#This file was created by <mhendrey> Thu May 11 15:07:19 2000
#LyX 1.0 (C) 1995-1999 Matthias Ettrich and the LyX Team
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\begin_preamble
\advisor{Professor Edward Ott}
\chairtitle{Chairman/Advisor}
\committee{Professor Thomas M. Antonsen, Jr. \\
                Dr. Parvez Guzdar \\
                Professor Rajarshi Roy \\
                Assoc. Professor Brian Hunt }
\department{Department of Physics}
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\layout Title

Effects of Inhomogeneities in the 
\newline 
Complex Ginzburg-Landau Equation
\layout Author

Matthew R.
 Hendrey
\layout Standard


\latex latex 

\backslash 
dedication{
\backslash 
centerline{To my loving wife and family.}}
\layout Date

2000
\layout Abstract

This is my abstract which will explain what I'm going to put into my dissertatio
n.
 
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comment{
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This is where I can make all my comments on how the paper is going.
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}
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acknowledgements{
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This is where I make any acknowledgements if I have any.
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}
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makefrontmatter
\layout Chapter

Spiral Wave Dynamics in the Complex Ginzburg-Landau Equation with Broken
 Chiral Symmetry
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Introduction
\layout Standard

Spiral waves occur in the Belousov-Zhabotinsky (BZ) reaction, mulitmode
 lasers, colonies of social amoebae, cardiac arrythmias, and Rayleigh-Benard
 convection 
\begin_inset LatexCommand \cite{Cross93}

\end_inset 

, 
\begin_inset Formula 
\begin{equation}
\label{CGLE_homo}
\frac{\partial A}{\partial t}=A-(1+i\alpha )|A|^{2}A+(1+i\beta )\nabla ^{2}A,
\end{equation}

\end_inset 

 where 
\begin_inset Formula \( A \)
\end_inset 

 is the complex order parameter which governs the slow spatial and temporal
 behavior of the system, and 
\begin_inset Formula \( \alpha  \)
\end_inset 

 and 
\begin_inset Formula \( \beta  \)
\end_inset 

 are real numbers.
 This equation is known to arise naturally for spatially extended systems
 in the vicinity of a Hopf bifurcation.
\layout Bibliography
\bibitem {Cross93}

For a general review on pattern formation see M.
 C.
 Cross and P.
 C.
 Hohenberg, Rev.
 Mod.
 Phys.
 
\series bold 
65
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, 851 (1993).
\the_end