HIGH-INTENSITY ULTRASONIC FIELDS
|
|
- Janis Neal
- 6 years ago
- Views:
Transcription
1 HIGH-INTENSITY ULTRASONIC FIELDS
2 ULTRASONIC TECHNOLOGY A Series of Monographs General Editor Lewis Balamuth Ultrasonic Systems, Inc., Farmingdale, N. Y. 1967: RAYLEIGH AJ'jl> LAMB WAVES Physical Theory and Applications I. A. Viktorov 1969: SOURCES OF IDGH-INTENSITY ULTRASOUND Volume 1 Edited by L. D. Rozenberg SOURCES OF IDGH I~"TENSITY ULTRASOUND Volume 2 Edited by L. D. Rozenberg 1971: ULTRASONIC TRANSDUCER MATERIALS Edited by 0. E. Mattiat IDGH-INTENSITY ULTRASONIC FIELDS Edited by L. D. Rozenberg
3 HIGH-INTENSITY ULTRASONIC FIELDS Edited by L.D. Rozenberg Acoustics Institute Academy of Sciences of the USSR Moscow, USSR Translated from Russian by James S. Wood 9? SPRINGER SCIENCE+BUSINESS MEDIA, LLC 1971
4 The original Russian text, published by Nauka Press for the Acoustics Institute, Academy of Sciences of the USSR, in 1968, has been corrected for the present edition. The English translation is published under an agreement with Mezhdunarodnaya Kniga, the Soviet book export agency. JI.,ll. P03EHBEPr MOillHhiE Y JlbTPA3BYKOBbiE nomj MOSHCHNYEUL~RAZVUKOVYEPOLYA Library of Congress Catalog Card Number ISBN ISBN (ebook) DOI / Springer Science+Business Media New York Originally published by Plenum Press. New York in 1971 All rights reserved No part of this publication may be reproduced in any form without written permission from the publisher
5 Dedicated to Nikolai Nikolaevich.Andreev Preface This is the second volume in the series, "Physics and Engineering of High-Intensity Ultrasound,"* and is devoted to the specific characteristics of high-intensity sound fields. The characteristics of such fields constitute the subject of nonlinear acoustics, and the boo.k submitted herewith does not aspire to be an exhaustive treatise in that area. As the reader is aware, nonlinear processes are typified by interrelatedness and the inadmissibility of superposition, so that one should properly investigate the whole complex of phenomena in the large. However, the state of the art of research in this direction is such that we cannot yet pursue that approach and must be content to treat isolated aspects of nonlinear sound fields. This approach, of course, while only approximate, nevertheless has distinct advantages. Our orientation in this area is still, so to speak, "linear," and by the investigation of individual effects we are better able to grasp their physical significance, i.e., they are more comprensible to us. Consequently, the investigation of individual aspects of nonlinear sound fields, which can lead us to qualitative and sometimes quantitative insight, is not only of practical importance, but also fits better into our accustomed "linear way of thinking. As far as the individual aspects are concerned, they have been set apart not only for the extent to which they can be utilized to construct the physical foundations of ultrasonic technology, but also from considerations of their timeliness and the contributions of Soviet scientists, particularly members of the Acoustics Insti- "Reference here is to the series of Russian works, of which sources of High Intensity Ultrasound was the first translated as part of the present series- Publisher. v
6 vi PREFACE tute of the Academy of Sciences of the USSR. Thus, the book does not contain material on the nonlinear interaction of nonlinear absorption of high-intensity acoustic oscillations in solids, etc. Although the main body of the text generally encompasses the results of the author of the given part of the book, the materials of other Soviet and foreign researchers working in the particular field are also incorporated in the interest of clarity and completeness. Part I presents a survey of the results of investigations conducted by the author in the nonlinear absorption of,sound in liquids and gases. Of special interest are the effects on nonlinear absorption in convergent and divergent cylindrical and spherical fronts. Part n is based on results obtained by the author largely during his tenure at the Acoustics Institute. It is given over to the rather complex and beguiling problem of the radiation pressure, an area that is often imprecisely and at times incorrectly handled. Part lli comprises a survey of our knowledge concerning acoustic streaming. Even though the advances made in this area at the Acoustics Institute are relatively limited, the subject is still important enough to warrant its inclusion as an independent part of the book. The last three parts (IV, V, and VI) are concerned with a problem that is exceedingly complex, multifaceted, and often vague, despite the great many papers that have been published on it, namely ultrasonic cavitation. As the reader is aware, cavitation is the most active factor in a large majority of practical applications; moreover, it is extremely important as a unique physical process in itself. There is a certain arbitrariness in the breakdown of the subject into three parts. All three parts are based on investigations conducted at the Acoustics Institute and marked by many conceptually new quantitative and qualitative materials. For example, Part IV represents a probing analysis of the equations describing the motion of an individual bubble and an assessment of the instability effect. The results are compared with the data of highspeed motion pictures of cavitation bubbles. Part V describes the recently discovered effect of the multiplication of cavitation bubbles, a procedure developed for determining the acoustic energy losses in the formation of cavitation bubbles, and an investigation of the very interesting effects of the static pressure on the be-
