From 8cbef7b502ce7d798a112ace105747f181f735a6 Mon Sep 17 00:00:00 2001
From: mdeluci <mdeluci@purdue.edu>
Date: Wed, 19 Jun 2024 18:57:45 +0000
Subject: [PATCH] =?UTF-8?q?Deploying=20to=20gh-pages=20from=20@=20mdeluci/?=
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 blog/2015/code/index.html             | 2 +-
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 delete mode 100644 blog/2015/math/index.html
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diff --git a/404.html b/404.html
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diff --git a/blog/2015/code/index.html b/blog/2015/code/index.html
index 1cbde853..28c9161d 100644
--- a/blog/2015/code/index.html
+++ b/blog/2015/code/index.html
@@ -65,4 +65,4 @@
     <span class="k">return</span> <span class="mi">0</span><span class="p">;</span>
 
 <span class="p">}</span>
-</pre></td> </tr></tbody></table></code></pre></figure> </div> </article> <br> <hr> <br> <ul class="list-disc pl-8"></ul> <h2 class="text-3xl font-semibold mb-4 mt-12">Enjoy Reading This Article?</h2> <p class="mb-2">Here are some more articles you might like to read next:</p> <li class="my-2"> <a class="text-pink-700 underline font-semibold hover:text-pink-800" href="/blog/2023/tables/">displaying beautiful tables with Bootstrap Tables</a> </li> <li class="my-2"> <a class="text-pink-700 underline font-semibold hover:text-pink-800" href="/blog/2015/math/">Solving the Cahn-Hilliard equation on complex geometries</a> </li> <li class="my-2"> <a class="text-pink-700 underline font-semibold hover:text-pink-800" href="/blog/2015/images/">a post with images</a> </li> </div> </div> <footer class="fixed-bottom" role="contentinfo"> <div class="container mt-0"> © Copyright 2024 Mario de Lucio. </div> </footer> <script src="https://cdn.jsdelivr.net/npm/jquery@3.6.0/dist/jquery.min.js" 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-<!DOCTYPE html> <html lang="en"> <head> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> <meta charset="utf-8"> <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"> <meta http-equiv="X-UA-Compatible" content="IE=edge"> <title> a post with images | Mario de Lucio's website </title> <meta name="author" content="Mario de Lucio"> <meta name="description" content="this is what included images could look like"> <meta name="keywords" content="Computational Mechanics, Multiphysics Simulation, Biomechanics, Transport phenomena"> <link rel="stylesheet" href="/assets/css/bootstrap.min.css?a4b3f509e79c54a512b890d73235ef04"> <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/mdbootstrap@4.20.0/css/mdb.min.css" integrity="sha256-jpjYvU3G3N6nrrBwXJoVEYI/0zw8htfFnhT9ljN3JJw=" crossorigin="anonymous"> <link defer rel="stylesheet" href="/assets/css/academicons.min.css?f0b7046b84e425c55f3463ac249818f5"> <link defer rel="stylesheet" type="text/css" href="https://fonts.googleapis.com/css?family=Roboto:300,400,500,700|Roboto+Slab:100,300,400,500,700|Material+Icons&amp;display=swap"> <link defer rel="stylesheet" href="/assets/css/jekyll-pygments-themes-github.css?591dab5a4e56573bf4ef7fd332894c99" media="" id="highlight_theme_light"> <link rel="shortcut icon" href="/assets/img/webicon.png?b6c2349ccb452e30289be5faff27b580"> <link rel="stylesheet" href="/assets/css/main.css?d41d8cd98f00b204e9800998ecf8427e"> <link rel="canonical" href="https://mdeluci.github.io/blog/2015/images/"> <script src="/assets/js/theme.js?9a0c749ec5240d9cda97bc72359a72c0"></script> <link defer rel="stylesheet" href="/assets/css/jekyll-pygments-themes-native.css?5847e5ed4a4568527aa6cfab446049ca" media="none" id="highlight_theme_dark"> <script>initTheme();</script> </head> <body class="fixed-top-nav "> <header> <nav id="navbar" class="navbar navbar-light navbar-expand-sm fixed-top" role="navigation"> <div class="container"> <a class="navbar-brand title font-weight-lighter" href="/"> Mario de Lucio's website </a> <button class="navbar-toggler collapsed ml-auto" type="button" data-toggle="collapse" data-target="#navbarNav" aria-controls="navbarNav" aria-expanded="false" aria-label="Toggle navigation"> <span class="sr-only">Toggle navigation</span> <span class="icon-bar top-bar"></span> <span class="icon-bar middle-bar"></span> <span class="icon-bar bottom-bar"></span> </button> <div class="collapse navbar-collapse text-right" id="navbarNav"> <ul class="navbar-nav ml-auto flex-nowrap"> <li class="nav-item "> <a class="nav-link" href="/">About </a> </li> <li class="nav-item "> <a class="nav-link" href="/publications/">Publications </a> </li> <li class="nav-item "> <a class="nav-link" href="/blog/">Blog </a> </li> <li class="nav-item "> <a class="nav-link" href="/cv/">CV </a> </li> <li class="nav-item "> <a class="nav-link" href="/teaching/">Teaching </a> </li> <li class="nav-item "> <a class="nav-link" href="/videos/">Videos </a> </li> <li class="nav-item"> <button id="search-toggle" title="Search" onclick="openSearchModal()"> <span class="nav-link">ctrl k <i class="ti ti-search"></i></span> </button> </li> <li class="toggle-container"> <button id="light-toggle" title="Change theme"> <i class="ti ti-sun-moon" id="light-toggle-system"></i> <i class="ti ti-moon-filled" id="light-toggle-dark"></i> <i class="ti ti-sun-filled" id="light-toggle-light"></i> </button> </li> </ul> </div> </div> </nav> <progress id="progress" value="0"> <div class="progress-container"> <span class="progress-bar"></span> </div> </progress> </header> <div class="container mt-5" role="main"> <div class="post"> <header class="post-header"> <h1 class="post-title">a post with images</h1> <p class="post-meta"> Created in May 15, 2015 </p> <p class="post-tags"> <a href="/blog/2015"> <i class="fa-solid fa-calendar fa-sm"></i> 2015 </a>   ·   <a href="/blog/tag/formatting"> <i class="fa-solid fa-hashtag fa-sm"></i> formatting</a>   <a href="/blog/tag/images"> <i class="fa-solid fa-hashtag fa-sm"></i> images</a>   ·   <a href="/blog/category/sample-posts"> <i class="fa-solid fa-tag fa-sm"></i> sample-posts</a> </p> </header> <article class="post-content"> <div id="markdown-content"> <p>This is an example post with image galleries.</p> <div class="row mt-3"> <div class="col-sm mt-3 mt-md-0"> <figure> <picture> <source class="responsive-img-srcset" srcset="/assets/img/9-480.webp 480w,/assets/img/9-800.webp 800w,/assets/img/9-1400.webp 1400w," sizes="95vw" type="image/webp"></source> <img src="/assets/img/9.jpg" class="img-fluid rounded z-depth-1" width="100%" height="auto" loading="eager" onerror="this.onerror=null; $('.responsive-img-srcset').remove();"> </picture> </figure> </div> <div class="col-sm mt-3 mt-md-0"> <figure> <picture> <source class="responsive-img-srcset" srcset="/assets/img/7-480.webp 480w,/assets/img/7-800.webp 800w,/assets/img/7-1400.webp 1400w," sizes="95vw" type="image/webp"></source> <img src="/assets/img/7.jpg" class="img-fluid rounded z-depth-1" width="100%" height="auto" loading="eager" onerror="this.onerror=null; $('.responsive-img-srcset').remove();"> </picture> </figure> </div> </div> <div class="caption"> A simple, elegant caption looks good between image rows, after each row, or doesn't have to be there at all. </div> <p>Images can be made zoomable. Simply add <code class="language-plaintext highlighter-rouge">data-zoomable</code> to <code class="language-plaintext highlighter-rouge">&lt;img&gt;</code> tags that you want to make zoomable.</p> <div class="row mt-3"> <div class="col-sm mt-3 mt-md-0"> <figure> <picture> <source class="responsive-img-srcset" srcset="/assets/img/8-480.webp 480w,/assets/img/8-800.webp 800w,/assets/img/8-1400.webp 1400w," sizes="95vw" type="image/webp"></source> <img src="/assets/img/8.jpg" class="img-fluid rounded z-depth-1" width="100%" height="auto" data-zoomable="" loading="eager" onerror="this.onerror=null; $('.responsive-img-srcset').remove();"> </picture> </figure> </div> <div class="col-sm mt-3 mt-md-0"> <figure> <picture> <source class="responsive-img-srcset" srcset="/assets/img/10-480.webp 480w,/assets/img/10-800.webp 800w,/assets/img/10-1400.webp 1400w," sizes="95vw" type="image/webp"></source> <img src="/assets/img/10.jpg" class="img-fluid rounded z-depth-1" width="100%" height="auto" data-zoomable="" loading="eager" onerror="this.onerror=null; $('.responsive-img-srcset').remove();"> </picture> </figure> </div> </div> <p>The rest of the images in this post are all zoomable, arranged into different mini-galleries.</p> <div class="row mt-3"> <div class="col-sm mt-3 mt-md-0"> <figure> <picture> <source class="responsive-img-srcset" srcset="/assets/img/11-480.webp 480w,/assets/img/11-800.webp 800w,/assets/img/11-1400.webp 1400w," sizes="95vw" type="image/webp"></source> <img src="/assets/img/11.jpg" class="img-fluid rounded z-depth-1" width="100%" height="auto" data-zoomable="" loading="lazy" onerror="this.onerror=null; $('.responsive-img-srcset').remove();"> </picture> </figure> </div> <div class="col-sm mt-3 mt-md-0"> <figure> <picture> <source class="responsive-img-srcset" srcset="/assets/img/12-480.webp 480w,/assets/img/12-800.webp 800w,/assets/img/12-1400.webp 1400w," sizes="95vw" type="image/webp"></source> <img src="/assets/img/12.jpg" class="img-fluid rounded z-depth-1" width="100%" height="auto" data-zoomable="" loading="lazy" onerror="this.onerror=null; $('.responsive-img-srcset').remove();"> </picture> </figure> </div> <div class="col-sm mt-3 mt-md-0"> <figure> <picture> <source class="responsive-img-srcset" srcset="/assets/img/7-480.webp 480w,/assets/img/7-800.webp 800w,/assets/img/7-1400.webp 1400w," sizes="95vw" type="image/webp"></source> <img src="/assets/img/7.jpg" class="img-fluid rounded z-depth-1" width="100%" height="auto" data-zoomable="" loading="lazy" onerror="this.onerror=null; $('.responsive-img-srcset').remove();"> </picture> </figure> </div> </div> </div> </article> <br> <hr> <br> <ul class="list-disc pl-8"></ul> <h2 class="text-3xl font-semibold mb-4 mt-12">Enjoy Reading This Article?</h2> <p class="mb-2">Here are some more articles you might like to read next:</p> <li class="my-2"> <a class="text-pink-700 underline font-semibold hover:text-pink-800" href="/blog/2023/tables/">displaying beautiful tables with Bootstrap 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+<!DOCTYPE html> <html lang="en"> <head> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> <meta charset="utf-8"> <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"> <meta http-equiv="X-UA-Compatible" content="IE=edge"> <title> a post with images | Mario de Lucio's website </title> <meta name="author" content="Mario de Lucio"> <meta name="description" content="this is what included images could look like"> <meta name="keywords" content="Computational Mechanics, Multiphysics Simulation, Biomechanics, Transport phenomena"> <link rel="stylesheet" href="/assets/css/bootstrap.min.css?a4b3f509e79c54a512b890d73235ef04"> <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/mdbootstrap@4.20.0/css/mdb.min.css" integrity="sha256-jpjYvU3G3N6nrrBwXJoVEYI/0zw8htfFnhT9ljN3JJw=" crossorigin="anonymous"> <link defer rel="stylesheet" href="/assets/css/academicons.min.css?f0b7046b84e425c55f3463ac249818f5"> <link defer rel="stylesheet" type="text/css" href="https://fonts.googleapis.com/css?family=Roboto:300,400,500,700|Roboto+Slab:100,300,400,500,700|Material+Icons&amp;display=swap"> <link defer rel="stylesheet" href="/assets/css/jekyll-pygments-themes-github.css?591dab5a4e56573bf4ef7fd332894c99" media="" id="highlight_theme_light"> <link rel="shortcut icon" href="/assets/img/webicon.png?b6c2349ccb452e30289be5faff27b580"> <link rel="stylesheet" href="/assets/css/main.css?d41d8cd98f00b204e9800998ecf8427e"> <link rel="canonical" href="https://mdeluci.github.io/blog/2015/images/"> <script src="/assets/js/theme.js?9a0c749ec5240d9cda97bc72359a72c0"></script> <link defer rel="stylesheet" href="/assets/css/jekyll-pygments-themes-native.css?5847e5ed4a4568527aa6cfab446049ca" media="none" id="highlight_theme_dark"> <script>initTheme();</script> </head> <body class="fixed-top-nav "> <header> <nav id="navbar" class="navbar navbar-light navbar-expand-sm fixed-top" role="navigation"> <div class="container"> <a class="navbar-brand title font-weight-lighter" href="/"> Mario de Lucio's website </a> <button class="navbar-toggler collapsed ml-auto" type="button" data-toggle="collapse" data-target="#navbarNav" aria-controls="navbarNav" aria-expanded="false" aria-label="Toggle navigation"> <span class="sr-only">Toggle navigation</span> <span class="icon-bar top-bar"></span> <span class="icon-bar middle-bar"></span> <span class="icon-bar bottom-bar"></span> </button> <div class="collapse navbar-collapse text-right" id="navbarNav"> <ul class="navbar-nav ml-auto flex-nowrap"> <li class="nav-item "> <a class="nav-link" href="/">About </a> </li> <li class="nav-item "> <a class="nav-link" href="/publications/">Publications </a> </li> <li class="nav-item "> <a class="nav-link" href="/blog/">Blog </a> </li> <li class="nav-item "> <a class="nav-link" href="/cv/">CV </a> </li> <li class="nav-item "> <a class="nav-link" href="/teaching/">Teaching </a> </li> <li class="nav-item "> <a class="nav-link" href="/videos/">Videos </a> </li> <li class="nav-item"> <button id="search-toggle" title="Search" onclick="openSearchModal()"> <span class="nav-link">ctrl k <i class="ti ti-search"></i></span> </button> </li> <li class="toggle-container"> <button id="light-toggle" title="Change theme"> <i class="ti ti-sun-moon" id="light-toggle-system"></i> <i class="ti ti-moon-filled" id="light-toggle-dark"></i> <i class="ti ti-sun-filled" id="light-toggle-light"></i> </button> </li> </ul> </div> </div> </nav> <progress id="progress" value="0"> <div class="progress-container"> <span class="progress-bar"></span> </div> </progress> </header> <div class="container mt-5" role="main"> <div class="post"> <header class="post-header"> <h1 class="post-title">a post with images</h1> <p class="post-meta"> Created in May 15, 2015 </p> <p class="post-tags"> <a href="/blog/2015"> <i class="fa-solid fa-calendar fa-sm"></i> 2015 </a>   ·   <a href="/blog/tag/formatting"> <i class="fa-solid fa-hashtag fa-sm"></i> formatting</a>   <a href="/blog/tag/images"> <i class="fa-solid fa-hashtag fa-sm"></i> images</a>   ·   <a href="/blog/category/sample-posts"> <i class="fa-solid fa-tag fa-sm"></i> sample-posts</a> </p> </header> <article class="post-content"> <div id="markdown-content"> <p>This is an example post with image galleries.</p> <div class="row mt-3"> <div class="col-sm mt-3 mt-md-0"> <figure> <picture> <source class="responsive-img-srcset" srcset="/assets/img/9-480.webp 480w,/assets/img/9-800.webp 800w,/assets/img/9-1400.webp 1400w," sizes="95vw" type="image/webp"></source> <img src="/assets/img/9.jpg" class="img-fluid rounded z-depth-1" width="100%" height="auto" loading="eager" onerror="this.onerror=null; $('.responsive-img-srcset').remove();"> </picture> </figure> </div> <div class="col-sm mt-3 mt-md-0"> <figure> <picture> <source class="responsive-img-srcset" srcset="/assets/img/7-480.webp 480w,/assets/img/7-800.webp 800w,/assets/img/7-1400.webp 1400w," sizes="95vw" type="image/webp"></source> <img src="/assets/img/7.jpg" class="img-fluid rounded z-depth-1" width="100%" height="auto" loading="eager" onerror="this.onerror=null; $('.responsive-img-srcset').remove();"> </picture> </figure> </div> </div> <div class="caption"> A simple, elegant caption looks good between image rows, after each row, or doesn't have to be there at all. </div> <p>Images can be made zoomable. Simply add <code class="language-plaintext highlighter-rouge">data-zoomable</code> to <code class="language-plaintext highlighter-rouge">&lt;img&gt;</code> tags that you want to make zoomable.</p> <div class="row mt-3"> <div class="col-sm mt-3 mt-md-0"> <figure> <picture> <source class="responsive-img-srcset" srcset="/assets/img/8-480.webp 480w,/assets/img/8-800.webp 800w,/assets/img/8-1400.webp 1400w," sizes="95vw" type="image/webp"></source> <img src="/assets/img/8.jpg" class="img-fluid rounded z-depth-1" width="100%" height="auto" data-zoomable="" loading="eager" onerror="this.onerror=null; $('.responsive-img-srcset').remove();"> </picture> </figure> </div> <div class="col-sm mt-3 mt-md-0"> <figure> <picture> <source class="responsive-img-srcset" srcset="/assets/img/10-480.webp 480w,/assets/img/10-800.webp 800w,/assets/img/10-1400.webp 1400w," sizes="95vw" type="image/webp"></source> <img src="/assets/img/10.jpg" class="img-fluid rounded z-depth-1" width="100%" height="auto" data-zoomable="" loading="eager" onerror="this.onerror=null; $('.responsive-img-srcset').remove();"> </picture> </figure> </div> </div> <p>The rest of the images in this post are all zoomable, arranged into different mini-galleries.</p> <div class="row mt-3"> <div class="col-sm mt-3 mt-md-0"> <figure> <picture> <source class="responsive-img-srcset" srcset="/assets/img/11-480.webp 480w,/assets/img/11-800.webp 800w,/assets/img/11-1400.webp 1400w," sizes="95vw" type="image/webp"></source> <img src="/assets/img/11.jpg" class="img-fluid rounded z-depth-1" width="100%" height="auto" data-zoomable="" loading="lazy" onerror="this.onerror=null; $('.responsive-img-srcset').remove();"> </picture> </figure> </div> <div class="col-sm mt-3 mt-md-0"> <figure> <picture> <source class="responsive-img-srcset" srcset="/assets/img/12-480.webp 480w,/assets/img/12-800.webp 800w,/assets/img/12-1400.webp 1400w," sizes="95vw" type="image/webp"></source> <img src="/assets/img/12.jpg" class="img-fluid rounded z-depth-1" width="100%" height="auto" data-zoomable="" loading="lazy" onerror="this.onerror=null; $('.responsive-img-srcset').remove();"> </picture> </figure> </div> <div class="col-sm mt-3 mt-md-0"> <figure> <picture> <source class="responsive-img-srcset" srcset="/assets/img/7-480.webp 480w,/assets/img/7-800.webp 800w,/assets/img/7-1400.webp 1400w," sizes="95vw" type="image/webp"></source> <img src="/assets/img/7.jpg" class="img-fluid rounded z-depth-1" width="100%" height="auto" data-zoomable="" loading="lazy" onerror="this.onerror=null; $('.responsive-img-srcset').remove();"> </picture> </figure> </div> </div> </div> </article> <br> <hr> <br> <ul class="list-disc pl-8"></ul> <h2 class="text-3xl font-semibold mb-4 mt-12">Enjoy Reading This Article?</h2> <p class="mb-2">Here are some more articles you might like to read next:</p> <li class="my-2"> <a class="text-pink-700 underline font-semibold hover:text-pink-800" href="/blog/2024/math/">Solving the Cahn-Hilliard equation on complex geometries</a> </li> <li class="my-2"> <a class="text-pink-700 underline font-semibold hover:text-pink-800" href="/blog/2023/tables/">displaying beautiful tables with Bootstrap Tables</a> </li> <li class="my-2"> <a class="text-pink-700 underline font-semibold hover:text-pink-800" href="/blog/2015/code/">a post with code</a> </li> </div> </div> <footer class="fixed-bottom" role="contentinfo"> <div class="container mt-0"> © Copyright 2024 Mario de Lucio. </div> </footer> <script src="https://cdn.jsdelivr.net/npm/jquery@3.6.0/dist/jquery.min.js" integrity="sha256-/xUj+3OJU5yExlq6GSYGSHk7tPXikynS7ogEvDej/m4=" crossorigin="anonymous"></script> <script src="/assets/js/bootstrap.bundle.min.js"></script> <script src="https://cdn.jsdelivr.net/npm/mdbootstrap@4.20.0/js/mdb.min.js" integrity="sha256-NdbiivsvWt7VYCt6hYNT3h/th9vSTL4EDWeGs5SN3DA=" crossorigin="anonymous"></script> <script defer src="https://cdn.jsdelivr.net/npm/masonry-layout@4.2.2/dist/masonry.pkgd.min.js" 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-<!DOCTYPE html> <html lang="en"> <head> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> <meta charset="utf-8"> <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"> <meta http-equiv="X-UA-Compatible" content="IE=edge"> <title> Solving the Cahn-Hilliard equation on complex geometries | Mario de Lucio's website </title> <meta name="author" content="Mario de Lucio"> <meta name="description" content="We solve the Cahn-Hilliard equation on a quarter of annulus by means of isogeometric analysis. We adopt the split form of the equation to avoid introducing fourth-order operators and facilitate the imposition of the boundary conditions on the circular geometry,"> <meta name="keywords" content="Computational Mechanics, Multiphysics Simulation, Biomechanics, Transport phenomena"> <link rel="stylesheet" href="/assets/css/bootstrap.min.css?a4b3f509e79c54a512b890d73235ef04"> <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/mdbootstrap@4.20.0/css/mdb.min.css" integrity="sha256-jpjYvU3G3N6nrrBwXJoVEYI/0zw8htfFnhT9ljN3JJw=" crossorigin="anonymous"> <link defer rel="stylesheet" href="/assets/css/academicons.min.css?f0b7046b84e425c55f3463ac249818f5"> <link defer rel="stylesheet" type="text/css" href="https://fonts.googleapis.com/css?family=Roboto:300,400,500,700|Roboto+Slab:100,300,400,500,700|Material+Icons&amp;display=swap"> <link defer rel="stylesheet" href="/assets/css/jekyll-pygments-themes-github.css?591dab5a4e56573bf4ef7fd332894c99" media="" id="highlight_theme_light"> <link rel="shortcut icon" href="/assets/img/webicon.png?b6c2349ccb452e30289be5faff27b580"> <link rel="stylesheet" href="/assets/css/main.css?d41d8cd98f00b204e9800998ecf8427e"> <link rel="canonical" href="https://mdeluci.github.io/blog/2015/math/"> <script src="/assets/js/theme.js?9a0c749ec5240d9cda97bc72359a72c0"></script> <link defer rel="stylesheet" href="/assets/css/jekyll-pygments-themes-native.css?5847e5ed4a4568527aa6cfab446049ca" media="none" id="highlight_theme_dark"> <script>initTheme();</script> </head> <body class="fixed-top-nav "> <header> <nav id="navbar" class="navbar navbar-light navbar-expand-sm fixed-top" role="navigation"> <div class="container"> <a class="navbar-brand title font-weight-lighter" href="/"> Mario de Lucio's website </a> <button class="navbar-toggler collapsed ml-auto" type="button" data-toggle="collapse" data-target="#navbarNav" aria-controls="navbarNav" aria-expanded="false" aria-label="Toggle navigation"> <span class="sr-only">Toggle navigation</span> <span class="icon-bar top-bar"></span> <span class="icon-bar middle-bar"></span> <span class="icon-bar bottom-bar"></span> </button> <div class="collapse navbar-collapse text-right" id="navbarNav"> <ul class="navbar-nav ml-auto flex-nowrap"> <li class="nav-item "> <a class="nav-link" href="/">About </a> </li> <li class="nav-item "> <a class="nav-link" href="/publications/">Publications </a> </li> <li class="nav-item "> <a class="nav-link" href="/blog/">Blog </a> </li> <li class="nav-item "> <a class="nav-link" href="/cv/">CV </a> </li> <li class="nav-item "> <a class="nav-link" href="/teaching/">Teaching </a> </li> <li class="nav-item "> <a class="nav-link" href="/videos/">Videos </a> </li> <li class="nav-item"> <button id="search-toggle" title="Search" onclick="openSearchModal()"> <span class="nav-link">ctrl k <i class="ti ti-search"></i></span> </button> </li> <li class="toggle-container"> <button id="light-toggle" title="Change theme"> <i class="ti ti-sun-moon" id="light-toggle-system"></i> <i class="ti ti-moon-filled" id="light-toggle-dark"></i> <i class="ti ti-sun-filled" id="light-toggle-light"></i> </button> </li> </ul> </div> </div> </nav> <progress id="progress" value="0"> <div class="progress-container"> <span class="progress-bar"></span> </div> </progress> </header> <div class="container mt-5" role="main"> <div class="post"> <header class="post-header"> <h1 class="post-title">Solving the Cahn-Hilliard equation on complex geometries</h1> <p class="post-meta"> Created in October 20, 2015 </p> <p class="post-tags"> <a href="/blog/2015"> <i class="fa-solid fa-calendar fa-sm"></i> 2015 </a>   ·   <a href="/blog/tag/cahn-hilliard"> <i class="fa-solid fa-hashtag fa-sm"></i> Cahn-Hilliard</a>   <a href="/blog/tag/pdes"> <i class="fa-solid fa-hashtag fa-sm"></i> PDEs</a>   <a href="/blog/tag/iga"> <i class="fa-solid fa-hashtag fa-sm"></i> IGA</a>   ·   <a href="/blog/category/sample-posts"> <i class="fa-solid fa-tag fa-sm"></i> sample-posts</a> </p> </header> <article class="post-content"> <div id="markdown-content"> <h2 id="the-cahn-hilliard-equation">The Cahn-Hilliard equation</h2> <p>The Cahn–Hilliard equation describes the process of phase separation, by which the two components of a binary fluid spontaneously separate and form domains pure in each component. It was originally proposed in 1958 to model phase separation in binary alloys \cite{Cahn-Hilliard, Cahn-Hilliard2}. Since then it has been used to describe various phenomena, such as spinodal decomposition \cite{MARALDI201231}, diblock copolymer \cite{Choksi,JEONG20141263}, image inpainting \cite{4032803}, tumor growth simulation \cite{tumor,WISE2008524} or multiphase fluid flows \cite{BADALASSI2003371, Kotschote}.</p> <p>There are two main approaches to describing phase transition phenomena: sharp-interface models and phase-field models. Sharp-interface models involve the resolution of a moving boundary problem, meaning that partial differential equations have to be solved for each phase. This can lead to physical \cite{Anderson} and computational complications \cite{Barrett}, such as jump discontinuities across the interface. Phase-field models replace sharp-interfaces by thin transitions regions where the interfacial forces are smoothly distributed (diffuse interfaces). For this reason, phase-field models are also referred to as \emph{diffuse interface} models, and they are emerging as a promising tool to treat problems with interfaces.</p> <p>From the mathematical point of view, the Cahn-Hilliard equation is a stiff, fourth-order, nonlinear parabolic partial differential equation. The elementary form of the Cahn-Hilliard equation is given by</p> <p>\begin{equation} \frac{\partial \phi}{\partial t}=\nabla \cdot \left(m\left(\phi\right) \nabla \left(W’\left(\phi\right) -\epsilon ^2 \Delta \phi \right) \right) \label{element} \end{equation}</p> <p>where \(\phi\left(\mathbf{x},t\right) \in [-1,1]\) represents the phase-field variable, which describes the location of different components (e.g., \(\phi=-1\) in oil and \(\phi=1\) in water), \(m\left(\phi\right)\) is the mobility, \(W\left(\phi\right)\) is the so-called double-well potential, and \(\epsilon\) is a length scale related to the thickness of the diffuse interface.</p> <p>Two different approaches have been used to solve the Cahn-Hilliard equation: solving the original form given by Eqn.\eqref{element}, which involves fourth-order operators, or by splitting it into two second order partial differential equations by introducing an auxiliary variable — the chemical potential \(\mu\). The split version of the equation is given by</p> <p>\begin{equation} \frac{\partial \phi}{\partial t}=\nabla \cdot \left(m\left(\phi\right) \nabla \mu \right) \label{split1} \end{equation} \begin{equation} \mu=W’\left(\phi \right) - \epsilon^2 \Delta \phi. \label{chempot} \end{equation}</p> <p>The splitting strategy was proposed by Elliot \cite{Elliott1989ASO} to avoid constraints related to the continuity of the basis functions when using the finite element method with a primal formulation. It also facilitates the imposition of the boundary conditions on a circular geometry, which is the case we are interested in. Unfortunately, this comes at a price of an additional degree of freedom introduced into the solver. Nevertheless, this reformulation reduces the complexity of the problem from the numerical point of view (see \cite{M2AN_2009__43_5_1003_0,Zee}).</p> <p>The spatial discretization of the governing equations is performed using isogeometric analysis (IGA) \cite{HUGHES20054135}. IGA is a generalization of the finite-element method that uses non-uniform rational B-splines (NURBS) to define the discrete spaces. A significant advantage of IGA with respect to finite element analysis is that the basis functions can be constructed with controllable continuity across the element boundaries, even on mapped geometries. The higher-order global continuity of the basis functions has been shown to produce higher accuracy than classical \(\mathcal{C}^0\)-continuous finite elements for the same number of degrees of freedom \cite{akkerman2008role,evans2009n}; and has been widely used to solve partial differential equations with high-order spatial derivatives \cite{GOMEZ20084333, GOMEZ20101828, GOMEZ201252}. Here, we will use \(\mathcal{C}^1\)-continuous quadratic splines for \(\phi\) and \(\mu\).</p> <h2 id="strong-form">Strong form</h2> <p>The strong form of the problem is formulated as follows: find \(\phi:\Omega \times \left[0,T\right]\rightarrow \mathbb{R}\) and \(\mu:\Omega \times \left[0,T\right]\rightarrow \mathbb{R}\) (being \(\mu\) an auxiliary variable) such that:</p> <p>\begin{equation} \frac{\partial \phi}{\partial t}=\nabla \cdot \left(m\left(\phi\right) \nabla \mu\right) \quad \text{in} \ \Omega \times \left[0,T\right], \label{st1} \end{equation} <br> \begin{equation} \mu=W’\left(\phi\right)-\epsilon^2 \Delta \phi \quad \text{in} \ \Omega \times \left[0,T\right], \label{st2} \end{equation} \begin{equation} \phi=g \quad \text{on} \ \Gamma_g \times \left[0,T\right], \label{st3} \end{equation} \begin{equation} <br> m\left(\phi\right)\epsilon^2\Delta\phi=q \quad \text{on} \ \Gamma_q \times \left[0,T\right], \label{st4} \end{equation} \begin{equation} \nabla\left(m\left(\phi\right)\mu\right)\cdot \mathbf{n}=s \quad \text{on} \ \Gamma_s \times \left[0,T\right], \label{st5} \end{equation} \begin{equation} \nabla\left(m\left(\phi\right)\phi\right)\cdot \mathbf{n}=h \quad \text{on} \ \Gamma_h \times \left[0,T\right], \label{st6}<br> \end{equation} \begin{equation} \phi\left(\mathbf{x},0\right)=\phi_0\left(\mathbf{x}\right) \quad \text{in} \ \Omega. \label{st7}<br> \end{equation}</p> <p>The double well function \(W\left(\phi\right)\) is defined such that it has two local minima, which makes possible the coexistence of the different phases. Some important examples of double well functions can be found in \cite{Gomez2}. In this work we will take the classical quartic potential</p> <p>\begin{equation} W\left(\phi\right)=\frac{1}{4}\left(1-\phi^2\right)^2, \end{equation}</p> <p>which is a qualitative approximation of the logarithmic double well.