Related papers: Numerical treatment of the Boltzmann equation for …
Considering a gas of self-propelled particles with binary interactions, we derive the hydrodynamic equations governing the density and velocity fields from the microscopic dynamics, in the framework of the associated Boltzmann equation.…
The transport of charged particles or photons in a scattering medium can be modelled with a Boltzmann equation. The mathematical treatment for scattering in such scenarios is often simplified if evaluated in a frame where the scattering…
We study analytically the emergence of spontaneous collective motion within large bidimensional groups of self-propelled particles with noisy local interactions, a schematic model for assemblies of biological organisms. As a central result,…
We introduce a novel mesoscopic computational model based on a multiphase-multicomponent lattice Boltzmann method for the simulation of self-phoretic particles in the presence of liquid-liquid interfaces. Our model features fully resolved…
We study the spatially homogeneous phases of polar active particles in the low density limit, and specifically the transition from the isotropic phase to collective polar motion. We show that the fundamental quantity of interest for the…
The Boltzmann equation describes the evolution of the phase-space probability distribution of classical particles under binary collisions. Approximations to it underlie the basis for several scholarly fields, including aerodynamics and…
Using methods of kinetic theory and liquid state theory we propose a description of the non-equilibrium behavior of molecular fluids which takes into account their microscopic structure and thermodynamic properties. The present work…
The Boltzmann equation has been a driving force behind significant mathematical research over the years. Its challenging theoretical complexity, combined with a wide variety of current scientific and technological problems that require…
We study the non-equilibrium statistical mechanics of a system of freely moving particles, in which binary encounters lead either to an elastic collision or to the disappearance of the pair. Such a system of {\em ballistic annihilation}…
Generic models of propelled particle systems posit that the emergence of polar order is driven by the competition between local alignment and noise. Although this notion has been confirmed employing the Boltzmann equation, the range of…
We study a set of models of self-propelled particles that achieve collective motion through similar alignment-based dynamics, considering versions with and without repulsive interactions that do not affect the heading directions. We explore…
We develop a theoretical and computational approach to deal with systems that involve a disparate range of spatio-temporal scales, such as those comprised of colloidal particles or polymers moving in a fluidic molecular environment. Our…
We study the bosonic Boltzmann-Nordheim kinetic equation, which describes the kinetic regime of weakly interacting bosons with s-wave scattering only. We consider a spatially homogeneous fluid with an isotropic momentum distribution. The…
We present a Lattice-Boltzmann method for simulating self-propelling (active) colloidal particles in two-dimensions. Active particles with symmetric and asymmetric force distribution on its surface are considered. The velocity field…
We describe a technique for solving the combined collisionless Boltzmann and Poisson equations in a discretised, or lattice, phase space. The time and the positions and velocities of `particles' take on integer values, and the forces are…
We present a novel method to solve the spatially homogeneous and isotropic relativistic Boltzmann equation. We employ a basis set of orthogonal polynomials dynamically adapted to allow for emergence of chemical non-equilibrium. Two time…
We study numerically and analytically a model of self-propelled polar disks on a substrate in two dimensions. The particles interact via isotropic repulsive forces and are subject to rotational noise, but there is no aligning interaction.…
We consider a coarse-grained description of a system of self-propelled particles given by hydrodynamic equations for the density and polarization fields. We find that the ordered moving or flocking state of the system is unstable to spatial…
This paper presents a systematic and accurate treatment of the evolution of cosmological perturbations in self-interacting dark matter models, for particles which decoupled from the primordial plasma while relativistic. We provide a…
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…