Kinetic roughening and nontrivial scaling in the Kardar–Parisi–Zhang growth with long-range temporal correlations

Abstract

Long-range spatiotemporal correlations may play important roles in nonequilibrium surface growth process. In order to explore the effects of long-range temporal correlation on dynamic scaling of growing surfaces, we carry out extensive numerical simulations of the (1+1)-and (2+1)-dimensional Kardar-Parisi-Zhang (KPZ) growth system in the presence of temporally correlated noise, and compare our results with previous theoretical predictions and numerical simulations. We find that surface morphologies are obviously affected with long-range temporal correlations, and as the temporal correlation exponent increases, the KPZ surfaces develop gradually faceted patterns in the saturated growth regimes. Our results show that the temporal correlated KPZ system displays evidently nontrivial dynamic properties when 0 0.5   , the characteristic roughness exponents satisfy s    , and loc  exhibiting non-universal scaling within local window sizes, which differs with the existing dynamic scaling hypotheses, both in the (1+1)-and (2+1)-dimensions.

Random Walk on a Rough Surface: Renormalization Group Analysis of a Simple Model

“…However, we did not find a nontrivial point that would correspond to the frozen limit (13). This follows from the fact that the function β g in (30) becomes trivial for u → 0: β g = −εg.…”

“…Over decades, stochastic growth processes, kinetic roughening phenomena and fluctuating surfaces or interfaces have been attracting constant attention. The most prominent examples include deposition of a substance on a surface and the growth of the corresponding phase boundary; propagation of flame, smoke, and solidification fronts; growth of vicinal surfaces and bacterial colonies; erosion of landscapes and seabed profiles; molecular beam epitaxy and many others; see [1]- [13] and references therein.…”

Field-Theoretic Renormalization Group in Models of Growth Processes, Surface Roughening and Non-Linear Diffusion in Random Environment: Mobilis in Mobili

“…Numerous modifications of the original KPZ equation have been proposed: "colored" noise f with finite correlation time [90,91], "quenched" h-dependent and time-independent noise [92,93], vector or matrix field h [94][95][96], random coupling constant [66], inclusion of superdiffusion [97], long-range temporal correlations [98], inclusion of anisotropy [92,[99][100][101], conservation law for the field h [102][103][104], modified non-linearity V(h) [105] and so on.…”

Random Walk on a Rough Surface: Renormalization Group Analysis of a Simple Model

“…The point (iv) corresponds to the limiting case (13) when the field h, in comparison with θ, behaves as if it was δ correlated in time.…”

“…Over decades, stochastic growth processes, kinetic roughening phenomena, and fluctuating surfaces or interfaces have been attracting constant attention. The most prominent examples include the deposition of a substance on a surface and the growth of the corresponding phase boundary; propagation of flame, smoke, and solidification fronts; growth of vicinal surfaces and bacterial colonies; erosion of landscapes and seabed profiles; molecular beam epitaxy; and many others, see [1][2][3][4][5][6][7][8][9][10][11][12][13] and references therein.…”