We extend a recently developed relation between the master equation describing the Parrondo’s games and the formalism of the Fokker–Planck equation to the case in which the games are modified with the introduction of “self–transition probabilities”. This accounts for the possibility that the capital can neither increase nor decrease during a game. Using this exact relation, we obtain expression...

In this article we study a system of nonlinear PDEs modelling the electrokinetics nematic electrolyte material consisting various ions species contained in liquid crystal. style='text-indent:20px;'>The evolution is described by coupling Nernst-Planck for concentrations with Maxwell's equation electrostatics governing electrostatic potential, Navier-Stokes velocity f...

We model the behavior of an ideal liquid junction, across a porous and possibly charged medium between two ion-containing solutions, by means of the Nernst–Planck equation for the stationary state, in conditions of local electroneutrality. An analytical solution of the equation was found long ago by Planck for the uncharged junction with only ions of valences +1 and −1. Other analytical results...

• Theory for ion transport in multicomponent electrolytes electrodialysis. Selective removal of nitrate over chloride is observed. Strategies to increase selectivity are evaluated. Increasing the membrane thickness results an increased selectivity. Decreasing charge density We analyze selective anions electrodialysis (ED) from a mixture where all ions monovalent, both experimentally, and by mod...

‎In this paper‎, ‎we obtain exact solutions involving parameters of some nonlinear PDEs in mathmatical physics; namely the one-‎dimensional modified complex Ginzburg-Landau equation by using the $ (G'/G) $ expansion method‎, homogeneous balance method, extended F-expansion method‎. ‎By ‎using homogeneous balance principle and the extended F-expansion, more periodic wave solutions expressed by j...