</p> <p>The mobility \(m\left(\phi\right)\), which can be linked with the diffusivity, controls the time scale of the problem. The most common approach is to set it as a constant, \(m\left(\phi\right)=m\). Such an approach is extensively applied in both analytical and numerical studies \cite{Rajagopal,polymer,CuetoFelgueroso2008ATF}. We will take \(m\) constant and equal to one as recommended in \cite{GOMEZ20084333}.</p> <p>The parameter \(\epsilon\) is a positive constant that defines the length scale for the problem. According to \cite{GOMEZ20084333}, the solution to the Cahn-Hilliard equations depends only on the dimensionless number</p> <p>\begin{equation} \alpha=\frac{L_0^2}{3\epsilon^2} \end{equation}</p> <p>also referred to as sharpness parameter, where \(L_0\) is a length scale of the problem. Here, we will assume that \(L_0\) is a measure of the computational domain size. Without loss of generality, \(L_0=R_2=1.0\) will be the outer radius of the quarter of annulus. The sharpness parameter $\alpha$ usually takes values in the range \(10^3-10^4\) \cite{GOMEZ20084333,Gomez2}. We will study the evolution of the phase-field variable for different values of \(\alpha\).</p> <div class="row mt-3"> <div class="col-sm mt-3 mt-md-0"> <figure> <picture> <source class="responsive-img-srcset" srcset="/assets/img/fig2_ch-480.webp 480w,/assets/img/fig2_ch-800.webp 800w,/assets/img/fig2_ch-1400.webp 1400w," sizes="95vw" type="image/webp"></source> <img src="/assets/img/fig2_ch.png" class="img-fluid rounded z-depth-1" width="100%" height="auto" loading="eager" onerror="this.onerror=null; $('.responsive-img-srcset').remove();"> </picture> </figure> </div> <div class="col-sm mt-3 mt-md-0"> <figure> <picture> <source class="responsive-img-srcset" srcset="/assets/img/fig3_ch-480.webp 480w,/assets/img/fig3_ch-800.webp 800w,/assets/img/fig3_ch-1400.webp 1400w," sizes="95vw" type="image/webp"></source> <img src="/assets/img/fig3_ch.png" class="img-fluid rounded z-depth-1" width="100%" height="auto" loading="eager" onerror="this.onerror=null; $('.responsive-img-srcset').remove();"> </picture> </figure> </div> </div> <div class="caption"> Evolution of the phase-field from a randomly perturbed initial condition for $$\alpha=1500$$ and $$\bar{\phi}=0.3$$ (left). Evolution of the phase-field from a randomly perturbed initial condition for $$\alpha=3000$$ and $$\bar{\phi}=0.1$$ (right). </div> </div> </article> </div> </div> <footer class="fixed-bottom" role="contentinfo"> <div class="container mt-0"> © Copyright 2024 Mario de Lucio. </div> </footer> <script src="https://cdn.jsdelivr.net/npm/jquery@3.6.0/dist/jquery.min.js" integrity="sha256-/xUj+3OJU5yExlq6GSYGSHk7tPXikynS7ogEvDej/m4=" crossorigin="anonymous"></script> <script src="/assets/js/bootstrap.bundle.min.js"></script> <script src="https://cdn.jsdelivr.net/npm/mdbootstrap@4.20.0/js/mdb.min.js" integrity="sha256-NdbiivsvWt7VYCt6hYNT3h/th9vSTL4EDWeGs5SN3DA=" crossorigin="anonymous"></script> <script defer src="https://cdn.jsdelivr.net/npm/masonry-layout@4.2.2/dist/masonry.pkgd.min.js" integrity="sha256-Nn1q/fx0H7SNLZMQ5Hw5JLaTRZp0yILA/FRexe19VdI=" crossorigin="anonymous"></script> <script defer src="https://cdn.jsdelivr.net/npm/imagesloaded@5.0.0/imagesloaded.pkgd.min.js" integrity="sha256-htrLFfZJ6v5udOG+3kNLINIKh2gvoKqwEhHYfTTMICc=" crossorigin="anonymous"></script> <script defer src="/assets/js/masonry.js" type="text/javascript"></script> <script defer src="https://cdn.jsdelivr.net/npm/medium-zoom@1.1.0/dist/medium-zoom.min.js" integrity="sha256-ZgMyDAIYDYGxbcpJcfUnYwNevG/xi9OHKaR/8GK+jWc=" crossorigin="anonymous"></script> <script defer src="/assets/js/zoom.js?85ddb88934d28b74e78031fd54cf8308"></script> <script src="/assets/js/no_defer.js?2781658a0a2b13ed609542042a859126"></script> <script defer src="/assets/js/common.js?06cae41083477f121be8cd9797ad8e2f"></script> <script defer src="/assets/js/copy_code.js?12775fdf7f95e901d7119054556e495f" type="text/javascript"></script> <script defer src="/assets/js/jupyter_new_tab.js?d9f17b6adc2311cbabd747f4538bb15f"></script> <script async src="https://d1bxh8uas1mnw7.cloudfront.net/assets/embed.js"></script> <script async src="https://badge.dimensions.ai/badge.js"></script> <script type="text/javascript">window.MathJax={tex:{tags:"ams"}};</script> <script defer type="text/javascript" id="MathJax-script" src="https://cdn.jsdelivr.net/npm/mathjax@3.2.0/es5/tex-mml-chtml.min.js" integrity="sha256-rjmgmaB99riUNcdlrDtcAiwtLIojSxNyUFdl+Qh+rB4=" crossorigin="anonymous"></script> <script defer src="https://cdnjs.cloudflare.com/polyfill/v3/polyfill.min.js?features=es6" crossorigin="anonymous"></script> <script type="text/javascript">function progressBarSetup(){"max"in document.createElement("progress")?(initializeProgressElement(),$(document).on("scroll",function(){progressBar.attr({value:getCurrentScrollPosition()})}),$(window).on("resize",initializeProgressElement)):(resizeProgressBar(),$(document).on("scroll",resizeProgressBar),$(window).on("resize",resizeProgressBar))}function getCurrentScrollPosition(){return $(window).scrollTop()}function initializeProgressElement(){let e=$("#navbar").outerHeight(!0);$("body").css({"padding-top":e}),$("progress-container").css({"padding-top":e}),progressBar.css({top:e}),progressBar.attr({max:getDistanceToScroll(),value:getCurrentScrollPosition()})}function getDistanceToScroll(){return $(document).height()-$(window).height()}function resizeProgressBar(){progressBar.css({width:getWidthPercentage()+"%"})}function getWidthPercentage(){return getCurrentScrollPosition()/getDistanceToScroll()*100}const progressBar=$("#progress");window.onload=function(){setTimeout(progressBarSetup,50)};</script> <script src="/assets/js/vanilla-back-to-top.min.js?f40d453793ff4f64e238e420181a1d17"></script> <script>addBackToTop();</script> <script type="module" src="/assets/js/search/ninja-keys.min.js?601a2d3465e2a52bec38b600518d5f70"></script> <ninja-keys hidebreadcrumbs noautoloadmdicons placeholder="Type to start searching"></ninja-keys> <script>let searchTheme=determineComputedTheme();const ninjaKeys=document.querySelector("ninja-keys");"dark"===searchTheme?ninjaKeys.classList.add("dark"):ninjaKeys.classList.remove("dark");const openSearchModal=()=>{const e=$("#navbarNav");e.hasClass("show")&&e.collapse("hide"),ninjaKeys.open()};</script> <script>const ninja=document.querySelector("ninja-keys");ninja.data=[{id:"nav-about",title:"About",section:"Navigation",handler:()=>{window.location.href="/"}},{id:"nav-publications",title:"Publications",description:"Ordered by most recent.",section:"Navigation",handler:()=>{window.location.href="/publications/"}},{id:"nav-blog",title:"Blog",description:"",section:"Navigation",handler:()=>{window.location.href="/blog/"}},{id:"nav-cv",title:"CV",description:"",section:"Navigation",handler:()=>{window.location.href="/cv/"}},{id:"nav-teaching",title:"Teaching",description:"Materials for courses you taught. 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diff --git a/blog/2023/index.html b/blog/2023/index.html
index 44ef15c3..8c8c418e 100644
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+++ b/blog/2023/index.html
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diff --git a/blog/2023/tables/index.html b/blog/2023/tables/index.html
index 59f32b22..52f215d1 100644
--- a/blog/2023/tables/index.html
+++ b/blog/2023/tables/index.html
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-</code></pre></div></div> <table data-click-to-select="true" data-height="460" data-pagination="true" data-search="true" data-toggle="table" data-url="/assets/json/table_data.json"> <thead> <tr> <th data-checkbox="true"></th> <th data-field="id" data-halign="left" data-align="center" data-sortable="true">ID</th> <th data-field="name" data-halign="center" data-align="right" data-sortable="true">Item Name</th> <th data-field="price" data-halign="right" data-align="left" data-sortable="true">Item Price</th> </tr> </thead> </table> </div> </article> <br> <hr> <br> <ul class="list-disc pl-8"></ul> <h2 class="text-3xl font-semibold mb-4 mt-12">Enjoy Reading This Article?</h2> <p class="mb-2">Here are some more articles you might like to read next:</p> <li class="my-2"> <a class="text-pink-700 underline font-semibold hover:text-pink-800" href="/blog/2015/math/">Solving the Cahn-Hilliard equation on complex geometries</a> </li> <li class="my-2"> <a class="text-pink-700 underline font-semibold hover:text-pink-800" href="/blog/2015/code/">a post with code</a> </li> <li class="my-2"> <a class="text-pink-700 underline font-semibold hover:text-pink-800" href="/blog/2015/images/">a post with images</a> </li> <div id="giscus_thread" style="max-width: 930px; margin: 0 auto;"> <script>let giscusTheme=determineComputedTheme(),giscusAttributes={src:"https://giscus.app/client.js","data-repo":"mdeluci/mdeluci.github.io","data-repo-id":"","data-category":"Comments","data-category-id":"","data-mapping":"title","data-strict":"1","data-reactions-enabled":"1","data-emit-metadata":"0","data-input-position":"bottom","data-theme":giscusTheme,"data-lang":"en",crossorigin:"anonymous",async:""},giscusScript=document.createElement("script");Object.entries(giscusAttributes).forEach(([t,e])=>giscusScript.setAttribute(t,e)),document.getElementById("giscus_thread").appendChild(giscusScript);</script> <noscript>Please enable JavaScript to view the <a href="http://giscus.app/?ref_noscript" rel="external 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+</code></pre></div></div> <table data-click-to-select="true" data-height="460" data-pagination="true" data-search="true" data-toggle="table" data-url="/assets/json/table_data.json"> <thead> <tr> <th data-checkbox="true"></th> <th data-field="id" data-halign="left" data-align="center" data-sortable="true">ID</th> <th data-field="name" data-halign="center" data-align="right" data-sortable="true">Item Name</th> <th data-field="price" data-halign="right" data-align="left" data-sortable="true">Item Price</th> </tr> </thead> </table> </div> </article> <br> <hr> <br> <ul class="list-disc pl-8"></ul> <h2 class="text-3xl font-semibold mb-4 mt-12">Enjoy Reading This Article?</h2> <p class="mb-2">Here are some more articles you might like to read next:</p> <li class="my-2"> <a class="text-pink-700 underline font-semibold hover:text-pink-800" href="/blog/2024/math/">Solving the Cahn-Hilliard equation on complex geometries</a> </li> <li class="my-2"> <a class="text-pink-700 underline font-semibold 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+<!DOCTYPE html> <html lang="en"> <head> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> <meta charset="utf-8"> <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"> <meta http-equiv="X-UA-Compatible" content="IE=edge"> <title> Solving the Cahn-Hilliard equation on complex geometries | Mario de Lucio's website </title> <meta name="author" content="Mario de Lucio"> <meta name="description" content="We solve the Cahn-Hilliard equation on a quarter of annulus by means of isogeometric analysis. We adopt the split form of the equation to avoid introducing fourth-order operators and facilitate the imposition of the boundary conditions on the circular geometry,"> <meta name="keywords" content="Computational Mechanics, Multiphysics Simulation, Biomechanics, Transport phenomena"> <link rel="stylesheet" href="/assets/css/bootstrap.min.css?a4b3f509e79c54a512b890d73235ef04"> <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/mdbootstrap@4.20.0/css/mdb.min.css" integrity="sha256-jpjYvU3G3N6nrrBwXJoVEYI/0zw8htfFnhT9ljN3JJw=" crossorigin="anonymous"> <link defer rel="stylesheet" href="/assets/css/academicons.min.css?f0b7046b84e425c55f3463ac249818f5"> <link defer rel="stylesheet" type="text/css" href="https://fonts.googleapis.com/css?family=Roboto:300,400,500,700|Roboto+Slab:100,300,400,500,700|Material+Icons&amp;display=swap"> <link defer rel="stylesheet" href="/assets/css/jekyll-pygments-themes-github.css?591dab5a4e56573bf4ef7fd332894c99" media="" id="highlight_theme_light"> <link rel="shortcut icon" href="/assets/img/webicon.png?b6c2349ccb452e30289be5faff27b580"> <link rel="stylesheet" href="/assets/css/main.css?d41d8cd98f00b204e9800998ecf8427e"> <link rel="canonical" href="https://mdeluci.github.io/blog/2024/math/"> <script src="/assets/js/theme.js?9a0c749ec5240d9cda97bc72359a72c0"></script> <link defer rel="stylesheet" href="/assets/css/jekyll-pygments-themes-native.css?5847e5ed4a4568527aa6cfab446049ca" media="none" id="highlight_theme_dark"> <script>initTheme();</script> </head> <body class="fixed-top-nav "> <header> <nav id="navbar" class="navbar navbar-light navbar-expand-sm fixed-top" role="navigation"> <div class="container"> <a class="navbar-brand title font-weight-lighter" href="/"> Mario de Lucio's website </a> <button class="navbar-toggler collapsed ml-auto" type="button" data-toggle="collapse" data-target="#navbarNav" aria-controls="navbarNav" aria-expanded="false" aria-label="Toggle navigation"> <span class="sr-only">Toggle navigation</span> <span class="icon-bar top-bar"></span> <span class="icon-bar middle-bar"></span> <span class="icon-bar bottom-bar"></span> </button> <div class="collapse navbar-collapse text-right" id="navbarNav"> <ul class="navbar-nav ml-auto flex-nowrap"> <li class="nav-item "> <a class="nav-link" href="/">About </a> </li> <li class="nav-item "> <a class="nav-link" href="/publications/">Publications </a> </li> <li class="nav-item "> <a class="nav-link" href="/blog/">Blog </a> </li> <li class="nav-item "> <a class="nav-link" href="/cv/">CV </a> </li> <li class="nav-item "> <a class="nav-link" href="/teaching/">Teaching </a> </li> <li class="nav-item "> <a class="nav-link" href="/videos/">Videos </a> </li> <li class="nav-item"> <button id="search-toggle" title="Search" onclick="openSearchModal()"> <span class="nav-link">ctrl k <i class="ti ti-search"></i></span> </button> </li> <li class="toggle-container"> <button id="light-toggle" title="Change theme"> <i class="ti ti-sun-moon" id="light-toggle-system"></i> <i class="ti ti-moon-filled" id="light-toggle-dark"></i> <i class="ti ti-sun-filled" id="light-toggle-light"></i> </button> </li> </ul> </div> </div> </nav> <progress id="progress" value="0"> <div class="progress-container"> <span class="progress-bar"></span> </div> </progress> </header> <div class="container mt-5" role="main"> <div class="post"> <header class="post-header"> <h1 class="post-title">Solving the Cahn-Hilliard equation on complex geometries</h1> <p class="post-meta"> Created in June 19, 2024 </p> <p class="post-tags"> <a href="/blog/2024"> <i class="fa-solid fa-calendar fa-sm"></i> 2024 </a>   ·   <a href="/blog/tag/cahn-hilliard"> <i class="fa-solid fa-hashtag fa-sm"></i> Cahn-Hilliard</a>   <a href="/blog/tag/pdes"> <i class="fa-solid fa-hashtag fa-sm"></i> PDEs</a>   <a href="/blog/tag/iga"> <i class="fa-solid fa-hashtag fa-sm"></i> IGA</a>   ·   <a href="/blog/category/projects"> <i class="fa-solid fa-tag fa-sm"></i> Projects</a> </p> </header> <article class="post-content"> <div id="markdown-content"> <h2 id="the-cahn-hilliard-equation">The Cahn-Hilliard equation</h2> <p>The Cahn–Hilliard equation describes the process of phase separation, by which the two components of a binary fluid spontaneously separate and form domains pure in each component. It was originally proposed in 1958 to model phase separation in binary alloys \cite{Cahn-Hilliard, Cahn-Hilliard2}. Since then it has been used to describe various phenomena, such as spinodal decomposition \cite{MARALDI201231}, diblock copolymer \cite{Choksi,JEONG20141263}, image inpainting \cite{4032803}, tumor growth simulation \cite{tumor,WISE2008524} or multiphase fluid flows \cite{BADALASSI2003371, Kotschote}.</p> <p>There are two main approaches to describing phase transition phenomena: sharp-interface models and phase-field models. Sharp-interface models involve the resolution of a moving boundary problem, meaning that partial differential equations have to be solved for each phase. This can lead to physical \cite{Anderson} and computational complications \cite{Barrett}, such as jump discontinuities across the interface. Phase-field models replace sharp-interfaces by thin transitions regions where the interfacial forces are smoothly distributed (diffuse interfaces). For this reason, phase-field models are also referred to as \emph{diffuse interface} models, and they are emerging as a promising tool to treat problems with interfaces.</p> <p>From the mathematical point of view, the Cahn-Hilliard equation is a stiff, fourth-order, nonlinear parabolic partial differential equation. The elementary form of the Cahn-Hilliard equation is given by</p> <p>\begin{equation} \frac{\partial \phi}{\partial t}=\nabla \cdot \left(m\left(\phi\right) \nabla \left(W’\left(\phi\right) -\epsilon ^2 \Delta \phi \right) \right) \label{element} \end{equation}</p> <p>where \(\phi\left(\mathbf{x},t\right) \in [-1,1]\) represents the phase-field variable, which describes the location of different components (e.g., \(\phi=-1\) in oil and \(\phi=1\) in water), \(m\left(\phi\right)\) is the mobility, \(W\left(\phi\right)\) is the so-called double-well potential, and \(\epsilon\) is a length scale related to the thickness of the diffuse interface.</p> <p>Two different approaches have been used to solve the Cahn-Hilliard equation: solving the original form given by Eqn.\eqref{element}, which involves fourth-order operators, or by splitting it into two second order partial differential equations by introducing an auxiliary variable — the chemical potential \(\mu\). The split version of the equation is given by</p> <p>\begin{equation} \frac{\partial \phi}{\partial t}=\nabla \cdot \left(m\left(\phi\right) \nabla \mu \right) \label{split1} \end{equation} \begin{equation} \mu=W’\left(\phi \right) - \epsilon^2 \Delta \phi. \label{chempot} \end{equation}</p> <p>The splitting strategy was proposed by Elliot \cite{Elliott1989ASO} to avoid constraints related to the continuity of the basis functions when using the finite element method with a primal formulation. It also facilitates the imposition of the boundary conditions on a circular geometry, which is the case we are interested in. Unfortunately, this comes at a price of an additional degree of freedom introduced into the solver. Nevertheless, this reformulation reduces the complexity of the problem from the numerical point of view (see \cite{M2AN_2009__43_5_1003_0,Zee}).</p> <p>The spatial discretization of the governing equations is performed using isogeometric analysis (IGA) \cite{HUGHES20054135}. IGA is a generalization of the finite-element method that uses non-uniform rational B-splines (NURBS) to define the discrete spaces. A significant advantage of IGA with respect to finite element analysis is that the basis functions can be constructed with controllable continuity across the element boundaries, even on mapped geometries. The higher-order global continuity of the basis functions has been shown to produce higher accuracy than classical \(\mathcal{C}^0\)-continuous finite elements for the same number of degrees of freedom \cite{akkerman2008role,evans2009n}; and has been widely used to solve partial differential equations with high-order spatial derivatives \cite{GOMEZ20084333, GOMEZ20101828, GOMEZ201252}. Here, we will use \(\mathcal{C}^1\)-continuous quadratic splines for \(\phi\) and \(\mu\).</p> <h2 id="strong-form">Strong form</h2> <p>The strong form of the problem is formulated as follows: find \(\phi:\Omega \times \left[0,T\right]\rightarrow \mathbb{R}\) and \(\mu:\Omega \times \left[0,T\right]\rightarrow \mathbb{R}\) (being \(\mu\) an auxiliary variable) such that:</p> <p>\begin{equation} \frac{\partial \phi}{\partial t}=\nabla \cdot \left(m\left(\phi\right) \nabla \mu\right) \quad \text{in} \ \Omega \times \left[0,T\right], \label{st1} \end{equation} <br> \begin{equation} \mu=W’\left(\phi\right)-\epsilon^2 \Delta \phi \quad \text{in} \ \Omega \times \left[0,T\right], \label{st2} \end{equation} \begin{equation} \phi=g \quad \text{on} \ \Gamma_g \times \left[0,T\right], \label{st3} \end{equation} \begin{equation} <br> m\left(\phi\right)\epsilon^2\Delta\phi=q \quad \text{on} \ \Gamma_q \times \left[0,T\right], \label{st4} \end{equation} \begin{equation} \nabla\left(m\left(\phi\right)\mu\right)\cdot \mathbf{n}=s \quad \text{on} \ \Gamma_s \times \left[0,T\right], \label{st5} \end{equation} \begin{equation} \nabla\left(m\left(\phi\right)\phi\right)\cdot \mathbf{n}=h \quad \text{on} \ \Gamma_h \times \left[0,T\right], \label{st6}<br> \end{equation} \begin{equation} \phi\left(\mathbf{x},0\right)=\phi_0\left(\mathbf{x}\right) \quad \text{in} \ \Omega. \label{st7}<br> \end{equation}</p> <p>The double well function \(W\left(\phi\right)\) is defined such that it has two local minima, which makes possible the coexistence of the different phases. Some important examples of double well functions can be found in \cite{Gomez2}. In this work we will take the classical quartic potential</p> <p>\begin{equation} W\left(\phi\right)=\frac{1}{4}\left(1-\phi^2\right)^2, \end{equation}</p> <p>which is a qualitative approximation of the logarithmic double well.</p> <p>The mobility \(m\left(\phi\right)\), which can be linked with the diffusivity, controls the time scale of the problem. The most common approach is to set it as a constant, \(m\left(\phi\right)=m\). Such an approach is extensively applied in both analytical and numerical studies \cite{Rajagopal,polymer,CuetoFelgueroso2008ATF}. We will take \(m\) constant and equal to one as recommended in \cite{GOMEZ20084333}.</p> <p>The parameter \(\epsilon\) is a positive constant that defines the length scale for the problem. According to \cite{GOMEZ20084333}, the solution to the Cahn-Hilliard equations depends only on the dimensionless number</p> <p>\begin{equation} \alpha=\frac{L_0^2}{3\epsilon^2} \end{equation}</p> <p>also referred to as sharpness parameter, where \(L_0\) is a length scale of the problem. Here, we will assume that \(L_0\) is a measure of the computational domain size. Without loss of generality, \(L_0=R_2=1.0\) will be the outer radius of the quarter of annulus. The sharpness parameter $\alpha$ usually takes values in the range \(10^3-10^4\) \cite{GOMEZ20084333,Gomez2}. We will study the evolution of the phase-field variable for different values of \(\alpha\).</p> <div class="row mt-3"> <div class="col-sm mt-3 mt-md-0"> <figure> <picture> <source class="responsive-img-srcset" srcset="/assets/img/fig2_ch-480.webp 480w,/assets/img/fig2_ch-800.webp 800w,/assets/img/fig2_ch-1400.webp 1400w," sizes="95vw" type="image/webp"></source> <img src="/assets/img/fig2_ch.png" class="img-fluid rounded z-depth-1" width="100%" height="auto" loading="eager" onerror="this.onerror=null; $('.responsive-img-srcset').remove();"> </picture> </figure> </div> <div class="col-sm mt-3 mt-md-0"> <figure> <picture> <source class="responsive-img-srcset" srcset="/assets/img/fig3_ch-480.webp 480w,/assets/img/fig3_ch-800.webp 800w,/assets/img/fig3_ch-1400.webp 1400w," sizes="95vw" type="image/webp"></source> <img src="/assets/img/fig3_ch.png" class="img-fluid rounded z-depth-1" width="100%" height="auto" loading="eager" onerror="this.onerror=null; $('.responsive-img-srcset').remove();"> </picture> </figure> </div> </div> <div class="caption"> Evolution of the phase-field from a randomly perturbed initial condition for $$\alpha=1500$$ and $$\bar{\phi}=0.3$$ (left). Evolution of the phase-field from a randomly perturbed initial condition for $$\alpha=3000$$ and $$\bar{\phi}=0.1$$ (right). </div> </div> </article> </div> </div> <footer class="fixed-bottom" role="contentinfo"> <div class="container mt-0"> © Copyright 2024 Mario de Lucio. </div> </footer> <script src="https://cdn.jsdelivr.net/npm/jquery@3.6.0/dist/jquery.min.js" integrity="sha256-/xUj+3OJU5yExlq6GSYGSHk7tPXikynS7ogEvDej/m4=" crossorigin="anonymous"></script> <script src="/assets/js/bootstrap.bundle.min.js"></script> <script src="https://cdn.jsdelivr.net/npm/mdbootstrap@4.20.0/js/mdb.min.js" integrity="sha256-NdbiivsvWt7VYCt6hYNT3h/th9vSTL4EDWeGs5SN3DA=" crossorigin="anonymous"></script> <script defer src="https://cdn.jsdelivr.net/npm/masonry-layout@4.2.2/dist/masonry.pkgd.min.js" integrity="sha256-Nn1q/fx0H7SNLZMQ5Hw5JLaTRZp0yILA/FRexe19VdI=" crossorigin="anonymous"></script> <script defer src="https://cdn.jsdelivr.net/npm/imagesloaded@5.0.0/imagesloaded.pkgd.min.js" integrity="sha256-htrLFfZJ6v5udOG+3kNLINIKh2gvoKqwEhHYfTTMICc=" crossorigin="anonymous"></script> <script defer src="/assets/js/masonry.js" type="text/javascript"></script> <script defer src="https://cdn.jsdelivr.net/npm/medium-zoom@1.1.0/dist/medium-zoom.min.js" integrity="sha256-ZgMyDAIYDYGxbcpJcfUnYwNevG/xi9OHKaR/8GK+jWc=" crossorigin="anonymous"></script> <script defer src="/assets/js/zoom.js?85ddb88934d28b74e78031fd54cf8308"></script> <script src="/assets/js/no_defer.js?2781658a0a2b13ed609542042a859126"></script> <script defer src="/assets/js/common.js?06cae41083477f121be8cd9797ad8e2f"></script> <script defer src="/assets/js/copy_code.js?12775fdf7f95e901d7119054556e495f" type="text/javascript"></script> <script defer src="/assets/js/jupyter_new_tab.js?d9f17b6adc2311cbabd747f4538bb15f"></script> <script async src="https://d1bxh8uas1mnw7.cloudfront.net/assets/embed.js"></script> <script async src="https://badge.dimensions.ai/badge.js"></script> <script type="text/javascript">window.MathJax={tex:{tags:"ams"}};</script> <script defer type="text/javascript" id="MathJax-script" src="https://cdn.jsdelivr.net/npm/mathjax@3.2.0/es5/tex-mml-chtml.min.js" integrity="sha256-rjmgmaB99riUNcdlrDtcAiwtLIojSxNyUFdl+Qh+rB4=" crossorigin="anonymous"></script> <script defer src="https://cdnjs.cloudflare.com/polyfill/v3/polyfill.min.js?features=es6" crossorigin="anonymous"></script> <script type="text/javascript">function progressBarSetup(){"max"in document.createElement("progress")?(initializeProgressElement(),$(document).on("scroll",function(){progressBar.attr({value:getCurrentScrollPosition()})}),$(window).on("resize",initializeProgressElement)):(resizeProgressBar(),$(document).on("scroll",resizeProgressBar),$(window).on("resize",resizeProgressBar))}function getCurrentScrollPosition(){return $(window).scrollTop()}function initializeProgressElement(){let e=$("#navbar").outerHeight(!0);$("body").css({"padding-top":e}),$("progress-container").css({"padding-top":e}),progressBar.css({top:e}),progressBar.attr({max:getDistanceToScroll(),value:getCurrentScrollPosition()})}function getDistanceToScroll(){return $(document).height()-$(window).height()}function resizeProgressBar(){progressBar.css({width:getWidthPercentage()+"%"})}function getWidthPercentage(){return getCurrentScrollPosition()/getDistanceToScroll()*100}const progressBar=$("#progress");window.onload=function(){setTimeout(progressBarSetup,50)};</script> <script src="/assets/js/vanilla-back-to-top.min.js?f40d453793ff4f64e238e420181a1d17"></script> <script>addBackToTop();</script> <script type="module" src="/assets/js/search/ninja-keys.min.js?601a2d3465e2a52bec38b600518d5f70"></script> <ninja-keys hidebreadcrumbs noautoloadmdicons placeholder="Type to start searching"></ninja-keys> <script>let searchTheme=determineComputedTheme();const ninjaKeys=document.querySelector("ninja-keys");"dark"===searchTheme?ninjaKeys.classList.add("dark"):ninjaKeys.classList.remove("dark");const openSearchModal=()=>{const e=$("#navbarNav");e.hasClass("show")&&e.collapse("hide"),ninjaKeys.open()};</script> <script>const ninja=document.querySelector("ninja-keys");ninja.data=[{id:"nav-about",title:"About",section:"Navigation",handler:()=>{window.location.href="/"}},{id:"nav-publications",title:"Publications",description:"Ordered by most recent.",section:"Navigation",handler:()=>{window.location.href="/publications/"}},{id:"nav-blog",title:"Blog",description:"",section:"Navigation",handler:()=>{window.location.href="/blog/"}},{id:"nav-cv",title:"CV",description:"",section:"Navigation",handler:()=>{window.location.href="/cv/"}},{id:"nav-teaching",title:"Teaching",description:"Materials for courses you taught. 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We adopt the split form of the equation to avoid introducing fourth-order operators and facilitate the imposition of the boundary conditions on the circular geometry,</p> <p class="post-meta"> 6 min read   ·   October 20, 2015 </p> <p class="post-tags"> <a href="/blog/2015"> <i class="fa-solid fa-calendar fa-sm"></i> 2015 </a>   ·   <a href="/blog/tag/cahn-hilliard"> <i class="fa-solid fa-hashtag fa-sm"></i> Cahn-Hilliard</a>   <a href="/blog/tag/pdes"> <i class="fa-solid fa-hashtag fa-sm"></i> PDEs</a>   <a href="/blog/tag/iga"> <i class="fa-solid fa-hashtag fa-sm"></i> IGA</a>   ·   <a href="/blog/category/sample-posts"> <i class="fa-solid fa-tag fa-sm"></i> sample-posts</a> </p> </li> <li> <h3> <a class="post-title" href="/blog/2015/code/">a post with code</a> </h3> <p>an example of a blog post with some code</p> <p class="post-meta"> 4 min read   ·   July 15, 2015 </p> <p class="post-tags"> <a href="/blog/2015"> <i class="fa-solid fa-calendar fa-sm"></i> 2015 </a>   ·   <a href="/blog/tag/formatting"> <i class="fa-solid fa-hashtag fa-sm"></i> formatting</a>   <a href="/blog/tag/code"> <i class="fa-solid fa-hashtag fa-sm"></i> code</a>   ·   <a href="/blog/category/sample-posts"> <i class="fa-solid fa-tag fa-sm"></i> sample-posts</a> </p> </li> <li> <div class="row"> <div class="col-sm-9"> <h3> <a class="post-title" href="/blog/2015/images/">a post with images</a> </h3> <p>this is what included images could look like</p> <p class="post-meta"> 3 min read   ·   May 15, 2015 </p> <p class="post-tags"> <a href="/blog/2015"> <i class="fa-solid fa-calendar fa-sm"></i> 2015 </a>   ·   <a href="/blog/tag/formatting"> <i class="fa-solid fa-hashtag fa-sm"></i> formatting</a>   <a href="/blog/tag/images"> <i class="fa-solid fa-hashtag fa-sm"></i> images</a>   ·   <a href="/blog/category/sample-posts"> <i class="fa-solid fa-tag fa-sm"></i> sample-posts</a> </p> </div> <div class="col-sm-3"> <img class="card-img" src="/assets/img/9.jpg" style="object-fit: cover; 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We adopt the split form of the equation to avoid introducing fourth-order operators and facilitate the imposition of the boundary conditions on the circular geometry,</p> <p class="post-meta"> 6 min read   ·   June 19, 2024 </p> <p class="post-tags"> <a href="/blog/2024"> <i class="fa-solid fa-calendar fa-sm"></i> 2024 </a>   ·   <a href="/blog/tag/cahn-hilliard"> <i class="fa-solid fa-hashtag fa-sm"></i> Cahn-Hilliard</a>   <a href="/blog/tag/pdes"> <i class="fa-solid fa-hashtag fa-sm"></i> PDEs</a>   <a href="/blog/tag/iga"> <i class="fa-solid fa-hashtag fa-sm"></i> IGA</a>   ·   <a href="/blog/category/projects"> <i class="fa-solid fa-tag fa-sm"></i> Projects</a> </p> </li> <li> <h3> <a class="post-title" href="/blog/2023/tables/">displaying beautiful tables with Bootstrap Tables</a> </h3> <p>an example of how to use Bootstrap Tables</p> <p class="post-meta"> 3 min read   ·   March 20, 2023 </p> <p class="post-tags"> <a href="/blog/2023"> <i class="fa-solid fa-calendar fa-sm"></i> 2023 </a>   ·   <a href="/blog/tag/formatting"> <i class="fa-solid fa-hashtag fa-sm"></i> formatting</a>   <a href="/blog/tag/tables"> <i class="fa-solid fa-hashtag fa-sm"></i> tables</a>   ·   <a href="/blog/category/sample-posts"> <i class="fa-solid fa-tag fa-sm"></i> sample-posts</a> </p> </li> <li> <h3> <a class="post-title" href="/blog/2015/code/">a post with code</a> </h3> <p>an example of a blog post with some code</p> <p class="post-meta"> 4 min read   ·   July 15, 2015 </p> <p class="post-tags"> <a href="/blog/2015"> <i class="fa-solid fa-calendar fa-sm"></i> 2015 </a>   ·   <a href="/blog/tag/formatting"> <i class="fa-solid fa-hashtag fa-sm"></i> formatting</a>   <a href="/blog/tag/code"> <i class="fa-solid fa-hashtag fa-sm"></i> code</a>   ·   <a href="/blog/category/sample-posts"> <i class="fa-solid fa-tag fa-sm"></i> sample-posts</a> </p> </li> <li> <div class="row"> <div class="col-sm-9"> <h3> <a class="post-title" href="/blog/2015/images/">a post with images</a> </h3> <p>this is what included images could look like</p> <p class="post-meta"> 3 min read   ·   May 15, 2015 </p> <p class="post-tags"> <a href="/blog/2015"> <i class="fa-solid fa-calendar fa-sm"></i> 2015 </a>   ·   <a href="/blog/tag/formatting"> <i class="fa-solid fa-hashtag fa-sm"></i> formatting</a>   <a href="/blog/tag/images"> <i class="fa-solid fa-hashtag fa-sm"></i> images</a>   ·   <a href="/blog/category/sample-posts"> <i class="fa-solid fa-tag fa-sm"></i> sample-posts</a> </p> </div> <div class="col-sm-3"> <img class="card-img" src="/assets/img/9.jpg" style="object-fit: cover; 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diff --git a/blog/tag/code/index.html b/blog/tag/code/index.html
