The book provides a broad overview of the full spectrum of state-of-the-art computational activities in multiphase flow as presented by top practitioners in the field. Starting with well-established approaches (point-particle models, volume-of-fluid, level set, and front capturing for free-surface flows) it builds up to newer methods for large-eddy simulations, extended particles in Navier-Stokes flows, the lattice-Boltzmann method, molecular dynamics techniques and compressible flows with shock waves. These methods are illustrated with applications to a broad spectrum of problems involving particle dispersion and deposition, turbulence modulation, environmental flows, fluidized beds, bubbly flows, and many others.

This book is a continuation of 'Acoustic and Elastic Wave Fields in Geophysics, Part I' published in 2000. The second volume is dedicated to propagation of linear plane, spherical and cylindrical acoustic waves in different media. Chapter 1 is devoted to principles of geometric acoustic in plane wave approximation. The eikonal and transport equations are derived. Ray tracing and wavefront construction techniques are explained. Chapter 2 deals with dynamic properties of wave fields. The behavior of pressure and displacements amplitudes in zero approximation is analysed in two ways: using Poynting vector and solving the transport equation. This chapter contains several examples related to shadow zones and caustics. In Chapter 3 using the results of analysis of high-frequency wave kinematics and dynamics some fundamental aspects of Kirchhoff migration are described. Chapters 4 and 5 are devoted to propagation of plane waves in media with flat boundaries in the case of normal and oblique incidence. Special attention is paid to the case when an incident angle exceeds the critical angles. Formation of normal modes in the waveguide is discussed. Chapter 6 deals with a spherical wave reflection and refraction. The steepest descent method is introduced to describe the behavior of reflected, transmitted, head and evanescent waves. In Chapter 7 propagation of stationary and transient waves in a waveguide formed by a flat layer with low velocity are investigated. Normal modes and waves related to the branch points of integrands under consideration are studied. Dispersive properties of normal modes are discussed. Chapter 8 describes wave propagation inside cylinder in acoustic media. Several appendices are added to help the reader understand different aspects of mathematics used in the book.

The present set of lectures and tutorial reviews deals with various topical aspects related to instabilities of interfacial processes and driven flows from both the theoretical and experimental point of views. New research has been spurred by demands for many applications in material sciences (melting, solidification, electro deposition), biomedical engineering and processing in microgravity environments. This book is intended as both a modern source of reference for researchers in the field as well as an introduction to postgraduate students and non-specialists from related areas.

This overview of the development of continuum mechanics throughout the twentieth century is unique and ambitious. Utilizing a historical perspective, it combines an exposition on the technical progress made in the field and a marked interest in the role played by remarkable individuals and scientific schools and institutions on a rapidly evolving social background. It underlines the newly raised technical questions and their answers, and the ongoing reflections on the bases of continuum mechanics associated, or in competition, with other branches of the physical sciences, including thermodynamics. The emphasis is placed on the development of a more realistic modeling of deformable solids and the exploitation of new mathematical tools. The book presents a balanced appraisal of advances made in various parts of the world. The author contributes his technical expertise, personal recollections, and international experience to this general overview, which is very informative albeit concise.

Introduce every concept in the simplest setting and to maintain a level of treatment that is as rigorous as possible without being unnecessarily abstract.

Contains unique recent developments of various finite elements such as nonconforming, mixed, discontinuous, characteristic, and adaptive finite elements, along with their applications.

Describes unique recent applications of finite element methods to important fields such as multiphase flows in porous media and semiconductor modelling.

Treats the three major types of partial differential equations, i.e., elliptic, parabolic, and hyperbolic equations.

The book is comprised of lectures and selected contributions presented at the Enzo Levi and XVI Annual Meeting of the Fluid Dynamic Division of the Mexican Physical Society in 2010. It is aimed at fourth year undergraduate and graduate students, as well as scientists in the fields of physics, engineering and chemistry with an interest in fluid dynamics from the experimental and theoretical point of view. The lectures are introductory and avoid the use of complicated mathematics. The other selected contributions are also geared to fourth year undergraduate and graduate students. The fluid dynamics applications include multiphase flow, convection, diffusion, heat transfer, rheology, granular material, viscous flow, porous media flow, geophysics and astrophysics. The material contained in the book includes recent advances in experimental and theoretical fluid dynamics and will be of great use to those involved in either teaching and/or research.

The objective of Volume III is to lay down the proper mathematical foundations of the two-dimensional theory of shells. To this end, it provides, without any recourse to any "a priori" assumptions of a geometrical or mechanical nature, a mathematical justification of two-dimensional nonlinear and linear shell theories, by means of asymptotic methods, with the thickness as the "small" parameter.

