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The nonequilibrium phase transition in a system of diffusing, coagulating particles in the presence of a steady input and evaporation of particles is studied. The system undergoes a transition from a phase in which the average number of…
In this paper, we study the non-linear diffusion equation associated with a particle system where the common drift depends on the rate of absorption of particles at a boundary. We provide an interpretation as a structural credit risk model…
We study the dynamics of inertial particles in turbulence using datasets obtained from both direct numerical simulations and laboratory experiments of turbulent swirling flows. By analyzing time series of particle velocity increments at…
We propose the deterministic dynamics of a free particle in a physical vacuum, which is considered as a discrete (quantum) medium. The motion of the particle is studied taking into account its interactions with the medium. It is assumed…
Dynamics simulations of constrained particles can greatly aid in understanding the temporal and spatial evolution of biological processes such as lateral transport along membranes and self-assembly of viruses. Most theoretical efforts in…
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…
The movement of motor particles consisting of one or several molecular motors bound to a cargo particle is studied theoretically. The particles move on patterns of immobilized filaments. Several patterns are described for which the motor…
We perform molecular dynamic simulations of liquid nanoparticles deposited on a disordered substrate. The motion of the nanoparticle is characterised by a 'stick and roll' diffusive process. Long simulation times ($\simeq \mu s$), analysis…
In this paper we introduce and analyze a class of diffusion type equations related to certain non-Markovian stochastic processes. We start from the forward drift equation which is made non-local in time by the introduction of a suitable…
We consider Brownian particles immersed in the fluid which flow is turbulent. We study the limit where the particles' inertia is weak and their velocity relaxes fast to the velocity of the flow. The trajectories of the particles in this…
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…
Diffusion of self-propelled particles in the presence of randomly distributed obstacles in three dimensions is studied using molecular dynamics simulations. It is found that depending on the magnitude of the propelling force and the…
We present an exact expression for the mean exit time through the cap of a confining sphere for particles alternating phases of surface and of bulk diffusion. The present approach is based on an integral equation which can be solved…
The lateral diffusion coefficient of a Brownian particle on a two-dimensional random surface is studied in the quenched limit for which the surface configuration is time-independent. We start with the stochastic equation of motion for a…
The horizontal dynamics of a bouncing ball interacting with an irregular surface is investigated and is found to demonstrate behavior analogous to a random walk. Its stochastic character is substantiated by the calculation of a permutation…
The dynamics of viscous thin-film particle-laden flows down inclined surfaces are commonly modeled with one of two approaches: a diffusive flux model or a suspension balance model. The diffusive flux model assumes that the particles migrate…
We prove a limit theorem for an integral functional of a Markov process. The Markovian dynamics is characterized by a linear Boltzmann equation modeling a one-dimensional test particle of mass $\lambda^{-1}\gg 1$ in an external periodic…
Molecular dynamics (MD) simulation based on Langevin equation has been widely used in the study of structural, thermal properties of matters in difference phases. Normally, the atomic dynamics are described by classical equations of motion…
Diffusion of small particles is omnipresent in a plentiful number of processes occurring in Nature. As such, it is widely studied and exerted in almost all branches of sciences. It constitutes such a broad and often rather complex subject…
Diverse processes -- e.g., environmental pollution, groundwater remediation, oil recovery, filtration, and drug delivery -- involve the transport of colloidal particles in porous media. Using confocal microscopy, we directly visualize this…