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+++ b/blog/tag/code/index.html
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diff --git a/blog/tag/images/index.html b/blog/tag/images/index.html
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diff --git a/blog/tag/pdes/index.html b/blog/tag/pdes/index.html
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mt-3 p-3"> <h3 class="card-title font-weight-medium">General Information</h3> <div> <table class="table table-cv table-sm table-borderless table-responsive"> <tr> <td class="p-1 pr-2 font-weight-bold"> <b>Full Name</b> </td> <td class="p-1 pl-2 font-weight-light text">Mario de Lucio</td> </tr> <tr> <td class="p-1 pr-2 font-weight-bold"> <b>Place of Birth</b> </td> <td class="p-1 pl-2 font-weight-light text">Laredo, Cantabria, Spain</td> </tr> <tr> <td class="p-1 pr-2 font-weight-bold"> <b>Date of Birth</b> </td> <td class="p-1 pl-2 font-weight-light text">22nd August 1994</td> </tr> <tr> <td class="p-1 pr-2 font-weight-bold"> <b>Languages</b> </td> <td class="p-1 pl-2 font-weight-light text">Spanish, English, Galician</td> </tr> </table> </div> </div> <a class="anchor" id="Education"></a> <div class="card mt-3 p-3"> <h3 class="card-title font-weight-medium">Education</h3> <div> <ul class="card-text font-weight-light list-group list-group-flush"> <li class="list-group-item"> <div class="row"> <div class="col-xs-2 cl-sm-2 col-md-2 text-center" style="width: 75px"> <table class="table-cv"> <tbody> <tr> <td> <span class="badge font-weight-bold danger-color-dark text-uppercase align-middle" style="min-width: 75px">2020-2024</span> </td> </tr> </tbody> </table> </div> <div class="col-xs-10 cl-sm-10 col-md-10 mt-2 mt-md-0"> <h6 class="title font-weight-bold ml-1 ml-md-4">PhD in Mechanical Engineering</h6> <table class="table-cv ml-1 ml-md-4 institution"> <tbody> <tr> <td style="vertical-align: top; text-align: center" class="institution"> <i class="fa-solid fa-building-columns iconinstitution"></i> </td> <td class="institution">Purdue University, IN, USA</td> </tr> </tbody> </table> <ul class="items"> <li> <span class="item">Concentration in <a href="https://www.purdue.edu/gradschool/cigp/about/index.html" rel="external nofollow noopener" target="_blank">Computational Science and Engineering</a> and Solid Mechanics.</span> </li> <li> <span class="item">Ph.D. thesis <a href="https://hammer.purdue.edu/articles/thesis/Numerical_Simulation_and_Poromechanical_Modeling_of_Subcutaneous_Injection_of_Monoclonal_Antibodies/25674240" rel="external nofollow noopener" target="_blank">"Numerical simulation and poromechanical modeling of subcutaneous injection of monoclonal antibodies"</a></span> </li> </ul> </div> </div> </li> <li class="list-group-item"> <div class="row"> <div class="col-xs-2 cl-sm-2 col-md-2 text-center" style="width: 75px"> <table class="table-cv"> <tbody> <tr> <td> <span class="badge font-weight-bold danger-color-dark text-uppercase align-middle" style="min-width: 75px">2017-2019</span> </td> </tr> </tbody> </table> </div> <div class="col-xs-10 cl-sm-10 col-md-10 mt-2 mt-md-0"> <h6 class="title font-weight-bold ml-1 ml-md-4">MSc in Civil Engineering (Graduated with Honors, ranked 1st)</h6> <table class="table-cv ml-1 ml-md-4 institution"> <tbody> <tr> <td style="vertical-align: top; text-align: center" class="institution"> <i class="fa-solid fa-building-columns iconinstitution"></i> </td> <td class="institution">University of A Coruna, Spain</td> </tr> </tbody> </table> <ul class="items"> <li> <span class="item">Concentration in Structural and Construction Engineering</span> </li> <li> <span class="item">Master’s thesis <a href="https://www.researchgate.net/publication/329707429_A_multi-layered_in-silico_model_for_rupture_risk_assessment_of_abdominal_aortic_aneurysms_with_non-atherosclerotic_intimal_thickening" rel="external nofollow noopener" target="_blank">"A multi-layered in-silico model for rupture risk assessment of abdominal aortic aneurysms with non-atherosclerotic intimal thickening"</a></span> </li> <li> <span class="item">Professional master’s project <a href="https://dialnet.unirioja.es/servlet/articulo?codigo=7486537" rel="external nofollow noopener" target="_blank">"Cable-stayed bridge over the San Martin Strait to connect the towns of Laredo and Santoña, Cantabria, Northern Spain"</a></span> </li> </ul> </div> </div> </li> <li class="list-group-item"> <div class="row"> <div class="col-xs-2 cl-sm-2 col-md-2 text-center" style="width: 75px"> <table class="table-cv"> <tbody> <tr> <td> <span class="badge font-weight-bold danger-color-dark text-uppercase align-middle" style="min-width: 75px">2013-2017</span> </td> </tr> </tbody> </table> </div> <div class="col-xs-10 cl-sm-10 col-md-10 mt-2 mt-md-0"> <h6 class="title font-weight-bold ml-1 ml-md-4">BSc in Civil Engineering (Graduated with Honors, ranked 1st)</h6> <table class="table-cv ml-1 ml-md-4 institution"> <tbody> <tr> <td style="vertical-align: top; text-align: center" class="institution"> <i class="fa-solid fa-building-columns iconinstitution"></i> </td> <td class="institution">University of A Coruna, Spain</td> </tr> </tbody> </table> <ul class="items"> <li> <span class="item">Concentration in Structural and Geotechnical Engineering</span> </li> <li> <span class="item">Bachelor’s thesis <a href="https://ruc.udc.es/dspace/handle/2183/19429" rel="external nofollow noopener" target="_blank">"Environmental Restoration and Channeling of Juan Diaz River in Panama City"</a></span> </li> </ul> </div> </div> </li> </ul> </div> </div> <a class="anchor" id="Experience"></a> <div class="card mt-3 p-3"> <h3 class="card-title font-weight-medium">Experience</h3> <div> <ul class="card-text font-weight-light list-group list-group-flush"> <li class="list-group-item"> <div class="row"> <div class="col-xs-2 cl-sm-2 col-md-2 text-center" style="width: 75px"> <table class="table-cv"> <tbody> <tr> <td> <span class="badge font-weight-bold danger-color-dark text-uppercase align-middle" style="min-width: 75px">Jul 2024 - Present</span> </td> </tr> </tbody> </table> </div> <div class="col-xs-10 cl-sm-10 col-md-10 mt-2 mt-md-0"> <h6 class="title font-weight-bold ml-1 ml-md-4">Research Scientist</h6> <table class="table-cv ml-1 ml-md-4 institution"> <tbody> <tr> <td style="vertical-align: top; text-align: center" class="institution"> <i class="fa-solid fa-building-columns iconinstitution"></i> </td> <td class="institution"> <a href="https://www.purdue.edu/research/rche/" rel="external nofollow noopener" target="_blank">Regenstrief Center for Healthcare Engineering</a>, Purdue University, IN, USA</td> </tr> </tbody> </table> <ul class="items"> <li> <span class="item">Engaged in a strategic collaboration between Eli Lilly and Purdue University, concentrating on the analysis and optimization of injectable medicine delivery systems.</span> </li> <li> <span class="item">Conducted advanced numerical simulations to enhance understanding of the auto-injection process mechanics, aiming to improve drug bioavailability, minimize injection site pain, and boost patient compliance and overall health. - Developed high-fidelity computational models using the Finite Element Method and Isogeometric Analysis to understand and and predict tissue deformation and fluid pressure build-up as well as their impact on drug transport and absorption.</span> </li> <li> <span class="item">Explored innovative approaches and technologies for improving drug delivery systems, focusing on device design, injection parameters, and drug formulation</span> </li> <li> <span class="item">Supported and advanced the strategic collaboration between Eli Lilly and Purdue University, promoting the translation of research findings into practical applications within the pharmaceutical industry.</span> </li> <li> <span class="item">Demonstrated expertise in advanced computational methods, quantitative analysis, Bayesian and causal inference modeling, and AI methods in health and life sciences.</span> </li> <li> <span class="item">Contributed to research grant writing, project management, and publication in reputable healthcare, medical, and biomedical journals.</span> </li> </ul> </div> </div> </li> <li class="list-group-item"> <div class="row"> <div class="col-xs-2 cl-sm-2 col-md-2 text-center" style="width: 75px"> <table class="table-cv"> <tbody> <tr> <td> <span class="badge font-weight-bold danger-color-dark text-uppercase align-middle" style="min-width: 75px">Jan 2020 - Jul 2024</span> </td> </tr> </tbody> </table> </div> <div class="col-xs-10 cl-sm-10 col-md-10 mt-2 mt-md-0"> <h6 class="title font-weight-bold ml-1 ml-md-4">Research Assistant</h6> <table class="table-cv ml-1 ml-md-4 institution"> <tbody> <tr> <td style="vertical-align: top; text-align: center" class="institution"> <i class="fa-solid fa-building-columns iconinstitution"></i> </td> <td class="institution">Purdue University, IN, USA</td> </tr> </tbody> </table> <ul class="items"> <li> <span class="item">Involved in a project within a strategic collaboration between Eli Lilly and Purdue University, focusing on the analysis of the delivery of injectable medicines.</span> </li> <li> <span class="item">Performed numerical simulations to analyze the delivery of injectable medicines with the overall goals of better understanding the fundamental mechanics of the auto-injection process and its effect on skin, improved drug bioavailability, and reducing injection site pain in order to better patient compliance and enhance overall health.</span> </li> <li> <span class="item">Developed high-fidelity computational models using the Finite Element Method and Isogeometric Analysis to understand and and predict tissue deformation and fluid pressure build-up as well as their impact on drug transport and absorption.</span> </li> <li> <span class="item">Investigated innovative approaches and technologies to improve drug delivery systems, considering factors such as device design, injection parameters, and drug formulation.</span> </li> <li> <span class="item">Utilized data from computational models to drive informed decision-making in medical device development, enabling effective optimization and innovation in design and functionality.</span> </li> <li> <span class="item">Supported the strategic collaboration between Eli Lilly and Purdue University, fostering innovation and facilitating the translation of research findings into practical applications in the pharmaceutical industry.</span> </li> </ul> </div> </div> </li> <li class="list-group-item"> <div class="row"> <div class="col-xs-2 cl-sm-2 col-md-2 text-center" style="width: 75px"> <table class="table-cv"> <tbody> <tr> <td> <span class="badge font-weight-bold danger-color-dark text-uppercase align-middle" style="min-width: 75px">Jul 2019 - Dec 2019</span> </td> </tr> </tbody> </table> </div> <div class="col-xs-10 cl-sm-10 col-md-10 mt-2 mt-md-0"> <h6 class="title font-weight-bold ml-1 ml-md-4">Visiting Researcher</h6> <table class="table-cv ml-1 ml-md-4 institution"> <tbody> <tr> <td style="vertical-align: top; text-align: center" class="institution"> <i class="fa-solid fa-building-columns iconinstitution"></i> </td> <td class="institution">Purdue University, IN, USA</td> </tr> </tbody> </table> <ul class="items"> <li> <span class="item">Developed computational methods utilizing isogeometric analysis, poroelasticity, and data-driven tissue geometries to model the complex dynamics of high-volume, high-speed subcutaneous injection of monoclonal antibodies.</span> </li> <li> <span class="item">Developed highly sophisticated numerical algorithms capable of running in parallel, utilizing 200+ processors in Purdue’s Rosen Center for Advanced Computing.</span> </li> <li> <span class="item">Leveraged the computational power and parallel processing capabilities to efficiently simulate and analyze the complex fluid-structure interactions during the subcutaneous injection process.</span> </li> <li> <span class="item">Conducted extensive simulations using the developed computational methods to investigate the effects of injection parameters, tissue properties, and geometrical variations on the injection dynamics and the resulting distribution of monoclonal antibodies.</span> </li> </ul> </div> </div> </li> <li class="list-group-item"> <div class="row"> <div class="col-xs-2 cl-sm-2 col-md-2 text-center" style="width: 75px"> <table class="table-cv"> <tbody> <tr> <td> <span class="badge font-weight-bold danger-color-dark text-uppercase align-middle" style="min-width: 75px">Jul 2018 - Sep 2018</span> </td> </tr> </tbody> </table> </div> <div class="col-xs-10 cl-sm-10 col-md-10 mt-2 mt-md-0"> <h6 class="title font-weight-bold ml-1 ml-md-4">Graduate Research Assistant</h6> <table class="table-cv ml-1 ml-md-4 institution"> <tbody> <tr> <td style="vertical-align: top; text-align: center" class="institution"> <i class="fa-solid fa-building-columns iconinstitution"></i> </td> <td class="institution"> <a href="https://www.ntnu.edu/casa" rel="external nofollow noopener" target="_blank">Norwegian University of Science and Technology</a>, Trondheim, Norway</td> </tr> </tbody> </table> <ul class="items"> <li> <span class="item">Acted as a main collaborator in the project "Industrial Implementation of 3D printed AlSi10Mg components under quasi-static loading".</span> </li> <li> <span class="item">Conducted experimental tests on structures under both quasi-static and dynamic conditions, specifically focusing on extreme deformations and crushing.</span> </li> <li> <span class="item">Utilized Digital Image Correlation (DIC) tools to postprocess experimental results, enabling precise measurements and analysis of structural behavior.</span> </li> <li> <span class="item">Applied crashworthiness optimization techniques to enhance the performance and efficiency of the structures.</span> </li> <li> <span class="item">Developed finite element models to simulate the behavior of aluminum alloy thin-walled structures.</span> </li> <li> <span class="item">Developed comprehensive material card for AlSi10Mg 3D printed aluminum, encompassing mechanical, thermal, and viscoelastic properties for accurate simulation in engineering analyses.</span> </li> <li> <span class="item">Collaborated closely with industry partners to ensure the successful implementation of 3D printed components under quasi-static loading.</span> </li> </ul> </div> </div> </li> <li class="list-group-item"> <div class="row"> <div class="col-xs-2 cl-sm-2 col-md-2 text-center" style="width: 75px"> <table class="table-cv"> <tbody> <tr> <td> <span class="badge font-weight-bold danger-color-dark text-uppercase align-middle" style="min-width: 75px">Oct 2017 - Jul 2018</span> </td> </tr> </tbody> </table> </div> <div class="col-xs-10 cl-sm-10 col-md-10 mt-2 mt-md-0"> <h6 class="title font-weight-bold ml-1 ml-md-4">Graduate Research Assistant</h6> <table class="table-cv ml-1 ml-md-4 institution"> <tbody> <tr> <td style="vertical-align: top; text-align: center" class="institution"> <i class="fa-solid fa-building-columns iconinstitution"></i> </td> <td class="institution"> <a href="http://gme.udc.es/en" rel="external nofollow noopener" target="_blank">University of A Coruna</a>, A Coruna, Spain</td> </tr> </tbody> </table> <ul class="items"> <li> <span class="item">Awarded a prestigious fellowship by the Spanish Ministry of Education and Science to serve as a principal investigator, collaborating with the Department of Cardiovascular Surgery at the Complejo Universitario Hospitalario de A Coruna (CHUAC), to conduct research on the risk of rupture of abdominal aortic aneurysms (AAA) with atherosclerotic intimal thickening.</span> </li> <li> <span class="item">Developed an in-house code, called AneuPy, to generate idealized geometrical models of AAAs using clinical data. This code facilitated the creation of accurate and representative computational models for further analysis.</span> </li> <li> <span class="item">Performed cardiovascular fluid-structure interaction simulations of AAAs using different constitutive models for aortic tissue that allowed to better determine the risk of rupture.</span> </li> <li> <span class="item">Analyzed the stress distribution, deformation patterns, and hemodynamic factors within the AAA models to gain insights into the potential mechanisms of rupture.</span> </li> <li> <span class="item">Collaborated closely with the Department of Cardiovascular Surgery at CHUAC, exchanging knowledge and expertise to bridge the gap between research and clinical applications.</span> </li> </ul> </div> </div> </li> <li class="list-group-item"> <div class="row"> <div class="col-xs-2 cl-sm-2 col-md-2 text-center" style="width: 75px"> <table class="table-cv"> <tbody> <tr> <td> <span class="badge font-weight-bold danger-color-dark text-uppercase align-middle" style="min-width: 75px">Sep 2016 - Jul 2017</span> </td> </tr> </tbody> </table> </div> <div class="col-xs-10 cl-sm-10 col-md-10 mt-2 mt-md-0"> <h6 class="title font-weight-bold ml-1 ml-md-4">Undergraduate Research Assistant</h6> <table class="table-cv ml-1 ml-md-4 institution"> <tbody> <tr> <td style="vertical-align: top; text-align: center" class="institution"> <i class="fa-solid fa-building-columns iconinstitution"></i> </td> <td class="institution"> <a href="http://gme.udc.es/en" rel="external nofollow noopener" target="_blank">University of A Coruna</a>, A Coruna, Spain</td> </tr> </tbody> </table> <ul class="items"> <li> <span class="item">Granted with a research scholarship from the University of A Coruña to conduct research under the project "Mechanical Characterization of Structural Adhesives for Crashworthiness Applications".</span> </li> <li> <span class="item">Analyzed the mechanical behavior of various structural adhesives through rigorous experimental tests (single lap, double lap, thermal tests).</span> </li> <li> <span class="item">Developed computational models with cohesive elements and nonlinear contact mechanics to accurately reproduce the structural behavior of the adhesives.</span> </li> <li> <span class="item">Successfully replicated the adhesive’s structural behavior in the computational model, validating the quality of the mechanical characterization.</span> </li> <li> <span class="item">Provided engineers and researchers with a reliable tool for assessing adhesive performance and optimizing their, use in various industries.</span> </li> </ul> </div> </div> </li> <li class="list-group-item"> <div class="row"> <div class="col-xs-2 cl-sm-2 col-md-2 text-center" style="width: 75px"> <table class="table-cv"> <tbody> <tr> <td> <span class="badge font-weight-bold danger-color-dark text-uppercase align-middle" style="min-width: 75px">Jun 2016 - Sep 2016</span> </td> </tr> </tbody> </table> </div> <div class="col-xs-10 cl-sm-10 col-md-10 mt-2 mt-md-0"> <h6 class="title font-weight-bold ml-1 ml-md-4">Project Manager Assistant</h6> <table class="table-cv ml-1 ml-md-4 institution"> <tbody> <tr> <td style="vertical-align: top; text-align: center" class="institution"> <i class="fa-solid fa-building-columns iconinstitution"></i> </td> <td class="institution"> <a href="https://ihcantabria.com/en/" rel="external nofollow noopener" target="_blank">Environmental Hydraulics Institute of Cantabria</a>, Santander, Spain</td> </tr> </tbody> </table> <ul class="items"> <li> <span class="item">Worked as a hydraulic modeler on large-scale flood management projects in Panama and Venezuela in collaboration with the World Bank and the Inter-American Development Bank.</span> </li> <li> <span class="item">Conducted two and three-dimensional numerical simulations of free surface flow in rivers and estuaries to assess and quantify the level of flood hazard in densely populated urban areas.</span> </li> <li> <span class="item">Utilized advanced numerical models to assess the level of flood hazard and create accurate flood risk maps, providing valuable information for urban planning and disaster management strategies.</span> </li> <li> <span class="item">Generated accurate flood risk maps by analyzing the hydraulic behavior of water bodies, considering factors such as water flow, topography, and urban infrastructure.</span> </li> <li> <span class="item">Designed and proposed innovative solutions including flood barriers, coastal defenses, waterfront parks, floodresilient buildings and landscapes, reducing flood hazards by up to 60%.</span> </li> <li> <span class="item">Conducted feasibility studies and cost-benefit analyses to evaluate the economic and environmental implications of proposed flood mitigation solutions, assisting decision-makers in selecting the most suitable approaches.</span> </li> </ul> </div> </div> </li> </ul> </div> </div> <a class="anchor" id="Honors and Awards"></a> <div class="card mt-3 p-3"> <h3 class="card-title font-weight-medium">Honors and Awards</h3> <div> <ul class="card-text font-weight-light list-group list-group-flush"> <li class="list-group-item"> <div class="row"> <div class="col-xs-2 cl-sm-2 col-md-2 text-center" style="width: 75px"> <table class="table-cv"> <tbody> <tr> <td> <span class="badge font-weight-bold danger-color-dark text-uppercase align-middle" style="min-width: 75px">2023</span> </td> </tr> </tbody> </table> </div> <div class="col-xs-10 cl-sm-10 col-md-10 mt-2 mt-md-0"> <ul class="items"> <li> <span class="item"><a href="https://engineering.purdue.edu/ME/News/2023/purdue-me-grad-students-receive-fellowships-and-scholarships" rel="external nofollow noopener" target="_blank">Ben M. Hillberry Graduate Scholarship</a>, for PhD students pursuing research in the areas of biomechanics and materials, School of Mechanical Engineering, Purdue University.</span> </li> <li> <span class="item"><a href="https://engineering.purdue.edu/Engr/Trailblazers/Fellows/2023/Lucio" rel="external nofollow noopener" target="_blank">2023 Trailblazers in Engineering Fellow</a>, Purdue University College of Engineering.</span> </li> <li> <span class="item">Winner of the <a href="https://www.asce.org/communities/institutes-and-technical-groups/engineering-mechanics-institute/news/emi-2023-student-winners" rel="external nofollow noopener" target="_blank">2023 Poromechanics Student Competition</a>, Engineering Mechanics Institute, American Society of Civil Engineers.</span> </li> <li> <span class="item">College of Engineering Conference Travel Grant, Purdue University.</span> </li> <li> <span class="item">Purdue Graduate Student Government Doctoral Travel Grant, Purdue University.</span> </li> </ul> </div> </div> </li> <li class="list-group-item"> <div class="row"> <div class="col-xs-2 cl-sm-2 col-md-2 text-center" style="width: 75px"> <table class="table-cv"> <tbody> <tr> <td> <span class="badge font-weight-bold danger-color-dark text-uppercase align-middle" style="min-width: 75px">2020</span> </td> </tr> </tbody> </table> </div> <div class="col-xs-10 cl-sm-10 col-md-10 mt-2 mt-md-0"> <ul class="items"> <li> <span class="item"><a href="https://www.youtube.com/watch?v=hUmzbm_o9N0&amp;t=2047s" rel="external nofollow noopener" target="_blank">National Award to the best Master's Thesis in Civil Engineering by the Spanish Institution of Civil Engineers</a></span> </li> </ul> </div> </div> </li> <li class="list-group-item"> <div class="row"> <div class="col-xs-2 cl-sm-2 col-md-2 text-center" style="width: 75px"> <table class="table-cv"> <tbody> <tr> <td> <span class="badge font-weight-bold danger-color-dark text-uppercase align-middle" style="min-width: 75px">2019</span> </td> </tr> </tbody> </table> </div> <div class="col-xs-10 cl-sm-10 col-md-10 mt-2 mt-md-0"> <ul class="items"> <li> <span class="item">Award to the highest cumulative GPA of the School of Civil Engineering, University of A Coruna</span> </li> <li> <span class="item">Outstanding Civil Engineering Student Award, Galician Civil Engineering Foundation</span> </li> <li> <span class="item">Award to the best Master's Thesis in Structural Engineering by Grupo Puentes</span> </li> <li> <span class="item"><a href="https://www.copasagroup.com/es/premios-copasa-2019/" rel="external nofollow noopener" target="_blank">Award to the best Master's Thesis in Construction Engineering by COPASA</a></span> </li> </ul> </div> </div> </li> <li class="list-group-item"> <div class="row"> <div class="col-xs-2 cl-sm-2 col-md-2 text-center" style="width: 75px"> <table class="table-cv"> <tbody> <tr> <td> <span class="badge font-weight-bold danger-color-dark text-uppercase align-middle" style="min-width: 75px">2017</span> </td> </tr> </tbody> </table> </div> <div class="col-xs-10 cl-sm-10 col-md-10 mt-2 mt-md-0"> <ul class="items"> <li> <span class="item">Award to the highest cumulative GPA of the School of Civil Engineering, University of A Coruna</span> </li> <li> <span class="item">Outstanding Civil Engineering Student Award, Galician Civil Engineering Foundation</span> </li> <li> <span class="item">Award to the best Bachelor's Thesis in the field of Hydraulic Engineering by Gas Natural Fenosa</span> </li> </ul> </div> </div> </li> <li class="list-group-item"> <div class="row"> <div class="col-xs-2 cl-sm-2 col-md-2 text-center" style="width: 75px"> <table class="table-cv"> <tbody> <tr> <td> <span class="badge font-weight-bold danger-color-dark text-uppercase align-middle" style="min-width: 75px">2016</span> </td> </tr> </tbody> </table> </div> <div class="col-xs-10 cl-sm-10 col-md-10 mt-2 mt-md-0"> <ul class="items"> <li> <span class="item">Best Undergraduate Poster Award at the 2016 Graduate &amp; Undergraduate Research Symposium, University of A Coruña</span> </li> </ul> </div> </div> </li> </ul> </div> </div> <a class="anchor" id="Skills"></a> <div class="card mt-3 p-3"> <h3 class="card-title font-weight-medium">Skills</h3> <div> <ul class="card-text font-weight-light list-group list-group-flush"> <li class="list-group-item">Research, FEM, Python, FORTRAN, MATLAB, FEnics, PetIGA, Abaqus</li> </ul> </div> </div> </div> </article> </div> </div> <footer class="fixed-bottom" role="contentinfo"> <div class="container mt-0"> © Copyright 2024 Mario de Lucio. </div> </footer> <script src="https://cdn.jsdelivr.net/npm/jquery@3.6.0/dist/jquery.min.js" integrity="sha256-/xUj+3OJU5yExlq6GSYGSHk7tPXikynS7ogEvDej/m4=" crossorigin="anonymous"></script> <script src="/assets/js/bootstrap.bundle.min.js"></script> <script src="https://cdn.jsdelivr.net/npm/mdbootstrap@4.20.0/js/mdb.min.js" integrity="sha256-NdbiivsvWt7VYCt6hYNT3h/th9vSTL4EDWeGs5SN3DA=" crossorigin="anonymous"></script> <script defer src="https://cdn.jsdelivr.net/npm/masonry-layout@4.2.2/dist/masonry.pkgd.min.js" integrity="sha256-Nn1q/fx0H7SNLZMQ5Hw5JLaTRZp0yILA/FRexe19VdI=" crossorigin="anonymous"></script> <script defer src="https://cdn.jsdelivr.net/npm/imagesloaded@5.0.0/imagesloaded.pkgd.min.js" integrity="sha256-htrLFfZJ6v5udOG+3kNLINIKh2gvoKqwEhHYfTTMICc=" crossorigin="anonymous"></script> <script defer src="/assets/js/masonry.js" type="text/javascript"></script> <script defer src="https://cdn.jsdelivr.net/npm/medium-zoom@1.1.0/dist/medium-zoom.min.js" integrity="sha256-ZgMyDAIYDYGxbcpJcfUnYwNevG/xi9OHKaR/8GK+jWc=" crossorigin="anonymous"></script> <script defer src="/assets/js/zoom.js?85ddb88934d28b74e78031fd54cf8308"></script> <script src="/assets/js/no_defer.js?2781658a0a2b13ed609542042a859126"></script> <script defer src="/assets/js/common.js?06cae41083477f121be8cd9797ad8e2f"></script> <script defer src="/assets/js/copy_code.js?12775fdf7f95e901d7119054556e495f" type="text/javascript"></script> <script defer src="/assets/js/jupyter_new_tab.js?d9f17b6adc2311cbabd747f4538bb15f"></script> <script async src="https://d1bxh8uas1mnw7.cloudfront.net/assets/embed.js"></script> <script async src="https://badge.dimensions.ai/badge.js"></script> <script type="text/javascript">window.MathJax={tex:{tags:"ams"}};</script> <script defer type="text/javascript" id="MathJax-script" src="https://cdn.jsdelivr.net/npm/mathjax@3.2.0/es5/tex-mml-chtml.min.js" integrity="sha256-rjmgmaB99riUNcdlrDtcAiwtLIojSxNyUFdl+Qh+rB4=" crossorigin="anonymous"></script> <script defer src="https://cdnjs.cloudflare.com/polyfill/v3/polyfill.min.js?features=es6" crossorigin="anonymous"></script> <script type="text/javascript">function progressBarSetup(){"max"in document.createElement("progress")?