Scaling properties of driven interfaces: Symmetries, conservation laws, and the role of constraints

Z. Rácz, M. Siegert, D. Liu, M. Plischke

Research output: Contribution to journalArticle

64 Citations (Scopus)

Abstract

One-dimensional models of surface dynamics are studied analytically and by numerical simulation. In all cases the number of particles that form the deposit is conserved. We find that an initially flat surface, in general, roughens as a function of time and can be characterized by a width which obeys the scaling form (L,t)=Lf(t/Lz) for a deposit on a substrate of linear dimension L. Restricted solid-on-solid (RSOS) -type models in which the microscopic dynamics obeys detailed balance are shown to be in the free-field universality class with exponents z=4 and =1/2. On the other hand, if detailed balance is broken, several universality classes exist. As the maximum-height-difference constraint in a RSOS model is varied, one can observe a phase transition between a flat phase (z=2, =0) and a grooved phase characterized by a steady-state exponent =1 but with no scaling in the relaxation process. At the transition point, a nontrivially rough surface emerges with exponents (z3.67, 0.33) close to those of the conserved Kardar-Parisi-Zhang equation. We propose a phenomenological model that may account for these observations.

Original languageEnglish
Pages (from-to)5275-5283
Number of pages9
JournalPhysical Review A
Volume43
Issue number10
DOIs
Publication statusPublished - 1991

Fingerprint

conservation laws
scaling
exponents
symmetry
deposits
transition points
flat surfaces
simulation

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Atomic and Molecular Physics, and Optics

Cite this

Scaling properties of driven interfaces : Symmetries, conservation laws, and the role of constraints. / Rácz, Z.; Siegert, M.; Liu, D.; Plischke, M.

In: Physical Review A, Vol. 43, No. 10, 1991, p. 5275-5283.

Research output: Contribution to journalArticle

Rácz, Z. ; Siegert, M. ; Liu, D. ; Plischke, M. / Scaling properties of driven interfaces : Symmetries, conservation laws, and the role of constraints. In: Physical Review A. 1991 ; Vol. 43, No. 10. pp. 5275-5283.
@article{f041e6b3458e4fb1872b57c98440ebc8,
title = "Scaling properties of driven interfaces: Symmetries, conservation laws, and the role of constraints",
abstract = "One-dimensional models of surface dynamics are studied analytically and by numerical simulation. In all cases the number of particles that form the deposit is conserved. We find that an initially flat surface, in general, roughens as a function of time and can be characterized by a width which obeys the scaling form (L,t)=Lf(t/Lz) for a deposit on a substrate of linear dimension L. Restricted solid-on-solid (RSOS) -type models in which the microscopic dynamics obeys detailed balance are shown to be in the free-field universality class with exponents z=4 and =1/2. On the other hand, if detailed balance is broken, several universality classes exist. As the maximum-height-difference constraint in a RSOS model is varied, one can observe a phase transition between a flat phase (z=2, =0) and a grooved phase characterized by a steady-state exponent =1 but with no scaling in the relaxation process. At the transition point, a nontrivially rough surface emerges with exponents (z3.67, 0.33) close to those of the conserved Kardar-Parisi-Zhang equation. We propose a phenomenological model that may account for these observations.",
author = "Z. R{\'a}cz and M. Siegert and D. Liu and M. Plischke",
year = "1991",
doi = "10.1103/PhysRevA.43.5275",
language = "English",
volume = "43",
pages = "5275--5283",
journal = "Physical Review A",
issn = "2469-9926",
publisher = "American Physical Society",
number = "10",

}

TY - JOUR

T1 - Scaling properties of driven interfaces

T2 - Symmetries, conservation laws, and the role of constraints

AU - Rácz, Z.

AU - Siegert, M.

AU - Liu, D.

AU - Plischke, M.

PY - 1991

Y1 - 1991

N2 - One-dimensional models of surface dynamics are studied analytically and by numerical simulation. In all cases the number of particles that form the deposit is conserved. We find that an initially flat surface, in general, roughens as a function of time and can be characterized by a width which obeys the scaling form (L,t)=Lf(t/Lz) for a deposit on a substrate of linear dimension L. Restricted solid-on-solid (RSOS) -type models in which the microscopic dynamics obeys detailed balance are shown to be in the free-field universality class with exponents z=4 and =1/2. On the other hand, if detailed balance is broken, several universality classes exist. As the maximum-height-difference constraint in a RSOS model is varied, one can observe a phase transition between a flat phase (z=2, =0) and a grooved phase characterized by a steady-state exponent =1 but with no scaling in the relaxation process. At the transition point, a nontrivially rough surface emerges with exponents (z3.67, 0.33) close to those of the conserved Kardar-Parisi-Zhang equation. We propose a phenomenological model that may account for these observations.

AB - One-dimensional models of surface dynamics are studied analytically and by numerical simulation. In all cases the number of particles that form the deposit is conserved. We find that an initially flat surface, in general, roughens as a function of time and can be characterized by a width which obeys the scaling form (L,t)=Lf(t/Lz) for a deposit on a substrate of linear dimension L. Restricted solid-on-solid (RSOS) -type models in which the microscopic dynamics obeys detailed balance are shown to be in the free-field universality class with exponents z=4 and =1/2. On the other hand, if detailed balance is broken, several universality classes exist. As the maximum-height-difference constraint in a RSOS model is varied, one can observe a phase transition between a flat phase (z=2, =0) and a grooved phase characterized by a steady-state exponent =1 but with no scaling in the relaxation process. At the transition point, a nontrivially rough surface emerges with exponents (z3.67, 0.33) close to those of the conserved Kardar-Parisi-Zhang equation. We propose a phenomenological model that may account for these observations.

UR - http://www.scopus.com/inward/record.url?scp=0013402752&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0013402752&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.43.5275

DO - 10.1103/PhysRevA.43.5275

M3 - Article

AN - SCOPUS:0013402752

VL - 43

SP - 5275

EP - 5283

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 10

ER -