A model of random deposition with relaxation on fractal substrates

초록

A model of random deposition with relaxation on both Sierpinski gasket and checkerboard fractal substrates is studied. The interface width W grows as t(beta) at early time t and it follows La for the saturated regime t >> L(z), where L is the system size. We obtain beta approximate to 0.158, alpha approximate to 0.374 for the Sierpinski gasket and beta approximate to 0.203, alpha approximate to 0.507 for the checkerboard fractal. The dynamic exponent z approximate to 2.35 for the Sierpinski gasket and z approximate to 2.50 for the checkerboard fractal were obtained by using the relation z = alpha/beta. They satisfy the scaling relation 2 alpha+ d(f) = z, where d(f) is the fractal dimension of the substrate, and they are in good agreement with the predictions of a fractional Langevin equation.

키워드