Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as weil as the clas sical techniques of applied mathematics. This renewal of interest, bothin research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high Ievel of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathematical Seiences (AMS) series, which will focus on advanced textbooks and research Ievel monographs. Preface This book is based on a one-term coursein fluid mechanics originally taught in the Department of Mathematics of the U niversity of California, Berkeley, during the spring of 1978. The goal of the course was not to provide an exhaustive account of fluid mechanics, nor to assess the engineering value of various approximation procedures."

The Tenth International Symposium on Gaseous Dielectrics was held at the Astir Palace Vouliagmeni Hotel, Athens, Greece, March 29-April 2, 2004. The symposium. continued the interdisciplinary character and comprehensive approach of the preceding nine symposia. Gaseous Dielectrics X is a detailed record of the symposium proceedings. It covers recent advances and developments in a wide range of basic, applied, and industrial areas of gaseous dielectrics. It is hoped that Gaseous Dielectrics X will aid future research and development in, and encourage wider industrial use of, gaseous dielectrics. The Organizing Committee of the Tenth International Symposium on Gaseous Dielectrics consisted of L. G. Christophorou (Chainnan, Greece), J. K. Olthoff (co-Chainnan, USA), A. Bulinski (Canada), A. H. Cookson (USA), C. T. Dervos (Greece), J. de Urquijo (Mexico), J. Blackman (USA), O. Farish (UK), M. E. Frechette (Canada), I. Gillimberti (Italy), A. Garscadden (USA), A. Gleizes (France), H. Hama (Japan), T. Kawamura (Japan), E. Marode (France), I. W. McAllister (Denmark), H. Morrison (Canada), A. H. Mufti (Saudi Arabia), L. Niemeyer (Switzerland), W. Pfeiffer (Germany), Y. Qiu (China), I. Sauers (USA), M. Schmidt (Germany), H.-H. Schramm (Germany), L. van der Zel (USA), S. Yanabu (Japan), Y. Wang (USA), and J. W. Wetzer (The Netherlands). The Local Arrangements Committee consisted of J. N. Avaritsiotis, P. Vassiliou, C. T. Dervos of The National Technical University of Athens, C. A. Stassinopoulos of the Aristotelian University of Thessaloniki, and D.

From the reviews: "Researchers in fluid dynamics and applied mathematics will enjoy this book for its breadth of coverage, hands-on treatment of important ideas, many references, and historical and philosophical remarks." Mathematical Reviews

Munson, Young, and Okiishi's Fundamentals of Fluid Mechanics is intended for undergraduate engineering students for use in a first course on fluid mechanics. Building on the well-established principles of fluid mechanics, the book offers improved and evolved academic treatment of the subject. Each important concept or notion is considered in terms of simple and easy-to-understand circumstances before more complicated features are introduced. The presentation of material allows for the gradual development of student confidence in fluid mechanics problem solving. This International Adaptation of the book comes with some new topics and updates on concepts that clarify, enhance, and expand certain ideas and concepts. The new examples and problems build upon the understanding of engineering applications of fluid mechanics and the edition has been completely updated to use SI units.

This symposium continues a long tradition for IUGGjIUTAM symposia going back to "Fundamental Problems in Thrbulence and their Relation to Geophysics" Marseille, 1961. The five topics that were emphasized were: turbulence modeling, statistics of small scales and coherent structures, con vective turbulence, stratified turbulence, and historical developments. The objective was to consider the ubiquitous nature of turbulence in a variety of geophysical problems and related flows. Some history of the contribu tions of NCAR and its alumni were discussed, including those of Jackson R Herring, who has been a central figure at NCAR since 1972. To the original topics we added rotation, which appeared in many places. This includes rotating stratified turbulence, rotating convective turbulence, horizontal rotation that appears in flows over terrain and the role of small scale vorticity in many flows. These complicated flows have recently begun to be simulated by several groups from around the world and this meeting provided them with an excellent forum for exchanging results, plus inter actions with those doing more fundamental work on rotating stratified and convective flows. New work on double diffusive convection was given in two presentations. The history of Large Eddy Simulations was presented and several new approaches to this field were given. This meeting also spawned some interesting interactions between observational side and how to inter pret the observations with modeling and simulations around the theme of particle dispersion in these flows.

