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.

Fluid turbulence is often referred to as `the unsolved problem of classical physics'. Yet, paradoxically, its mathematical description resembles quantum field theory. The present book addresses the idealised problem posed by homogeneous, isotropic turbulence, in order to concentrate on the fundamental aspects of the general problem. It is written from the perspective of a theoretical physicist, but is designed to be accessible to all researchers in turbulence, both theoretical and experimental, and from all disciplines. The book is in three parts, and begins with a very simple overview of the basic statistical closure problem, along with a summary of current theoretical approaches. This is followed by a precise formulation of the statistical problem, along with a complete set of mathematical tools (as needed in the rest of the book), and a summary of the generally accepted phenomenology of the subject. Part 2 deals with current issues in phenomenology, including the role of Galilean invariance, the physics of energy transfer, and the fundamental problems inherent in numerical simulation. Part 3 deals with renormalization methods, with an emphasis on the taxonomy of the subject, rather than on lengthy mathematical derivations. The book concludes with some discussion of current lines of research and is supplemented by three appendices containing detailed mathematical treatments of the effect of isotropy on correlations, the properties of Gaussian distributions, and the evaluation of coefficients in statistical theories.

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

The book focuses on the physical and mathematical foundations of model-based turbulence control: reduced-order modelling and control design in simulations and experiments. Leading experts provide elementary self-consistent descriptions of the main methods and outline the state of the art. Covered areas include optimization techniques, stability analysis, nonlinear reduced-order modelling, model-based control design as well as model-free and neural network approaches. The wake stabilization serves as unifying benchmark control problem.

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.

Computational Fluid Dynamics (CFD) has been applied extensively to great benefit in the food processing sector. Its numerous applications include: predicting the gas flow pattern and particle histories, such as temperature, velocity, residence time, and impact position during spray drying;modeling of ovens to provide information about temperature and airflow pattern throughout the baking chamber to enhance heat transfer and in turn final product quality; designing hybrid heating ovens, such as microwave-infrared, infrared-electrical or microwave-electrical ovens for rapid baking; model the dynamics of gastrointestinal contents during digestion based on the motor response of the GI tract and the physicochemical properties of luminal contents; retort processing of canned solid and liquid foods for understanding and optimization of the heat transfer processes. This Brief will recapitulate the various applications of CFD modeling, discuss the recent developments in this field, and identify the strengths and weaknesses of CFD when applied in the food industry. "

This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem. In addition to minor corrections and updates throughout, this new edition includes materials on higher order Melnikov theory and the bifurcation of limit cycles for planar systems of differential equations.

Physically correct boundary conditions on vapor-liquid interfaces are essential in order to make an analysis of flows of a liquid including bubbles or of a gas including droplets. Suitable boundary conditions do not exist at the present time. This book is concerned with the kinetic boundary condition for both the plane and curved vapor-liquid interfaces, and the fluid dynamics boundary condition for Navier-Stokes(fluid dynamics) equations. The kinetic boundary condition is formulated on the basis of molecular dynamics simulations and the fluid dynamics boundary condition is derived by a perturbation analysis of Gaussian-BGK Boltzmann equation applicable to polyatomic gases. The fluid dynamics boundary condition is applied to actual flow problems of bubbles in a liquid and droplets in a gas.

This monograph is intended as a concise and self-contained guide to practitioners and graduate students for applying approaches in computational fluid dynamics (CFD) to real-world problems that require a quantification of viscous incompressible flows. In various projects related to NASA missions, the authors have gained CFD expertise over many years by developing and utilizing tools especially related to viscous incompressible flows. They are looking at CFD from an engineering perspective, which is especially useful when working on real-world applications. From that point of view, CFD requires two major elements, namely methods/algorithm and engineering/physical modeling. As for the methods, CFD research has been performed with great successes. In terms of modeling/simulation, mission applications require a deeper understanding of CFD and flow physics, which has only been debated in technical conferences and to a limited scope. This monograph fills the gap by offering in-depth examples for students and engineers to get useful information on CFD for their activities. The procedural details are given with respect to particular tasks from the authors' field of research, for example simulations of liquid propellant rocket engine subsystems, turbo-pumps and the blood circulations in the human brain as well as the design of artificial heart devices. However, those examples serve as illustrations of computational and physical challenges relevant to many other fields. Unlike other books on incompressible flow simulations, no abstract mathematics are used in this book. Assuming some basic CFD knowledge, readers can easily transfer the insights gained from specific CFD applications in engineering to their area of interest.

