Diffusion in poro‐plastic media

A model is developed for the flow of a slightly compressible fluid through a saturated inelastic porous medium. The initial‐boundary‐value problem is a system that consists of the diffusion equation for the fluid coupled to the momentum equation for the porous solid together with a constitutive law which includes a possibly hysteretic relation of elasto‐visco‐plastic type. The variational form of this problem in Hilbert space is a non‐linear evolution equation for which the existence and uniqueness of a global strong solution is proved by means of monotonicity methods. Various degenerate situations are permitted, such as incompressible fluid, negligible porosity, or a quasi‐static momentum equation. The essential sufficient conditions for the well‐posedness of the system consist of an ellipticity condition on the term for diffusion of fluid and either a viscous or a hardening assumption in the constitutive relation for the porous solid. Copyright © 2004 John Wiley & Sons, Ltd.     

Functionalization of substituted 2-(1H)pyridones. II. Synthetic pathways to c-6 modified 3-cyano- and 3-carboxy-2-(1H)pyridones from a common precursor

Starting from readily available 1,2-dihydro-6-methyl-2-oxo-3-pyridinecarbonitrile, 1, viable synthetic pathways to a number of C-6 functionalized 1,2-dihydro-2-oxo-3-pyridinecarbonitriles and corresponding acids are presented. Through the utilization of dianion chemistry, the C-6 methyl substituent is selectively functionalized to three different oxidation levels.     

Thin-film capacitance models

Models for distributed capacitance in a thin film are derived in the form of a system of local RC diffusion equations coupled by a global elliptic equation. Such models contain the local geometry of the distributed capacitance on which charge pis stored and the exchange of current flux on its interface with the medium. Certain singular limits are characterized, and the resulting degenerate initial-boundary-value problems are shown to be well posed.     

Self-segregation of competitive chaotic populations

The dynamical behavior of species competing for a common resource is studied with a reaction-diffusion system based on cubic autocatalysis. Randomly seeded populations self-segregate to form a complex network of domains separated by distinct interfaces. For chaotic populations in one-dimensional media, the interfaces exhibit irregular motions on long time scales. In two-dimensional media, the interface motions are governed by curvature-induced drift.     

Homogenization of the layered medium equation

A new partial differential equation to be called the layered medium equation is introduced, and it is proved that certain relevant initial or periodic boundary conditions give well-posed problems. Then, the homogenized limit of the layered medium equation is studied. It is shown to be preserved in limit in the limit in the physical problem in which the coefficients that arise from the dielectric layer are both proportional to thickness. Otherwise, a non-local problem is obtained as the limiting form