In structure mechanics analysis, finite element methods are now well estab lished and well documented techniques; their advantage lies in a higher flexibility, in particular for: (i) The representation of arbitrary complicated boundaries; (ii) Systematic rules for the developments of stable numerical schemes ap proximating mathematically wellposed problems, with various types of boundary conditions. On the other hand, compared to finite difference methods, this flexibility is paid by: an increased programming complexity; additional storage require ment. The application of finite element methods to fluid mechanics has been lagging behind and is relatively recent for several types of reasons: (i) Historical reasons: the early methods were invented by engineers for the analysis of torsion, flexion deformation of bearns, plates, shells, etc ... (see the historics in Strang and Fix (1972) or Zienckiewicz (1977. (ii) Technical reasons: fluid flow problems present specific difficulties: strong gradients, l of the velocity or temperature for instance, may occur which a finite mesh is unable to properly represent; a remedy lies in the various upwind finite element schemes which recently turned up, and which are reviewed in chapter 2 (yet their effect is just as controversial as in finite differences). Next, waves can propagate (e.g. in ocean dynamics with shallowwaters equations) which will be falsely distorted by a finite non regular mesh, as Kreiss (1979) pointed out. We are concerned in this course with the approximation of incompressible, viscous, Newtonian fluids, i.e. governed by N avier Stokes equations."

Stochastic Dynamics, born almost 100 years ago with the early explanations of Brownian motion by physicists, is nowadays a quickly expanding field of research within nonequilibrium statistical physics. The present volume provides a survey on the influence of fluctuations in nonlinear dynamics. It addresses specialists, although the intention of this book is to provide teachers and students with a reliable resource for seminar work. In particular, the reader will find many examples illustrating the theory as well as a host of recent findings.

The second Workshop on "Quality and Reliability of Large-Eddy Simulations", QLES2009, was held at the University of Pisa from September 9 to September 11, 2009. Its predecessor, QLES2007, was organized in 2007 in Leuven (Belgium). The focus of QLES2009 was on issues related to predicting, assessing and assuring the quality of LES. The main goal of QLES2009 was to enhance the knowledge on error sources and on their interaction in LES and to devise criteria for the prediction and optimization of simulation quality, by bringing together mathematicians, physicists and engineers and providing a platform specifically addressing these aspects for LES. Contributions were made by leading experts in the field. The present book contains the written contributions to QLES2009 and is divided into three parts, which reflect the main topics addressed at the workshop: (i) SGS modeling and discretization errors; (ii) Assessment and reduction of computational errors; (iii) Mathematical analysis and foundation for SGS modeling.

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.

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.

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.

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.

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.

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.

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.

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 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."

The new series, International Mathematical Series founded by Kluwer / Plenum Publishers and the Russian publisher, Tamara Rozhkovskaya is published simultaneously in English and in Russian and starts with two volumes dedicated to the famous Russian mathematician Professor Olga Aleksandrovna Ladyzhenskaya, on the occasion of her 80th birthday. O.A. Ladyzhenskaya graduated from the Moscow State University. But throughout her career she has been closely connected with St. Petersburg where she works at the V.A. Steklov Mathematical Institute of the Russian Academy of Sciences. Many generations of mathematicians have become familiar with the nonlinear theory of partial differential equations reading the books on quasilinear elliptic and parabolic equations written by O.A. Ladyzhenskaya with V.A. Solonnikov and N.N. Uraltseva. Her results and methods on the Navier-Stokes equations, and other mathematical problems in the theory of viscous fluids, nonlinear partial differential equations and systems, the regularity theory, some directions of computational analysis are well known. So it is no surprise that these two volumes attracted leading specialists in partial differential equations and mathematical physics from more than 15 countries, who present their new results in the various fields of mathematics in which the results, methods, and ideas of O.A. Ladyzhenskaya played a fundamental role. Nonlinear Problems in Mathematical Physics and Related Topics I presents new results from distinguished specialists in the theory of partial differential equations and analysis. A large part of the material is devoted to the Navier-Stokes equations, which play an important role in the theory of viscous fluids. In particular, the existence of a local strong solution (in the sense of Ladyzhenskaya) to the problem describing some special motion in a Navier-Stokes fluid is established. Ladyzhenskaya's results on axially symmetric solutions to the Navier-Stokes fluid are generalized and solutions with fast decay of nonstationary Navier-Stokes equations in the half-space are stated. Application of the Fourier-analysis to the study of the Stokes wave problem and some interesting properties of the Stokes problem are presented. The nonstationary Stokes problem is also investigated in nonconvex domains and some Lp-estimates for the first-order derivatives of solutions are obtained. New results in the theory of fully nonlinear equations are presented. Some asymptotics are derived for elliptic operators with strongly degenerated symbols. New results are also presented for variational problems connected with phase transitions of means in controllable dynamical systems, nonlocal problems for quasilinear parabolic equations, elliptic variational problems with nonstandard growth, and some sufficient conditions for the regularity of lateral boundary. Additionally, new results are presented on area formulas, estimates for eigenvalues in the case of the weighted Laplacian on Metric graph, application of the direct Lyapunov method in continuum mechanics, singular perturbation property of capillary surfaces, partially free boundary problem for parametric double integrals.

