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Despite the fact that fluid dynamics and filtration through porous
media and mathematics, there are classical research areas in
engineering, physics, are still many industrial processes that
require the study of new mathemat ical models for flows of
particular complexity, due to the peculiar properties of the
systems involved. The aim of this book is to provide a number of
examples showing how frequently such situations arise in various
branches of industrial technology. The selection of the subjects
was motivated not only by their industrial rel evance and
mathematical interest. What I had in mind was a collection of
problems having a really distinctive character, thus bringing some
fresh air into one of the oldest and most revered domains of
applied mathematics. The incredible richness of nonstandard flow
problems in industrial appli cations has always been, and still is,
a constant surprise to me. Therefore I tried to offer a very large
spectrum of subjects, with special attention devoted to those
problems in which the modeling phase is far from being obvious, and
the mathematical content is absolutely nontrivial. With such a view
to diversity, topics have been selected from a variety of sources
(such as glass industry, polymers science, coffee brewing, fuels
pipelining), and contributors from different backgrounds
(mathematics, physics, chemical engineering) have been included.
Consequently, the mathematical nature of the problems formulated
spans over a large range, so that their theoret ical investigation
and numerical computation require a variety of different
techniques."
This book illustrates applications of mathematics to various
processes (physiological or artificial) involving flowing blood,
including hemorheology, microcirculation, coagulation, kidney
filtration and dialysis, offering a historical overview of each
topic. Mathematical models are used to simulate processes normally
occurring in flowing blood and to predict the effects of
dysfunctions (e.g. bleeding disorders, renal failure), as well as
the effects of therapies with an eye to improving treatments. Most
of the models have a completely new approach that makes
patient-specific simulations possible. The book is mainly intended
for mathematicians interested in medical applications, but it is
also useful for clinicians such as hematologists, nephrologists,
cardio-surgeons, and bioengineers. Some parts require no specific
knowledge of mathematics. The book is a valuable addition to
mathematics, medical, biology, and bioengineering libraries.
This book illustrates applications of mathematics to various
processes (physiological or artificial) involving flowing blood,
including hemorheology, microcirculation, coagulation, kidney
filtration and dialysis, offering a historical overview of each
topic. Mathematical models are used to simulate processes normally
occurring in flowing blood and to predict the effects of
dysfunctions (e.g. bleeding disorders, renal failure), as well as
the effects of therapies with an eye to improving treatments. Most
of the models have a completely new approach that makes
patient-specific simulations possible. The book is mainly intended
for mathematicians interested in medical applications, but it is
also useful for clinicians such as hematologists, nephrologists,
cardio-surgeons, and bioengineers. Some parts require no specific
knowledge of mathematics. The book is a valuable addition to
mathematics, medical, biology, and bioengineering libraries.
This volume presents a review of advanced technological problems in
the glass industry and of the mathematics involved. It is amazing
that such a seemingly small research area is extremely rich and
calls for an impressively large variety of mathematical methods,
including numerical simulations of considerable complexity. The
problems treated here are very typical of the field of glass
manufacturing and cover a large spectrum of complementary subjects:
injection molding by various techniques, radiative heat transfer in
glass, nonisothermal flows and fibre spinning. The book can
certainly be useful not only to applied mathematicians, but also to
physicists and engineers, who can find in it an overview of the
most advanced models and methods.
The 1990 CIME course on Mathematical Modelling of Industrial
Processes set out to illustrate some advances in questions of
industrial mathematics, i.e.of the applications of mathematics
(with all its "academic" rigour) to real-life problems. The papers
describe the genesis of the models and illustrate their relevant
mathematical characteristics. Among the themesdealt with are:
thermally controlled crystal growth, thermal behaviour of a
high-pressure gas-discharge lamp, the sessile-drop problem, etching
processes, the batch-coil- annealing process, inverse problems in
classical dynamics, image representation and dynamical systems,
scintillation in rear projections screens, identification of
semiconductor properties, pattern recognition with neural networks.
