Math Physics ML

Cahn-Hilliard phase separation

The Cahn-Hilliard model describes the phase separation process in a binary mixture, such as oil and water. The system's evolution in terms of concentrations obeys the following partial differential equation: $$ \frac{\partial c}{\partial t} = D \nabla^2 (c^3-c-\gamma\nabla^2 c) $$ where $c\in[-1,1]$ is the concentration of fluid, -1 means highest concentration of species $A$, 1 means highest concentration of species $B$.
Parameters: $D$ is a diffusion coefficient and $\gamma$ characterizes the sharpness of transition regions. Periodic boundary conditions are applied to the simulation domain.



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$D$ = 1.5

$\gamma$ = 0.7

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The behavior of this model shows similarity to the Ising model where neighboring cells influence each other on a 2 state grid space, however, here, the value on each point of the grid has values in $[-1,1]$.