Related papers: A model for slowing particles in random media
We consider the fully-coupled McKean-Vlasov equation with multi-time-scale potentials, and all the coefficients depend on the distributions of both the slow component and the fast motion. By studying the smoothness of the solution of the…
We consider an ensemble of mass collisionless particles, which interact mutually either by an attraction of Newton's law of gravitation or by an electrostatic repulsion of Coulomb's law, under a background downward gravity in a…
We consider one-dimensional random walks in random environment which are transient to the right. Our main interest is in the study of the sub-ballistic regime, where at time $n$ the particle is typically at a distance of order $O(n^\kappa)$…
We present a simple stochastic quadrant model for calculating the transport and de- position of heavy particles in a fully developed turbulent boundary layer based on the statistics of wall-normal fluid velocity fluctuations obtained from a…
We study finite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which…
The motion of a freely rotating prolate spheroid in a simple shear flow of a dilute polymeric solution is examined in the limit of large particle aspect ratio, $\kappa$. A regular perturbation expansion in the polymer concentration, $c$, a…
We measure acceleration statistics of neutrally buoyant spherical particles with diameter 0.4 < d/eta <27 in intense turbulence (400< R_lambda <815). High speed cameras image polystyrene tracer particles in a flow between counter-rotating…
The kinetics of the annihilation process, $A+A\to 0$, with ballistic particle motion is investigated when the distribution of particle velocities is {\it discrete}. This discreteness is the source of many intriguing phenomena. In the mean…
The transport of an infinitely thin, hard rod in a random, dense array of point obstacles is investigated by molecular dynamics simulations. Our model mimics the sterically hindered dynamics in dense needle liquids. The center-of-mass…
We review the derivation of the Kac master equation model for random collisions of particles, its relationship to the Poisson process, and existing algorithms for simulating values from the marginal distribution of velocity for a single…
We study the problem of minimal resistance for a body moving with constant velocity in a rarefied medium of chaotically moving point particles, in Euclidean space R^d. The particles distribution over velocities is radially symmetric. Under…
The effect of crowding on the run-and-tumble dynamics of swimmers such as bacteria is studied using a discrete lattice model of mutually excluding particles that move with constant velocity along a direction that is randomized at a rate…
We investigate two models for traffic flow with modified acceleration ('slow-to-start') rules. Even in the simplest case $v_{max}=1$ these rules break the 'particle-hole` symmetry of the model. We determine the fundamental diagram…
(abbreviated) In this note we consider, in a weak-field limit, a relativistic linear motion of two particles with opposite signs of masses having a small difference between their absolute values $m_{1,2}=\pm (\mu\pm \Delta \mu) $, $\mu >…
We study statistical properties of a one dimensional infinite system of coalescing particles. Each particle moves with constant velocity $\pm v$ towards its closest neighbor and merges with it upon collision. We propose a mean-field theory…
Consider $N$ particles performing random walks on the $\epsilon$-grid $(\epsilon Z)^d$, $\epsilon>0$ with branching and density-dependent selection: When one of the particles branches, a particle is removed from the most populated site. The…
In this paper, we developed a mathematical model for the sedimentation process of small particles in a lid-driven cavity flow with an obstacle to model the transport of microplastic particles in rivers. A stationary incompressible…
The asymptotic analysis of kinetic models describing the behavior of particles interacting through alignment is performed. We will analyze the asymptotic regime corresponding to large alignment frequency where the alignment effects are…
We study the settling of rigid oblates in quiescent fluid using interface-resolved Direct Numerical Simulations. In particular, an immersed boundary method is used to account for the dispersed solid phase together with lubrication…
The cohesive collective motion (flocking, swarming) of autonomous agents is ubiquitously observed and exploited in both natural and man-made settings, thus, minimal models for its description are essential. In a model with continuous space…