Related papers: Drift and trapping in biased diffusion on disorder…
Random walks with a fixed bias direction on randomly diluted cubic lattices far above the percolation threshold exhibit log-periodic oscillations in the effective exponent versus time. A scaling argument accounts for the numerical results…
We prove that bridges of subelliptic diffusions on a compact manifold, with distinct ends, satisfy a large deviation principle in a space of Holder continuous functions, with a good rate function, when the travel time tends to 0. This leads…
Bounce-averaged theories provide a framework for simulating relatively slow processes, such as collisional transport and quasilinear diffusion, by averaging these processes over the fast periodic motions of a particle on a closed orbit.…
We study the effect of particle mobility on phase transitions in a spin fluid in two dimensions. The presence of a phase transition of the BKT universality class is shown in an off-lattice model of particles with purely repulsive…
The analysis of the Rayleigh-B\'enard instability due to the mass diffusion in a fluid-saturated horizontal porous layer is reconsidered. The standard diffusion theory based on the variance of the molecular position growing linearly in time…
As a model of trapping by biased motion in random structure, we study the time taken for a biased random walk to return to the root of a subcritical Galton-Watson tree. We do so for trees in which these biases are randomly chosen,…
We consider a tracer particle performing a random walk on a two-dimensional lattice in the presence of immobile hard obstacles. Starting from equilibrium, a constant force pulling on the particle is switched on, driving the system to a new…
A disordered version of the one dimensional asymmetric exclusion model where the particle hopping rates are quenched random variables is studied. The steady state is solved exactly by use of a matrix product. It is shown how the phenomenon…
For a stopped diffusion process in a multidimensional time-dependent domain $\D$, we propose and analyse a new procedure consisting in simulating the process with an Euler scheme with step size $\Delta$ and stopping it at discrete times…
Recently an exact solution has been found (M.Henkel and H.Hinrichsen, cond-mat/0010062) for the 1d coagulation production process: 2A ->A, A0A->3A with equal diffusion and coagulation rates. This model evolves into the inactive phase…
We study here the random diffusion model. This is a continuum model for a conserved scalar density field $\phi$ driven by diffusive dynamics. The interesting feature of the dynamics is that the {\it bare} diffusion coefficient $D$ is…
We study the first-passage properties of a jump process with constant drift where jump amplitudes and inter-arrival times follow arbitrary light-tailed distributions with smooth densities. Using a mapping to an effective discrete-time…
We study the mixing time of the unit-rate zero-range process on the complete graph, in the regime where the number $n$ of sites tends to infinity while the density of particles per site stabilizes to some limit $\rho>0$. We prove that the…
We introduce a fractional Bessel process with constant negative drift, defined as a time-changed Bessel process via the inverse of a stable subordinator, independent of the base process. This construction yields a model capable of capturing…
A system of drift-diffusion equations with electric field under Dirichlet boundary conditions is analyzed. The system of strongly coupled parabolic equations for particle density and spin density vector describes the spin-polarized…
As a dynamical complex system, traffic is characterized by a transition from free flow to congestions, which is mostly studied in highways. However, despite its importance in developing congestion mitigation strategies, the understanding of…
Of stochastic differential equations, diffusion processes have been adopted in numerous applications, as more relevant and flexible models. This paper studies diffusion processes in a different setting, where for a given stationary…
We quantify the asymptotic behaviour of multidimensional drifltess diffusions in domains unbounded in a single direction, with asymptotically normal reflections from the boundary. We identify the critical growth/contraction rates of the…
We consider a specific random graph which serves as a disordered medium for a particle performing biased random walk. Take a two-sided infinite horizontal ladder and pick a random spanning tree with a certain edge weight $c$ for the…
Bias plays an important role in the enhancement of diffusion in periodic potentials. Using the continuous-time random walk in the presence of a bias, we provide a novel mechanism for the enhancement of diffusion in a random energy…