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Nonlinear partial differential equations abound in modern physics.
The problems arising in these fields lead to fascinating questions
and, at the same time, progress in understanding the mathematical
structures is of great importance to the models. Nevertheless,
activity in one of the approaches is not always sufficiently in
touch with developments in the other field. The book presents the
joint efforts of mathematicians and physicists involved in
modelling reactive flows, in particular superconductivity and
superfluidity. Certain contributions are fundamental to an
understanding of such cutting-edge research topics as rotating
Bose-Einstein condensates, Kolmogorov-Zakharov solutions for weak
turbulence equations, and the propagation of fronts in
heterogeneous media.
Nonlinear partial differential equations abound in modern physics.
The problems arising in these fields lead to fascinating questions
and, at the same time, progress in understanding the mathematical
structures is of great importance to the models. Nevertheless,
activity in one of the approaches is not always sufficiently in
touch with developments in the other field. The book presents the
joint efforts of mathematicians and physicists involved in
modelling reactive flows, in particular superconductivity and
superfluidity. Certain contributions are fundamental to an
understanding of such cutting-edge research topics as rotating
Bose-Einstein condensates, Kolmogorov-Zakharov solutions for weak
turbulence equations, and the propagation of fronts in
heterogeneous media.
CARGESE INSTITUfE ON DISORDER AND MIXING Convection, diffusion and
reaction are the three basic mechanisms in physico-chemical
hydrodynamics and chemical engineering. Both convective and
diffusive processes are strongly influenced by the effect of
disorder of granular matter in porous media, suspensions, fluidized
beds or/and by the randomness caused in turbulent flow field. This
book has been initiated by a NATO summer institute held in Cargese
(Corsica, FRANCE) from June 15 th to 27 th 1987 . Its aim was to
associate statistical physicists, fluid mechanicians and
specialists of chemical engineering on the problems of the relation
between disorder and mixing and, in this respect, this is a "
premiere ." This book is made of chapters based on lectures given
in the meeting. However we have paid a considerable attention to
harmonize the contents and styles of chapters made by scientists
trained in different communities and using different languages and
techniques to describe similar problems. The Prelude by the editors
of the book introduces the different points and is a biased view of
some of the important and most active aspects of the subjects
developed. We wish to thank all contributors and students of the
institute who gave the style of the present interdisciplinary
approach. We also greatly thank Elisabeth Charlaix who has shared
with us the scientific and practical organisation of the institute,
and Marie-France Hanseler for her technical support.
CARGESE INSTITUfE ON DISORDER AND MIXING Convection, diffusion and
reaction are the three basic mechanisms in physico-chemical
hydrodynamics and chemical engineering. Both convective and
diffusive processes are strongly influenced by the effect of
disorder of granular matter in porous media, suspensions, fluidized
beds or/and by the randomness caused in turbulent flow field. This
book has been initiated by a NATO summer institute held in Cargese
(Corsica, FRANCE) from June 15 th to 27 th 1987 . Its aim was to
associate statistical physicists, fluid mechanicians and
specialists of chemical engineering on the problems of the relation
between disorder and mixing and, in this respect, this is a "
premiere ." This book is made of chapters based on lectures given
in the meeting. However we have paid a considerable attention to
harmonize the contents and styles of chapters made by scientists
trained in different communities and using different languages and
techniques to describe similar problems. The Prelude by the editors
of the book introduces the different points and is a biased view of
some of the important and most active aspects of the subjects
developed. We wish to thank all contributors and students of the
institute who gave the style of the present interdisciplinary
approach. We also greatly thank Elisabeth Charlaix who has shared
with us the scientific and practical organisation of the institute,
and Marie-France Hanseler for her technical support.
This book provides an introduction to topics in non-equilibrium
quantum statistical physics for both mathematicians and theoretical
physicists. The first part introduces a kinetic equation, of
Kolmogorov type, which is needed to describe an isolated atom
(actually, in experiments, an ion) under the effect of a classical
pumping electromagnetic field which keeps the atom in its excited
state(s) together with the random emission of fluorescence photons
which put it back into its ground state. The quantum kinetic theory
developed in the second part is an extension of Boltzmann's
classical (non-quantum) kinetic theory of a dilute gas of quantum
bosons. This is the source of many interesting fundamental
questions, particularly because, if the temperature is low enough,
such a gas is known to have at equilibrium a transition, the
Bose-Einstein transition, where a finite portion of the particles
stay in the quantum ground state. An important question considered
is how a Bose gas condensate develops in time if its energy is
initially low enough.
We experience elasticity everywhere in daily life: in the
straightening or curling of hairs, the irreversible deformations of
car bodies after a crash, or the bouncing of elastic balls in
ping-pong or soccer. The theory of elasticity is essential to the
recent developments of applied and fundamental science, such as the
bio-mechanics of DNA filaments and other macro-molecules, and the
animation of virtual characters in computer graphics and materials
science. In this book, the emphasis is on the elasticity of thin
bodies (plates, shells, rods) in connection with geometry. It
covers such topics as the mechanics of hairs (curled and straight),
the buckling instabilities of stressed plates, including folds and
conical points appearing at larger stresses, the geometric rigidity
of elastic shells, and the delamination of thin compressed films.
It applies general methods of classical analysis, including
advanced nonlinear aspects (bifurcation theory, boundary layer
analysis), to derive detailed, fully explicit solutions to specific
problems. These theoretical concepts are discussed in connection
with experiments. Mathematical prerequisites are vector analysis
and differential equations. The book can serve as a concrete
introduction to nonlinear methods in analysis.
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