Renewal theory for anomalous transport processes

1998 ◽  
Vol 92 (4) ◽  
pp. 4085-4096 ◽  
Author(s):  
V. Uchaikin
Keyword(s):  
Renewal Theory ◽  
Transport Processes ◽  
Anomalous Transport

scholarly journals Stochastic scattering model of anomalous diffusion in arrays of steady vortices

2020 ◽  
Vol 476 (2238) ◽  
pp. 20200183
Author(s):  
Salvatore Buonocore ◽  
Mihir Sen ◽  
Fabio Semperlotti
Keyword(s):  
Transport Mechanism ◽  
Transport Processes ◽  
Anomalous Transport ◽  
Continuum Models ◽  
Particle Dynamic ◽  
Tracer Particles ◽  
Non Local ◽  
Heavy Tailed ◽  
Steady Vortices ◽  
Local Nature

We investigate the occurrence of anomalous transport phenomena associated with tracer particles propagating through arrays of steady vortices. The mechanism responsible for the occurrence of anomalous transport is identified in the particle dynamic, which is characterized by long collision-less trajectories (Lévy flights) interrupted by chaotic interactions with vortices. The process is studied via stochastic molecular models that are able to capture the underlying non-local nature of the transport mechanism. These models, however, are not well suited for problems where computational efficiency is an enabling factor. We show that fractional-order continuum models provide an excellent alternative that is able to capture the non-local nature of anomalous transport processes in turbulent environments. The equivalence between stochastic molecular and fractional continuum models is demonstrated both theoretically and numerically. In particular, the onset and the temporal evolution of heavy-tailed diffused fields are shown to be accurately captured, from a macroscopic perspective, by a fractional diffusion equation. The resulting anomalous transport mechanism, for the selected ranges of density of the vortices, shows a superdiffusive nature.

Kinetic theory of anomalous transport processes in tokamaks

1987 ◽  
Vol 27 (3) ◽  
pp. 453-470 ◽  
Author(s):  
A.V. Gurevich ◽  
K.P. Zybin ◽  
Ya.N. Istomin
Keyword(s):  
Kinetic Theory ◽  
Transport Processes ◽  
Anomalous Transport

scholarly journals Kinetic Simulations of Neoclassical and Anomalous Transport Processes in Helical Systems

2012 ◽  
Vol 7 (0) ◽  
pp. 2403094-2403094 ◽  
Author(s):  
Hideo SUGAMA ◽  
Tomohiko WATANABE ◽  
Masanori NUNAMI ◽  
Shinsuke SATAKE ◽  
Seikichi MATSUOKA ◽  
...  
Keyword(s):  
Transport Processes ◽  
Anomalous Transport

scholarly journals Anomalous transport processes in turbulent non-Abelian plasmas

2011 ◽  
Vol 854 (1) ◽  
pp. 76-80 ◽  
Author(s):  
Masayuki Asakawa ◽  
Steffen A. Bass ◽  
Berndt Müller
Keyword(s):  
Transport Processes ◽  
Anomalous Transport

Anomalous transport processes near a levitated coil immersed in a plasma

1992 ◽  
Vol 32 (10) ◽  
pp. 1725-1733 ◽  
Author(s):  
V.P Pastukhov ◽  
A.Yu Sokolov
Keyword(s):  
Transport Processes ◽  
Anomalous Transport

scholarly journals A phenomenological approach to anomalous transport in complex or disordered media

2021 ◽  
Author(s):  
Ugur Saglam ◽  
Deniz Deger
Keyword(s):  
Master Equation ◽  
Initial Conditions ◽  
Stochastic Theory ◽  
Planck Equation ◽  
Phenomenological Approach ◽  
Transport Processes ◽  
Amorphous Semiconductors ◽  
Anomalous Transport ◽  
Disordered Media ◽  
Conductivity Behavior

We aim to derive a phenomenological approach to link the theories of anomalous transport governed by fractional calculus and stochastic theory with the conductivity behavior governed by the semi-empirical conductivity formalism involving Debye, Cole-Cole, Cole-Davidson, and Havriliak-Negami type conductivity equations. We want to determine the anomalous transport processes in the amorphous semiconductors and insulators by developing a theoretical approach over some mathematical instruments and methods. In this paper, we obtain an analytical expression for the average behavior of conductivity in complex or disordered media via using the fractional-stochastic differential equation, the Fourier-Laplace transform, some natural boundary-initial conditions, and familiar physical relations. We start with the stochastic equation of motion called the Langevin equation, develop its equivalent master equation called Klein-Kramers or Fokker-Planck equation, and consider the time-fractional generalization of the master equation. Once we derive the fractional master equation, then determine the expressions for the mean value of the variables or observables through some calculations and conditions. Finally, we use these expressions in the current density relation to obtain the average conductivity behavior.

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