A Finite Volume Method for Continuum Limit Equations of Nonlocally Interacting Active Chiral Particles

08/19/2020
by   Nikita Kruk, et al.
0

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.

READ FULL TEXT

page 20

page 21

page 22

page 24

page 27

research
09/14/2023

A Convergent Finite Volume Method for a Kinetic Model for Interacting Species

We propose an upwind finite volume method for a system of two kinetic eq...
research
02/09/2022

A degenerating convection-diffusion system modelling froth flotation with drainage

Froth flotation is a common unit operation used in mineral processing. I...
research
05/29/2023

Combining Particle and Tensor-network Methods for Partial Differential Equations via Sketching

In this paper, we propose a general framework for solving high-dimension...
research
10/14/2021

Learning Mean-Field Equations from Particle Data Using WSINDy

We develop a weak-form sparse identification method for interacting part...
research
06/01/2020

Interacting particle solutions of Fokker-Planck equations through gradient-log-density estimation

Fokker-Planck equations are extensively employed in various scientific f...
research
11/08/2019

Coupled Systems of Differential-Algebraic and Kinetic Equations with Application to the Mathematical Modelling of Muscle Tissue

We consider a coupled system composed of a differential-algebraic equati...
research
03/21/2020

Parameter robust preconditioning by congruence for multiple-network poroelasticity

The mechanical behaviour of a poroelastic medium permeated by multiple i...

Please sign up or login with your details

Forgot password? Click here to reset