(initializeProgressElement(),$(document).on("scroll",function(){progressBar.attr({value:getCurrentScrollPosition()})}),$(window).on("resize",initializeProgressElement)):(resizeProgressBar(),$(document).on("scroll",resizeProgressBar),$(window).on("resize",resizeProgressBar))}function getCurrentScrollPosition(){return $(window).scrollTop()}function initializeProgressElement(){let e=$("#navbar").outerHeight(!0);$("body").css({"padding-top":e}),$("progress-container").css({"padding-top":e}),progressBar.css({top:e}),progressBar.attr({max:getDistanceToScroll(),value:getCurrentScrollPosition()})}function getDistanceToScroll(){return $(document).height()-$(window).height()}function resizeProgressBar(){progressBar.css({width:getWidthPercentage()+"%"})}function getWidthPercentage(){return getCurrentScrollPosition()/getDistanceToScroll()*100}const progressBar=$("#progress");window.onload=function(){setTimeout(progressBarSetup,50)};</script> <script src="/assets/js/vanilla-back-to-top.min.js?f40d453793ff4f64e238e420181a1d17"></script> <script>addBackToTop();</script> <script type="module" src="/assets/js/search/ninja-keys.min.js?601a2d3465e2a52bec38b600518d5f70"></script> <ninja-keys hidebreadcrumbs noautoloadmdicons placeholder="Type to start searching"></ninja-keys> <script>let searchTheme=determineComputedTheme();const ninjaKeys=document.querySelector("ninja-keys");"dark"===searchTheme?ninjaKeys.classList.add("dark"):ninjaKeys.classList.remove("dark");const openSearchModal=()=>{const e=$("#navbarNav");e.hasClass("show")&&e.collapse("hide"),ninjaKeys.open()};</script> <script>const ninja=document.querySelector("ninja-keys");ninja.data=[{id:"nav-about",title:"About",section:"Navigation",handler:()=>{window.location.href="/"}},{id:"nav-publications",title:"Publications",description:"Ordered by most recent.",section:"Navigation",handler:()=>{window.location.href="/publications/"}},{id:"nav-blog",title:"Blog",description:"",section:"Navigation",handler:()=>{window.location.href="/blog/"}},{id:"nav-cv",title:"CV",description:"",section:"Navigation",handler:()=>{window.location.href="/cv/"}},{id:"nav-teaching",title:"Teaching",description:"Materials for courses you taught. 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+<!DOCTYPE html> <html lang="en"> <head> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> <meta charset="utf-8"> <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"> <meta http-equiv="X-UA-Compatible" content="IE=edge"> <title> CV | Mario de Lucio's website </title> <meta name="author" content="Mario de Lucio"> <meta name="description" content="Mario de Lucio's website "> <meta name="keywords" content="Computational Mechanics, Multiphysics Simulation, Biomechanics, Transport phenomena"> <link rel="stylesheet" href="/assets/css/bootstrap.min.css?a4b3f509e79c54a512b890d73235ef04"> <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/mdbootstrap@4.20.0/css/mdb.min.css" integrity="sha256-jpjYvU3G3N6nrrBwXJoVEYI/0zw8htfFnhT9ljN3JJw=" crossorigin="anonymous"> <link defer rel="stylesheet" href="/assets/css/academicons.min.css?f0b7046b84e425c55f3463ac249818f5"> <link defer rel="stylesheet" type="text/css" 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mt-3 p-3"> <h3 class="card-title font-weight-medium">General Information</h3> <div> <table class="table table-cv table-sm table-borderless table-responsive"> <tr> <td class="p-1 pr-2 font-weight-bold"> <b>Full Name</b> </td> <td class="p-1 pl-2 font-weight-light text">Mario de Lucio</td> </tr> <tr> <td class="p-1 pr-2 font-weight-bold"> <b>Place of Birth</b> </td> <td class="p-1 pl-2 font-weight-light text">Laredo, Cantabria, Spain</td> </tr> <tr> <td class="p-1 pr-2 font-weight-bold"> <b>Date of Birth</b> </td> <td class="p-1 pl-2 font-weight-light text">22nd August 1994</td> </tr> <tr> <td class="p-1 pr-2 font-weight-bold"> <b>Languages</b> </td> <td class="p-1 pl-2 font-weight-light text">Spanish, English, Galician</td> </tr> </table> </div> </div> <a class="anchor" id="Education"></a> <div class="card mt-3 p-3"> <h3 class="card-title font-weight-medium">Education</h3> <div> <ul class="card-text font-weight-light list-group list-group-flush"> <li class="list-group-item"> <div class="row"> <div class="col-xs-2 cl-sm-2 col-md-2 text-center" style="width: 75px"> <table class="table-cv"> <tbody> <tr> <td> <span class="badge font-weight-bold danger-color-dark text-uppercase align-middle" style="min-width: 75px">2020-2024</span> </td> </tr> </tbody> </table> </div> <div class="col-xs-10 cl-sm-10 col-md-10 mt-2 mt-md-0"> <h6 class="title font-weight-bold ml-1 ml-md-4">PhD in Mechanical Engineering</h6> <table class="table-cv ml-1 ml-md-4 institution"> <tbody> <tr> <td style="vertical-align: top; text-align: center" class="institution"> <i class="fa-solid fa-building-columns iconinstitution"></i> </td> <td class="institution">Purdue University, IN, USA</td> </tr> </tbody> </table> <ul class="items"> <li> <span class="item">Concentration in <a href="https://www.purdue.edu/gradschool/cigp/about/index.html" rel="external nofollow noopener" target="_blank">Computational Science and Engineering</a> and Solid Mechanics.</span> </li> <li> <span class="item">Ph.D. thesis <a href="https://hammer.purdue.edu/articles/thesis/Numerical_Simulation_and_Poromechanical_Modeling_of_Subcutaneous_Injection_of_Monoclonal_Antibodies/25674240" rel="external nofollow noopener" target="_blank">"Numerical simulation and poromechanical modeling of subcutaneous injection of monoclonal antibodies"</a></span> </li> </ul> </div> </div> </li> <li class="list-group-item"> <div class="row"> <div class="col-xs-2 cl-sm-2 col-md-2 text-center" style="width: 75px"> <table class="table-cv"> <tbody> <tr> <td> <span class="badge font-weight-bold danger-color-dark text-uppercase align-middle" style="min-width: 75px">2017-2019</span> </td> </tr> </tbody> </table> </div> <div class="col-xs-10 cl-sm-10 col-md-10 mt-2 mt-md-0"> <h6 class="title font-weight-bold ml-1 ml-md-4">MSc in Civil Engineering (Graduated with Honors, ranked 1st)</h6> <table class="table-cv ml-1 ml-md-4 institution"> <tbody> <tr> <td style="vertical-align: top; text-align: center" class="institution"> <i class="fa-solid fa-building-columns iconinstitution"></i> </td> <td class="institution">University of A Coruna, Spain</td> </tr> </tbody> </table> <ul class="items"> <li> <span class="item">Concentration in Structural and Construction Engineering</span> </li> <li> <span class="item">Master’s thesis <a href="https://www.researchgate.net/publication/329707429_A_multi-layered_in-silico_model_for_rupture_risk_assessment_of_abdominal_aortic_aneurysms_with_non-atherosclerotic_intimal_thickening" rel="external nofollow noopener" target="_blank">"A multi-layered in-silico model for rupture risk assessment of abdominal aortic aneurysms with non-atherosclerotic intimal thickening"</a></span> </li> <li> <span class="item">Professional master’s project <a href="https://dialnet.unirioja.es/servlet/articulo?codigo=7486537" rel="external nofollow noopener" target="_blank">"Cable-stayed bridge over the San Martin Strait to connect the towns of Laredo and Santoña, Cantabria, Northern Spain"</a></span> </li> </ul> </div> </div> </li> <li class="list-group-item"> <div class="row"> <div class="col-xs-2 cl-sm-2 col-md-2 text-center" style="width: 75px"> <table class="table-cv"> <tbody> <tr> <td> <span class="badge font-weight-bold danger-color-dark text-uppercase align-middle" style="min-width: 75px">2013-2017</span> </td> </tr> </tbody> </table> </div> <div class="col-xs-10 cl-sm-10 col-md-10 mt-2 mt-md-0"> <h6 class="title font-weight-bold ml-1 ml-md-4">BSc in Civil Engineering (Graduated with Honors, ranked 1st)</h6> <table class="table-cv ml-1 ml-md-4 institution"> <tbody> <tr> <td style="vertical-align: top; text-align: center" class="institution"> <i class="fa-solid fa-building-columns iconinstitution"></i> </td> <td class="institution">University of A Coruna, Spain</td> </tr> </tbody> </table> <ul class="items"> <li> <span class="item">Concentration in Structural and Geotechnical Engineering</span> </li> <li> <span class="item">Bachelor’s thesis <a href="https://ruc.udc.es/dspace/handle/2183/19429" rel="external nofollow noopener" target="_blank">"Environmental Restoration and Channeling of Juan Diaz River in Panama City"</a></span> </li> </ul> </div> </div> </li> </ul> </div> </div> <a class="anchor" id="Experience"></a> <div class="card mt-3 p-3"> <h3 class="card-title font-weight-medium">Experience</h3> <div> <ul class="card-text font-weight-light list-group list-group-flush"> <li class="list-group-item"> <div class="row"> <div class="col-xs-2 cl-sm-2 col-md-2 text-center" style="width: 75px"> <table class="table-cv"> <tbody> <tr> <td> <span class="badge font-weight-bold danger-color-dark text-uppercase align-middle" style="min-width: 75px">Jul 2024 - Present</span> </td> </tr> </tbody> </table> </div> <div class="col-xs-10 cl-sm-10 col-md-10 mt-2 mt-md-0"> <h6 class="title font-weight-bold ml-1 ml-md-4">Research Scientist</h6> <table class="table-cv ml-1 ml-md-4 institution"> <tbody> <tr> <td style="vertical-align: top; text-align: center" class="institution"> <i class="fa-solid fa-building-columns iconinstitution"></i> </td> <td class="institution"> <a href="https://www.purdue.edu/research/rche/" rel="external nofollow noopener" target="_blank">Regenstrief Center for Healthcare Engineering</a>, Purdue University, IN, USA</td> </tr> </tbody> </table> <ul class="items"> <li> <span class="item">Engaged in a strategic collaboration between Eli Lilly and Purdue University, concentrating on the analysis and optimization of injectable medicine delivery systems.</span> </li> <li> <span class="item">Conducted advanced numerical simulations to enhance understanding of the auto-injection process mechanics, aiming to improve drug bioavailability, minimize injection site pain, and boost patient compliance and overall health. - Developed high-fidelity computational models using the Finite Element Method and Isogeometric Analysis to understand and and predict tissue deformation and fluid pressure build-up as well as their impact on drug transport and absorption.</span> </li> <li> <span class="item">Explored innovative approaches and technologies for improving drug delivery systems, focusing on device design, injection parameters, and drug formulation</span> </li> <li> <span class="item">Supported and advanced the strategic collaboration between Eli Lilly and Purdue University, promoting the translation of research findings into practical applications within the pharmaceutical industry.</span> </li> <li> <span class="item">Demonstrated expertise in advanced computational methods, quantitative analysis, Bayesian and causal inference modeling, and AI methods in health and life sciences.</span> </li> <li> <span class="item">Contributed to research grant writing, project management, and publication in reputable healthcare, medical, and biomedical journals.</span> </li> </ul> </div> </div> </li> <li class="list-group-item"> <div class="row"> <div class="col-xs-2 cl-sm-2 col-md-2 text-center" style="width: 75px"> <table class="table-cv"> <tbody> <tr> <td> <span class="badge font-weight-bold danger-color-dark text-uppercase align-middle" style="min-width: 75px">Jan 2020 - Jul 2024</span> </td> </tr> </tbody> </table> </div> <div class="col-xs-10 cl-sm-10 col-md-10 mt-2 mt-md-0"> <h6 class="title font-weight-bold ml-1 ml-md-4">Research Assistant</h6> <table class="table-cv ml-1 ml-md-4 institution"> <tbody> <tr> <td style="vertical-align: top; text-align: center" class="institution"> <i class="fa-solid fa-building-columns iconinstitution"></i> </td> <td class="institution">Purdue University, IN, USA</td> </tr> </tbody> </table> <ul class="items"> <li> <span class="item">Involved in a project within a strategic collaboration between Eli Lilly and Purdue University, focusing on the analysis of the delivery of injectable medicines.</span> </li> <li> <span class="item">Performed numerical simulations to analyze the delivery of injectable medicines with the overall goals of better understanding the fundamental mechanics of the auto-injection process and its effect on skin, improved drug bioavailability, and reducing injection site pain in order to better patient compliance and enhance overall health.</span> </li> <li> <span class="item">Developed high-fidelity computational models using the Finite Element Method and Isogeometric Analysis to understand and and predict tissue deformation and fluid pressure build-up as well as their impact on drug transport and absorption.</span> </li> <li> <span class="item">Investigated innovative approaches and technologies to improve drug delivery systems, considering factors such as device design, injection parameters, and drug formulation.</span> </li> <li> <span class="item">Utilized data from computational models to drive informed decision-making in medical device development, enabling effective optimization and innovation in design and functionality.</span> </li> <li> <span class="item">Supported the strategic collaboration between Eli Lilly and Purdue University, fostering innovation and facilitating the translation of research findings into practical applications in the pharmaceutical industry.</span> </li> </ul> </div> </div> </li> <li class="list-group-item"> <div class="row"> <div class="col-xs-2 cl-sm-2 col-md-2 text-center" style="width: 75px"> <table class="table-cv"> <tbody> <tr> <td> <span class="badge font-weight-bold danger-color-dark text-uppercase align-middle" style="min-width: 75px">Jul 2019 - Dec 2019</span> </td> </tr> </tbody> </table> </div> <div class="col-xs-10 cl-sm-10 col-md-10 mt-2 mt-md-0"> <h6 class="title font-weight-bold ml-1 ml-md-4">Visiting Researcher</h6> <table class="table-cv ml-1 ml-md-4 institution"> <tbody> <tr> <td style="vertical-align: top; text-align: center" class="institution"> <i class="fa-solid fa-building-columns iconinstitution"></i> </td> <td class="institution">Purdue University, IN, USA</td> </tr> </tbody> </table> <ul class="items"> <li> <span class="item">Developed computational methods utilizing isogeometric analysis, poroelasticity, and data-driven tissue geometries to model the complex dynamics of high-volume, high-speed subcutaneous injection of monoclonal antibodies.</span> </li> <li> <span class="item">Developed highly sophisticated numerical algorithms capable of running in parallel, utilizing 200+ processors in Purdue’s Rosen Center for Advanced Computing.</span> </li> <li> <span class="item">Leveraged the computational power and parallel processing capabilities to efficiently simulate and analyze the complex fluid-structure interactions during the subcutaneous injection process.</span> </li> <li> <span class="item">Conducted extensive simulations using the developed computational methods to investigate the effects of injection parameters, tissue properties, and geometrical variations on the injection dynamics and the resulting distribution of monoclonal antibodies.</span> </li> </ul> </div> </div> </li> <li class="list-group-item"> <div class="row"> <div class="col-xs-2 cl-sm-2 col-md-2 text-center" style="width: 75px"> <table class="table-cv"> <tbody> <tr> <td> <span class="badge font-weight-bold danger-color-dark text-uppercase align-middle" style="min-width: 75px">Jul 2018 - Sep 2018</span> </td> </tr> </tbody> </table> </div> <div class="col-xs-10 cl-sm-10 col-md-10 mt-2 mt-md-0"> <h6 class="title font-weight-bold ml-1 ml-md-4">Graduate Research Assistant</h6> <table class="table-cv ml-1 ml-md-4 institution"> <tbody> <tr> <td style="vertical-align: top; text-align: center" class="institution"> <i class="fa-solid fa-building-columns iconinstitution"></i> </td> <td class="institution"> <a href="https://www.ntnu.edu/casa" rel="external nofollow noopener" target="_blank">Norwegian University of Science and Technology</a>, Trondheim, Norway</td> </tr> </tbody> </table> <ul class="items"> <li> <span class="item">Acted as a main collaborator in the project "Industrial Implementation of 3D printed AlSi10Mg components under quasi-static loading".</span> </li> <li> <span class="item">Conducted experimental tests on structures under both quasi-static and dynamic conditions, specifically focusing on extreme deformations and crushing.</span> </li> <li> <span class="item">Utilized Digital Image Correlation (DIC) tools to postprocess experimental results, enabling precise measurements and analysis of structural behavior.</span> </li> <li> <span class="item">Applied crashworthiness optimization techniques to enhance the performance and efficiency of the structures.</span> </li> <li> <span class="item">Developed finite element models to simulate the behavior of aluminum alloy thin-walled structures.</span> </li> <li> <span class="item">Developed comprehensive material card for AlSi10Mg 3D printed aluminum, encompassing mechanical, thermal, and viscoelastic properties for accurate simulation in engineering analyses.</span> </li> <li> <span class="item">Collaborated closely with industry partners to ensure the successful implementation of 3D printed components under quasi-static loading.</span> </li> </ul> </div> </div> </li> <li class="list-group-item"> <div class="row"> <div class="col-xs-2 cl-sm-2 col-md-2 text-center" style="width: 75px"> <table class="table-cv"> <tbody> <tr> <td> <span class="badge font-weight-bold danger-color-dark text-uppercase align-middle" style="min-width: 75px">Oct 2017 - Jul 2018</span> </td> </tr> </tbody> </table> </div> <div class="col-xs-10 cl-sm-10 col-md-10 mt-2 mt-md-0"> <h6 class="title font-weight-bold ml-1 ml-md-4">Graduate Research Assistant</h6> <table class="table-cv ml-1 ml-md-4 institution"> <tbody> <tr> <td style="vertical-align: top; text-align: center" class="institution"> <i class="fa-solid fa-building-columns iconinstitution"></i> </td> <td class="institution"> <a href="http://gme.udc.es/en" rel="external nofollow noopener" target="_blank">University of A Coruna</a>, A Coruna, Spain</td> </tr> </tbody> </table> <ul class="items"> <li> <span class="item">Awarded a prestigious fellowship by the Spanish Ministry of Education and Science to serve as a principal investigator, collaborating with the Department of Cardiovascular Surgery at the Complejo Universitario Hospitalario de A Coruna (CHUAC), to conduct research on the risk of rupture of abdominal aortic aneurysms (AAA) with atherosclerotic intimal thickening.</span> </li> <li> <span class="item">Developed an in-house code, called AneuPy, to generate idealized geometrical models of AAAs using clinical data. This code facilitated the creation of accurate and representative computational models for further analysis.</span> </li> <li> <span class="item">Performed cardiovascular fluid-structure interaction simulations of AAAs using different constitutive models for aortic tissue that allowed to better determine the risk of rupture.</span> </li> <li> <span class="item">Analyzed the stress distribution, deformation patterns, and hemodynamic factors within the AAA models to gain insights into the potential mechanisms of rupture.</span> </li> <li> <span class="item">Collaborated closely with the Department of Cardiovascular Surgery at CHUAC, exchanging knowledge and expertise to bridge the gap between research and clinical applications.</span> </li> </ul> </div> </div> </li> <li class="list-group-item"> <div class="row"> <div class="col-xs-2 cl-sm-2 col-md-2 text-center" style="width: 75px"> <table class="table-cv"> <tbody> <tr> <td> <span class="badge font-weight-bold danger-color-dark text-uppercase align-middle" style="min-width: 75px">Sep 2016 - Jul 2017</span> </td> </tr> </tbody> </table> </div> <div class="col-xs-10 cl-sm-10 col-md-10 mt-2 mt-md-0"> <h6 class="title font-weight-bold ml-1 ml-md-4">Undergraduate Research Assistant</h6> <table class="table-cv ml-1 ml-md-4 institution"> <tbody> <tr> <td style="vertical-align: top; text-align: center" class="institution"> <i class="fa-solid fa-building-columns iconinstitution"></i> </td> <td class="institution"> <a href="http://gme.udc.es/en" rel="external nofollow noopener" target="_blank">University of A Coruna</a>, A Coruna, Spain</td> </tr> </tbody> </table> <ul class="items"> <li> <span class="item">Granted with a research scholarship from the University of A Coruña to conduct research under the project "Mechanical Characterization of Structural Adhesives for Crashworthiness Applications".</span> </li> <li> <span class="item">Analyzed the mechanical behavior of various structural adhesives through rigorous experimental tests (single lap, double lap, thermal tests).</span> </li> <li> <span class="item">Developed computational models with cohesive elements and nonlinear contact mechanics to accurately reproduce the structural behavior of the adhesives.</span> </li> <li> <span class="item">Successfully replicated the adhesive’s structural behavior in the computational model, validating the quality of the mechanical characterization.</span> </li> <li> <span class="item">Provided engineers and researchers with a reliable tool for assessing adhesive performance and optimizing their, use in various industries.</span> </li> </ul> </div> </div> </li> <li class="list-group-item"> <div class="row"> <div class="col-xs-2 cl-sm-2 col-md-2 text-center" style="width: 75px"> <table class="table-cv"> <tbody> <tr> <td> <span class="badge font-weight-bold danger-color-dark text-uppercase align-middle" style="min-width: 75px">Jun 2016 - Sep 2016</span> </td> </tr> </tbody> </table> </div> <div class="col-xs-10 cl-sm-10 col-md-10 mt-2 mt-md-0"> <h6 class="title font-weight-bold ml-1 ml-md-4">Project Manager Assistant</h6> <table class="table-cv ml-1 ml-md-4 institution"> <tbody> <tr> <td style="vertical-align: top; text-align: center" class="institution"> <i class="fa-solid fa-building-columns iconinstitution"></i> </td> <td class="institution"> <a href="https://ihcantabria.com/en/" rel="external nofollow noopener" target="_blank">Environmental Hydraulics Institute of Cantabria</a>, Santander, Spain</td> </tr> </tbody> </table> <ul class="items"> <li> <span class="item">Worked as a hydraulic modeler on large-scale flood management projects in Panama and Venezuela in collaboration with the World Bank and the Inter-American Development Bank.</span> </li> <li> <span class="item">Conducted two and three-dimensional numerical simulations of free surface flow in rivers and estuaries to assess and quantify the level of flood hazard in densely populated urban areas.</span> </li> <li> <span class="item">Utilized advanced numerical models to assess the level of flood hazard and create accurate flood risk maps, providing valuable information for urban planning and disaster management strategies.</span> </li> <li> <span class="item">Generated accurate flood risk maps by analyzing the hydraulic behavior of water bodies, considering factors such as water flow, topography, and urban infrastructure.</span> </li> <li> <span class="item">Designed and proposed innovative solutions including flood barriers, coastal defenses, waterfront parks, floodresilient buildings and landscapes, reducing flood hazards by up to 60%.</span> </li> <li> <span class="item">Conducted feasibility studies and cost-benefit analyses to evaluate the economic and environmental implications of proposed flood mitigation solutions, assisting decision-makers in selecting the most suitable approaches.</span> </li> </ul> </div> </div> </li> </ul> </div> </div> <a class="anchor" id="Honors and Awards"></a> <div class="card mt-3 p-3"> <h3 class="card-title font-weight-medium">Honors and Awards</h3> <div> <ul class="card-text font-weight-light list-group list-group-flush"> <li class="list-group-item"> <div class="row"> <div class="col-xs-2 cl-sm-2 col-md-2 text-center" style="width: 75px"> <table class="table-cv"> <tbody> <tr> <td> <span class="badge font-weight-bold danger-color-dark text-uppercase align-middle" style="min-width: 75px">2023</span> </td> </tr> </tbody> </table> </div> <div class="col-xs-10 cl-sm-10 col-md-10 mt-2 mt-md-0"> <ul class="items"> <li> <span class="item"><a href="https://engineering.purdue.edu/ME/News/2023/purdue-me-grad-students-receive-fellowships-and-scholarships" rel="external nofollow noopener" target="_blank">Ben M. Hillberry Graduate Scholarship</a>, for PhD students pursuing research in the areas of biomechanics and materials, School of Mechanical Engineering, Purdue University.</span> </li> <li> <span class="item"><a href="https://engineering.purdue.edu/Engr/Trailblazers/Fellows/2023/Lucio" rel="external nofollow noopener" target="_blank">2023 Trailblazers in Engineering Fellow</a>, Purdue University College of Engineering.</span> </li> <li> <span class="item">Winner of the <a href="https://www.asce.org/communities/institutes-and-technical-groups/engineering-mechanics-institute/news/emi-2023-student-winners" rel="external nofollow noopener" target="_blank">2023 Poromechanics Student Competition</a>, Engineering Mechanics Institute, American Society of Civil Engineers.</span> </li> <li> <span class="item">College of Engineering Conference Travel Grant, Purdue University.</span> </li> <li> <span class="item">Purdue Graduate Student Government Doctoral Travel Grant, Purdue University.