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Books > Science & Mathematics > Physics > Atomic & molecular physics

Introduction to Atomic Physics (Hardcover): Harley Reynolds Introduction to Atomic Physics (Hardcover)
Harley Reynolds
R3,074 R2,787 Discovery Miles 27 870 Save R287 (9%) Ships in 18 - 22 working days
Interference of Atomic States (Paperback, Softcover reprint of the original 1st ed. 1993): Evgeny B. Alexandrov, Maria P.... Interference of Atomic States (Paperback, Softcover reprint of the original 1st ed. 1993)
Evgeny B. Alexandrov, Maria P. Chaika, Gennadij I. Khvostenko
R1,399 Discovery Miles 13 990 Ships in 18 - 22 working days

In this monograph we describe an important and relatively new class of phenomena in the field of high-resolution atomic spectroscopy: the interference effects manifest in the angular distribution and polarization of spontaneous radiation and absorption by atoms. Although the quantum-theoretical descrip tion of these interference effects is quite subtle, it turns out - as so often in quantum mechanics - that a simple classical or semi-classical description offers much insight and can even explain quantitative features. In this presentation, however, we attempt to give the full story. Beginning with the simple semi classical description, we then present the quantum-mechanical analysis based on the density-matrix formalism and the statistical tensor. The remaining two chapters discuss experimental observations and data analysis. A great variety of effects have now been observed and can be used to obtain highly accu rate information about hyperfine structure, atomic constants, interaction con stants, etc. The authors have assumed only a basic knowledge of quantum mechanics and electromagnetism, thus making the book accessible to those beginning a graduate studies program. It is also aimed at practising spectroscopists and all researchers for whom atomic spectroscopy is an important tool - for these readers it will hopefully offer some new solutions and ideas for furthering their research. February 1993 E. B. Alexandrov M. P. Chaika G. I. Khvostenko Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2. Classical Description of Interference Phenomena in Radiation 2. 1 The Classical Oscillator Model of Atomic Emission . ."

Multiphoton Processes in Atoms (Hardcover, 2nd Revised edition): Nikolai B. Delone, Vladmir P. Krainov Multiphoton Processes in Atoms (Hardcover, 2nd Revised edition)
Nikolai B. Delone, Vladmir P. Krainov
R2,416 Discovery Miles 24 160 Ships in 18 - 22 working days

Multiphoton processes in atoms in intense laser-light fields is gaining ground as a spectroscopic diagnostic tool. This text presents descriptions of processes occurring in atoms under the action of strong electromagnetic radiation, in particular, the shift, broadening and mixing of atomic states. The topics covered include tunnelling ionization, above-threshold ionization, ionization of multiply charged ions, resonance-enhanced ionization, super-intense radiation fields, and properties of Rydberg states strongly perturbed by laser radiation.

The Elementary Structure of Matter - Proceedings of the Workshop, Les Houches, France, March 24-April 2, 1987 (Paperback,... The Elementary Structure of Matter - Proceedings of the Workshop, Les Houches, France, March 24-April 2, 1987 (Paperback, Softcover reprint of the original 1st ed. 1988)
Jean-Marc Richard, Elie Aslanides, Nino Boccara
R2,721 Discovery Miles 27 210 Ships in 18 - 22 working days

This book is the proceedings of a workshop on problems at the interface between elementary particle and nuclear physics. It deals with experimental and theoretical developments in the investigation of hadrons and nuclei and in the study of their interactions at low and high energies, including nonperturbative quantum chromodynamics, quark confinement, hadron spectroscopy, hadronic interactions, strange particles, hypernuclei, structure functions of nucleons and nuclei, antiproton annihilation on nucleons and nuclei, quark-gluon plasmas and heavy-ion collisions. Plans for new accelerators are evaluated and some related topics in astrophysics, such as supernovae and neutrinos, are discussed.

Electron-Atom Collisions - Quantum-Relativistic Theory and Exercises (Paperback): Maurizio Dapor Electron-Atom Collisions - Quantum-Relativistic Theory and Exercises (Paperback)
Maurizio Dapor
R2,133 R1,695 Discovery Miles 16 950 Save R438 (21%) Ships in 18 - 22 working days

Electron collisions with atoms, ions, and molecules have been investigated since the earliest years of the last century because of their pervasiveness and importance in fields ranging from astrophysics and plasma physics to atmospheric and condensed matter physics. Written in an accessible yet rigorous style, this book introduces the theory of electron-atom scattering into both the non-relativistic and relativistic quantum frameworks. The book also includes exercises with an increasing degree of difficulty to allow the reader to become familiar with the subject.

