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Title: Similarity of ensembles of trajectories of reversible and irreversible growth processes

Abstract

Models of bacterial growth tend to be "irreversible," allowing for the number of bacteria in a colony to increase but not to decrease. By contrast, models of molecular self-assembly are usually "reversible," allowing for the addition and removal of particles to a structure. Such processes differ in a fundamental way because only reversible processes possess an equilibrium. Here we show at the mean-field level that dynamic trajectories of reversible and irreversible growth processes are similar in that both feel the influence of attractors, at which growth proceeds without limit but the intensive properties of the system are invariant. Attractors of both processes undergo nonequilibrium phase transitions as model parameters are varied, suggesting a unified way of describing typical properties of reversible and irreversible growth. We also establish a connection at the mean-field level between an irreversible model of growth (the magnetic Eden model) and the equilibrium Ising model, supporting the findings made by other authors using numerical simulations.

Authors:
 [1];  [2];  [3]
  1. Univ. of California, Berkeley, CA (United States)
  2. Univ. of Nottingham (United Kingdom)
  3. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); National Science Foundation (NSF)
OSTI Identifier:
1601163
Alternate Identifier(s):
OSTI ID: 1399287
Grant/Contract Number:  
[AC02-05CH11231; EP/K01773X/1]
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review E
Additional Journal Information:
[ Journal Volume: 96; Journal Issue: 4]; Journal ID: ISSN 2470-0045
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Klymko, Katherine, Garrahan, Juan P., and Whitelam, Stephen. Similarity of ensembles of trajectories of reversible and irreversible growth processes. United States: N. p., 2017. Web. doi:10.1103/physreve.96.042126.
Klymko, Katherine, Garrahan, Juan P., & Whitelam, Stephen. Similarity of ensembles of trajectories of reversible and irreversible growth processes. United States. doi:10.1103/physreve.96.042126.
Klymko, Katherine, Garrahan, Juan P., and Whitelam, Stephen. Fri . "Similarity of ensembles of trajectories of reversible and irreversible growth processes". United States. doi:10.1103/physreve.96.042126. https://www.osti.gov/servlets/purl/1601163.
@article{osti_1601163,
title = {Similarity of ensembles of trajectories of reversible and irreversible growth processes},
author = {Klymko, Katherine and Garrahan, Juan P. and Whitelam, Stephen},
abstractNote = {Models of bacterial growth tend to be "irreversible," allowing for the number of bacteria in a colony to increase but not to decrease. By contrast, models of molecular self-assembly are usually "reversible," allowing for the addition and removal of particles to a structure. Such processes differ in a fundamental way because only reversible processes possess an equilibrium. Here we show at the mean-field level that dynamic trajectories of reversible and irreversible growth processes are similar in that both feel the influence of attractors, at which growth proceeds without limit but the intensive properties of the system are invariant. Attractors of both processes undergo nonequilibrium phase transitions as model parameters are varied, suggesting a unified way of describing typical properties of reversible and irreversible growth. We also establish a connection at the mean-field level between an irreversible model of growth (the magnetic Eden model) and the equilibrium Ising model, supporting the findings made by other authors using numerical simulations.},
doi = {10.1103/physreve.96.042126},
journal = {Physical Review E},
number = [4],
volume = [96],
place = {United States},
year = {2017},
month = {10}
}

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Works referenced in this record:

Structure and phase transitions of grown and equilibrated alloys
journal, June 1990


The Magnetic eden Model
journal, October 2008

  • Candia, JuliÁN; Albano, Ezequiel V.
  • International Journal of Modern Physics C, Vol. 19, Issue 10
  • DOI: 10.1142/S0129183108013163

Comparative study of an Eden model for the irreversible growth of spins and the equilibrium Ising model
journal, May 2001


Self-Assembly at a Nonequilibrium Critical Point
journal, April 2014


Statistical Mechanics of Probabilistic Cellular Automata
journal, December 1985


Dynamic Order-Disorder in Atomistic Models of Structural Glass Formers
journal, March 2009


Role of Reversibility in Viral Capsid Growth: A Paradigm for Self-Assembly
journal, October 2008


Far-from-equilibrium growth of magnetic thin films with Blume-Capel impurities
journal, April 2015


A general method for numerically simulating the stochastic time evolution of coupled chemical reactions
journal, December 1976


Dynamic Pathways for Viral Capsid Assembly
journal, July 2006


Nucleation: theory and applications to protein solutions and colloidal suspensions
journal, January 2007


Growth-induced breaking and unbreaking of ergodicity in fully-connected spin systems
journal, August 2014


Reversible self-assembly of patchy particles into monodisperse icosahedral clusters
journal, August 2007

  • Wilber, Alex W.; Doye, Jonathan P. K.; Louis, Ard A.
  • The Journal of Chemical Physics, Vol. 127, Issue 8
  • DOI: 10.1063/1.2759922

Model for growth of binary alloys with fast surface equilibration
journal, May 1997


Minimal physical requirements for crystal growth self-poisoning
journal, February 2016

  • Whitelam, Stephen; Dahal, Yuba Raj; Schmit, Jeremy D.
  • The Journal of Chemical Physics, Vol. 144, Issue 6
  • DOI: 10.1063/1.4941457

Classical Nucleation Theory Description of Active Colloid Assembly
journal, September 2016