This IMA Volume in Mathematics and its Applications COMPUTATIONAL MODELING IN BIOLOGICAL FLUID DYNAMICS is based on the proceedings of a very successful workshop with the same title. The workshop was an integral part of the September 1998 to June 1999 IMA program on "MATHEMATICS IN BIOLOGY." I would like to thank the organizing committee: Lisa J. Fauci of Tulane University and Shay Gueron of Technion - Israel Institute of Technology for their excellent work as organizers of the meeting and for editing the proceedings. I also take this opportunity to thank the National Science Founda tion (NSF), whose financial support of the IMA made the Mathematics in Biology program possible. Willard Miller, Jr., Professor and Director Institute for Mathematics and its Applications University of Minnesota 400 Lind Hall, 207 Church St. SE Minneapolis, MN 55455-0436 612-624-6066, FAX 612-626-7370 [email protected] World Wide Web: http://www.ima.umn.edu v PREFACE A unifying theme in biological fluid dynamics is the interaction of moving, elastic boundaries with a surrounding fluid. A complex dynami cal system describes the motion of red blood cells through the circulatory system, the movement of spermatazoa in the reproductive tract, cilia of microorganisms, or a heart pumping blood. The revolution in computa tional technology has allowed tremendous progress in the study of these previously intractable fluid-structure interaction problems.

Mathematical modeling and numerical simulation in fluid mechanics are topics of great importance both in theory and technical applications. The present book attempts to describe the current status in various areas of research. The 10 chapters, mostly survey articles, are written by internationally renowned specialists and offer a range of approaches to and views of the essential questions and problems. In particular, the theories of incompressible and compressible Navier-Stokes equations are considered, as well as stability theory and numerical methods in fluid mechanics. Although the book is primarily written for researchers in the field, it will also serve as a valuable source of information to graduate students.

In recent years kinetic theory has developed in many areas of the physical sciences and engineering, and has extended the borders of its traditional fields of application. This monograph is a self-contained presentation of such recently developed aspects of kinetic theory, as well as a comprehensive account of the fundamentals of the theory. Emphasizing modeling techniques and numerical methods, the book provides a unified treatment of kinetic equations not found in more focused works. Specific applications presented include plasma kinetic models, traffic flow models, granular media models, and coagulation-fragmentation problems. The work may be used for self-study, as a reference text, or in graduate-level courses in kinetic theory and its applications.

This study is one of the first attempts to bridge the theoretical models of variational dynamics of perfect fluids and some practical approaches worked out in chemical and mechanical engineering in the field newly called thermo-hydrodynamics. In recent years, applied mathematicians and theoretical physicists have made significant progress in formulating analytical tools to describe fluid dynamics through variational methods. These tools are much loved by theoretists, and rightly so, because they are quite powerful and beautiful theoretical tools. Chemists, physicists and engineers, however, are limited in their ability to use these tools, because presently they are applicable only to "perfect fluids" (i. e. those fluids without viscosity, heat transfer, diffusion and chemical reactions). To be useful, a model must take into account important transport and rate phenomena, which are inherent to real fluid behavior and which cannot be ignored. This monograph serves to provide the beginnings of a means by which to extend the mathematical analyses to include the basic effects of thermo-hydrodynamics. In large part a research report, this study uses variational calculus as a basic theoretical tool, without undo compromise to the integrity of the mathematical analyses, while emphasizing the conservation laws of real fluids in the context of underlying thermodynamics --reversible or irreversible. The approach of this monograph is a new generalizing approach, based on Nother's theorem and variational calculus, which leads to the energy-momentum tensor and the related conservation or balance equations in fluids.

Starting in 1996, a sequence of articles appeared in the Journal of Nonlinear Science dedicated to the memory of one of its original editors, Juan-Carlos Simo, Applied Me chanics, Stanford University. Sadly, Juan-Carlos passed away at an early age in 1994. We lost a brilliant colleague and a wonderful person. These articles are collected in the present volume. Many of them are updated and corrected especially for this occasion. These essays are in areas of scientific interest of Juan-Carlos, including mechanics (particles, rigid bodies, fluids, elasticity, plastic ity, etc.), geometry, applied dynamics, and, of course, computation. His interests were extremely broad-he did not see boundaries between computation, mathematics, me chanics, and dynamics, and, in that sense, he ideally reflected the spirit of the journal and many of the most exciting areas of current scientific interest. Juan-Carlos was one of those select and gifted people who could cross interdisci plinary boundaries with extremely high quality and productive interactions of lasting value. His contributions, ranging from concrete engineering problems to fundamental mathematical theorems in geometric mechanics, are remarkable. In current conferences as well as in scientific books and articles, and over a wide range of subjects, one frequently hears how his ideas as well as specific results are often used and quoted-this is one indication of just how profound and fundamental his work has impacted the community.

