Beyond KPZ: Simulations of 1-d Surface Growth with memory Open Access

Abstract

Growing interfaces are ubiquitous in the nature. They are categorized by different universality classes, the most well known of which is the Kardar-Parisi-Zhang (KPZ) class, which describes a variety of well-known growth processes, including sticky ballistic deposition. KPZ and other common growth processes assume that interfaces spread without memory. In contrast, recent experiments on living systems show that, in some cases, for an interface to spread, it must not slow down, and must have reached the current position only very recently. In other words, the interface possesses memory, and hence cannot be modeled by KPZ-style processes. Here we propose a model of ballistic deposition with memory aimed to describe such processes. We calculate dynamical growth exponents for this process using numerical simulations and we observe that universality classes with these exponents have not been studied before. 

Table of Contents

1 Background 1

2 Introduction 4

2.1 BallisticDeposition............................ 4

2.2 DynamicScaling ............................. 7

2.3 KPZUniversalityClass.......................... 11

3 Simulation of BD 13

3.1 BDwithdifferentLs ........................... 13

3.2 ScalingExponents ............................ 14

4 BD with Memory 19

4.1 TheBDMModel ............................. 19

4.2 Effects of r ................................ 21

4.3 ScalingRelation.............................. 26

4.4 ScalingExponents ............................ 26

References 34 

About this Honors Thesis

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School	Emory College
Department	Physics
Degree	B.S.
Submission	Honors Thesis
Language	English
Research Field	Physics, General Biophysics, General Physics, Theory
Keyword	Memory Surface Growth KPZ
Committee Chair / Thesis Advisor	Ilya Nemenman, Emory University
Committee Members	Stefan Boettcher, Emory University Gordon Berman, Emory University

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