Related papers: Diffusion between evolving interfaces
Diffusion of a two component fluid is studied in the framework of differential equations, but where these equations are systematically derived from a well-defined microscopic model. The model has a finite carrying capacity imposed upon it…
We consider a diffusion process on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ an energetic variational approach with both surface divergence and transport theorems to derive…
This paper reviews (and expands) some recent results on the modeling of aggregation-diffusion phenomena at various scales, focusing on the emergence of collective dynamics as a result of the competition between attractive and repulsive…
This paper considers particle propagation in a cylindrical molecular communication channel, e.g. a simplified model of a blood vessel. Emitted particles are influenced by diffusion, flow, and a vertical force induced e.g. by gravity or…
We study the transport properties of particles draining from a silo using imaging and direct particle tracking. The particle displacements show a universal transition from super-diffusion to normal diffusion, as a function of the distance…
Diffusion is a fundamental phenomenon that occurs ubiquitously in nature and remains the subject of continuous research interest. Understanding diffusion is a key to understanding leaving systems. In this Chapter, I discuss diffusion of…
Dispersion curves to a oscillatory reaction-diffusion system with the self-consistent flow have obtained by means of numerical calculations. The flow modulates the shape of dispersion curves and characteristics of traveling waves. The point…
Viscous fingering patterns can form at the interface between two immiscible fluids confined in the gap between a pair of flat plates; whenever the fluid with lower viscosity displaces the one of higher viscosity the interface is unstable.…
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is…
This article is an invitation. It is, first, an invitation to consider as a subject worthy of attention the wide range of situations where small discrete elements, either bubbles, droplets or solid particles, are embedded in turbulent…
We consider a basic one-dimensional model of diffusion which allows to obtain a diversity of diffusive regimes whose speed depends on the moments of the per-site trapping time. This model is closely related to the continuous time random…
Periodic forcing of flow in compressible porous media is an important driver for solute dispersion and mixing in geological and engineered porous media subject for example to tides, pumping and recharge cycles, or fluid injection and…
The critical dimension necessary for a flame to propagate in suspensions of fuel particles in oxidizer is studied analytically and numerically. Two types of models are considered: First, a continuum model, wherein the individual particulate…
This article presents a multi-physics methodology for the numerical simulation of physical systems that involve the non-linear interaction of multi-phase reactive fluids and elastoplastic solids, inducing high strain-rates and high…
We derive and study a theoretical description for single file diffusion, i.e., diffusion in a one dimensional lattice of particles with hard core interaction. It is well known that for this system a tagged particle has anomalous diffusion…
A partial differential equation governing the global evolution of the joint probability distribution of an arbitrary number of local flow observations, drawn randomly from a control volume, is derived and applied to examples involving…
The possibility of different interpretations of the stochastic term (or calculi) in the overdamped Langevin equation for the motion of a particle in an inhomogeneous medium is often referred to as the "Ito--Stratonovich dilemma," although…
The transport of an infinitely thin, hard rod in a random, dense array of point obstacles is investigated by molecular dynamics simulations. Our model mimics the sterically hindered dynamics in dense needle liquids. The center-of-mass…
Explicit analytical expressions for the drag and diffusion coefficients of a spherical particle attached to the interface between two immiscible fluids are constructed for the case of a small viscosity ratio between the fluid phases. The…
Direct sampling of multi-dimensional systems with quantum Monte Carlo methods allows exact account of many-body effects or particle correlations. The most straightforward approach to solve the Schr\"odinger equation, Diffusion Monte Carlo,…