Written for researchers and advanced students the book exhibits a combination of various methods and tools required to describe the complexity of the chemical and physical behaviour of fluid surfaces. The common denominator for all the contributions presented here is the simultaneous use of concepts from surface chemistry and physics and from hydrodynamics where external force fields can be introduced. Theoretical and experimental work is equally represented. Most of the basic problems in the area of nonequilibrium multiphase systems have not yet received extensive treatment. This volume should be a reference for physicists, physico-chemists, and chemical engineers and will serve as a jumping-off point for new directions and new points of view.

This volume brings together five contributions to mathematical fluid mechanics, a classical but still very active research field which overlaps with physics and engineering. The contributions cover not only the classical Navier-Stokes equations for an incompressible Newtonian fluid, but also generalized Newtonian fluids, fluids interacting with particles and with solids, and stochastic models. The questions addressed in the lectures range from the basic problems of existence of weak and more regular solutions, the local regularity theory and analysis of potential singularities, qualitative and quantitative results about the behavior in special cases, asymptotic behavior, statistical properties and ergodicity.

This volume contains the proceedings of the Summer Program on Nonlinear Conservation Laws and Applications held at the IMA on July 13--31, 2009. Hyperbolic conservation laws is a classical subject, which has experienced vigorous growth in recent years. The present collection provides a timely survey of the state of the art in this exciting field, and a comprehensive outlook on open problems. Contributions of more theoretical nature cover the following topics: global existence and uniqueness theory of one-dimensional systems, multidimensional conservation laws in several space variables and approximations of their solutions, mathematical analysis of fluid motion, stability and dynamics of viscous shock waves, singular limits for viscous systems, basic principles in the modeling of turbulent mixing, transonic flows past an obstacle and a fluid dynamic approach for isometric embedding in geometry, models of nonlinear elasticity, the Monge problem, and transport equations with rough coefficients. In addition, there are a number of papers devoted to applications. These include: models of blood flow, self-gravitating compressible fluids, granular flow, charge transport in fluids, and the modeling and control of traffic flow on networks.

Liquid helium has been studied for its intrinsic interest through much of the 20th century. In the past decade, much has been learned about heat transfer in liquid helium because of the need to cool superconducting magnets and other devices. The topic of the Seventh Oregon Conference on Low Temperature Physics was an applied one, namely the use of liquid and gaseous helium to generate high Reynolds number flows. The low kinematic viscosity of liquid helium automatically makes high Reynolds numbers accessible and the question addressed in this conference was to explore various possibilities to see what practical devices might be built using liquid or gaseous helium. There are a number of possibilities: construction of a wind tunnel using critical helium gas, free surface testing, low speed flow facilities using helium I and helium ll. At the time of the conference, most consideration had been given to the last possibility because it seemed both possible and useful to build a flow facility which could reach unprecedented Reynolds numbers. Such a device could be useful in pure research for studying turbulence, and in applied research for testing models much as is done in a water tunnel. In order to examine these possibilities in detail, we invited a wide range of experts to Eugene in October 1989 to present papers on their own specialties and to listen to presentations on the liquid helium proposals.

"Hydrothermal and Supercritical Water Processes" presents an overview on the properties and applications of water at elevated temperatures and pressures. It combines fundamentals with production process aspects. Water is an extraordinary substance. At elevated temperatures (and pressures)its properties change dramatically due to the modifications of the molecular structure of bulk water that varies from a stable three-dimensional network, formed by hydrogen bonds at low and moderate temperatures, to an assembly of separated polar water molecules at high and supercritical temperatures. With varying pressure and temperature, water is turned from a solvent for ionic species to a solvent for polar and non-polar substances. This variability and an enhanced reactivity of water have led to many practical applications and to even more research activities, related to such areas as energy transfer, extraction of functional molecules, unique chemical reactions, biomass conversion and fuel materials processing, destruction of dangerous compounds and recycling of useful ones, growth of monolithic crystals, and preparation of metallic nanoparticles.