</span> </li> </ul> </div> </div> </li> <li class="list-group-item"> <div class="row"> <div class="col-xs-2 cl-sm-2 col-md-2 text-center" style="width: 75px"> <table class="table-cv"> <tbody> <tr> <td> <span class="badge font-weight-bold danger-color-dark text-uppercase align-middle" style="min-width: 75px">2020</span> </td> </tr> </tbody> </table> </div> <div class="col-xs-10 cl-sm-10 col-md-10 mt-2 mt-md-0"> <ul class="items"> <li> <span class="item"><a href="https://www.youtube.com/watch?v=hUmzbm_o9N0&amp;t=2047s" rel="external nofollow noopener" target="_blank">National Award to the best Master's Thesis in Civil Engineering by the Spanish Institution of Civil Engineers</a></span> </li> </ul> </div> </div> </li> <li class="list-group-item"> <div class="row"> <div class="col-xs-2 cl-sm-2 col-md-2 text-center" style="width: 75px"> <table class="table-cv"> <tbody> <tr> <td> <span class="badge font-weight-bold danger-color-dark text-uppercase align-middle" style="min-width: 75px">2019</span> </td> </tr> </tbody> </table> </div> <div class="col-xs-10 cl-sm-10 col-md-10 mt-2 mt-md-0"> <ul class="items"> <li> <span class="item">Award to the highest cumulative GPA of the School of Civil Engineering, University of A Coruna</span> </li> <li> <span class="item">Outstanding Civil Engineering Student Award, Galician Civil Engineering Foundation</span> </li> <li> <span class="item">Award to the best Master's Thesis in Structural Engineering by Grupo Puentes</span> </li> <li> <span class="item"><a href="https://www.copasagroup.com/es/premios-copasa-2019/" rel="external nofollow noopener" target="_blank">Award to the best Master's Thesis in Construction Engineering by COPASA</a></span> </li> </ul> </div> </div> </li> <li class="list-group-item"> <div class="row"> <div class="col-xs-2 cl-sm-2 col-md-2 text-center" style="width: 75px"> <table class="table-cv"> <tbody> <tr> <td> <span class="badge font-weight-bold danger-color-dark text-uppercase align-middle" style="min-width: 75px">2017</span> </td> </tr> </tbody> </table> </div> <div class="col-xs-10 cl-sm-10 col-md-10 mt-2 mt-md-0"> <ul class="items"> <li> <span class="item">Award to the highest cumulative GPA of the School of Civil Engineering, University of A Coruna</span> </li> <li> <span class="item">Outstanding Civil Engineering Student Award, Galician Civil Engineering Foundation</span> </li> <li> <span class="item">Award to the best Bachelor's Thesis in the field of Hydraulic Engineering by Gas Natural Fenosa</span> </li> </ul> </div> </div> </li> <li class="list-group-item"> <div class="row"> <div class="col-xs-2 cl-sm-2 col-md-2 text-center" style="width: 75px"> <table class="table-cv"> <tbody> <tr> <td> <span class="badge font-weight-bold danger-color-dark text-uppercase align-middle" style="min-width: 75px">2016</span> </td> </tr> </tbody> </table> </div> <div class="col-xs-10 cl-sm-10 col-md-10 mt-2 mt-md-0"> <ul class="items"> <li> <span class="item">Best Undergraduate Poster Award at the 2016 Graduate &amp; Undergraduate Research Symposium, University of A Coruña</span> </li> </ul> </div> </div> </li> </ul> </div> </div> <a class="anchor" id="Skills"></a> <div class="card mt-3 p-3"> <h3 class="card-title font-weight-medium">Skills</h3> <div> <ul class="card-text font-weight-light list-group list-group-flush"> <li class="list-group-item">Research, FEM, Python, FORTRAN, MATLAB, FEnics, PetIGA, Abaqus</li> </ul> </div> </div> </div> </article> </div> </div> <footer class="fixed-bottom" role="contentinfo"> <div class="container mt-0"> © Copyright 2024 Mario de Lucio. </div> </footer> <script src="https://cdn.jsdelivr.net/npm/jquery@3.6.0/dist/jquery.min.js" integrity="sha256-/xUj+3OJU5yExlq6GSYGSHk7tPXikynS7ogEvDej/m4=" crossorigin="anonymous"></script> <script src="/assets/js/bootstrap.bundle.min.js"></script> <script src="https://cdn.jsdelivr.net/npm/mdbootstrap@4.20.0/js/mdb.min.js" integrity="sha256-NdbiivsvWt7VYCt6hYNT3h/th9vSTL4EDWeGs5SN3DA=" crossorigin="anonymous"></script> <script defer src="https://cdn.jsdelivr.net/npm/masonry-layout@4.2.2/dist/masonry.pkgd.min.js" integrity="sha256-Nn1q/fx0H7SNLZMQ5Hw5JLaTRZp0yILA/FRexe19VdI=" crossorigin="anonymous"></script> <script defer src="https://cdn.jsdelivr.net/npm/imagesloaded@5.0.0/imagesloaded.pkgd.min.js" integrity="sha256-htrLFfZJ6v5udOG+3kNLINIKh2gvoKqwEhHYfTTMICc=" crossorigin="anonymous"></script> <script defer src="/assets/js/masonry.js" type="text/javascript"></script> <script defer src="https://cdn.jsdelivr.net/npm/medium-zoom@1.1.0/dist/medium-zoom.min.js" integrity="sha256-ZgMyDAIYDYGxbcpJcfUnYwNevG/xi9OHKaR/8GK+jWc=" crossorigin="anonymous"></script> <script defer src="/assets/js/zoom.js?85ddb88934d28b74e78031fd54cf8308"></script> <script src="/assets/js/no_defer.js?2781658a0a2b13ed609542042a859126"></script> <script defer src="/assets/js/common.js?06cae41083477f121be8cd9797ad8e2f"></script> <script defer src="/assets/js/copy_code.js?12775fdf7f95e901d7119054556e495f" type="text/javascript"></script> <script defer src="/assets/js/jupyter_new_tab.js?d9f17b6adc2311cbabd747f4538bb15f"></script> <script async src="https://d1bxh8uas1mnw7.cloudfront.net/assets/embed.js"></script> <script async src="https://badge.dimensions.ai/badge.js"></script> <script type="text/javascript">window.MathJax={tex:{tags:"ams"}};</script> <script defer type="text/javascript" id="MathJax-script" src="https://cdn.jsdelivr.net/npm/mathjax@3.2.0/es5/tex-mml-chtml.min.js" integrity="sha256-rjmgmaB99riUNcdlrDtcAiwtLIojSxNyUFdl+Qh+rB4=" crossorigin="anonymous"></script> <script defer src="https://cdnjs.cloudflare.com/polyfill/v3/polyfill.min.js?features=es6" crossorigin="anonymous"></script> <script type="text/javascript">function progressBarSetup(){"max"in document.createElement("progress")?(initializeProgressElement(),$(document).on("scroll",function(){progressBar.attr({value:getCurrentScrollPosition()})}),$(window).on("resize",initializeProgressElement)):(resizeProgressBar(),$(document).on("scroll",resizeProgressBar),$(window).on("resize",resizeProgressBar))}function getCurrentScrollPosition(){return $(window).scrollTop()}function initializeProgressElement(){let e=$("#navbar").outerHeight(!0);$("body").css({"padding-top":e}),$("progress-container").css({"padding-top":e}),progressBar.css({top:e}),progressBar.attr({max:getDistanceToScroll(),value:getCurrentScrollPosition()})}function getDistanceToScroll(){return $(document).height()-$(window).height()}function resizeProgressBar(){progressBar.css({width:getWidthPercentage()+"%"})}function getWidthPercentage(){return getCurrentScrollPosition()/getDistanceToScroll()*100}const progressBar=$("#progress");window.onload=function(){setTimeout(progressBarSetup,50)};</script> <script src="/assets/js/vanilla-back-to-top.min.js?f40d453793ff4f64e238e420181a1d17"></script> <script>addBackToTop();</script> <script type="module" src="/assets/js/search/ninja-keys.min.js?601a2d3465e2a52bec38b600518d5f70"></script> <ninja-keys hidebreadcrumbs noautoloadmdicons placeholder="Type to start searching"></ninja-keys> <script>let searchTheme=determineComputedTheme();const ninjaKeys=document.querySelector("ninja-keys");"dark"===searchTheme?ninjaKeys.classList.add("dark"):ninjaKeys.classList.remove("dark");const openSearchModal=()=>{const e=$("#navbarNav");e.hasClass("show")&&e.collapse("hide"),ninjaKeys.open()};</script> <script>const ninja=document.querySelector("ninja-keys");ninja.data=[{id:"nav-about",title:"About",section:"Navigation",handler:()=>{window.location.href="/"}},{id:"nav-publications",title:"Publications",description:"Ordered by most recent.",section:"Navigation",handler:()=>{window.location.href="/publications/"}},{id:"nav-blog",title:"Blog",description:"",section:"Navigation",handler:()=>{window.location.href="/blog/"}},{id:"nav-cv",title:"CV",description:"",section:"Navigation",handler:()=>{window.location.href="/cv/"}},{id:"nav-teaching",title:"Teaching",description:"Materials for courses you taught. 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-<?xml version="1.0" encoding="utf-8"?><feed xmlns="http://www.w3.org/2005/Atom" xml:lang="en"><generator uri="https://jekyllrb.com/" version="4.3.3">Jekyll</generator><link href="https://mdeluci.github.io/feed.xml" rel="self" type="application/atom+xml"/><link href="https://mdeluci.github.io/" rel="alternate" type="text/html" hreflang="en"/><updated>2024-06-19T18:53:06+00:00</updated><id>https://mdeluci.github.io/feed.xml</id><title type="html">Mario de Lucio’s website</title><subtitle>Mario de Lucio&apos;s website </subtitle><entry><title type="html">displaying beautiful tables with Bootstrap Tables</title><link href="https://mdeluci.github.io/blog/2023/tables/" rel="alternate" type="text/html" title="displaying beautiful tables with Bootstrap Tables"/><published>2023-03-20T18:37:00+00:00</published><updated>2023-03-20T18:37:00+00:00</updated><id>https://mdeluci.github.io/blog/2023/tables</id><content type="html" xml:base="https://mdeluci.github.io/blog/2023/tables/"><![CDATA[<p>Using markdown to display tables is easy. Just use the following syntax:</p> <div class="language-markdown highlighter-rouge"><div class="highlight"><pre class="highlight"><code>| Left aligned | Center aligned | Right aligned |
+<?xml version="1.0" encoding="utf-8"?><feed xmlns="http://www.w3.org/2005/Atom" xml:lang="en"><generator uri="https://jekyllrb.com/" version="4.3.3">Jekyll</generator><link href="https://mdeluci.github.io/feed.xml" rel="self" type="application/atom+xml"/><link href="https://mdeluci.github.io/" rel="alternate" type="text/html" hreflang="en"/><updated>2024-06-19T18:54:13+00:00</updated><id>https://mdeluci.github.io/feed.xml</id><title type="html">Mario de Lucio’s website</title><subtitle>Mario de Lucio&apos;s website </subtitle><entry><title type="html">Solving the Cahn-Hilliard equation on complex geometries</title><link href="https://mdeluci.github.io/blog/2024/math/" rel="alternate" type="text/html" title="Solving the Cahn-Hilliard equation on complex geometries"/><published>2024-06-19T06:52:00+00:00</published><updated>2024-06-19T06:52:00+00:00</updated><id>https://mdeluci.github.io/blog/2024/math</id><content type="html" xml:base="https://mdeluci.github.io/blog/2024/math/"><![CDATA[<h2 id="the-cahn-hilliard-equation">The Cahn-Hilliard equation</h2> <p>The Cahn–Hilliard equation describes the process of phase separation, by which the two components of a binary fluid spontaneously separate and form domains pure in each component. It was originally proposed in 1958 to model phase separation in binary alloys \cite{Cahn-Hilliard, Cahn-Hilliard2}. Since then it has been used to describe various phenomena, such as spinodal decomposition \cite{MARALDI201231}, diblock copolymer \cite{Choksi,JEONG20141263}, image inpainting \cite{4032803}, tumor growth simulation \cite{tumor,WISE2008524} or multiphase fluid flows \cite{BADALASSI2003371, Kotschote}.</p> <p>There are two main approaches to describing phase transition phenomena: sharp-interface models and phase-field models. Sharp-interface models involve the resolution of a moving boundary problem, meaning that partial differential equations have to be solved for each phase. This can lead to physical \cite{Anderson} and computational complications \cite{Barrett}, such as jump discontinuities across the interface. Phase-field models replace sharp-interfaces by thin transitions regions where the interfacial forces are smoothly distributed (diffuse interfaces). For this reason, phase-field models are also referred to as \emph{diffuse interface} models, and they are emerging as a promising tool to treat problems with interfaces.</p> <p>From the mathematical point of view, the Cahn-Hilliard equation is a stiff, fourth-order, nonlinear parabolic partial differential equation. The elementary form of the Cahn-Hilliard equation is given by</p> <p>\begin{equation} \frac{\partial \phi}{\partial t}=\nabla \cdot \left(m\left(\phi\right) \nabla \left(W’\left(\phi\right) -\epsilon ^2 \Delta \phi \right) \right) \label{element} \end{equation}</p> <p>where \(\phi\left(\mathbf{x},t\right) \in [-1,1]\) represents the phase-field variable, which describes the location of different components (e.g., \(\phi=-1\) in oil and \(\phi=1\) in water), \(m\left(\phi\right)\) is the mobility, \(W\left(\phi\right)\) is the so-called double-well potential, and \(\epsilon\) is a length scale related to the thickness of the diffuse interface.</p> <p>Two different approaches have been used to solve the Cahn-Hilliard equation: solving the original form given by Eqn.\eqref{element}, which involves fourth-order operators, or by splitting it into two second order partial differential equations by introducing an auxiliary variable — the chemical potential \(\mu\). The split version of the equation is given by</p> <p>\begin{equation} \frac{\partial \phi}{\partial t}=\nabla \cdot \left(m\left(\phi\right) \nabla \mu \right) \label{split1} \end{equation} \begin{equation} \mu=W’\left(\phi \right) - \epsilon^2 \Delta \phi. \label{chempot} \end{equation}</p> <p>The splitting strategy was proposed by Elliot \cite{Elliott1989ASO} to avoid constraints related to the continuity of the basis functions when using the finite element method with a primal formulation. It also facilitates the imposition of the boundary conditions on a circular geometry, which is the case we are interested in. Unfortunately, this comes at a price of an additional degree of freedom introduced into the solver. Nevertheless, this reformulation reduces the complexity of the problem from the numerical point of view (see \cite{M2AN_2009__43_5_1003_0,Zee}).</p> <p>The spatial discretization of the governing equations is performed using isogeometric analysis (IGA) \cite{HUGHES20054135}. IGA is a generalization of the finite-element method that uses non-uniform rational B-splines (NURBS) to define the discrete spaces. A significant advantage of IGA with respect to finite element analysis is that the basis functions can be constructed with controllable continuity across the element boundaries, even on mapped geometries. The higher-order global continuity of the basis functions has been shown to produce higher accuracy than classical \(\mathcal{C}^0\)-continuous finite elements for the same number of degrees of freedom \cite{akkerman2008role,evans2009n}; and has been widely used to solve partial differential equations with high-order spatial derivatives \cite{GOMEZ20084333, GOMEZ20101828, GOMEZ201252}. Here, we will use \(\mathcal{C}^1\)-continuous quadratic splines for \(\phi\) and \(\mu\).</p> <h2 id="strong-form">Strong form</h2> <p>The strong form of the problem is formulated as follows: find \(\phi:\Omega \times \left[0,T\right]\rightarrow \mathbb{R}\) and \(\mu:\Omega \times \left[0,T\right]\rightarrow \mathbb{R}\) (being \(\mu\) an auxiliary variable) such that:</p> <p>\begin{equation} \frac{\partial \phi}{\partial t}=\nabla \cdot \left(m\left(\phi\right) \nabla \mu\right) \quad \text{in} \ \Omega \times \left[0,T\right], \label{st1} \end{equation} <br/> \begin{equation} \mu=W’\left(\phi\right)-\epsilon^2 \Delta \phi \quad \text{in} \ \Omega \times \left[0,T\right], \label{st2} \end{equation} \begin{equation} \phi=g \quad \text{on} \ \Gamma_g \times \left[0,T\right], \label{st3} \end{equation} \begin{equation} <br/> m\left(\phi\right)\epsilon^2\Delta\phi=q \quad \text{on} \ \Gamma_q \times \left[0,T\right], \label{st4} \end{equation} \begin{equation} \nabla\left(m\left(\phi\right)\mu\right)\cdot \mathbf{n}=s \quad \text{on} \ \Gamma_s \times \left[0,T\right], \label{st5} \end{equation} \begin{equation} \nabla\left(m\left(\phi\right)\phi\right)\cdot \mathbf{n}=h \quad \text{on} \ \Gamma_h \times \left[0,T\right], \label{st6}<br/> \end{equation} \begin{equation} \phi\left(\mathbf{x},0\right)=\phi_0\left(\mathbf{x}\right) \quad \text{in} \ \Omega. \label{st7}<br/> \end{equation}</p> <p>The double well function \(W\left(\phi\right)\) is defined such that it has two local minima, which makes possible the coexistence of the different phases. Some important examples of double well functions can be found in \cite{Gomez2}. In this work we will take the classical quartic potential</p> <p>\begin{equation} W\left(\phi\right)=\frac{1}{4}\left(1-\phi^2\right)^2, \end{equation}</p> <p>which is a qualitative approximation of the logarithmic double well.</p> <p>The mobility \(m\left(\phi\right)\), which can be linked with the diffusivity, controls the time scale of the problem. The most common approach is to set it as a constant, \(m\left(\phi\right)=m\). Such an approach is extensively applied in both analytical and numerical studies \cite{Rajagopal,polymer,CuetoFelgueroso2008ATF}. We will take \(m\) constant and equal to one as recommended in \cite{GOMEZ20084333}.</p> <p>The parameter \(\epsilon\) is a positive constant that defines the length scale for the problem. According to \cite{GOMEZ20084333}, the solution to the Cahn-Hilliard equations depends only on the dimensionless number</p> <p>\begin{equation} \alpha=\frac{L_0^2}{3\epsilon^2} \end{equation}</p> <p>also referred to as sharpness parameter, where \(L_0\) is a length scale of the problem. Here, we will assume that \(L_0\) is a measure of the computational domain size. Without loss of generality, \(L_0=R_2=1.0\) will be the outer radius of the quarter of annulus. The sharpness parameter $\alpha$ usually takes values in the range \(10^3-10^4\) \cite{GOMEZ20084333,Gomez2}. We will study the evolution of the phase-field variable for different values of \(\alpha\).</p> <div class="row mt-3"> <div class="col-sm mt-3 mt-md-0"> <figure> <picture> <source class="responsive-img-srcset" srcset="/assets/img/fig2_ch-480.webp 480w,/assets/img/fig2_ch-800.webp 800w,/assets/img/fig2_ch-1400.webp 1400w," sizes="95vw" type="image/webp"/> <img src="/assets/img/fig2_ch.png" class="img-fluid rounded z-depth-1" width="100%" height="auto" loading="eager" onerror="this.onerror=null; $('.responsive-img-srcset').remove();"/> </picture> </figure> </div> <div class="col-sm mt-3 mt-md-0"> <figure> <picture> <source class="responsive-img-srcset" srcset="/assets/img/fig3_ch-480.webp 480w,/assets/img/fig3_ch-800.webp 800w,/assets/img/fig3_ch-1400.webp 1400w," sizes="95vw" type="image/webp"/> <img src="/assets/img/fig3_ch.png" class="img-fluid rounded z-depth-1" width="100%" height="auto" loading="eager" onerror="this.onerror=null; $('.responsive-img-srcset').remove();"/> </picture> </figure> </div> </div> <div class="caption"> Evolution of the phase-field from a randomly perturbed initial condition for $$\alpha=1500$$ and $$\bar{\phi}=0.3$$ (left). Evolution of the phase-field from a randomly perturbed initial condition for $$\alpha=3000$$ and $$\bar{\phi}=0.1$$ (right). </div>]]></content><author><name></name></author><category term="Projects"/><category term="Cahn-Hilliard"/><category term="PDEs"/><category term="IGA"/><summary type="html"><![CDATA[We solve the Cahn-Hilliard equation on a quarter of annulus by means of isogeometric analysis. We adopt the split form of the equation to avoid introducing fourth-order operators and facilitate the imposition of the boundary conditions on the circular geometry,]]></summary></entry><entry><title type="html">displaying beautiful tables with Bootstrap Tables</title><link href="https://mdeluci.github.io/blog/2023/tables/" rel="alternate" type="text/html" title="displaying beautiful tables with Bootstrap Tables"/><published>2023-03-20T18:37:00+00:00</published><updated>2023-03-20T18:37:00+00:00</updated><id>https://mdeluci.github.io/blog/2023/tables</id><content type="html" xml:base="https://mdeluci.github.io/blog/2023/tables/"><![CDATA[<p>Using markdown to display tables is easy. Just use the following syntax:</p> <div class="language-markdown highlighter-rouge"><div class="highlight"><pre class="highlight"><code>| Left aligned | Center aligned | Right aligned |
 | :----------- | :------------: | ------------: |
 | Left 1       |    center 1    |       right 1 |
 | Left 2       |    center 2    |       right 2 |
@@ -29,7 +29,7 @@
     <span class="nt">&lt;/tr&gt;</span>
   <span class="nt">&lt;/thead&gt;</span>
 <span class="nt">&lt;/table&gt;</span>
-</code></pre></div></div> <table data-click-to-select="true" data-height="460" data-pagination="true" data-search="true" data-toggle="table" data-url="/assets/json/table_data.json"> <thead> <tr> <th data-checkbox="true"></th> <th data-field="id" data-halign="left" data-align="center" data-sortable="true">ID</th> <th data-field="name" data-halign="center" data-align="right" data-sortable="true">Item Name</th> <th data-field="price" data-halign="right" data-align="left" data-sortable="true">Item Price</th> </tr> </thead> </table>]]></content><author><name></name></author><category term="sample-posts"/><category term="formatting"/><category term="tables"/><summary type="html"><![CDATA[an example of how to use Bootstrap Tables]]></summary></entry><entry><title type="html">Solving the Cahn-Hilliard equation on complex geometries</title><link href="https://mdeluci.github.io/blog/2015/math/" rel="alternate" type="text/html" title="Solving the Cahn-Hilliard equation on complex geometries"/><published>2015-10-20T15:12:00+00:00</published><updated>2015-10-20T15:12:00+00:00</updated><id>https://mdeluci.github.io/blog/2015/math</id><content type="html" xml:base="https://mdeluci.github.io/blog/2015/math/"><![CDATA[<h2 id="the-cahn-hilliard-equation">The Cahn-Hilliard equation</h2> <p>The Cahn–Hilliard equation describes the process of phase separation, by which the two components of a binary fluid spontaneously separate and form domains pure in each component. It was originally proposed in 1958 to model phase separation in binary alloys \cite{Cahn-Hilliard, Cahn-Hilliard2}. Since then it has been used to describe various phenomena, such as spinodal decomposition \cite{MARALDI201231}, diblock copolymer \cite{Choksi,JEONG20141263}, image inpainting \cite{4032803}, tumor growth simulation \cite{tumor,WISE2008524} or multiphase fluid flows \cite{BADALASSI2003371, Kotschote}.</p> <p>There are two main approaches to describing phase transition phenomena: sharp-interface models and phase-field models. Sharp-interface models involve the resolution of a moving boundary problem, meaning that partial differential equations have to be solved for each phase. This can lead to physical \cite{Anderson} and computational complications \cite{Barrett}, such as jump discontinuities across the interface. Phase-field models replace sharp-interfaces by thin transitions regions where the interfacial forces are smoothly distributed (diffuse interfaces). For this reason, phase-field models are also referred to as \emph{diffuse interface} models, and they are emerging as a promising tool to treat problems with interfaces.</p> <p>From the mathematical point of view, the Cahn-Hilliard equation is a stiff, fourth-order, nonlinear parabolic partial differential equation. The elementary form of the Cahn-Hilliard equation is given by</p> <p>\begin{equation} \frac{\partial \phi}{\partial t}=\nabla \cdot \left(m\left(\phi\right) \nabla \left(W’\left(\phi\right) -\epsilon ^2 \Delta \phi \right) \right) \label{element} \end{equation}</p> <p>where \(\phi\left(\mathbf{x},t\right) \in [-1,1]\) represents the phase-field variable, which describes the location of different components (e.g., \(\phi=-1\) in oil and \(\phi=1\) in water), \(m\left(\phi\right)\) is the mobility, \(W\left(\phi\right)\) is the so-called double-well potential, and \(\epsilon\) is a length scale related to the thickness of the diffuse interface.</p> <p>Two different approaches have been used to solve the Cahn-Hilliard equation: solving the original form given by Eqn.\eqref{element}, which involves fourth-order operators, or by splitting it into two second order partial differential equations by introducing an auxiliary variable — the chemical potential \(\mu\). The split version of the equation is given by</p> <p>\begin{equation} \frac{\partial \phi}{\partial t}=\nabla \cdot \left(m\left(\phi\right) \nabla \mu \right) \label{split1} \end{equation} \begin{equation} \mu=W’\left(\phi \right) - \epsilon^2 \Delta \phi. \label{chempot} \end{equation}</p> <p>The splitting strategy was proposed by Elliot \cite{Elliott1989ASO} to avoid constraints related to the continuity of the basis functions when using the finite element method with a primal formulation. It also facilitates the imposition of the boundary conditions on a circular geometry, which is the case we are interested in. Unfortunately, this comes at a price of an additional degree of freedom introduced into the solver. Nevertheless, this reformulation reduces the complexity of the problem from the numerical point of view (see \cite{M2AN_2009__43_5_1003_0,Zee}).</p> <p>The spatial discretization of the governing equations is performed using isogeometric analysis (IGA) \cite{HUGHES20054135}. IGA is a generalization of the finite-element method that uses non-uniform rational B-splines (NURBS) to define the discrete spaces. A significant advantage of IGA with respect to finite element analysis is that the basis functions can be constructed with controllable continuity across the element boundaries, even on mapped geometries. The higher-order global continuity of the basis functions has been shown to produce higher accuracy than classical \(\mathcal{C}^0\)-continuous finite elements for the same number of degrees of freedom \cite{akkerman2008role,evans2009n}; and has been widely used to solve partial differential equations with high-order spatial derivatives \cite{GOMEZ20084333, GOMEZ20101828, GOMEZ201252}. Here, we will use \(\mathcal{C}^1\)-continuous quadratic splines for \(\phi\) and \(\mu\).</p> <h2 id="strong-form">Strong form</h2> <p>The strong form of the problem is formulated as follows: find \(\phi:\Omega \times \left[0,T\right]\rightarrow \mathbb{R}\) and \(\mu:\Omega \times \left[0,T\right]\rightarrow \mathbb{R}\) (being \(\mu\) an auxiliary variable) such that:</p> <p>\begin{equation} \frac{\partial \phi}{\partial t}=\nabla \cdot \left(m\left(\phi\right) \nabla \mu\right) \quad \text{in} \ \Omega \times \left[0,T\right], \label{st1} \end{equation} <br/> \begin{equation} \mu=W’\left(\phi\right)-\epsilon^2 \Delta \phi \quad \text{in} \ \Omega \times \left[0,T\right], \label{st2} \end{equation} \begin{equation} \phi=g \quad \text{on} \ \Gamma_g \times \left[0,T\right], \label{st3} \end{equation} \begin{equation} <br/> m\left(\phi\right)\epsilon^2\Delta\phi=q \quad \text{on} \ \Gamma_q \times \left[0,T\right], \label{st4} \end{equation} \begin{equation} \nabla\left(m\left(\phi\right)\mu\right)\cdot \mathbf{n}=s \quad \text{on} \ \Gamma_s \times \left[0,T\right], \label{st5} \end{equation} \begin{equation} \nabla\left(m\left(\phi\right)\phi\right)\cdot \mathbf{n}=h \quad \text{on} \ \Gamma_h \times \left[0,T\right], \label{st6}<br/> \end{equation} \begin{equation} \phi\left(\mathbf{x},0\right)=\phi_0\left(\mathbf{x}\right) \quad \text{in} \ \Omega. \label{st7}<br/> \end{equation}</p> <p>The double well function \(W\left(\phi\right)\) is defined such that it has two local minima, which makes possible the coexistence of the different phases. Some important examples of double well functions can be found in \cite{Gomez2}. In this work we will take the classical quartic potential</p> <p>\begin{equation} W\left(\phi\right)=\frac{1}{4}\left(1-\phi^2\right)^2, \end{equation}</p> <p>which is a qualitative approximation of the logarithmic double well.</p> <p>The mobility \(m\left(\phi\right)\), which can be linked with the diffusivity, controls the time scale of the problem. The most common approach is to set it as a constant, \(m\left(\phi\right)=m\). Such an approach is extensively applied in both analytical and numerical studies \cite{Rajagopal,polymer,CuetoFelgueroso2008ATF}. We will take \(m\) constant and equal to one as recommended in \cite{GOMEZ20084333}.</p> <p>The parameter \(\epsilon\) is a positive constant that defines the length scale for the problem. According to \cite{GOMEZ20084333}, the solution to the Cahn-Hilliard equations depends only on the dimensionless number</p> <p>\begin{equation} \alpha=\frac{L_0^2}{3\epsilon^2} \end{equation}</p> <p>also referred to as sharpness parameter, where \(L_0\) is a length scale of the problem. Here, we will assume that \(L_0\) is a measure of the computational domain size. Without loss of generality, \(L_0=R_2=1.0\) will be the outer radius of the quarter of annulus. The sharpness parameter $\alpha$ usually takes values in the range \(10^3-10^4\) \cite{GOMEZ20084333,Gomez2}. We will study the evolution of the phase-field variable for different values of \(\alpha\).</p> <div class="row mt-3"> <div class="col-sm mt-3 mt-md-0"> <figure> <picture> <source class="responsive-img-srcset" srcset="/assets/img/fig2_ch-480.webp 480w,/assets/img/fig2_ch-800.webp 800w,/assets/img/fig2_ch-1400.webp 1400w," sizes="95vw" type="image/webp"/> <img src="/assets/img/fig2_ch.png" class="img-fluid rounded z-depth-1" width="100%" height="auto" loading="eager" onerror="this.onerror=null; $('.responsive-img-srcset').remove();"/> </picture> </figure> </div> <div class="col-sm mt-3 mt-md-0"> <figure> <picture> <source class="responsive-img-srcset" srcset="/assets/img/fig3_ch-480.webp 480w,/assets/img/fig3_ch-800.webp 800w,/assets/img/fig3_ch-1400.webp 1400w," sizes="95vw" type="image/webp"/> <img src="/assets/img/fig3_ch.png" class="img-fluid rounded z-depth-1" width="100%" height="auto" loading="eager" onerror="this.onerror=null; $('.responsive-img-srcset').remove();"/> </picture> </figure> </div> </div> <div class="caption"> Evolution of the phase-field from a randomly perturbed initial condition for $$\alpha=1500$$ and $$\bar{\phi}=0.3$$ (left). Evolution of the phase-field from a randomly perturbed initial condition for $$\alpha=3000$$ and $$\bar{\phi}=0.1$$ (right). </div>]]></content><author><name></name></author><category term="sample-posts"/><category term="Cahn-Hilliard"/><category term="PDEs"/><category term="IGA"/><summary type="html"><![CDATA[We solve the Cahn-Hilliard equation on a quarter of annulus by means of isogeometric analysis. We adopt the split form of the equation to avoid introducing fourth-order operators and facilitate the imposition of the boundary conditions on the circular geometry,]]></summary></entry><entry><title type="html">a post with code</title><link href="https://mdeluci.github.io/blog/2015/code/" rel="alternate" type="text/html" title="a post with code"/><published>2015-07-15T15:09:00+00:00</published><updated>2015-07-15T15:09:00+00:00</updated><id>https://mdeluci.github.io/blog/2015/code</id><content type="html" xml:base="https://mdeluci.github.io/blog/2015/code/"><![CDATA[<p>This theme implements a built-in Jekyll feature, the use of Rouge, for syntax highlighting. It supports more than 100 languages. This example is in C++. All you have to do is wrap your code in markdown code tags:</p> <div class="language-markdown highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="p">```</span><span class="nl">c++
