Classical mechanics Books

Trade Review“This hefty tome offers a comprehensive introduction to fluid dynamics, mainly with application to planetary science and astrophysics in mind. ... it is a useful resource for course development. It certainly offers a wealth of interesting insights into fluid dynamics and plasma physics for those with experience, and I found it to be an enjoyable and informative read.” (David A. Burton, The Observatory, Vol. 137 (1260), October, 2017)“Modern Fluid Dynamics for Physics and Astrophysics is a welcome addition that helps fill the gap between introductory and advanced books. … The textbook is especially suited for graduate courses, but I believe that it can also be easily used for senior undergraduate courses. … Modern Fluid Dynamics for Physics and Astrophysics to be a very good resource, not just for astrophysics and geophysics courses but for any physics course that covers the fundamental topic of fluid dynamics.” (Giuseppe Lodato, Physics Today, May, 2017)Table of Contents

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Book SynopsisThis work focuses on computational methods in continuum thermomechanics. The text is based on the author's lectures, which ensures a didactical and coherent buildup. The main emphasis is put on the presentation of ideas and qualitative considerations, illustrated by specific examples and applications. Conditions and explanations that are essential for the practical application of methods are discussed thoroughly.Table of ContentsPreface Notation Part I. Basic equations of continuum mechanics Chapter 1. Basic equations of continuum media Part II. Theory of finite-difference schemes Chapter 2. The basics of the theory of finite-difference schemes Chapter 3. Methods for solving systems of algebraic equations Chapter 4. Methods for solving boundary value problems for systems of differential equations Part III. Finite-difference methods for solving nonlinear evolution equations of continuum mechanics Chapter 5. Wave propagation problems Chapter 6. Finite-difference splitting method for solving dynamic and quasistatic boundary value problems Chapter 7. Solution of elastoplastic dynamic and quasistatic problems with finite deformations References

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Book SynopsisVarious nanoclusters and microparticles are considered in excited and ionized gases, as well as various processes with their participation. The concepts of these processes were developed 50 - 100 years ago mostly for dense media, and basing on these concepts, we analyze these processes in gases in two opposite regimes, so that in the kinetic regime surrounding atoms of a buffer gas do not partake in processesinvolving small particles, and the diffusion regime corresponds to a dense gas where interaction of small particles with a buffer gas subjects to laws of hydrodynamics. For calculation or estimation of the rates of these processes, we are based on the liquid drop model for small particles which was introduced in physics by N. Bohr about 80 years ago for the analysis of properties of atomic nuclei including the nuclear fusion and the hard sphere model (or the model of billiard balls) which was used by J. C. Maxwell 150 years ago and helped to create the kinetic theory of gases. These models along with the analysis of their accuracy allow one to study various processes, such as transport processes in gases involving small particles, charging of small particles in gases, chemical processes, atom attachment and quenching of excited atomic particles on the surface of a small particle, nucleation processes for small particles including coagulation, coalescence and growth of fractal aggregates, chain aggregates, fractal fibres and aerogels. Each analysis is finished by analytic formulas or simple models which allow us to calculate the rate of a certain real process with a known accuracy or to estimate this, and criteria of validity are given for these expressions obtained. Examples of real objects and processes involving small particles are analyzed.

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Book SynopsisThis book presents current spatial and temporal multiscaling approaches of materials modeling. Recent results demonstrate the deduction of macroscopic properties at the device and component level by simulating structures and materials sequentially on atomic, micro- and mesostructural scales. The book covers precipitation strengthening and fracture processes in metallic alloys, materials that exhibit ferroelectric and magnetoelectric properties as well as biological, metal-ceramic and polymer composites. The progress which has been achieved documents the current state of art in multiscale materials modelling (MMM) on the route to full multi-scaling. Contents:Part I: Multi-time-scale and multi-length-scale simulations of precipitation and strengthening effectsLinking nanoscale and macroscaleMultiscale simulations on the coarsening of Cu-rich precipitates in α-Fe using kinetic Monte Carlo, Molecular Dynamics, and Phase-Field simulationsMultiscale modeling predictions of age hardening curves in Al-Cu alloysKinetic Monte Carlo modeling of shear-coupled motion of grain boundariesProduct Properties of a two-phase magneto-electric compositePart II: Multiscale simulations of plastic deformation and fractureNiobium/alumina bicrystal interface fractureAtomistically informed crystal plasticity model for body-centred cubic ironFE2AT ・ finite element informed atomistic simulationsMultiscale fatigue crack growth modeling for welded stiffened panelsMolecular dynamics study on low temperature brittleness in tungsten single crystalsMulti scale cellular automata and finite element based model for cold deformation and annealing of a ferritic-pearlitic microstructureMultiscale simulation of the mechanical behavior of nanoparticle-modified polyamide compositesPart III: Multiscale simulations of biological and bio-inspired materials, bio-sensors and compositesMultiscale Modeling of Nano-BiosensorsFinite strain compressive behaviour of CNT/epoxy nanocompositesPeptide・zinc oxide interaction

