Related papers: Diffusion properties of small-scale fractional tra…
We study transport of an inertial Brownian particle moving in a symmetric and periodic one-dimensional potential, and subjected to both a symmetric, unbiased external harmonic force as well as biased dichotomic noise $\eta(t)$ also known as…
Mathematical models based on probability density functions (PDF) have been extensively used in hydrology and subsurface flow problems, to describe the uncertainty in porous media properties (e.g., permeability modelled as random field).…
Fractional Gaussian noise models the time series with long-range dependence; when the Hurst index $H>1/2$, it has positive correlation reflecting a persistent autocorrelation structure. This paper studies the numerical method for solving…
Diffusion theory establishes a fundamental connection between stochastic differential equations and partial differential equations. The solution of a partial differential equation known as the Fokker-Planck equation describes the…
We present a field theory for the statistics of charge and current fluctuations in diffusive systems. The cumulant generating function is given by the saddle-point solution for the action of this field theory. The action depends on two…
Fractional kinetic equations employ non-integer calculus to model anomalous relaxation and diffusion in many systems. While this approach is well explored, it so far failed to describe an important class of transport in disordered systems.…
We develop a microscopic transport theory in a randomly driven fermionic model with and without linear potential. The operator dynamics arise from the competition between noisy and static couplings, leading to diffusion regardless of…
We consider overdamped Brownian dynamics in a periodic potential with temporally oscillating amplitude. We analyze the transport which shows effective diffusion enhanced by the oscillations and derive approximate expressions for the…
We investigate the stochastic dynamics of an active particle moving at a constant speed under the influence of a fluctuating torque. In our model the angular velocity is generated by a constant torque and random fluctuations described as a…
We consider the motion of a particle governed by a weakly random Hamiltonian flow. We identify temporal and spatial scales on which the particle trajectory converges to a spatial Brownian motion. The main technical issue in the proof is to…
A stochastic method is described for estimating Green's functions (GF's), appropriate to linear advection-diffusion-reaction transport problems, evolving in arbitrary geometries. By allowing straightforward construction of approximate,…
We define weighted fractional Brownian sheets, which are a class of Gaussian random fields with four parameters that include fractional Brownian sheets as special cases, and we give some of their properties. We show that for certain values…
The two--dimensional diffusive dynamics of test particles in a random electromagnetic field is studied. The synthetic electromagnetic fluctuations are generated through randomly placed magnetised ``clouds'' oscillating with a frequency…
In this paper, we consider nonlinear diffusion processes driven by space-time white noises, which have an interpretation in terms of partial differential equations. For a specific choice of coefficients, they correspond to the Landau…
We propose an alternative interpretation of Markovian transport models based on the well-mixedness condition, in terms of the properties of a random velocity field with second order structure functions scaling linearly in the space time…
We present a method to infer the arbitrary space-dependent drift and diffusion of a nonlinear stochastic model driven by multiplicative fractional Gaussian noise from a single trajectory. Our method, fractional Onsager-Machlup optimisation…
We introduce a particular construction of an autocorrelation matrix of a time series and its analysis based on the random-matrix theory ideas that is capable of unveiling the type of correlations information which is inaccessible to the…
Subdiffusion on graphs is often modeled by time-fractional diffusion equations, yet its structural and dynamical consequences remain unclear. We show that subdiffusive transport on graphs is a memory-driven process generated by a random…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
We review several results related to the problem of a quantum particle in a random environment. In an introductory part, we recall how several functionals of the Brownian motion arise in the study of electronic transport in weakly…