Random deposition with surface relaxation model in u v flower networks

Abstract

Abstract Random deposition with a relaxation model in (u, v) flower networks is studied. In a (2, 2) flower network, the surface width W(t, N) was found to grow as b ln t in the early period and follows a ln N in the saturated regime, where t and N are the evolution time and the number of nodes in the network, respectively. The dynamic exponent z, obtained by the relation z = a/b, was z ≈ 2.11(10), which is consistent with the random walk exponent d w = 2 in the network. For u + v ⩾ 5(u ⩾ 2, v ⩾ u), i.e. the (2, 3) and (3, 3) flower networks, the surface width grows following power-law behavior with some corrections, where the growth exponent β and roughness exponent α are controlled by spectral dimension d s and fractal dimension d f of the substrate network.