Séminaire

Vendredi 25 Septembre 2026 à 11h00.

Kinetic Theory for Active Brownian Particles

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The Active Brownian Particle (ABP) model has become a prototype of self-propelled particles. ABPs move persistently at a constant speed V along a direction that changes slowly by rotational diffusion, characterized by a coefficient Dr, and interact by excluded volume with diameter $\sigma$. When two ABPs collide, they slide along each other until they can continue their free motion. For persistence lengths much larger than the particle diameter, the directors do not change, but the collision can be modeled as producing a net displacement on the particles compared to their free motion in the absence of the encounter. With these elements, a Boltzmann--Enskog-like kinetic theory is built, where collisions, instead of producing instantaneous changes in velocity, change the particle positions.

For the the self-diffusion process of a tagged particle in an equilibrium ABP bath, on intermediate timescales, where many collisions have taken place but the director of the tagged particle has not yet changed, an effective stochastic dynamics emerges, characterized by an effective reduced streaming velocity Veff and anisotropic diffusion, with coefficients explicitly depending on density. On time scales larger than 1/Dr, the tagged particle shows an effective diffusive motion with a coefficient D=Veff^2/(2 Dr). A linear stability analysis of the homogeneous state predicts a density instability with full agreement with numerical simulations of the motility induced phase separation (MIPS). Applying the Chapman--Enskog method to the kinetic equation, we derive the hydrodynamic equations for the density and polarization fields, which reproduce the main phenomenology of MIPS. Also, it is possible to obtain the Active Model B+ equation for the density field, with explicit expressions for the non-variational transport coefficients. Finally, some ideas are presented on how the theory could be extended to high density regimes.

[1] R. Soto, M. Pinto, and R. Brito, Kinetic Theory of Motility Induced Phase Separation for Active Brownian Particles, Physical Review Letters 132, 208301 (2024)
[2] R. Soto, Self-diffusive dynamics of active Brownian particles at moderate densities, Physics of Fluids 37, 033309 (2025)
[3] J.P. Carrillo-Mora, M. Pires Monteiro, V.I. Marconi, M.L. Cordero, R. Brito, and R. Soto, Preventing clustering of active particles in microchannels, Communications Physics 8, 374 2025
[4] M. Pinto-Goldberg and R. Soto, Hydrodynamic equations for active Brownian particles in the high-persistence regime, Physical Review E 112, 065413, (2025)
[5] M. Pinto-Goldberg and R. Soto, Microscopic derivation of a field equation for active Brownian particles, arXiv:2608.11184

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