On 1/6/08, Eugene Salamin <gene_salamin@yahoo.com> wrote:

... On a square grid of 1 ohm resistors, the effective resistance between the node at (0,0) and the node at (p,q) is given by the following expression.

R[p,q] = (1/(4 pi^2)) int (F(x,y), x=-pi..pi, y=-pi..pi),

F(x,y) = [1 - cos(p x + q y)] / [2 - (cos x + cos y)].

This is pretty much identical to formula (18) in Cserti, for the 2-D case. No doubt one could be convinced of its correctness simply by checking that it satisfied the Kirchhoff-inspired equations I quoted earlier [ my u^{kl} being your R[p,q] ] : [Lat1] u^{00} = 0; [Lat2] u^{01} = 1/2; [Lat3] \del^2 u^{kl} = 0 for (k,l) <> (0,0); where \del^2 u^{kl} == u^{k,l-1} + u^{k,l+1} + u^{k-1,l} + u^{k+1,l} - 4 u_{kl} . But how did you arrive at it; and exactly what assumptions did you make in order to do so? Fred Lunnon