Related papers: Universal framework for the long-time position dis…
Random walkers characterized by random positions and random velocities lead to normal diffusion. A random walk was originally proposed by Einstein to model Brownian motion and to demonstrate the existence of atoms and molecules. Such a…
We show that dispersion in propulsion strength qualitatively alters collective behavior of active multi-particle systems interacting via short-range attractive potential, giving rise to novel ordered phases that combine spatial and…
The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's…
We consider a tracer particle performing a random walk on a two-dimensional lattice in the presence of immobile hard obstacles. Starting from equilibrium, a constant force pulling on the particle is switched on, driving the system to a new…
A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability…
We study the single-file dynamics of three classes of active particles: run-and-tumble particles, active Brownian particles and active Ornstein-Uhlenbeck particles. At high activity values, the particles, interacting via purely repulsive…
A rapidly increasing number of systems is identified in which the stochastic motion of tracer particles follows the Brownian law $\langle\mathbf{r}^2(t) \rangle\simeq Dt$ yet the distribution of particle displacements is strongly…
The stochastic dynamics of an active particle undergoing a constant speed and additionally driven by an overall fluctuating torque is investigated. The random torque forces are expressed by a stochastic differential equation for the angular…
We study the long time behavior of a Brownian particle moving in an anomalously diffusing field, the evolution of which depends on the particle position. We prove that the process describing the asymptotic behaviour of the Brownian particle…
In this work we present a general derivation of the non-Fickian behavior for the self-diffusion of identically interacting particle systems with excluded mutual passage. We show that the conditional probability distribution of finding a…
We prove the existence of solutions to a non-linear, non-local, degenerate equation which was previously derived as the formal hydrodynamic limit of an active Brownian particle system, where the particles are endowed with a position and an…
Stochastic differential equations in Hilbert space as random nonlinear modified Schroedinger equations have achieved great attention in recent years; of particular interest is the long time behavior of their solutions. In this note we…
The diffusion of chiral active Brownian particles in three-dimensional space is studied analytically, by consideration of the corresponding Fokker-Planck equation for the probability density of finding a particle at position…
Consider a massive (inert) particle impinged from above by N Brownian particles that are instantaneously reflected upon collision with the inert particle. The velocity of the inert particle increases due to the influence of an external…
We propose a model for the motion of a single active particle in a heterogeneous environment where the heterogeneity may arise due to the crowding, conformational fluctuations and/or slow rearrangement of the surroundings. Describing the…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
We study the effect of randomly distributed diffusivities and speeds in two models for active particle dynamics with active and passive fluctuations. We demonstrate how non-Gaussian displacement distributions emerge in these models in the…
We study the dynamics of a single inertial run-and-tumble particle on a straight line. The motion of this particle is characterized by two intrinsic time-scales, namely, an inertial and an active time-scale. We show that interplay of these…
In this work, we obtain third order linear differential equation for stationary distributions of run-and-tumble particles in two-dimensions in a harmonic trap. The equation represents the condition $j = 0$ where $j$ is a flux and is…
Many active particles are embedded in environments that exhibit viscoelastic properties. An important class of such media lacks a single characteristic relaxation timescale when subjected to a time-dependent stress. Rather, the stress…