The universal scaling properties of the original and modified versions of the Villain–Lai–Das Sarma (VLDS) growth system are investigated numerically in both (1 + 1) and (2 + 1) dimensions. The modified VLDS equation with instability suppression by an exponentially decreasing function is equivalent to the VLDS with infinitely many weakly relevant nonlinear terms (VLDS_∞). The growth instability and scaling properties are discussed based on the modification of the VLDS growth system. Our results show that the existence of infinitely many weakly relevant nonlinear terms in the modified VLDS system could: (i) lead to nontrivial scaling behavior in a generic way, such as anomalous scaling; (ii) be partially effective at suppressing numerical instabilities in the normal VLDS equation.

对Villain–Lai–Das Sarma（VLDS）生长系统原始版本和修改版本的通用缩放特性进行了数值（1 +1）和（2 +1）维度的研究。修改后的VLDS方程不稳定性抑制由一个指数递减函数等效于VLDS与无穷多个弱相关的非线性项（VLDS _∞）。基于VLDS生长系统的修改，讨论了生长的不稳定性和结垢特性。我们的结果表明，在改进的VLDS系统中存在无限多个弱相关的非线性项可以：（i）以通用方式导致非平凡的缩放行为，例如异常缩放；（ii）在抑制正常VLDS方程中的数值不稳定性方面部分有效。