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.

Now in its fully updated fourth edition, this leading text in its field is an exhaustive monograph on turbulence in fluids in its theoretical and applied aspects. The authors examine a number of advanced developments using mathematical spectral methods, direct-numerical simulations, and large-eddy simulations. The book remains a hugely important contribution to the literature on a topic of great importance for engineering and environmental applications, and presents a very detailed presentation of the field.

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.

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.

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.

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.

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.

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.

"

A follow on from the author's work "Finite Elements in Heat Transfer" which we published 11/94, and which is a powerful CFD programme that will run on a PC. The fluid flow market is larger than the previous, and this package is good value in comparison with other software packages in Computational Fluid Dynamics, which are generally very expensive. The work in general copes with non-Newtonian laminar flow using the finite element method, and some basic theory of the subject is included in the opening chapters of the book.

Along with almost a hundred research communications this volume contains six invited lectures of lasting value. They cover modeling in plasma dynamics, the use of parallel computing for simulations and the applications of multigrid methods to Navier-Stokes equations, as well as other surveys on important techniques. An inaugural talk on computational fluid dynamics and a survey that relates dynamical systems, turbulence and numerical solutions of the Navier-Stokes equations give an exciting view on scientific computing and its importance for engineering, physics and mathematics.

This critical overview describes fluid flow driven by the thermocapillary effect in models of crystal growth. Simple models are the floating-zone technique and the open-boat technique. Basic equations, boundary layer scaling, stability analysis, pattern formation and additional buoyancy are discussed. Particular emphasis is given to the understanding of the physics of flow. This reference book gives a state-of-the-art report and reviews the literature available.

The development of water resources has proceeded at an amazing speed around the world in the last few decades. The hydraulic engineer has played his part: in constructing much larger artificial channels than ever before, larger and more sophisticated control structures, and systems of irrigation, drainage and water supply channels in which the flow by its nature is complex and unsteady requiring computer-based techniques at both the design and operation stage. It seemed appropriate to look briefly at some of the developments in hydraulic design resulting from this situation. Hence the idea of the Conference was formed. The Proceedings of the Conference show that hydraulic engineers have been able to acquire a very substantial base of design capability from the experience of the period referred to. The most outstanding development to have occurred is in the combination of physical and mathematical modelling, which in hydraulic engineering has followed a parallel path to that in other branches of engineering science. The Proceedings of this Conference will give to the reader an awareness of the current state of hydraulic design in open channel flow and open channel control structures. K.V.H. Smith Editor 1. CONTROL AND DIVERSION STRUCTURES 1-3 FACTORS AFFECTING BRINK DEPTH IN RECTANGULAR OVERFALLS G.C. Christodoulou, G.C. Noutsopoulos and S.A. Andreou Dept. of Civil Engineering, National Technical Univ. of Athens, Greece.

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 short primer provides a concise and tutorial-style introduction to transport phenomena in Newtonian fluids , in particular the transport of mass, energy and momentum. The reader will find detailed derivations of the transport equations for these phenomena, as well as selected analytical solutions to the transport equations in some simple geometries. After a brief introduction to the basic mathematics used in the text, Chapter 2, which deals with momentum transport, presents a derivation of the Navier-Stokes-Duhem equation describing the basic flow in a Newtonian fluid. Also provided at this stage are the derivations of the Bernoulli equation, the pressure equation and the wave equation for sound waves. The boundary layer, turbulent flow and flow separation are briefly reviewed. Chapter 3, which addresses energy transport caused by thermal conduction and convection, examines a derivation of the heat transport equation. Finally, Chapter 4, which focuses on mass transport caused by diffusion and convection, discusses a derivation of the mass transport equation.

Increasing possibilities of computer-aided data processing have caused a new revival of optical techniques in many areas of mechanical and chemical engi neering. Optical methods have a long tradition in heat and mass transfer and in fluid dynamics. Global experimental information is not sufficient for de veloping constitution equations to describe complicated phenomena in fluid dynamics or in transfer processes by a computer program. Furthermore, a detailed insight with high local and temporal resolution into the thermo and fluiddynamic situations is necessary. Sets of equations for computer program in thermo dynamics and fluid dynamics usually consist of two types of formulations: a first one derived from the conservation laws for mass, energy and momentum, and a second one mathematically modelling transport processes like laminar or turbulent diffusion. For reliably predicting the heat transfer, for example, the velocity and temperature field in the boundary layer must be known, or a physically realistic and widely valid correlation describing the turbulence must be avail able. For a better understanding of combustion processes it is necessary to know the local concentration and temperature just ahead of the flame and in the ignition zone."

The International Conference on Differential Equations, theor*y, nu- merics and applications(ICDE'96-Bandung) was held successfully at the West Aula of Institut TeknoIogi Bandung on September 29 - October 2, 1996, hosted by the Center of Mathematics and the Department of Mathe- matics ITB. This was the first international conference on differential equa- tions in the region and attended by participants from 12 countries: Aus- tralia, Cambodia, Hong Kong, France, IndonE'sia, Malaysia, Netherlands, Philippine, Thailand, Singapore, USA and Vietnam. We would like to express our gratitude to the following organizations and institution: Directorate General of Higher Education of Indonesia (through Center Grant Project), Institut Teknologi Bandung, UNESCO (through Participating Programme and ROSTSEA Programme), European Economic Community(through the Joint Research Project between the Faculty of Ap- plied Mathematics, Universiteit Twente and the Department of Mathemat- ics, Institut Teknologi Bandung), South East Asian Mathematical Society (SEAMS), French Embassy in Jakarta and local sponsors for their generolls support which have made this conference possible.

