The year has been divided into three segments, with a total of nine
workshops. In each case, we aim to bring together researchers
with overlapping interests who may move in disjoint scientific
circles, and expose applied mathematicians to activity in the
selected area of the workshop. The overall focus will be on
identifying situations where an infusion of existing mathematical
technology can lead to rapid progress, as well as recognizing
areas where the existing theoretical framework needs to be
Fall
Quarter (September - December, 1999)
Combustion
Although
combustion has a long history and the subject is of great economical
and technological importance, its emergence as a science is
of relatively recent origin. Applied mathematicians "discovered"
Combustion only about thirty years ago, and the scientific,
analytical and computational challenges of the field have now
made combustion an important application area of applied mathematics.
Fluid
mechanics, chemical reaction, and thermodynamics are the essential
ingredients of combustion. The governing equations are conservation
laws of compressible flow, augmented by chemical kinetics. Nonlinearities
and disparate scales abound. Even in the simplest of combustible
mixtures, there is a bewildering array of chemical reactions
among myriad species. When multiple phases are encountered,
there is a lack of consensus even on the governing equations.
It is clear, then, that the field continues to Offer major opportunities
to the modeller, analyst, and numericist alike.
aim of the quarter of concentration on combustion is to focus
on three specific contexts in the field of combustion (each
a workshop topic), to review recent successes, and to acquaint
the participant with the challenges that remain.
Winter Quarter(January - March, 2000)
Natural Resources and Environment
This
term will focus on the increasingly important role that reaction-transport
processes play in the recovery of natural resources and in the
confinement and remediation of environmental hazards. Geochemical
phenomena which are essential to the understanding of the processes
involved in enhanced oil recovery are also critical to developing
effective strategies for the bioremediation of petroleum wastes.
In both cases the effects of the chemical reactions enter the
mathematical model not only as lower order terms in the reaction-transport
equation but also can be nonlinearly coupled to the transport
through concentration-dependent diffusion and permeability coefficients.
Mechanical effects are also becoming important in these processes.
During this term we will study the phenomena which arise from
the full coupling of these reaction, transport and mechanical
effects. We shall also be interested in studying them in the context
of "real life", strategically important processes such as enhanced
oil recovery, location of mineral deposits, chemical and nuclear
waste repository dynamics, bioremediation of petroleum wastes,
spread of pollutants in the atmosphere and lakes, etc. Experts
in the modeling, analysis and numerical simulation of such processes
will be brought together with experimentalists and participants
from industry during the period.
Spring Quarter (April - June, 2000)
Multiscale and Transition Regimes
This
term will focus on modeling processes for which transport is one
of the most complicated components. This includes processes that
include length scales that range from the order of mean-free paths
to many times over different spatial-temporal regions of the problem,
thereby requiring different transport models in each region for
effective modeling. In some cases the underlying kinetic description
is understood, such as the Boltzmann equation for rarified gases,
or the transport equation for radiation. In such cases the main
issue is one of economy, a fully resolved kinetic simulation being
impractical, and one therefore develops homogenization, stochastic,
or moment based subgrid models. Such is the focus of two of the
workshops: "Model Hierarchies for the Evolution of Surfaces under
Chemically Reacting Flows" and "Tr
nsport Phenomena in Transition
Regimes." In other cases there is considerable disagreement about
the underlying kinetic description, especially when dispersive
effects become macroscopic, for example due to quantum effects
in semiconductors and superfluids. These disagreements are the
focus of the workshop: "Dispersive Corrections to Transport Equations".