Victor Barcilon

Nonlinear waves in compacting media

An investigation of the mathematical model of a compacting medium proposed by McKenzie (1984) for the purpose of understanding the migration and segregation of melts in the Earth is presented. The numerical observation that the governing equations admit solutions in the form of nonlinear one-dimensional waves of permanent shape is confirmed analytically. The properties of these solitary waves are presented, namely phase speed as a function of melt content, nonlinear interaction and conservation quantities. The information at hand suggests that these waves are not solitons.

Qualitative properties of steady-state Poisson-Nernst-Planck systems: perturbation and simulation study

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 quotient of the Debye and characteristic length scales, serves as the singular perturbation parameter. The regions of validity are carefully analyzed by critical comparisons and contrasts between the simulation and the perturbation solution, which can be represented in closed form.

Ion flow through narrow membrane channels: part I

This paper is devoted to the study of the electrostatic potential in a composite dielectric medium. The geometry consists of a membrane-like layer with one dielectric constant, perforated by a hole filled with a material with a different dielectric constant. The field is due to a known, but otherwise arbitrary, distribution

Solitary waves in magma dynamics

f(z)

Inverse Problem for the Vibrating Beam in the Free--Clamped Configuration

of charges in the hole, where z is the coordinate along the axis of the hole. The induced surface charge at the interface between the two media is found as an asymptotic series in the small aspect ratio

Iterative solution of the inverse Sturm‐Liouville problem

\alpha

Steady flow of a viscous ice stream across a no-slip/free-slip transition at the bed

of the hole, for the case in which

Explicit Solution of the Inverse Problem for a Vibrating String.

f(z)

Barrier crossing with concentration boundary conditions in biological channels and chemical reactions

vanishes at the endpoints and is

On the Multiplicity of Solutions of the Inverse Problem for a Vibrating Beam

C^1