On the relation between a fluctuating diffusion equation and long time tails in stationary random media

1986 ◽  
Vol 42 (5-6) ◽  
pp. 935-940 ◽  
Author(s):  
Alan K. Harrison ◽  
Robert Zwanzig
Keyword(s):  
Diffusion Equation ◽  
Random Media ◽  
Long Time Tails ◽  
Long Time

Long time tails in stationary random media II: Applications

1984 ◽  
Vol 35 (3-4) ◽  
pp. 413-442 ◽  
Author(s):  
J. Machta ◽  
M. H. Ernst ◽  
H. van Beijeren ◽  
J. R. Dorfman
Keyword(s):  
Random Media ◽  
Long Time Tails ◽  
Long Time

scholarly journals Long time tails in stationary random media. I. Theory

1984 ◽  
Vol 34 (3-4) ◽  
pp. 477-495 ◽  
Author(s):  
M. H. Ernst ◽  
J. Machta ◽  
J. R. Dorfman ◽  
H. van Beijeren
Keyword(s):  
Random Media ◽  
Long Time Tails ◽  
Long Time

Experimental observation of “long time tails”?

1976 ◽  
Vol 55 (7) ◽  
pp. 391-392 ◽  
Author(s):  
J.P. Boon ◽  
A. Bouiller
Keyword(s):  
Experimental Observation ◽  
Long Time Tails ◽  
Long Time

NUMERICAL SIMULATIONS FOR SPACE–TIME FRACTIONAL DIFFUSION EQUATIONS

2013 ◽  
Vol 10 (02) ◽  
pp. 1341001 ◽  
Author(s):  
LEEVAN LING ◽  
MASAHIRO YAMAMOTO
Keyword(s):  
Diffusion Equation ◽  
Fractional Derivative ◽  
Time Derivative ◽  
Fundamental Solutions ◽  
Fractional Diffusion ◽  
Space Time ◽  
Fractional Diffusion Equation ◽  
Long Time ◽  
Liouville Fractional Derivative ◽  
Time Fractional Diffusion Equation

We consider the solutions of a space–time fractional diffusion equation on the interval [-1, 1]. The equation is obtained from the standard diffusion equation by replacing the second-order space derivative by a Riemann–Liouville fractional derivative of order between one and two, and the first-order time derivative by a Caputo fractional derivative of order between zero and one. As the fundamental solution of this fractional equation is unknown (if exists), an eigenfunction approach is applied to obtain approximate fundamental solutions which are then used to solve the space–time fractional diffusion equation with initial and boundary values. Numerical results are presented to demonstrate the effectiveness of the proposed method in long time simulations.

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