The high temperatures generated in gases by shock waves give rise to physical and chemical phenomena such as molecular vibrational excitation, dissociation, ionization, chemical reactions and inherently related radiation. In continuum regime, these processes start from the wave front, so that generally the gaseous media behind shock waves may be in a thermodynamic and chemical non-equilibrium state. This book presents the state of knowledge of these phenomena. Thus, the thermodynamic properties of high temperature gases, including the plasma state are described, as well as the kinetics of the various chemical phenomena cited above. Numerous results of measurement and computation of vibrational relaxation times, dissociation and reaction rate constants are given, and various ionization and radiative mechanisms and processes are presented. The coupling between these different phenomena is taken into account as well as their interaction with the flow-field. Particular points such as the case of rarefied flows and the inside of the shock wave itself are also examined. Examples of specific non-equilibrium flows are given, generally corresponding to those encountered during spatial missions or in shock tube experiments.

This volume is an introduction to nonlinear waves and soliton theory in the special environment of compact spaces such a closed curves and surfaces and other domain contours. It assumes familiarity with basic soliton theory and nonlinear dynamical systems. The first part of the book introduces the mathematical concept required for treating the manifolds considered, providing relevant notions from topology and differential geometry. An introduction to the theory of motion of curves and surfaces - as part of the emerging field of contour dynamics - is given. The second and third parts discuss the modeling of various physical solitons on compact systems, such as filaments, loops and drops made of almost incompressible materials thereby intersecting with a large number of physical disciplines from hydrodynamics to compact object astrophysics. This book is intended for graduate students and researchers in mathematics, physics and engineering. This new edition has been thoroughly revised, expanded and updated.

This book proposes an introduction to the mathematical modeling of the respiratory system. A detailed introduction on the physiological aspects makes it accessible to a large audience without any prior knowledge on the lung. Different levels of description are proposed, from the lumped models with a small number of parameters (Ordinary Differential Equations), up to infinite dimensional models based on Partial Differential Equations. Besides these two types of differential equations, two chapters are dedicated to resistive networks, and to the way they can be used to investigate the dependence of the resistance of the lung upon geometrical characteristics. The theoretical analysis of the various models is provided, together with state-of-the-art techniques to compute approximate solutions, allowing comparisons with experimental measurements. The book contains several exercises, most of which are accessible to advanced undergraduate students.

This book explores the interplay of bubble dynamics and shock waves, covering shock wave emission by laser generated bubbles, pulsating bubbles near boundaries, interaction of shock waves with bubble clouds, applications in shock wave lithotripsy, and more.

The "Turbulence and Interactions 2006" (TI2006) conference was held on the island of Porquerolles, France, May 29-June 2, 2006. The scientific sponsors of the conference were * Association Francaise de Mecanique, * CD-adapco, * DGA * Ecole Polytechnique Federale de Lausanne (EPFL), * ERCOFTAC : European Research Community on Flow, Turbulence and Combustion, * FLUENT, * The French Ministery of Foreign Affairs, * Laboratoire de Modelisation en Mecanique, Paris 6, * ONERA. The conference was a unique event. Never before have so many organisations concerned with turbulence works come together in one conference. As the title "Turbulence and Interactions" anticipated, the workshop was not run with parallel sessions but instead of one united gathering where people had strong interactions and discussions. Many of the 85 or so attendants were veterans of previous ERCOFTAC conferences. Some young researchers attended their very first int- national meeting. The organisers were fortunate in obtaining the presence of the following - vited speakers: N. Adams (TUM, Germany), C. Cambon (ECL, France), J.-P. Dussauge (Polytech Marseille, France), D.A. Gosman (Imperial College, UK), Y. Kaneda (Nagoya University, Japan), O. Simonin (IMFT, France), G. Tryggvason (WPI, USA), D. Veynante (ECP, France), F. Waleffe (University of Wisconsin, USA), Y.K. Zhou (University of California, USA). The topics covered by the 59 papers ranged from experimental results through theory to computations. The papers of the conference went through the usual - viewing process for two special issues of international journals : Computers and Fluids, and Flow, Turbulence and Combustion.