7 PREFACE vii havior of cavitation bubbles, primarily on the enhancement of cavitation eros ion. Part VI is devoted to the vital, though so far, comparatively neglected problem of the behavior of the cavitation zone in general. The work in this area is currently in the state of development, but the results to date already permit a clear conceptualization of the phenomena evolving in a cavitation zone and occassionally certain inferences useful for practical applications. The pioneer in the formulation and development of problems in nonlinear acoustics in the large is Academician N. N. Andreev, on whose initiative some of the earliest investigations in this area were undertaken. The editor is grateful to V. S. Grigor 'ev and G. A. Ostroumov, who assumed the task of reviewing the manuscript of the book and offered many valuable comments. Also deserving acknowledgment is the considerable service rendered by V. A. Akulichev in preparing the manuscript for publication. L. D. Rozenberg
8 Contents PART I- ABSORPTION OF FINITE-AMPLITUDE WAVES K. A. Naugol 'nykh Introduction Chapter 1 - Plane Waves of Finite Amplitude Absorption of a!..ow-intensity Sound Wave Qualitative Description of the Propagation of Finite-Amplitude Waves Fundamental Equations Formation of First-Order Discontinuities in a Sound '"'ave Variation of the Spectral Composition of a Finite-Amplitude Wave during Propagation Absorption of a Finite-Amplitude Wave.. 30 Chapter 2 - Spherical and Cylindrical Waves of Finite Amplitude Formation of First-Order Discontinuities in Spherical Waves Variation of the Spectral Composition of Spherical and Cylindrical Waves Absorption of Spherical and Cylindrical Waves of Finite-Amplitude Chapter 3 - Dependence of the Gain of a Focusing System on Sound Intensity In.troduction ix
9 X CONTE::-ITS 2. Spherical Concentrator Cylindrical Concentrator Chapter 4 - Absorption of Finite-Amplitude Waves in Relaxing Media and in Solids Sound Absorption in Relaxing Media The Absorption of Finite-Amplitude Sound in Sol ids References PART II- ACOUSTIC RADIATION PRESSURE Z A. Gol' dbe rg Introduction Chapter 1 - The Initial Equations Initial Equations in Euler Variables Initial Equation in Lagrange Variables Chapter 2 - The Radiation Pressure General The Rayleigh Radiation Pressure The Langevin Radiation Pressure Chapter 3 - Problems Associated with the Radiation Pressure The Energy of Sound Waves Momentum Flux in Sound Waves Chapter 4 - Radiation Forces Acting on a Particle in a Sound Field Derivation of the Initial Equation Forces Acting on a Spherical Obstacle Forces Acting on a Disk Chapter 5 -Radiation Pressure Effects and Their Applications The Fountain Effect Absolute Measurement of the Field Intensity Nonlinear Properties of a Medium Acoustic Streaming Velocity and the Coefficient of Sound Absorption. 126 References
10 CONTENTS xi PART ill - ACOUSTIC STREAMING L. K. Zarembo Introduction Chapter 1 -Theory of Stationary Streaming in a Sound Field General Theory of Stationary Acoustic Streaming in the Second Approximation (Slow Streaming) Eckart Streaming Streaming Outside the Boundary Layer Acoustic Streaming in the Boundary Layer 159 Chapter 2 - The Experimental Investigation of Acoustic Streaming Methods for the <llservation of Streaming and Measurement of Its Velocity Streaming Near <llstacles, Microstreaming, and Streaming in Standing Waves Eckart Streaming References PART IV- PULSATIONS OF CAVITATION VOIDS V. A. Akulichev Introduction Chapter 1 - Fundamental Equations for the Pulsations of a Cavitation Void Pulsations of a Void in an Incompressible Liquid Pulsations of a Void with Regard for Compressibility of the Liquid Chapter 2 - Investigation of the Pulsations of Cavitation Voids Similarity of the Solutions of the Equations for Different frequencies of the Ultrasonic Field Structure of the Solutions; Structural Stability Collapse of Cavitation Voids
11 xii CONTEJ.'ITS 4. Analysis of the Solutions of the Equations in the Phase Plane Experimental Investigation of the Pulsations of Cavitation Voids Chapter 3 - Relationship of the Pulsations of Cavitation Voids to the Emission of Shock Waves and Cavitation Noise Shock Waves in Cavitation Discrete Spectral Components of Cavitation Noise The Continuous Cavitation Noise Spectrum Conclusion References PART V -EXPERIMENTAL INVESTIGATIONS U..l.<' ULTRASONIC CAVITATION M. G. Sirotyuk Introduction Chapter 1 -The Strength of Liquids Theoretical and Actual Strength Cavitation Nuclei The Cavitation Strength Size Distribution of the Nuclei Chapter 2- Characteristics of Cavitation Bubbles and Properties of the Cavitation Zone Oscillations of Cavitation Bubbles in a Sound Field Acoustic Pressure in the Cavitation Zone Maximum Cavitation Bubble Radius Gas Pressure in a Bubble at the Time of Collapse; the Gas Content Parameter The Collapse Time The Cavitation Zone and Number of Cavitation Bubbles Chapter 3 - Energy Balance of the Sound Field in Cavitation Cavitation Formation Energy; Streaming. 315
