28 Jan
2011
28 Jan
'11
11:29 a.m.
R[m_, n_] := Integrate[(1 - Cos[m p + n q])/(2 - Cos[p] - Cos[q]), {p, 0, 2 Pi}, {q, 0, 2 Pi}]/(2 Pi)^2 R[5,0] = (-3760 + 1203 pi)/(6 pi]) = 1.02580 R[4,3] = (48 - 5 pi)/(10 pi) = 1.02789 You can superimpose two symmetric circuit solutions, one where unit current is injected at [0,0] and the other where unit current is extracted at [1,0], to argue R[1,0] = 1/2. Veit On Jan 28, 2011, at 12:53 PM, Cordwell, William R wrote:
If I recall correctly, for the resistance between diagonal points, one might need Fourier series, but there is a simple method for nearest lattice points.