With regard to both the environmental sustainability and operating efficiency demands, modern combustion research has to face two main objectives, the optimization of combustion efficiency and the reduction of pollutants. This book reports on the combustion research activities carried out within the Collaborative Research Center (SFB) 568 "Flow and Combustion in Future Gas Turbine Combustion Chambers" funded by the German Research Foundation (DFG). This aimed at designing a completely integrated modeling and numerical simulation of the occurring very complex, coupled and interacting physico-chemical processes, such as turbulent heat and mass transport, single or multi-phase flows phenomena, chemical reactions/combustion and radiation, able to support the development of advanced gas turbine chamber concepts

This book reports on important nonlinear aspects or deterministic chaos issues in the systems of multi-phase reactors. The reactors treated in the book include gas-liquid bubble columns, gas-liquid-solid fluidized beds and gas-liquid-solid magnetized fluidized beds. The authors take pressure fluctuations in the bubble columnsas time series for nonlinear analysis, modeling and forecasting. They present qualitative and quantitative non-linear analysis tools which include attractor phase plane plot, correlation dimension, Kolmogorov entropy and largest Lyapunov exponent calculations and local non-linear short-term prediction."

The "Turbulence and Interactions 2009" (TI2009) conference was held in Saint- Luce on the island of La Martinique, France, on May 31-June 5, 2009. The sci- tific sponsors of the conference were * DGA * Ecole Polytechnique Federale de Lausanne (EPFL), * ERCOFTAC : European Research Community on Flow, Turbulence and Combustion, * Institut Jean Le Rond d'Alembert, Paris, * ONERA. This second TI conference was very successful as it attracted 65 researchers from 17 countries. The magnificent venue and the beautiful weather helped the participants to discuss freely and casually, share ideas and projects, and spend very good times all together. The organisers were fortunate in obtaining the presence of the following - vited speakers: L. Fuchs (KTH, Stockholm and Lund University), J. Jimenez (Univ. Politecnica Madrid), C.-H. Moeng (NCAR), A. Scotti (University of North Carolina), L. Shen (Johns Hopkins University) and A.J. Smits (Princeton Univ- sity). The topics covered by the 62 contributed papers ranged from experimental results through theory to computations. They represent a snapshot of the state-- the-art in turbulence research. The papers of the conference went through the usual reviewing process and the result is given in this book of Proceedings. In the present volume, the reader will find the keynote lectures followed by the contributed talks given in alphabetical order of the first author.

Hermann Schlichting is one of the internationally leading scientists in the field of th fluid mechanics during the 20 century. He contributed largely to modern theories of viscous flows and aircraft aerodynamics. His famous monographies Boundary Layer Theory and Aerodynamics of Aircraft are known worldwide and they appeared in six languages. He held Chairs of Aerodynamics and Fluid Mechanics at Technische U- versitat Braunschweig during 37 years and directed the Institute of Aerodynamics of the Deutsche Forschungsanstalt fur Luftfahrt in Braunschweig. He also directed the Aerodynamische Versuchsanstalt Goettingen and served in the Executive Board of the German Aerospace Center (DFVLR). Hermann Schlichting played a leading role in the rebuilding of aerospace research in Germany after the Second World War. th The occasion of his 100 birthday in the year 2007 was an excellent opportunity to acknowledge important ideas and accomplishments that Hermann Schlichting c- tributed to science. The editors of this volume are the present successors of Hermann Schlichting in his role as director of the two research institutes in Braunschweig. We were glad to host a scientific colloquium in his honor on 28 September 2007. Invited former scholars of Hermann Schlichting reviewed his work in boundary layer theory and in aircraft aerodynamics followed by presentations of important research results of his institutes today.