12 CONTENTS xiii 2. Cavitation Energy Cavitation Efficiency Chapter 4 -Influence of the Acoustic Pressure and Characteristics of the Liquid on the Shock Wave In.tensity The Acoustic Pressure Temperature and Gas Content of the Liquid The Hydrostatic Pressure 333 Conclusion References PART VI- THE CAVITATION ZONE L. D. Rozenberg Introduction Chapter 1 - Phenomenological Treatment The Cavitation Index Uniformity of the Cavitation Zone Energy Losses in the Formation of the Cavitation Zone The Loss Function and Its Application The Developed Cavitation Zone (in a High- Intensity Focusing Concentrator) Experimental Determination of the Cavitation Index Chapter 2 - Oscillations of a Bubble in a Cavitation Zone Statement of the Problem On the Interaction of Adjacent Bubbles Experimental Estimation of the Interaction Criterion Chapter 3 - Variationofthe Average Acoustical Characteristics of the Medium The One-Dimensional Cavitation Zone Experimental Investigations of the Equivalent Wave Resistance in Cavitation Compressibility of Cavitation Bubbles Chapter 4 -The Cavitation Efficiency. 389
13 xiv CONTENTS 1. Fundamental Definitions Experimental Determination of "K On the Measurement of the Acoustic Energy Cavitation Efficiency Estimation of T/T Chapter 5 -Analysis of Bubble Oscillations Introductory Considerations The Cavitation Zone in a Plane Wave Cavitation in a Convergent Spherical Wave Acoustic Streaming Induced by the Formation of Cavitation References Index
THEORY OF MOLECULAR EXCITONS
THEORY OF MOLECULAR EXCITONS THEORY OF MOLECULAR EXCITONS A. S. Davydov Kiev State University Kiev, USSR Translated from Russian by Stephen B. Dresner g? SPRINGER SCIENCE+BUSINESS MEDIA, LLC 1971 Aleksandr
More informationRarefied Gas Dynamics
Rarefied Gas Dynamics Rarefied Gas Dynamics Mikhail N. Kogan Computer Center Academy of Sciences of the USSR Moscow Translated from Russian Translation Editor Leon Trilling Department of Aeronautics and
More informationTWILIGHT. Georgii Vladimirovich Rozenberg Deputy Director Institute of Physics of the Atmosphere Academy of Sciences of the USSR
TWILIGHT TWILIGHT A STUDY IN ATMOSPHERIC OPTICS Georgii Vladimirovich Rozenberg Deputy Director Institute of Physics of the Atmosphere Academy of Sciences of the USSR With a Preface by J. V. Dave National
More informationPROGRESS IN MATHEMATICS. Valurne 10. Mathematical Analysis
PROGRESS IN MATHEMATICS Valurne 10 Mathematical Analysis PROGRESS IN MATHEMATICS Translations of Itogi Nauki- Seriya Matematika 1968: Volume 1- Mathematical Analysis Volume 2 - Mathematical Analysis 1969:
More informationNONLINEAR OPTICS NELINEINAYA OPTIKA. HEJH1HEHHAH OnTHKA
NONLINEAR OPTICS NELINEINAYA OPTIKA HEJH1HEHHAH OnTHKA The Lebedev Physics Institute Series Editor: Academician D. V. Skobel'tsyn Director, P. N. Lebedev Physics Institute, Academy of Sciences of the USSR
More informationDIPOLE MOMENTS IN ORGANIC CHEMISTRY
DIPOLE MOMENTS IN ORGANIC CHEMISTRY PHYSICAL METHODS IN ORGANIC CHEMISTRY B. I. lonin and B. A. Ershov NMR Spectroscopy in Organic Chemistry, 1970 V. I. Minkin, O. A. Osipov, and Yu. A. Zhdanov Dipole
More informationELECTRONICS IN EXPERIMENTAL PHYSICS ELEKTRONIKA V FIZICHESKOM EKSPERIMENTE. 8JIEKTPOHMRA B <DM3J:IqECKOM 81\CIIEP.l:IMEHTE
ELECTRONICS IN EXPERIMENTAL PHYSICS ELEKTRONIKA V FIZICHESKOM EKSPERIMENTE 8JIEKTPOHMRA B
More informationMOLECULES AND LIFE. An Introduction to Molecular Biology
MOLECULES AND LIFE An Introduction to Molecular Biology MOLECULES AND LIFE An Introduction to Molecular Biology Mikhail V. Vol'kenshtein Institute of Molecular Biology Academy of Sciences of the USSR,
More informationQUANTUM SCATTERING THEORY FOR SEVERAL PARTICLE SYSTEMS
.: ' :,. QUANTUM SCATTERING THEORY FOR SEVERAL PARTICLE SYSTEMS Mathematical Physics and Applied Mathematics Editors: M. Plato, Universite de Bourgogne, Dijon, France The titles published in this series
More informationTHEORY OF PLASMAS TEORIYA PLAZMY. TEOPMH lljla3mbi
THEORY OF PLASMAS TEORIYA PLAZMY TEOPMH lljla3mbi The Lebedev Physics Institute Series Editors: Academicians D. V. Skobel'tsyn and N. G. Basov P. N. Lebedev Physics Institute, Academy of Sciences of the
More informationAN INTRODUCTION TO HYDRODYNAMICS AND WATER WAVES
AN INTRODUCTION TO HYDRODYNAMICS AND WATER WAVES HYDRODYNAMICA SIVE DE VIRIBUS ET MOTIBUS FLUIDORUM COMMENTARII 'Remember, when discoursing about water, to induce first experience, then reason.' - Leonardo
More informationProbability Theory, Random Processes and Mathematical Statistics
Probability Theory, Random Processes and Mathematical Statistics Mathematics and Its Applications Managing Editor: M.HAZEWINKEL Centre for Mathematics and Computer Science, Amsterdam, The Netherlands Volume
