In January 1992, the Sixth Workshop on Optimization and Numerical Analysis was held in the heart of the Mixteco-Zapoteca region, in the city of Oaxaca, Mexico, a beautiful and culturally rich site in ancient, colonial and modern Mexican civiliza tion. The Workshop was organized by the Numerical Analysis Department at the Institute of Research in Applied Mathematics of the National University of Mexico in collaboration with the Mathematical Sciences Department at Rice University, as were the previous ones in 1978, 1979, 1981, 1984 and 1989. As were the third, fourth, and fifth workshops, this one was supported by a grant from the Mexican National Council for Science and Technology, and the US National Science Foundation, as part of the joint Scientific and Technical Cooperation Program existing between these two countries. The participation of many of the leading figures in the field resulted in a good representation of the state of the art in Continuous Optimization, and in an over view of several topics including Numerical Methods for Diffusion-Advection PDE problems as well as some Numerical Linear Algebraic Methods to solve related pro blems. This book collects some of the papers given at this Workshop."

The present volume, published at the occasion of his 100th birthday anniversary, is a collection of articles that reviews the impact of Kolomogorov's work in the physical sciences and provides an introduction to the modern developments that have been triggered in this way to encompass recent applications in biology, chemistry, information sciences and finance.

Advances in Mechanics and Mathematics (AMMA) is intended to bridge the gap by providing multi-disciplinary publications. This volume, AMMA 2002, includes two parts with three articles by four subject experts. Part 1 deals with nonsmooth static and dynamic systems. A systematic mathematical theory for multibody dynamics with unilateral and frictional constraints and a brief introduction to hemivariational inequalities together with some new developments in nonsmooth semi-linear elliptic boundary value problems are presented. Part 2 provides a comprehensive introduction and the latest research on dendritic growth in fluid mechanics, one of the most profound and fundamental subjects in the area of interfacial pattern formation, a commonly observed phenomenon in crystal growth and solidification processes.

This book presents comprehensive and authoritative coverage of the wide field of concentrated vortices observed in nature and technique. The methods for research of their kinematics and dynamics are considered. Special attention is paid to the flows with helical symmetry. The authors have described models of vortex structures used for interpretation of experimental data which serve as a ground for development of theoretical and numerical approaches to vortex investigation.

The need for properties is ever increasing to make processes more economical. A good survey of the viscosity data, its critical evaluation and correlation would help design engineers, scientists and technologists in their areas of interest. This type of work assumes more importance as the amount of experimental work in collection and correlation of properties such as viscosity, thermal conductivity, heat capacities, etc has reduced drastically both at the industry, universities, and national laboratories. One of the c o-authors, Professor Viswanath, co-authored a book jointly with Dr. Natarajan Data Book on the Viscosity of Liquids in 1989 which mainly presented collected and evaluated liquid viscosity data from the literature. Although it is one of its kinds in the field, Prof. Viswanath recognized that the design engineers, scientists and technologists should have a better understanding of theories, experimental procedures, and operational aspects of viscometers. Also, rarely the data are readily available at the conditions that are necessary for design of the equipment or for other calculations. Therefore, the data must be interpolated or extrapolated using the existing literature data and using appropriate correlations or models. We have tried to address these issues in this book."

Hydronamics of Explosion presents the research results for the problems of underwater explosions and contains a detailed analysis of the structure and the parameters of the wave fields generated by explosions of cord and spiral charges, a description of the formation mechanisms for a wide range of cumulative flows at underwater explosions near the free surface, and the relevant mathematical models. Shock-wave transformation in bubbly liquids, shock-wave amplification due to collision and focusing, and the formation of bubble detonation waves in reactive bubbly liquids are studied in detail. Particular emphasis is placed on the investigation of wave processes in cavitating liquids, which incorporates the concepts of the strength of real liquids containing natural microinhomogeneities, the relaxation of tensile stress, and the cavitation fracture of a liquid as the inversion of its two-phase state under impulsive (explosive) loading. The problems are classed among essentially nonlinear processes that occur under shock loading of liquids and may be of interest to researchers in physical acoustics, mechanics of multiphase media, shock-wave processes in condensed media, explosive hydroacoustics, and cumulation.

The need for tsunami research and analysis has grown dramatically following the devastating tsunami of December 2004, which affected Southern Asia. This book pursues a detailed theoretical and mathematical analysis of the fundamentals of tsunamis, especially the evolution and dynamics of tsunamis and other great waves. Of course, it includes specific measurement results from the 2004 tsunami, but the emphasis is on the nature of the waves themselves and their links to nonlinear phenomena.

