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We study systems of Brownian particles on the real line, which interact by splitting the local times of collisions among themselves in an asymmetric manner. We prove the strong existence and uniqueness of such processes and identify them…
We develop a theory of Brownian motion of a massive particle, including the effects of inertia (Kramers' problem), in spaces with curvature and torsion. This is done by invoking the recently discovered generalized equivalence principle,…
It is well known that understanding the transport properties of liquid crystals (LCs) is crucial to optimise their performance in a number of technological applications. In this work, we analyse the effect of shape anisotropy on the…
We study the Brownian motion of ellipsoidal particles lying on an agitated granular bath composed of magnetic particles. We quantify the mobility of different floating ellipsoidal particles using the mean square displacement and the mean…
We investigate the construction of diffusions consisting of infinitely numerous Brownian particles moving in $\mathbb{R}^d$ and interacting via logarithmic functions (two-dimensional Coulomb potentials). These potentials are very strong and…
A simple model of an active colloid consisting of dumbbell-shaped particles that cyclically change their length without propelling themselves is proposed and analyzed. At nanoscales, it represents an idealization for bacterial cytoplasm or…
A micro-hydrodynamics model based on elastic collisions of light point solvent particles with a heavy solute particle is investigated in the setting where the light particles have velocity distribution corresponding to a background flow.…
We propose a new approach to describe the effective microscopic dynamics of (power-law) nonlinear Fokker-Planck equations. Our formalism is based on a nonextensive generalization of the Wiener process. This allow us to obtain, in addition…
A dynamical treatment of Markovian diffusion is presented and several applications discussed. The stochastic interpretation of quantum mechanics is considered within this framework. A model for Brownian movement which includes second order…
Although the dynamics of colloids in the vicinity of a solid interface has been widely characterized in the past, experimental studies of Brownian diffusion close to an air-water interface are rare and limited to particle-interface gap…
Two deterministic models for Brownian motion are investigated by means of numerical simulations and kinetic theory arguments. The first model consists of a heavy hard disk immersed in a rarefied gas of smaller and lighter hard disks acting…
In this paper we study macroscopic density equations in which the diffusion coefficient depends on a weighted spatial average of the density itself. We show that large differences (not present in the local density-dependence case) appear…
Based on Brownian dynamics simulations we study the collective behavior of a twodimensional system of repulsively interacting colloidal particles, where each particle is propelled by a repulsive feedback force with time delay $\tau$.…
Brownian motion (BM) is pivotal in natural science for the stochastic motion of microscopic droplets. In this study, we investigate BM driven by thermal composition noise at sub-micro scales, where inter-molecular diffusion and surface…
Diffusion of colloidal particles in a complex environment such as polymer networks or biological cells is a topic of high complexity with significant biological and medical relevance. In such situations, the interaction between the…
We consider the collective motion of finite-sized, overdamped Brownian particles (e.g., motor proteins) in a periodic potential. Simulations of our model have revealed a number of novel cooperative transport phenomena, including (i) the…
The effects of Brownian motion on particle interactions with heterogeneous collectors are evaluated by adding stochastic Brownian displacements to the particle trajectories and comparing those trajectories to those where Brownian motion is…
Classical diffusion in a random medium involves an exponential functional of Brownian motion. This functional also appears in the study of Brownian diffusion on a Riemann surface of constant negative curvature. We analyse in detail this…
We have considered the underdamped motion of a Brownian particle in the presence of a correlated external random force. The force is modeled by an Ornstein-Uhlenbeck process. We investigate the fluctuations of the work done by the external…
We derive diffusive macroscopic equations for the particle and energy density of a system whose time evolution is described by a kinetic equation for the one particle position and velocity function f(r,v,t) that consists of a part that…