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- Title
GENERAL SCALING RELATIONS IN ANOMALOUS DIFFUSION.
- Authors
FERREIRA, R. M. S.; LAPAS, L. C.; OLIVEIRA, F. A.
- Abstract
Diffusion regimes most frequently found in nature are described in terms of asymptotic behaviors. In this work, we use a generalization of the final-value theorem for Laplace transform in order to investigate the anomalous diffusion phenomenon for asymptotic times. We generalize the concept of the diffusion exponent, including a wide variety of asymptotic behaviors than the power law. A method is proposed to obtain the diffusion coefficient analytically through the introduction of a time scaling factor, λ. We obtain as well an exact expression for λ, which makes possible to describe all diffusive regimes featuring a universal parameter determined by the diffusion exponent. We show the existence of two kinds of ballistic diffusion, ergodic and non-ergodic. The method is general and may be applied to many types of stochastic problem.
- Subjects
ANOMALOUS Hall effect; HEAT equation; ASYMPTOTIC distribution; GENERALIZATION; THERMAL diffusivity; LAPLACE transformation; TIME factors (Learning); BALLISTICS
- Publication
Acta Physica Polonica B, 2013, Vol 44, Issue 5, p1085
- ISSN
0587-4254
- Publication type
Article
- DOI
10.5506/APhysPolB.44.1085