A collection of contributions on a variety of mathematical, physical and engineering subjects related to turbulence. Topics include mathematical issues, control and related problems, observational aspects, two- and quasi-two-dimensional flows, basic aspects of turbulence modeling, statistical issues and passive scalars.

The main objective of the First International Symposium on Lubricated Transport of Viscous Materials was to bring together scientists and engineers from academia and industryto discuss current research work and exchange ideas in this newly emerging field. It is an area offluid dynamics devoted to laying bare the principlesofthe lubricated transport of viscous materials such as crude oil, concentrated oil/water emulsion, slurries and capsules. It encompasses several types of problem. Studies of migration of particulates away from walls, Segre-Silverberg effects, lubrication versus lift and shear-induced migration belong to one category. Some of the technological problems are the fluid dynamics ofcore flows emphasizing studies ofstability, problems of start-up, lift-off and eccentric flow where gravity causes the core flow to stratify. Another category of problems deals with the fouling of pipe walls with oil, with undesirable increases in pressure gradients and even blocking. This study involves subjects like adhesion and dynamic contact angles. The topics ofshear-induced diffusion ofsmall particles and wall slip in slow flow are other appropriate subjects. Computer intensive studiesofflow-induced microstructures and moving interface problems are yet additional research directions. The general consensus was that the Symposium was a tremendous success, although the number of presentations fell below expectations. Scientists from the petroleum industry, and this includes INTEVEP (Venezuela), Schlumberger and Syncrude Canada Ltd., and consultants to oil companies actively participated in the Symposium. The meeting produced new insights which should lead to further interesting research work and established contacts for possiblejoint investigations."

Whilst most contemporary books in the aerospace propulsion field are dedicated primarily to gas turbine engines, there is often little or no coverage of other propulsion systems and devices such as propeller and helicopter rotors or detailed attention to rocket engines. By taking a wider viewpoint, "Powered Flight - The Engineering of Aerospace Propulsion" aims to provide a broader context, allowing observations and comparisons to be made across systems that are overlooked by focusing on a single aspect alone. The physics and history of aerospace propulsion are built on step-by-step, coupled with the development of an appreciation for the mathematics involved in the science and engineering of propulsion.

Combining the author s experience as a researcher, an industry professional and a lecturer in graduate and undergraduate aerospace engineering, "Powered Flight - The Engineering of Aerospace Propulsion" covers its subject matter both theoretically and with an awareness of the practicalities of the industry. To ensure that the content is clear, representative but also interesting the text is complimented by a range of relevant graphs and photographs including representative engineering, in addition to several propeller performance charts. These items provide excellent reference and support materials for graduate and undergraduate projects and exercises.

Students in the field of aerospace engineering will find that "Powered Flight - The Engineering of Aerospace Propulsion" supports their studies from the introductory stage and throughout more intensive follow-on studies. "

This research monograph deals with a modeling theory of the system of Navier-Stokes-Fourier equations for a Newtonian fluid governing a compressible viscous and heat conducting flows. The main objective is threefold. First , to 'deconstruct' this Navier-Stokes-Fourier system in order to unify the puzzle of the various partial simplified approximate models used in Newtonian Classical Fluid Dynamics and this, first facet, have obviously a challenging approach and a very important pedagogic impact on the university education. The second facet of the main objective is to outline a rational consistent asymptotic/mathematical theory of the of fluid flows modeling on the basis of a typical Navier-Stokes-Fourier initial and boundary value problem. The third facet is devoted to an illustration of our rational asymptotic/mathematical modeling theory for various technological and geophysical stiff problems from: aerodynamics, thermal and thermocapillary convections and also meteofluid dynamics.

The Earth's atmosphere is often portrayed as a thin and finite blanket covering our planet, separate from the emptiness of outer space. In reality, the transition is gradual and a tiny fraction of the atmophere gases is still present at the altitude of low orbiting satellites. The very high velocities of these satellites ensure that their orbital motion can still be considerably affected by air density and wind. This influence can be measured using accelerometers and satellite tracking techniques. The opening chapters of this thesis provide an excellent introduction to the various disciplines that are involved in the interpretation of these observations: orbital mechanics, satellite aerodynamics and upper atmospheric physics. A subsequent chapter, at the heart of this work, covers advances in the algorithms used for processing satellite accelerometry and Two-Line Element (TLE) orbit data. The closing chapters provide an elaborate analysis of the resulting density and wind products, which are generating many opportunities for further research, to improve the modelling and understanding of the thermosphere system and its interactions with the lower atmosphere, the ionosphere-magnetosphere system and the Sun.

