Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles
Abstract
Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization [Phys. Rev. Lett. 112, 218304 (2014)]. Here we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, mean-field description starting from the microscopic dynamics. The effective free energy emerging from this approach has the form of a conventional Ginzburg-Landau function. On the coarsest scale, our results thus agree with the mapping of active phase separation onto that of passive fluids with attractive interactions through a global effective free energy (mobility-induced phase transition). Particular attention is paid to the square-gradient term necessary for the dynamics. We finally discuss results from numerical simulations corroborating the analytical results.
Keywords
Cite
@article{arxiv.1503.08412,
title = {Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles},
author = {Thomas Speck and Andreas M. Menzel and Julian Bialké and Hartmut Löwen},
journal= {arXiv preprint arXiv:1503.08412},
year = {2015}
}