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A generalized Fokker-Planck equation is derived to describe particle kinetics in specific situations when the probability transition function (PTF) has a long tail in momentum space. The equation is valid for an arbitrary value of the…
The diffusion equation is the primary tool to study the movement dynamics of a free Brownian particle, but when spatial heterogeneities in the form of permeable interfaces are present, no fundamental equation has been derived. Here we…
A Langevin equation with a special type of additive random source is considered. This random force presents a fractional order derivative of white noise, and leads to a power-law time behavior of the mean square displacement of a particle,…
Advection properties of passive particles in flows generated by point vortices are considered. Transport properties are anomalous with characteristic transport exponent $\mu \sim 1.5$. This behavior is linked back to the presence of…
This dissertation resolves a longstanding discussion of a mathematical problem important in contaminant hydrogeology and chemical-reaction engineering, the proper mathematical description for a miscible solute undergoing longitudinal…
We study dynamical fluctuations in overdamped diffusion processes driven by time periodic forces. This is done by studying fluctuation functionals (rate functions from large deviation theory), of fluctuations around the non-equilibrium…
It has been observed in many numerical simulations, experiments and from various theoretical treatments that heat transport in one-dimensional systems of interacting particles cannot be described by the phenomenological Fourier's law. The…
We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fractal function of control parameters. A modified continuous time random walk theory yields its coarse functional form and correctly describes a…
We consider the inverse problem of reconstructing the scattering and absorption coefficients using boundary measurements for a time dependent radiative transfer equation (RTE). As the measurement is mostly polluted by errors, both…
Using the analytical Fick-Jacobs approximation formalism and extensive Brownian dynamics simulations we study particle transport through two-dimensional periodic channels with triangularly shaped walls. Directed motion is caused by the…
We study the transport properties of passive inertial particles in a $2-d$ incompressible flows. Here the particle dynamics is represented by the $4-d$ dissipative embedding map of $2-d$ area-preserving standard map which models the…
The study of fluctuation-induced transport is concerned with the directed motion of particles on a substrate when subjected to a fluctuating external field. Work over the last two decades provides now precise clues on how the average…
In this article, we study the unique determination of convection term and the time-dependent density coefficient appearing in a convection-diffusion equation from partial Dirichlet to Neumann map measured on boundary.
We consider a nonlinear Fokker-Planck equation driven by a deterministic rough path which describes the conditional probability of a McKean-Vlasov diffusion with "common" noise. To study the equation we build a self-contained framework of…
Most existing works on transportation dynamics focus on networks of a fixed structure, but networks whose nodes are mobile have become widespread, such as cell-phone networks. We introduce a model to explore the basic physics of…
The calculation of transport profiles from experimental measurements belongs in the category of inverse problems which are known to come with issues of ill-conditioning or singularity. A reformulation of the calculation, the matricial…
A generalized continuum framework for the theory of solute transport in fluids is proposed and systematically developed. This framework rests on the introduction of a generic force balance for the solute, a balance distinct from the…
We define the Dyson diffusion process on a curved smooth closed contour in the plane and derive the Fokker-Planck equation for probability density. Its stationary solution is shown to be the Boltzmann weight for the logarithmic gas confined…
The longitudinal transport problem (the current is applied parallel to some bias magnetic field) in type-II superconductors is analyzed theoretically. Based on analytical results for simplified configurations, and relying on numerical…
Instabilities driven by strong gradients appear in a wide variety of physical systems, including plasmas, neutral fluids, and self-gravitating systems. This work develops an analytic formulation to describe the transport structure and…