Bi-flux theory applied to the dispersion of particles in anisotropic substratum

Nonlinear Galerkin finite element methods for fourth-order Bi-flux diffusion model with nonlinear reaction term

“…For sufficient large time t > t * the singularity fades out and the concentration becomes positive for all points of the interval [−4, 4]. This singular behavior is characteristic of the fourth order equation as reported in the references (Bevilacqua et al 2016;Jiang et al 2018). The long time behavior tends to remove the negative values for the Bi-flux model.…”

“…A numerical solution for the Bi-flux diffusion model leading to a fourth-order PDE (Bevilacqua et al 2011(Bevilacqua et al , 2013(Bevilacqua et al , 2016Jiang et al 2018) was developed in this paper. With the Bi-flux approach to reaction diffusion behaviors it is possible to simulate several peculiar isotropic diffusion phenomena in several scientific fields, as biology and chemistry.…”

“…The Bi-flux approach to diffusion problems has been recently proposed, using a discrete formulation (Bevilacqua et al 2011(Bevilacqua et al , 2013(Bevilacqua et al , 2016Jiang et al 2018), to deal with peculiar evolution processes. The theory leads to the bifurcation of the flux into two distinct streams corresponding to two independent potentials.…”

Energy exchange in a bi-flux diffusion process consisting of particles of the same nature split into two distinct microstates

“…Several cases of particles sensitive to particular disturbances in the dispersing medium can be solved with the bi-flux equation. The presence of a pheromone in a restrict region of the dispersing medium is a typical example [18]. The fourth order term is introduced to take into account the disturbance introduced by the external player in a restrict region.…”

Estudo do Coeficiente de Difusão Secundária em Problema de Difusão com Fluxo Bimodal

“…Resultados obtidos da simulação da Eq. (1.3), ou da sua versão em duas dimensões, foram obtidos por diversos autores empregando variadas metodologias para solução numérica de equações diferenciais, tais como o Método de Volumes Finitos [24] para o modelo unidimensional e estacionário, a Técnica da Transformada Integral Generalizada [23] e o Método de Elementos Finitos [9]. Contudo, em casos já documentados [3,8,19], valores fisicamente irreais foram observados em decorrência de uma aceleração inicial no fluxo associadaàs condições inicial e de contorno.…”