Growth Equation with Conservation Law

TL;DR

This paper introduces a unified growth equation with a conservation law, encompassing several known models, and uses renormalization-group analysis to determine critical exponents and universality classes.

Contribution

It presents a generalized growth equation with an integral kernel that unifies various growth models and analyzes their critical behavior.

Findings

Identifies critical exponents for growth models with conservation laws.

Classifies universality classes for these growth equations.

Provides a framework for analyzing growth equations with a conservation law.

Abstract

A growth equation with a generalized conservation law characterized by an integral kernel is introduced. The equation contains the Kardar-Parisi-Zhang, Sun-Guo-Grant, and Molecular-Beam Epitaxy growth equations as special cases and allows for a unified investigation of growth equations. From a dynamic renormalization-group analysis critical exponents and universality classes are determined for growth models with a conservation law.