A population model with nonlinear diffusion

AbstractA model is presented for a single species population moving in a limited one-dimensional environment. The birth-death process is specialized by assuming a constant death modulus and a birth modulus which is an exponential in the age. The diffusion mechanism is nonlinear and results in a problem for the space population density which has a degenerate parabolic form and is similarly to the porous media equation. It is shown that the effect of the nonlinearity in the diffusion is to produce an approach to steady state even when the process is birth dominant. The interaction of the birth-death and diffusion processes is studied and is shown to yield a modified birth-death mechanism which is both time and space dependent

Solution procedures for three-dimensional eddy current problems

AbstractThe problem under consideration is that of the scattering of time periodic electromagnetic fields by metallic obstacles. A common approximation here is that in which the metal is assumed to have infinite conductivity. The resulting problem, called the perfect conductor problem, involves solving Maxwell's equations in the region exterior to the obstacle with the tangential component of the electric field zero on the obstacle surface. In the interface problem different sets of Maxwell equations must be solved in the obstacle and outside while the tangential components of both electric and magnetic fields are continuous across the obstacle surface. Solution procedures for this problem are given. There is an exact integral equation procedure for the interface problem and an asymptotic procedure for large conductivity. Both are based on a new integral equation procedure for the perfect conductor problem. The asymptotic procedure gives an approximate solution by solving a sequence of problems analogous to the one for perfect conductors

A skin effect approximation for eddy current problems

SIGLEDEGerman

A boundary element method for an exterior problem for three-dimensional Maxwell's equations

SIGLEDEGerman