Intermittent Motion, Nonlinear Diffusion Equation and Tsallis Formalism

Intermittent Motion, Nonlinear Diffusion Equation and Tsallis Formalism

E. K. Lenzi, L. R. da Silva, M. K. Lenzi, M. A. F. dos Santos, H. V. Ribeiro, L. R. Evangelista, Entropy 19, 42 (2017). PDF | DOI

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.