Structure and thermodynamics in restricted primitive model electrolytes are examined using three recently developed versions of a linear form the modified Poisson-Boltzmann equation. Analytical expressions for osmotic coefficient electrical part mean activity obtained results coefficients compared with that from more established spherical approximation, symmetric Poisson-Boltzmann, theories, av...

Stein’s (1972) method is a very general tool for assessing the quality of approximation of the distribution of a random element by another, often simpler, distribution. In applications of Stein’s method, one needs to establish a Stein identity for the approximating distribution, solve the Stein equation and estimate the behaviour of the solutions in terms of the metrics under study. For some St...

We are concerned with the study of the diffusion and homogenization approximation of the Boltzmann-Poisson system in presence of a spatially oscillating electrostatic potential. By analyzing the relative entropy, we prove uniform energy estimate for well prepared boundary data. An averaging lemma and two scale convergence techniques are used to prove rigorously the convergence of the scaled Bol...