A discrete model on Sierpinski gasket substrate for a conserved current equation with a conservative noise

초록

A conserved discrete model on the Sierpinski gasket substrate is studied. The interface width W in the model follows the Family-Vicsek dynamic scaling form with growth exponent beta approximate to 0.0542, roughness exponent alpha approximate to 0.240 and dynamic exponent z approximate to 4.42. They satisfy a scaling relation alpha + z = 2z(rw), where z(rw) is the random walk exponent of the fractal substrate. Also, they are in a good agreement with the predicted values of a fractional Langevin equation partial derivative h/partial derivative t = del(zrw) [-nu del(zrw) h + lambda/2 (del(zrw/2) h)(2)] + eta(c), where eta(c) is a conservative noise.

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