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Probability distributions for kinetic roughening in the Kardar-Parisi-Zhang growth with long-range temporal and spatial correlations by Chang, Zhichao; Xia, Hui is a scholarly article available to read on EtoBox.

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We investigate numerically the effects of long-range temporal and spatial correlations based on the rescaled distributions of the squared interface width $W^2(L,t)$ and the interface height $h(x,t)$ in the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) growth system within the early growth regimes. Through extensive numerical simulations, we find that long-range temporally correlated noise could not significantly impact the distribution form of the interface width. Generally, $W^2(L,t)$ obeys approximately lognormal distribution when the temporal correlation exponent $\theta \ge 0$. On the other hand, the effects of long-range spatially correlated noise are evidently different from the temporally correlated case. Our results show that, when the spatial correlation exponent $\rho \le 0.20$, the distribution forms of $W^2(L,t)$ approach the lognormal distribution, and when $\rho > 0.20$, the distribution becomes more asymmetric, steep, and fat-tailed, and tends to an unknown distribution form. As a comparison, probability distributions of the interface height are also provided in the temporally and spatially correlated KPZ system, exhibiting quite different characteristics from each oth

Author

Chang, Zhichao; Xia, Hui

Published

2022

Language

EN