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Book SynopsisThe book provides a concise and rigor introduction to the fundamentals of methods for solving the principal problems of modern non-linear dynamics. This monograph covers the basic issues of the theory of integrable systems and the theory of dynamical chaos both in nonintegrable conservative and in dissipative systems. A distinguishing feature of the material exposition is to add some comments, historical information, brief biographies and portraits of the researchers who made the most significant contribution to science. This allows one to present the material as accessible and attractive to students to acquire indepth scientific knowledge of nonlinear mechanics, feel the atmosphere where those or other important discoveries were made. The book can be used as a textbook for advanced undergraduate and graduate students majoring in high-tech industries and high technology (the science based on high technology) to help them to develop lateral thinking in early stages of training. Contents:Nonlinear OscillationsIntegrable SystemsStability of Motion and Structural StabilityChaos in Conservative SystemsChaos and Fractal Attractors in Dissipative SystemsConclusionReferencesIndex

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Book SynopsisThis monograph covers new variational and projection methods to study the dynamics within solid structures. To cope with the underlying initial-boundary value problems, the method of integrodifferential relations is employed. Applications and examples in physics, mechanics and control engineering range from natural vibrations or forced motions of elastic and viscoelastic bodies to heat and mass transfer processes. ContentsGeneralized formulations of parabolic and hyperbolic problemsVariational principles in linear elasticityVariational statements in structural mechanicsRitz method for initial-boundary value problemsVariational and projection techniques with semi-discretizationIntegrodifferential approach to eigenvalue problemsSpatial vibrations of elastic beams with convex cross-sectionsDouble minimization in optimal control problemsSemi-discrete approximations in inverse dynamic problemsModeling and control in mechatronics

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Book SynopsisThis book presents a detailed description of a robust pseudomultigrid algorithm for solving (initial-)boundary value problems on structured grids in a black-box manner. To overcome the problem of robustness, the presented Robust Multigrid Technique (RMT) is based on the application of the essential multigrid principle in a single grid algorithm. It results in an extremely simple, very robust and highly parallel solver with close-to-optimal algorithmic complexity and the least number of problem-dependent components. Topics covered include an introduction to the mathematical principles of multigrid methods, a detailed description of RMT, results of convergence analysis and complexity, possible expansion on unstructured grids, numerical experiments and a brief description of multigrid software, parallel RMT and estimations of speed-up and efficiency of the parallel multigrid algorithms, and finally applications of RMT for the numerical solution of the incompressible Navier Stokes equations. Potential readers are graduate students and researchers working in applied and numerical mathematics as well as multigrid practitioners and software programmers. ContentsIntroduction to multigridRobust multigrid techniqueParallel multigrid methodsApplications of multigrid methods in computational fluid dynamics

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Book SynopsisThis two-volume work presents state-of-the-art mathematical theories and results on infinite-dimensional dynamical systems. Inertial manifolds, approximate inertial manifolds, discrete attractors and the dynamics of small dissipation are discussed in detail. The unique combination of mathematical rigor and physical background makes this work an essential reference for researchers and graduate students in applied mathematics and physics. The main emphasis in the first volume is on the mathematical analysis of attractors and inertial manifolds. This volume deals with the existence of global attractors, inertial manifolds and with the estimation of Hausdorff fractal dimension for some dissipative nonlinear evolution equations in modern physics. Known as well as many new results about the existence, regularity and properties of inertial manifolds and approximate inertial manifolds are also presented in the first volume. The second volume will be devoted to modern analytical tools and methods in infinite-dimensional dynamical systems. ContentsAttractor and its dimension estimationInertial manifoldThe approximate inertial manifold Table of ContentsTable of contentsChapter 1 The Attractor and Its Estimation of DimensionChapter 2 Inertial ManifoldChapter 3 The Approximate Inertial ManifoldChapter 4 Discrete Attractor and Approximate CalculationChapter 5 Some Properties of Global AttractorChapter 6 The dynamics with small dissipationChapter 7 Existence and Stability of Solitary WavesChapter 8 Numerical computation method for some nonlinear evolution equationsReferences

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Book SynopsisThis monograph develops adaptive stochastic methods in computational mathematics. The authors discuss the basic ideas of the algorithms and ways to analyze their properties and efficiency. Methods of evaluation of multidimensional integrals and solutions of integral equations are illustrated by multiple examples from mechanics, theory of elasticity, heat conduction and fluid dynamics. Contents Part I: Evaluation of IntegralsFundamentals of the Monte Carlo Method to Evaluate Definite IntegralsSequential Monte Carlo Method and Adaptive IntegrationMethods of Adaptive Integration Based on Piecewise ApproximationMethods of Adaptive Integration Based on Global ApproximationNumerical ExperimentsAdaptive Importance Sampling Method Based on Piecewise Constant Approximation Part II: Solution of Integral EquationsSemi-Statistical Method of Solving Integral Equations NumericallyProblem of Vibration ConductivityProblem on Ideal-Fluid Flow Around an AirfoilFirst Basic Problem of Elasticity TheorySecond Basic Problem of Elasticity TheoryProjectional and Statistical Method of Solving Integral Equations Numerically

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Book SynopsisRegularized equations of motion can improve numerical integration for the propagation of orbits, and simplify the treatment of mission design problems. This monograph discusses standard techniques and recent research in the area. While each scheme is derived analytically, its accuracy is investigated numerically. Algebraic and topological aspects of the formulations are studied, as well as their application to practical scenarios such as spacecraft relative motion and new low-thrust trajectories.

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Table of ContentsFrontmatter -- Preface -- Contents -- General Scheme of Notations -- 1. Introduction -- 2. Geometry of Physical Space -- 3. Essentials of Non-Linear Elasticity Theory -- 4. Geometric Formalization of the Body and Its Representation in Physical Space -- 5. Strain Measures -- 6. Motion -- 7. Stress Measures -- 8. Material Uniformity and Inhomogeneity -- 9. Material Connections -- 10. Balance Equations -- 11. The Evolutionary Problem – Examples -- 12. Algebraic Structures -- 13. Review of Smooth Manifolds and Vector Bundles -- 14. Connections on Principal Bundles -- Bibliography -- Index

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Book SynopsisThis two-volume work presents state-of-the-art mathematical theories and results on infinite-dimensional dynamical systems. Inertial manifolds, approximate inertial manifolds, discrete attractors and the dynamics of small dissipation are discussed in detail. The unique combination of mathematical rigor and physical background makes this work an essential reference for researchers and graduate students in applied mathematics and physics. The main emphasis in the fi rst volume is on the existence and properties for attractors and inertial manifolds. This volume highlights the use of modern analytical tools and methods such as the geometric measure method, center manifold theory in infinite dimensions, the Melnihov method, spectral analysis and so on for infinite-dimensional dynamical systems. The second volume includes the properties of global attractors, the calculation of discrete attractors, structures of small dissipative dynamical systems, and the existence and stability of solitary waves. 　 ContentsDiscrete attractor and approximate calculation Some properties of global attractor Structures of small dissipative dynamical systems Existence and stability of solitary waves Table of ContentsTable of contentsChapter 1 The Attractor and Its Estimation of DimensionChapter 2 Inertial ManifoldChapter 3 The Approximate Inertial ManifoldChapter 4 Discrete Attractor and Approximate CalculationChapter 5 Some Properties of Global AttractorChapter 6 The dynamics with small dissipationChapter 7 Existence and Stability of Solitary WavesChapter 8 Numerical computation method for some nonlinear evolution equationsReferences