More informationFUNDAMENTALS OF OCEAN ACOUSTICS
FUNDAMENTALS OF OCEAN ACOUSTICS Third Edition L.M. Brekhovskikh Yu.P. Lysanov Moscow, Russia With 120 Figures Springer Contents Preface to the Third Edition Preface to the Second Edition Preface to the
More informationMOLECULES AND LIFE. An Introduction to Molecular Biology
MOLECULES AND LIFE An Introduction to Molecular Biology MOLECULES AND LIFE An Introduction to Molecular Biology Mikhail V. Vol'kenshtein Institute of Molecular Biology Academy of Sciences of the USSR,
More informationLinear Partial Differential Equations for Scientists and Engineers
Tyn Myint-U Lokenath Debnath Linear Partial Differential Equations for Scientists and Engineers Fourth Edition Birkhäuser Boston Basel Berlin Tyn Myint-U 5 Sue Terrace Westport, CT 06880 USA Lokenath Debnath
More informationTECHNIQUES AND METHODS OF RADIO-ASTRONOMIC RECEPTION TEKHNIKA I METODY RADIO-ASTRONOMICHESKOGO PRIEMA
TECHNIQUES AND METHODS OF RADIO-ASTRONOMIC RECEPTION TEKHNIKA I METODY RADIO-ASTRONOMICHESKOGO PRIEMA TEXHIIKA II METO)J,bl PA,IJ,IIO-ACTPOHOlVlIIqECKOrO IIPIIEMA The Lebedev Physics Institute Series Editors:
More informationTHE TRANSURANIUM ELEMENTS
THE TRANSURANIUM ELEMENTS STUDIES IN SOVIET SCIENCE 1973 Motile Muscle and Cell Models N. I. Arronet Densification of Metal Powders during Sintering V. A. Ivensen The Transuranium Elements V. I. Goldanskii
More informationDissipative Ordered Fluids
Dissipative Ordered Fluids Andr é M. Sonnet Epifanio G. Virga Dissipative Ordered Fluids Theories for Liquid Crystals Andr é M. Sonnet Department of Mathematics and Statistics University of Strathclyde
More informationNumerical Methods for the Solution of Ill-Posed Problems
Numerical Methods for the Solution of Ill-Posed Problems Mathematics and Its Applications Managing Editor: M.HAZEWINKEL Centre for Mathematics and Computer Science, Amsterdam, The Netherlands Volume 328
More informationMachine Tool Vibrations and Cutting Dynamics
Machine Tool Vibrations and Cutting Dynamics Brandon C. Gegg l Albert C.J. Luo C. Steve Suh Machine Tool Vibrations and Cutting Dynamics Brandon C. Gegg Dynacon Inc. Winches and Handling Systems 831 Industrial
More informationThe Theory of the Top Volume II
Felix Klein Arnold Sommerfeld The Theory of the Top Volume II Development of the Theory in the Case of the Heavy Symmetric Top Raymond J. Nagem Guido Sandri Translators Preface to Volume I by Michael Eckert
More informationSEMINARS IN MATHEMATICS V. А. STEKLOV МАТНЕМАТIСАL INSTITUTE, LENINGRAD
SEMINARS IN MATHEMATICS V. А. STEKLOV МАТНЕМАТIСАL INSTITUTE, LENINGRAD ZAPISКI NAUCHNYKH SEMINAROV LENINGRADSKOGO OГDELENIY А MATEMATICHESKOGO INSTITUTA lm. V. А. STEKLOVA AN SSSR ЗАПИСКИ НАУЧНЫХ СЕМИНАРОВ
More informationFunctional Integrals: Approximate Evaluation and Applications
Functional Integrals: Approximate Evaluation and Applications Mathematics and Its Applications Managing Editor: M. HAZEWINKEL Centre for Mathematics and Computer Science. Amsterdam. The Netherlands Volume
More informationThermal Plasmas. Fundamentals and Applications. Volume 1
Thermal Plasmas Fundamentals and Applications Volume 1 Thermal Plasmas Fundamentals and Applications Volume 1 Maher I. Boulos University 0/ Sherbrooke Sherbrooke, Quebec, Canada Pierre Fauchais University
More informationPHYSICAL PROCESSES IN SOLAR FLARES
PHYSICAL PROCESSES IN SOLAR FLARES ASTROPHYSICS AND SPACE SCIENCE LIBRARY A SERIES OF BOOKS ON THE RECENT DEVELOPMENTS OF SPACE SCIENCE AND OF GENERAL GEOPHYSICS AND ASTROPHYSICS PUBLISHED IN CONNECTION
More informationAdvanced Calculus of a Single Variable
Advanced Calculus of a Single Variable Tunc Geveci Advanced Calculus of a Single Variable 123 Tunc Geveci Department of Mathematics and Statistics San Diego State University San Diego, CA, USA ISBN 978-3-319-27806-3
More informationELECTRODYNAMICS OF CONTINUOUS MEDIA
ELECTRODYNAMICS OF CONTINUOUS MEDIA by L. D. LANDAU and E. M. LIFSHITZ Institute of Physical Problems, USSR Academy of Sciences Volume 8 of Course of Theoretical Physics Translated from the Russian by
More informationGraduate Texts in Mathematics 51
Graduate Texts in Mathematics 51 Editorial Board F. W. Gehring P. R. Halmos M anaging Editor c. C. Moore Wilhelm Klingenberg ACoursein Differential Geometry Translated by David Hoffman Springer Science+Business
More informationACOUSTIC EFFECTS OCCURRING IN OPTICAL BREAKDOWN WITH A LIQUID BY LASER RADIATION
The 21 st International Congress on Sound and Vibration 13-17 July, 2014, Beijing/China ACOUSTIC EFFECTS OCCURRING IN OPTICAL BREAKDOWN WITH A LIQUID BY LASER RADIATION Bulanov Alexey V.I. Il'ichev Pacific
More informationMETHODS FOR PROTEIN ANALYSIS
METHODS FOR PROTEIN ANALYSIS Robert A. Copeland, PhD The DuPont Merck Pharmaceutical Company Experimental Station P.O. Box 80400 Wilmington, DE 19880-0400 METHODS FOR PROTEIN ANALYSIS A Practical Guide
More informationTHE SOLAR CHROMOSPHERE AND CORONA: QUIET SUN
