论文标题
非局部相互作用的活动性手性颗粒的连续限量方程的有限体积方法
A Finite Volume Method for Continuum Limit Equations of Nonlocally Interacting Active Chiral Particles
论文作者
论文摘要
活动粒子系统的连续描述是一种有效的仪器，用于分析有限尺寸粒子动力学以大量粒子的极限。但是，通常情况下，这种方程式似乎是非线性间差方程，并且纯粹的分析处理变得非常有限。我们提出了一个有限体积方法（FVM）的一般框架，以求解局限于二维的非局部相互作用的手性活动粒子系统的连续限制的部分微分方程（PDE）。我们证明了该方法在空间均质问题上的性能，在该问题上，可以使用与分析结果的比较，以及在一般的空间不均匀方程式上进行的，其中动力学理论预测了模式形成。我们在数值上研究了在空间均匀和不均匀的方案中特定问题的相变，并报告存在不同的一阶和二阶转变的存在。
The continuum description of active particle systems is an efficient instrument to analyze a finite size particle dynamics in the limit of a large number of particles. However, it is often the case that such equations appear as nonlinear integro-differential equations and purely analytical treatment becomes quite limited. We propose a general framework of finite volume methods (FVMs) to numerically solve partial differential equations (PDEs) of the continuum limit of nonlocally interacting chiral active particle systems confined to two dimensions. We demonstrate the performance of the method on spatially homogeneous problems, where the comparison to analytical results is available, and on general spatially inhomogeneous equations, where pattern formation is predicted by kinetic theory. We numerically investigate phase transitions of particular problems in both spatially homogeneous and inhomogeneous regimes and report the existence of different first and second order transitions.
