We model fluid-fluid displacement in d = 2 by a diffusion-limited-aggregation (DLA) algorithm which takes random capillary forces into account. Interpore surface tension is neglected. The invading fluid is nonviscous. We find a crossover length L c . On length scales much smaller (larger) than L f , invasion percolation (DLA) patterns are obtained. We argue by scaling, and check by simulations, that L c -(Ap/Ca) s ; Ap stands for a measure of spatial variations of the capillary pressure, Ca is the capillary number, and D s is the interface fractal dimension on small length scales (we find D s ~ 1.3).

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We investigate the magneto-conductance (MC) anisotropy in the variable range hopping regime, caused by quantum interference effects in three dimensions. When no spin-orbit scattering is included, there is an increase in the localization length (as in two dimensions), producing a large positive MC. By contrast, with spin-orbit scattering present, there is no change in the localization length, and only a small increase in the overall tunneling amplitude.The numerical data for small magnetic fields B, and hopping lengths t, can be collapsed by using scaling variables B ⊥ t 3/2 , and B t in the perpendicular and parallel field orientations respectively. This is in agreement with the flux through a 'cigar'-shaped region with a diffusive transverse dimension proportional to √ t. If a single hop dominates the conductivity of the sample, this leads to a characteristic orientational 'finger print' for the MC anisotropy.However, we estimate that many hops contribute to conductivity of typical

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