THE SOLAR CHROMOSPHERE AND CORONA: QUIET SUN ASTROPHYSICS AND SPACE SCIENCE LIBRARY A SERIES OF BOOKS ON THE RECENT DEVELOPMENTS OF SPACE SCIENCE AND OF GENERAL GEOPHYSICS AND ASTROPHYSICS PUBLISHED IN
More informationGeophysical Interpretation using Integral Equations
Geophysical Interpretation using Integral Equations Geophysical Interpretation using Integral Equations L. ESKOLA Head of the Geophysics Department, Geological Survey of Finland 1~lll SPRINGER-SCIENCE+BUSINESS
More informationStability Theorems in Geometry and Analysis
Stability Theorems in Geometry and Analysis Mathematics and Its Applications Managing Editor: M. HAZEWINKEL Centre for Mathematics and Computer Science, Amsterdam, The Netherlands Volume 304 Stability
More informationElectromagnetism PATHS TO RESEARCH
Electromagnetism PATHS TO RESEARCH Electromagnetism PATHS TO RESEARCH Edited by DORIS TEPLITZ SPRINGER SCIENCE+BUSINESS MEDIA, LLC Main entry under title: Library of Congress Cataloging in Publication
More informationCOSSERAT THEORIES: SHELLS, RODS AND POINTS
COSSERAT THEORIES: SHELLS, RODS AND POINTS SOLID MECHANICS AND ITS APPLICATIONS Volume 79 Series Editor: G.M.L. GLADWELL Department of Civil Engineering University of Waterloo Waterloo, Ontario, Canada
More informationNonlinear Parabolic and Elliptic Equations
Nonlinear Parabolic and Elliptic Equations Nonlinear Parabolic and Elliptic Equations c. V. Pao North Carolina State University Raleigh, North Carolina Plenum Press New York and London Library of Congress
More informationIntroduction to physical acoustics
Loughborough University Institutional Repository Introduction to physical acoustics This item was submitted to Loughborough University's Institutional Repository by the/an author. Citation: KRASIL'NIKOV,
More informationIntroduction to Numerical Analysis
J. Stoer R. Bulirsch Introduction to Numerical Analysis Translated by R. Bartels, W. Gautschi, and C. Witzgall Springer Science+Business Media, LLC J. Stoer R. Bulirsch Institut fiir Angewandte Mathematik
More informationThe Physics of Fluids and Plasmas
The Physics of Fluids and Plasmas An Introduction for Astrophysicists ARNAB RAI CHOUDHURI CAMBRIDGE UNIVERSITY PRESS Preface Acknowledgements xiii xvii Introduction 1 1. 3 1.1 Fluids and plasmas in the
More informationTopics in Number Theory
Topics in Number Theory THE UNIVERSITY SERIES IN MATHEMATICS Series Editor: Joseph J. Kohn Princeton University THE CLASSIFICATION OF FINITE SIMPLE GROUPS Daniel Gorenstein VOLUME 1: GROUPS OF NONCHARACTERISTIC
More informationQUANTUM MECHANICS SECOND EDITION G. ARULDHAS
QUANTUM MECHANICS SECOND EDITION G. ARULDHAS Formerly, Professor and Head of Physics and Dean, Faculty of Science University of Kerala New Delhi-110001 2009 QUANTUM MECHANICS, 2nd Ed. G. Aruldhas 2009
More informationATOMIC SPECTROSCOPY: Introduction to the Theory of Hyperfine Structure
ATOMIC SPECTROSCOPY: Introduction to the Theory of Hyperfine Structure ATOMIC SPECTROSCOPY: Introduction to the Theory of Hyperfine Structure ANATOLI ANDREEV M.V. Lomonosov Moscow State University Moscow.
More informationCRYOGENIC LABORATORY EQUIPMENT
CRYOGENIC LABORATORY EQUIPMENT Fig. 3.6. Model 200 ADL-Collins helium liquefier. (Photo: Arth THE INTERNATIONAL CRYOGENICS MONOGRAPH SE RIES General Editors I Dr. K. Mendelssohn, F. R. S. The Clarendon
More informationOSCILLATION THEORY FOR DIFFERENCE AND FUNCTIONAL DIFFERENTIAL EQUATIONS
OSCILLATION THEORY FOR DIFFERENCE AND FUNCTIONAL DIFFERENTIAL EQUATIONS Oscillation Theory for Difference and Functional Differential Equations by Ravi P. Agarwal Department of Mathematics, National University
More informationLatif M. Jiji. Heat Convection. With 206 Figures and 16 Tables
Heat Convection Latif M. Jiji Heat Convection With 206 Figures and 16 Tables Prof. Latif M. Jiji City University of New York School of Engineering Dept. of Mechanical Engineering Convent Avenue at 138th
More informationSpringerBriefs in Mathematics
SpringerBriefs in Mathematics For further volumes: http://www.springer.com/series/10030 George A. Anastassiou Advances on Fractional Inequalities 123 George A. Anastassiou Department of Mathematical Sciences
More informationINTRODUCTION TO SOL-GEL PROCESSING
INTRODUCTION TO SOL-GEL PROCESSING THE KLUWER INTERNATIONAL SERIES in SOL-GEL PROCESSING: TECHNOLOGY AND APPLICATIONS Consulting Editor Lisa Klein Rutgers, the State University of New Jersey INTRODUCTION
More informationNMR SPECTROSCOPY IN ORGANIC CHEMISTRY
NMR SPECTROSCOPY IN ORGANIC CHEMISTRY PHYSICAL METHODS IN ORGANIC CHEMISTRY B. I. lonin and B. A. Ershov NMR Spectroscopy in Organic Chemistry, 1970 v. I. Minkin, O. A. Osipov, and Yu. A. Zhdanov Dipole
More informationChemical Kinetics and Catalysis
Chemical Kinetics and Catalysis FUNDAMENTAL AND APPLIED CATALYSIS Series Editors: M. V. Twigg Johnson Matthey Catalytic Systems Division Royston, Hertfordshire, United Kingdom M. S. Spencer School of Chemistry
More informationContents. I Introduction 1. Preface. xiii
Contents Preface xiii I Introduction 1 1 Continuous matter 3 1.1 Molecules................................ 4 1.2 The continuum approximation.................... 6 1.3 Newtonian mechanics.........................
