Related papers: Subdiffusion on a Fractal Comb
A simple Markov process is considered involving a diffusion in one direction and a transport in a transverse direction. Quantitative mixing rate estimates are obtained with limited assumptions about the transport field, which might be…
A distributed order fractional diffusion equation is considered. Distributed order derivatives are fractional derivatives that have been integrated over the order of the derivative within a given range. In this paper sub-diffusive cases are…
This paper provides a new model to compute the fractal dimension of a subset on a generalized-fractal space. Recall that fractal structures are a perfect place where a new definition of fractal dimension can be given, so we perform a…
We analyse deterministic diffusion in a simple, one-dimensional setting consisting of a family of four parameter dependent, chaotic maps defined over the real line. When iterated under these maps, a probability density function spreads out…
We construct a theory of distributions in the setting of analysis on post-critically finite self-similar fractals, and on fractafolds and products based on such fractals. The results include basic properties of test functions and…
A problem of diffraction by an elongated body of revolution is studied. The incident wave falls along the axis. The wavelength is small comparatively to the dimensions of the body. The parabolic equation of the diffraction theory is used to…
A conditional diffusion model has been developed to analyze intricate conductance fluctuations called universal conductance fluctuations or quantum fingerprints appearing in quantum transport phenomena. The model reconstructs impurity…
The present work is aimed to find suitable exchange conditions for saturated fluid flow in a porous medium, when a fractal microstructure is embedded in the porous matrix. Two different deterministic models are introduced and rigorously…
The formulation of combinatorial differential forms, proposed by Forman for analysis of topological properties of discrete complexes, is extended by defining the operators required for analysis of physical processes dependent on scalar…
Dynamical zeta functions provide a powerful method to analyze low dimensional dynamical systems when the underlying symbolic dynamics is under control. On the other hand even simple one dimensional maps can show an intricate structure of…
Anomalous heat diffusion is investigated for biological tissues displaying a fractal structure and long-term thermal memory, which is modeled via a fractional derivative. For increasing values of the fractional derivation order, the tissue…
There are various notions of dimension in fractal geometry to characterise (random and non-random) subsets of $\mathbb R^d$. In this expository text, we discuss their analogues for infinite subsets of $\mathbb Z^d$ and, more generally, for…
Analysis of signal fluctuations of a locally fixed probe, caused by molecules diffusing under the probe, can be used to determine diffusion coefficients. Theoretical treatments so far have been limited to point-like particles or to…
Fractals have been at the heart of geophysical and geospatial studies in the recent past. We examine the emergent fractal character of water vapor distributions above the surface of the Earth as a function of both image resolution (number…
In many physical situations involving diverse length scales, waves or rays representing them travel through media characterized by spatially smooth, random, modest refactive index variations. "Primary" diffraction (by individual…
We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phenomena. This yields a system of equations with possibly…
A problem of the crossover from percolation to diffusion transport is considered. A general scaling theory is proposed. It introduces phenomenologically four critical exponents which are connected by two equations. One exponent is…
We study a diffusion process on a three-dimensional comb under stochastic resetting. We consider three different types of resetting: global resetting from any point in the comb to the initial position, resetting from a finger to the…
The motion of energetic particles in magnetic turbulence across a mean magnetic field is explored analytically. The approach presented here allows for a full time-dependent description of the transport, including compound sub-diffusion. The…
We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two indistinguishable fluids. The enhancement of the diffusive transport depends on the system size L and grows…