Related papers: Diffusion on Fractal Ces\`aro Curve
A new approach to the modeling of nonfree particle diffusion is presented. The approach uses a general setup based on geometric graphs (networks of curves), which means that particle diffusion in anything from arrays of barriers and pore…
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…
The fractional diffusion equation is derived from the master equation of continuous-time random walks (CTRWs) via a straightforward application of the Gnedenko-Kolmogorov limit theorem. The Cauchy problem for the fractional diffusion…
Possible formulations of the problem of cosmic rays acceleration in the interstellar galactic medium are considered with the use of fractional differential equations. The applied technique has been physically justified. A Fermi result has…
The~numerical solutions to a non-linear Fractional Fokker--Planck (FFP) equation are studied estimating the generalized diffusion coefficients. The~aim is to model anomalous diffusion using an FFP description with fractional velocity…
Subdiffusion on a fractal comb is considered. A mechanism of subdiffusion with a transport exponent different from 1/2 is suggested. It is shown that the transport exponent is determined by the fractal geometry of the comb.
Diffusion is a reoccurring phenomena in many fields and is affected by the geometry in which it takes place. Here we investigate the effects of geometry on diffusion in a Brick and Mortar model system. The tortuous effects are evaluated…
Using a microfluidics device filled with a colloidal suspension of microspheres, we test the laws of diffusion in the limit of small particle numbers. Our focus is not just on average properties such as the mean flux, but rather on the…
A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector…
We find Feynman-Kac type representation theorems for generalized diffusions. To do this we need to establish existence, uniqueness and regularity results for equations with measure-valued coefficients.
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…
A well studied family of random fractals called fractal percolation is discussed. We focus on the projections of fractal percolation on the plane. Our goal is to present stronger versions of the classical Marstrand theorem, valid for almost…
The thesis deals with applications of fractional calculus to fractals. It introduces the notion of local fractional derivative (LFD). Fractal and multifractal functions have been studied in the thesis using LFD. New kind of equations are…
The small-angle scattering of neutrons on large scale inhomogeneities of two-component systems in refraction range is considered. We supposed, that neutrons acquire phase shifts describing by the Gaussian distribution function. It is shown…
In [arXiv:2305.05022], Cohen proved a higher dimensional fractal uncertainty principle for line porous sets. The purpose of this expository note is to provide a different point of view on some parts of Cohen's proof, particularly suited to…
Opals are structures composed of the closed packing of spheres in the size range of nano-to-micro meter. They are sintered to create small necks at the points of contact. We have solved the diffusion problem in such structures. The relation…
In the present work, we propose a new parameterization for the concentration flux using fractional derivatives. The fractional order differential equation in the longitudinal and vertical directions is used to obtain the concentration…
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.…
In analogy to recent results on non-universal roughening in surface growth [Lam and Sander, Phys. Rev. Lett. {\bf 69}, 3338 (1992)], we propose a variant of diffusion-limited aggregation ($DLA$) in which the radii of the particles are…
In this paper, a multi-dimensional fractional wave equation that describes propagation of the damped waves is introduced and analyzed. In contrast to the fractional diffusion-wave equation, the fractional wave equation contains fractional…