In this work, we are interested in effects of a simple profile of permanent charges on ionic flows. We determine when a permanent charge produces current reversal. We adopt the classical Poisson-NernstPlanck models of ionic flows for this study. The starting point of our analysis is the recently developed geometric singular perturbation approach for Poisson-Nernst-Planck models. Under the setti...

In biological systems, intercellular communication is mediated by membrane proteins and ion channels that regulate traffic of ions and small molecules across cell membranes. A bioelectronic device with ion channels that control ionic flow across a supported lipid bilayer (SLB) should therefore be ideal for interfacing with biological systems. Here, we demonstrate a biotic-abiotic bioprotonic de...

Oxygen reduction on the surface of a rotating disk electrode RDE in 0.5 M H2SO4 is simulated by including mass transfer, adsorption, and charge transfer. A generalized model for the adsorption and reaction of several species is introduced. The oxygen reduction reaction is simulated as a limiting case where oxygen is the only species adsorbed, and oxygen reduction is the only reaction that takes...

Recently measured water permeability through bilayers of different lipids is most strongly correlated with the area per lipid A rather than with other structural quantities such as the thickness. This paper presents a simple three-layer theory that incorporates the area dependence in a physically realistic way and also includes the thickness as a secondary modulating parameter. The theory also ...

We investigate a system of N Brownian particles with the Coulomb interaction in any dimension d ≥ 2, and we assume that the initial data are independent and identically distributed with a common density ρ0 satisfying ∫ Rd ρ0 ln ρ0 dx < ∞ and ρ0 ∈ L 2d d+2 (Rd ) ∩ L1(Rd, (1+ |x|2) dx). We prove that there exists a unique global strong solution for this interacting partsicle system and there is n...

A multielectrode setup for protein OFFGEL electrophoresis that significantly improves protein separation efficiency has been developed. Here, the electric field is applied by segments between seven electrodes connected in series to six independent power supplies. The aim of this strategy is to distribute evenly the electric field along the multiwell system, and as a consequence to enhance elect...

The dielectric boundary force (DBF) is the force that induced charges at dielectric boundaries exert on the charge that induced them. The DBF is present in any electrostatic problem with a non-uniform dielectric constant, and is important in the case of charged particles near dielectric boundaries. Yet, it is absent in common continuum theories of charge distribution and of charge transport, su...

We deal with the transmembrane sodium diffusion in a nerve. We study amathematical model of a nerve fibre in response to an imposed extracellular stimulus. The presentedmodel is constituted by a diffusion-drift vectorial equation in a bidomain, that is, two parabolic equations defined in each of the intraand extra-regions. This system of partial differential equations can be understood as a red...

Conformal mapping has been applied mostly to harmonic functions, i.e. solutions of Laplace’s equation. In this paper, it is noted that some other equations are also conformally invariant and thus equally well suited for conformal mapping in two dimensions. In physics, these include steady states of various nonlinear diffusion equations, the advection-diffusion equations for potential flows, and...

Conformal mapping has been applied mostly to harmonic functions, i.e. solutions of Laplace’s equation. In this paper, it is noted that some other equations are also conformally invariant and thus equally well suited for conformal mapping in two dimensions. In physics, these include steady states of various nonlinear diffusion equations, the advection-diffusion equations for potential flows, and...