Title page for ETD etd-04102001-113110


Type of Document Dissertation
Author Triampo, Wannapong
Author's Email Address wtriampo@yahoo.com
URN etd-04102001-113110
Title Non-Equilibrium Disordering Processes In binary Systems Due to an Active Agent
Degree PhD
Department Physics
Advisory Committee
Advisor Name Title
Schmittmann, Beate Committee Chair
Heflin, James R. Committee Member
Ritter, Alfred L. Committee Member
Tauber, Uwe C. Committee Member
Zia, Royce K. P. Committee Member
Keywords
  • Vacancy-mediated dynamics
  • Non-equilibrium processes
  • Monte Carlo
  • Brownian motion
  • Dynamic scaling
  • Random walk
  • Disordering process
  • Mean-field theory
  • Ising model
  • Data corruption
Date of Defense 2001-04-10
Availability unrestricted
Abstract
In this thesis, we study the kinetic disordering of systems

interacting with an agent or a walker. Our studies divide naturally into two

classes: for the first, the dynamics of the walker conserves the total

magnetization of the system, for the second, it does not. These distinct

dynamics are investigated in part I and II respectively.

In part I, we investigate the disordering of an initially

phase-segregated binary alloy due to a highly mobile vacancy which exchanges

with the alloy atoms. This dynamics clearly conserves the total

magnetization. We distinguish three versions of dynamic rules for the

vacancy motion, namely a pure random walk , an ``active' and a biased walk.

For the random walk case, we review and reproduce earlier work by Z.

Toroczkai et. al.,~cite{TKSZ} which will serve as our base-line. To test

the robustness of these findings and to make our model more accessible to

experimental studies, we investigated the effects of finite temperatures

(``active walks') as well as external fields (biased walks). To monitor the

disordering process, we define a suitable disorder parameter, namely the

number of broken bonds, which we study as a function of time, system size

and vacancy number. Using Monte Carlo simulations and a coarse-grained field

theory, we observe that the disordering process exhibits three well

separated temporal regimes. We show that the later stages exhibit dynamic

scaling, characterized by a set of exponents and scaling functions. For the

random and the biased case, these exponents and scaling functions are

computed analytically in excellent agreement with the simulation results.

The exponents are remarkably universal. We conclude this part with some

comments on the early stage, the interfacial roughness and other related

features.

In part II, we introduce a model of binary data corruption induced

by a Brownian agent or random walker. Here, the magnetization is not

conserved, being related to the density of corrupted bits }$ ho ${small .}

{small Using both continuum theory and computer simulations, we study the

average density of corrupted bits, and the

associated density-density correlation function, as well as several other

related quantities. In the second half, we

extend our investigations in three main directions which allow us to make

closer contact with real binary systems. These are i) a detailed analysis of

two dimensions, ii) the case of competing agents, and iii) the cases of

asymmetric and quenched random couplings. Our analytic results are in good

agreement with simulation results. The remarkable finding of this study is

the robustness of the phenomenological model which provides us with the tool,

continuum theory, to understand the nature of such a simple model.

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