Poisson-Nernst-Planck (PNP) systems are considered in the case of vanishing permanent charge. A detailed case study, based on natural categories described by system boundary conditions and flux, is carried out via simulation and singular perturbation analysis. Our results confirm the rich structure inherent in these systems. A natural quantity, the quotientâ€¦ (More)

together with suitable boundary conditions is examined. It is shown that n + 1 spectra associated with n + 1 distinct sets of boundary conditions are required in order to reconstruct the unknown coefficients pl, . . . ,p , . The sixth order case is analogous to the eigenvalue problem for the spheroidal modes of vibrations of earth which have been used toâ€¦ (More)

Syncytial tissues consist of many cells whose intracellular spaces are electrically coupled one to another. Such tissues typically include narrow, tortuous extracellular space and often have specialized membranes at their outer surface. We derive differential equations to describe the potentials induced when a sinusoidal or steady current is applied to theâ€¦ (More)

Ions enter cells through pores in proteins that are holes in dielectrics. The energy of interaction between ion and charge induced on the dielectric is many kT, and so the dielectric properties of channel and pore are important. We describe ionic movement by (three-dimensional) Nemst-Planck equations (including flux and net charge). Potential is describedâ€¦ (More)

An analysis is presented of the displacement of potential recorded when one microelectrode is used both to apply current to and record potential from a spherical cell. There are three significant components of the displacement in potential: a component produced inside the microelectrode, a time-independent component representing the spatially nonuniformâ€¦ (More)