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Book SynopsisDieses Buch erläutert die Mechanik weitgehend auf der Grundlage algebraischer Vorstellungen und Methoden, so wie sie in der Quantenmechanik oder in der Feldtheorie entwickelt wurden. Das Mechanik-Lehrbuch ist damit zugleich eine Einführung in diese Methoden und dient daher als Vorbereitung auf andere Bereiche der theoretischen Physik: Bereits die Struktur des Raumes oder die Newtonschen Gesetze führt der Autor beispielsweise so ein, dass sie Raum lassen für neue, weitergehende Vorstellungen.Trade ReviewAus den Rezensionen:"Hervorgegangen aus Vorlesungen an der Universität Karlsruhe und München. … Laut Verlagstext legt ‘Dieses Buch der Mechanik weitgehend algebraische Vorstellungen und Methoden … zugrunde.‘ So werden Methoden der Physik dargestellt. die auch in anderen Bereichen der theoretischen Physik relevant sind. An Universitätsorten unbedingt anschaffen." (Ruge, in: ekz-Informationsdienst Einkaufszentrale für öffentliche Bibliotheken, 2008, Issue 15)“... Bereits ein erster Blick in das Buch ... zeigt, dass hier die Physik primär als Pate diente. … Es ist ... leicht zu erkennen, dass die Methoden der ‘Newtonschen Mechanik‘ universell einsetzbar sind. ... Alle Elemente werden mit der notwendigen Genauigkeit ... hinsichtlich der Mathematik dargeboten, so dass man zahlreiche Darlegungen in einer modernen mathematischen Darstellung findet. Der Nachweis der Nützlichkeit wird über die Beispiele erbracht. … Eine Erweiterung der Newtonschen Mechanik in dieser Richtung ist nicht schwierig und würde theoretisch interessierten Lesern neue Horizonte öffnen.“ (Holm Altenbach, in: ZAMM Zeitschrift für Angewandte Mathematik und Mechanik, 2010, Vol. 90, Issue 1, S. 64)Table of ContentsPunktmechanik.- Newton’sche Gesetze und einfache mechanische Systeme.- Erhaltungssätze und Stoßprozesse.- Zweikörperproblem.- Schwingungen.- Vielteilchenprobleme und der Übergang zum Kontinuum.- Variationsprinzip und relativistische Mechanik.- Variationsprinzip und relativistische Mechanik.- Kanonische Mechanik.- Kanonische Mechanik.- Der starre Körper.- Der starre Körper.

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Book SynopsisDas Lehrbuch bietet eine kompakte und prägnante Darstellung der Mechanik elastischer Körper und Strukturen. Es beschränkt die Stofffülle auf das Wesentliche, schlägt aber auch Brücken zu Spezialdisziplinen Struktur- und Festkörpermechanik und zur immer wichtiger werdenden Computer-orientierten Mechanik. Nach einer Einführung in die Grundlagen werden ebene Probleme, räumliche Probleme, Variations- und Energieprinzipien behandelt. Weitere Kapitel gehen auf die Mechanik von Platten, Rotationsschalen und ebenen Laminaten ein. Ein Buch für Studenten des Maschinenbaus und Bauingenieurwesens an Universitäten und Fachhochschulen ebenso wie für Fachleute und Praktiker in Industrie und Forschung.Table of Contents1. Grundlagen (Spannungszustand, Deformation und Verzerrung, Elastizitätsgesetz, Grundgleichungen der linearen Elastizitätstheorie) 2. Ebene Probleme (Ebener Verzerrungszustand, Ebener Spannungszustand, Airysche Spannungsfunktion, Scheibengleichung, Lösungen der Bipotentialgleichung, Anwendungsbeispiele, Methode der komplexen Potentiale, Anwendungsbeispiele der komplexen Methode) 3. Räumliche Probleme (Papkovich-Neuber-Potentiale, Einzelkraft im elastischen Körper, Kelvin-Lösung, Normalkraft auf elastischen Halbraum, Boussinesq-Lösung, Tangentialkraft auf elastischen Halbraum, Cerruti-Lösung, kugelförmiger Einschluß) 4. Variations- und Energieprinzipien (Allgemeiner Arbeitssatz, Prinzip der virtuellen Verrückungen, Prinzip der virtuellen Kräfte, Extremalprinzipien, Sätze von Castigliano, Menabrea, Clapeyron und Betti, verallgemeinerte Energieprinzipien, Rayleigh-Ritz- und Galerkin-Verfahren, Methode der finiten Elemente, Randelemente-Methode) 5. Platten (Kirchhoffsche Plattentheorie, Lösungen der Plattengleichungen, Elastisch gebettete Platte, Die orthotrope Platte, Mindlinsche Plattentheorie) 6. Rotationsschalen (Grundgleichungen, Biegetheorie, Membrantheorie, Kreiszylinderschale, Kugelschale) 7. Ebene Laminate (Verhalten einer Laminat-Einzelschicht, Klassische Laminattheorie, Hygrothermische Probleme, Festigkeit, Höhere Laminattheorien, Composite-Mikromechanik) ANHANG.- Literatur.- Englische Fachausdrücke.- Sachverzeichnis.

