Random walk diffusion model for a restricted solid-on-solid condition

Random walk diffusion model with restricted solid on solid condition on fractal substrates

“…The scaling plot of W 2 (L, t)/L 2α as a function of t/L z with α = 0.92 and z = 3.4 is shown in figure 4, where the good data collapse is obtained. Combining with the information z rw ≈ 2.32, and d f = 1.58 of the Sierpinski gasket, we can predict β ≈ 0.282, α ≈ 1.02, and z ≈ 3.62 from equation (11). Our numerical results of the exponents are a little smaller than, but consistent with, the predicted values.…”

“…There also exists a scaling relation α + z = 4. Through the study of the random walk diusion model on regular substrates, we found the values of the growth exponents which are in good agreement with the results obtained from equation (7) [11]. It is interesting that the ordinary RSOS growth model without any diusion [4,5] has the KPZ nonlinearity (∇h) 2 and the model with random walk diusion has the conserved nonlinearity ∇ 2 (∇h) 2 of equation (5).…”

“…There are some other studies in conserved growth models, where the deposited particle is attached to the surface without evaporation [7][8][9][10]. Recently we introduced a modified RSOS model with random walk diusion on a regular lattice [11]. The growth algorithm of the model is to deposit a particle on a randomly selected site.…”

“…Because the random walk of the deposited particle has some relevance to the diusion process, we expect that the model can produce a conserved non-linear term λ∇ 2 (∇h) 2 [11]. Actually there is a conserved KPZ equation [7,8,10,13], so called Lai, Das Sarma and Villain equation…”