This is the first thorough examination of weakly nonlocal solitary waves, which are just as important in applications as their classical counterparts. The book describes a class of waves that radiate away from the core of the disturbance but are nevertheless very long-lived nonlinear disturbances.

This book contains papers presented at a workshop, jointly organized by the EUROPIV 2 project, the PivNet 2 Thematic Network, and the ERCOFTAC Spe cial Interest Group on PIV (SIG 32). EUROPIV 2 was a research program, funded by the European Community which started in April 2000 and ended in June 2003. The aim of this project was to develop and demonstrate the Particle Image Velocimetry technique (PIV), which allows to measure the velocity of large flow fields instantaneously, in order to make it available as an operational tool for the European aeronautical industry. A total of 17 teams from 5 different countries cooperated during these 3 years to im prove the method, both hardware and software, and to demonstrate its capabilities in large industrial wind tunnels. PivNet 2 is a European thematic network devoted to the transfer of the PIV technique to IndUStry. It has started in April 2002 for four years. It is coordinated by Dr J. Kompenhans from DLR Gottingen. Details on PivNnet 2 can be found at http: //pivnet.sm.go.dlr.de. ERCOFTAC (European Research Community on Flow, Turbulence and Com bustion) is an international association with the aim to promote research and coop eration in Europe on fluid flows, turbulence and combustion. Details can be found at http: //www.ercoftac.org and http: //www.univ-lillellpivnet."

Progress in fluid mechanics depends heavily on the availability of good experimental data which can inspire new ideas and concepts but which are also necessary to check and validate theories and numerical calculations. With the advent of new recording and image analysis techniques new and promising experimental methods in fluid flows have presented themselves which are rather newly developed techniques such as particle tracking velocimetry (PTV), particle image velocimetry (PIV) and laser fluorescene (LIF). This volume presents state-of-the-art research on these techniques and their application to fluid flow. Selected papers from the EUROMECH conference on Image Analysis are published in this volume.

The position taken in this collection of pedagogically written essays is that conjugate gradient algorithms and finite element methods complement each other extremely well.

Via their combinations practitioners have been able to solve complicated, direct and inverse, multidemensional problems modeled by ordinary or partial differential equations and inequalities, not necessarily linear, optimal control and optimal design being part of these problems.

The aim of this book is to present both methods in the context of complicated problems modeled by linear and nonlinear partial differential equations, to provide an in-depth discussion on their implementation aspects. The authors show that conjugate gradient methods and finite element methods apply to the solution of real-life problems. They address graduate students as well as experts in scientific computing.

In the present book the reader will find a review of methods for constructing a certain class of asymptotic solutions, which we call self-stabilizing solutions. This class includes solitons, kinks, traveling waves, etc. It can be said that either the solutions from this class or their derivatives are localized in the neighborhood of a certain curve or surface. For the present edition, the book published in Moscow by the Nauka publishing house in 1987, was almost completely revised, essentially up-dated, and shows our present understanding of the problems considered. The new results, obtained by the authors after the Russian edition was published, are referred to in footnotes. As before, the book can be divided into two parts: the methods for constructing asymptotic solutions ( Chapters I-V) and the application of these methods to some concrete problems (Chapters VI-VII). In Appendix a method for justification some asymptotic solutions is discussed briefly. The final formulas for the asymptotic solutions are given in the form of theorems. These theorems are unusual in form, since they present the results of calculations. The authors hope that the book will be useful to specialists both in differential equations and in the mathematical modeling of physical and chemical processes. The authors express their gratitude to Professor M. Hazewinkel for his attention to this work and his support.

The problems of transient interaction of deformable bodies with surrounding media are of great practical and theoretical importance. When solving the problems of this kind, the main difficulty is in the necessity to integrate jointly the system of equations which describe motion of the body and the system of equations which describe motion of the medium under the boundary conditions predetermined at the unknown (movable) curvilinear interfaces. At that, the position of these interfaces should be determined as part of the solution process. That is why, the known exact solutions in this area of mechanics of continuum have been derived mainly for the cases of idealized rigid bodies. Different aspects of the problems of transient interaction of bodies and structures with continuum (derivation of the efficient mathematical mod els for the phenomenon, development of the theoretical and experimental methods to be used for study of the transient problems of mechanics, etc.) were considered in the books by S.U. Galiev, A.N. Guz, V.D. Kubenko, V.B. Poruchikov, L.L Slepyan, A.S. Volmir, and Yu.S. Yakovlev. The results presented by these authors make interest when solving a great variety of problems and show a necessity of joint usage of the results obtained in differ ent areas: aerohydrodynamics, theory of elasticity and plasticity, mechanics of soils, theory of shells and plates, applied and computational mathemat ics, etc.