The investigation of minor solar system bodies, such as comets and asteroids, using spacecraft requires an understanding of orbital motion in strongly perturbed environments. The solutions to a wide range of complex and challenging problems in this field are reviewed in this comprehensive and authoritative work.

This volume contains selected presentations of the "EUROMECH Colloquium 412 on LES of complex transitional and turbulent flows" held at the Munich University of Technology from 4 to 6 October 2000.

The articles focus on new developments in the field of large-eddy simulation of complex flows and are related to the topics: modelling and analysis of subgrid scales, numerical issues in LES cartesian grids for complex geometries, curvilinear and non-structured grids for complex geometries. DES and RANS-LES coupling, aircraft wake vortices, combustion and magnetohydrodynamics.

Progress has been made not only in understanding and modelling the dynamics of unresolved scales, but also in designing means that prevent the contamination of LES predictions by discretization errors. Progress is reported as well on the use of cartesian and curvilinear coordinates to compute flow in and around complex geometries and in the field of LES with unstructured grids. A chapter is dedicated to the detached-eddy simulation technique and its recent achievements and to the promising technique of coupling RANS and LES solutions in order to push the resolution-based Reynolds number limit of wall-resolving LES to higher values.

Complexity due to physical mechanisms links the last two chapters. It is shown that LES constitutes the tool to analyse the physics of aircraft wake vortices during landing and takeoff. Its thorough understanding is a prerequisite for reliable predictions of the distance between consecutive landing airplanes. Subgrid combustion modelling for LES of single and two-phase reacting flows is demonstrated to have the potential to deal with finite-rate kinetics in high Reynolds numberflows of full-scale gas turbine engines. Fluctuating magnetic fields are more reliably predicted by LES when tensor-diffusivity rather than gradient-diffusion models are used. An encouraging result in the context of turbulence control by magnetic fields.

Musical Sound, Instruments, and Equipment offers a basic understanding of sound, musical instruments and music equipment, geared towards a general audience and non-science majors. The book begins with an introduction of the fundamental properties of sound waves, and the perception of the characteristics of sound. The relation between intensity and loudness, and the relation between frequency and pitch are discussed. The basics of propagation of sound waves, and the interaction of sound waves with objects and structures of various sizes are introduced. Standing waves, harmonics and resonance are explained in simple terms, using graphics that provide a visual understanding.

This new edition of this standard work adds several new information the book, so that sound engineering and architects can better assess the acoustic value of a Rock and Pop Venue. In particular, new insights to the influence of sound absorbers in reflected and important ISO standards are included into the new edition. Based on the first ever scientific investigations on recommendable acoustics for amplified music conducted by the author, this book sets forward precise guidelines for acoustical engineers to optimize the acoustics in existing or future halls for amplified music. It Gives precise guidelines on how to design the acoustics in venues that present amplified music Debates essential construction details, including placement of sound system and use of possible building materials, in the architectural design of new venues or the renovation of old ones Portrays 75 well-known European Rock & Pop venues, their architecture and acoustic properties. 20 venues were rated for their acoustics by music professionals leading to an easy-to-use assessment methodology

The book presents a history of classical mechanics by focusing on issues of equilibrium. The historical point of view adopted here restricts attention to cases where the effectiveness of forces is assessed on the basis of the virtual motion of their points of application. For completeness, hints of the alternative approach are also referred, the Archimedean for ancient mechanics and the Newtonian for modern mechanics. The laws resulting from consideration of virtual motions are named laws of virtual work. The modern formulations of the principle of virtual work are only a particular form of them. The book begins with the first documented formulations of laws of virtual work in the IV century BC in Greece and proceeds to the end of the XIX century AD in Europe. A significant space is devoted to Arabic and Latin mechanics of Middle Ages. With the Renaissance it began to appear slightly different wordings of the laws, which were often proposed as unique principles of statics. The process reached its apex with Bernoulli and Lagrange in the XVIII century. The book ends with some chapters dealing with the discussions that took place in the French school on the role of the Lagrangian version of the law of virtual work and its applications to continuum mechanics.

The symposiumwas motivatedby theincreasing need for modelling of material behaviourundervarious mechan icalconditions. This need is driven by the evolut ion ofcomputer capac ityand the resulting ability for engineers and scien tiststo address complexproblems . Reliable models formaterialbehaviour, including accurate numericalvalues of parameters ,are necessary for a continued beneficial development ofthe computational side of solid mechanics .High rate plasticity ,thermally assisted creep and phasetransformationsare only a fewexamplesof areas where more accurate modelsare needed. Experiments are necessary for the establishment ofmodels and parameters , and modified versionsof conventional test methods can make important contributions . Also modern optical methodsoffer a highpotentialfor futureexperimental development. Numerical simulations ofexperiments and so-called inverse modelling arealso frequentlyused techniques. The aim of the symposium was to bring together researchers with an interest in the areaofexperimental and computational aspects ofmaterial modelling for exchange and discussionofpromising methodsandresults. Abisko,a national park in the Swedish mountain district about 200 km north of the arctic circle and about one hourve dri from the airport ofKiruna,was chosen for the symposium. The tourist hotel in the park , overlookinga beautiful lake , offered a suitablevenue for the symposium. This environment with tracks for short walks (and long hikes),goals for small excursions and a hotel with restaurant and bar ve the ga delegatesmany opportunitiesto meet , socialiseand discuss during breaks and evenings.

