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The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Generalized fractional diffusion equations for accelerating subdiffusion and truncated Lévy flights
A V Chechkin1, V Yu Gonchar, R Gorenflo
1Institute for Theoretical Physics NSC KIPT, Akademicheskaya street, 1, 61108 Kharkov, Ukraine.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2008
Summary
Diffusion equations with distributed order fractional derivatives describe anomalous processes. This study explores their use for phenomena becoming less anomalous over time, like accelerating subdiffusion and decelerating superdiffusion.
Area of Science:
- Physics
- Mathematics
- Complex Systems
Background:
- Fractional diffusion equations model anomalous diffusion where displacement scales with time.
- Distributed order fractional derivatives describe processes lacking simple scaling.
Purpose of the Study:
- To investigate diffusion equations with distributed order fractional derivatives for phenomena becoming less anomalous over time.
- To model accelerating subdiffusion and decelerating superdiffusion.
Main Methods:
- Analysis of diffusion equations with distributed order fractional derivatives.
- Examination of specific examples for accelerating subdiffusion and decelerating superdiffusion.
- Mathematical modeling of time-varying diffusion exponents and Lévy stable distribution evolution.
Main Results:
- Demonstrated effectiveness of the proposed equations for accelerating subdiffusion with time-varying diffusion exponents.
- Showcased the evolution of power-law truncated Lévy stable distributions towards a Gaussian core with power-law tails.
- Identified that extreme orders dominate asymptotic behavior in the special case of two different orders.
Conclusions:
- Distributed order fractional diffusion equations provide a framework for describing anomalous diffusion that becomes less anomalous over time.
- These models capture complex relaxation and diffusion dynamics, including evolving anomalous exponents.
- The findings offer insights into the behavior of complex systems exhibiting time-dependent anomalous diffusion.
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