\documentclass{article} 
\begin{document} 

\begin{center} 
{\bf An Entropy Based Theory of the Grain Boundary\\
 Character Distribution}

\vspace{.10in}  


K. Barmak\\
Department of Materials Science and Engineering\\
Carnegie Mellon University\\
Pittsburgh, PA 15213\\
katayun@andrew.cmu.edu

\vspace{.10in}

E. Eggeling\\
Fraunhofer Austria Research GmbH\\
Visual Computing, A-8010 Graz

\vspace{.10in}

M. Emelianenko\\
Department of Mathematical Sciences\\
 George Mason University\\
 Fairfax, VA  22030\\
memelian@gmu.edu

\vspace{.10in}

Y. Epshteyn\\
Department of Mathematics\\
 The University of Utah\\
 Salt Lake City, UT, 84112\\
epshteyn@math.utah.edu

\vspace{.10in}

D. Kinderlehrer\\
Department of Mathematical Sciences\\
 Carnegie Mellon University\\
 Pittsburgh, PA 15213\\
davidk@andrew.cmu.edu

\vspace{.10in}

R. Sharp\\
Department of Mathematical Sciences\\
Carnegie Mellon University\\
 Pittsburgh, PA 15213\\

\vspace{.10in}

S. Ta'asan\\
Department of Mathematical Sciences\\
 Carnegie Mellon University\\
 Pittsburgh, PA 15213\\
shlomo@andrew.cmu.edu

\end{center} 

\vspace{.10in} 

\noindent {\bf Abstract}: Cellular networks are ubiquitous in nature. They
exhibit behavior on many ditechnologically useful materials are
polycrystalline microstructures composed of a myriad of small monocrystalline
grains separated by grain boundaries.  The energetics and connectivity of the
grain boundary network plays a crucial role in determining the properties of a
material across a wide range of scales.  A central problem in materials
science is to develop technologies capable of producing an arrangement of
grains|a texture|appropriate for a desired set of material properties. Here we
discuss the role of energy in texture development, measured by a character
distribution. We derive an entropy based theory based on mass transport and a
Kantorovich-Rubinstein-Wasserstein metric to suggest that, to rst
approximation, this distribution behaves like the solution to a Fokker-Planck
Equation.  

\end{document}
