The generalised resistance between connected points a distance L apart on fractal networks of nonlinear (V approximately Ialpha) resistors scales as Lzeta (/alpha ). It is shown that zeta ( alpha ) for alpha =- infinity , -1, 0-, 0+, 1 and infinity , describes physically relevant geometrical properties and d zeta /d alpha <or=0. For percolating clusters approximants are given for zeta for - infinity < alpha < infinity in 2-6 dimensions. For alpha <0 a family of solutions to Kirchhoff's equations exists, reminiscent of metastable states in spin glasses.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy (all)