Reaction-diffusion equations
갤러리
Reaction-diffusion equations
Allen-Cahn equation: describes phase separation of two media.
Rock-Paper-Scissors-Lizard-Spock equation: describes 5 competing chemicals
공식
- \partial_t u = \Delta u + u - u^3
Solution of the 2D Allen-Cahn equation
저작권 CC BY-NC-SA-3.0
공식
- \begin{align} \partial_t u_1 &= \Delta u_1 + u_1(1 - \rho - au_2 - au_4) \\ \partial_t u_2 &= \Delta u_2 + u_2(1 - \rho - au_3 - au_5) \\ \partial_t u_3 &= \Delta u_3 + u_3(1 - \rho - au_4 - au_1) \\ \partial_t u_4 &= \Delta u_4 + u_4(1 - \rho - au_5 - au_2) \\ \partial_t u_5 &= \Delta u_5 + u_5(1 - \rho - au_1 - au_3) \\ \rho &= \sum_{i=1}^5 u_i, a = 0.75 \end{align}
Rock-Paper-Scissors-Lizard-Spock reaction-diffusion equation
Solution of a reaction-diffusion equation with five competing chemicals.
저작권 CC BY-NC-SA-3.0
공식
- \begin{align} \partial_t u_1 &= \Delta u_1 + u_1(1 - \rho - au_2 - b(t)u_4) \\ \partial_t u_2 &= \Delta u_2 + u_2(1 - \rho - au_3 - b(t)u_5) \\ \partial_t u_3 &= \Delta u_3 + u_3(1 - \rho - au_4 - b(t)u_1) \\ \partial_t u_4 &= \Delta u_4 + u_4(1 - \rho - au_5 - b(t)u_2) \\ \partial_t u_5 &= \Delta u_5 + u_5(1 - \rho - au_1 - b(t)u_3) \\ \rho &= \sum_{i=1}^5 u_i, a = 0.75 \end{align}
Asymmetric Rock-Paper-Scissors-Lizard-Spock reaction-diffusion equation
저작권 CC BY-NC-SA-3.0
