Doctoral Dissertations

Author

Man Young Lee

Abstract

"Nonequilibrium systems can undergo continuous phase transitions between different steady states. These transitions are characterized by collective fluctuations over large distances and long times similar to the behavior of equilibrium critical points. They also can be divided into different universality classes according to their critical behavior.

This dissertation considers two types of nonequilibrium transitions. First study concerns absorbing state transitions on a randomly diluted lattice. Second study deals with nonequilibrium models with several absorbing states. We investigate two specific nonequilibrium lattice models, i.e., the contact process and the generalized contact process by means of both theoretical and computational approaches.

In section 1, we introduce the basic arguments and theories to support our investigations for both problems. In sections 2 and 3, we investigate nonequilibrium phase transitions of the contact process and the generalized contact process on a percolating lattice, focusing on the transition across the lattice percolation threshold. In this study, we show that the interplay between geometric criticality due to percolation and dynamical fluctuations of the nonequilibrium system leads to a new universality class. The critical point is characterized by ultra-slow activated dynamical scaling and accompanied by strong Griffiths singularities. We support our theory by extensive Monte-Carlo simulations. In sections 4 and 5, we investigate the generalized contact process on one and two-dimensional lattices. We treat the creation rate of active sites between inactive domains as an independent parameter. It turns out that this model has an unusual phase diagram with two different nonequilibrium phase transitions. The special point separating them shares some characteristics with a multicritical point. For one dimension, a small boundary rate takes the system from the directed percolation universality class to the parity-conserved class. For two dimensions, the critical behavior on the generic transition line is of mean-field type with logarithmic corrections suggesting that the two-dimensional generalized contact process is in the generalized voter universality class"--Abstract, page iv.

Advisor(s)

Vojta, Thomas

Committee Member(s)

Wilemski, Gerald
Tauber, Uwe C.
Medvedeva, Julia E.
Parris, Paul Ernest, 1954-

Department(s)

Physics

Degree Name

Ph. D. in Physics

Publisher

Missouri University of Science and Technology

Publication Date

Spring 2011

Journal article titles appearing in thesis/dissertation

  • Nonequilibrium phase transition on a randomly diluted lattice
  • Absorbing state phase transitions on percolating lattices
  • Phase transitions of the generalized contact process with two absorbing states
  • Generalized contact process with two symmetric absorbing states in two dimensions

Pagination

xiv, 107 pages

Note about bibliography

Includes bibliographical references.

Rights

© 2011 Man Young Lee, All rights reserved.

Document Type

Dissertation - Open Access

File Type

text

Language

English

Library of Congress Subject Headings

Nonequilibrium statistical mechanics
Percolation
Phase transformations (Statistical physics)

Thesis Number

T 9779

Print OCLC #

775016032

Electronic OCLC #

747952791

Included in

Physics Commons

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