+</code></pre></div></div> <table data-click-to-select="true" data-height="460" data-pagination="true" data-search="true" data-toggle="table" data-url="/assets/json/table_data.json"> <thead> <tr> <th data-checkbox="true"></th> <th data-field="id" data-halign="left" data-align="center" data-sortable="true">ID</th> <th data-field="name" data-halign="center" data-align="right" data-sortable="true">Item Name</th> <th data-field="price" data-halign="right" data-align="left" data-sortable="true">Item Price</th> </tr> </thead> </table>]]></content><author><name></name></author><category term="sample-posts"/><category term="formatting"/><category term="tables"/><summary type="html"><![CDATA[an example of how to use Bootstrap Tables]]></summary></entry><entry><title type="html">a post with code</title><link href="https://mdeluci.github.io/blog/2015/code/" rel="alternate" type="text/html" title="a post with code"/><published>2015-07-15T15:09:00+00:00</published><updated>2015-07-15T15:09:00+00:00</updated><id>https://mdeluci.github.io/blog/2015/code</id><content type="html" xml:base="https://mdeluci.github.io/blog/2015/code/"><![CDATA[<p>This theme implements a built-in Jekyll feature, the use of Rouge, for syntax highlighting. It supports more than 100 languages. This example is in C++. All you have to do is wrap your code in markdown code tags:</p> <div class="language-markdown highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="p">```</span><span class="nl">c++
 </span><span class="n">code</span> <span class="n">code</span> <span class="n">code</span>
 <span class="p">```</span>
 </code></pre></div></div> <div class="language-c++ highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="kt">int</span> <span class="nf">main</span><span class="p">(</span><span class="kt">int</span> <span class="n">argc</span><span class="p">,</span> <span class="kt">char</span> <span class="k">const</span> <span class="err">\</span><span class="o">*</span><span class="n">argv</span><span class="p">[])</span>
diff --git a/index.html b/index.html
index c1b1f299..99cd121b 100644
--- a/index.html
+++ b/index.html
@@ -5,4 +5,4 @@
   <span class="na">year</span> <span class="p">=</span> <span class="s">{2024}</span><span class="p">,</span>
   <span class="na">doi</span> <span class="p">=</span> <span class="s">{10.1007/s10439-024-03477-1}</span><span class="p">,</span>
   <span class="na">publisher</span> <span class="p">=</span> <span class="s">{Springer}</span>
-<span class="p">}</span></code></pre></figure> </div> </div> </div> </li></ol> </div> <div class="social"> <div class="contact-icons"> <a href="mailto:%6D%64%65%6C%75%63%69@%70%75%72%64%75%65.%65%64%75" title="email"><i class="fa-solid fa-envelope"></i></a> <a href="https://orcid.org/0000-0003-1168-2249" title="ORCID" rel="external nofollow noopener" target="_blank"><i class="ai ai-orcid"></i></a> <a href="https://scholar.google.com/citations?user=ykpA5ZsAAAAJ" title="Google Scholar" rel="external nofollow noopener" target="_blank"><i class="ai ai-google-scholar"></i></a> <a href="https://www.researchgate.net/profile/Mario-De-Lucio/" title="ResearchGate" rel="external nofollow noopener" target="_blank"><i class="ai ai-researchgate"></i></a> <a href="https://github.com/mdeluci" title="GitHub" rel="external nofollow noopener" target="_blank"><i class="fa-brands fa-github"></i></a> <a href="https://www.linkedin.com/in/mario-de-lucio" title="LinkedIn" rel="external nofollow noopener" 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The PhD thesis committee was composed by Prof. Hector Gomez (Chair), Prof. Adrian Buganza Tepole, Prof. Arezoo M. Ardekani and Prof. Luis Solorio.</p> </div> </article> </div> </div> <footer class="fixed-bottom" role="contentinfo"> <div class="container mt-0"> © Copyright 2024 Mario de Lucio. </div> </footer> <script src="https://cdn.jsdelivr.net/npm/jquery@3.6.0/dist/jquery.min.js" integrity="sha256-/xUj+3OJU5yExlq6GSYGSHk7tPXikynS7ogEvDej/m4=" crossorigin="anonymous"></script> <script src="/assets/js/bootstrap.bundle.min.js"></script> <script src="https://cdn.jsdelivr.net/npm/mdbootstrap@4.20.0/js/mdb.min.js" integrity="sha256-NdbiivsvWt7VYCt6hYNT3h/th9vSTL4EDWeGs5SN3DA=" crossorigin="anonymous"></script> <script defer src="https://cdn.jsdelivr.net/npm/masonry-layout@4.2.2/dist/masonry.pkgd.min.js" integrity="sha256-Nn1q/fx0H7SNLZMQ5Hw5JLaTRZp0yILA/FRexe19VdI=" crossorigin="anonymous"></script> <script defer src="https://cdn.jsdelivr.net/npm/imagesloaded@5.0.0/imagesloaded.pkgd.min.js" integrity="sha256-htrLFfZJ6v5udOG+3kNLINIKh2gvoKqwEhHYfTTMICc=" crossorigin="anonymous"></script> <script defer src="/assets/js/masonry.js" type="text/javascript"></script> <script defer src="https://cdn.jsdelivr.net/npm/medium-zoom@1.1.0/dist/medium-zoom.min.js" integrity="sha256-ZgMyDAIYDYGxbcpJcfUnYwNevG/xi9OHKaR/8GK+jWc=" crossorigin="anonymous"></script> <script defer src="/assets/js/zoom.js?85ddb88934d28b74e78031fd54cf8308"></script> <script src="/assets/js/no_defer.js?2781658a0a2b13ed609542042a859126"></script> <script defer src="/assets/js/common.js?06cae41083477f121be8cd9797ad8e2f"></script> <script defer src="/assets/js/copy_code.js?12775fdf7f95e901d7119054556e495f" type="text/javascript"></script> <script defer src="/assets/js/jupyter_new_tab.js?d9f17b6adc2311cbabd747f4538bb15f"></script> <script async src="https://d1bxh8uas1mnw7.cloudfront.net/assets/embed.js"></script> <script async src="https://badge.dimensions.ai/badge.js"></script> <script type="text/javascript">window.MathJax={tex:{tags:"ams"}};</script> <script defer type="text/javascript" id="MathJax-script" src="https://cdn.jsdelivr.net/npm/mathjax@3.2.0/es5/tex-mml-chtml.min.js" integrity="sha256-rjmgmaB99riUNcdlrDtcAiwtLIojSxNyUFdl+Qh+rB4=" crossorigin="anonymous"></script> <script defer src="https://cdnjs.cloudflare.com/polyfill/v3/polyfill.min.js?features=es6" crossorigin="anonymous"></script> <script type="text/javascript">function progressBarSetup(){"max"in document.createElement("progress")?(initializeProgressElement(),$(document).on("scroll",function(){progressBar.attr({value:getCurrentScrollPosition()})}),$(window).on("resize",initializeProgressElement)):(resizeProgressBar(),$(document).on("scroll",resizeProgressBar),$(window).on("resize",resizeProgressBar))}function getCurrentScrollPosition(){return $(window).scrollTop()}function initializeProgressElement(){let e=$("#navbar").outerHeight(!0);$("body").css({"padding-top":e}),$("progress-container").css({"padding-top":e}),progressBar.css({top:e}),progressBar.attr({max:getDistanceToScroll(),value:getCurrentScrollPosition()})}function getDistanceToScroll(){return $(document).height()-$(window).height()}function resizeProgressBar(){progressBar.css({width:getWidthPercentage()+"%"})}function getWidthPercentage(){return getCurrentScrollPosition()/getDistanceToScroll()*100}const progressBar=$("#progress");window.onload=function(){setTimeout(progressBarSetup,50)};</script> <script src="/assets/js/vanilla-back-to-top.min.js?f40d453793ff4f64e238e420181a1d17"></script> <script>addBackToTop();</script> <script type="module" src="/assets/js/search/ninja-keys.min.js?601a2d3465e2a52bec38b600518d5f70"></script> <ninja-keys hidebreadcrumbs noautoloadmdicons placeholder="Type to start searching"></ninja-keys> <script>let searchTheme=determineComputedTheme();const ninjaKeys=document.querySelector("ninja-keys");"dark"===searchTheme?ninjaKeys.classList.add("dark"):ninjaKeys.classList.remove("dark");const openSearchModal=()=>{const e=$("#navbarNav");e.hasClass("show")&&e.collapse("hide"),ninjaKeys.open()};</script> <script>const ninja=document.querySelector("ninja-keys");ninja.data=[{id:"nav-about",title:"About",section:"Navigation",handler:()=>{window.location.href="/"}},{id:"nav-publications",title:"Publications",description:"Ordered by most recent.",section:"Navigation",handler:()=>{window.location.href="/publications/"}},{id:"nav-blog",title:"Blog",description:"",section:"Navigation",handler:()=>{window.location.href="/blog/"}},{id:"nav-cv",title:"CV",description:"",section:"Navigation",handler:()=>{window.location.href="/cv/"}},{id:"nav-teaching",title:"Teaching",description:"Materials for courses you taught. 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+<!DOCTYPE html> <html lang="en"> <head> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> <meta charset="utf-8"> <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"> <meta http-equiv="X-UA-Compatible" content="IE=edge"> <title> PhD thesis defense | Mario de Lucio's website </title> <meta name="author" content="Mario de Lucio"> <meta name="description" content="Mario de Lucio's website "> <meta name="keywords" content="Computational Mechanics, Multiphysics Simulation, Biomechanics, Transport phenomena"> <link rel="stylesheet" href="/assets/css/bootstrap.min.css?a4b3f509e79c54a512b890d73235ef04"> <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/mdbootstrap@4.20.0/css/mdb.min.css" integrity="sha256-jpjYvU3G3N6nrrBwXJoVEYI/0zw8htfFnhT9ljN3JJw=" crossorigin="anonymous"> <link defer rel="stylesheet" href="/assets/css/academicons.min.css?f0b7046b84e425c55f3463ac249818f5"> <link defer rel="stylesheet" type="text/css" href="https://fonts.googleapis.com/css?family=Roboto:300,400,500,700|Roboto+Slab:100,300,400,500,700|Material+Icons&amp;display=swap"> <link defer rel="stylesheet" href="/assets/css/jekyll-pygments-themes-github.css?591dab5a4e56573bf4ef7fd332894c99" media="" id="highlight_theme_light"> <link rel="shortcut icon" href="/assets/img/webicon.png?b6c2349ccb452e30289be5faff27b580"> <link rel="stylesheet" href="/assets/css/main.css?d41d8cd98f00b204e9800998ecf8427e"> <link rel="canonical" href="https://mdeluci.github.io/news/PhD_defense/"> <script src="/assets/js/theme.js?9a0c749ec5240d9cda97bc72359a72c0"></script> <link defer rel="stylesheet" href="/assets/css/jekyll-pygments-themes-native.css?5847e5ed4a4568527aa6cfab446049ca" media="none" id="highlight_theme_dark"> <script>initTheme();</script> </head> <body class="fixed-top-nav "> <header> <nav id="navbar" class="navbar navbar-light navbar-expand-sm fixed-top" role="navigation"> <div class="container"> <a class="navbar-brand title font-weight-lighter" href="/"> Mario de Lucio's website </a> <button class="navbar-toggler collapsed ml-auto" type="button" data-toggle="collapse" data-target="#navbarNav" aria-controls="navbarNav" aria-expanded="false" aria-label="Toggle navigation"> <span class="sr-only">Toggle navigation</span> <span class="icon-bar top-bar"></span> <span class="icon-bar middle-bar"></span> <span class="icon-bar bottom-bar"></span> </button> <div class="collapse navbar-collapse text-right" id="navbarNav"> <ul class="navbar-nav ml-auto flex-nowrap"> <li class="nav-item "> <a class="nav-link" href="/">About </a> </li> <li class="nav-item "> <a class="nav-link" href="/publications/">Publications </a> </li> <li class="nav-item "> <a class="nav-link" href="/blog/">Blog </a> </li> <li class="nav-item "> <a class="nav-link" href="/cv/">CV </a> </li> <li class="nav-item "> <a class="nav-link" href="/teaching/">Teaching </a> </li> <li class="nav-item "> <a class="nav-link" href="/videos/">Videos </a> </li> <li class="nav-item"> <button id="search-toggle" title="Search" onclick="openSearchModal()"> <span class="nav-link">ctrl k <i class="ti ti-search"></i></span> </button> </li> <li class="toggle-container"> <button id="light-toggle" title="Change theme"> <i class="ti ti-sun-moon" id="light-toggle-system"></i> <i class="ti ti-moon-filled" id="light-toggle-dark"></i> <i class="ti ti-sun-filled" id="light-toggle-light"></i> </button> </li> </ul> </div> </div> </nav> <progress id="progress" value="0"> <div class="progress-container"> <span class="progress-bar"></span> </div> </progress> </header> <div class="container mt-5" role="main"> <div class="post"> <header class="post-header"> <h1 class="post-title">PhD thesis defense</h1> <p class="post-meta"> Created in April 03, 2024 </p> <p class="post-tags"> <i class="fa-solid fa-calendar fa-sm"></i> 2024 </p> </header> <article class="post-content"> <div id="markdown-content"> <p>I have successfully defended my PhD Dissertation titled “Numerical Simulation and Poromechanical Modeling of Subcutaneous Injection of Monoclonal Antibodies”. The PhD thesis committee was composed by Prof. Hector Gomez (Chair), Prof. Adrian Buganza Tepole, Prof. Arezoo M. Ardekani and Prof. Luis Solorio.</p> </div> </article> </div> </div> <footer class="fixed-bottom" role="contentinfo"> <div class="container mt-0"> © Copyright 2024 Mario de Lucio. </div> </footer> <script src="https://cdn.jsdelivr.net/npm/jquery@3.6.0/dist/jquery.min.js" integrity="sha256-/xUj+3OJU5yExlq6GSYGSHk7tPXikynS7ogEvDej/m4=" crossorigin="anonymous"></script> <script src="/assets/js/bootstrap.bundle.min.js"></script> <script src="https://cdn.jsdelivr.net/npm/mdbootstrap@4.20.0/js/mdb.min.js" integrity="sha256-NdbiivsvWt7VYCt6hYNT3h/th9vSTL4EDWeGs5SN3DA=" crossorigin="anonymous"></script> <script defer src="https://cdn.jsdelivr.net/npm/masonry-layout@4.2.2/dist/masonry.pkgd.min.js" integrity="sha256-Nn1q/fx0H7SNLZMQ5Hw5JLaTRZp0yILA/FRexe19VdI=" crossorigin="anonymous"></script> <script defer src="https://cdn.jsdelivr.net/npm/imagesloaded@5.0.0/imagesloaded.pkgd.min.js" integrity="sha256-htrLFfZJ6v5udOG+3kNLINIKh2gvoKqwEhHYfTTMICc=" crossorigin="anonymous"></script> <script defer src="/assets/js/masonry.js" type="text/javascript"></script> <script defer src="https://cdn.jsdelivr.net/npm/medium-zoom@1.1.0/dist/medium-zoom.min.js" integrity="sha256-ZgMyDAIYDYGxbcpJcfUnYwNevG/xi9OHKaR/8GK+jWc=" crossorigin="anonymous"></script> <script defer src="/assets/js/zoom.js?85ddb88934d28b74e78031fd54cf8308"></script> <script src="/assets/js/no_defer.js?2781658a0a2b13ed609542042a859126"></script> <script defer src="/assets/js/common.js?06cae41083477f121be8cd9797ad8e2f"></script> <script defer src="/assets/js/copy_code.js?12775fdf7f95e901d7119054556e495f" type="text/javascript"></script> <script defer src="/assets/js/jupyter_new_tab.js?d9f17b6adc2311cbabd747f4538bb15f"></script> <script async src="https://d1bxh8uas1mnw7.cloudfront.net/assets/embed.js"></script> <script async src="https://badge.dimensions.ai/badge.js"></script> <script type="text/javascript">window.MathJax={tex:{tags:"ams"}};</script> <script defer type="text/javascript" id="MathJax-script" src="https://cdn.jsdelivr.net/npm/mathjax@3.2.0/es5/tex-mml-chtml.min.js" integrity="sha256-rjmgmaB99riUNcdlrDtcAiwtLIojSxNyUFdl+Qh+rB4=" crossorigin="anonymous"></script> <script defer src="https://cdnjs.cloudflare.com/polyfill/v3/polyfill.min.js?features=es6" crossorigin="anonymous"></script> <script type="text/javascript">function progressBarSetup(){"max"in document.createElement("progress")?(initializeProgressElement(),$(document).on("scroll",function(){progressBar.attr({value:getCurrentScrollPosition()})}),$(window).on("resize",initializeProgressElement)):(resizeProgressBar(),$(document).on("scroll",resizeProgressBar),$(window).on("resize",resizeProgressBar))}function getCurrentScrollPosition(){return $(window).scrollTop()}function initializeProgressElement(){let e=$("#navbar").outerHeight(!0);$("body").css({"padding-top":e}),$("progress-container").css({"padding-top":e}),progressBar.css({top:e}),progressBar.attr({max:getDistanceToScroll(),value:getCurrentScrollPosition()})}function getDistanceToScroll(){return $(document).height()-$(window).height()}function resizeProgressBar(){progressBar.css({width:getWidthPercentage()+"%"})}function getWidthPercentage(){return getCurrentScrollPosition()/getDistanceToScroll()*100}const progressBar=$("#progress");window.onload=function(){setTimeout(progressBarSetup,50)};</script> <script src="/assets/js/vanilla-back-to-top.min.js?f40d453793ff4f64e238e420181a1d17"></script> <script>addBackToTop();</script> <script type="module" src="/assets/js/search/ninja-keys.min.js?601a2d3465e2a52bec38b600518d5f70"></script> <ninja-keys hidebreadcrumbs noautoloadmdicons placeholder="Type to start searching"></ninja-keys> <script>let searchTheme=determineComputedTheme();const ninjaKeys=document.querySelector("ninja-keys");"dark"===searchTheme?ninjaKeys.classList.add("dark"):ninjaKeys.classList.remove("dark");const openSearchModal=()=>{const e=$("#navbarNav");e.hasClass("show")&&e.collapse("hide"),ninjaKeys.open()};</script> <script>const ninja=document.querySelector("ninja-keys");ninja.data=[{id:"nav-about",title:"About",section:"Navigation",handler:()=>{window.location.href="/"}},{id:"nav-publications",title:"Publications",description:"Ordered by most recent.",section:"Navigation",handler:()=>{window.location.href="/publications/"}},{id:"nav-blog",title:"Blog",description:"",section:"Navigation",handler:()=>{window.location.href="/blog/"}},{id:"nav-cv",title:"CV",description:"",section:"Navigation",handler:()=>{window.location.href="/cv/"}},{id:"nav-teaching",title:"Teaching",description:"Materials for courses you taught. 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The PhD thesis committee was composed by Prof. Hector Gomez (Chair), Prof. Adrian Buganza Tepole, Prof. Arezoo M. Ardekani and Prof. Luis Solorio.</p> <p><img src="/assets/img/phd_defense.jpg" alt="PhD Defense" width="750"></p> <blockquote> <p>To my parents, Ana and Rafael, whose teachings I can encapsulate in the following words by the most important writer of all time: “Since you are not experienced in things of the world, all things that are a bit difficult seem impossible to you. 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+<!DOCTYPE html> <html lang="en"> <head> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> <meta charset="utf-8"> <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"> <meta http-equiv="X-UA-Compatible" content="IE=edge"> <title> Mario succesfully defended his PhD thesis | Mario de Lucio's website </title> <meta name="author" content="Mario de Lucio"> <meta name="description" content="Mario de Lucio's website "> <meta name="keywords" content="Computational Mechanics, Multiphysics Simulation, Biomechanics, Transport phenomena"> <link rel="stylesheet" href="/assets/css/bootstrap.min.css?a4b3f509e79c54a512b890d73235ef04"> <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/mdbootstrap@4.20.0/css/mdb.min.css" integrity="sha256-jpjYvU3G3N6nrrBwXJoVEYI/0zw8htfFnhT9ljN3JJw=" crossorigin="anonymous"> <link defer rel="stylesheet" href="/assets/css/academicons.min.css?f0b7046b84e425c55f3463ac249818f5"> <link defer rel="stylesheet" type="text/css" href="https://fonts.googleapis.com/css?family=Roboto:300,400,500,700|Roboto+Slab:100,300,400,500,700|Material+Icons&amp;display=swap"> <link defer rel="stylesheet" href="/assets/css/jekyll-pygments-themes-github.css?591dab5a4e56573bf4ef7fd332894c99" media="" id="highlight_theme_light"> <link rel="shortcut icon" href="/assets/img/webicon.png?b6c2349ccb452e30289be5faff27b580"> <link rel="stylesheet" href="/assets/css/main.css?d41d8cd98f00b204e9800998ecf8427e"> <link rel="canonical" href="https://mdeluci.github.io/news/announcement_2/"> <script src="/assets/js/theme.js?9a0c749ec5240d9cda97bc72359a72c0"></script> <link defer rel="stylesheet" href="/assets/css/jekyll-pygments-themes-native.css?5847e5ed4a4568527aa6cfab446049ca" media="none" id="highlight_theme_dark"> <script>initTheme();</script> </head> <body class="fixed-top-nav "> <header> <nav id="navbar" class="navbar navbar-light navbar-expand-sm fixed-top" role="navigation"> <div class="container"> <a class="navbar-brand title font-weight-lighter" href="/"> Mario de Lucio's website </a> <button class="navbar-toggler collapsed ml-auto" type="button" data-toggle="collapse" data-target="#navbarNav" aria-controls="navbarNav" aria-expanded="false" aria-label="Toggle navigation"> <span class="sr-only">Toggle navigation</span> <span class="icon-bar top-bar"></span> <span class="icon-bar middle-bar"></span> <span class="icon-bar bottom-bar"></span> </button> <div class="collapse navbar-collapse text-right" id="navbarNav"> <ul class="navbar-nav ml-auto flex-nowrap"> <li class="nav-item "> <a class="nav-link" href="/">About </a> </li> <li class="nav-item "> <a class="nav-link" href="/publications/">Publications </a> </li> <li class="nav-item "> <a class="nav-link" href="/blog/">Blog </a> </li> <li class="nav-item "> <a class="nav-link" href="/cv/">CV </a> </li> <li class="nav-item "> <a class="nav-link" href="/teaching/">Teaching </a> </li> <li class="nav-item "> <a class="nav-link" href="/videos/">Videos </a> </li> <li class="nav-item"> <button id="search-toggle" title="Search" onclick="openSearchModal()"> <span class="nav-link">ctrl k <i class="ti ti-search"></i></span> </button> </li> <li class="toggle-container"> <button id="light-toggle" title="Change theme"> <i class="ti ti-sun-moon" id="light-toggle-system"></i> <i class="ti ti-moon-filled" id="light-toggle-dark"></i> <i class="ti ti-sun-filled" id="light-toggle-light"></i> </button> </li> </ul> </div> </div> </nav> <progress id="progress" value="0"> <div class="progress-container"> <span class="progress-bar"></span> </div> </progress> </header> <div class="container mt-5" role="main"> <div class="post"> <header class="post-header"> <h1 class="post-title">Mario succesfully defended his PhD thesis</h1> <p class="post-meta"> Created in April 03, 2024 </p> <p class="post-tags"> <i class="fa-solid fa-calendar fa-sm"></i> 2024 </p> </header> <article class="post-content"> <div id="markdown-content"> <p>Mario has successfully defended his PhD Dissertation titled “Numerical Simulation and Poromechanical Modeling of Subcutaneous Injection of Monoclonal Antibodies”. The PhD thesis committee was composed by Prof. Hector Gomez (Chair), Prof. Adrian Buganza Tepole, Prof. Arezoo M. Ardekani and Prof. Luis Solorio.</p> <p><img src="/assets/img/phd_defense.jpg" alt="PhD Defense" width="750"></p> <blockquote> <p>To my parents, Ana and Rafael, whose teachings I can encapsulate in the following words by the most important writer of all time: “Since you are not experienced in things of the world, all things that are a bit difficult seem impossible to you. Trust time; it usually provides a sweet way out of many bitter challenges.” —Miguel de Cervantes Saavedra, Don Quixote</p> </blockquote> </div> </article> </div> </div> <footer class="fixed-bottom" role="contentinfo"> <div class="container mt-0"> © Copyright 2024 Mario de Lucio. </div> </footer> <script src="https://cdn.jsdelivr.net/npm/jquery@3.6.0/dist/jquery.min.js" integrity="sha256-/xUj+3OJU5yExlq6GSYGSHk7tPXikynS7ogEvDej/m4=" crossorigin="anonymous"></script> <script src="/assets/js/bootstrap.bundle.min.js"></script> <script src="https://cdn.jsdelivr.net/npm/mdbootstrap@4.20.0/js/mdb.min.js" integrity="sha256-NdbiivsvWt7VYCt6hYNT3h/th9vSTL4EDWeGs5SN3DA=" crossorigin="anonymous"></script> <script defer src="https://cdn.jsdelivr.net/npm/masonry-layout@4.2.2/dist/masonry.pkgd.min.js" integrity="sha256-Nn1q/fx0H7SNLZMQ5Hw5JLaTRZp0yILA/FRexe19VdI=" crossorigin="anonymous"></script> <script defer src="https://cdn.jsdelivr.net/npm/imagesloaded@5.0.0/imagesloaded.pkgd.min.js" integrity="sha256-htrLFfZJ6v5udOG+3kNLINIKh2gvoKqwEhHYfTTMICc=" crossorigin="anonymous"></script> <script defer src="/assets/js/masonry.js" type="text/javascript"></script> <script defer src="https://cdn.jsdelivr.net/npm/medium-zoom@1.1.0/dist/medium-zoom.min.js" integrity="sha256-ZgMyDAIYDYGxbcpJcfUnYwNevG/xi9OHKaR/8GK+jWc=" crossorigin="anonymous"></script> <script defer src="/assets/js/zoom.js?85ddb88934d28b74e78031fd54cf8308"></script> <script src="/assets/js/no_defer.js?2781658a0a2b13ed609542042a859126"></script> <script defer src="/assets/js/common.js?06cae41083477f121be8cd9797ad8e2f"></script> <script defer src="/assets/js/copy_code.js?12775fdf7f95e901d7119054556e495f" type="text/javascript"></script> <script defer src="/assets/js/jupyter_new_tab.js?d9f17b6adc2311cbabd747f4538bb15f"></script> <script async src="https://d1bxh8uas1mnw7.cloudfront.net/assets/embed.js"></script> <script async src="https://badge.dimensions.ai/badge.js"></script> <script type="text/javascript">window.MathJax={tex:{tags:"ams"}};</script> <script defer type="text/javascript" id="MathJax-script" src="https://cdn.jsdelivr.net/npm/mathjax@3.2.0/es5/tex-mml-chtml.min.js" integrity="sha256-rjmgmaB99riUNcdlrDtcAiwtLIojSxNyUFdl+Qh+rB4=" crossorigin="anonymous"></script> <script defer src="https://cdnjs.cloudflare.com/polyfill/v3/polyfill.min.js?features=es6" crossorigin="anonymous"></script> <script type="text/javascript">function progressBarSetup(){"max"in document.createElement("progress")?(initializeProgressElement(),$(document).on("scroll",function(){progressBar.attr({value:getCurrentScrollPosition()})}),$(window).on("resize",initializeProgressElement)):(resizeProgressBar(),$(document).on("scroll",resizeProgressBar),$(window).on("resize",resizeProgressBar))}function getCurrentScrollPosition(){return $(window).scrollTop()}function initializeProgressElement(){let e=$("#navbar").outerHeight(!0);$("body").css({"padding-top":e}),$("progress-container").css({"padding-top":e}),progressBar.css({top:e}),progressBar.attr({max:getDistanceToScroll(),value:getCurrentScrollPosition()})}function getDistanceToScroll(){return $(document).height()-$(window).height()}function resizeProgressBar(){progressBar.css({width:getWidthPercentage()+"%"})}function getWidthPercentage(){return getCurrentScrollPosition()/getDistanceToScroll()*100}const progressBar=$("#progress");window.onload=function(){setTimeout(progressBarSetup,50)};</script> <script src="/assets/js/vanilla-back-to-top.min.js?f40d453793ff4f64e238e420181a1d17"></script> <script>addBackToTop();</script> <script type="module" src="/assets/js/search/ninja-keys.min.js?601a2d3465e2a52bec38b600518d5f70"></script> <ninja-keys hidebreadcrumbs noautoloadmdicons placeholder="Type to start searching"></ninja-keys> <script>let searchTheme=determineComputedTheme();const ninjaKeys=document.querySelector("ninja-keys");"dark"===searchTheme?ninjaKeys.classList.add("dark"):ninjaKeys.classList.remove("dark");const openSearchModal=()=>{const e=$("#navbarNav");e.hasClass("show")&&e.collapse("hide"),ninjaKeys.open()};</script> <script>const ninja=document.querySelector("ninja-keys");ninja.data=[{id:"nav-about",title:"About",section:"Navigation",handler:()=>{window.location.href="/"}},{id:"nav-publications",title:"Publications",description:"Ordered by most recent.",section:"Navigation",handler:()=>{window.location.href="/publications/"}},{id:"nav-blog",title:"Blog",description:"",section:"Navigation",handler:()=>{window.location.href="/blog/"}},{id:"nav-cv",title:"CV",description:"",section:"Navigation",handler:()=>{window.location.href="/cv/"}},{id:"nav-teaching",title:"Teaching",description:"Materials for courses you taught. 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Hillberry Graduate Scholarship | Mario de Lucio's website </title> <meta name="author" content="Mario de Lucio"> <meta name="description" content="Mario de Lucio's website "> <meta name="keywords" content="Computational Mechanics, Multiphysics Simulation, Biomechanics, Transport phenomena"> <link rel="stylesheet" href="/assets/css/bootstrap.min.css?a4b3f509e79c54a512b890d73235ef04"> <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/mdbootstrap@4.20.0/css/mdb.min.css" integrity="sha256-jpjYvU3G3N6nrrBwXJoVEYI/0zw8htfFnhT9ljN3JJw=" crossorigin="anonymous"> <link defer rel="stylesheet" href="/assets/css/academicons.min.css?f0b7046b84e425c55f3463ac249818f5"> <link defer rel="stylesheet" type="text/css" href="https://fonts.googleapis.com/css?family=Roboto:300,400,500,700|Roboto+Slab:100,300,400,500,700|Material+Icons&amp;display=swap"> <link defer rel="stylesheet" href="/assets/css/jekyll-pygments-themes-github.css?591dab5a4e56573bf4ef7fd332894c99" media="" id="highlight_theme_light"> <link rel="shortcut icon" href="/assets/img/webicon.png?b6c2349ccb452e30289be5faff27b580"> <link rel="stylesheet" href="/assets/css/main.css?d41d8cd98f00b204e9800998ecf8427e"> <link rel="canonical" href="https://mdeluci.github.io/news/announcement_3/"> <script src="/assets/js/theme.js?9a0c749ec5240d9cda97bc72359a72c0"></script> <link defer rel="stylesheet" href="/assets/css/jekyll-pygments-themes-native.css?5847e5ed4a4568527aa6cfab446049ca" media="none" id="highlight_theme_dark"> <script>initTheme();</script> </head> <body class="fixed-top-nav "> <header> <nav id="navbar" class="navbar navbar-light navbar-expand-sm fixed-top" role="navigation"> <div class="container"> <a class="navbar-brand title font-weight-lighter" href="/"> Mario de Lucio's website </a> <button class="navbar-toggler collapsed ml-auto" type="button" data-toggle="collapse" data-target="#navbarNav" aria-controls="navbarNav" aria-expanded="false" aria-label="Toggle navigation"> <span class="sr-only">Toggle navigation</span> <span class="icon-bar top-bar"></span> <span class="icon-bar middle-bar"></span> <span class="icon-bar bottom-bar"></span> </button> <div class="collapse navbar-collapse text-right" id="navbarNav"> <ul class="navbar-nav ml-auto flex-nowrap"> <li class="nav-item "> <a class="nav-link" href="/">About </a> </li> <li class="nav-item "> <a class="nav-link" href="/publications/">Publications </a> </li> <li class="nav-item "> <a class="nav-link" href="/blog/">Blog </a> </li> <li class="nav-item "> <a class="nav-link" href="/cv/">CV </a> </li> <li class="nav-item "> <a class="nav-link" href="/teaching/">Teaching </a> </li> <li class="nav-item "> <a class="nav-link" href="/videos/">Videos </a> </li> <li class="nav-item"> <button id="search-toggle" title="Search" onclick="openSearchModal()"> <span class="nav-link">ctrl k <i class="ti ti-search"></i></span> </button> </li> <li class="toggle-container"> <button id="light-toggle" title="Change theme"> <i class="ti ti-sun-moon" id="light-toggle-system"></i> <i class="ti ti-moon-filled" id="light-toggle-dark"></i> <i class="ti ti-sun-filled" id="light-toggle-light"></i> </button> </li> </ul> </div> </div> </nav> <progress id="progress" value="0"> <div class="progress-container"> <span class="progress-bar"></span> </div> </progress> </header> <div class="container mt-5" role="main"> <div class="post"> <header class="post-header"> <h1 class="post-title">Mario is awarded the Ben M. Hillberry Graduate Scholarship</h1> <p class="post-meta"> Created in November 10, 2023 </p> <p class="post-tags"> <i class="fa-solid fa-calendar fa-sm"></i> 2023 </p> </header> <article class="post-content"> <div id="markdown-content"> <p>Mario has been awarded the 2023 <a href="https://engineering.purdue.edu/ME/News/2023/purdue-me-grad-students-receive-fellowships-and-scholarships" rel="external nofollow noopener" target="_blank">Ben M. Hillberry</a> departmental scholarship for his PhD work in computational biomechanics. The Ben M. Hillberry Graduate Scholarship is sponsored by the students and friends of Professor Ben M. Hillberry in honor of his years of dedication to the School of Mechanical Engineering. The scholarship is for ME graduate students with a preference for students studying in biomechanics or materials. Selection of the recipients will be based on academic merit. Each recipient will receive a scholarship of $4,000. 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Hillberry Graduate Scholarship</h1> <p class="post-meta"> Created in November 10, 2023 </p> <p class="post-tags"> <i class="fa-solid fa-calendar fa-sm"></i> 2023 </p> </header> <article class="post-content"> <div id="markdown-content"> <p>Mario has been awarded the 2023 <a href="https://engineering.purdue.edu/ME/News/2023/purdue-me-grad-students-receive-fellowships-and-scholarships" rel="external nofollow noopener" target="_blank">Ben M. Hillberry</a> departmental scholarship for his PhD work in computational biomechanics. The Ben M. Hillberry Graduate Scholarship is sponsored by the students and friends of Professor Ben M. Hillberry in honor of his years of dedication to the School of Mechanical Engineering. The scholarship is for ME graduate students with a preference for students studying in biomechanics or materials. Selection of the recipients will be based on academic merit. Each recipient will receive a scholarship of $4,000. 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diff --git a/news/index.html b/news/index.html
