Search results for "anomalous diffusion"
showing 10 items of 33 documents
A mechanical picture of fractional-order Darcy equation
2015
Abstract In this paper the authors show that fractional-order force-flux relations are obtained considering the flux of a viscous fluid across an elastic porous media. Indeed the one-dimensional fluid mass transport in an unbounded porous media with power-law variation of geometrical and physical properties yields a fractional-order relation among the ingoing flux and the applied pressure to the control section. As a power-law decay of the physical properties from the control section is considered, then the flux is related to a Caputo fractional derivative of the pressure of order 0 ⩽ β ≤ 1 . If, instead, the physical properties of the media show a power-law increase from the control sectio…
On fractional diffusion and continuous time random walks
2003
Abstract A continuous time random walk model is presented with long-tailed waiting time density that approaches a Gaussian distribution in the continuum limit. This example shows that continuous time random walks with long time tails and diffusion equations with a fractional time derivative are in general not asymptotically equivalent.
Anomalous tracer diffusion in film forming colloidal dispersions
2000
Film forming colloidal dispersions can be conceived as a material composed of interpenetrating hydrophobic (polymer) and hydrophilic (partially broken interfaces) phases where the transport properties of one phase are influenced by the geometric confinement effect imposed by the other. We studied the transport properties of film forming colloidal dispersions by introducing hydrophobic dye molecules into the colloidal particles and determining their motion with forced Rayleigh Scattering as a function of length scale (grating distance A) and water content. At water contents between 18 and 3 weight percent we find signatures of anomalous tracer diffusion, namely stretched exponential decay cu…
Scattering lengths and universality in superdiffusive L\'evy materials
2012
We study the effects of scattering lengths on L\'evy walks in quenched one-dimensional random and fractal quasi-lattices, with scatterers spaced according to a long-tailed distribution. By analyzing the scaling properties of the random-walk probability distribution, we show that the effect of the varying scattering length can be reabsorbed in the multiplicative coefficient of the scaling length. This leads to a superscaling behavior, where the dynamical exponents and also the scaling functions do not depend on the value of the scattering length. Within the scaling framework, we obtain an exact expression for the multiplicative coefficient as a function of the scattering length both in the a…
Anomalous diffusion in polymer melts
2002
Abstract We present a study of the anomalous diffusion regimes in polymer melt dynamics performing a Monte Carlo (MC) simulation of the bond-fluctuation lattice model. Special emphasis is laid on the crossover from a Rouse-like motion to the behavior predicted by reptation theory. For the longest chains of N=400 the high statistical accuracy of the data allows for clear identification of the subdiffusive regimes in the center of mass motion and the monomer displacement. They are well compatible with those predicted by reptation theory. Furthermore a detailed analysis of the different short time anomalous diffusion regimes in the melt dynamics of polymer chains is presented and it is shown t…
Switching times in long-overlap Josephson junctions subject to thermal fluctuations and non-Gaussian noise sources
2014
We investigate the superconducting lifetime of long current-biased Josephson junctions, in the presence of Gaussian and non-Gaussian noise sources. In particular, we analyze the dynamics of a Josephson junction as a function of the noise signal intensity, for different values of the parameters of the system and external driving currents. We find that the mean lifetime of the superconductive state is characterized by nonmonotonic behavior as a function of noise intensity, driving frequency and junction length. We observe that these nonmonotonic behaviours are connected with the dynamics of the junction phase string during the switching towards the resistive state. An important role is played…
Single trajectory characterization via machine learning
2020
[EN] In order to study transport in complex environments, it is extremely important to determine the physical mechanism underlying diffusion and precisely characterize its nature and parameters. Often, this task is strongly impacted by data consisting of trajectories with short length (either due to brief recordings or previous trajectory segmentation) and limited localization precision. In this paper, we propose a machine learning method based on a random forest architecture, which is able to associate single trajectories to the underlying diffusion mechanism with high accuracy. In addition, the algorithm is able to determine the anomalous exponent with a small error, thus inherently provi…
Critical Phenomena and Diffusion in Complex Systems
2008
Wait-and-switch stochastic model of the non-Debye relaxation. Derivation of the Burr survival probability
2006
Abstract Stochastic mechanism of relaxation, in which a dipole waits until a favourable condition for reorientation exists, is discussed. Assuming that an imposed direction of a dipole moment may be changed when a migrating defect reaches the dipole, we present a mathematically rigorous scheme relating the local random characteristics of a macroscopic system to its effective relaxation behaviour. We derive a relaxation function (the Burr survival probability) that is characterized by the stretched exponential or the power-law behaviour.