This volume contains twenty contributions of work, conducted since 1996 in the French- German Research Programme "Numerical Flow Simulation" of the Centre National de la Recherche Scientifique (CNRS) and the Deutsche Forschungsgemeinschaft (DFG). The main purpose of this publication is to give an overview over the work conducted in this programme, and to make the results obtained available to the pUblic. The reports are grouped under the four headings "Development of Solution Techniques", "Crystal Growth and Melts", "Flows of Reacting Gases" and "Turbulent Flows". AIl contributions to this publica- tion were reviewed by a board consisting of T. Alziary de Roquefort (Poitiers, France), P. Bontoux (Marseille, France), JA Desideri (Sophia-Antipolis, France), W. Kordulla (G6t- tingen, Germany), R. Peyret (Nice, France), R. Rannacher (Heidelberg, Germany), G. War- necke (Magdeburg, ,Germany), and the editor. The responsibility for the contents of the reports nevertheless lies with the authors. E. H. Hirschel Editor Preface The Colloquium on "Numerical Simulation of Flows", Marseille, November 21 and 22, th 1997, was the 6 Joint CNRS-DFG Colloquium organized in the frame of the French- German Research Collaboration on Computational Fluid Dynamics. This Collaborative Program was elaborated progressively since 1991, when the two major research groups were brought together: the Priority Program "Flow Simulation with Super Computers" from the DFG in Germany and the Groupement de Recherche de "Mecanique des Fluides NumCrique" (GDR MFN) from the CNRS in France.

This technical book considers the application side of LDA techniques. Starting from the basic theories that are crucial for each LDA user, the main subject of the book is focused on diverse application methods. In details, it deals with universal methodical techniques that have been mostly developed in the last 15 years. The book thus gives for the first time an application reference for LDA users in improving the optical conditions and enhancing the measurement accuracies. It also provides the guidelines for simplifying the measurements and correcting measurement errors as well as for clarifying the application limits and extending the application areas of LDA techniques. Beside the treatments of some traditional optical and flow mechanical features influencing the measurement accuracies, the book shows a broad spectrum of LDA application methods in the manner of measuring the flow turbulence, resolving the secondary flow structures, and quantifying the optical aberrations at measurements of internal flows etc.. Thus, it also supports the further developments of both the hard- and software of LDA instrumentations.

Computers are widely used for the analysis, design, and operation of water resource projects. This gives accurate results, allowing the analysis of complex systems which may not have been possible otherwise, and the investigation and comparison of several different alternatives in a short time, thereby reducing the project costs, optimizing design, and efficient utilization of resources. This volume compiles an edited version of the lecture notes specially prepared by 14 well-known European and North American researchers. Part I deals with free-surface flows. Governing equations are derived and their solution by the finite-difference, finite-element, and boundary-integral methods are discussed. Then, turbulence models, three-dimensional models, dam-break flow models, sediment transport models, and flood routing models are presented. Part II is related to the modeling of steady and transient pressurized flows. Governing equations for both single and two-component flows are derived and numerical methods for their solution are presented. The modeling of water quality in pipe networks, of cooling water systems, and slow and rapid transients is then discussed.

With continuous development of modern computing hardware and applicable - merical methods, computational ?uid dynamics (CFD) has reached certain level of maturity so that it is being used routinely by scientists and engineers for ?uid ?ow analysis. Since most of the real-life applications involve some kind of optimization, it has been natural to extend the use of CFD tools from ?ow simulation to simu- tion based optimization. However, the transition from simulation to optimization is not straight forward, it requires proper interaction between advanced CFD meth- ologies and state-of-the-art optimization algorithms. The ultimate goal is to achieve optimal solution at the cost of few ?ow solutions. There is growing number of - search activities to achieve this goal. This book results from my work done on simulation based optimization problems at the Department of Mathematics, University of Trier, and reported in my postd- toral thesis ("Habilitationsschrift") accepted by the Faculty-IV of this University in 2008. The focus of the work has been to develop mathematical methods and - gorithms which lead to ef?cient and high performance computational techniques to solve such optimization problems in real-life applications. Systematic development of the methods and algorithms are presented here. Practical aspects of implemen- tions are discussed at each level as the complexity of the problems increase, suppo- ing with enough number of computational examples.