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-<!DOCTYPE html> <html lang="en"> <head> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> <meta charset="utf-8"> <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"> <meta http-equiv="X-UA-Compatible" content="IE=edge"> <title> news | Mario de Lucio's website </title> <meta name="author" content="Mario de Lucio"> <meta name="description" content="Mario de Lucio's website "> <meta name="keywords" content="Computational Mechanics, Multiphysics Simulation, Biomechanics, Transport phenomena"> <link rel="stylesheet" href="/assets/css/bootstrap.min.css?a4b3f509e79c54a512b890d73235ef04"> <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/mdbootstrap@4.20.0/css/mdb.min.css" integrity="sha256-jpjYvU3G3N6nrrBwXJoVEYI/0zw8htfFnhT9ljN3JJw=" crossorigin="anonymous"> <link defer rel="stylesheet" href="/assets/css/academicons.min.css?f0b7046b84e425c55f3463ac249818f5"> <link defer rel="stylesheet" type="text/css" href="https://fonts.googleapis.com/css?family=Roboto:300,400,500,700|Roboto+Slab:100,300,400,500,700|Material+Icons&amp;display=swap"> <link defer rel="stylesheet" href="/assets/css/jekyll-pygments-themes-github.css?591dab5a4e56573bf4ef7fd332894c99" media="" id="highlight_theme_light"> <link rel="shortcut icon" href="/assets/img/webicon.png?b6c2349ccb452e30289be5faff27b580"> <link rel="stylesheet" href="/assets/css/main.css?d41d8cd98f00b204e9800998ecf8427e"> <link rel="canonical" href="https://mdeluci.github.io/news/"> <script src="/assets/js/theme.js?9a0c749ec5240d9cda97bc72359a72c0"></script> <link defer rel="stylesheet" href="/assets/css/jekyll-pygments-themes-native.css?5847e5ed4a4568527aa6cfab446049ca" media="none" id="highlight_theme_dark"> <script>initTheme();</script> </head> <body class="fixed-top-nav "> <header> <nav id="navbar" class="navbar navbar-light navbar-expand-sm fixed-top" role="navigation"> <div class="container"> <a class="navbar-brand title font-weight-lighter" href="/"> Mario de Lucio's website </a> <button class="navbar-toggler collapsed ml-auto" type="button" data-toggle="collapse" data-target="#navbarNav" aria-controls="navbarNav" aria-expanded="false" aria-label="Toggle navigation"> <span class="sr-only">Toggle navigation</span> <span class="icon-bar top-bar"></span> <span class="icon-bar middle-bar"></span> <span class="icon-bar bottom-bar"></span> </button> <div class="collapse navbar-collapse text-right" id="navbarNav"> <ul class="navbar-nav ml-auto flex-nowrap"> <li class="nav-item "> <a class="nav-link" href="/">About </a> </li> <li class="nav-item "> <a class="nav-link" href="/publications/">Publications </a> </li> <li class="nav-item "> <a class="nav-link" href="/blog/">Blog </a> </li> <li class="nav-item "> <a class="nav-link" href="/cv/">CV </a> </li> <li class="nav-item "> <a class="nav-link" href="/teaching/">Teaching </a> </li> <li class="nav-item "> <a class="nav-link" href="/videos/">Videos </a> </li> <li class="nav-item"> <button id="search-toggle" title="Search" onclick="openSearchModal()"> <span class="nav-link">ctrl k <i class="ti ti-search"></i></span> </button> </li> <li class="toggle-container"> <button id="light-toggle" title="Change theme"> <i class="ti ti-sun-moon" id="light-toggle-system"></i> <i class="ti ti-moon-filled" id="light-toggle-dark"></i> <i class="ti ti-sun-filled" id="light-toggle-light"></i> </button> </li> </ul> </div> </div> </nav> <progress id="progress" value="0"> <div class="progress-container"> <span class="progress-bar"></span> </div> </progress> </header> <div class="container mt-5" role="main"> <div class="post"> <header class="post-header"> <h1 class="post-title">news</h1> <p class="post-description"></p> </header> <article> <div class="news"> <div class="table-responsive"> <table class="table table-sm table-borderless"> <tr> <th scope="row" style="width: 20%">Apr 03, 2024</th> <td> I have successfully defended my PhD Dissertation titled “Numerical Simulation and Poromechanical Modeling of Subcutaneous Injection of Monoclonal Antibodies”. The PhD thesis committee was composed by Prof. Hector Gomez (Chair), Prof. Adrian Buganza Tepole, Prof. Arezoo M. Ardekani and Prof. Luis Solorio. </td> </tr> <tr> <th scope="row" style="width: 20%">Apr 03, 2024</th> <td> <a class="news-title" href="/news/announcement_2/">Mario succesfully defended his PhD thesis</a> </td> </tr> <tr> <th scope="row" style="width: 20%">Nov 10, 2023</th> <td> <a class="news-title" href="/news/announcement_3/">Mario is awarded the Ben M. 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+<!DOCTYPE html> <html lang="en"> <head> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> <meta charset="utf-8"> <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"> <meta http-equiv="X-UA-Compatible" content="IE=edge"> <title> news | Mario de Lucio's website </title> <meta name="author" content="Mario de Lucio"> <meta name="description" content="Mario de Lucio's website "> <meta name="keywords" content="Computational Mechanics, Multiphysics Simulation, Biomechanics, Transport phenomena"> <link rel="stylesheet" href="/assets/css/bootstrap.min.css?a4b3f509e79c54a512b890d73235ef04"> <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/mdbootstrap@4.20.0/css/mdb.min.css" integrity="sha256-jpjYvU3G3N6nrrBwXJoVEYI/0zw8htfFnhT9ljN3JJw=" crossorigin="anonymous"> <link defer rel="stylesheet" href="/assets/css/academicons.min.css?f0b7046b84e425c55f3463ac249818f5"> <link defer rel="stylesheet" type="text/css" href="https://fonts.googleapis.com/css?family=Roboto:300,400,500,700|Roboto+Slab:100,300,400,500,700|Material+Icons&amp;display=swap"> <link defer rel="stylesheet" href="/assets/css/jekyll-pygments-themes-github.css?591dab5a4e56573bf4ef7fd332894c99" media="" id="highlight_theme_light"> <link rel="shortcut icon" href="/assets/img/webicon.png?b6c2349ccb452e30289be5faff27b580"> <link rel="stylesheet" href="/assets/css/main.css?d41d8cd98f00b204e9800998ecf8427e"> <link rel="canonical" href="https://mdeluci.github.io/news/"> <script src="/assets/js/theme.js?9a0c749ec5240d9cda97bc72359a72c0"></script> <link defer rel="stylesheet" href="/assets/css/jekyll-pygments-themes-native.css?5847e5ed4a4568527aa6cfab446049ca" media="none" id="highlight_theme_dark"> <script>initTheme();</script> </head> <body class="fixed-top-nav "> <header> <nav id="navbar" class="navbar navbar-light navbar-expand-sm fixed-top" role="navigation"> <div class="container"> <a class="navbar-brand title font-weight-lighter" href="/"> Mario de Lucio's website </a> <button class="navbar-toggler collapsed ml-auto" type="button" data-toggle="collapse" data-target="#navbarNav" aria-controls="navbarNav" aria-expanded="false" aria-label="Toggle navigation"> <span class="sr-only">Toggle navigation</span> <span class="icon-bar top-bar"></span> <span class="icon-bar middle-bar"></span> <span class="icon-bar bottom-bar"></span> </button> <div class="collapse navbar-collapse text-right" id="navbarNav"> <ul class="navbar-nav ml-auto flex-nowrap"> <li class="nav-item "> <a class="nav-link" href="/">About </a> </li> <li class="nav-item "> <a class="nav-link" href="/publications/">Publications </a> </li> <li class="nav-item "> <a class="nav-link" href="/blog/">Blog </a> </li> <li class="nav-item "> <a class="nav-link" href="/cv/">CV </a> </li> <li class="nav-item "> <a class="nav-link" href="/teaching/">Teaching </a> </li> <li class="nav-item "> <a class="nav-link" href="/videos/">Videos </a> </li> <li class="nav-item"> <button id="search-toggle" title="Search" onclick="openSearchModal()"> <span class="nav-link">ctrl k <i class="ti ti-search"></i></span> </button> </li> <li class="toggle-container"> <button id="light-toggle" title="Change theme"> <i class="ti ti-sun-moon" id="light-toggle-system"></i> <i class="ti ti-moon-filled" id="light-toggle-dark"></i> <i class="ti ti-sun-filled" id="light-toggle-light"></i> </button> </li> </ul> </div> </div> </nav> <progress id="progress" value="0"> <div class="progress-container"> <span class="progress-bar"></span> </div> </progress> </header> <div class="container mt-5" role="main"> <div class="post"> <header class="post-header"> <h1 class="post-title">news</h1> <p class="post-description"></p> </header> <article> <div class="news"> <div class="table-responsive"> <table class="table table-sm table-borderless"> <tr> <th scope="row" style="width: 20%">Apr 03, 2024</th> <td> I have successfully defended my PhD Dissertation titled “Numerical Simulation and Poromechanical Modeling of Subcutaneous Injection of Monoclonal Antibodies”. The PhD thesis committee was composed by Prof. Hector Gomez (Chair), Prof. Adrian Buganza Tepole, Prof. Arezoo M. Ardekani and Prof. Luis Solorio. </td> </tr> <tr> <th scope="row" style="width: 20%">Apr 03, 2024</th> <td> <a class="news-title" href="/news/announcement_2/">Mario succesfully defended his PhD thesis</a> </td> </tr> <tr> <th scope="row" style="width: 20%">Nov 10, 2023</th> <td> <a class="news-title" href="/news/announcement_3/">Mario is awarded the Ben M. Hillberry Graduate Scholarship</a> </td> </tr> </table> </div> </div> </article> </div> </div> <footer class="fixed-bottom" role="contentinfo"> <div class="container mt-0"> © Copyright 2024 Mario de Lucio. </div> </footer> <script src="https://cdn.jsdelivr.net/npm/jquery@3.6.0/dist/jquery.min.js" integrity="sha256-/xUj+3OJU5yExlq6GSYGSHk7tPXikynS7ogEvDej/m4=" crossorigin="anonymous"></script> <script src="/assets/js/bootstrap.bundle.min.js"></script> <script src="https://cdn.jsdelivr.net/npm/mdbootstrap@4.20.0/js/mdb.min.js" integrity="sha256-NdbiivsvWt7VYCt6hYNT3h/th9vSTL4EDWeGs5SN3DA=" crossorigin="anonymous"></script> <script defer src="https://cdn.jsdelivr.net/npm/masonry-layout@4.2.2/dist/masonry.pkgd.min.js" integrity="sha256-Nn1q/fx0H7SNLZMQ5Hw5JLaTRZp0yILA/FRexe19VdI=" crossorigin="anonymous"></script> <script defer src="https://cdn.jsdelivr.net/npm/imagesloaded@5.0.0/imagesloaded.pkgd.min.js" integrity="sha256-htrLFfZJ6v5udOG+3kNLINIKh2gvoKqwEhHYfTTMICc=" crossorigin="anonymous"></script> <script defer src="/assets/js/masonry.js" type="text/javascript"></script> <script defer src="https://cdn.jsdelivr.net/npm/medium-zoom@1.1.0/dist/medium-zoom.min.js" integrity="sha256-ZgMyDAIYDYGxbcpJcfUnYwNevG/xi9OHKaR/8GK+jWc=" crossorigin="anonymous"></script> <script defer src="/assets/js/zoom.js?85ddb88934d28b74e78031fd54cf8308"></script> <script src="/assets/js/no_defer.js?2781658a0a2b13ed609542042a859126"></script> <script defer src="/assets/js/common.js?06cae41083477f121be8cd9797ad8e2f"></script> <script defer src="/assets/js/copy_code.js?12775fdf7f95e901d7119054556e495f" type="text/javascript"></script> <script defer src="/assets/js/jupyter_new_tab.js?d9f17b6adc2311cbabd747f4538bb15f"></script> <script async src="https://d1bxh8uas1mnw7.cloudfront.net/assets/embed.js"></script> <script async src="https://badge.dimensions.ai/badge.js"></script> <script type="text/javascript">window.MathJax={tex:{tags:"ams"}};</script> <script defer type="text/javascript" id="MathJax-script" src="https://cdn.jsdelivr.net/npm/mathjax@3.2.0/es5/tex-mml-chtml.min.js" integrity="sha256-rjmgmaB99riUNcdlrDtcAiwtLIojSxNyUFdl+Qh+rB4=" crossorigin="anonymous"></script> <script defer src="https://cdnjs.cloudflare.com/polyfill/v3/polyfill.min.js?features=es6" crossorigin="anonymous"></script> <script type="text/javascript">function progressBarSetup(){"max"in document.createElement("progress")?(initializeProgressElement(),$(document).on("scroll",function(){progressBar.attr({value:getCurrentScrollPosition()})}),$(window).on("resize",initializeProgressElement)):(resizeProgressBar(),$(document).on("scroll",resizeProgressBar),$(window).on("resize",resizeProgressBar))}function getCurrentScrollPosition(){return $(window).scrollTop()}function initializeProgressElement(){let e=$("#navbar").outerHeight(!0);$("body").css({"padding-top":e}),$("progress-container").css({"padding-top":e}),progressBar.css({top:e}),progressBar.attr({max:getDistanceToScroll(),value:getCurrentScrollPosition()})}function getDistanceToScroll(){return $(document).height()-$(window).height()}function resizeProgressBar(){progressBar.css({width:getWidthPercentage()+"%"})}function getWidthPercentage(){return getCurrentScrollPosition()/getDistanceToScroll()*100}const progressBar=$("#progress");window.onload=function(){setTimeout(progressBarSetup,50)};</script> <script src="/assets/js/vanilla-back-to-top.min.js?f40d453793ff4f64e238e420181a1d17"></script> <script>addBackToTop();</script> <script type="module" src="/assets/js/search/ninja-keys.min.js?601a2d3465e2a52bec38b600518d5f70"></script> <ninja-keys hidebreadcrumbs noautoloadmdicons placeholder="Type to start searching"></ninja-keys> <script>let searchTheme=determineComputedTheme();const ninjaKeys=document.querySelector("ninja-keys");"dark"===searchTheme?ninjaKeys.classList.add("dark"):ninjaKeys.classList.remove("dark");const openSearchModal=()=>{const e=$("#navbarNav");e.hasClass("show")&&e.collapse("hide"),ninjaKeys.open()};</script> <script>const ninja=document.querySelector("ninja-keys");ninja.data=[{id:"nav-about",title:"About",section:"Navigation",handler:()=>{window.location.href="/"}},{id:"nav-publications",title:"Publications",description:"Ordered by most recent.",section:"Navigation",handler:()=>{window.location.href="/publications/"}},{id:"nav-blog",title:"Blog",description:"",section:"Navigation",handler:()=>{window.location.href="/blog/"}},{id:"nav-cv",title:"CV",description:"",section:"Navigation",handler:()=>{window.location.href="/cv/"}},{id:"nav-teaching",title:"Teaching",description:"Materials for courses you taught. 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   <span class="nt">&lt;/div&gt;</span>
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-</code></pre></div></div> </article> <h2>References</h2> <div class="publications"> </div> </div> </div> <footer class="fixed-bottom" role="contentinfo"> <div class="container mt-0"> © Copyright 2024 Mario de Lucio. </div> </footer> <script src="https://cdn.jsdelivr.net/npm/jquery@3.6.0/dist/jquery.min.js" integrity="sha256-/xUj+3OJU5yExlq6GSYGSHk7tPXikynS7ogEvDej/m4=" crossorigin="anonymous"></script> <script src="/assets/js/bootstrap.bundle.min.js"></script> <script src="https://cdn.jsdelivr.net/npm/mdbootstrap@4.20.0/js/mdb.min.js" integrity="sha256-NdbiivsvWt7VYCt6hYNT3h/th9vSTL4EDWeGs5SN3DA=" crossorigin="anonymous"></script> <script defer src="https://cdn.jsdelivr.net/npm/masonry-layout@4.2.2/dist/masonry.pkgd.min.js" integrity="sha256-Nn1q/fx0H7SNLZMQ5Hw5JLaTRZp0yILA/FRexe19VdI=" crossorigin="anonymous"></script> <script defer src="https://cdn.jsdelivr.net/npm/imagesloaded@5.0.0/imagesloaded.pkgd.min.js" integrity="sha256-htrLFfZJ6v5udOG+3kNLINIKh2gvoKqwEhHYfTTMICc=" crossorigin="anonymous"></script> <script defer src="/assets/js/masonry.js" type="text/javascript"></script> <script defer src="https://cdn.jsdelivr.net/npm/medium-zoom@1.1.0/dist/medium-zoom.min.js" integrity="sha256-ZgMyDAIYDYGxbcpJcfUnYwNevG/xi9OHKaR/8GK+jWc=" crossorigin="anonymous"></script> <script defer src="/assets/js/zoom.js?85ddb88934d28b74e78031fd54cf8308"></script> <script src="/assets/js/no_defer.js?2781658a0a2b13ed609542042a859126"></script> <script defer src="/assets/js/common.js?06cae41083477f121be8cd9797ad8e2f"></script> <script defer src="/assets/js/copy_code.js?12775fdf7f95e901d7119054556e495f" type="text/javascript"></script> <script defer src="/assets/js/jupyter_new_tab.js?d9f17b6adc2311cbabd747f4538bb15f"></script> <script async src="https://d1bxh8uas1mnw7.cloudfront.net/assets/embed.js"></script> <script async src="https://badge.dimensions.ai/badge.js"></script> <script type="text/javascript">window.MathJax={tex:{tags:"ams"}};</script> <script defer type="text/javascript" id="MathJax-script" src="https://cdn.jsdelivr.net/npm/mathjax@3.2.0/es5/tex-mml-chtml.min.js" integrity="sha256-rjmgmaB99riUNcdlrDtcAiwtLIojSxNyUFdl+Qh+rB4=" crossorigin="anonymous"></script> <script defer src="https://cdnjs.cloudflare.com/polyfill/v3/polyfill.min.js?features=es6" crossorigin="anonymous"></script> <script type="text/javascript">function progressBarSetup(){"max"in document.createElement("progress")?(initializeProgressElement(),$(document).on("scroll",function(){progressBar.attr({value:getCurrentScrollPosition()})}),$(window).on("resize",initializeProgressElement)):(resizeProgressBar(),$(document).on("scroll",resizeProgressBar),$(window).on("resize",resizeProgressBar))}function getCurrentScrollPosition(){return $(window).scrollTop()}function initializeProgressElement(){let e=$("#navbar").outerHeight(!0);$("body").css({"padding-top":e}),$("progress-container").css({"padding-top":e}),progressBar.css({top:e}),progressBar.attr({max:getDistanceToScroll(),value:getCurrentScrollPosition()})}function getDistanceToScroll(){return $(document).height()-$(window).height()}function resizeProgressBar(){progressBar.css({width:getWidthPercentage()+"%"})}function getWidthPercentage(){return getCurrentScrollPosition()/getDistanceToScroll()*100}const progressBar=$("#progress");window.onload=function(){setTimeout(progressBarSetup,50)};</script> <script src="/assets/js/vanilla-back-to-top.min.js?f40d453793ff4f64e238e420181a1d17"></script> <script>addBackToTop();</script> <script type="module" src="/assets/js/search/ninja-keys.min.js?601a2d3465e2a52bec38b600518d5f70"></script> <ninja-keys hidebreadcrumbs noautoloadmdicons placeholder="Type to start searching"></ninja-keys> <script>let searchTheme=determineComputedTheme();const ninjaKeys=document.querySelector("ninja-keys");"dark"===searchTheme?ninjaKeys.classList.add("dark"):ninjaKeys.classList.remove("dark");const openSearchModal=()=>{const e=$("#navbarNav");e.hasClass("show")&&e.collapse("hide"),ninjaKeys.open()};</script> <script>const ninja=document.querySelector("ninja-keys");ninja.data=[{id:"nav-about",title:"About",section:"Navigation",handler:()=>{window.location.href="/"}},{id:"nav-publications",title:"Publications",description:"Ordered by most recent.",section:"Navigation",handler:()=>{window.location.href="/publications/"}},{id:"nav-blog",title:"Blog",description:"",section:"Navigation",handler:()=>{window.location.href="/blog/"}},{id:"nav-cv",title:"CV",description:"",section:"Navigation",handler:()=>{window.location.href="/cv/"}},{id:"nav-teaching",title:"Teaching",description:"Materials for courses you taught. 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\ No newline at end of file
+</code></pre></div></div> </article> <h2>References</h2> <div class="publications"> </div> </div> </div> <footer class="fixed-bottom" role="contentinfo"> <div class="container mt-0"> © Copyright 2024 Mario de Lucio. </div> </footer> <script src="https://cdn.jsdelivr.net/npm/jquery@3.6.0/dist/jquery.min.js" integrity="sha256-/xUj+3OJU5yExlq6GSYGSHk7tPXikynS7ogEvDej/m4=" crossorigin="anonymous"></script> <script src="/assets/js/bootstrap.bundle.min.js"></script> <script src="https://cdn.jsdelivr.net/npm/mdbootstrap@4.20.0/js/mdb.min.js" integrity="sha256-NdbiivsvWt7VYCt6hYNT3h/th9vSTL4EDWeGs5SN3DA=" crossorigin="anonymous"></script> <script defer src="https://cdn.jsdelivr.net/npm/masonry-layout@4.2.2/dist/masonry.pkgd.min.js" integrity="sha256-Nn1q/fx0H7SNLZMQ5Hw5JLaTRZp0yILA/FRexe19VdI=" crossorigin="anonymous"></script> <script defer src="https://cdn.jsdelivr.net/npm/imagesloaded@5.0.0/imagesloaded.pkgd.min.js" integrity="sha256-htrLFfZJ6v5udOG+3kNLINIKh2gvoKqwEhHYfTTMICc=" crossorigin="anonymous"></script> <script defer src="/assets/js/masonry.js" type="text/javascript"></script> <script defer src="https://cdn.jsdelivr.net/npm/medium-zoom@1.1.0/dist/medium-zoom.min.js" integrity="sha256-ZgMyDAIYDYGxbcpJcfUnYwNevG/xi9OHKaR/8GK+jWc=" crossorigin="anonymous"></script> <script defer src="/assets/js/zoom.js?85ddb88934d28b74e78031fd54cf8308"></script> <script src="/assets/js/no_defer.js?2781658a0a2b13ed609542042a859126"></script> <script defer src="/assets/js/common.js?06cae41083477f121be8cd9797ad8e2f"></script> <script defer src="/assets/js/copy_code.js?12775fdf7f95e901d7119054556e495f" type="text/javascript"></script> <script defer src="/assets/js/jupyter_new_tab.js?d9f17b6adc2311cbabd747f4538bb15f"></script> <script async src="https://d1bxh8uas1mnw7.cloudfront.net/assets/embed.js"></script> <script async src="https://badge.dimensions.ai/badge.js"></script> <script type="text/javascript">window.MathJax={tex:{tags:"ams"}};</script> <script defer type="text/javascript" id="MathJax-script" src="https://cdn.jsdelivr.net/npm/mathjax@3.2.0/es5/tex-mml-chtml.min.js" integrity="sha256-rjmgmaB99riUNcdlrDtcAiwtLIojSxNyUFdl+Qh+rB4=" crossorigin="anonymous"></script> <script defer src="https://cdnjs.cloudflare.com/polyfill/v3/polyfill.min.js?features=es6" crossorigin="anonymous"></script> <script type="text/javascript">function progressBarSetup(){"max"in document.createElement("progress")?(initializeProgressElement(),$(document).on("scroll",function(){progressBar.attr({value:getCurrentScrollPosition()})}),$(window).on("resize",initializeProgressElement)):(resizeProgressBar(),$(document).on("scroll",resizeProgressBar),$(window).on("resize",resizeProgressBar))}function getCurrentScrollPosition(){return $(window).scrollTop()}function initializeProgressElement(){let e=$("#navbar").outerHeight(!0);$("body").css({"padding-top":e}),$("progress-container").css({"padding-top":e}),progressBar.css({top:e}),progressBar.attr({max:getDistanceToScroll(),value:getCurrentScrollPosition()})}function getDistanceToScroll(){return $(document).height()-$(window).height()}function resizeProgressBar(){progressBar.css({width:getWidthPercentage()+"%"})}function getWidthPercentage(){return getCurrentScrollPosition()/getDistanceToScroll()*100}const progressBar=$("#progress");window.onload=function(){setTimeout(progressBarSetup,50)};</script> <script src="/assets/js/vanilla-back-to-top.min.js?f40d453793ff4f64e238e420181a1d17"></script> <script>addBackToTop();</script> <script type="module" src="/assets/js/search/ninja-keys.min.js?601a2d3465e2a52bec38b600518d5f70"></script> <ninja-keys hidebreadcrumbs noautoloadmdicons placeholder="Type to start searching"></ninja-keys> <script>let searchTheme=determineComputedTheme();const ninjaKeys=document.querySelector("ninja-keys");"dark"===searchTheme?ninjaKeys.classList.add("dark"):ninjaKeys.classList.remove("dark");const openSearchModal=()=>{const e=$("#navbarNav");e.hasClass("show")&&e.collapse("hide"),ninjaKeys.open()};</script> <script>const ninja=document.querySelector("ninja-keys");ninja.data=[{id:"nav-about",title:"About",section:"Navigation",handler:()=>{window.location.href="/"}},{id:"nav-publications",title:"Publications",description:"Ordered by most recent.",section:"Navigation",handler:()=>{window.location.href="/publications/"}},{id:"nav-blog",title:"Blog",description:"",section:"Navigation",handler:()=>{window.location.href="/blog/"}},{id:"nav-cv",title:"CV",description:"",section:"Navigation",handler:()=>{window.location.href="/cv/"}},{id:"nav-teaching",title:"Teaching",description:"Materials for courses you taught. 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diff --git a/projects/2_project/index.html b/projects/2_project/index.html
index 99a8790a..a966b80a 100644
--- a/projects/2_project/index.html
+++ b/projects/2_project/index.html
@@ -12,4 +12,4 @@
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   <span class="nt">&lt;/div&gt;</span>
 <span class="nt">&lt;/div&gt;</span>
-</code></pre></div></div> </article> <div id="giscus_thread" style="max-width: 930px; margin: 0 auto;"> <script>let giscusTheme=determineComputedTheme(),giscusAttributes={src:"https://giscus.app/client.js","data-repo":"mdeluci/mdeluci.github.io","data-repo-id":"","data-category":"Comments","data-category-id":"","data-mapping":"title","data-strict":"1","data-reactions-enabled":"1","data-emit-metadata":"0","data-input-position":"bottom","data-theme":giscusTheme,"data-lang":"en",crossorigin:"anonymous",async:""},giscusScript=document.createElement("script");Object.entries(giscusAttributes).forEach(([t,e])=>giscusScript.setAttribute(t,e)),document.getElementById("giscus_thread").appendChild(giscusScript);</script> <noscript>Please enable JavaScript to view the <a href="http://giscus.app/?ref_noscript" rel="external nofollow noopener" target="_blank">comments powered by giscus.</a> </noscript> </div> </div> </div> <footer class="fixed-bottom" role="contentinfo"> <div class="container 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diff --git a/projects/4_project/index.html b/projects/4_project/index.html
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diff --git a/projects/5_project/index.html b/projects/5_project/index.html
index abad3aa0..d72364ef 100644
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diff --git a/projects/6_project/index.html b/projects/6_project/index.html