Two-fluid dynamics is a challenging subject rich in physics and prac tical applications. Many of the most interesting problems are tied to the loss of stability which is realized in preferential positioning and shaping of the interface, so that interfacial stability is a major player in this drama. Typically, solutions of equations governing the dynamics of two fluids are not uniquely determined by the boundary data and different configurations of flow are compatible with the same data. This is one reason why stability studies are important; we need to know which of the possible solutions are stable to predict what might be observed. When we started our studies in the early 1980's, it was not at all evident that stability theory could actu ally work in the hostile environment of pervasive nonuniqueness. We were pleasantly surprised, even astounded, by the extent to which it does work. There are many simple solutions, called basic flows, which are never stable, but we may always compute growth rates and determine the wavelength and frequency of the unstable mode which grows the fastest. This proce dure appears to work well even in deeply nonlinear regimes where linear theory is not strictly valid, just as Lord Rayleigh showed long ago in his calculation of the size of drops resulting from capillary-induced pinch-off of an inviscid jet.

This book presents state-of-the-art lectures on complex flows of fundamental and industrial interest in the subsonic, supersonic and hypersonic regimes. Experimental investigations of unsteady separated flows, high-enthalpy flows, 3D configurations, laminar and transitional flows are addressed. Theoretical predictions of aerodynamic performances are provided along with analyses of supersonic combustion, detonation, simulation of reactive mixing layer and non-equilibrium flow. Computational Fluid Dynamics methods for the simulation of viscous compressible flow, inviscidviscous flow interactions, real-gas effects in rarefied flow, flows about bodies with permeable walls and supersonic turbulent flows are finally developed and analysed.

This book is about two special topics in rheological fluid mechanics: the elasticity of liquids and asymptotic theories of constitutive models. The major emphasis of the book is on the mathematical and physical consequences of the elasticity of liquids; seventeen of twenty chapters are devoted to this. Constitutive models which are instantaneously elastic can lead to some hyperbolicity in the dynamics of flow, waves of vorticity into rest (known as shear waves), to shock waves of vorticity or velocity, to steady flows of transonic type or to short wave instabilities which lead to ill-posed problems. Other kinds of models, with small Newtonian viscosities, give rise to perturbed instantaneous elasticity, associated with smoothing of discontinuities as in gas dynamics. There is no doubt that liquids will respond like elastic solids to impulses which are very rapid compared to the time it takes for the molecular order associated with short range forces in the liquid, to relax. After this, all liquids look viscous with signals propagating by diffusion rather than by waves. For small molecules this time of relaxation is estimated as lQ-13 to 10-10 seconds depending on the fluids. Waves associated with such liquids move with speeds of 1 QS cm/s, or even faster. For engineering applications the instantaneous elasticity of these fluids is of little interest; the practical dynamics is governed by diffusion, .say, by the Navier-Stokes equations. On the other hand, there are other liquids which are known to have much longer times of relaxation."

The book introduces readers to and summarizes the current ideas and theories about the basic mechanisms for transport in chaotic flows. Typically no single paradigmatic approach exists as this topic is relevant for fields as diverse as plasma physics, geophysical flows and various branches of engineering. Accordingly, the dispersion of matter in chaotic or turbulent flows is analyzed from different perspectives. Partly based on lecture courses given by the author, this book addresses both graduate students and researchers in search of a high-level but approachable and broad introduction to the topic.

This book covers a wide area of topics, from fundamental theories to industrial applications. It serves as a useful reference for all interested in computational modeling of partial differential equations pertinent primarily to aeronautical applications. The reader will find five survey articles on cartesian mesh methods, on numerical studies of turbulent boundary layers, on efficient computation of compressible flows, on the use of Riemann-solvers and on numerical procedures in complex flows.

