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Entropy 2017, 19(1), 42; doi:10.3390/e19010042

Intermittent Motion, Nonlinear Diffusion Equation and Tsallis Formalism

1
Departamento de Física, Universidade Estadual de Ponta Grossa, Ponta Grossa, PR 87030-900, Brazil
2
National Institute of Science and Technology for Complex Systems, Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, RJ 22290-180, Brazil
3
Departamento de Física, Universidade Federal do Rio Grande do Norte, Natal, RN 59072-970, Brazil
4
Departamento de Engenharia Química, Universidade Federal do Paraná, Curitiba, PR 81531-990, Brazil
5
Departamento de Física, Universidade Estadual de Maringá, Maringá, PR 87020-900, Brazil
6
National Institute of Science and Technology on Complex Fluids, Instituto de Física da USP, São Paulo, SP 05508-090, Brazil
*
Author to whom correspondence should be addressed.
Academic Editors: Kevin H. Knuth and Angelo Plastino
Received: 25 November 2016 / Revised: 15 January 2017 / Accepted: 17 January 2017 / Published: 21 January 2017
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Abstract

We investigate an intermittent process obtained from the combination of a nonlinear diffusion equation and pauses. We consider the porous media equation with reaction terms related to the rate of switching the particles from the diffusive mode to the resting mode or switching them from the resting to the movement. The results show that in the asymptotic limit of small and long times, the spreading of the system is essentially governed by the diffusive term. The behavior exhibited for intermediate times depends on the rates present in the reaction terms. In this scenario, we show that, in the asymptotic limits, the distributions for this process are given by in terms of power laws which may be related to the q-exponential present in the Tsallis statistics. Furthermore, we also analyze a situation characterized by different diffusive regimes, which emerges when the diffusive term is a mixing of linear and nonlinear terms. View Full-Text
Keywords: anomalous diffusion; nonlinear diffusion equation; Tsallis entropy anomalous diffusion; nonlinear diffusion equation; Tsallis entropy
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MDPI and ACS Style

Lenzi, E.K.; da Silva, L.R.; Lenzi, M.K.; dos Santos, M.A.F.; Ribeiro, H.V.; Evangelista, L.R. Intermittent Motion, Nonlinear Diffusion Equation and Tsallis Formalism. Entropy 2017, 19, 42.

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