Related papers: Fractal properties of the diffusion coefficient in…
Within the point vortex model, we compute the probability distribution function of the velocity fluctuations induced by same-signed vortices scattered within a disk according to a fractal distribution of distances to origin $\sim…
A non--linear diffusion equation is derived by taking into account hopping rates depending on the occupation of next neighbouring sites. There appears additonal repulsive and attractive forces leading to a changed local mobiltiy. The…
Motivated by networked systems in random environment and controlled hybrid stochastic dynamic systems, this work focuses on modeling and analysis of a class of switching diffusions consisting of continuous and discrete components. Novel…
We present a finite element approach for diffusion problems with thermal fluctuations based on a fluctuating hydrodynamics model. The governing transport equations are stochastic partial differential equations with a fluctuating forcing…
We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…
This work analyzes fractional continuous-time random walks on two-layer multiplexes. A node-centric dynamics is used, in which it is assumed a Poisson distribution of a walker to become active, while a jump to one of its neighbors depends…
Analysis with the characteristic functional of stochastic motion is used for the gradient spin echo measurement of restricted motion to clarify details of the diffraction-like effect in a porous structure. It gives the diffusive diffraction…
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…
This paper studies a basic model of a dynamical distribution network, where the network topology is given by a directed graph with storage variables corresponding to the vertices and flow inputs corresponding to the edges. We aim at…
The Levy diffusion processes are a form of non ordinary statistical mechanics resting, however, on the conventional Markov property. As a consequence of this, their dynamic derivation is possible provided that (i) a source of randomness is…
The method of iterated conformal maps allows to study the harmonic measure of Diffusion Limited Aggregates with unprecedented accuracy. We employ this method to explore the multifractal properties of the measure, including the scaling of…
The small-angle scattering curves of deterministic mass fractals are studied and analyzed in the momentum space. In the fractal region, the curve I(q)q^D is found to be log-periodic with a good accuracy, and the period is equal to the…
Fluctuation properties of the Langevin equation including a multiplicative, power-law noise and a quadratic potential are discussed. The noise has the Levy stable distribution. If this distribution is truncated, the covariance can be…
The purpose of this paper is to study the fractal phenomena in large data sets and the associated questions of dimension reduction. We examine situations where the classical Principal Component Analysis is not effective in identifying the…
In this paper we present a study of anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives. The distribution functions are found using numerical means for varying degree of fractionality observing the…
The B/C ratio is used in cosmic-ray physics to constrain the transport parameters. However, from the same set of data, the various published values show a puzzling large scatter of these parameters. We investigate the impact of using…
We study the Sinai model for the diffusion of a particle in a one dimensional quenched random energy landscape. We consider the particular case of discrete energy landscapes made of random +/- 1 jumps on the semi infinite line Z+ with a…
We review some exact results for the motion of a tagged particle in simple models. Then, we study the density dependence of the self diffusion coefficient, $D_N(\rho)$, in lattice systems with simple symmetric exclusion in which the…
Diffusion coefficient usually decreases when friction increases. We analyze the opposite behavior in the paradigmatic system consisting of an inertial Brownian particle moving in a symmetric spatially periodic potential and driven by an…
We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer…