The need for properties is ever increasing to make processes more economical. A good survey of the viscosity data, its critical evaluation and correlation would help design engineers, scientists and technologists in their areas of interest. This type of work assumes more importance as the amount of experimental work in collection and correlation of properties such as viscosity, thermal conductivity, heat capacities, etc has reduced drastically both at the industry, universities, and national laboratories. One of the c o-authors, Professor Viswanath, co-authored a book jointly with Dr. Natarajan Data Book on the Viscosity of Liquids in 1989 which mainly presented collected and evaluated liquid viscosity data from the literature. Although it is one of its kinds in the field, Prof. Viswanath recognized that the design engineers, scientists and technologists should have a better understanding of theories, experimental procedures, and operational aspects of viscometers. Also, rarely the data are readily available at the conditions that are necessary for design of the equipment or for other calculations. Therefore, the data must be interpolated or extrapolated using the existing literature data and using appropriate correlations or models. We have tried to address these issues in this book."

The emphasis of this book is on engineering aspects of fluid turbulence. The book explains for example how to tackle turbulence in industrial applications. It is useful to several disciplines, such as, mechanical, civil, chemical, aerospace engineers and also to professors, researchers, beginners, under graduates and post graduates. The following issues are emphasized in the book: - Modeling and computations of engineering flows: The author discusses in detail the quantities of interest for engineering turbulent flows and how to select an appropriate turbulence model; Also, a treatment of the selection of appropriate boundary conditions for the CFD simulations is given. - Modeling of turbulent convective heat transfer: This is encountered in several practical situations. It basically needs discussion on issues of treatment of walls and turbulent heat fluxes. - Modeling of buoyancy driven flows, for example, smoke issuing from chimney, pollutant discharge into water bodies, etc

In 1998 the chairman of the Russian National Committee of TMM Professor Arcady Bessonov, recommended one of authors of this book to be come a member of the IFToMM Permanent Commission on the History of Mechanisms and Machines Sciences (PC HMMS). Willy-nilly from this time the history of technique, as hobby passed on to a serious the employment in the history of engineering science. Interest history of a subject is natural for Professor, a leading a course of Theory of Mechanisms and Machines in Bauman University. This interest is supported by the fact that Bauman University is one of the oldest technical universities in Russia, and the course "Applied Mechanics" - later "Theory of Mechanisms and Machines" was the first systematic course in Russia. The second author supervises a cycle of laboratory works on TMM. Models of mechanisms are placed in laboratory in show-windows of ancient cases quite possibly coevals of the first course. He became interested in contents of these cases: firstly in models, and then in their origin. Later he occupied himself with the creation of a web-site "The Collection of mechanisms in department TMM in Bauman University". Gradually both authors had the idea of cooperation, although several years previously, we could not imagine this happening. We took an active part in the work of PC HMMS from 2000. It was promoted by of chairman of the commission Professor Marco Ceccarelli.

Ando establishes a theory of subjective preference of the sound field in a concert hall, based on preference theory with a model of human auditory- brain system. The model uses the autocorrelation function and the interaural crosscorrelation function for signals arriving at two ear entrances and considers the specialization of human cerebral hemispheres. The theory may be applied to describe primary sensations such as pitch or missing fundamental, loudness, timbre, and duration. The theory may also be applied to visual sensations as well as subjective preference of visual environments. Remarkable findings in activities in both auditory-brain and visual-brain systems in relation to subjective preference as a primitive response are described.

This book is comprehensive in its classical mathematical physics presentation, providing the reader with detailed instructions for obtaining Green's functions from scratch. Green's functions is an instrument easily accessible to practitioners who are engaged in design and exploitation of machines and structures in modern engineering practice. To date, there are no books available on the market that are devoted to the Green's function formalism for equations covered in this volume. The reader, with an undergraduate background in applied mathematics, can become an active user of the Green's function approach. For the first time, Green's functions are discussed for a specific class of problems dealing with potential fields induced in thin-wall structures and therefore, the reader will have first-hand access to a novel issue. This Work is accessible to researchers in applied mathematics, mechanics, and relevant disciplines such as engineering, as well as to upper level undergraduates and graduate students.

