Journal ArticleDOI
Anomalous diffusion approach to non-exponential relaxation in complex physical systems
TLDR
A direct (one-to-one) relationship between the method of random relaxation rates and the anomalous diffusion approach based on subordination of random processes that are applied for the theory of relaxation phenomena is discovered.About:
This article is published in Communications in Nonlinear Science and Numerical Simulation.The article was published on 2015-07-01. It has received 25 citations till now. The article focuses on the topics: Relaxation (physics) & Anomalous diffusion.read more
Citations
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Journal ArticleDOI
Models of dielectric relaxation based on completely monotone functions
TL;DR: In this paper, the relaxation properties of dielectric materials are described, in the frequency domain, according to one of the several models proposed over the years: Kohlrausch-Williams-Watts, Cole-Cole, ColeDavidson, Havriliak-Negami (with its modified version) and Excess wing model.
Journal ArticleDOI
Models of dielectric relaxation based on completely monotone functions
TL;DR: The relaxation properties of dielectric materials are described, in the frequency domain, according to one of the several models proposed over the years: Kohlrausch-Williams-Watts (KW), Cole-Cole, Cole-Davidson, Havriliak-Negami (with its modified version), and Excess wing model.
Journal ArticleDOI
Relaxation and diffusion models with non-singular kernels
TL;DR: In this paper, a legitimate extension of the previous derivative is proposed by replacing the exponential kernel with a stretched exponential kernel, implying the potential applicability of the new derivative in quantifying real-world, anomalous relaxation and diffusion processes.
Journal ArticleDOI
The Havriliak–Negami relaxation and its relatives: the response, relaxation and probability density functions
Journal ArticleDOI
Stochastic Tools Hidden Behind the Empirical Dielectric Relaxation Laws
TL;DR: In this article, the authors present probabilistic implications for the study of the relaxation-rate distribution models in complex systems, in which relaxing entities form random clusters interacting with each other and single entities.
References
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Journal ArticleDOI
An Introduction to Probability Theory and Its Applications.
Book
Stochastic processes in physics and chemistry
TL;DR: In this article, the authors introduce the Fokker-planck equation, the Langevin approach, and the diffusion type of the master equation, as well as the statistics of jump events.
Journal ArticleDOI
The random walk's guide to anomalous diffusion: a fractional dynamics approach
Ralf Metzler,Joseph Klafter +1 more
TL;DR: Fractional kinetic equations of the diffusion, diffusion-advection, and Fokker-Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns.
Stochastic Processes in Physics and Chemistry
Abstract: Preface to the first edition. Preface to the second edition. Abbreviated references. I. Stochastic variables. II. Random events. III. Stochastic processes. IV. Markov processes. V. The master equation. VI. One-step processes. VII. Chemical reactions. VIII. The Fokker-Planck equation. IX. The Langevin approach. X. The expansion of the master equation. XI. The diffusion type. XII. First-passage problems. XIII. Unstable systems. XIV. Fluctuations in continuous systems. XV. The statistics of jump events. XVI. Stochastic differential equations. XVII. Stochastic behavior of quantum systems.
Related Papers (5)
The random walk's guide to anomalous diffusion: a fractional dynamics approach
Ralf Metzler,Joseph Klafter +1 more