Over the last few years it has become apparent that fluid turbulence shares many common features with plasma turbulence, such as coherent structures and self-organization phenomena, passive scalar transport and anomalous diffusion. This book gathers very high level, current papers on these subjects. It is intended for scientists and researchers, lecturers and graduate students because of the review style of the papers.

This volume contains a selection of the papers presented at the Fourth Symposium on Numerical and Physical Aspects of Aerodynamic Flows, which was held at the California State University, Long Beach, from 16-19 January 1989. It includes the Stewartson Memorial Lecture of Professor J. H. Whitelaw, and is divided into three parts. The first is a collection of papers that describe the status of current technology in two- and three-dimensional steady flows, the second deals with two- and three-dimensional unsteady flows, and the papers in the third address stability and transition. Each of the three parts begins with an overview of current research, as described in the following chapters. The individual papers are edited versions of the selected papers originally submitted to the symposium. Four years have passed since the Third Symposium, and certain trends be come clear if one compares the papers contained in this volume with those of previous volumes. There are more three- than two-dimensional problems consid ered in Part 1 and the latter address more difficult problems than in the past, for example, the extension to higher angles of attack, to transonic flow, to leading edge ice accretion, and to thick hydrofoils. The large number of papers in the first part reflects the emphasis of current research and development and the needs of industry."

Soft matter and biological systems pose many challenges for theoretical, experimental and computational research. From the computational point of view, these many-body systems cover variations in relevant time and length scales over many orders of magnitude. Indeed, the macroscopic properties of materials and complex fluids are ultimately to be deduced from the dynamics of the microsopic, molecular level. In these lectures, internationally renowned experts offer a tutorial presentation of novel approaches for bridging these space and time scales in realistic simulations. This volume addresses graduate students and nonspecialist researchers from related areas seeking a high-level but accessible introduction to the state of the art in soft matter simulations.

This immensely practical guide to PIV provides a condensed, yet exhaustive guide to most of the information needed for experiments employing the technique. This second edition has updated chapters on the principles and extra information on microscopic, high-speed and three component measurements as well as a description of advanced evaluation techniques. What's more, the huge increase in the range of possible applications has been taken into account as the chapter describing these applications of the PIV technique has been expanded.

I used the opportunity of this edition to correct some minor mistakes and clarify, wherever it possible, exposition of the theory in comparison with the previous edition of this book (Kluwer, Dordrechtet cet, 2000). It provokes - largement of the book, though I tried to present the modern theory of thermic motion of long macromolecules in compact form. I have tried to accumulate the common heritage and to take into account di?erent approaches in the theory of dynamics of linear polymers, at least, to understand and make clear the importance of various ideas for explanation of relaxation phenomena in linear polymers, to present recent development in the ?eld. The theory of non-equilibrium phenomena in polymer systems is based on the fundamental principles of statistical physics. However, the peculiarities of thestructureandthebehaviourofthesystemsnecessitatetheimplementation of special methods and heuristic models that are di?erent from those for gases and solids, so that polymer dynamics has appeared to be a special branch of physicsnow. Themonographcontainsdiscussionsofthemainprinciplesofthe theoryof slowrelaxationphenomena in linearpolymers, elaborated inthe last decades. The basic model of a macromolecule, which allows us a consistent explanation of di?erent relaxation phenomena (di?usion, neutron scattering, viscoelasticity, optical birefringence), remains to be a coarse-grained or be- spring model, considered in di?erent environments: viscous, to describe the behaviourofdilutesolutions,orviscoelastic,todescribethebehaviourofboth weakly and strongly entangled systems.

This volume contains 27 contributions to the Forth Russian-German Advanced Research Workshop on Computational Science and High Performance Computing presented in October 2009 in Freiburg, Germany. The workshop was organized jointly by the High Performance Computing Center Stuttgart (HLRS), the Institute of Computational Technologies of the Siberian Branch of the Russian Academy of Sciences (ICT SB RAS) and the Section of Applied Mathematics of the University of Freiburg (IAM Freiburg) The contributions range from computer science, mathematics and high performance computing to applications in mechanical and aerospace engineering. They show a wealth of theoretical work and simulation experience with a potential of bringing together theoretical mathematical modelling and usage of high performance computing systems presenting the state of the art of computational technologies.

This volume will contain selected papers from the lectures held at the BAIL 2010 Conference, which took place from July 5th to 9th, 2010 in Zaragoza (Spain). The papers present significant advances in the modeling, analysis and construction of efficient numerical methods to solve boundary and interior layers appearing in singular perturbation problems. Special emphasis is put on the mathematical foundations of such methods and their application to physical models. Topics in scientific fields such as fluid dynamics, quantum mechanics, semiconductor modeling, control theory, elasticity, chemical reactor theory, and porous media are examined in detail.