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We propose a unified framework to study the turbulent transport problem from the perspective of nonequilibrium statistical mechanics. By combining Krarichnan's turbulence thermalization assumption and Ruelle's recent work on nonequilibrium…
Quasilinear perpendicular diffusion of charged particles in fluctuating electromagnetic fields is the focus of this paper. A general transport parameter for perpendicular diffusion is presented being valid for an arbitrary turbulence…
In this paper, a new fractional operator of variable order with the use of the monotonic increasing function is proposed in sense of Caputo type. The properties in term of the Laplace and Fourier transforms are analyzed and the results for…
Mass transport problems are ubiquitous in diverse fields of physics and engineering. With the development of fractional calculus, many have taken to studying problems of fractional mass transport either through numerical simulations or…
Understanding the transport behavior of quantum many-body systems constitutes an important physical endeavor, both experimentally and theoretically. While a reliable classification into normal and anomalous dynamics is known to be…
Transport events in turbulent tokamak plasmas often exhibit non-local or non-diffusive action at a distance features that so far have eluded a conclusive theoretical description. In this paper a theory of non-local transport is investigated…
In many biological systems, the movement of individual agents is commonly characterized as having multiple qualitatively distinct behaviors that arise from various biophysical states. This is true for vesicles in intracellular transport,…
Tracer tests in natural porous media sometimes show abnormalities that suggest considering a fractional variant of the Advection Diffusion Equation supplemented by a time derivative of non-integer order. We are describing an inverse method…
Probabilistic interpretation of transition from the dispersive transport regime to the quasi-Gaussian one in disordered semiconductors is given in terms of truncated Levy distributions. Corresponding transport equations with fractional…
I will discuss, from a dynamical systems point of view, some recent attempts to rigorously derive the macroscopic laws of transport (e.g. the heat equation) from deterministic microscopic dynamics.
We prove transportation-cost inequalities for the law of SDE solutions driven by general Gaussian processes. Examples include the fractional Brownian motion, but also more general processes like bifractional Brownian motion. In case of…
The extraction of natural gas from the earth has been shown to be governed by differential equations concerning flow through a porous material. Recently, models such as fractional differential equations have been developed to model this…
We review a semi-classical transport theory for non-Abelian plasmas based on a classical picture of coloured point particles. Within this formalism, kinetic equations for the mean particle distribution, the mean fields and their…
In this paper, we show how to study the evolution of a system, given imprecise knowledge about the state of the system and the dynamics laws. Our approach is based on Fuzzy Set Theory, and it will be shown that the \emph{Fuzzy Dynamics} of…
Many important transport phenomena are described by simple mathematical models rooted in the diffusion equation. Geometrical constraints present in such phenomena often have influence of a universal sort and manifest themselves in scaling…
In this Letter, we clarify the physical origin of effective transport in periodic and tilted periodic systems. When Brownian dynamics is examined on the scale of a single period, the particle displacement admits a natural separation into a…
We introduce a formalism of fractional diffusion on networks based on a fractional Laplacian matrix that can be constructed directly from the eigenvalues and eigenvectors of the Laplacian matrix. This fractional approach allows random walks…
Fractional Levy motion (fLm) is the natural generalization of fractional Brownian motion in the context of self-similar stochastic processes and stable probability distributions. In this paper we give an explicit derivation of the…
We describe a method for computing transport coefficients from the direct evaluation of large deviation function. This method is general, relying on only equilibrium fluctuations, and is statistically efficient, employing trajectory based…
In this paper, a new family of implicit compact finite difference schemes for computation of unsteady convection-diffusion equation with variable convection coefficient is proposed. The schemes are fourth order accurate in space and second…