Related papers: Comparison between Smoluchowski and Boltzmann appr…
We study the kinetic regime of the Bose-condensation of scalar particles with weak $\lambda \phi^4$ self-interaction. The Boltzmann equation is solved numerically. We consider two kinetic stages. At the first stage the condensate is still…
We study a system of self-propelled particles which interact with their neighbors via alignment and repulsion. The particle velocities result from self-propulsion and repulsion by close neighbors. The direction of self-propulsion is…
We consider a bound system of charged particles moving in an external electromagnetic field, including leading relativistic corrections. The difference from the point particle with a magnetic moment comes from the presence of…
A recent kinetic approach for Vicsek-like models of active particles is reviewed. The theory is based on an exact Chapman-Kolmogorov equation in phase space. It can handle discrete time dynamics and "exotic" multi-particle interactions. A…
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…
Point polarizable molecules at fixed spatial positions have solvable electrostatic properties in classical approximation, the most familiar being the Clausius-Mossotti (CM) formula. This paper generalizes the model and imagines various…
We show from experiments and simulations on vibration-activated granular matter that self-propelled polar rods in an elastic medium on a substrate turn and move towards each other. We account for this effective attraction through a…
We present a generic framework for describing interacting, spinning, active polar particles, aimed at modelling dense cell aggregates, where cells are treated as polar, rotating objects that interact mechanically with one another and their…
In this note, we study the phase transitions arising in a modified Smoluchowski equation on the sphere with dipolar potential. This equation models the competition between alignment and diffusion, and the modification consists in taking the…
Polar solitons, i.e., solitonic waves accompanying asymmetry of geometry or phase, have garnered attention in polar systems, such as ferroelectric or magnetoelectric materials, where they play a critical role in topological transitions and…
We investigate numerically by a conservative difference scheme in complex arithmetic the head-on and takeover collision dynamics of the solitary waves as solutions of linearly Coupled Nonlinear Schr\"odinger Equations for various initial…
We study the role of electron-electron interactions for spin polarized transport using the Boltzmann equation and derive a set of coupled transport equations. For spin polarized transport the electron-electron interactions are important,…
A linear Boltzmann equation with nonautonomous collision operator is rigorously derived in the Boltzmann-Grad limit for the deterministic dynamics of a Rayleigh gas where a tagged particle is undergoing hard-sphere collisions with…
Systems composed of strongly interacting self-propelled particles can form a spontaneously flowing polar active fluid. The study of the connection between the microscopic dynamics of a single such particle and the macroscopic dynamics of…
Using experiments with anisotropic vibrated rods and quasi-2D numerical simulations, we show that shape plays an important role in the collective dynamics of self-propelled (SP) particles. We demonstrate that SP rods exhibit local ordering,…
For the system with inhomogeneous distribution of macroscopic parameters we obtain thermodynamic relation which depends on the spatial point (coordinate). In our approach, to obtain such a relation we use the basic ideas of the method of…
We study a collection of polar self-propelled particles confined to a long two-dimensional channel. We write the coupled hydrodynamic equations of motion for density and polarisation order parameter. At two confined boundaries, density is…
A quantum linear Boltzmann equation is proposed, constructed in terms of the operator-valued dynamic structure factor of the macroscopic system the test particle is interacting with. Due to this operator structure it is a non-Abelian linear…
We study the spontaneous motion, binary collisions, and collective dynamics of "polar disks", i.e. purpose-built particles which, when vibrated between two horizontal plates, move coherently along a direction strongly correlated to their…
Despite their fundamentally non-equilibrium nature, the individual and collective behavior of active systems with polar propulsion and isotropic interactions (polar-isotropic active systems) are remarkably well captured by equilibrium…