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We present a detailed derivation of Fourier's law in a class of stochastic energy exchange systems that naturally characterize two-dimensional mechanical systems of locally confined particles in interaction. The stochastic systems consist…
Polymer self-consistent field theory techniques are used to derive quantum density functional theory without the use of the theorems of density functional theory. Instead, a free energy is obtained from a partition function that is…
Precipitation and dissolution are prime processes in carbonate rocks and being able to monitor them is of major importance for aquifer and reservoir exploitation or environmental studies. Electrical conductivity is a physical property…
We begin with a brief overview of the most commonly used fractional derivatives, namely the Caputo and Riemann-Liouville derivatives. We then focus on the study of the fractional time wave equation with the Riemann-Liouville derivative,…
We presented a general approach for obtaining the generalized transport equations with fractional derivatives by using the Liouville equation with fractional derivatives for a system of classical particles and Zubarev's nonequilibrium…
In recent works it has been demonstrated that using an appropriate rescaling, linear Boltzmann-type equations give rise to a scalar fractional diffusion equation in the limit of a small mean free path. The equilibrium distributions are…
Several classes of physical systems exhibit ultraslow diffusion for which the mean squared displacement at long times grows as a power of the logarithm of time ("strong anomaly") and share the interesting property that the probability…
Brownian yet non-Gaussian processes have recently been observed in numerous biological systems and the corresponding theories have been built based on random diffusivity models. Considering the particularity of random diffusivity, this…
Traction-separation relationship is an important material characteristic describing the fracture behaviour of quasi-brittle solids. A new numerical scheme for identification of the traction-separation relation by inverse analysis of data…
The variability of temporal (or spatial) fluctuations of any variable is represented in conventional statistical theory by the relative dispersion equal to the standard deviation divided by the mean . The Relative Dispersion decreases with…
We consider and compare two different approaches to the fractional subdiffusion and transport in washboard potentials. One is based on the concept of random fractal time and is associated with the fractional Fokker-Planck equation. Another…
We investigate the well-posedness of a coupled Navier-Stokes-Fokker-Planck system with a time-fractional derivative. Such systems arise in the kinetic theory of dilute solutions of polymeric liquids, where the motion of noninteracting…
The fractal distribution of charged particles is considered. An example of this distribution is the charged particles that are distributed over fractal. The fractional integrals are used to describe fractal distribution. These integrals are…
This article is in continuation of our earlier article [37] in which computational solution of an unified reaction-diffusion equation of distributed order associated with Caputo derivatives as the time-derivative and Riesz-Feller derivative…
Saturated random sequential adsorption packings built of two-dimensional ellipses, spherocylinders, rectangles, and dimers placed on a one-dimensional line are studied to check analytical prediction concerning packing growth kinetics [A.…
Anomalous relaxation and diffusion processes have been widely characterized by fractional derivative models, where the definition of the fractional-order derivative remains a historical debate due to the singular memory kernel that…
The behaviour of the solutions of the time-fractional diffusion equation, based on the Caputo derivative, is studied and its dependence on the fractional exponent is analysed. The time-fractional convection-diffusion equation is also solved…
The paper provides a macro-microscopic coupled constitutive model for fluid-saturated porous media with respect to the compressibility of the solid skeleton, the real solid material and the fluid phase. The derivation of the model is…
In this note we analyse the propagation of a small density perturbation in a one-dimensional compressible fluid by means of fractional calculus modelling, replacing thus the ordinary time derivative with the Caputo fractional derivative in…
We study average flow properties in porous media using a two-dimensional network simulator. It models the dynamics of two-phase immiscible bulk flow where film flow can be neglected. The boundary conditions are biperiodic which provide a…