This is a simple phase separation model, where particles with different colors repel each other, while particles with the same color attract each other. Read more...
In this phase separation model, the particles have two fundamental properties: color and interaction strength. The particles interact with each other according to the following potential energy function:
$$V(r) = \begin{cases} A (1 - \frac{r}{R})^2 & r \leq R \\ 0 & r > R \end{cases}$$
Where $V(r)$ represents the interaction potential energy between two particles, $r$ is the distance between them, $A$ is the interaction strength, and $R$ is the interaction range.
The model also incorporates a simple equation of motion for the particles, given by:
$$\frac{d\mathbf{r}_i}{dt} = -\frac{1}{\zeta} \sum_{j \neq i} \nabla V_{ij}$$
Here, $\mathbf{r}_i$ is the position of particle $i$, $\zeta$ is the drag coefficient, and $\nabla V_{ij}$ is the gradient of the potential energy with respect to the positions of particles $i$ and $j$.
Based on these equations, the simulation evolves the particle system in time and demonstrates the emergence of phase separation behavior.
这是一个简单的相分离模型，其中不同颜色的粒子互相排斥，而相同颜色的粒子互相吸引。阅读更多...
在这个相分离模型中，粒子有两个基本属性：颜色和相互作用强度。粒子之间根据以下势能函数相互作用：
$$V(r) = \begin{cases} A (1 - \frac{r}{R})^2 & r \leq R \\ 0 & r > R \end{cases}$$
其中 $V(r)$ 代表两个粒子之间的相互作用势能，$r$ 是它们之间的距离，$A$ 是相互作用强度，$R$ 是相互作用范围。
该模型还引入了粒子的简单运动方程，表示为：
$$\frac{d\mathbf{r}_i}{dt} = -\frac{1}{\zeta} \sum_{j \neq i} \nabla V_{ij}$$
这里，$\mathbf{r}_i$ 是粒子 $i$ 的位置，$\zeta$ 是阻力系数，$\nabla V_{ij}$ 是关于粒子 $i$
和 $j$ 的位置的势能梯度。
基于这些方程，模拟在时间内演化粒子系统并展示相分离行为的出现。