Related papers: A Paradox of State-Dependent Diffusion and How to …
We show that observing the trajectories of confined particles in a thermal equilibrium state yields an estimate on the free-space diffusion coefficient. For generic trapping potentials and interactions between particles, the estimate comes…
Instabilities and pattern formation is the rule in nonequilibrium systems. Selection of a persistent lengthscale, or coarsening (increase of the lengthscale with time) are the two major alternatives. When and under which conditions one…
We consider a drift-diffusion model, with an unknown function depending on the spatial variable and an additional structural variable, the amount of ingested lipid. The diffusion coefficient depends on this additional variable. The drift…
We present results on tagged particle diffusion in a meso-scale lattice model for sheared amorphous material in athermal quasi-static conditions. We find a short time diffusive regime and a long time diffusive regime whose diffusion…
We consider a run an tumble particle with two velocity states $\pm v_0$, in an inhomogeneous force field $f(x)$ in one dimension. We obtain exact formulae for its velocity $V_L$ and diffusion constant $D_L$ for arbitrary periodic $f(x)$ of…
We study an interacting particle system whose dynamics depends on an interacting random environment. As the number of particles grows large, the transition rate of the particles slows down (perhaps because they share a common resource of…
This article deals with the issues of global-in-time existence and asymptotic analysis of a fluid-particle interaction model in the so-called bubbling regime. The mixture occupies the physical space $\Omega \subset \mathbb{R}^3$ which may…
Local diffusion coefficients in disordered systems such as spin glass systems and living cells are highly heterogeneous and may change over time. Such a time-dependent and spatially heterogeneous environment results in irreproducibility of…
We discuss a reaction-diffusion model in one dimension subjected to an external driving force. Each lattice site may be occupied by at most one particle. The particles hop with asymmetric rates (the sum of which is one) to the right or left…
Collective diffusion coefficient in a two-dimensional lattice gas on a nonhomogeneous substrate is investigated using variational approach. Particles reside at adsorption sites with different well depths potentials and jump randomly between…
The diffusion of particles trapped in long narrow channels occurs predominantly in one dimension. Here, molecular dynamics simulation is used to study the inertial dynamics of two-dimensional hard disks, confined to long, narrow,…
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…
We review some exact results for the motion of a tagged particle in simple models. Then, we study the density dependence of the self diffusion coefficient, $D_N(\rho)$, in lattice systems with simple symmetric exclusion in which the…
A non--linear diffusion equation is derived by taking into account hopping rates depending on the occupation of next neighbouring sites. There appears additonal repulsive and attractive forces leading to a changed local mobiltiy. The…
We study the spreading of a quantum-mechanical wavepacket in a one-dimensional tight-binding model with a noisy potential, and analyze the emergence of classical diffusion from the quantum dynamics due to decoherence. We consider a finite…
Conditional diffusion models provide a natural framework for probabilistic prediction of dynamical systems and have been successfully applied to fluid dynamics and weather prediction. However, in many settings, the available information at…
In the framework of Gibbs statistical theory, the issue of the distribution of particle sizes forming the statistical system and the moments of this distribution are considered. This task is relevant for a wide variety of applications. The…
Recently a new theory for the transport of energetic particles across a mean magnetic field was presented. Compared to other non-linear theories the new approach has the advantage that it provides a full time-dependent description of the…
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…
The equation which describes a particle diffusing in a logarithmic potential arises in diverse physical problems such as momentum diffusion of atoms in optical traps, condensation processes, and denaturation of DNA molecules. A detailed…