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Book SynopsisWAVE TURBULENCE is a state of a system of many simultaneously excited and interacting waves characterized by an energy distribution which is not in any sense close to thermodynamic equilibrium. Such situations in a choppy sea, in a hot plasma, in dielectrics under arise, for example, a powerful laser beam, in magnets placed in a strong microwave field, etc. Among the great variety of physical situations in which wave turbulence arises, it is possible to select two large limiting groups which allow a detailed analysis. The first is fully developed wave turbulence arising when energy pumping and dissipation have essentially different space scales. In this case there is a wide power spectrum of turbulence. This type of turbulence is described in detail e. g. in Zakharov et al. 1 In the second limiting case the scales in which energy pumping and dissipation occur are the same. As a rule, in this case a narrow, almost singular spectrum of turbulence appears which is concentrated near surfaces, curves or even points in k-space. One of the most important, widely investigated and instructive examples of this kind of turbulence is parametric wave turbulence appearing as a result of the evolution of a parametric instability of waves in media under strong external periodic modulation (laser beam, microwave electromagnetic field, etc. ). The present book deals with parametric wave turbulence.Table of Contents1 Introduction to Nonlinear Wave Dynamics.- 1.1 Hamiltonian Method for Description of Waves in a Continuous Medium.- 1.1.1 Hamiltonian Equations of Motion.- 1.1.2 Transfer to Complex Variables.- 1.1.3 Hamiltonian Structure Under Small Nonlinearity.- 1.1.4 Dynamic Perturbation Theory. Elimination of “Non-Resonant” Terms from the Hamiltonian.- 1.2 Dimensional Estimation of Hamiltonian Coefficients.- 1.3 Dynamic Equations of Motion for Weakly Non-Conservative Wave Systems.- 1.3.1 Taking into Account Linear Wave Damping.- 1.3.2 Allowing for Thermal Noise.- 1.3.3 Nonlinearity of Wave Damping.- 1.4 Three-Wave Processes.- 1.4.1 Confluence of Two Waves and Other Induced Processes.- 1.4.2 Decay Instability.- 1.4.3 Interaction of Three Waves with Finite Amplitude.- 1.4.4 Explosive Three-Wave Instability.- 1.5 Four-Wave Processes.- 1.5.1 Modulation Instability of the Plane Wave.- 1.5.2 Equation for the Envelopes.- 1.5.3 Package Evolution in Unbounded Media.- 2 The General Properties of Magnetodielectrics.- 2.1 Classification of Substances by Their Magnetic Properties.- 2.1.1 Diamagnets.- 2.1.2 Superconductors.- 2.1.3 Paramagnets.- 2.1.4 Magnetically Ordered Substances (Magnets).- 2.2 Nature of Interaction of Magnetic Moments.- 2.2.1 Exchange Interaction in the Hydrogen Molecule.- 2.2.2 Interatomic Exchange.- 2.2.3 Interatomic Exchange of Large Spins.- 2.2.4 Indirect Exchange Interactions.- 2.2.5 Relativistic Interactions.- 2.3 Energy of Ferromagnets in the Continuum Approximation.- 2.4 Magnetic and Crystallographic Structure of Some Magnets.- 2.4.1 Crystals with Spinel Structure.- 2.4.2 Crystals with Garnet Structure.- 2.4.3 Crystals with Hexagonal Structure.- 2.4.4 Crystals with Rhombohedral Structures.- 3 Spin Waves (Magnons) in Magnetically Ordered Dielectrics.- 3.1 Hamiltonian of Magnons in Ferromagnets (FM).- 3.1.1 Spectrum of Magnons in Cubic Ferromagnets.