CONTENTS: H.K. Kuiken: Mathematical Modelling of Industrial
Processes.- B. Forte: Inverse Problems in Mathematics for
Industry.- S. Busenberg: Case Studies in Industrial Mathematics.
Analytical Mechanics is the investigation of motion with the
rigorous tools of mathematics, with remarkable applications to many
branches of physics (Astronomy, Statistical and Quantum Mechanics,
etc.). Rooted in the works of Lagrange, Euler, and Poincare, it is
a classical subject with fascinating developments and still rich
with open problems. It addresses such fundamental questions as: Is
the solar system stable? Is there a unifying "economy" principle in
mechanics? How can a point mass be described as a "wave"? This book
was written to fill a gap between elementary expositions and more
advanced (and clearly more stimulating) material. It takes the
challenge to explain the most relevant ideas and to show the most
important applications using plain language and "simple"
mathematics, often through an original approach. Basic calculus is
enough for the reader to proceed through the book and when more is
required, the new mathematical concepts are illustrated, again in
plain language. The book is conceived in such a way that some
difficult chapters can be bypassed, whilst still grasping the main
ideas. However, anybody wishing to go deeper in some directions
will find at least the flavour of recent developments and many
bibliographical references. Theory is always accompanied by
examples. Many problems are suggested and some are completely
worked out at the end of each chapter. The book may effectively be
used (and it is in several Italian Universities) for undergraduate
as well as for PhD courses in Physics and Mathematics at various
levels.
Despite the fact that fluid dynamics and filtration through porous
media and mathematics, there are classical research areas in
engineering, physics, are still many industrial processes that
require the study of new mathemat ical models for flows of
particular complexity, due to the peculiar properties of the
systems involved. The aim of this book is to provide a number of
examples showing how frequently such situations arise in various
branches of industrial technology. The selection of the subjects
was motivated not only by their industrial rel evance and
mathematical interest. What I had in mind was a collection of
problems having a really distinctive character, thus bringing some
fresh air into one of the oldest and most revered domains of
applied mathematics. The incredible richness of nonstandard flow
problems in industrial appli cations has always been, and still is,
a constant surprise to me. Therefore I tried to offer a very large
spectrum of subjects, with special attention devoted to those
problems in which the modeling phase is far from being obvious, and
the mathematical content is absolutely nontrivial. With such a view
to diversity, topics have been selected from a variety of sources
(such as glass industry, polymers science, coffee brewing, fuels
pipelining), and contributors from different backgrounds
(mathematics, physics, chemical engineering) have been included.
Consequently, the mathematical nature of the problems formulated
spans over a large range, so that their theoret ical investigation
and numerical computation require a variety of different
techniques.
Analytical Mechanics is the investigation of motion with the
rigorous tools of mathematics. Rooted in the works of Lagrange,
Euler, Poincare (to mention just a few), it is a very classical
subject with fascinating developments and still rich of open
problems. It addresses such fundamental questions as: Is the solar
system stable? Is there a unifying 'economy' principle in
mechanics? How can a point mass be described as a 'wave'? And has
remarkable applications to many branches of physics (Astronomy,
Statistical mechanics, Quantum Mechanics).
This book was written to fill a gap between elementary expositions
and more advanced (and clearly more stimulating) material. It takes
up the challenge to explain the most relevant ideas (generally
highly non-trivial) and to show the most important applications
using a plain language and 'simple' mathematics, often through an
original approach. Basic calculus is enough for the reader to
proceed through the book. New mathematical concepts are fully
introduced and illustrated in a simple, student-friendly language.
More advanced chapters can be omitted while still following the
main ideas. Anybody wishing to go deeper in some direction will
find at least the flavor of recent developments and many
bibliographical references. The theory is always accompanied by
examples. Many problems are suggested and some are completely
worked out at the end of each chapter. The book may effectively be
used (and has been used at several Italian Universities) for
undergraduate as well as for PhD courses in Physics and Mathematics
at various levels.
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