In September 2000, the University of Bayreuth, Germany, hosted the Fourth International Meeting on Thermodi?usion (IMT4). TheIMTconferenceswerebornfromtheideaofbringingtogetherresearchers in the ?eld of thermodi?usion. Under the auspices of the European Group of Research in Thermodi?usion(EGRT)theconferenceseriesstartedin1994with IMT1 in Toulouse and has been continued every other year with IMT2 (Pau, 1996), IMT3 (Mons, 1998), and IMT4 (Bayreuth, 2000). The next conference, IMT5, will be held in 2002 in Lyngby, Denmark. Thermodi?usion, alsocalledthermaldi?usionortheLudwig-Sorete?ect, - scribes the coupling between a temperature gradient and a resulting mass ?ux. Although the e?ect was already discovered in the 19th century by Ludwig and Soret, it has gained growing interest during the last years due to improved - perimentaltechniqueslikestate-of-the-artthermogravitationalcolumns, modern opticalmethods, ?owchannels, andmicrogravityexperiments, tomentiononlya few. We are still far from a detailed microscopic picture, but analytical theories have been improved and the availability of fast computers and e?cient al- rithmsfornonequilibriummoleculardynamicssimulationshasprovidedvaluable input from the theoretical side. TheIMTconferencescoverallaspectsofthermodi?usionfromfundamentals to new applications. Traditionally, the focus has been on the ?uid state, ra- ing from mixtures of simple liquids to more complex systems such as critical mixtures, electrolytes, polymers, colloidal dispersions, or magnetic ?uids. IMT4 tried to widen the scope by including a plenary lecture about thermodi?usion in ionic solids. Scienti?c input comes from diverse disciplines such as physics, chemistry, engineering, and geophysics. Sadly, Leo Kempers passed away while this book was being prepared. Many ofushavelostafriendandrespectedcolleague.Hismanuscripthasbeenbrought into its ?nal state by A. Shapiro, whom we want to thank

This volume contains revised and edited forms of papers presented at the Symposium on Numerical and Physical Aspects of Aerodynamic Flows, held at the California State University from 19 to 21 January 1981. The Symposium was organized to bring together leading research workers in those aspects of aerodynamic flows represented by the five parts and to fulfill the following purposes: first, to allow the presentation of technical papers which provide a basis for research workers to assess the present status of the subject and to formulate priorities for the future; and second, to promote informal discussion and thereby to assist the communication and develop ment of novel concepts. The format ofthe content ofthe volume is similar to that ofthe Symposium and addresses, in separate parts: Numerical Fluid Dynamics, Interactive Steady Boundary Layers, Singularities in Unsteady Boundary Layers, Transonic Flows, and Experimental Fluid Dynamics. The motivation for most of the work described relates to the internal and extern al aerodynamics of aircraft and to the development and appraisal of design methods based on numerical solutions to conservation equations in differential forms, for corresponding components. The chapters concerned with numerical fluid dynamics can, perhaps, be interpreted in a more general context, but the emphasis on boundary-Iayer flows and the special consideration oftransonic flows reflects the interest in external flows and the recent advances which have allowed the calculation methods to encompass transonic regions."

Small-scale structures in turbulent flows appear as a subtle mixture of order and chaos that could play an important role in the energetics. The aim here is a better understanding of the similarities and differences between vortex and current dynamics, and of the influence of these structures on the statistical and transport properties of hydrodynamic and magnetohydrodynamic turbulence, with special concern for fusion plasmas, and solar or magnetospheric environments. Special emphasis is given to the intermittency at inertial scales and to the coherent structures at small scales. Magnetic reconnection and the dynamo effect are also discussed, together with the effect of stratification and inhomogeneity. The impact of hydrodynamic concepts on astro and geophysical observations are reviewed.

This book contains a collection of the main contributions from the first five workshops held by Ercoftac Special Interest Group on Synthetic Turbulence Models (SIG42. It is intended as an illustration of the sig s activities and of the latest developments in the field.

Thisvolume investigates the use of Kinematic Simulation (KS) and other synthetic turbulence models for the particular application to environmental flows.