The principal object of this volume is the creation of a mathematical theory of deformations for elastic anisotropic thermodynamic piezoelastic plates, beams and shells with variable thickness. The book is divided into two parts. The first part deals with problems related to the construction of refined theories (such as those of Richhof-Love, von Karman-A. Fioppl, and Reissner) and their equivalent new models (depending on arbitrary control functions). These are investigated by means of a new variational principle. Methods of reduction, containing regular processes of study of spatial problems, are also studied. Topics treated include problems of solvability, error estimations, convergence of processes in Sobolev spaces and construction of effective schemes of solutions of two-dimensional boundary value problems for systems of partial differential equations. The second part considers stable projective methods, using classical orthogonal polynomials and a new class of spline-functions as coordinate systems, and their numerical realizations for a design of one- and two- dimensional boundary value problems from the first part. These efficient methods increase the possibilities of classical finite-difference, exponential- fitted, variational-discrete and alternating-direction methods. Audience: This book will be of interest to researchers and graduate students whose work involves mechanics, analysis, numerics and computation, mathematical modelling and industrial mathematics, calculus of variations, and design engineering.

This book will reveal cost reductions and how to slash your energy costs without investing big money. The three pillars of costs reduction will discussed: Assembling your options and analyzing your risk; developing options with your utility; and cutting out obvious waste in your operation. Those who will benefit from this excellent text are business owners, CFOs, plant managers, plant engineers, and energy managers. You will learn how to distill what savings are possible and how you can quickly accomplish those savings from what you already know and can expect to walk away at the end of this book with confidence and a realistic plan of action for reducing your costs.

Designing new structural materials, extending lifetimes and guarding against fracture in service are among the preoccupations of engineers, and to deal with these they need to have command of the mechanics of material behaviour. The first volume of this two-volume work deals with elastic and elastoplastic behaviour; this second volume continues with viscoelasticity, damage, fracture (resistance to cracking) and contact mechanics. As in Volume I, the treatment starts from the active mechanisms on the microscopic scale and develops the laws of macroscopic behaviour. Chapter I deals with viscoplastic behaviour, as shown, for example, at low temperatures by the effects of oscillatory loads and at high temperatures by creep under steady load. Chapter 2 treats damage phenomena encountered in all materials - for example, metals, polymers, glasses, concretes - such as cavitation, fatigue and stress-corrosion cracking. Chapter 3 treats those concepts of fracture mechanics that are needed for the understanding of resistance to cracking and Chapter 4 completes the volume with a survey of the main concepts of contact mechanics. As with Volume I, each chapter has a set of exercises, either with solutions or with indications of how to attack the problem; and there are many explanatory diagrams and other illustrations.

The text of the Persian poet Rum - - ?, written some eight centuries ago, and reproduced at the beginning of this book is still relevant to many of our pursuits of knowledge, not least of turbulence. The text illustrates the inability people have in seeing the whole thing, the 'big picture'. Everybody looks into the problem from his/her vi- point, and that leads to disagreement and controversy. If we could see the whole thing, our understanding would become complete and there would be no cont- versy. The turbulent motion of the atmosphere and oceans, at the heart of the observed general circulation, is undoubtedly very complex and dif?cult to understand in its entirety. Even 'bare' turbulence, without rotation and strati?cation whose effects are paramount in the atmosphere and oceans, still poses great fundamental ch- lenges for understanding after a century of research. Rotating strati?ed turbulence is a relatively new research topic. It is also far richer, exhibiting a host of distinct wave types interacting in a complicated and often subtle way with long-lived - herent structures such as jets or currents and vortices. All of this is tied together by basic ?uid-dynamical nonlinearity, and this gives rise to a multitude of phen- ena: spontaneous wave emission, wave-induced transport, both direct and inverse energy scale cascades, lateral and vertical anisotropy, fronts and transport barriers, anomalous transport in coherent vortices, and a very wide range of dynamical and thermodynamical instabilities.