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.

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

Parallel CFD 2008, the twentieth in the high-level international series of meetings featuring different aspect of parallel computing in computational?uid dynamics and other modern scienti?c domains was held May 19?22, 2008 in Lyon, France. The themes of the 2008 meeting included the traditional emphases of this c- ference, and experiences with contemporary architectures. Around 70 presentations were included into the conference program in the following sessions: Parallel Algorithms and solvers Parallel performances with contemporary architectures Structured and unstructured grid methods, boundary methods software framework and components architecture CFD applications(Bio ?uid, environmentalproblem)Lattice Boltzmannmethodand SPH Optimisation in Aerodynamics This book presents an up-to-date overviewof the state of the art in Parallel C- putational Fluid Dynamics from Asia, Europe, and North America. This reviewed proceedingsincluded about sixty percent of the oral lectures presented at the conf- ence. The editors. VI Preface Parallel CFD 2008 was organized by the Institut Camille Jordan of the Univ- sity of Lyon 1 in collaboration with the Center for the Development of the Parallel Scienti?c Computing. The Scienti?c Committee and Local Organizers of Parallel CFD 2008 are - lighted to acknowledge the generous sponsorship of the following organizations, through ?nancial or in-kind assistance. Assistance of our sponsors allowed to - ganize scienti?c as well as social program of the conference.

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."

Computational Fluid Dynamics (CFD) has made remarkable progress in the last two decades and is becoming an important, if not inevitable, analytical tool for both fundamental and practical fluid dynamics research. The analysis of flow fields is important in the sense that it improves the researcher's understanding of the flow features. CFD analysis also indirectly helps the design of new aircraft and/or spacecraft. However, design methodologies are the real need for the development of aircraft or spacecraft. They directly contribute to the design process and can significantly shorten the design cycle. Although quite a few publications have been written on this subject, most of the methods proposed were not used in practice in the past due to an immature research level and restrictions due to the inadequate computing capabilities. With the progress of high-speed computers, the time has come for such methods to be used practically. There is strong evidence of a growing interest in the development and use of aerodynamic inverse design and optimization techniques. This is true, not only for aerospace industries, but also for any industries requiring fluid dynamic design. This clearly shows the matured engineering need for optimum aerodynamic shape design methodologies. Therefore, it seems timely to publish a book in which eminent researchers in this area can elaborate on their research efforts and discuss it in conjunction with other efforts.

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."

This volume contains papers presented at the IUTAM Symposium on Bubble Dynamics and Interface Phenomena held at the University of Birmingham from 6-9 September 1993. In many respects it follows on a decade later from the very successful IUTAM Symposium held at CALTECH in June 1981 on the Mechanics and physics of bubbles in liquids which was organised by the late Milton Plesset and Leen van Wijngaarden. The intervening period has seen major development with both experiment and theory. On the experimental side there have been ad vances with very high speed photography and data recording that provide detailed information on fluid and interface motion. Major developments in both computer hardware and software have also led to extensive improvement in our understand ing of bubble and interface dynamics although development is still limited by the sheer complexity of the laminar and turbulent flow regimes often associated with bubbly flows. The symposium attracts wide and extensive interest from engineers, physical, chemical, biological and medical scientists and applied mathematicians. The sci entific committee sought to achieve a balance between theory and experiment over a range of fields in bubble dynamics and interface phenomena. It was our intention to emphasise both the breadth and recent developments in these various fields and to encourage cross-fertilisation of ideas on both experimental techniques and theo retical developments. The programme, and the proceedings recorded herein, cover bubble dynamics, sound and wave propagation, bubbles in flow, sonoluminescence, acoustic cavitation, underwater explosions, bursting bubbles and ESWL.

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.

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.

Across the centuries, the development and growth of mathematical concepts have been strongly stimulated by the needs of mechanics. Vector algebra was developed to describe the equilibrium of force systems and originated from Stevin's experiments (1548-1620). Vector analysis was then introduced to study velocity fields and force fields. Classical dynamics required the differential calculus developed by Newton (1687). Nevertheless, the concept of particle acceleration was the starting point for introducing a structured spacetime. Instantaneous velocity involved the set of particle positions in space. Vector algebra theory was not sufficient to compare the different velocities of a particle in the course of time. There was a need to (parallel) transport these velocities at a single point before any vector algebraic operation. The appropriate mathematical structure for this transport was the connection. I The Euclidean connection derived from the metric tensor of the referential body was the only connection used in mechanics for over two centuries. Then, major steps in the evolution of spacetime concepts were made by Einstein in 1905 (special relativity) and 1915 (general relativity) by using Riemannian connection. Slightly later, nonrelativistic spacetime which includes the main features of general relativity I It took about one and a half centuries for connection theory to be accepted as an independent theory in mathematics. Major steps for the connection concept are attributed to a series of findings: Riemann 1854, Christoffel 1869, Ricci 1888, Levi-Civita 1917, WeyJ 1918, Cartan 1923, Eshermann 1950.