Thisvolume offers the best syntheses on the research status in KS, which iswidely used in various domains, including Lagrangian aspects in turbulence mixing/stirring, particle dispersion/clustering, and last but not least, aeroacoustics. Flow realizations with complete spatial, and sometime spatio-temporal, dependency, are generated via superposition of random modes (mostly spatial, and sometime spatial and temporal, Fourier modes), with prescribed constraints such as: strict incompressibility (divergence-free velocity field at each point), high Reynolds energy spectrum. Recent improvements consisted in incorporating linear dynamics, for instance in rotating and/or stably-stratified flows, with possible easy generalization to MHD flows, and perhaps to plasmas. KS for channel flows have also been validated. However, the absence of "sweeping effects" in present conventional KS versions is identified as a major drawback in very different applications: inertial particle clustering as well as in aeroacoustics. Nevertheless, this issue was addressed in some reference papers, and merits to be revisited in the light of new studies in progress. "

Over the last decade, flow visualization has advanced in step with the progress in laser and computer technologies. The scope of the International Symposium on Flow Visualiza- tion will be broader than ever, covering the range of infor- mation generally thought of as nonvisual and reflecting the inclusion of computer - aided methodologies. The Sixth In- ternational Symposium on Flow Visualization aims to attract the participation of experts and users of flow viualizing techniques on furthering an advanced philosophy for the de- velopment of the methods and their applications.

Focuses on the methods of solving incompressible flows, although flows with significant property change due to heat transfer are also covered. Covers turbulent flow simulation, unstructured mesh, and two-phase flows. Uses a practical approach for CFD to build a foundation for those planning to work on low-speed flows. Provides detailed steps of solving 1-D and 2-D flow examples and MATLAB (R) codes of important algorithms. Includes numerous real-word examples and worked problems.

Modern experiments and numerical simulations show that the long-known coherent structures in turbulence take the form of elongated vortex tubes and vortex sheets. The evolution of vortex tubes may result in spiral structures which can be associated with the spectral power laws of turbulence. The mutual stretching of skewed vortex tubes, when they are close to each other, causes rapid growth of vorticity. Whether this process may or may not lead to a finite-time singularity is one of the famous open problems of fluid dynamics.

This book contains the proceedings of the NATO ARW and IUTAM Symposium held in Zakopane, Poland, 2-7 September 2001. The papers presented, carefully reviewed by the International Scientific Committee, cover various aspects of the dynamics of vortex tubes and sheets and of their analogues in magnetohydrodynamics and in quantum turbulence. The book should be a useful reference for all researchers and students of modern fluid dynamics.

This book will consist of a coherent collection of recent results on near wall turbulence including theory, new experiments, DNS, and modeling with RANS, LES and Low Order Dynamical Systems.

Addressing students and researchers as well as Computational Fluid Dynamics practitioners, this book is the most comprehensive review of high-resolution schemes based on the principle of Flux-Corrected Transport (FCT). The foreword by J.P. Boris and historical note by D.L. Book describe the development of the classical FCT methodology for convection-dominated transport problems, while the design philosophy behind modern FCT schemes is explained by S.T. Zalesak. The subsequent chapters present various improvements and generalizations proposed over the past three decades.
In this new edition, recent results are integrated into existing chapters in order to describe significant advances since the publication of the first edition. Also, 3 new chapters were added in order to cover the following topics: algebraic flux correction for finite elements, iterative and linearized FCT schemes, TVD-like flux limiters, acceleration of explicit and implicit solvers, mesh adaptation, failsafe limiting for systems of conservation laws, flux-corrected interpolation (remapping), positivity preservation in RANS turbulence models, and the use of FCT as an implicit subgrid scale model for large eddy simulations.

The second, enlarged edition of this established reference integrates many new insights into wastewater hydraulics. This work serves as a reference for researchers but also is a basis for practicing engineers. It can be used as a text book for graduate students, although it has the characteristics of a reference book. It addresses mainly the sewer hydraulician but also general hydraulic engineers who have to tackle many a problem in daily life, and who will not always find an appropriate solution. Each chapter is introduced with a summary to outline the contents. To illustrate application of the theory, examples are presented to explain the computational procedures. Further, to relate present knowledge to the history of hydraulics, some key dates on noteworthy hydraulicians are quoted. A historical note on the development of wastewater hydraulics is also added. References are given at the end of each chapter, and they are often helpful starting points for further reading. Each notation is defined when introduced, and listed alphabetically at the end of each chapter. This new edition includes in particular sideweirs with throttling pipes, drop shafts with an account on the two-phase flow features, as well as conduit choking due to direct or undular hydraulic jumps.

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."