Stratospheric processes play a signi?cant role in regulating the weather and c- mate of the Earth system. Solar radiation, which is the primary source of energy for the tropospheric weather systems, is absorbed by ozone when it passes through the stratosphere, thereby modulating the solar-forcing energy reaching into the t- posphere. The concentrations of the radiatively sensitive greenhouse gases present in the lower atmosphere, such as water vapor, carbon dioxide, and ozone, control the radiation balance of the atmosphere by the two-way interaction between the stratosphere and troposphere. The stratosphere is the transition region which interacts with the weather s- tems in the lower atmosphere and the richly ionized upper atmosphere. Therefore, this part of the atmosphere provides a long list of challenging scienti?c problems of basic nature involving its thermal structure, energetics, composition, dynamics, chemistry, and modeling. The lower stratosphere is very much linked dynamically, radiatively, and chemically with the upper troposphere, even though the temperature characteristics of these regions are different. The stratosphere is a region of high stability, rich in ozone and poor in water - por and temperature increases with altitude. The lower stratospheric ozone absorbs the harmful ultraviolet (UV) radiation from the sun and protects life on the Earth. On the other hand, the troposphere has high concentrations of water vapor, is low in ozone, and temperature decreases with altitude. The convective activity is more in the troposphere than in the stratospher

This book deals with the role of water in cell function. Long recognized to be central to cell function, water 's role has not received the attention lately that it deserves. This book brings the role of water front and central. It presents the most recent work of the leading authorities on the subject, culminating in a series of sometimes astonishing observations. This volume will be of interest to a broad audience.

Since the publication of "Spectral Methods in Fluid Dynamics" 1988, spectral methods have become firmly established as a mainstream tool for scientific and engineering computation. The authors of that book have incorporated into this new edition the many improvements in the algorithms and the theory of spectral methods that have been made since then. This latest book retains the tight integration between the theoretical and practical aspects of spectral methods, and the chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is also greatly expanded.

A consistent, up-to-date description of the extremely manifold and varied experimental techniques which nowadays enable work with neutral particles. Th book lays the physical foundations of the various experimental techniques, which utilize methods from most fields in physics.

This work brings together previously unpublished notes contributed by participants of the IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence (Moscow, 25-30 August 2006). The study of vortex motion is of great interest to fluid and gas dynamics: since all real flows are vortical in nature, applications of the vortex theory are extremely diverse, many of them (e.g. aircraft dynamics, atmospheric and ocean phenomena) being especially important.

Proceedings of the second conference on Applied Mathematics and Scientific Computing, held June 4-9, 2001 in Dubrovnik, Croatia.

The main idea of the conference was to bring together applied mathematicians both from outside academia, as well as experts from other areas (engineering, applied sciences) whose work involves advanced mathematical techniques.

During the meeting there were one complete mini-course, invited presentations, contributed talks and software presentations. A mini-course Schwarz Methods for Partial Differential Equations was given by Prof Marcus Sarkis (Worcester Polytechnic Institute, USA), and invited presentations were given by active researchers from the fields of numerical linear algebra, computational fluid dynamics, matrix theory and mathematical physics (fluid mechanics and elasticity).

This volume contains the mini-course and review papers by invited speakers (Part I), as well as selected contributed presentations from the field of analysis, numerical mathematics, and engineering applications.

This is a rapidly developing field to which the author is a leading contributor

New methods in quantum dynamics and computational techniques, with applications to interesting physical problems, are brought together in this book

Useful to both students and researchers

This volume contains the proceedings of the IUTAM Symposium on Computational Physics and New Perspectives in Turbulence, held at Nagoya University, Nagoya, Japan, in September 2006. With special emphasis given to fundamental aspects of the physics of turbulence, coverage includes experimental approaches to fundamental problems in turbulence, turbulence modeling and numerical methods, and geophysical and astrophysical turbulence.

Magnetic control of the properties and the flow of liquids is a challenging field for basic research and for applications. This book is meant to be both an introduction to, and a state-of-the-art review of, this topic. Written in the form of a set of lectures and tutorial reviews, the book addresses the synthesis and characterization of magnetic fluids, their hydrodynamical description and their rheological properties. The book closes with an account of magnetic drug targeting.

Elements of Continuum Mechanics and Conservation Laws presents a systematization of different models in mathematical physics, a study of the structure of conservation laws, thermodynamical identities, and connection with criteria for well-posedness of the corresponding mathematical problems.
The theory presented in this book stems from research carried out by the authors concerning the formulations of differential equations describing explosive deformations of metals. In such processes, elasticity equations are used in some zones, whereas hydrodynamics equations are stated in other zones. Plastic deformations appear in transition zones, which leads to residual stresses. The suggested model contains some relaxation terms which simulate these plastic deformations. Certain laws of thermodynamics are used in order to describe and study differential equations simulating the physical processes. This leads to the special formulation of differential equations using generalized thermodynamical potentials.

This volume contains new trends of computational fluid dynamics for the 21st century and consists of papers especially useful to the younger generation of scientists and engineers in this field. Topics include cartesian, gridless and higher-order schemes, and flow-visualization techniques.