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.

This book gives a detailed, up-to-date account of the Lense-Thirring effect and its implications for physics and astrophysics. Starting from a profound intuition of Lense and Thirring in 1918, based on a simple solution to the linearized Einstein field equations, this has emerged in the past four decades as a phenomenon of extraordinary importance in cosmology, radio jets in quasars, and the physics of neutron stars and black holes, besides leading to some of the most sophisticated experiments ever performed in the space surrounding our planet. The book contains the contributions presented at the "Third William Fairbank Meeting," which have been expanded by adding a complete set of classical and prominent contemporary papers on this subject and a general introduction by R Ruffini.

This thesis presents valuable contributions to several aspects of the rapidly growing field of gravitational wave astrophysics. The potential sources of gravitational waves in globular clusters are analyzed using sophisticated dynamics simulations involving intermediate mass black holes and including, for the first time, high-order post-Newtonian corrections to the equations of motion. The thesis further demonstrates our ability to accurately measure the parameters of the sources involved in intermediate-mass-ratio inspirals of stellar-mass compact objects into hundred-solar-mass black holes. Lastly, it proposes new techniques for the computationally efficient inference on gravitational waves. On 14 September 2015, the LIGO observatory reported the first direct detection of gravitational waves from the merger of a pair of black holes. For a brief fraction of a second, the power emitted by this merger exceeded the combined output of all stars in the visible universe. This has since been followed by another confirmed detection and a third candidate binary black hole merger. These detections heralded the birth of an exciting new field: gravitational-wave astrophysics.

This volume contains the papers of a German Symposium dealing with research and project work in numerical and experimental aerodynamics and fluidmechanics for aerospace and other applications. Results are reported from universities, research-establishments and industry. It therefore gives a broad overview over the ongoing work in this field in Germany.

As mentioned in the Introduction to Volume I, the present monograph is intended both for mathematicians interested in applications of the theory of linear operators and operator-functions to problems of hydrodynamics, and for researchers of applied hydrodynamic problems, who want to study these problems by means of the most recent achievements in operator theory. The second volume considers nonself-adjoint problems describing motions and normal oscillations of a homogeneous viscous incompressible fluid. These ini tial boundary value problems of mathematical physics include, as a rule, derivatives in time of the unknown functions not only in the equation, but in the boundary conditions, too. Therefore, the spectral problems corresponding to such boundary value problems include the spectral parameter in the equation and in the bound ary conditions, and are nonself-adjoint. In their study, we widely used the theory of nonself-adjoint operators acting in a Hilbert space and also the theory of operator pencils. In particular, the methods of operator pencil factorization and methods of operator theory in a space with indefinite metric find here a wide application. We note also that this volume presents both the now classical problems on oscillations of a homogeneous viscous fluid in an open container (in an ordinary state and in weightlessness) and a new set of problems on oscillations of partially dissipative hydrodynamic systems, and problems on oscillations of a visco-elastic or relaxing fluid. Some of these problems need a more careful additional investigation and are rather complicated."

The priority research, Analysis, Modelling and Numerical Calculations ofMul tiphase Flows" was running for 6 years (from 1996 to 2002) and financially sup ported by the Deutsche Forschungsgemeinschaft (DFG). The main objective ofthe research programme was to provide a better understanding of the physical basis for multiphase gas-liquid flows as they are found in numerous chemical and bio chemical reactors. The research comprised steady and unsteady multiphase flows in three frequently found reactor configurations, namely bubble columns without interiors, loop reactors, and aerated stirred vessels. For this purpose, new and im proved measurement techniques should be developed. From the resulting knowl edge and data, new and refined models for describing the underlying physical processes should result, which can be used for the establishment and improvement of analytic as well as numerical methods for predicting multiphase reactors. Thereby, the development, lay-out and scale-up ofsuch processes should be pos sible on a more reliable basis. For achieving this objective three research areas were defined: development and improvement of experimental techniques which allow accu rate measurements in steady and unsteady multiphase flows elaboration of new modelling approaches in order to describe the basic trans port processes for mass, momentum, and heat in bubbly flows development of analytical and numerical methods supplemented by the new modelling strategies in order to support optimisation and lay-out of technical multiphase processes."