This text is the primary recommendation of the UK Engineering Council Faculty of Technology to all British universities as of approved standard and quality for use as a text for the Board's own examinations. It introduces the fundamental concepts and principles of statics and stress analysis as the essential reading for first year engineering students. Worked examples from the authors experience reinforce comprehension of key concepts. Tutorial solutions with explanation in extended detail have been provided for students. Key elements include: use of free-body diagrams to help problem solving; coverage of composite materials; torsion of circular and non-circular sections; and the matrix-displacement method.
Introduces the fundamental concepts and principles of statistics and stress analysis and applies these concepts and principles to a large number of practical problemsThe primary recommendation of the UK Engineering Council Faculty of Technology to all British universities

This collection is dedicated to the 70th jubilee of Yu. N. Savchenko, and presents experimental, theoretical, and numerical investigations written by an international group of well-known authors. The contributions solve very important problems of the high-speed hydrodynamics, such as supersonic motion in water, drag diminishing, dynamics and stability of supercavitating vehicles, water entry and hydrodynamic performances of hydrofoils, ventilated cavities after a disc and under the ship bottom.
The book is written for researches, scientists, engineers, and students interested in problems of hydromechanics."

This volume contains the Proceedings of the IUTAM Symposium held in Liverpool in 2002. It includes the articles presenting the results of recent work in mathematical modelling that covers the following areas of continuum mechanics and theoretical physics: *-Perturbation problems for partial differential equations and their applications in mechanics; * Analysis of singular fields; * Homogenisation theory in models of composite structures; * Mathematical models of cracks in solids; * Wave propagation, scattering; * Models of photonic and phononic band gap composite structures; * Advanced numerical techniques.

This monograph gives a comprehensive description of the relationship and connections between kinetic theory and fluid dynamics, mainly for a time-independent problem in a general domain. Ambiguities in this relationship are clarified, and the incompleteness of classical fluid dynamics in describing the behavior of a gas in the continuum limita "recently reported as the ghost effecta "is also discussed. The approach used in this work engages an audience of theoretical physicists, applied mathematicians, and engineers.

By a systematic asymptotic analysis, fluid-dynamic-type equations and their associated boundary conditions that take into account the weak effect of gas rarefaction are derived from the Boltzmann system. Comprehensive information on the Knudsen-layer correction is also obtained. Equations and their boundary conditions are carefully classified depending on the physical context of problems. Applications are presented to various physically interesting phenomena, including flows induced by temperature fields, evaporation and condensation problems, examples of the ghost effect, and bifurcation of flows.

Key features:

* many applications and physical models of practical interest

* experimental works such as the Knudsen compressor are examined to supplement theory

* engineers will not be overwhelmed by sophisticated mathematical techniques

* mathematicians will benefit from clarity of definitions and precise physical descriptions given in mathematical terms

* appendices collect key derivations and formulas, important to the practitioner, but not easily found in the literature

Kinetic Theory and Fluid Dynamics serves as a bridge for those working indifferent communities where kinetic theory or fluid dynamics is important: graduate students, researchers and practitioners in theoretical physics, applied mathematics, and various branches of engineering. The work can be used in graduate-level courses in fluid dynamics, gas dynamics, and kinetic theory; some parts of the text can be used in advanced undergraduate courses.

This book presents a unified hierarchical formulation of theories for three-dimensional continua, two-dimensional shells, one-dimensional rods, and zero-dimensional points. It allows readers with varying backgrounds easy access to fundamental understanding of these powerful Cosserat theories.

Hard spheres and related objects (hard disks and mixtures of hard systems) are paradigmatic systems: indeed, they have served as a basis for the theoretical and numerical development of a number of fields, such as general liquids and fluids, amorphous solids, liquid crystals, colloids and granular matter, to name but a few. The present volume introduces and reviews some important basics and progress in the study of such systems. Their structure, thermodynamic properties, equations of state, as well as kinetic and transport properties are considered from different and complementary points of view. This book addresses graduate students, lecturers as well as researchers in statistical mechanics, physics of liquids, physical chemistry and chemical engineering.

This book provides an introduction to turbulence in vortex systems, and to turbulence theory for incompressible flow described in terms of the vorticity field. It is the author's hope that by the end of the book the reader will believe that these subjects are identical, and constitute a special case of fairly standard statistical mechanics, with both equilibrium and non-equilibrium aspects. The author's main goal is to relate turbulence to statistical mechanics. The book is organized as follows: the first three chapters constitute a fairly standard introduction to homogeneous turbulence in incompressible flow; a quick review of fluid mechanics; a summary of the appropriate Fourier theory; a summary of Kolmogorov's theory of the inertial range. The next four chapters present the statistical theory of vortex notion, and the vortex dynamics of turbulence. The book ends with the major conclusion that turbulence can no longer be viewed as incomprehensible. This book will be appropriate for professionals in the fields of applied mathematics, mechanical engineering, or physics, as well as graduate students in these noted areas.