Related papers: Subdiffusion on a Fractal Comb
Electrodynamics of composite materials with fractal geometry is studied in the framework of fractional calculus. This consideration establishes a link between fractal geometry of the media and fractional integro-differentiation. The…
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.…
By considering subexponential contributions in large deviation theory, we determine the fine structure in the probability distribution of the observable displacement of a bead coupled to a molecular motor. More generally, for any stochastic…
We consider random walks on comb- and brush-like graphs consisting of a base (of fractal dimension $D$) decorated with attached side-groups. The graphs are also characterized by the fractal dimension $D_a$ of a set of anchor points where…
The Interstellar Medium seems to have an underlying fractal structure, which can be characterized through its fractal dimension (Df). However, several factors may affect the determination of Df, such as distortions due to projection, low…
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.…
We propose a novel method to measure the fractal dimension of a submonolayer metal adatom system grown under conditions of limited diffusivity on a surface. The method is based on measuring the specular peak attenuation of He atoms…
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…
In this paper we present a systematic and rigorous method for calculating the diffusion tensor for a Brownian particle moving in a periodic potential which is valid in arbitrary dimensions and for all values of the dissipation. We use this…
In this paper, the scattering/transmission inside a step-modulated subwavelength metal slit is investigated in detail. We firstly investigate the scattering in a junction structure by two types of structural changes. The variation of…
Many physical phenomena occur on domains that grow in time. When the timescales of the phenomena and domain growth are comparable, models must include the dynamics of the domain. A widespread intrinsically slow transport process is…
A transport theory for atomic matter waves in low-dimensional waveguides is outlined. The thermal fluctuation spectrum of magnetic near fields leaking out of metallic microstructures is estimated. The corresponding scattering rate for…
Dispersion engineering is among the most important steps towards a promising optical frequency comb. We propose a new and general approach to trim frequency combs using a self-adaptive boundary of the optical mode at different wavelengths…
We investigate front propagation in systems with diffusive and sub-diffusive behavior. The scaling behavior of moments of the diffusive problem, both in the standard and in the anomalous cases, is not enough to determine the features of the…
We investigate evolution equations for anomalous diffusion employing fractional derivatives in space and time. Linkage between the space-time variables leads to a new type of fractional derivative operator. Fractional diffusion equations…
We discuss some aspects of a recently proposed semi-classical transport theory for QCD plasmas based on coloured point particles. This includes the derivation of effective transport equations for mean fields and fluctuations which relies on…
Fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time. For processes lacking such scaling the corresponding description may be given by…
Polymer's network is treated as an anisotropic fractal with fractional dimensionality D = 1 + \epsilon close to one. Percolation model on such a fractal is studied. Using the real space renormalization group approach of Migdal and Kadanoff…
The soft physics approach to form factors and Compton scattering at moderately large momentum transfer is reviewed. It will be argued that in that approach the Compton cross section is given by the Klein-Nishina cross section multiplied by…
Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with…