This book contains advanced-level research material in the area of lubrication theory and related aspects, presented by eminent researchers during the International Conference on Advances in Tribology and Engineering Systems (ICATES 2013) held at Gujarat Technological University, Ahmedabad, India during October 15 17, 2013. The material in this book represents the advanced field of tribology and reflects the work of many eminent researchers from both India and abroad. The treatment of the presentations is the result of the contributions of several professionals working in the industry and academia. This book will be useful for students, researchers, academicians, and professionals working in the area of tribology, in general, and bearing performance characteristics, in particular, especially from the point-of-view of design. This book will also appeal to researchers and professionals working in fluid-film lubrication and other practical applications of tribology. A wide range of topics has been included despite space and time constraints. Basic concepts and fundamentals techniques have been emphasized upon, while also including highly specialized topics and methods (such as nanotribology, bio-nanotribology). Care has been taken to generate interest for a wide range of readers, considering the interdisciplinary nature of the subject."

This book covers the basics of the hydrodynamics and vibration of structures subjected to environmental loads. It describes the interaction of hydrodynamics with the associated vibration of structures, giving simple explanations. Emphasis is placed on the applications of the theory to practical problems. Several case studies are provided to show how the theory outlined in the book is applied in the design of structures. Background material needed for understanding fluid-induced vibrations of structures is given to make the book reasonably self-sufficient. Examples are taken mainly from the novel structures that are of interest today, including ocean and offshore structures and components.Besides being a text for undergraduates, this book can serve as a handy reference for design engineers and consultants involved in the design of structures subjected to dynamics and vibration.

These proceedings collect the selected contributions of participants of the First Karl Schwarzschild Meeting on Gravitational Physics, held in Frankfurt, Germany to celebrate the 140th anniversary of Schwarzschild's birth. They are grouped into 4 main themes: I. The Life and Work of Karl Schwarzschild; II. Black Holes in Classical General Relativity, Numerical Relativity, Astrophysics, Cosmology, and Alternative Theories of Gravity; III. Black Holes in Quantum Gravity and String Theory; IV. Other Topics in Contemporary Gravitation. Inspired by the foundational principle ``By acknowledging the past, we open a route to the future", the week-long meeting, envisioned as a forum for exchange between scientists from all locations and levels of education, drew participants from 15 countries across 4 continents. In addition to plenary talks from leading researchers, a special focus on young talent was provided, a feature underlined by the Springer Prize for the best student and junior presentations.

This book details a systematic characteristics-based finite element procedure to investigate incompressible, free-surface and compressible flows. Several sections derive the Fluid Dynamics equations from first thermo-mechanics principles and develop this multi-dimensional and infinite-directional upstream procedure by combining a finite element discretization with an implicit non-linearly stable Runge-Kutta time integration for the numerical solution of the Euler and Navier Stokes equations.

This book includes the proceedings of the Workshop held in Madrid, April 1999 to celebrate 2 years of successful operation of the first Spanish small scientific satellite in orbit. It contains discussions about the overall philosophy of small mission programs, the design of the satellite and its payload as well as the most relevant scientific outcome of the mission. Also included are additional contributions to the workshop, which are of importance to Minisat 01 in order to put its results within context. Finally, the future of small missions for space sciences is reviewed together with the main technological challenges for new studies. Out of the technological and scientific results of Minisat 01, the measurement of the EUV airglow spectrum and the flux of some stars in the same range can be highlighted together with the dismiss of the massive neutrino decay theory. The high-energy experiment analyzed the characterization of the radiation environment in LEO and the behaviour of different kind of detectors, as well as the use of coded masks for imaging and the measurement of some specific sources. The book's level is intended for specialists in EUV and Hard X-Ray astrophysicists as well as for engineers and technicians involved in space science experiments and missions.

