Boundary-induced heterogeneous absorbing states

Juan A. Bonachela, Miguel A. Muñoz

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We study two different types of systems with many absorbing states (with and without a conservation law) and scrutinize the effect of walls/boundaries (either absorbing or reflecting) into them. In some cases, non-trivial structured absorbing configurations (characterized by a background field) develop around the wall. We study such structures using a mean-field approach as well as computer simulations. The main results are: i) for systems in the directed percolation class, a very fast (exponential) convergence of the background to its bulk value is observed; ii) for systems with a conservation law, power-law decaying landscapes are induced by both types of walls: while for absorbing walls this effect is already present in the mean-field approximation, for reflecting walls the structured background is a noise-induced effect. The landscapes are shown to converge to their asymptotic bulk values with an exponent equal to the inverse of the bulk correlation length exponent. Finally, the implications of these results in the context of self-organizing systems are discussed.

LanguageEnglish
Pages204-211
Number of pages8
JournalAIP Conference Proceedings
Volume1091
DOIs
Publication statusPublished - 23 Apr 2009

Fingerprint

conservation laws
exponents
self organizing systems
computerized simulation
configurations
approximation

Keywords

  • absorbing states
  • non-equilibrium phase transition
  • self-organized criticality

Cite this

Bonachela, Juan A. ; Muñoz, Miguel A. / Boundary-induced heterogeneous absorbing states. In: AIP Conference Proceedings. 2009 ; Vol. 1091. pp. 204-211.
@article{c3cc527d027e4acab49e2647348406cc,
title = "Boundary-induced heterogeneous absorbing states",
abstract = "We study two different types of systems with many absorbing states (with and without a conservation law) and scrutinize the effect of walls/boundaries (either absorbing or reflecting) into them. In some cases, non-trivial structured absorbing configurations (characterized by a background field) develop around the wall. We study such structures using a mean-field approach as well as computer simulations. The main results are: i) for systems in the directed percolation class, a very fast (exponential) convergence of the background to its bulk value is observed; ii) for systems with a conservation law, power-law decaying landscapes are induced by both types of walls: while for absorbing walls this effect is already present in the mean-field approximation, for reflecting walls the structured background is a noise-induced effect. The landscapes are shown to converge to their asymptotic bulk values with an exponent equal to the inverse of the bulk correlation length exponent. Finally, the implications of these results in the context of self-organizing systems are discussed.",
keywords = "absorbing states, non-equilibrium phase transition, self-organized criticality",
author = "Bonachela, {Juan A.} and Mu{\~n}oz, {Miguel A.}",
year = "2009",
month = "4",
day = "23",
doi = "10.1063/1.3082283",
language = "English",
volume = "1091",
pages = "204--211",
journal = "AIP Conference Proceedings",
issn = "0094-243X",

}

Boundary-induced heterogeneous absorbing states. / Bonachela, Juan A.; Muñoz, Miguel A.

In: AIP Conference Proceedings, Vol. 1091, 23.04.2009, p. 204-211.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Boundary-induced heterogeneous absorbing states

AU - Bonachela, Juan A.

AU - Muñoz, Miguel A.

PY - 2009/4/23

Y1 - 2009/4/23

N2 - We study two different types of systems with many absorbing states (with and without a conservation law) and scrutinize the effect of walls/boundaries (either absorbing or reflecting) into them. In some cases, non-trivial structured absorbing configurations (characterized by a background field) develop around the wall. We study such structures using a mean-field approach as well as computer simulations. The main results are: i) for systems in the directed percolation class, a very fast (exponential) convergence of the background to its bulk value is observed; ii) for systems with a conservation law, power-law decaying landscapes are induced by both types of walls: while for absorbing walls this effect is already present in the mean-field approximation, for reflecting walls the structured background is a noise-induced effect. The landscapes are shown to converge to their asymptotic bulk values with an exponent equal to the inverse of the bulk correlation length exponent. Finally, the implications of these results in the context of self-organizing systems are discussed.

AB - We study two different types of systems with many absorbing states (with and without a conservation law) and scrutinize the effect of walls/boundaries (either absorbing or reflecting) into them. In some cases, non-trivial structured absorbing configurations (characterized by a background field) develop around the wall. We study such structures using a mean-field approach as well as computer simulations. The main results are: i) for systems in the directed percolation class, a very fast (exponential) convergence of the background to its bulk value is observed; ii) for systems with a conservation law, power-law decaying landscapes are induced by both types of walls: while for absorbing walls this effect is already present in the mean-field approximation, for reflecting walls the structured background is a noise-induced effect. The landscapes are shown to converge to their asymptotic bulk values with an exponent equal to the inverse of the bulk correlation length exponent. Finally, the implications of these results in the context of self-organizing systems are discussed.

KW - absorbing states

KW - non-equilibrium phase transition

KW - self-organized criticality

UR - http://www.scopus.com/inward/record.url?scp=64849084244&partnerID=8YFLogxK

U2 - 10.1063/1.3082283

DO - 10.1063/1.3082283

M3 - Article

VL - 1091

SP - 204

EP - 211

JO - AIP Conference Proceedings

T2 - AIP Conference Proceedings

JF - AIP Conference Proceedings

SN - 0094-243X

ER -