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The purpose of this four volume series is to make available for
college teachers and students samples of important and realistic
applications of mathematics which can be covered in undergraduate
programs. The goal is to provide illustrations of how modem
mathematics is actually employed to solve relevant contemporary
problems. Although these independent chapters were prepared
primarily for teachers in the general mathematical sciences, they
should prove valuable to students, teachers, and research
scientists in many of the fields of application as well.
Prerequisites for each chapter and suggestions for the teacher are
provided. Several of these chapters have been tested in a variety
of classroom settings, and all have undergone extensive peer review
and revision. Illustrations and exercises are included in most
chapters. Some units can be covered in one class, whereas others
provide sufficient material for a few weeks of class time. Volume 1
contains 23 chapters and deals with differential equations and, in
the last four chapters, problems leading to partial differential
equations. Applications are taken from medicine, biology, traffic
systems and several other fields. The 14 chapters in Volume 2 are
devoted mostly to problems arising in political science, but they
also address questions appearing in sociology and ecology. Topics
covered include voting systems, weighted voting, proportional
representation, coalitional values, and committees. The 14 chapters
in Volume 3 emphasize discrete mathematical methods such as those
which arise in graph theory, combinatorics, and networks.
This IMA Volume in Mathematics and its Applications PARTICULATE
FLOWS: PROCESSING AND RHEOLOGY is based on the proceedings of a
very successful one-week workshop with the same title, which was an
integral part of the 1995-1996 IMA program on "Mathematical Methods
in Materials Science." We would like to thank Donald A. Drew,
Daniel D. Joseph, and Stephen L. Passman for their excellent work
as organizers of the meeting. We also take this opportunity to
thank the National Science Foun dation (NSF), the Army Research
Office (ARO) and the Office of Naval Research (ONR), whose
financial support made the workshop possible. A vner Friedman
Robert Gulliver v PREFACE The workshop on Particulate Flows:
Processing and Rheology was held January 8-12, 1996 at the
Institute for Mathematics and its Applications on the University of
Minnesota Twin Cities campus as part of the 1995- 96 Program on
Mathematical Methods in Materials Science. There were about forty
participants, and some lively discussions, in spite of the fact
that bad weather on the east coast kept some participants from
attending, and caused scheduling changes throughout the workshop.
Heterogeneous materials can behave strangely, even in simple flow
sit uations. For example, a mixture of solid particles in a liquid
can exhibit behavior that seems solid-like or fluid-like, and
attempting to measure the "viscosity" of such a mixture leads to
contradictions and "unrepeatable" experiments. Even so, such
materials are commonly used in manufacturing and processing."
An exposition of the derivation and use of equations of motion for
two-phase flow. The approach taken derives the equations of motion
using ensemble averaging, and compares them with those derived from
control volume methods. Closure for dispersed flows is discussed,
and some fundamental solutions are given. The work focuses on the
fundamental aspects of two-phase flow, and is intended to give the
reader a background for understanding the dynamics as well as a
system of equations that can be used in predictions of the behavior
of dispersed two-phase flows. The exposition in terms of ensemble
averaging is new, and combining it with modern continuum mechanics
concepts makes this book unique. Intended for engineering,
mathematics and physics researchers and advanced graduate students
working in the field.
An exposition of the derivation and use of equations of motion for two-phase flow. The approach taken derives the equations of motion using ensemble averaging, and compares them with those derived from control volume methods. Closure for dispersed flows is discussed, and some fundamental solutions are given. The work focuses on the fundamental aspects of two-phase flow, and is intended to give the reader a background for understanding the dynamics as well as a system of equations that can be used in predictions of the behavior of dispersed two-phase flows. The exposition in terms of ensemble averaging is new, and combining it with modern continuum mechanics concepts makes this book unique. Intended for engineering, mathematics and physics researchers and advanced graduate students working in the field.
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