Related papers: Fractional diffusion on a fractal grid comb
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.
We suggest a modification of a comb model to describe anomalous transport in spiny dendrites. Geometry of the comb structure consisting of a one-dimensional backbone and lateral branches makes it possible to describe anomalous diffusion,…
We give an exact analytical results for diffusion with a power-law position dependent diffusion coefficient along the main channel (backbone) on a comb and grid comb structures. For the mean square displacement along the backbone of the…
A possible mechanism of superdiffusion of ultra-cold atoms in a one-dimensional polarization optical lattice, observed experimentally in [Phys. Rev. Lett. \textbf{108}, 093002 (2012)], is suggested. The analysis is based on a consideration…
An exact analytical analysis of anomalous diffusion on a fractal mesh is presented. The fractal mesh structure is a direct product of two fractal sets which belong to a main branch of backbones and side branch of fingers. The fractal sets…
Anomalous transport in a circular comb is considered. The circular motion takes place for a fixed radius, while radii are continuously distributed along the circle. Two scenarios of the anomalous transport, related to the reflecting and…
A Cattaneo equation for a comb structure is considered. We present a rigorous analysis of the obtained fractional diffusion equation, and corresponding solutions for the probability distribution function are obtained in the form of the Fox…
The diffusion in the comb structures is a popular model of geometrically induced anomalous diffusion. In the present work we concentrate on the diffusion along the backbone in a system where sidebranches are planes, and the diffusion…
Recent experimental findings on anomalous diffusion have demanded novel models that combine annealed (temporal) and quenched (spatial or static) disorder mechanisms. The comb-model is a simplified description of diffusion on percolation…
We study a transport of impurity particles on a comb structure in the presence of advection. The main body concentration and asymptotic concentration distributions are obtained. Seven different transport regimes occur on the comb structure…
Fractional transport of particles on a comb structure in the presence of an inhomogeneous convection flow is studied. The large scale asymptotics is considered. It is shown that a contaminant spreads superdiffusively in the direction…
This chapter is a contribution in the "Handbook of Applications of Chaos Theory" ed. by Prof. Christos H Skiadas. The chapter is organized as follows. First we study the statistical properties of combs and explain how to reduce the effect…
The comb model is a simplified description for anomalous diffusion under geometric constraints. It represents particles spreading out in a two-dimensional space where the motions in the x-direction are allowed only when the y coordinate of…
A fractional diffusion equation with advection term is rigorously derived from a kinetic transport model with a linear turning operator, featuring a fat-tailed equilibrium distribution and a small directional bias due to a given vector…
The motion of contaminant particles through complex environments such as fractured rocks or porous sediments is often characterized by anomalous diffusion: the spread of the transported quantity is found to grow sublinearly in time due to…
We address the problem of diffusion on a comb whose teeth display a varying length. Specifically, the length $\ell$ of each tooth is drawn from a probability distribution displaying the large-$\ell$ behavior $P(\ell) \sim…
We study specific properties of particles transport by exploring an exact solvable model, a so-called comb structure, where diffusive transport of particles leads to subdiffusion. A performance of L\'evy -- like process enriches this…
We present a rigorous result on ultra-slow diffusion by solving a Fokker-Planck equation, which describes anomalous transport in a three dimensional (3D) comb. This 3D cylindrical comb consists of a cylinder of discs threaten on a backbone.…
Diffusion in complex heterogeneous media such as biological tissues or porous materials typically involves constrained displacements in tortuous structures and {\em sticky} environments. Therefore, diffusing particles experience both…
Superdiffusion is an anomalous transport behavior. Recently, a new mechanism, termed the ``nodal mechanism," has been proposed to induce superdiffusion in quantum models. However, existing realizations of the nodal mechanism have so far…