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Welcome to the Investigations wiki! Here's a list of investigations, organised by are

Here are some suggested investigations, organised by course

Dynamics

• Buckling beams outside of the nonlinear regime. See [http://link.springer.com/article/10.1007/BF02429861]

Waves and Oscillations

• Nonlinear oscillations of a pendulum
• Ripples from a central source with gravity and capillary wave dispersion (minimal group velocity gives caustic)
• Kelvin wedge
• Rainbows
• Swimming pool caustics
• Multiple scattering from Foldy--Lax
• Whispering gallery modes (as at the Northern line platform at Kings Cross)

Electromagnetism

Visualising field lines

Theories of Quantum Matter

• Solution of the Bethe equations for the Lieb--Liniger model
• Numerical renormalization group calculations in the Kondo problem
• Vortex lattices from imaginary time GPE (see Ryan Barnett work)

Advanced Quantum Physics

• Self consistent field approach for multi-electron atoms
• The Talbot effect for dispersive waves on periodic domains
• Methods for time dependent dynamics. Split step and refinements. Finite element methods and stability.

TP2

• Aharonov--Bohm scattering, and scattering of water waves on a vortex
• Kicked rotor
• Transfer matrix for 1D scattering and applications to band structure, disorder, etc.
• Hofstadter problem
• High orders of perturbation theory
• Violations of adiabaticity. Particle production

Mathematics

• Composing Möbius transformations (see Indra's Pearls)