This book provides an introduction into the wide range of activities that are possible in aqueous mixtures. It is organized to facilitate understanding of the main features, outlines the main applications, and gives access to further information
Summarizes fundamental properties of water for engineering applicationsCompares process and reactor designs Evaluates processes from thermodynamic, economic, and social impact viewpoints"

Filling the gap between the mathematical literature and applications to domains, the authors have chosen to address the problem of wave collapse by several methods ranging from rigorous mathematical analysis to formal aymptotic expansions and numerical simulations.

Computation of Unsteady Internal Flows provides an in-depth understanding of unsteady flow modeling and algorithms. This understanding enables suitable algorithms and approaches for particular fields of application to be selected. In addition, the understanding of the behavior of algorithms gained allows practitioners to use them more safely in existing codes, enabling meaningful results to be produced more economically. Features of Computation of Unsteady Internal Flows: * Specialized unsteady flow modeling algorithms, their traits, and practical tips relating to their use are presented. * Case studies considering complex, practically significant problems are given. * Source code and set-up files are included. Intended to be of a tutorial nature, these enable the reader to reproduce and extend case studies and to further explore algorithm performances. * Mathematical derivations are used in a fashion that illuminates understanding of the physical implications of different numerical schemes. Physically intuitive mathematical concepts are used. * New material on adaptive time stepping is included.GBP/LISTGBP Audience: Researchers in both the academic and industrial areas who wish to gain in-depth knowledge of unsteady flow modeling will find Computation of Unsteady Internal Flows invaluable. It can also be used as a text in courses centered on computational fluid dynamics.

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.

Turbulence is a major problem facing modern societies. It makes airline passengers return to their seats and fasten their seatbelts but it also creates drag on the aircraft that causes it to use more fuel and create more pollution. The same applies to cars, ships and the space shuttle. The mathematical theory of turbulence has been an unsolved problems for 500 years and the development of the statistical theory of the Navier-Stokes equations describes turbulent flow has been an open problem. The Kolmogorov-Obukhov Theory of Turbulence develops a statistical theory of turbulence from the stochastic Navier-Stokes equation and the physical theory, that was proposed by Kolmogorov and Obukhov in 1941. The statistical theory of turbulence shows that the noise in developed turbulence is a general form which can be used to present a mathematical model for the stochastic Navier-Stokes equation. The statistical theory of the stochastic Navier-Stokes equation is developed in a pedagogical manner and shown to imply the Kolmogorov-Obukhov statistical theory. This book looks at a new mathematical theory in turbulence which may lead to many new developments in vorticity and Lagrangian turbulence. But even more importantly it may produce a systematic way of improving direct Navier-Stokes simulations and lead to a major jump in the technology both preventing and utilizing turbulence.

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.

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.

Stabilization of Navier-Stokes Flows presents recent notable progress in the mathematical theory of stabilization of Newtonian fluid flows. Finite-dimensional feedback controllers are used to stabilize exponentially the equilibrium solutions of Navier-Stokes equations, reducing or eliminating turbulence. Stochastic stabilization and robustness of stabilizable feedback are also discussed. The analysis developed here provides a rigorous pattern for the design of efficient stabilizable feedback controllers to meet the needs of practical problems and the conceptual controllers actually detailed will render the reader's task of application easier still. Stabilization of Navier-Stokes Flows avoids the tedious and technical details often present in mathematical treatments of control and Navier-Stokes equations and will appeal to a sizeable audience of researchers and graduate students interested in the mathematics of flow and turbulence control and in Navier-Stokes equations in particular.

This book surveys significant modern contributions to the mathematical theories of generalized heat wave equations. The first three chapters form a comprehensive survey of most modern contributions also describing in detail the mathematical properties of each model. Acceleration waves and shock waves are the focus in the next two chapters. Numerical techniques, continuous data dependence, and spatial stability of the solution in a cylinder, feature prominently among other topics treated in the following two chapters. The final two chapters are devoted to a description of selected applications and the corresponding formation of mathematical models. Illustrations are taken from a broad range that includes nanofluids, porous media, thin films, nuclear reactors, traffic flow, biology, and medicine, all of contemporary active technological importance and interest.

This book will be of value to applied mathematicians, theoretical engineers and other practitioners who wish to know both the theory and its relevance to diverse applications.

"

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."

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.