More informationNumerical Approximation Methods for Elliptic Boundary Value Problems
Numerical Approximation Methods for Elliptic Boundary Value Problems Olaf Steinbach Numerical Approximation Methods for Elliptic Boundary Value Problems Finite and Boundary Elements Olaf Steinbach Institute
More informationDifferential criterion of a bubble collapse in viscous liquids
PHYSICAL REVIEW E VOLUME 60, NUMBER 1 JULY 1999 Differential criterion of a bubble collapse in viscous liquids Vladislav A. Bogoyavlenskiy* Low Temperature Physics Department, Moscow State University,
More informationPublication of the Museum of Nature South Tyrol Nr. 11
Publication of the Museum of Nature South Tyrol Nr. 11 ThiS is a FM Blank Page Erika Pignatti Sandro Pignatti Plant Life of the Dolomites Vegetation Tables Erika Pignatti Sandro Pignatti Rome Italy Publication
More informationMiao Boya and An Yu Department of Physics, Tsinghua University, Beijing , People s Republic of China
Localization in an acoustic cavitation cloud Miao Boya and An Yu Department of Physics, Tsinghua University, Beijing 100084, People s Republic of China Using a nonlinear sound wave equation for a bubbly
More informationTyn Myint-U Lokenath Debnath. Linear Partial Differential Equations for Scientists and Engineers. Fourth Edition. Birkhauser Boston Basel Berlin
Tyn Myint-U Lokenath Debnath Linear Partial Differential Equations for Scientists and Engineers Fourth Edition Birkhauser Boston Basel Berlin Preface to the Fourth Edition Preface to the Third Edition
More informationEgon Krause. Fluid Mechanics
Egon Krause Fluid Mechanics Egon Krause Fluid Mechanics With Problems and Solutions, and an Aerodynamic Laboratory With 607 Figures Prof. Dr. Egon Krause RWTH Aachen Aerodynamisches Institut Wüllnerstr.5-7
More informationGraduate Texts in Mathematics 22
Graduate Texts in Mathematics 22 Managing Editors: P. R. Halmos C. C. Moore Donald W. Barnes lohn M. Mack An Aigebraic Introduction to Mathematical Logic Springer Science+Business Media, LLC Donald W.
More informationData Analysis Using the Method of Least Squares
Data Analysis Using the Method of Least Squares J. Wolberg Data Analysis Using the Method of Least Squares Extracting the Most Information from Experiments With Figures and Tables 123 John Wolberg Technion-Israel
More informationElectrochemical Process Engineering. A Guide to the Design of Electrolytic Plant
Electrochemical Process Engineering A Guide to the Design of Electrolytic Plant Electrochemical Process Engineering A Guide to the Design of Electrolytic Plant F. Goodridge and K. Scott University of Newcastle
More informationUndergraduate Texts in Mathematics. Editors J. H. Ewing F. W. Gehring P. R. Halmos
Undergraduate Texts in Mathematics Editors J. H. Ewing F. W. Gehring P. R. Halmos Springer Books on Elemeritary Mathematics by Serge Lang MATH! Encounters with High School Students 1985, ISBN 96129-1 The
More informationAPPLIED PARTIM DIFFERENTIAL EQUATIONS with Fourier Series and Boundary Value Problems
APPLIED PARTIM DIFFERENTIAL EQUATIONS with Fourier Series and Boundary Value Problems Fourth Edition Richard Haberman Department of Mathematics Southern Methodist University PEARSON Prentice Hall PEARSON
More informationResearch Techniques for High Pressure and High Temperature
Research Techniques for High Pressure and High Temperature Research Techniques for High Pressure and High Temperature Edited by Gene C. Ulmer Springer-Verlag New York Heidelberg Berlin 1971 All rights
More informationIgor Emri Arkady Voloshin. Statics. Learning from Engineering Examples
Statics Igor Emri Arkady Voloshin Statics Learning from Engineering Examples Igor Emri University of Ljubljana Ljubljana, Slovenia Arkady Voloshin Lehigh University Bethlehem, PA, USA ISBN 978-1-4939-2100-3
More informationReliability Evaluation of Engineering Systems:
Reliability Evaluation of Engineering Systems: Concepts and Techniques Roy Billinton PhD, DSc, FEIC, FRSC, FIEEE, PE c. J. MacKenzie Professor of Electrical Engineering University of Saskatchewan and Ronald
More informationNON-EQUILIBRIUM THERMODYNAMICS
NON-EQUILIBRIUM THERMODYNAMICS S. R. DE GROOT Professor of Theoretical Physics University of Amsterdam, The Netherlands E MAZUR Professor of Theoretical Physics University of Leiden, The Netherlands DOVER
More informationExercises in Basic Ring Theory
Exercises in Basic Ring Theory Kluwer Texts in the Mathematical Sciences VOLUME 20 A Graduate-Level Book Series The titles published in this series are listed at the end of this volume. Exercises in Basic
More informationPHASE PORTRAITS OF PLANAR QUADRATIC SYSTEMS
PHASE PORTRAITS OF PLANAR QUADRATIC SYSTEMS Mathematics and Its Applications Managing Editor: M. HAZEWINKEL Centre for Mathematics and Computer Science, Amsterdam, The Netherlands Volume 583 PHASE PORTRAITS
More informationAdvanced Engineering. Dynamics. H. R. Harrison. T. Nettleton. Formerly Department of Mechanical Engineering & Aeronautics City University London
