KPZ Equation and Surface Growth Model
Masato Hisakado
TL;DR
This paper explores the ultra-discrete Burgers equation, classifies its behavior, and constructs automata models for the KPZ surface growth, including noise effects and connections to known models like ASEP.
Contribution
It introduces automata models for the KPZ equation derived from the ultra-discrete Burgers equation, linking discrete surface growth models with established stochastic models.
Findings
Classified the ultra-discrete Burgers equation into five parameter regions.
Constructed deterministic surface growth models from the equation.
Presented automata models corresponding to the KPZ equation and related models.
Abstract
We consider the ultra-discrete Burgers equation. All variables of the equation are discrete. We classify the equation into five regions in the parameter space. We discuss behavior of solutions. Using this equation we construct the deterministic surface growth models respectively. Furthermore we introduce noise into the ultra-discrete Burgers equation. We present the automata models of the KPZ equation. One model corresponds to the discrete version of the ASEP and the other to the Kim-Kosterlitz model.
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Taxonomy
TopicsAdhesion, Friction, and Surface Interactions · Fluid Dynamics and Heat Transfer · Surface Modification and Superhydrophobicity