Neutronics of Advanced Nuclear Systems (Hardcover, 1st ed. 2019): Yican Wu Neutronics of Advanced Nuclear Systems (Hardcover, 1st ed. 2019)
Yican Wu
R4,322 Discovery Miles 43 220 Ships in 18 - 22 working days

This book provides a systematic and comprehensive introduction to the neutronics of advanced nuclear systems, covering all key aspects, from the fundamental theories and methodologies to a wide range of advanced nuclear system designs and experiments. It is the first-ever book focusing on the neutronics of advanced nuclear systems in the world. Compared with traditional nuclear systems, advanced nuclear systems are characterized by more complex geometry and nuclear physics, and pose new challenges in terms of neutronics. Based on the achievements and experiences of the author and his team over the past few decades, the book focuses on the neutronics characteristics of advanced nuclear systems and introduces novel neutron transport methodologies for complex systems, high-fidelity calculation software for nuclear design and safety evaluation, and high-intensity neutron source and technologies for neutronics experiments. At the same time, it describes the development of various neutronics designs for advanced nuclear systems, including neutronics design for ITER, CLEAR and FDS series reactors. The book not only summarizes the progress and achievements of the author's research work, but also highlights the latest advances and investigates the forefront of the field and the road ahead.

Proton Transfer in Hydrogen-bonded Systems - Proceedings of a NATO ARW Held in Crete, Greece, May 21-25, 1991 (Hardcover, New):... Proton Transfer in Hydrogen-bonded Systems - Proceedings of a NATO ARW Held in Crete, Greece, May 21-25, 1991 (Hardcover, New)
T. Bountis
R2,466 Discovery Miles 24 660 Ships in 10 - 15 working days

Introduction: From Fluid Particles to Physical Particles; M. Mareschal, B.L. Holian. Non-Equilibrium Molecular Dynamics: Theoretical Foundation and Rheological Application of NonEquilibrium Molecular Dynamics; G. Ciccotti, et al. Lattice Gases: Lattice Boltzmann Simulation of High Reynolds Number Fluid Flow in Two Dimensions; G. McNamara, B.J. Alder. Other Simulation Methods: A Contemporary Implementation of the Direct Simulation Monte Carlo Method; G.A. Bird. Chaos, Turbulence, and Irreversibility: Lyapunov Exponents and Bulk Transport Coefficients; D. Evans, et al. Related Topics: Statistical Fracture Mechanics; A. Chudnovsky, B. Kunin. Recollections: The Long Time Tail Story; B.J. Adler. 22 additional articles. Index.

X-Ray Structure Analysis (Paperback): Theo Siegrist X-Ray Structure Analysis (Paperback)
Theo Siegrist
R1,646 R1,333 Discovery Miles 13 330 Save R313 (19%) Ships in 18 - 22 working days

This book offers a compact overview on crystallography, symmetry, and applications of symmetry concepts. The author explains the theory behind scattering and diffraction of electromagnetic radiation. X-ray diffraction on single crystals as well as quantitative evaluation of powder patterns are discussed.

Intelligent Materials and Structures (Paperback, 2nd Edition): Haim Abramovich Intelligent Materials and Structures (Paperback, 2nd Edition)
Haim Abramovich
R2,381 R1,903 Discovery Miles 19 030 Save R478 (20%) Ships in 18 - 22 working days

This new edition of our 2016 book provides insight into designing intelligent materials and structures for special application in engineering. Literature is updated throughout and a new chapter on optics fibers has been added. The book discusses simulation and experimental determination of physical material properties, such as piezoelectric effects, shape memory, electro-rheology, and distributed control for vibrations minimization.

