Neumann Boundary Problem Research Articles

Eigenvalue Comparison Theorems of Neumann Laplacian for Graphs.

In this paper, the spectrum of the Neumann Laplacian for a graph with boundary is studied. Two comparison theorems of the Neumann Laplacian for a graph are shown. Namely, the optimal upper and lower bounds of the first eigenvalue of the Neumann boundary problem of the combinatorial Laplacian for a graph with boundary are given.

Decomposition of Plane Waves into Irreducible Representations of Space Groups

Abstract Using a relation between representation theory of crystallographic space groups and a Dirichlet type of boundary problem for the Laplacian, we derive the solutions for the Dirichlet problem, as well as for a similar Neumann boundary problem, by a complete decomposition of plane waves into irreducible representations of a particular space group. This decomposition corresponds to a basis transformation in L2(Ω) and yields a new set of basis functions adapted to the symmetry of the lattice considered.

Asymptotic behavior of a reaction-diffusion system in bacteriology

This paper is concerned with the asymptotic behavior of the solution for a coupled system of reaction-diffusion equations which describes the bacteria growth and the diffusion of histidine and buffer concentrations. Under the basic boundary condition of Neumann type or mixed type the coupled system can have infinitely many steady-state solutions. The present paper gives some explicit information on the asymptotic limit of the time-dependent solution in relation to these steady states. This information exhibits some rather distinct properties of the solutions between the Neumann boundary problem and the Dirichlet or mixed boundary problem.

A boundary integral equation method for a Neumann boundary problem for force-free fields

A Neumann boundary value problem for the equation rot ν−λν=0 is considered in 29-1 and 29-2. The approach is by transforming the boundary value problem into an equivalent boundary integral equation deduced from a representation formula for solutions of rot ν−λν=0 based on the fundamental solution of the Helmholtz equation. In particular, for the two-dimensional case a detailed discussion of the integral equation is carried out including the approximate solution by numerical integration.

Direct solution of laplace's equation for coronal magnetic fields using line-of-sight boundary conditions

A new fast mathematical method is described for computing potential magnetic field solutions in the solar atmosphere from the observed line-of-sight component of the photospheric magnetic field. As in a standard Neumann boundary problem the orthogonality relation of the spherical harmonics is used to determine the coefficients of the harmonic expansion. This leads to a very simple set of recursion formulae that determines the harmonic coefficients successively.

Use of Ritz and Bubnow-Galerkin methods for calculation of inductance and impedance of conductors

It is shown that the Ritz and Bubnow-Galerkin methods can be applied for the calculation of the inductance and the impedance, respectively. Moreover it is shown that the calculation of the impedance by the Bubnow-Galerkin method is a generalization of the calculation of the inductance by the Ritz method in the case of a nonhomogeneous Neumann boundary problem. For the illustration of these methods the inductance of a rectangular ferromagnetic conductor and the inner impedance of a rectangular conductor placed in a semi-closed slot are calculated.