- 3.1.2 Amplitudes of Three-and Four-Magnon Interaction.- 3.1.3 Three-Magnon Hamiltonian.- 3.1.4 Four-Magnon Interaction Hamiltonian.- 3.2 Hamiltonian Function of Magnons in Antiferromagnets.- 3.2.1 Magnon Spectrum in Antiferromagnets (AFM).- 3.2.2 Interaction Hamiltonian in “Easy-Plane” Antiferromagnets.- 3.2.3 Nuclear Magnons in “Easy-Plane” Antiferromagnets.- 3.3 Comments at the Road Fork.- 3.4 Calculation of Magnon Hamiltonian.- 3.4.1 Equation of Motion of Magnetic Moment.- 3.4.2 Canonical Variables for Spin Waves in Ferromagnets (FM).- 3.4.3 Calculation of Frequencies and Interaction Amplitudes of Waves.- 4 Nonlinear Dynamics of Narrow Packets of Spin Waves.- 4.1 Elementary Processes of Spin Wave Interaction.- 4.1.1 Three-Magnon Processes.- 4.1.2 Modulation Instability of Spin Waves.- 4.2 Self-Focusing of Magnetoelastic Waves in Antiferromagnets (AFM).- 4.2.1 Structure of Basic Equations.- 4.2.2 Properties of Unidimensional Equations.- 4.2.3 Stability of Solitons and Self-Focusing Theorem.- 4.2.4 Evolution of Magnetoelastic Waves in the Absence of a Linear Bond Between Magnons and Phonons.- 4.3 Methods of Parametric Excitation of Spin Waves.- 4.3.1 Transverse Pumping of Spin Waves in FM.- 4.3.2 Parallel Pumping of Spin Waves in FM.- 4.3.3 “Oblique” Pumping of Spin Waves in FM.- 4.3.4 Suhl Instability of the Second Order in FM.- 4.3.5 Parallel Pumping in“Easy-Plane”Antiferromagnets.- 4.3.6 Parametric Pumping of Nuclear Magnons.- 5 Stationary Nonlinear Behavior of Parametrically Excited Waves. Basic S-Theory.- 5.1 History of the Problem.- 5.2 Statement of a Problem of Nonlinear Wave Behavior.- 5.3 Phase Relations and Mechanisms for Amplitude Limitation.- 5.3.1 Analysis of Phase Relations.- 5.3.2 Nonlinear Mechanisms for Limiting Parametric Instability.- 5.4 Basic Equations of Motion in the S-Theory.- 5.4.1 Statistical Properties of a Non-Interacting Field.- 5.4.2 Mean-Field Approximation.- 5.4.3 General Analysis of Basic Equations of S-Theory.- 5.5 Ground State of System of Interacting Parametric Waves.- 5.5.1 Stationary States and Analysis of Instability.- 5.5.2 Ground State Under Low Supercriticality.- 5.5.3 Threshold of Generation of Second Group of Pairs.- 5.5.4 Ground State Under High Supercriticality.- 5.5.5 Nonlinear Susceptibilities of Parametric Waves.- 6 Advanced S-Theory: Supplementary Sections.- 6.1 Ground State Evolution of System with Increasing Pumping Amplitude.- 6.1.1 Ground State of Parametric Waves for Complex Pair Interaction Amplitudes.- 6.1.2 The Second and Intermediate Thresholds.- 6.1.3 Nonlinear Behavior of Non-Analytic Pair Interaction Amplitudes.- 6.2 Influence of Nonlinear Damping on Parametric Excitation.- 6.2.1 Simple Theory.- 6.2.2 Influence of Non-Analyticity on Nonlinear Damping.- 6.3 Parametric Excitation Under the Feedback Effect on Pumping.- 6.3.1 Hamiltonian of the Problem.- 6.3.2 General Analysis of the Equations of Motion.- 6.3.3 First-Order Processes.- 6.3.4 Second-Order Processes.- 6.4 Nonlinear Theory of Parametric Wave Excitation at Finite Temperatures.- 6.4.1 Different Time Correlators and Frequency Spectrum.- 6.4.2 Basic Equations of Temperature S-Theory.- 6.4.3 Separation of Waves into Parametric and Thermal.- 6.4.4 Two-Dimensional Reduction of Basic Equations.- 6.4.5 Distribution of Parametric Waves in k.- 6.4.6 Spectrum of Parametric Waves.- 6.4.7 Heating Below Threshold.