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With already demonstrated in previous work the equations that describe the space dependence of the electric potential are determined by the solution of the equation of Poisson-Boltzmann. In this work we consider these solutions for the membrane of the human neuron, using a model simplified for this structure considering the distribution of electrolytes in each side of the membrane, as well as the effect of glycocalyx and the lipidic bilayer. It was assumed that on both sides of the membrane the charges are homogeneously distributed and that the potential depends only on coordinate z.
We consider the problem of computing approximate solution of Poisson equation in the low-parametric tensor formats. We propose a new algorithm to compute the solution based on the cross approximation algorithm in the frequency space, and it has bette
In numerical simulations of many charged systems at the micro/nano scale, a common theme is the repeated solution of the Poisson-Boltzmann equation. This task proves challenging, if not entirely infeasible, largely due to the nonlinearity of the equa
The Chapman-Enskog method of solution of the relativistic Boltzmann equation is generalized in order to admit a time-derivative term associated to a thermodynamic force in its first order solution. Both existence and uniqueness of such a solution are
The Poisson-Boltzmann equation is a widely used model to study the electrostatics in molecular solvation. Its numerical solution using a boundary integral formulation requires a mesh on the molecular surface only, yielding accurate representations of
A non-linear Boltzmann equation describing the time evolution of a partonic system in the central rapidity region after a heavy ion collision is solved numerically. A particular model of the collinear logarithmic divergences due to small angle scatte