scholarly journals Fronts in anomalous diffusion–reaction systems

2013 ◽  
Vol 371 (1982) ◽  
pp. 20120179 ◽  
Author(s):  
V. A. Volpert ◽  
Y. Nec ◽  
A. A. Nepomnyashchy
Keyword(s):  
Anomalous Diffusion ◽  
Diffusion Reaction ◽  
Lévy Flights ◽  
Reaction Systems ◽  
Unstable Phase ◽  
Levy Flights ◽  
Recent Developments ◽  
Front Dynamics

A review of recent developments in the field of front dynamics in anomalous diffusion–reaction systems is presented. Both fronts between stable phases and those propagating into an unstable phase are considered. A number of models of anomalous diffusion with reaction are discussed, including models with Lévy flights, truncated Lévy flights, subdiffusion-limited reactions and models with intertwined subdiffusion and reaction operators.

Anomalous diffusion and Lévy flights in channeling

2004 ◽  
Vol 324 (1) ◽  
pp. 82-85 ◽  
Author(s):  
A.A Greenenko ◽  
A.V Chechkin ◽  
N.F Shul'ga
Keyword(s):  
Anomalous Diffusion ◽  
Lévy Flights ◽  
Levy Flights

REACTION-FRONT DYNAMICS IN A+B→C WITH INITIALLY-SEPARATED REACTANTS

Fractals ◽  
1993 ◽  
Vol 01 (03) ◽  
pp. 405-415 ◽  
Author(s):  
S. HAVLIN ◽  
M. ARAUJO ◽  
H. LARRALDE ◽  
A. SHEHTER ◽  
H.E. STANLEY
Keyword(s):  
Reaction Front ◽  
Reaction Rate ◽  
Reaction System ◽  
Diffusion Reaction ◽  
Dimensional System ◽  
Scaling Exponent ◽  
One Dimensional ◽  
Recent Developments ◽  
The One ◽  
Front Dynamics

We review recent developments in the study of the diffusion reaction system of the type A+B→C in which the reactants are initially separated. We consider the case where the A and B particles are initially placed uniformly in Euclidean space at x>0 and x<0 respectively. We find that whereas for d≥2 a single scaling exponent characterizes the width of the reaction zone, a multiscaling approach is needed to describe the one-dimensional system. We also present analytical and numerical results for the reaction rate on fractals and percolation systems.

scholarly journals Lévy flights and anomalous diffusion in the stratosphere

2000 ◽  
Vol 105 (D10) ◽  
pp. 12295-12302 ◽  
Author(s):  
Kyong-Hwan Seo ◽  
Kenneth P. Bowman
Keyword(s):  
Anomalous Diffusion ◽  
Lévy Flights ◽  
Levy Flights

scholarly journals Two-Species Reaction-Diffusion System: the Effect of Long-Range Spreading

2020 ◽  
Vol 226 ◽  
pp. 02005
Author(s):  
Šarlota Birnšteinová ◽  
Michal Hnatič ◽  
Tomáš Lučivjanský
Keyword(s):  
Long Range ◽  
Anomalous Diffusion ◽  
Particle Density ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Group Method ◽  
Theoretic Approach ◽  
Lévy Flights ◽  
Levy Flights

We study fluctuation effects in the two-species reaction-diffusion system A + B → Ø and A + A → (Ø, A). In contrast to the usually assumed ordinary short-range diffusion spreading of the reactants we consider anomalous diffusion due to microscopic long-range hops. In order to describe the latter, we employ the Lévy stochastic ensemble. The probability distribution for the Lévy flights decays in d dimensions with the distance r according to a power-law r−d−σ. For anomalous diffusion (including Lévy flights) the critical dimension dc = σ depends on the control parameter σ, 0 < σ ≤ 2. The model is studied in terms of the field theoretic approach based on the Feynman diagrammatic technique and perturbative renormalization group method. We demonstrate the ideas behind the B particle density calculation.

Observation of anomalous diffusion and Lévy flights in a two-dimensional rotating flow

1993 ◽  
Vol 71 (24) ◽  
pp. 3975-3978 ◽  
Author(s):  
T. H. Solomon ◽  
Eric R. Weeks ◽  
Harry L. Swinney
Keyword(s):  
Anomalous Diffusion ◽  
Rotating Flow ◽  
Two Dimensional ◽  
Lévy Flights ◽  
Levy Flights
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