PHASE SEPARATION IN SYSTEMS OF INTERACTING ACTIVE BROWNIAN PARTICLES

Bruna M, Burger M, Esposito A, Schulz SM (2022)

Publication Type: Journal article

Publication year: 2022

Journal

SIAM Journal on Applied Mathematics Society for Industrial and Applied Mathematics

Book Volume: 82

Pages Range: 1635-1660

Journal Issue: 4

DOI: 10.1137/21M1452524

Abstract

The aim of this paper is to discuss the mathematical modeling of Brownian active particle systems, a recently popular paradigmatic system for self-propelled particles. We present four microscopic models with different types of repulsive interactions between particles and their associated macroscopic models, which are formally obtained using different coarse-graining methods. The macroscopic limits are integro-differential equations for the density in phase space (positions and orientations) of the particles and may include nonlinearities in both the diffusive and advective components. In contrast to passive particles, systems of active particles can undergo phase separation without any attractive interactions, a mechanism known as motility-induced phase separation (MIPS). We explore the onset of such a transition for each model in the parameter space of occupied volume fraction and Péclet number via a linear stability analysis and numerical simulations at both the microscopic and macroscopic levels. We establish that one of the models, namely, the mean-field model which assumes long-range repulsive interactions, cannot explain the emergence of MIPS. In contrast, MIPS is observed for the remaining three models that assume short-range interactions that localize the interaction terms in space.

Authors with CRIS profile

Martin Burger Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

Involved external institutions

University of Cambridge GB United Kingdom (GB) University of Oxford GB United Kingdom (GB) University of Wisconsin - Madison US United States (USA) (US)

How to cite

APA:

Bruna, M., Burger, M., Esposito, A., & Schulz, S.M. (2022). PHASE SEPARATION IN SYSTEMS OF INTERACTING ACTIVE BROWNIAN PARTICLES. SIAM Journal on Applied Mathematics, 82(4), 1635-1660. https://dx.doi.org/10.1137/21M1452524

MLA:

Bruna, Maria, et al. "PHASE SEPARATION IN SYSTEMS OF INTERACTING ACTIVE BROWNIAN PARTICLES." SIAM Journal on Applied Mathematics 82.4 (2022): 1635-1660.

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