- 6.4.8 Influence of Thermal Bath on Total Characteristics.- 6.5 Introduction to Spatially Inhomogeneous S-Theory.- 6.5.1 Basic Equations.- 6.5.2 Parametric Threshold in Inhomogeneous Media.- 6.5.3 Stationary State in Non-Homogeneous Media.- 6.6 Nonlinear Behavior of Parametric Waves from Various Branches. Asymmetrical S-Theory.- 6.6.1 Derivation of Basic Equations.- 6.6.2 Stationary States in Isotropic Case.- 6.7 Parametric Excitation of Waves by Noise Pumping.- 6.7.1 Equations of S-Theory Under Noise Pumping.- 6.7.2 Distribution of Parametric Waves Above Threshold.- 7 Non-Stationary Behavior of Parametrically Excited Waves.- 7.1 Spectrum of Collective Oscillations (CO).- 7.1.1 Spectrum of Spatially Homogeneous CO in the Non-Dissipation Limit.- 7.1.2 Influence of Wave Damping on the CO Spectrum.- 7.1.3 Spectrum of Spatially Non-Homogeneous CO.- 7.2 Linear Theory of CO Resonance Excitation.- 7.2.1 Basic Equations and Their Solution.- 7.2.2 CO Excitation by a Microwave Field.- 7.2.3 Direct CO Excitation by a Radio Frequency Field.- 7.2.4 Coupled Motions of Collective Excitations of Parametric Waves and Sound.- 7.3 Threshold Under Periodic Modulation of Dispersion Law.- 7.4 Large-Amplitude Collective Oscillations and Double Parametric Resonance.- 7.4.1 Stationary State Under Periodic Modulation.- 7.4.2 Parametric Excitation of CO of Parametric Wave System.- 7.5 Transient Processes when Pumping is Turned on.- 7.5.1 Small Supercriticality Range.- 7.5.2 High Supercriticality Range.- 7.6 Parametric Excitation Under Sweeping of Wave Frequency.- 7.6.1 Qualitative Analysis of the Problem.- 7.6.2 Basic Equations of S-Theory Under Frequency Sweeping.- 7.6.3 Solution of S-Theory Equations.- 7.6.4 Dependence of the Number of Waves on the Pumping Amplitude.- 7.7 Problems.- 8 Secondary Parametric Wave Turbulence.- 8.1 Instability of Ground State and Auto-Oscillations.- 8.1.1 Properties and Nature of Spin Wave Oscillations.- 8.1.2 Numerical Simulation of Auto-Oscillation in the S-Theory.- 8.1.3 Conditions for Excitation of Auto-Oscillations.- 8.2 Route to Chaos in Dynamic Systems.- 8.2.1 Introduction.- 8.2.2 Elementary Concepts of Theory of Dynamic Chaos.- 8.2.3 Chaos of Parametric Magnons in CsMnF3.- 8.3 Geometry of Attractors of Secondary Parametric Turbulence of Magnons.- 8.3.1 Effective Phase Space and Dimensionality of Inclusion.- 8.3.2 Experimental Study of Attractor Structure in CsMnF3.- 8.4 Secondary Turbulence and Collapses in Narrow Parametric Wave Packets.- 8.4.1 Equations for Envelopes.- 8.4.2 Stationary Solitons.- 8.4.3 Average Characteristics of Secondary Turbulence.- 8.4.4 Destruction of Parametric Solitons with Large Amplitude.- 8.4.5 Soliton Mechanism of Amplitude Limitation.- 9 Experimental Investigations of Parametrically Excited Magnons.- 9.1 Experimental Investigations of Parametric Instability of Magnons.- 9.1.1 Methods and Materials Investigated.- 9.1.2 Measurements of Constants in Spin Wave Spectra.- 9.1.3 Spin Wave Damping.- 9.2 Nonlinear Behavior of Parametric Magnons — General Information.- 9.2.1 Measuring Technique for Susceptibilities X? and X?.- 9.2.2 Comparison of S-Theory and Experiment for Susceptibilities.- 9.2.3 Measurements of Interaction (Frequency Shift) Amplitude.- 9.2.4 Nonlinear Ferromagnetic Resonance.- 9.3 Investigations of Stationary State With One Group of Pairs.