Related papers: Diffusion of particles moving with constant speed
The diffusion in two dimensions of non-interacting active particles that follow an arbitrary motility pattern is considered for analysis. Accordingly, the transport equation is generalized to take into account an arbitrary distribution of…
A stationary distribution function that describes the entire processes of propagation of relativistic particles, including the transition between the ballistic and diffusion regimes, is obtained. The spacial component of the constructed…
Fractional Brownian motion is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically fractional Brownian motion confined to a finite…
We study the dynamics of a self-propelled particle advected by a steady laminar flow. The persistent motion of the self-propelled particle is described by an active Ornstein-Uhlenbeck process. We focus on the diffusivity properties of the…
We formulate the the problem of persistent diffusion in three dimensions from the perspective of the Frenet--Serret equations. In contrast to one and two dimensional systems, in three dimensions persistent diffusion is, in general, a third…
We study a Brownian particle diffusing under a time-modulated stochastic resetting mechanism to a fixed position. The rate of resetting r(t) is a function of the time t since the last reset event. We derive a sufficient condition on r(t)…
We study spectral properties of the Fokker-Planck operator that represents particles moving via a combination of diffusion and advection in a time-independent random velocity field, presenting in detail work outlined elsewhere [J. T.…
Front propagation described by Huygens' principle is a fundamental mechanism of spatial spreading of a property or an effect, occurring in optics, acoustics, ecology and combustion. If the local front speed varies randomly due to…
The photon density operator function is used to calculate light beam propagation through turbulent atmosphere. A kinetic equation for the photon distribution function is derived and solved using the method of characteristics. Optical wave…
We develop a straightforward analytical framework for the propagation of spatial light modes through a turbulent atmosphere. Built upon the split-step approach with the mode-based optical field representation, it directly assesses how…
We suggest a governing equation which describes the process of polymer chain translocation through a narrow pore and reconciles the seemingly contradictory features of such dynamics: (i) a Gaussian probability distribution of the…
The empirical velocity of a reaction-diffusion front, propagating into an unstable state, fluctuates because of the shot noises of the reactions and diffusion. Under certain conditions these fluctuations can be described as a diffusion…
We prove finite speed of propagation for stochastic porous media equations perturbed by linear multiplicative space-time rough signals. Explicit and optimal estimates for the speed of propagation are given. The result applies to any…
The present paper discusses the diffusion approximation of the linear Boltzmann equation in cases where the collision frequency is not uniformly large in the spatial domain. Our results apply for instance to the case of radiative transfer…
We investigate propagation of few-photon pulses in waveguides coupled to a two-level system by means of the method of distribution functions in coordinate-momentum space that provides a detailed description of photon systems. We find that…
We study here the escape time for the fastest diffusing particle from the boundary of an interval with point-sink killing sources. Killing represents a degradation that leads to the probabilistic removal of the moving Brownian particles. We…
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…
In the first paper of this series, I investigated whether a wavefunction model of a heavy particle and a collection of light particles might generate "Brownian-Motion-Like" trajectories of the heavy particle. I concluded that it was…
The diffusion model is used to calculate the time-averaged flow of particles in stochastic media and the propagation of waves averaged over ensembles of disordered static configurations. For classical waves exciting static disordered…
Scattering through natural porous formations (by far the most ubiquitous example of disordered media) represents a formidable tool to identify effective flow and transport properties. In particular, we are interested here in the scattering…