Bioinorganic Chemistry - Some New Facets (Paperback): Ram Charitra Maurya Bioinorganic Chemistry - Some New Facets (Paperback)
Ram Charitra Maurya
R2,076 R1,668 Discovery Miles 16 680 Save R408 (20%) Ships in 18 - 22 working days

The book includes several topics as per Universities curriculum of M.Sc. and M.Phil. course work in Chemistry. This covers different Physiological aspects of Bioinorganic Chemistry in terms of 4 Chapters with in-depth and up-to-date coverage. The book symmetrically presents (i) Coordination chemistry of chlorophylls/bacteriochlophylls and its functional aspects in photosynthesis, (ii) Complexes containing nitric oxide: Synthesis, reactivity, structure, bonding, and therapeutic aspects of nitric oxide releasing molecules (NORMS) in human beings and plants, (iv) Complexes containing carbon monoxide: Synthesis, reactivity, structure, bonding, and therapeutic aspects of carbon monoxide releasing molecules (CORMS) in human beings and plants, and (iv) Advantageous role of gaseous signaling molecule, H2S: Hydrogen sulphide and their respective donors, in ophthalmic diseases and physiological implications in plants. At the end, three relevant topics are included as appendices for updating students and faculty members.

Intermolecular and Surface Forces (Hardcover, 3rd edition): Jacob N. Israelachvili Intermolecular and Surface Forces (Hardcover, 3rd edition)
Jacob N. Israelachvili
R2,718 R2,506 Discovery Miles 25 060 Save R212 (8%) Ships in 10 - 15 working days

This reference describes the role of various intermolecular and interparticle forces in determining the properties of simple systems such as gases, liquids and solids, with a special focus on more complex colloidal, polymeric and biological systems. The book provides a thorough foundation in theories and concepts of intermolecular forces, allowing researchers and students to recognize which forces are important in any particular system, as well as how to control these forces. This third edition is expanded into three sections and contains five new chapters over the previous edition.
. starts from the basics and builds up to more complex systems
. covers all aspects of intermolecular and interparticle forces both at the fundamental and applied levels
. multidisciplinary approach: bringing together and unifying phenomena from different fields
. This new edition has an expanded Part III and new chapters on non-equilibrium (dynamic) interactions, and tribology (friction forces)"

Crystallography in Materials Science - From Structure-Property Relationships to Engineering (Paperback): Susan Schorr, Claudia... Crystallography in Materials Science - From Structure-Property Relationships to Engineering (Paperback)
Susan Schorr, Claudia Weidenthaler
R2,207 R1,763 Discovery Miles 17 630 Save R444 (20%) Ships in 18 - 22 working days

The knowledge about crystal structure and its correlation with physical properties is the prerequisite for designing new materials with taylored properties. This work provides for researchers and graduates a valuable resource on various techniques for crystal structure determinations. By discussing a broad range of different materials and tools the authors enable the understanding of why a material might be suitable for a particular application.

Physics of Massive Neutrinos (Hardcover, 2nd Revised edition): Felix Boehm, Petr Vogel Physics of Massive Neutrinos (Hardcover, 2nd Revised edition)
Felix Boehm, Petr Vogel
R3,547 Discovery Miles 35 470 Ships in 10 - 15 working days

Neutrinos play a decisive part in nuclear and elementary particle physics, as well as in astrophysics and cosmology. Because they interact so weakly with matter, some of their basic properties, such as mass charge conjugation symmetry, are largely unknown. These subjects are considered in detail by authors, who also discuss such topics as neutrino mixing, neutrino decay, neutrino oscillations, double beta decay and related ideas. Physical concepts are stressed, and both theoretical methods and experimental techniques are presented. This second edition contains an expanded coverage of new experimental results and recent theoretical advances. In the intervening years since the first edition, many then unresolved problems such as tritium beta decay and reactor neutrino oscillations have been clarified. This edition also gives expanded coverage of solar and supernova neutrinos.

High-Energy Physics and Cosmology - Celebrating the Impact of 25 Years of Coral Gables Conferences - Proceedings of the... High-Energy Physics and Cosmology - Celebrating the Impact of 25 Years of Coral Gables Conferences - Proceedings of the International Conference on Orbis Scientiate 1997 Held in Miami Beach, Florida, January 23-26, 1997 (Hardcover, New)
Kursunoglu Behram, Etc
R2,423 Discovery Miles 24 230 Ships in 18 - 22 working days