- 9.3.1 Nonlinear Susceptibility in the One-Group State.- 9.3.2 Direct Measurement of Pair Phase.- 9.4 Electromagnetic Radiation of Parametric Magnons.- 9.4.1 Frequency of Parametric Magnons.- 9.4.2 Frequency Width of Parametrically Excited Magnons.- 9.5 Collective Resonance of Parametric Magnons.- 9.5.1 Experimental Technique.- 9.5.2 Frequency of Collective Resonance.- 9.5.3 Susceptibility to Field of Weak Microwave Signal.- 9.5.4 Linewidth of Collective Resonance.- 9.5.5 Oscillations of Longitudinal Magnetization.- 9.5.6 Other Methods for Excitation of Collective Oscillations.- 9.6 Stepwise Excitation in YIG.- 9.6.1 Re-Radiation into the Transverse Channel.- 9.6.2 Interaction of Second-Group Magnons and Transverse Signal.- 9.7 Conditions of Excitation of Auto-Oscillations of Magnons.- 9.7.1 Experimental Setup.- 9.7.2 Intensive Auto-Oscillations of Mode m = 0.- 9.7.3 Crossing the Instability Boundary and Spatially Inhomogeneous Auto-Oscillations.- 9.7.4 Instability of Higher Collective Modes.- 9.8 Effect of Radio-Frequency Field Modulation on Parametric Resonance.- 9.8.1 Suppression of Parametric Instability by Modulation.- 9.8.2 Stationary State of Parametric Magnons Under Modulation of Their Frequency.- 9.9 Double Parametric Resonance and Inhomogeneous Collective Oscillations of Magnons.- 9.10 Parametric Excitation of Magnons Under Noise Modulation of their Frequencies.- 9.10.1 Threshold Amplitude of Noise Pumping.- 9.10.2 Efficiency of Phase Mechanism Under Noise Pumping.- 10 Nonlinear Kinetics of Parametrically Excited Waves.- 10.1 General Equations.- 10.2 Limit of the S-Theory.- 10.2.1 Form of the Green’s Function.- 10.2.2 Separation of the Waves into Parametric and Thermal.- 10.3 Nonlinear Theory of Parametric Excitation of Waves in Random Media.- 10.3.1 General Equations in the S,g2-Approximation.- 10.3.2 Distribution Function of Parametric Waves.- 10.3.3 Behavior of Parametrically Excited Waves Beyond the Threshold.- 10.4 Consistent Nonlinear Theory for Parametric Excitation of Waves.- 10.4.1 Spectral Density of Parametrically Excited Waves.- 10.4.2 Structure of the Distribution Function in k-Space.- References.

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Book SynopsisThe history of mechanics, and more particularly, the history of mechanics applied to constructions, constitutes a field of research that is relatively recent. This volume, together with the recent publication "Towards a History of Construction", is intended as an homage to the two eminent scholars who made a determinant contribution to the history of mechanics: Edoardo Benvenuto and Clifford Truesdell.Table of ContentsTruesdell and the History of the Theory of Structures.- Development of Studies in the History of Elasticity Theory and Structural Mechanics.- Coping With Error in the History of Mechanics.- The Development of the Deformation Method.- The Mechanics of Timbrel Vaults: a Historical Outline.- The Use of a Particular Form of the Parallelogram Law of Forces for the Building of Vaults (1650-1750).- Rose Windows.- Early Theories of Vectors.- The Ancients’ Inferno: The Slow and Tortuous Development of ‘Newtonian’ Principles of Motion in the Eighteenth Century.- A Historical Survey of Impact Theories.- What Can the Historian of Science Learn from the Historian of Fine Arts?.- Index of Names.

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