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\begin{document}
\title{VIGRE Application Part III $\cdot$ Spring 2010 \\
Statement of intellectual merit and broader impact
}
\author{John Kerl}
%\date{\today}
\date{November 4, 2009}
\maketitle

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% What is the intellectual merit of the proposed activity?
%
% How important is the proposed activity to advancing knowledge and
% understanding within its own field or across different fields?

Bose-Einstein condensates have received considerable interest in the
experimental and theoretical physics communities, sparked in no small part by
their 1995 realization in the laboratory by Cornell et al. and subsequent 2001
Nobel prize for that research team.  Moreover, BECs have attracted rigorous
mathematical interest by the likes of Lieb and Seiringer.  Ultimately, one
hopes to increase understanding of Bose-Einstein condensates through the
three-pronged approach of theory, simulation, and physical experiment.  The
simulations done for this dissertation work involve a simplified model,
somewhat far from the Bose gas, which serve as a milestone toward simulating
the Bose gas from the random-cycle perspective.
% How well qualified is the proposer (individual or team) to conduct the
% project?
My hard industrial software experience, combined my mathematical training
at the UA and the expert guidance of Daniel Ueltschi and Tom Kennedy,
uniquely position me to complete this project.
% To what extent does the proposed activity suggest and explore creative and
% original concepts?
This thorough an experimental investigation of the random-cycle model has not,
to our knowledge, ever been undertaken.  The worm algorithm, in particular,
is a novel adaptation of a path-integral Monte Carlo technique to a new
probability model.
% How well conceived and organized is the proposed activity?
% Is there sufficient access to resources?
My dissertation is largely complete; the portions which are incomplete are
clearly identified and well-contained.  CPU time on the University of Arizona's
ICE high-performance computing cluster has been scheduled and is adequate to
obtain desired results in time for a March 2010 dissertation defense.
Available resources are matched by low risk.

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% What are the broader impacts of the proposed activity?
%
% How well does the activity advance discovery and understanding while promoting
% teaching, training, and learning?
%
% How well does the proposed activity broaden the participation of
% underrepresented groups (e.g., gender, ethnicity, disability, geographic,
% etc.)?
%
% To what extent will it enhance the infrastructure for research and education,
% such as facilities, instrumentation, networks, and partnerships?
My work with undergraduate Howard Cheng and junior graduate Shane Passon serves
to spread my successful, hard-won software techniques.
% Will the results be disseminated broadly to enhance scientific and
% technological understanding?
A rough draft of my dissertation, just like the rest of my writings and lecture
notes, is already available on the World Wide Web.  With Daniel Ueltschi, I
will submit my results for publication before my graduation.
% What may be the benefits of the proposed activity to society?
One hopes that the work begun here will increase understanding of Bose-Einstein
condensates in unforeseeable ways.  Moreover, one hopes that the careful and
thorough explication of Markov chain Monte Carlo, thermalization,
autocorrelation, and finite-size scaling techniques will facilitate future work
by other researchers investigating this and other probability models.

\end{document}