In general, combustion is a spatially three-dimensional, highly complex physi co-chemical process oftransient nature. Models are therefore needed that sim to such a degree that it becomes amenable plify a given combustion problem to theoretical or numerical analysis but that are not so restrictive as to distort the underlying physics or chemistry. In particular, in view of worldwide efforts to conserve energy and to control pollutant formation, models of combustion chemistry are needed that are sufficiently accurate to allow confident predic tions of flame structures. Reduced kinetic mechanisms, which are the topic of the present book, represent such combustion-chemistry models. Historically combustion chemistry was first described as a global one-step reaction in which fuel and oxidizer react to form a single product. Even when detailed mechanisms ofelementary reactions became available, empirical one step kinetic approximations were needed in order to make problems amenable to theoretical analysis. This situation began to change inthe early 1970s when computing facilities became more powerful and more widely available, thereby facilitating numerical analysis of relatively simple combustion problems, typi cally steady one-dimensional flames, with moderately detailed mechanisms of elementary reactions. However, even on the fastest and most powerful com puters available today, numerical simulations of, say, laminar, steady, three dimensional reacting flows with reasonably detailed and hence realistic ki netic mechanisms of elementary reactions are not possible."

Photon correlation is a kind of spectroscopy designed to identify optical frequency shifts and line-broadening effects in the range of many MHz down to a few Hz. The optical intensity is measured in terms of single photon detection events which result in current pulses at the output of photomulti plier tubes. This signal is processed in real time in a special-purpose paral lel processor known as a correlator. The resulting photon correlation func tion, a function in the time domain, contains the desired spectral informa tion, which may be extracted by a suitable algorithm. Due to the non-intrusive nature and the sound theoretical basis of photon correlation, the phenomena under study are not disturbed, and the parameters in question can be precisely evaluated. For these reasons photon correlation has become a valuable and in many instances indispensable technique in two distinct fields. One of these is velocimetry in fluid flow. This includes hydro- and aerodynamic processes in liquids, gases, or flames where the velo city field may be stationary, time periodic, or turbulent, and may range from micrometers per second for motion inside biological cells to one kilometer per second for supersonic flow. The other major field is stochastic particle propagation due to Brownian motion."

This book provides a unique assembly of state-of-the-art articles concerned with a wide range of fundamental and applied issues, including turbulence parameterization, numerical uncertainty, complex turbulence, flow-structure interactions, atmosphere-ocean turbulence and turmachinery flows. The articles provide specific examples of the most recent applications of direct and large eddies methods. These methods have been very successful in providing new insight into the structure of turbulent flows and are becoming feasable in real engineering and environmental problems with complex geometries. This volume will be a very valuable source book for researchers and graduate students embarking on studies in turbulent flow simulation.

The purpose of this book is to gather contributions from scientists in fluid mechanics who use asymptotic methods to cope with difficult problems. The selected topics are as follows: vorticity and turbulence, hydrodynamic instability, non-linear waves, aerodynamics and rarefied gas flows. The last chapter of the book broadens the perspective with an overview of other issues pertaining to asymptotics, presented in a didactic way.

Global sustainable development of the world economy requires better understanding and utilization of natural recourses. In this endeavor rheology has an indispensable role. The Rheology Conferences are therefore always an important event for science and technology. The Fifth European Rheology Conference, held from September 6 to 11 in the Portoro-z, Slovenia, will be the first AlI-European rheology meeting after the formal constitution of the European Society ofRheology. As such it will be a special historical event. At this meeting the European Society of Rheology will introduce the Weissenberg Medal, to be bestowed every four years to an individual for hislhers contribution to the field of Rheology. The recipient ofthe first award will be professor G. Marrucci ofthe Universita degli Studi di Napoli, Italy. Two mini Symposia will be part of the Conference. The first, on Industrial Rheology, will commemorate the late professor G. Astarita. The second will honor the eightieth birthday of professor N.W. Tschoegl. This volume comprises extended abstracts of the 15 plenary and keynote lectures and about 300 oral and poster contributions presented at this conference. AII contributed papers were reviewed by members ofthe European Committee on Rheology, assuring the high standard ofthe Conference. Besides the scientific program, the Organizing Committee has prepared an extensive social program that wilI reveal the culture and the natural beauties of Slovenia.