Launching of the Coral Gables Conferences on High Energy Physics and Cosmology: The Launching of the Coral Gables Conferences on High Energy Physics and Cosmology and the Establishment of the Center for Theoretical Studies at the University of Miami; B.N. Kursunoglu. Neutrino Physics: Neutrino Oscillations at Accelerators; F. Vannucci. KARMEN: Present Neutrino Oscillation Limits and Perspectives after the Upgrade; G. Drexlin. Progress on New and Old Ideas: Exotic Hadrons; D.B. Lichtenberg. Orthogonal Mixing and CP Violation; P.H. Frampton. Round Trip Between Cosmology and Elementary Particles: Physics of Mass; B.N. Kursunoglu. Progress and Prospects in the Direct Search for Supersymmetric and Dark Matter Particles; D.B. Cline. Gauge Symmetries, Gravity and Srings: Gauge Symmetry in Fivebrane Conformal Field Theory; L. Dolan. Exact Local Supersymmetry Absence of Superpartners and Noncommutative; F. Mansouri. Light Cone Quantization: Adjoint QCD2 in Large N; S. Pinsky. Nonperturbative Renormalization in Light-Cone Quantization; J.R.Hiller. Current Experiments in High Energy Physics: Search for New Particles with DELPHI at LEP2; W. Adam. W Physics Results from DELPHI; H.T. Phillips. 8 Additional Articles. Index.

Principles of Atomic Physics (Hardcover): Titus Mason Principles of Atomic Physics (Hardcover)
Titus Mason
R3,044 R2,759 Discovery Miles 27 590 Save R285 (9%) Ships in 18 - 22 working days
Enrico Fermi - His Work And Legacy (Hardcover, 2004 ed.): Carlo Bernardini, Luisa Bonolis Enrico Fermi - His Work And Legacy (Hardcover, 2004 ed.)
Carlo Bernardini, Luisa Bonolis
R2,737 Discovery Miles 27 370 Ships in 18 - 22 working days

Enrico Fermia (TM)s scientific work, noted for its originality and breadth, has had lasting consequences throughout modern science. Written by close colleagues as well as scientists whose fields were profoundly influenced by Fermi, the papers collected here constitute a tribute to him and his scientific legacy. They were commissioned on the occasion of his 100th birthday by the Italian Physical Society and confirm that Fermi was a rare combination of theorist, experimentalist, teacher, and inspiring colleague. The book is organized into three parts: three biographical overviews by close colleagues, replete with personal insights; fourteen analyses of Fermi's impact by specialists in their fields, spanning physics, chemistry, mathematics, and engineering; and a year-by-year chronology of Fermia (TM)s scientific endeavors. Written for a general scientific audience, Enrico Fermi: His Work and Legacy offers a highly readable source on the life of one of the 20th century's most distinguished scientists and a must for everybody interested in the history of modern science.

Particle Production in Highly Excited Matter - Proceedings of a NATO ASI Held in Il Ciocco, Tuscany, Italy, July 12-24, 1992... Particle Production in Highly Excited Matter - Proceedings of a NATO ASI Held in Il Ciocco, Tuscany, Italy, July 12-24, 1992 (Hardcover, New)
Hans H. Gutbrod, Johann Rafelski
R2,507 Discovery Miles 25 070 Ships in 10 - 15 working days

Overview: Big Bang in the Laboratory; H.H. Gutbrod, J. Rafelski. Physics of Relativistic Nuclear Collisions; I. Otterlund. Towards the LHC; P. Giubellino. Hot Hadronic Matter: Fireball Spectra; U. Heinz, et al. Quark Matter in Equilibrium; F. Karsch. Towards Dynamical Theoretical Description: Cascade Models and Particle Production; J. Cugnon. Relativistic Hydrodynamics and Flavor Flow; L. Csernai, et al. Quark-Gluon Plasma Formation in UltraRelativistic Heavy Ion Collisions; K. Geiger. Diagnostic Methods and Recent Results: A Pedestrian's Guide to Particle Interferometry; W.A. Zajc. Strangeness in Ultrarelativistic NucleusNucleus Collisions; E. Quercigh. On the Trail of Quark-Gluon Plasma; J. Rafelski. Epilogue: The Quark-Gluon Plasma; P.A. Carruthers. 20 additional articles. Index.

