Abstract
The dynamics of dry active matter have implications for a diverse collection of biological phenomena spanning a range of length and time scales, such as animal flocking, cell tissue dynamics, and swarming of inserts and bacteria. Uniting these systems are a common set of symmetries and conservation laws, defining dry active fluids as a class of physical system. Many interesting behaviours have been observed at high densities, which remain difficult to simulate due to the computational demand. Here, we show how two-dimensional dry active fluids in a dense regime can be studied using a simple modification of the lattice Boltzmann method. We apply our method on a model that exhibits motility-induced phase separation, and an active model with contact inhibition of locomotion, which has relevance to collective cell migration. For the latter, we uncover multiple novel phase transitions: two first-order and one potentially critical. We further support our simulation results with an analytical treatment of the hydrodynamic equations obtained via a Chapman–Enskog coarse-graining procedure.
Highlights
Introduction ce pte an us criSymmetry serves a foundational role in all areas of physics today
By identifying the underlying symmetries of a classical many-body system, one can derive the hydrodynamic equations of motion (EOM) that govern the macroscopic dynamics of that system, and, crucially, any other system that respects the same symmetries and conservation laws [1]
Analysis of a hydrodynamic theory can elucidate the universal behaviour exhibited by all generic systems respecting the prescribed set of symmetries; any particular many-body system defined by microscopic rules that respect the same set of symmetries can be used to study the associated universal behaviour in the hydrodynamic limit
Summary
Our system involves the evolution of a distribution function fi (t, r), i ∈ {0, 1, ..., 6}, defined on a two-dimensional triangular lattice (D2Q7 in standard LBM notation [38]). The average velocity of the particles will align with the density gradient, and as a result there is a net flow towards regions of higher density. This is consistent with the observation that particles will congregate in areas of lower speeds or, equivalently, higher densities; we expect there to be a flow towards those regions. Ce separation, with the density in their liquid and gas phases given by the values on the blue and orange curves for that σ, respectively These results are consistent with previous studies in MIPS [13]. We have demonstrated that our lattice Boltzmann method is adaptable, and could be used to study MIPS in more detail
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