This book springs from the programme Quantized Vortex Dynamics and Sup- ?uid Turbulence held at the Isaac Newton Institute for Mathematical Sciences (University of Cambridge) in August 2000. What motivated the programme was the recognition that two recent developments have moved the study of qu- tized vorticity, traditionally carried out within the low-temperature physics and condensed-matter physics communities, into a new era. The ?rst development is the increasing contact with classical ?uid dynamics and its ideas and methods. For example, some current experiments with - lium II now deal with very classical issues, such as the measurement of velocity spectra and turbulence decay rates. The evidence from these experiments and many others is that super?uid turbulence and classical turbulence share many features. The challenge is now to explain these similarities and explore the time scales and length scales over which they hold true. The observed classical aspects have also attracted attention to the role played by the ?ow of the normal ?uid, which was somewhat neglected in the past because of the lack of direct ?ow visualization. Increased computing power is also making it possible to study the coupled motion of super?uid vortices and normal ?uids. Another contact with classical physics arises through the interest in the study of super?uid vortex - connections. Reconnections have been studied for some time in the contexts of classical ?uid dynamics and magneto-hydrodynamics (MHD), and it is useful to learn from the experience acquired in other ?elds.

This book completes the physical foundations and experimental techniques described in volume 1 with an updated review of the accessory equipment indispensable in molecular beam experiments. It extends the subject to cluster beams and beams of hyperthermal and subthermal energies.

This book is dedicated to the memory of a distinguished Russian engineer, Rostislav E. Alexeyev, who was the first in the world to develop the largest ground effect machine - Ekranoplan. One of Alexeyev's design concepts with the aerodynamic configuration of a jlying wing can be seen on the front page. The book presents a description of a mathematical model of flow past a lifting system, performing steady and unsteady motions in close proximity to the underlying solid surface (ground). This case is interesting for practical purposes because both the aerodynamic and the economic efficiency of the system near the ground are most pronounced. Use of the method of matched asymptotic expansions enables closed form solutions for the aerodynamic characteristics of the wings-in-ground effect. These can be used for design, identification, and processing of experimental data in the course of developing ground effect vehicles. The term extreme ground effect, widely used through out the book, is associated with very small relative ground clearances of the order of 10% or less. The theory of a lifting surface, moving in immediate proximity to the ground, represents one of the few limiting cases that can be treated analytically. The author would like to acknowledge that this work has been influenced by the ideas of Professor Sheila E. Widnall, who was the first to apply the matched asymptotics techniques to treat lifting flows with the ground effect. Saint Petersburg, Russia February 2000 Kirill V. Rozhdestvensky Contents 1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ."

Magnetohydrodynamics (MHD) studies the interaction between the flow of an electrically conducting fluid and magnetic fields. It involves such diverse topics as the evolution and dynamics of astrophysical objects, thermonuclear fusion, metallurgy and semiconductor crystal growth, etc. Although the first ideas in magnetohydrodynamics appeared at the beginning of the last century, the "explosion" in theoretical and experimental studies occurred in the 1950s-60s.

This state-of-the-art book aims at revising the evolution of ideas in various branches of magnetohydrodynamics (astrophysics, earth and solar dynamos, plasmas, MHD turbulence and liquid metals) and reviews current trends and challenges.

The book deals with the theme of incompressible flows of electrically conducting fluids in hydraulic components. The main content of the book is a result of engineering research associated with the design of liquid metal cooling systems for fusion reactors. The book is well suited to serve as a guide for utilising magnetohydrodynamic means in other engineering disciplines such as in material processing, metallurgical engineering and power engineering.

The present volume is an introduction to nonlinear waves and soliton theory in the special environment of compact spaces such as closed curves and surfaces and other domain contours.

The first part of the book introduces the mathematical concept required for treating the manifolds considered. An introduction to the theory of motion of curves and surfaces is given. The second and third parts discuss the modeling of various physical solitons on compact systems.

The English version of the book does not di?er essentially from the Rus- 1 sian version . Along with a few notes and new references I included Part II to Article 3 and added some new materials to the 'Nobel' autobiography. Furthermore, Article 7 (M. Cardona and W. Marx "Vitaly L. Ginzburg - a bibliometricstudy"), whichwaspublishedinJournalofSuperconductivityand NovelMagnetism, v.19, No.3-5, July 2006 is included as an appendix. My special thanks are due to Prof. Manuel Cardona and Prof. Werner Marx who kindly allowed publishing their paper as an appendix to this book (with some new minor author's amendments). Also, I am grateful to M.S. Aksent'eva, E.A. Frimer, G.M. Krasnikova and S.G.RudnevfortheirassistanceinthepreparationoftheEnglishmanuscript. Moscow, September 2008 V.L.Ginzburg 1 V.L.Ginzburg, Osverkhprovodimostiiosverkhtekuchesti.Avtobiogra?a (Moskva: Izdatel'styvo Fiziko-matematicheskoi literatury, 2006) Preface to the Russian Edition The Nobel Prize in Physics, 2003 was awarded to A.A. Abrikosov, A.J. L- gett and myself 'for pioneering contribution to the theory of superconductors and super?uids'. It does not mean that the contribution was made in joint works with these authors. Speci?cally, I do not have any joint publications with A.A. Abrikosov and A.J. Leggett.