This book is an outcome of a European collaboration on applications of stochastical methods to problems of science and engineering. The articles present methods allowing concrete calculations without neglecting the mathematical foundations. They address physicists and engineers interested in scientific computation and simulation techniques.
In particular the volume covers: simulation, stability theory, Lyapounov exponents, stochastic modelling, statistics on trajectories, parametric stochastic control, Fokker Planck equations, and Wiener filtering.

Published in honour of Marc Feix this book tries to give a thorough overview of mathematical methods, analytical and numerical techniques and simulations applied to a variety of problems from physics and engineering. The book addresses graduate students, researchers and especially engineers. The main emphasis is to apply the generality of methods to form a coherent and stimulating approach to practical investigations.

An international group of outstanding scientists presents a balanced discussion of various controversies in current turbulence theory. Six topics from the present-day approach to turbulence are each introduced by a survey, followed by three commentaries and a panel discussion. This analysis evaluates future developments of theories presently used for understanding and modelling turbulent flows.

An important new area of current research in combustion science is reviewed in the contributions to this volume. The complicated phenomena of combustion, such as chemical reactions, heat and mass transfer, and gaseous flows, have so far been studied predominantly by experiment and by phenomenological approaches. But asymptotic analysis and other recent developments are rapidly changing this situation. The contributions in this volume are devoted to mathematical modeling in three areas: high Mach number combustion, complex chemistry and physics, and flame modeling in small scale turbulent flow combustion.

The contributions in this volume focus on the use of general connectivity (unstructured) adaptive meshes for Lagrangian calculations but contain a substantial amount of material on Euler and arbitrary Lagrange-Euler techniques as well. Contributions on the smooth particle hydrodynamics method and on deterministic vortex methods broaden the scope of the material and allow comparisons of different, though allied, techniques to be made. The format of the conference was designedto optimize the interaction among the attendees. An edited version of roundtable discussions is included in these proceedings.

This monograph provides a detailed review of the state-of-the-art theoretical (analytical and numerical) methodologies for the analysis of dissipative wave dynamics and pattern formation on the surface of a film falling down a planar, inclined substrate. Particular emphasis is given to low-dimensional approximations for such flows through a hierarchy of modeling approaches, including equations of the boundary-layer type, averaged formulations based on weighted residuals approaches, and long-wave expansions.

Whenever possible, the link between theory and experiments is illustrated and, as a further bridge between the two, the development of order-of-magnitude estimates and scaling arguments is used to facilitate the understanding of the underlying basic physics.

The book will be of particular interest to advanced graduate students in applied mathematics, science or engineering undertaking research on interfacial fluid mechanics or studying fluid mechanics as part of their program; researchers working on both applied and fundamental theoretical and experimental aspects of thin film flows; and engineers and technologists dealing with processes involving thin films, either isothermal or heated.

Topics covered include:

Detailed derivations of governing equations and wall and free-surface boundary conditions for free-surface thin film flows in the presence of thermocapillary Marangoni effect; linear stability including Orr-Sommerfeld, absolute/convective instability and Floquet analysis of periodic waves; strongly nonlinear analysis including construction of bifurcation diagrams of periodic and solitary waves; weakly nonlinear prototypes such as Kuramoto-Sivashinsky equation; validity domain of the long-wave expansions; kinematic/dynamic waves, connection with shallow water and river flows/hydraulic jumps; dynamical systems approach, local and global bifurcations, homoclinicity and conditions for periodic, subsidiary and secondary homoclinic orbits; modulation instability of solitary waves to transverse perturbations; transition to two-dimensional solitary waves and interaction of two-dimensional solitary waves; and substrate heating and competition between solitary waves and rivulet formation in free-surface flows over heated substrates.

Tutorials and details of computational methodologies including computer programs:

Solution of the Orr-Sommerfeld eigenvalue problem; computational search via continuation for traveling wave solutions and their bifurcations; computation of systems of nonlinear pde s using finite differences; spectral representation and aliasing.

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