Time: From Earth Rotation to Atomic Physics (Hardcover, 2nd Revised edition): Dennis D. McCarthy, P.Kenneth Seidelmann Time: From Earth Rotation to Atomic Physics (Hardcover, 2nd Revised edition)
Dennis D. McCarthy, P.Kenneth Seidelmann
R2,230 Discovery Miles 22 300 Ships in 10 - 15 working days

In the twenty-first century, we take the means to measure time for granted, without contemplating the sophisticated concepts on which our time scales are based. This volume presents the evolution of concepts of time and methods of time keeping up to the present day. It outlines the progression of time based on sundials, water clocks, and the Earth's rotation, to time measurement using pendulum clocks, quartz crystal clocks, and atomic frequency standards. Time scales created as a result of these improvements in technology and the development of general and special relativity are explained. This second edition has been updated throughout to describe twentieth- and twenty-first-century advances and discusses the redefinition of SI units and the future of UTC. A new chapter on time and cosmology has been added. This broad-ranging reference benefits a diverse readership, including historians, scientists, engineers, educators, and it is accessible to general readers.

Fundamentals of van der Waals and Casimir Interactions (Hardcover, 1st ed. 2018): Bo E. Sernelius Fundamentals of van der Waals and Casimir Interactions (Hardcover, 1st ed. 2018)
Bo E. Sernelius
R3,573 R3,022 Discovery Miles 30 220 Save R551 (15%) Ships in 10 - 15 working days

This book presents a self-contained derivation of van der Waals and Casimir type dispersion forces, covering the interactions between two atoms but also between microscopic, mesoscopic, and macroscopic objects of various shapes and materials. It also presents detailed and general prescriptions for finding the normal modes and the interactions in layered systems of planar, spherical and cylindrical types, with two-dimensional sheets, such as graphene incorporated in the formalism. A detailed derivation of the van der Waals force and Casimir-Polder force between two polarizable atoms serves as the starting point for the discussion of forces: Dispersion forces, of van der Waals and Casimir type, act on bodies of all size, from atoms up to macroscopic objects. The smaller the object the more these forces dominate and as a result they play a key role in modern nanotechnology through effects such as stiction. They show up in almost all fields of science, including physics, chemistry, biology, medicine, and even cosmology. Written by a condensed matter physicist in the language of condensed matter physics, the book shows readers how to obtain the electromagnetic normal modes, which for metallic systems, is especially useful in the field of plasmonics.

Joint Polish-German Crystallographic Meeting, February 24-27, 2020, Wroclaw, Poland (Paperback): German Crystallographic... Joint Polish-German Crystallographic Meeting, February 24-27, 2020, Wroclaw, Poland (Paperback)
German Crystallographic Society, Polish Crystallographic Association
R5,328 Discovery Miles 53 280 Ships in 18 - 22 working days

Zeitschrift fur Kristallographie. Supplement Volume 40 presents the complete Abstracts of all contributions to the Joint Polish-German Crystallographic Meeting in Wroclaw (Poland) 2020: - Plenary Talks - Microsymposia - Poster Session Supplement Series of Zeitschrift fur Kristallographie publishes Abstracts of international conferences on the interdisciplinary field of crystallography.

Aspetti e Scambi della Materia o Energia - manoscritto inedito, trascrizione, introduzione e note di Claudio Cardella (Italian,... Aspetti e Scambi della Materia o Energia - manoscritto inedito, trascrizione, introduzione e note di Claudio Cardella (Italian, Hardcover)
Francesco Pannaria
R1,265 Discovery Miles 12 650 Ships in 18 - 22 working days
Plasma Atomic Physics (Hardcover, 1st ed. 2021): Frank B. Rosmej, Valery A. Astapenko, Valery S. Lisitsa Plasma Atomic Physics (Hardcover, 1st ed. 2021)
Frank B. Rosmej, Valery A. Astapenko, Valery S. Lisitsa
R4,358 Discovery Miles 43 580 Ships in 10 - 15 working days

