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There are three fundamental physical processes that gives rise to the morphology of a surface: deposition, surface diffusion and desorption. The characteristics of the interfaces generated by the combination of deposition and surface…
The transport of sediment by a fluid along the surface is responsible for dune formation, dust entrainment and for a rich diversity of patterns on the bottom of oceans, rivers, and planetary surfaces. Most previous models of sediment…
The adsorption of particles diffusing in a half-space bounded by the substrate and irreversibly sticking to the substrate upon contacts is investigated. We show that when absorbing particles are planar disks diffusing in the…
Diffusion in an evolving environment is studied by continuos-time Monte Carlo simulations. Diffusion is modelled by continuos-time random walkers on a lattice, in a dynamic environment provided by bubbles between two one-dimensional…
The study of fluctuation-induced transport is concerned with the directed motion of particles on a substrate when subjected to a fluctuating external field. Work over the last two decades provides now precise clues on how the average…
We consider a model system of persistent random walkers that can jam, pass through each other or jump apart (recoil) on contact. In a continuum limit, where particle motion between stochastic changes in direction becomes deterministic, we…
Analyzing complex fluid flow problems that involve multiple coupled domains, each with their respective set of governing equations, is not a trivial undertaking. Even more complicated is the elaborate and tedious task of specifying the…
Second initial boundary problem in narrow domains of width $\epsilon\ll 1$ for linear second order differential equations with nonlinear boundary conditions is considered in this paper. Using probabilistic methods we show that the solution…
Stochastic boundary conditions for interactions with a particle reservoir are discussed in many-particle systems. We introduce the boundary conditions with the injection rate and the momentum distribution of particles coming from a particle…
We introduce a notion of viscosity solutions for a nonlinear degenerate diffusion equation with a drift potential. We show that our notion of solutions coincide with the weak solutions defined via integration by parts. As an application of…
A diffusion's induced transport is defined for a linear model of a Fokker-Plank equation under periodic boundary conditions in one-dimensional geometry. The flow is generated by a diffusion and a periodic deriving force induced by a…
Non-local equations of motion contain an infinite number of derivatives and commonly appear in a number of string theory models. We review how these equations can be rewritten in the form of a diffusion-like equation with non-linear…
The transport of individual entities through interconnected structures is a process of practical relevance both in biology and technology. Examples are given by diffusive dynamics of molecules in porous structures. In soft environments,…
Deterministic diffusion in temporally oscillating convection is studied for particles with finite mass. The particles are assumed to obey a simple dissipative dynamical system and the particle diffusion is induced by the strange attractor.…
We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the…
Albeit the past intensive research, the governing equation of anomalous diffusion which is observed for the transport of particles underground is still an open problem. In this paper, as a governing equation, the advection-diffusion…
A solution is developed for a convection-diffusion equation describing chemical transport with sorption, decay, and production. The problem is formulated in a finite domain where the appropriate conservation law yields Robin conditions at…
The results of Direct Numerical Simulations of the oscillatory flow over a cohesionless bed of spherical particles, mimicking sediment grains, are described. The flow around the sediment particles is explicitly computed by using the…
The derivation of suitable analytical models is an important step for the design and analysis of molecular communication systems. However, many existing models have limited applicability in practical scenarios due to various simplifications…
We study the surface transport properties of stationary localized configurations of relativistic fluids to the first two non-trivial orders in a derivative expansion. By demanding that these finite lumps of relativistic fluid are described…