在生长的KPZ界面下的弹道沉积模式
Ballistic deposition patterns beneath a growing KPZ interface
摘要：
我们考虑一个（1+1）维弹道沉积过程的次近邻相互作用，它属于KPZ普适类，并引入一个类似于随机强迫连续Burgers方程的变分公式。这允许识别的特征结构的大部分增长的聚集体（“集群”和“裂缝”）与最小化和冲击的Burgers湍流，并引入一种新的装备艾里过程的弹道增长。我们称之为“毛艾里过程”，并调查其统计数字。我们还确定了标度律，其特征在于弹道沉积模式的散装：法律的“变薄”的森林集群的高度增加，法律的横向波动的集群边界，和集群的大小分布。相应的临界指数的确定正是基于与Burgers湍流的类比和简单的标度考虑。
英文摘要：
We consider a (1+1)-dimensional ballistic deposition process with next-nearest neighbor interaction, which belongs to the KPZ universality class, and introduce for this discrete model a variational formulation similar to that for the randomly forced continuous Burgers equation. This allows to identify the characteristic structures in the bulk of a growing aggregate ("clusters" and "crevices") with minimizers and shocks in the Burgers turbulence, and to introduce a new kind of equipped Airy process for ballistic growth. We dub it the "hairy Airy process" and investigate its statistics numerically. We also identify scaling laws that characterize the ballistic deposition patterns in the bulk: the law of "thinning" of the forest of clusters with increasing height, the law of transversal fluctuations of cluster boundaries, and the size distribution of clusters. The corresponding critical exponents are determined exactly based on the analogy with the Burgers turbulence and simple scaling considerations.
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