A Finite Volume Method for Continuum Limit Equations of Nonlocally Interacting Active Chiral Particles
arXiv:2008.08493 · doi:10.1016/j.jcp.2021.110275
Abstract
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.
References in corpus (34)
- Novel type of phase transition in a system of self-driven particles
- Chimera States for Coupled Oscillators
- Swimming in circles: Motion of bacteria near solid boundaries
- Coexistence of Coherence and Incoherence in Nonlocally Coupled Phase Oscillators
- Boltzmann and hydrodynamic description for self-propelled particles
- Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis
- A well-posedness theory in measures for some kinetic models of collective motion
- Transition from turbulent to coherent flows in confined three-dimensional active fluids
- Dynamical density functional theory for interacting Brownian particles: stochastic or deterministic?
- The Rotating Vicsek Model: Pattern Formation and Enhanced Flocking in Chiral Active Matter
- A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure
- The derivation of Swarming models: Mean-Field Limit and Wasserstein distances
- GEMPIC: Geometric ElectroMagnetic Particle-In-Cell Methods
- Kuramoto model of synchronization: Equilibrium and nonequilibrium aspects
- Simple and faithful nonlinear field equations for aligning self-propelled rods
- Collective Motion of Self-Propelled Particles with Memory
- Boltzmann-Ginzburg-Landau approach for continuous descriptions of generic Vicsek-like models
- Activity induced synchronization: From Mutual Flocking to Chiral Self-Sorting
- Long-time behaviour and phase transitions for the McKean--Vlasov equation on the torus
- A particle-field representation unifies paradigms in active matter
- Sounds and hydrodynamics of polar active fluids
- A discontinuous Galerkin method for nonlinear parabolic equations and gradient flow problems with interaction potentials
- Invasion-wave induced first-order phase transition in systems of active particles
- Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics
- Dynamics in a kinetic model of oriented particles with phase transition
- Phase Transitions in a kinetic flocking model of Cucker-Smale type
- Contractivity of the Wasserstein metric for the kinetic Kuramoto equation
- Understanding dense active nematics from microscopic models
- Traveling Bands, Clouds, and Vortices of Chiral Active Matter
- Self-propelled chimeras
- Numerical simulation of nonlinear continuity equations by evolving diffeomorphisms
- Superdiffusion, large-scale synchronization and topological defects
- Numerical treatment of the Boltzmann equation for self-propelled particle systems
- Structure preserving schemes for the continuum Kuramoto model: phase transitions