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.
翻译:对活性粒子系统的连续描述是一种有效的工具,用以分析在大量粒子的极限范围内的有限大小粒子动态,然而,这种方程式往往被看成是非线性内分泌异方程和纯分析性处理方法,因而相当有限。我们提出了一个有限体积方法总框架,用数字方式解决非局部互动的手性活性粒子系统在两个层面的连续性限制中的部分差异方程(PDEs)。我们展示了空间同质问题方法的性能,可与分析结果进行比较,以及一般空间异同质方程方法的性能,其模式形成是由动因理论预测的。我们用数字方式调查空间同质和不相容性系统中特定问题的阶段转变,并报告存在不同的第一和第二顺序转变。