From: utzoo!decvax!harpo!floyd!cmcl2!philabs!mcvax!vub!edgard Newsgroups: net.math,net.physics Title: Request solutn.Poisson problem-Neumann bound.cond.-cil.coord. Article-I.D.: vub.109 Posted: Mon Feb 21 10:51:11 1983 Received: Sun Feb 27 02:19:38 1983 We are in search for the solution of the following problem: What is the potential distribution on the surface of a homogeneous and isotropic conducting cylinder containing one point current source and one point current sink (both of the same time in- variant magnitude)? The cylinder is surrounded by an insulating medium. We have formulated this problem in cylindrical coordinates (r,fi,z). In its simplest form (sink at the origin/source on the symmetry axis /infinite cylinder), the mathematical expression becomes: -Basic differential equation: LAPLACIAN(p)=constant*(delta(x'-1'z*a)-delta(x')) (Poisson problem) (x' and 1'z are vector quantities; 1'z=unit vector in z-direction; delta is a Dirac function) delta(x') can be written as (delta(r)*delta(z))/(pi*r) and delta(x'-1'z*a) = (delta(r)*delta(z-a))/(pi*r). (no delta(fi)-factor because of axial symmetry) -Boundary conditions: p=0 at infinity and dp | -- | = 0 (Neumann type boundary condition) dr | |r=R d (R=radius of cylinder; -- = partial derivative ) dr All attempts to compute a plausible solution for our problem failed. (Our method was based on "Classical Electrodynamics" of J.D.Jackson -the most complete work we know for do-it-yourself potential problem solving. We think that the weak point in our strategy was the decomposition of delta(r)/r into a Fourier-Bessel series since this function is very badly behaved for r=0) In the literature one can almost only find solutions to problems in spherical coordinates or with Dirichlet boundary conditions (p=p(r,fi,z) implied at the boundaries). Did someone resolve a similar problem yet? Does anyone know any literature, describing the solution of this problem or describing a solution strategy for this class of problems? Please mail solutions and/or references to: ..!philabs!mcvax!vub!edgard or: Edgard NYSSEN Brussels Free University (VUB) Fac. of Medicine - unit HART Laarbeeklaan 103 1090 Brussel BELGIUM