• Corpus ID: 236957205

On the hydrodynamics of active matter models on a lattice

@inproceedings{Erignoux2021OnTH,
  title={On the hydrodynamics of active matter models on a lattice},
  author={Cl{\'e}ment Erignoux},
  year={2021}
}
Active matter has been widely studied in recent years because of its rich phenomenology, whose mathematical understanding is still partial. We present some results, based on [8, 17] linking microscopic lattice gases to their macroscopic limit, and explore how the mathematical state of the art allows to derive from various types of microscopic dynamics their hydrodynamic limit. We present some of the crucial aspects of this theory when applied to weakly asymmetric active models. We comment on… 

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References

SHOWING 1-10 OF 27 REFERENCES
Exact Hydrodynamic Description of Active Lattice Gases.
TLDR
Coupled partial differential equations describing the dynamics of the local density and polarization fields are derived and it is shown how they quantitatively predict the emerging properties of the macroscopic lattice gases.
Hydrodynamic limit for a facilitated exclusion process
Collective dynamics can be observed among many animal species, and have given rise in the last decades to an active and interdisciplinary eld of study. Such behaviors are often modeled by active
A continuum model for alignment of self-propelled particles with anisotropy and density-dependent parameters
We consider the macroscopic model derived by Degond and Motsch from a time-continuous version of the Vicsek model, describing the interaction orientation in a large number of self-propelled
Fluctuation-Induced Phase Separation in Metric and Topological Models of Collective Motion.
TLDR
It is shown that fluctuations induce a density-dependent shift of the onset of order, which in turn changes the nature of the transition into a phase-separation scenario.
Dynamics in a Kinetic Model of Oriented Particles with Phase Transition
TLDR
A rigorous prove of convergence of the solution to a steady-state as time goes to infinity is given, and it is shown that in the supercritical case, the only initial conditions leading to the uniform distribution in large time are those with vanishing momentum.
DIFFUSION IN A CONTINUUM MODEL OF SELF-PROPELLED PARTICLES WITH ALIGNMENT INTERACTION
In this paper, we provide the O(e) corrections to the hydrodynamic model derived by Degond and Motsch from a kinetic version of the model by Vicsek and co-authors describing flocking biological
Flocking with discrete symmetry: The two-dimensional active Ising model.
  • A. Solon, J. Tailleur
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2015
TLDR
A continuum theory is built which reproduces qualitatively the behavior of the microscopic model, and predicts analytically the shapes of the phase diagrams in the vicinity of the critical points, the binodal and spinodal densities at coexistence, and the speeds and shapes ofThe phase-separated profiles.
Phase transition and diffusion among socially interacting self-propelled agents
We consider a hydrodynamic model of swarming behavior derived from the kinetic description of a particle system combining a noisy Cucker-Smale consensus force and self-propulsion. In the large
Generalized thermodynamics of phase equilibria in scalar active matter.
TLDR
This work gives a general prescription for the mean densities of coexisting phases in flux-free steady states that amounts, at a hydrodynamics scale, to extremizing an effective free energy.
Collective motion of self-propelled particles interacting without cohesion.
TLDR
The onset of collective motion in Vicsek-style self-propelled particle models in two and three space dimensions is studied in detail and shown to be discontinuous (first-order-like), and the properties of the ordered, collectively moving phase are investigated.
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