Plasma Atomic Physics provides an overview of the elementary processes within atoms and ions in plasmas, and introduces readers to the language of atomic spectra and light emission, allowing them to explore the various and fascinating radiative properties of matter. The book familiarizes readers with the complex quantum-mechanical descriptions of electromagnetic and collisional processes, while also developing a number of effective qualitative models that will allow them to obtain adequately comprehensive descriptions of collisional-radiative processes in dense plasmas, dielectronic satellite emissions and autoionizing states, hollow ion X-ray emissions, polarized atoms and ions, hot electrons, charge exchange, atomic population kinetics, and radiation transport. Numerous applications to plasma spectroscopy and experimental data are presented, which concern magnetic confinement fusion, inertial fusion, laser-produced plasmas, and X-ray free-electron lasers' interaction with matter. Particular highlights include the development of quantum kinetics to a level surpassing the almost exclusively used quasi-classical approach in atomic population kinetics, the introduction of the recently developed Quantum-F-Matrix-Theory (QFMT) to study the impact of plasma microfields on atomic populations, and the Enrico Fermi equivalent photon method to develop the "Plasma Atom", where the response properties and oscillator strength distribution are represented with the help of a local plasma frequency of the atomic electron density. Based on courses held by the authors, this material will assist students and scientists studying the complex processes within atoms and ions in different kinds of plasmas by developing relatively simple but highly effective models. Considerable attention is paid to a number of qualitative models that deliver physical transparency, while extensive tables and formulas promote the practical and useful application of complex theories and provide effective tools for non-specialist readers.

An Introduction to the Atomic and Radiation Physics of Plasmas (Hardcover): G.J. Tallents An Introduction to the Atomic and Radiation Physics of Plasmas (Hardcover)
G.J. Tallents
R1,919 Discovery Miles 19 190 Ships in 10 - 15 working days

Plasmas comprise more than 99% of the observable universe. They are important in many technologies and are key potential sources for fusion power. Atomic and radiation physics is critical for the diagnosis, observation and simulation of astrophysical and laboratory plasmas, and plasma physicists working in a range of areas from astrophysics, magnetic fusion, and inertial fusion utilise atomic and radiation physics to interpret measurements. This text develops the physics of emission, absorption and interaction of light in astrophysics and in laboratory plasmas from first principles using the physics of various fields of study including quantum mechanics, electricity and magnetism, and statistical physics. Linking undergraduate level atomic and radiation physics with the advanced material required for postgraduate study and research, this text adopts a highly pedagogical approach and includes numerous exercises within each chapter for students to reinforce their understanding of the key concepts.

Quantum Chromodynamics Sum Rules (Paperback, 1st ed. 2018): Cesareo A. Dominguez Quantum Chromodynamics Sum Rules (Paperback, 1st ed. 2018)
Cesareo A. Dominguez
R1,974 Discovery Miles 19 740 Ships in 18 - 22 working days

This concise book provides the necessary background to allow interested readers to launch original research projects on the subject matter. Currently, this material is not available from one single source, and is either spread out over numerous journal publications, or covered in long and technical monographs. At the core of this book lies the sum rule approach to obtain analytic results in Quantum Chromodynamics (QCD), the current theory of strong interactions among quarks and gluons. This method fully complements Lattice QCD, the corresponding computational approach based on discretizing QCD on a space-time lattice. Applications include standard determinations of hadronic particle properties with extensions to finite temperature and density, and possibly involving the presence of extreme magnetic fields. The latter cases include stellar objects (e.g. neutron stars and magnetars) as well as high-energy proton-proton and heavy-ion collisions. Further topics concern the determination of the fundamental parameters of QCD, e.g. quark masses and the quark-gluon couplings, the hadronic contribution to the anomalous magnetic moment of the muon, and electromagnetic coupling at the the W-boson mass scale.

Optics f2f - From Fourier to Fresnel (Paperback): Charles S Adams, Ifan G. Hughes Optics f2f - From Fourier to Fresnel (Paperback)
Charles S Adams, Ifan G. Hughes
R1,411 Discovery Miles 14 110 Ships in 10 - 15 working days

This textbook on optics provides an introduction to key concepts of wave optics and light propagation. It uniquely makes extensive use of Fourier methods and the angular-spectrum approach, especially to provide a unified approach to Fraunhofer and Fresnel diffraction. A recurring theme is that simple building blocks such as plane and spherical waves can be summed to construct useful solutions. The text pays particular attention to analysing topics in contemporary optics such as propagation, dispersion, laser beams and wave guides, apodisation, tightly-focused vector fields, unconventional polarization states, and light-matter interactions. Throughout the text, the principles are applied through worked examples, and the book is copiously illustrated with more than 240 figures. The 200 end-of-chapter exercises offer further opportunities for testing the reader's understanding.

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