The term “classical Brownian motion” describes the random movement of microscopic, relatively big particles suspended in a liquid or gas.
1905: Albert Einstein produced his quantitative theory of Brownian motion, showing how to compute the probability (P) of a particle’s moving a certain distance (x) in any given direction, during a certain time interval (t) in a medium whose coefficient of diffusion (D).
D = R × T/(6π × Na × n × r) where:
- T: temperature. Na: Avogadro number n: viscosity of liquid.
- r: radius of the particle. R: gas constant. So, the displacement ∆x is equal to D multiplied by the square of the time interval between 2 consecutive positions, by a white noise, and by a probability density function following the normal law.
Solution:
∆x=noise*sqrt(T/N)*D*normrnd(0,1);
Using elastic collision between 2 sphers
The applications of "random theory" are:
- In modeling fluctuations in prices in financial markets.
- A simpler Model for stochastic phenomenal than random walk hypothesis.
- Modeling noise in images.
- Generating fractals.
It is subjected to no other interaction than shocks with the molecules of the surrounding environment, where the previous change in the value of a variable is unrelated to future or past changes.
in this work:
