相关论文: Drift-diffusion processes from elimination of fast…

In this paper a concentration inequality is proved for the deviation in the ergodic theorem in the case of discrete time observations of diffusion processes. The proof is based on the geometric ergodicity property for diffusion processes.…

Random walk has wide applications in many fields, such as machine learning, biology, physics, and chemistry. Random walk can be discrete or continuous in time and space. Asymmetric random walk could be described by drift-diffusion equation.…

We consider a heterogeneous diffusion equation and its corresponding generalization to the Cattaneo-Vernotte equation. It is derived by a combination of the continuity equation and the constitutive relation in various stochastic…

We consider a drift-diffusion process with a time-independent and divergence-free random drift that is of white-noise character. We are interested in the critical case of two space dimensions, where one has to impose a small-scale cut-off…

The diffusion type is determined not only by microscopic dynamics but also by the environment properties. For example, the environment's fractal structure is responsible for the emergence of subdiffusive scaling of the mean square…

Sampling from unnormalized densities is analogous to the generative modeling problem, but the target distribution is defined by a known energy function instead of data samples. Because evaluating the energy function is often costly, a…

Consider a reflecting diffusion in a domain in $R^d$ that acquires drift in proportion to the amount of local time spent on the boundary of the domain. We show that the stationary distribution for the joint law of the position of the…

Convection-diffusion equations provide the basis for describing heat and mass transfer phenomena as well as processes of continuum mechanics. To handle flows in porous media, the fundamental issue is to model correctly the convective…

We consider the motion of a particle in a periodic two dimensional flow perturbed by small (molecular) diffusion. The flow is generated by a divergence free zero mean vector field. The long time behavior corresponds to the behavior of the…

We study the absorbing state transition in particulate systems under spatially inhomogeneous driving using a modified random organization model. For smoothly varying driving the steady state results map onto the homogeneous absorbing state…

The presented explanations are provided for the one--dimensional diffusion process with constant drift by using forward Fokker--Planck technique. We are interested in the outflow probability in a finite interval, i.e. first passage time…

In this contribution, a variational diffuse modeling framework for cracks in heterogeneous media is presented. A static order parameter smoothly bridges the discontinuity at material interfaces, while an evolving phase-field captures the…

An expression for the two-particle relaxation time of collective excitations on a distorted Fermi surface in the diffusion approach to kinetic theory is obtained. The general case of momentum-dependent diffusion and drift coefficients is…

We propose an alternative method for one-dimensional continuum diffusion models with spatially variable (heterogeneous) diffusivity. Our method, which extends recent work on stochastic diffusion, assumes the constant-coefficient homogenized…

A mass transport directed from low to high density region in an inhomogeneous medium is modeled as a limiting case of a two-component lattice gas with excluded volume constraint and one of the components fixed. In the long-wavelength…

An asymmetric exclusion process comprising positive particles, negative particles and vacancies is introduced. The model is defined on a ring and the dynamics does not conserve the number of particles. We solve the steady state exactly and…

This paper addresses the nonparametric estimation of the drift function over a compact domain for a time-homogeneous diffusion process, based on high-frequency discrete observations from $N$ independent trajectories. We propose a neural…

We analyze numerically and analytically the non linear transport properties of a drift-diffusion equation in presence of a magnetic field and of a disorder potential. For a wide range of parameters this model exhibits a plateau where the…

The effect of diffusional relaxation on the random sequential deposition process is studied in the limit of fast deposition. Expression for the coverage as a function of time are analytically derived for both the short-time and long-time…

Drift-diffusion analysis has been introduced in physics as a method to study turbulent flows. In the current study, it is proposed to use the method to identify underlying dynamical models of particulate matter smog, ozone and nitrogen…