Among the variety of wave motions one can single out surface wave pr- agation since these surface waves often adjust the features of the energy transfer in the continuum (system), its deformation and fracture. Predicted by Rayleigh in 1885, surface waves represent waves localized in the vicinity ofextendedboundaries(surfaces)of?uidsorelasticmedia. Intheidealcase of an isotropic elastic half-space while the Rayleigh waves propagate along the surface, the wave amplitude (displacement) in the transverse direction exponentially decays with increasing distance away from the surface. As a resulttheenergyofsurfaceperturbationsislocalizedbytheRayleighwaves within a relatively narrow layer beneath the surface. It is this property of the surface waves that leads to the resonance phenomena that accompany the motion of the perturbation sources (like surface loads) with velocities close to the Rayleigh one; (see e. g. , R. V. Goldstein. Rayleigh waves and resonance phenomena in elastic bodies. Journal of Applied Mathematics and Mechanics (PMM), 1965, v. 29, N 3, pp. 608-619). It is essential to note that resonance phenomena are also inherent to the elastic medium in the case where initially there are no free (unloaded) surfaces. However, they occur as a result of an external action accompanied by the violation of the continuity of certain physical quantities, e. g. , by crack nucleation and dynamic propagation. Note that the aforementioned resonance phenomena are related to the nature of the surface waves as homogeneous solutions (eigenfunctions) of the dynamic elasticity equations for a half-space (i. e. nonzero solutions at vanishing boundary conditions).

This volume is dedicated to Jacob Aboudi, a ?ne scientist who has made seminal c- tributions in applied mechanics. The papers presented here re?ect the appreciation of many of Jacob's colleagues. A publication list f- lowing this introduction provides an indi- tion of his distinguished academic career, c- rently in its ?fth decade, and the breadth of hisknowledge. His papersconsistentlydem- strate originality, innovation and diligence. This list uncovers the methodical work of a dedicated researcher whose achievements established him as a leading authority in the area of mathematical modeling of the beh- ior of heterogeneous materials, the area which became known as homogenization theory. Starting in 1981, Jacob established a micromechanical model known as the Method of Cells (MOC) which evolved into the Generalized Method of Cells (GMC) that predicts the macroscopic response of composite materials as a function of the pr- erties, volume fractions, shapes, and constitutive behavior of its constituents. The versatility of the model has been demonstrated to effectively incorporate various types of constituent material behavior (i. e. , both coupled and uncoupled mecha- cal, thermal, electrical and magnetic effects). As a result of its potential in providing an ef?cient tool for the emerging ?eld of multiscale analysis, the method gained increasing attention and became a subject for further research.

Fluids, play an important role in environmental systems, appearing as surface water in rivers, lakes, and coastal regions or in the subsurface as well as in the atmosphere. Mechanics of environmental fluids is concerned with fluid motion, associated mass and heat transport in addition to deformation processes in subsurface systems. In this textbook the fundamental modelling approaches based on continuum mechanics for fluids in the environment are described, including porous media and turbulence. Numerical methods for solving the process governing equations and its object-oriented computer implementation are discussed and illustrated with examples. Finally the application of computer models in civil and environmental engineering is demonstrated.

The essential aim of the present book is to consider a wide set of problems arising in the mathematical modelling of mechanical systems under unilateral constraints. In these investigations elastic and non-elastic deformations, friction and adhesion phenomena are taken into account. All the necessary mathematical tools are given: local boundary value problem formulations, construction of variational equations and inequalities, and the transition to minimization problems, existence and uniqueness theorems, and variational transformations (Friedrichs and Young-Fenchel-Moreau) to dual and saddle-point search problems. Important new results concern contact problems with friction. The Coulomb friction law and some others are considered, in which relative sliding velocities appear.

The volume is devoted to the dynamics of rods, which is a branch of mech- ics of deformable bodies. The main goal of the book is to present systema- cally theoretical fundamentals of the mechanics of rods as well as numerical methods used for practical purposes. Linear and nonlinear equations governing a rod's oscillations are p- sented. Methods of determining eigenvalues and eigenfunctions in conser- tive and non-conservative problems along with numerical methods dealing with forced, parametric, and random oscillations of rods are given. Some - sues of interaction of rods with air (liquid) flows and the dynamics of spa- curved rods containing flows of liquid are considered. The book consists of nine chapters and appendices and may be conv- tionally divided into two parts. That is, Chapters 1 to 6 contain, in the main, theoretical material, whereas Chapters 7 to 9 illustrate the application of the theoretical results to problems of practical interest. Problems for self-study are found in Chapters 3, 5, and 7. The solutions to most of the problems are given in Appendix B. The monograph is addressed to undergraduate and postgraduate students and teaching staff of technical universities. It may also be useful for scientists and mechanical engineers working in a wide range of industries. I wish to express my deep appreciation to my colleagues, Dr. S.A. Voronov and C.B. Danilenko, for their help in preparing the manuscript.