Advanced Engineering Dynamics H. R. Harrison Formerly Department of Mechanical Engineering & Aeronautics City University London T. Nettleton Formerly Department of Mechanical Engineering & Aeronautics
More informationMETHODS IN THE QUANTUM THEORY OF MAGNETISM
METHODS IN THE QUANTUM THEORY OF MAGNETISM METHODS IN THE QUANTUM THEORY OF MAGNETISM Sergei Vladimirovich Tyablikov Chairman, Department of Statistical Mechanics V. A. Steklov Mathematical Institute Academy
More informationPhysics for Scientists & Engineers with Modern Physics Douglas C. Giancoli Fourth Edition
Physics for Scientists & Engineers with Modern Physics Douglas C. Giancoli Fourth Edition Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the
More information1000 Solved Problems in Classical Physics
1000 Solved Problems in Classical Physics Ahmad A. Kamal 1000 Solved Problems in Classical Physics An Exercise Book 123 Dr. Ahmad A. Kamal Silversprings Lane 425 75094 Murphy Texas USA anwarakamal@yahoo.com
More informationComputational Techniques for the Summation of Series
Computational Techniques for the Summation of Series Computational Techniques for the Summation of Series Anthony Sofa School of Computer Science and Mathematics Victoria University Melboume, Australia
More informationA Macmillan Physics Text
WAVES A Macmillan Physics Text Consulting Editor: Professor P. A. Matthews, F.R.S. Other titles MODERN ATOMIC PHYSICS: FUNDAMENTAL PRINCIPLES: B. Cagnacand J. -C. Pebay-Peyroula MODERN ATOMIC PHYSICS:
More informationNonlinear Dynamical Systems in Engineering
Nonlinear Dynamical Systems in Engineering . Vasile Marinca Nicolae Herisanu Nonlinear Dynamical Systems in Engineering Some Approximate Approaches Vasile Marinca Politehnica University of Timisoara Department
More informationWaves of Acoustically Induced Transparency in Bubbly Liquids: Theoretical Prediction and Experimental Validation
Waves of Acoustically Induced Transparency in Bubbly Liquids: Theoretical Prediction and Experimental Validation Nail A. Gumerov University of Maryland, USA Iskander S. Akhatov North Dakota State University,
More informationDoubt-Free Uncertainty In Measurement
Doubt-Free Uncertainty In Measurement Colin Ratcliffe Bridget Ratcliffe Doubt-Free Uncertainty In Measurement An Introduction for Engineers and Students Colin Ratcliffe United States Naval Academy Annapolis
More informationKazumi Tanuma. Stroh Formalism and Rayleigh Waves
Kazumi Tanuma Stroh Formalism and Rayleigh Waves Previously published in the Journal of Elasticity Volume 89, Issues 1Y3, 2007 Kazumi Tanuma Department of Mathematics Graduate School of Engineering Gunma
More informationSemiconductor Physical Electronics
Semiconductor Physical Electronics Sheng S. Li Semiconductor Physical Electronics Second Edition With 230 Figures Sheng S. Li Department of Electrical and Computer Engineering University of Florida Gainesville,
More informationUniversitext. Series Editors:
Universitext Universitext Series Editors: Sheldon Axler San Francisco State University, San Francisco, CA, USA Vincenzo Capasso Università degli Studi di Milano, Milan, Italy Carles Casacuberta Universitat
More informationProgress in Mathematical Physics
Progress in Mathematical Physics Volume 24 Editors-in-Chiej Anne Boutet de Monvel, Universite Paris VII Denis Diderot Gerald Kaiser, The Virginia Center for Signals and Waves Editorial Board D. Bao, University
More informationMechanisms of Interaction between Ultrasound and Sound in Liquids with Bubbles: Singular Focusing
Acoustical Physics, Vol. 47, No., 1, pp. 14 144. Translated from Akusticheskiœ Zhurnal, Vol. 47, No., 1, pp. 178 18. Original Russian Text Copyright 1 by Akhatov, Khismatullin. REVIEWS Mechanisms of Interaction
More informationResonant solitons in a polydisperse bubble medium
Journal of Physics: Conference Series PAPER OPEN ACCESS Resonant solitons in a polydisperse bubble medium To cite this article: I A Ogorodnikov 018 J. Phys.: Conf. Ser. 1105 01088 View the article online
More informationBoundary. DIFFERENTIAL EQUATIONS with Fourier Series and. Value Problems APPLIED PARTIAL. Fifth Edition. Richard Haberman PEARSON
APPLIED PARTIAL DIFFERENTIAL EQUATIONS with Fourier Series and Boundary Value Problems Fifth Edition Richard Haberman Southern Methodist University PEARSON Boston Columbus Indianapolis New York San Francisco
More informationCircuit Analysis for Power Engineering Handbook
Circuit Analysis for Power Engineering Handbook Circuit Analysis for Power Engineering Handbook Arieh L. Shenkman SPRINGER SCIENCE+BUSINESS MEDIA, B.V A c.i.p. Catalogue record for this book is available
More informationWith Modern Physics For Scientists and Engineers
With Modern Physics For Scientists and Engineers Third Edition Richard Wolfson Middlebury College Jay M. Pasachoff Williams College ^ADDISON-WESLEY An imprint of Addison Wesley Longman, Inc. Reading, Massachusetts
More informationLight and Vacuum Downloaded from by on 11/22/17. For personal use only.