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+</code></pre></div></div> </article> </div> </div> <footer class="fixed-bottom" role="contentinfo"> <div class="container mt-0"> © Copyright 2024 Mario de Lucio. </div> </footer> <script src="https://cdn.jsdelivr.net/npm/jquery@3.6.0/dist/jquery.min.js" integrity="sha256-/xUj+3OJU5yExlq6GSYGSHk7tPXikynS7ogEvDej/m4=" crossorigin="anonymous"></script> <script src="/assets/js/bootstrap.bundle.min.js"></script> <script src="https://cdn.jsdelivr.net/npm/mdbootstrap@4.20.0/js/mdb.min.js" integrity="sha256-NdbiivsvWt7VYCt6hYNT3h/th9vSTL4EDWeGs5SN3DA=" crossorigin="anonymous"></script> <script defer src="https://cdn.jsdelivr.net/npm/masonry-layout@4.2.2/dist/masonry.pkgd.min.js" integrity="sha256-Nn1q/fx0H7SNLZMQ5Hw5JLaTRZp0yILA/FRexe19VdI=" crossorigin="anonymous"></script> <script defer src="https://cdn.jsdelivr.net/npm/imagesloaded@5.0.0/imagesloaded.pkgd.min.js" integrity="sha256-htrLFfZJ6v5udOG+3kNLINIKh2gvoKqwEhHYfTTMICc=" crossorigin="anonymous"></script> <script defer src="/assets/js/masonry.js" type="text/javascript"></script> <script defer src="https://cdn.jsdelivr.net/npm/medium-zoom@1.1.0/dist/medium-zoom.min.js" integrity="sha256-ZgMyDAIYDYGxbcpJcfUnYwNevG/xi9OHKaR/8GK+jWc=" crossorigin="anonymous"></script> <script defer src="/assets/js/zoom.js?85ddb88934d28b74e78031fd54cf8308"></script> <script src="/assets/js/no_defer.js?2781658a0a2b13ed609542042a859126"></script> <script defer src="/assets/js/common.js?06cae41083477f121be8cd9797ad8e2f"></script> <script defer src="/assets/js/copy_code.js?12775fdf7f95e901d7119054556e495f" type="text/javascript"></script> <script defer src="/assets/js/jupyter_new_tab.js?d9f17b6adc2311cbabd747f4538bb15f"></script> <script async src="https://d1bxh8uas1mnw7.cloudfront.net/assets/embed.js"></script> <script async src="https://badge.dimensions.ai/badge.js"></script> <script type="text/javascript">window.MathJax={tex:{tags:"ams"}};</script> <script defer type="text/javascript" id="MathJax-script" src="https://cdn.jsdelivr.net/npm/mathjax@3.2.0/es5/tex-mml-chtml.min.js" integrity="sha256-rjmgmaB99riUNcdlrDtcAiwtLIojSxNyUFdl+Qh+rB4=" crossorigin="anonymous"></script> <script defer src="https://cdnjs.cloudflare.com/polyfill/v3/polyfill.min.js?features=es6" crossorigin="anonymous"></script> <script type="text/javascript">function progressBarSetup(){"max"in document.createElement("progress")?(initializeProgressElement(),$(document).on("scroll",function(){progressBar.attr({value:getCurrentScrollPosition()})}),$(window).on("resize",initializeProgressElement)):(resizeProgressBar(),$(document).on("scroll",resizeProgressBar),$(window).on("resize",resizeProgressBar))}function getCurrentScrollPosition(){return $(window).scrollTop()}function initializeProgressElement(){let e=$("#navbar").outerHeight(!0);$("body").css({"padding-top":e}),$("progress-container").css({"padding-top":e}),progressBar.css({top:e}),progressBar.attr({max:getDistanceToScroll(),value:getCurrentScrollPosition()})}function getDistanceToScroll(){return $(document).height()-$(window).height()}function resizeProgressBar(){progressBar.css({width:getWidthPercentage()+"%"})}function getWidthPercentage(){return getCurrentScrollPosition()/getDistanceToScroll()*100}const progressBar=$("#progress");window.onload=function(){setTimeout(progressBarSetup,50)};</script> <script src="/assets/js/vanilla-back-to-top.min.js?f40d453793ff4f64e238e420181a1d17"></script> <script>addBackToTop();</script> <script type="module" src="/assets/js/search/ninja-keys.min.js?601a2d3465e2a52bec38b600518d5f70"></script> <ninja-keys hidebreadcrumbs noautoloadmdicons placeholder="Type to start searching"></ninja-keys> <script>let searchTheme=determineComputedTheme();const ninjaKeys=document.querySelector("ninja-keys");"dark"===searchTheme?ninjaKeys.classList.add("dark"):ninjaKeys.classList.remove("dark");const openSearchModal=()=>{const e=$("#navbarNav");e.hasClass("show")&&e.collapse("hide"),ninjaKeys.open()};</script> <script>const ninja=document.querySelector("ninja-keys");ninja.data=[{id:"nav-about",title:"About",section:"Navigation",handler:()=>{window.location.href="/"}},{id:"nav-publications",title:"Publications",description:"Ordered by most recent.",section:"Navigation",handler:()=>{window.location.href="/publications/"}},{id:"nav-blog",title:"Blog",description:"",section:"Navigation",handler:()=>{window.location.href="/blog/"}},{id:"nav-cv",title:"CV",description:"",section:"Navigation",handler:()=>{window.location.href="/cv/"}},{id:"nav-teaching",title:"Teaching",description:"Materials for courses you taught. 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diff --git a/projects/7_project/index.html b/projects/7_project/index.html
index 56bca261..a9ab26f4 100644
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-</code></pre></div></div> </article> <h2>References</h2> <div class="publications"> </div> </div> </div> <footer class="fixed-bottom" role="contentinfo"> <div class="container mt-0"> © Copyright 2024 Mario de Lucio. </div> </footer> <script src="https://cdn.jsdelivr.net/npm/jquery@3.6.0/dist/jquery.min.js" integrity="sha256-/xUj+3OJU5yExlq6GSYGSHk7tPXikynS7ogEvDej/m4=" crossorigin="anonymous"></script> <script src="/assets/js/bootstrap.bundle.min.js"></script> <script src="https://cdn.jsdelivr.net/npm/mdbootstrap@4.20.0/js/mdb.min.js" integrity="sha256-NdbiivsvWt7VYCt6hYNT3h/th9vSTL4EDWeGs5SN3DA=" crossorigin="anonymous"></script> <script defer src="https://cdn.jsdelivr.net/npm/masonry-layout@4.2.2/dist/masonry.pkgd.min.js" integrity="sha256-Nn1q/fx0H7SNLZMQ5Hw5JLaTRZp0yILA/FRexe19VdI=" crossorigin="anonymous"></script> <script defer src="https://cdn.jsdelivr.net/npm/imagesloaded@5.0.0/imagesloaded.pkgd.min.js" integrity="sha256-htrLFfZJ6v5udOG+3kNLINIKh2gvoKqwEhHYfTTMICc=" crossorigin="anonymous"></script> <script defer src="/assets/js/masonry.js" type="text/javascript"></script> <script defer src="https://cdn.jsdelivr.net/npm/medium-zoom@1.1.0/dist/medium-zoom.min.js" integrity="sha256-ZgMyDAIYDYGxbcpJcfUnYwNevG/xi9OHKaR/8GK+jWc=" crossorigin="anonymous"></script> <script defer src="/assets/js/zoom.js?85ddb88934d28b74e78031fd54cf8308"></script> <script src="/assets/js/no_defer.js?2781658a0a2b13ed609542042a859126"></script> <script defer src="/assets/js/common.js?06cae41083477f121be8cd9797ad8e2f"></script> <script defer src="/assets/js/copy_code.js?12775fdf7f95e901d7119054556e495f" type="text/javascript"></script> <script defer src="/assets/js/jupyter_new_tab.js?d9f17b6adc2311cbabd747f4538bb15f"></script> <script async src="https://d1bxh8uas1mnw7.cloudfront.net/assets/embed.js"></script> <script async src="https://badge.dimensions.ai/badge.js"></script> <script type="text/javascript">window.MathJax={tex:{tags:"ams"}};</script> <script defer type="text/javascript" id="MathJax-script" src="https://cdn.jsdelivr.net/npm/mathjax@3.2.0/es5/tex-mml-chtml.min.js" integrity="sha256-rjmgmaB99riUNcdlrDtcAiwtLIojSxNyUFdl+Qh+rB4=" crossorigin="anonymous"></script> <script defer src="https://cdnjs.cloudflare.com/polyfill/v3/polyfill.min.js?features=es6" crossorigin="anonymous"></script> <script type="text/javascript">function progressBarSetup(){"max"in document.createElement("progress")?(initializeProgressElement(),$(document).on("scroll",function(){progressBar.attr({value:getCurrentScrollPosition()})}),$(window).on("resize",initializeProgressElement)):(resizeProgressBar(),$(document).on("scroll",resizeProgressBar),$(window).on("resize",resizeProgressBar))}function getCurrentScrollPosition(){return $(window).scrollTop()}function initializeProgressElement(){let e=$("#navbar").outerHeight(!0);$("body").css({"padding-top":e}),$("progress-container").css({"padding-top":e}),progressBar.css({top:e}),progressBar.attr({max:getDistanceToScroll(),value:getCurrentScrollPosition()})}function getDistanceToScroll(){return $(document).height()-$(window).height()}function resizeProgressBar(){progressBar.css({width:getWidthPercentage()+"%"})}function getWidthPercentage(){return getCurrentScrollPosition()/getDistanceToScroll()*100}const progressBar=$("#progress");window.onload=function(){setTimeout(progressBarSetup,50)};</script> <script src="/assets/js/vanilla-back-to-top.min.js?f40d453793ff4f64e238e420181a1d17"></script> <script>addBackToTop();</script> <script type="module" src="/assets/js/search/ninja-keys.min.js?601a2d3465e2a52bec38b600518d5f70"></script> <ninja-keys hidebreadcrumbs noautoloadmdicons placeholder="Type to start searching"></ninja-keys> <script>let searchTheme=determineComputedTheme();const ninjaKeys=document.querySelector("ninja-keys");"dark"===searchTheme?ninjaKeys.classList.add("dark"):ninjaKeys.classList.remove("dark");const openSearchModal=()=>{const e=$("#navbarNav");e.hasClass("show")&&e.collapse("hide"),ninjaKeys.open()};</script> <script>const ninja=document.querySelector("ninja-keys");ninja.data=[{id:"nav-about",title:"About",section:"Navigation",handler:()=>{window.location.href="/"}},{id:"nav-publications",title:"Publications",description:"Ordered by most recent.",section:"Navigation",handler:()=>{window.location.href="/publications/"}},{id:"nav-blog",title:"Blog",description:"",section:"Navigation",handler:()=>{window.location.href="/blog/"}},{id:"nav-cv",title:"CV",description:"",section:"Navigation",handler:()=>{window.location.href="/cv/"}},{id:"nav-teaching",title:"Teaching",description:"Materials for courses you taught. 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\ No newline at end of file
+</code></pre></div></div> </article> <h2>References</h2> <div class="publications"> </div> </div> </div> <footer class="fixed-bottom" role="contentinfo"> <div class="container mt-0"> © Copyright 2024 Mario de Lucio. </div> </footer> <script src="https://cdn.jsdelivr.net/npm/jquery@3.6.0/dist/jquery.min.js" integrity="sha256-/xUj+3OJU5yExlq6GSYGSHk7tPXikynS7ogEvDej/m4=" crossorigin="anonymous"></script> <script src="/assets/js/bootstrap.bundle.min.js"></script> <script src="https://cdn.jsdelivr.net/npm/mdbootstrap@4.20.0/js/mdb.min.js" integrity="sha256-NdbiivsvWt7VYCt6hYNT3h/th9vSTL4EDWeGs5SN3DA=" crossorigin="anonymous"></script> <script defer src="https://cdn.jsdelivr.net/npm/masonry-layout@4.2.2/dist/masonry.pkgd.min.js" integrity="sha256-Nn1q/fx0H7SNLZMQ5Hw5JLaTRZp0yILA/FRexe19VdI=" crossorigin="anonymous"></script> <script defer src="https://cdn.jsdelivr.net/npm/imagesloaded@5.0.0/imagesloaded.pkgd.min.js" integrity="sha256-htrLFfZJ6v5udOG+3kNLINIKh2gvoKqwEhHYfTTMICc=" crossorigin="anonymous"></script> <script defer src="/assets/js/masonry.js" type="text/javascript"></script> <script defer src="https://cdn.jsdelivr.net/npm/medium-zoom@1.1.0/dist/medium-zoom.min.js" integrity="sha256-ZgMyDAIYDYGxbcpJcfUnYwNevG/xi9OHKaR/8GK+jWc=" crossorigin="anonymous"></script> <script defer src="/assets/js/zoom.js?85ddb88934d28b74e78031fd54cf8308"></script> <script src="/assets/js/no_defer.js?2781658a0a2b13ed609542042a859126"></script> <script defer src="/assets/js/common.js?06cae41083477f121be8cd9797ad8e2f"></script> <script defer src="/assets/js/copy_code.js?12775fdf7f95e901d7119054556e495f" type="text/javascript"></script> <script defer src="/assets/js/jupyter_new_tab.js?d9f17b6adc2311cbabd747f4538bb15f"></script> <script async src="https://d1bxh8uas1mnw7.cloudfront.net/assets/embed.js"></script> <script async src="https://badge.dimensions.ai/badge.js"></script> <script type="text/javascript">window.MathJax={tex:{tags:"ams"}};</script> <script defer type="text/javascript" id="MathJax-script" src="https://cdn.jsdelivr.net/npm/mathjax@3.2.0/es5/tex-mml-chtml.min.js" integrity="sha256-rjmgmaB99riUNcdlrDtcAiwtLIojSxNyUFdl+Qh+rB4=" crossorigin="anonymous"></script> <script defer src="https://cdnjs.cloudflare.com/polyfill/v3/polyfill.min.js?features=es6" crossorigin="anonymous"></script> <script type="text/javascript">function progressBarSetup(){"max"in document.createElement("progress")?(initializeProgressElement(),$(document).on("scroll",function(){progressBar.attr({value:getCurrentScrollPosition()})}),$(window).on("resize",initializeProgressElement)):(resizeProgressBar(),$(document).on("scroll",resizeProgressBar),$(window).on("resize",resizeProgressBar))}function getCurrentScrollPosition(){return $(window).scrollTop()}function initializeProgressElement(){let e=$("#navbar").outerHeight(!0);$("body").css({"padding-top":e}),$("progress-container").css({"padding-top":e}),progressBar.css({top:e}),progressBar.attr({max:getDistanceToScroll(),value:getCurrentScrollPosition()})}function getDistanceToScroll(){return $(document).height()-$(window).height()}function resizeProgressBar(){progressBar.css({width:getWidthPercentage()+"%"})}function getWidthPercentage(){return getCurrentScrollPosition()/getDistanceToScroll()*100}const progressBar=$("#progress");window.onload=function(){setTimeout(progressBarSetup,50)};</script> <script src="/assets/js/vanilla-back-to-top.min.js?f40d453793ff4f64e238e420181a1d17"></script> <script>addBackToTop();</script> <script type="module" src="/assets/js/search/ninja-keys.min.js?601a2d3465e2a52bec38b600518d5f70"></script> <ninja-keys hidebreadcrumbs noautoloadmdicons placeholder="Type to start searching"></ninja-keys> <script>let searchTheme=determineComputedTheme();const ninjaKeys=document.querySelector("ninja-keys");"dark"===searchTheme?ninjaKeys.classList.add("dark"):ninjaKeys.classList.remove("dark");const openSearchModal=()=>{const e=$("#navbarNav");e.hasClass("show")&&e.collapse("hide"),ninjaKeys.open()};</script> <script>const ninja=document.querySelector("ninja-keys");ninja.data=[{id:"nav-about",title:"About",section:"Navigation",handler:()=>{window.location.href="/"}},{id:"nav-publications",title:"Publications",description:"Ordered by most recent.",section:"Navigation",handler:()=>{window.location.href="/publications/"}},{id:"nav-blog",title:"Blog",description:"",section:"Navigation",handler:()=>{window.location.href="/blog/"}},{id:"nav-cv",title:"CV",description:"",section:"Navigation",handler:()=>{window.location.href="/cv/"}},{id:"nav-teaching",title:"Teaching",description:"Materials for courses you taught. 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diff --git a/projects/8_project/index.html b/projects/8_project/index.html
index 9b55f3ed..5d69d4e8 100644
--- a/projects/8_project/index.html
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-</code></pre></div></div> </article> <div id="giscus_thread" style="max-width: 930px; margin: 0 auto;"> <script>let giscusTheme=determineComputedTheme(),giscusAttributes={src:"https://giscus.app/client.js","data-repo":"mdeluci/mdeluci.github.io","data-repo-id":"","data-category":"Comments","data-category-id":"","data-mapping":"title","data-strict":"1","data-reactions-enabled":"1","data-emit-metadata":"0","data-input-position":"bottom","data-theme":giscusTheme,"data-lang":"en",crossorigin:"anonymous",async:""},giscusScript=document.createElement("script");Object.entries(giscusAttributes).forEach(([t,e])=>giscusScript.setAttribute(t,e)),document.getElementById("giscus_thread").appendChild(giscusScript);</script> <noscript>Please enable JavaScript to view the <a href="http://giscus.app/?ref_noscript" rel="external nofollow noopener" target="_blank">comments powered by giscus.</a> </noscript> </div> </div> </div> <footer class="fixed-bottom" role="contentinfo"> <div class="container 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diff --git a/projects/index.html b/projects/index.html
index acb8c794..bc2c74b2 100644
--- a/projects/index.html
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@@ -1 +1 @@
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<div class="card h-100 hoverable"> <figure> <picture> <source class="responsive-img-srcset" srcset="/assets/img/12-480.webp 480w,/assets/img/12-800.webp 800w,/assets/img/12-1400.webp 1400w," sizes="250px" type="image/webp"></source> <img src="/assets/img/12.jpg" class="card-img-top" width="100%" height="auto" alt="project thumbnail" loading="eager" onerror="this.onerror=null; $('.responsive-img-srcset').remove();"> </picture> </figure> <div class="card-body"> <h2 class="card-title">project 1</h2> <p class="card-text">with background image</p> <div class="row ml-1 mr-1 p-0"> </div> </div> </div> </a> </div> <div class="col"> <a href="/projects/7_project/"> <div class="card h-100 hoverable"> <figure> <picture> <source class="responsive-img-srcset" srcset="/assets/img/4-480.webp 480w,/assets/img/4-800.webp 800w,/assets/img/4-1400.webp 1400w," sizes="250px" type="image/webp"></source> <img src="/assets/img/4.jpg" class="card-img-top" width="100%" height="auto" alt="project thumbnail" loading="eager" onerror="this.onerror=null; $('.responsive-img-srcset').remove();"> </picture> </figure> <div class="card-body"> <h2 class="card-title">project 7</h2> <p class="card-text">with background image</p> <div class="row ml-1 mr-1 p-0"> </div> </div> </div> </a> </div> <div class="col"> <a href="/projects/2_project/"> <div class="card h-100 hoverable"> <figure> <picture> <source class="responsive-img-srcset" srcset="/assets/img/3-480.webp 480w,/assets/img/3-800.webp 800w,/assets/img/3-1400.webp 1400w," sizes="250px" type="image/webp"></source> <img src="/assets/img/3.jpg" class="card-img-top" width="100%" height="auto" alt="project thumbnail" loading="eager" onerror="this.onerror=null; $('.responsive-img-srcset').remove();"> </picture> </figure> <div class="card-body"> <h2 class="card-title">project 2</h2> <p class="card-text">a project with a background image and giscus comments</p> <div class="row ml-1 mr-1 p-0"> </div> </div> </div> </a> </div> <div class="col"> <a href="/projects/8_project/"> <div class="card h-100 hoverable"> <figure> <picture> <source class="responsive-img-srcset" srcset="/assets/img/9-480.webp 480w,/assets/img/9-800.webp 800w,/assets/img/9-1400.webp 1400w," sizes="250px" type="image/webp"></source> <img src="/assets/img/9.jpg" class="card-img-top" width="100%" height="auto" alt="project thumbnail" loading="eager" onerror="this.onerror=null; $('.responsive-img-srcset').remove();"> </picture> </figure> <div class="card-body"> <h2 class="card-title">project 8</h2> <p class="card-text">an other project with a background image and giscus comments</p> <div class="row ml-1 mr-1 p-0"> </div> </div> </div> </a> </div> <div class="col"> <a href="https://unsplash.com" rel="external nofollow noopener" target="_blank"> <div class="card h-100 hoverable"> <figure> <picture> <source class="responsive-img-srcset" srcset="/assets/img/7-480.webp 480w,/assets/img/7-800.webp 800w,/assets/img/7-1400.webp 1400w," sizes="250px" type="image/webp"></source> <img src="/assets/img/7.jpg" class="card-img-top" width="100%" height="auto" alt="project thumbnail" loading="eager" onerror="this.onerror=null; $('.responsive-img-srcset').remove();"> </picture> </figure> <div class="card-body"> <h2 class="card-title">project 3 with very long name</h2> <p class="card-text">a project that redirects to another website</p> <div class="row ml-1 mr-1 p-0"> </div> </div> </div> </a> </div> </div> <a id="fun" href=".#fun"> <h2 class="category">fun</h2> </a> <div class="row row-cols-1 row-cols-md-3"> <div class="col"> <a href="/projects/4_project/"> <div class="card h-100 hoverable"> <div class="card-body"> <h2 class="card-title">project 4</h2> <p class="card-text">another without an image</p> <div class="row ml-1 mr-1 p-0"> </div> </div> </div> </a> </div> <div class="col"> <a href="/projects/5_project/"> <div class="card h-100 hoverable"> <figure> <picture> <source class="responsive-img-srcset" srcset="/assets/img/1-480.webp 480w,/assets/img/1-800.webp 800w,/assets/img/1-1400.webp 1400w," sizes="250px" type="image/webp"></source> <img src="/assets/img/1.jpg" class="card-img-top" width="100%" height="auto" alt="project thumbnail" loading="eager" onerror="this.onerror=null; $('.responsive-img-srcset').remove();"> </picture> </figure> <div class="card-body"> <h2 class="card-title">project 5</h2> <p class="card-text">a project with a background image</p> <div class="row ml-1 mr-1 p-0"> </div> </div> </div> </a> </div> <div class="col"> <a href="/projects/6_project/"> <div class="card h-100 hoverable"> <div class="card-body"> <h2 class="card-title">project 6</h2> <p class="card-text">a project with no image</p> <div class="row ml-1 mr-1 p-0"> </div> </div> </div> </a> </div> <div class="col"> <a href="/projects/9_project/"> <div class="card h-100 hoverable"> <figure> <picture> <source class="responsive-img-srcset" srcset="/assets/img/6-480.webp 480w,/assets/img/6-800.webp 800w,/assets/img/6-1400.webp 1400w," sizes="250px" type="image/webp"></source> <img src="/assets/img/6.jpg" class="card-img-top" width="100%" height="auto" alt="project thumbnail" loading="eager" onerror="this.onerror=null; $('.responsive-img-srcset').remove();"> </picture> </figure> <div class="card-body"> <h2 class="card-title">project 9</h2> <p class="card-text">another project with an image 🎉</p> <div class="row ml-1 mr-1 p-0"> </div> </div> </div> </a> </div> </div> </div> </article> </div> </div> <footer class="fixed-bottom" role="contentinfo"> <div class="container mt-0"> © Copyright 2024 Mario de Lucio. </div> </footer> <script src="https://cdn.jsdelivr.net/npm/jquery@3.6.0/dist/jquery.min.js" integrity="sha256-/xUj+3OJU5yExlq6GSYGSHk7tPXikynS7ogEvDej/m4=" crossorigin="anonymous"></script> <script src="/assets/js/bootstrap.bundle.min.js"></script> <script src="https://cdn.jsdelivr.net/npm/mdbootstrap@4.20.0/js/mdb.min.js" integrity="sha256-NdbiivsvWt7VYCt6hYNT3h/th9vSTL4EDWeGs5SN3DA=" 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index 1729e7a7..bf98a699 100644
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   <span class="na">year</span> <span class="p">=</span> <span class="s">{2018}</span><span class="p">,</span>
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-<span class="p">}</span></code></pre></figure> </div> </div> </div> </li></ol> </div> </article> </div> </div> <footer class="fixed-bottom" role="contentinfo"> <div class="container mt-0"> © Copyright 2024 Mario de Lucio. </div> </footer> <script src="https://cdn.jsdelivr.net/npm/jquery@3.6.0/dist/jquery.min.js" integrity="sha256-/xUj+3OJU5yExlq6GSYGSHk7tPXikynS7ogEvDej/m4=" crossorigin="anonymous"></script> <script src="/assets/js/bootstrap.bundle.min.js"></script> <script src="https://cdn.jsdelivr.net/npm/mdbootstrap@4.20.0/js/mdb.min.js" integrity="sha256-NdbiivsvWt7VYCt6hYNT3h/th9vSTL4EDWeGs5SN3DA=" crossorigin="anonymous"></script> <script defer src="https://cdn.jsdelivr.net/npm/masonry-layout@4.2.2/dist/masonry.pkgd.min.js" integrity="sha256-Nn1q/fx0H7SNLZMQ5Hw5JLaTRZp0yILA/FRexe19VdI=" crossorigin="anonymous"></script> <script defer src="https://cdn.jsdelivr.net/npm/imagesloaded@5.0.0/imagesloaded.pkgd.min.js" integrity="sha256-htrLFfZJ6v5udOG+3kNLINIKh2gvoKqwEhHYfTTMICc=" crossorigin="anonymous"></script> <script defer src="/assets/js/masonry.js" type="text/javascript"></script> <script defer src="https://cdn.jsdelivr.net/npm/medium-zoom@1.1.0/dist/medium-zoom.min.js" integrity="sha256-ZgMyDAIYDYGxbcpJcfUnYwNevG/xi9OHKaR/8GK+jWc=" crossorigin="anonymous"></script> <script defer src="/assets/js/zoom.js?85ddb88934d28b74e78031fd54cf8308"></script> <script src="/assets/js/no_defer.js?2781658a0a2b13ed609542042a859126"></script> <script defer src="/assets/js/common.js?06cae41083477f121be8cd9797ad8e2f"></script> <script defer src="/assets/js/copy_code.js?12775fdf7f95e901d7119054556e495f" type="text/javascript"></script> <script defer src="/assets/js/jupyter_new_tab.js?d9f17b6adc2311cbabd747f4538bb15f"></script> <script async src="https://d1bxh8uas1mnw7.cloudfront.net/assets/embed.js"></script> <script async src="https://badge.dimensions.ai/badge.js"></script> <script type="text/javascript">window.MathJax={tex:{tags:"ams"}};</script> <script defer type="text/javascript" id="MathJax-script" src="https://cdn.jsdelivr.net/npm/mathjax@3.2.0/es5/tex-mml-chtml.min.js" integrity="sha256-rjmgmaB99riUNcdlrDtcAiwtLIojSxNyUFdl+Qh+rB4=" crossorigin="anonymous"></script> <script defer src="https://cdnjs.cloudflare.com/polyfill/v3/polyfill.min.js?features=es6" crossorigin="anonymous"></script> <script type="text/javascript">function progressBarSetup(){"max"in document.createElement("progress")?(initializeProgressElement(),$(document).on("scroll",function(){progressBar.attr({value:getCurrentScrollPosition()})}),$(window).on("resize",initializeProgressElement)):(resizeProgressBar(),$(document).on("scroll",resizeProgressBar),$(window).on("resize",resizeProgressBar))}function getCurrentScrollPosition(){return $(window).scrollTop()}function initializeProgressElement(){let e=$("#navbar").outerHeight(!0);$("body").css({"padding-top":e}),$("progress-container").css({"padding-top":e}),progressBar.css({top:e}),progressBar.attr({max:getDistanceToScroll(),value:getCurrentScrollPosition()})}function getDistanceToScroll(){return $(document).height()-$(window).height()}function resizeProgressBar(){progressBar.css({width:getWidthPercentage()+"%"})}function getWidthPercentage(){return getCurrentScrollPosition()/getDistanceToScroll()*100}const progressBar=$("#progress");window.onload=function(){setTimeout(progressBarSetup,50)};</script> <script src="/assets/js/vanilla-back-to-top.min.js?f40d453793ff4f64e238e420181a1d17"></script> <script>addBackToTop();</script> <script type="module" src="/assets/js/search/ninja-keys.min.js?601a2d3465e2a52bec38b600518d5f70"></script> <ninja-keys hidebreadcrumbs noautoloadmdicons placeholder="Type to start searching"></ninja-keys> <script>let searchTheme=determineComputedTheme();const ninjaKeys=document.querySelector("ninja-keys");"dark"===searchTheme?ninjaKeys.classList.add("dark"):ninjaKeys.classList.remove("dark");const openSearchModal=()=>{const e=$("#navbarNav");e.hasClass("show")&&e.collapse("hide"),ninjaKeys.open()};</script> <script>const ninja=document.querySelector("ninja-keys");ninja.data=[{id:"nav-about",title:"About",section:"Navigation",handler:()=>{window.location.href="/"}},{id:"nav-publications",title:"Publications",description:"Ordered by most recent.",section:"Navigation",handler:()=>{window.location.href="/publications/"}},{id:"nav-blog",title:"Blog",description:"",section:"Navigation",handler:()=>{window.location.href="/blog/"}},{id:"nav-cv",title:"CV",description:"",section:"Navigation",handler:()=>{window.location.href="/cv/"}},{id:"nav-teaching",title:"Teaching",description:"Materials for courses you taught. 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diff --git a/repositories/index.html b/repositories/index.html
index 69ca25b1..c68cb9bb 100644
--- a/repositories/index.html
+++ b/repositories/index.html
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diff --git a/videos/index.html b/videos/index.html
index e0e83729..013afa55 100644
--- a/videos/index.html
+++ b/videos/index.html
@@ -1 +1 @@
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+<!DOCTYPE html> <html lang="en"> <head> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> <meta charset="utf-8"> <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"> <meta http-equiv="X-UA-Compatible" content="IE=edge"> <title> Videos | Mario de Lucio's website </title> <meta name="author" content="Mario de Lucio"> <meta name="description" content="Animations and videos"> <meta name="keywords" content="Computational Mechanics, Multiphysics Simulation, Biomechanics, Transport phenomena"> <link rel="stylesheet" href="/assets/css/bootstrap.min.css?a4b3f509e79c54a512b890d73235ef04"> <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/mdbootstrap@4.20.0/css/mdb.min.css" integrity="sha256-jpjYvU3G3N6nrrBwXJoVEYI/0zw8htfFnhT9ljN3JJw=" crossorigin="anonymous"> <link defer rel="stylesheet" href="/assets/css/academicons.min.css?f0b7046b84e425c55f3463ac249818f5"> <link defer rel="stylesheet" type="text/css" href="https://fonts.googleapis.com/css?family=Roboto:300,400,500,700|Roboto+Slab:100,300,400,500,700|Material+Icons&amp;display=swap"> <link defer rel="stylesheet" href="/assets/css/jekyll-pygments-themes-github.css?591dab5a4e56573bf4ef7fd332894c99" media="" id="highlight_theme_light"> <link rel="shortcut icon" href="/assets/img/webicon.png?b6c2349ccb452e30289be5faff27b580"> <link rel="stylesheet" href="/assets/css/main.css?d41d8cd98f00b204e9800998ecf8427e"> <link rel="canonical" href="https://mdeluci.github.io/videos/"> <script src="/assets/js/theme.js?9a0c749ec5240d9cda97bc72359a72c0"></script> <link defer rel="stylesheet" href="/assets/css/jekyll-pygments-themes-native.css?5847e5ed4a4568527aa6cfab446049ca" media="none" id="highlight_theme_dark"> <script>initTheme();</script> </head> <body class="fixed-top-nav "> <header> <nav id="navbar" class="navbar navbar-light navbar-expand-sm fixed-top" role="navigation"> <div class="container"> <a class="navbar-brand title font-weight-lighter" href="/"> Mario de Lucio's website </a> <button class="navbar-toggler collapsed ml-auto" type="button" data-toggle="collapse" data-target="#navbarNav" aria-controls="navbarNav" aria-expanded="false" aria-label="Toggle navigation"> <span class="sr-only">Toggle navigation</span> <span class="icon-bar top-bar"></span> <span class="icon-bar middle-bar"></span> <span class="icon-bar bottom-bar"></span> </button> <div class="collapse navbar-collapse text-right" id="navbarNav"> <ul class="navbar-nav ml-auto flex-nowrap"> <li class="nav-item "> <a class="nav-link" href="/">About </a> </li> <li class="nav-item "> <a class="nav-link" href="/publications/">Publications </a> </li> <li class="nav-item "> <a class="nav-link" href="/blog/">Blog </a> </li> <li class="nav-item "> <a class="nav-link" href="/cv/">CV </a> </li> <li class="nav-item "> <a class="nav-link" href="/teaching/">Teaching </a> </li> <li class="nav-item active"> <a class="nav-link" href="/videos/">Videos <span class="sr-only">(current)</span> </a> </li> <li class="nav-item"> <button id="search-toggle" title="Search" onclick="openSearchModal()"> <span class="nav-link">ctrl k <i class="ti ti-search"></i></span> </button> </li> <li class="toggle-container"> <button id="light-toggle" title="Change theme"> <i class="ti ti-sun-moon" id="light-toggle-system"></i> <i class="ti ti-moon-filled" id="light-toggle-dark"></i> <i class="ti ti-sun-filled" id="light-toggle-light"></i> </button> </li> </ul> </div> </div> </nav> <progress id="progress" value="0"> <div class="progress-container"> <span class="progress-bar"></span> </div> </progress> </header> <div class="container mt-5" role="main"> <div class="post"> <header class="post-header"> <h1 class="post-title">Videos</h1> <p class="post-description">Animations and videos</p> </header> <article> <h4 id="fluid-structure-interaction-simulation-of-an-abdominal-aortic-aneurysm">Fluid-structure interaction simulation of an abdominal aortic aneurysm</h4> <p>Simulations performed during my master’s studies at Universidade da Coruna</p> <div class="video-container"> <iframe width="560" height="315" src="https://www.youtube.com/embed/Q7G-yB3iWwQ" title="YouTube video player" frameborder="0" allow="accelerometer; 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