ABSTRACT


Abstract

This Focused Research Group brings together researchers from the
University of Michigan's Departments of Mathematics, Physics and
Chemical Engineering to address important problems of modeling,
simulation and analysis for dynamical processes where underlying
discreteness plays a non-negligible role in large scale descriptions
via deterministic continuum systems (generally systems of ordinary and
partial differential equations). This Focused Research Group combines
the investigators' expertise in theory, modeling, analysis and
scientific computation to study a suite of problems from materials
physics, chemical kinetics and the life sciences to elucidate the
fundamental scientific issues and develop appropriate quantitative
tools to analyze them. The specific problems to be studied are: (1)
Mesoscopic mathematical models of wound healing with cell proliferation
and migration, and including the biologically important effect of
cell-cell adhesion; (2) The application of new and improved simulation
techniques, direct solutions of the Becker-Doering equations, and
simulation and analysis of stochastic models to investigate the role of
microscopic correlations in Ostwald ripening; (3) The development of
analytic asymptotic methods for accurate reduced descriptions of slow
stochastic variables properly incorporating residual fluctuation
effects with applications to (bio)chemical reaction networks possessing
a wide spectrum of reaction rates; (4) An extension of modeling,
analysis and simulation methods developed for simple systems to
increasingly complex stochastic models in population biology and
epidemiology including epidemics in structured populations and
extinction of competing species; (5) Spatial inhomogeneities and
reaction-rate variations in the stochastic Fisher-Kolmogorov equation,
a fundamental paradigm of front propagation and pattern formation.

Results from this project will lead to the development of effective
mathematical descriptions and efficient computational schemes for
problems of increasing importance for small-scale physical and chemical
processes in materials science and nano-technology, and for
quantitative modeling in the life sciences. With regard to the even
broader impact of this project, it contributes to the development of
the scientific workforce by providing advanced training for
postdoctoral researchers and doctoral students in the natural,
engineering and applied mathematical sciences.

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