This page intentionally left blank World Scientific Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ
More informationNumerical Data Fitting in Dynamical Systems
Numerical Data Fitting in Dynamical Systems Applied Optimization Volume 77 Series Editors: Panos M. Pardalos University of Florida, U.S.A. Donald Hearn University of Florida, U.S.A. The titles published
More informationTile-Based Geospatial Information Systems
Tile-Based Geospatial Information Systems John T. Sample Elias Ioup Tile-Based Geospatial Information Systems Principles and Practices 123 John T. Sample Naval Research Laboratory 1005 Balch Blvd. Stennis
More informationFOUNDATION SCIENCE FOR ENGINEERS
FOUNDATION SCIENCE FOR ENGINEERS Other titles of interest to engineers Dynamics G.E. Drabble Electric Circuits P. Silvester Electromagnetism R.G. Powell Engineering Mathematics, fourth edition K.A. Stroud
More informationCERN LIBRARIES, GENEVA
JOINT INSTITUTE FOR NUCLEAR RESEARCH, DUBNA Report P13-6513 CERN LIBRARIES, GENEVA CM-P00100726 STUDY OF TRACK FORMATION OF IONIZING PARTICLES IN AN ULTRASONIC FIELD IN A LIQUID HYDROGEN BUBBLE CHAMBER
More informationION EXCHANGE TRAINING MANUAL
ION EXCHANGE TRAINING MANUAL GEORGE P. SIMON ~ SPRINGER SCIENCE+BUSINESS MEDIA, LLC Copyright 1991 by Springer Science+ Business Media New York Originally published by Van Nostrand Reinhold in 1991 Library
More informationThis content has been downloaded from IOPscience. Please scroll down to see the full text.
This content has been downloaded from IOPscience. Please scroll down to see the full text. Download details: IP Address: 46.3.203.124 This content was downloaded on 30/12/2017 at 22:16 Please note that
More informationVARIATIONS INTRODUCTION TO THE CALCULUS OF. 3rd Edition. Introduction to the Calculus of Variations Downloaded from
INTRODUCTION TO THE CALCULUS OF VARIATIONS 3rd Edition This page intentionally left blank INTRODUCTION TO THE CALCULUS OF VARIATIONS 3rd Edition Bernard Dacorogna Ecole Polytechnique Fédérale Lausanne,
More informationPractical Statistics for Geographers and Earth Scientists
Practical Statistics for Geographers and Earth Scientists Nigel Walford A John Wiley & Sons, Ltd., Publication Practical Statistics for Geographers and Earth Scientists Practical Statistics for Geographers
More informationChristian Okonek Michael Schneider Heinz SRindler. ector undies on omplex. rojective S aces
Christian Okonek Michael Schneider Heinz SRindler ector undies on omplex rojective S aces Progress in Mathe~natics Vol. 1: H. Gross, Quadratic Forms in Infinite-Dimensional Vector Spaces. XXII, 4!9 pages,!979
More informationQUANTUM MECHANICS OF ONE- AND TWO-ELECTRON ATOMS
QUANTUM MECHANICS OF ONE- AND TWO-ELECTRON ATOMS QUANTUM MECHANICS OF ONE- AND TWO-ELECTRON ATOMS HANS A. BETHE AND EDWIN E. SALPETER Cornell University Ithaca, New York A PLENUM/ROSETTA EDITION Library
More informationFRACTIONAL CALCULUS IN PHYSICS
APPLICATIONS OF FRACTIONAL CALCULUS IN PHYSICS APPLICATIONS OF FRACTIONAL CALCULUS IN PHYSICS Editor Universitat Mainz and Universitat Stuttgart Germany Vfe World Scientific «Singapore New Jersey London
More informationTHE BOUNDARY ELEMENT METHOD
THE BOUNDARY ELEMENT METHOD SOLID MECHANICS AND ITS APPLICATIONS Volume 27 Series Editor: G.M.L. GLADWELL Solid Mechanics Division, Faculty of Engineering University of Waterloo Waterloo, Ontario, Canada
More informationMathematics for Economics
Mathematics for Economics third edition Michael Hoy John Livernois Chris McKenna Ray Rees Thanasis Stengos The MIT Press Cambridge, Massachusetts London, England c 2011 Massachusetts Institute of Technology
More informationTRANSPORT PHENOMENA AND UNIT OPERATIONS
TRANSPORT PHENOMENA AND UNIT OPERATIONS TRANSPORT PHENOMENA AND UNIT OPERATIONS A COMBINED APPROACH Richard G. Griskey A JOHN WILEY & SONS, INC., PUBLICATION This book is printed on acid-free paper Copyright
More information