A new theory for anomalous diffusion with a bimodal flux distribution

作者：Bevilacqua L^*; Galeao A C N R; Simas J G; Rio Doce Ana Paula

来源：Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2013, 35(4): 431-440.

DOI：10.1007/s40430-013-0041-y

• Anomalous diffusion
• Multiflux
• Retention
• Fourth order PDE

This paper deals with a new governing equation for anomalous diffusion encompassing a large spectrum of phenomena with particular attention on delaying processes. The analysis starts with a discrete approach and a law of evolution introducing a partial retention of the diffusing particles at each time step. The resulting differential equation assuming that the concentration function belongs to class C-3 is a fourth-order differential equation. To fit this result into the framework of a new theory, a bi-modal flux distribution for the diffusion process associated with two energy states is proposed. The first energy state is related to the set of particles flowing according to the Fick%26apos;s law and the complementary set follows a new law. Two key parameters are introduced, namely, a parameter beta indicating the fraction of the particles in the principal energy state and a parameter R controlling the effect of the secondary flux. Some examples are presented characterizing different types of phenomena as function of the relative values of beta and R. The necessary conditions for the retention behavior are discussed for some particular cases.

• 出版日期2013-11