The Handbook of Mathematical Fluid Dynamics is a compendium of essays that provides a survey of the major topics in the subject. Each article traces developments, surveys the results of the past decade, discusses the current state of knowledge and presents major future directions and open problems. Extensive bibliographic material is provided. The book is intended to be useful both to experts in the field and to mathematicians and other scientists who wish to learn about or begin research in mathematical fluid dynamics. The Handbook illuminates an exciting subject that involves rigorous mathematical theory applied to an important physical problem, namely the motion of fluids.

The present volume celebrates the 60th birthday of Professor Giovanni Paolo Galdi and honors his remarkable contributions to research in the ?eld of Mathematical Fluid Mechanics. The book contains a collection of 35 peer reviewed papers, with authors from 20 countries, re?ecting the worldwide impact and great inspiration by his work over the years. These papers were selected from invited lectures and contributed talks presented at the International Conference on Mathematical Fluid Mechanics held in Estoril, Portugal, May 21-25, 2007 and organized on the oc- sion of Professor Galdi's 60th birthday. We express our gratitude to all the authors and reviewers for their important contributions. Professor Galdi devotes his career to research on the mathematical analysis of the Navier-Stokes equations and non-Newtonian ?ow problems, with special emphasis on hydrodynamic stability and ?uid-particle interactions, impressing the worldwide mathematical communities with his results. His numerous contributions have laid down signi?cant milestones in these ?elds, with a great in?uence on interdis- plinary research communities. He has advanced the careers of numerous young researchers through his generosity and encouragement, some directly through int- lectual guidance and others indirectly by pairing them with well chosen senior c- laborators. A brief review of Professor Galdi's activities and some impressions by colleagues and friends are included here.

This thesis presents a study of strong stratification and turbulence collapse in the planetary boundary layer, opening a new avenue in this field. It is the first work to study all regimes of stratified turbulence in a unified simulation framework without a break in the paradigms for representation of turbulence. To date, advances in our understanding and the parameterization of turbulence in the stable boundary layer have been hampered by difficulties simulating the strongly stratified regime, and the analysis has primarily been based on field measurements. The content presented here changes that paradigm by demonstrating the ability of direct numerical simulation to address this problem, and by doing so to remove the uncertainty of turbulence models from the analysis. Employing a stably stratified Ekman layer as a simplified physical model of the stable boundary layer, the three stratification regimes observed in nature- weakly, intermediately and strongly stratified-are reproduced, and the data is subsequently used to answer key, long-standing questions. The main part of the book is organized in three sections, namely a comprehensive introduction, numerics, and physics. The thesis ends with a clear and concise conclusion that distills specific implications for the study of the stable boundary layer. This structure emphasizes the physical results, but at the same time gives relevance to the technical aspects of numerical schemes and post-processing tools. The selection of the relevant literature during the introduction, and its use along the work appropriately combines literature from two research communities: fluid dynamics, and boundary-layer meteorology.

Intended as a textbook for courses in computational fluid dynamics at the senior undergraduate or graduate level, this book is a follow-up to the book Fundamentals of Computational Fluid Dynamics by the same authors, which was published in the series Scientific Computation in 2001. Whereas the earlier book concentrated on the analysis of numerical methods applied to model equations, this new book concentrates on algorithms for the numerical solution of the Euler and Navier-Stokes equations. It focuses on some classical algorithms as well as the underlying ideas based on the latest methods. A key feature of the book is the inclusion of programming exercises at the end of each chapter based on the numerical solution of the quasi-one-dimensional Euler equations and the shock-tube problem. These exercises can be included in the context of a typical course and sample solutions are provided in each chapter, so readers can confirm that they have coded the algorithms correctly.