Download or read book Waves and Rays in Elastic Continua written by Michael A. Slawinski and published by World Scientific. This book was released on 2010 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second edition of the textbook that was first published by Elsevier Science. Professor Slawinski has the copyright to the textbook and the second edition is significantly extended. The present book emphasizes the interdependence of mathematical formulation and physical meaning in the description of seismic phenomena. Herein, we use aspects of continuum mechanics, wave theory and ray theory to explain phenomena resulting from the propagation of seismic waves. The book is divided into three main sections: elastic continua, waves and rays and variational formulation of rays. There is also a fourth part, which consists of appendices. In Part 1, we use continuum mechanics to describe the material through which seismic waves propagate, and to formulate a system of equations to study the behaviour of such a material. In Part 2, we use these equations to identify the types of body waves propagating in elastic continua as well as to express their velocities and displacements in terms of the properties of these continua. To solve the equations of motion in anisotropic inhomogeneous continua, we use the high-frequency approximation and, hence, establish the concept of a ray. In Part 3, we show that, in elastic continua, a ray is tantamount to a trajectory along which a seismic signal propagates in accordance with the variational principle of stationary traveltime. Consequently, many seismic problems in elastic continua can be conveniently formulated and solved using the calculus of variations. In Part 4, we describe two mathematical concepts that are used in the book; namely, homogeneity of a function and Legendre's transformation. This section also contains a list of symbols.

Download or read book Waves And Rays In Elastic Continua 3rd Edition written by Michael A Slawinski and published by World Scientific Publishing Company. This book was released on 2014-12-15 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book — which is the third, significantly revised edition of the textbook originally published by Elsevier Science — emphasizes the interdependence of mathematical formulation and physical meaning in the description of seismic phenomena. Herein, we use aspects of continuum mechanics, wave theory and ray theory to explain phenomena resulting from the propagation of seismic waves.The book is divided into three main sections: Elastic Continua, Waves and Rays and Variational Formulation of Rays. There is also a fourth part, which consists of appendices.In Elastic Continua, we use continuum mechanics to describe the material through which seismic waves propagate, and to formulate a system of equations to study the behaviour of such a material. In Waves and Rays, we use these equations to identify the types of body waves propagating in elastic continua as well as to express their velocities and displacements in terms of the properties of these continua. To solve the equations of motion in anisotropic inhomogeneous continua, we invoke the concept of a ray. In Variational Formulation of Rays, we show that, in elastic continua, a ray is tantamount to a trajectory along which a seismic signal propagates in accordance with the variational principle of stationary traveltime. Consequently, many seismic problems in elastic continua can be conveniently formulated and solved using the calculus of variations. In the Appendices, we describe two mathematical concepts that are used in the book; namely, homogeneity of a function and Legendre's transformation. This section also contains a list of symbols.

Download or read book Seismic Waves and Rays in Elastic Media written by M.A. Slawinski and published by Elsevier. This book was released on 2003-08-04 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book seeks to explore seismic phenomena in elastic media and emphasizes the interdependence of mathematical formulation and physical meaning. The purpose of this title - which is intended for senior undergraduate and graduate students as well as scientists interested in quantitative seismology - is to use aspects of continuum mechanics, wave theory and ray theory to describe phenomena resulting from the propagation of waves.The book is divided into three parts: Elastic continua, Waves and rays, and Variational formulation of rays. In Part I, continuum mechanics are used to describe the material through which seismic waves propagate, and to formulate a system of equations to study the behaviour of such material. In Part II, these equations are used to identify the types of body waves propagating in elastic continua as well as to express their velocities and displacements in terms of the properties of these continua. To solve the equations of motion in anisotropic inhomogeneous continua, the high-frequency approximation is used and establishes the concept of a ray. In Part III, it is shown that in elastic continua a ray is tantamount to a trajectory along which a seismic signal propagates in accordance with the variational principle of stationary travel time.

Download or read book Waves And Rays In Seismology Answers To Unasked Questions Second Edition written by Michael A Slawinski and published by World Scientific. This book was released on 2018-05-04 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'In summary, Professor Slawinski has written an engaging volume covering an unfamiliar topic in a highly accessible fashion. Non-specialists will gain a significant appreciation of the unique complexities associated with seismology.'Contemporary PhysicsThe author dedicates this book to readers who are concerned with finding out the status of concepts, statements and hypotheses, and with clarifying and rearranging them in a logical order. It is thus not intended to teach tools and techniques of the trade, but to discuss the foundations on which seismology — and in a larger sense, the theory of wave propagation in solids — is built. A key question is: why and to what degree can a theory developed for an elastic continuum be used to investigate the propagation of waves in the Earth, which is neither a continuum nor fully elastic. But the scrutiny of the foundations goes much deeper: material symmetry, effective tensors, equivalent media; the influence (or, rather, the lack thereof) of gravitational and thermal effects and the rotation of the Earth, are discussed ab initio. The variational principles of Fermat and Hamilton and their consequences for the propagation of elastic waves, causality, Noether's theorem and its consequences on conservation of energy and conservation of linear momentum are but a few topics that are investigated in the process to establish seismology as a science and to investigate its relation to subjects like realism and empiricism in natural sciences, to the nature of explanations and predictions, and to experimental verification and refutation.In the second edition, new sections, figures, examples, exercises and remarks are added. Most importantly, however, four new appendices of about one-hundred pages are included, which can serve as a self-contained continuum-mechanics course on finite elasticity. Also, they broaden the scope of elasticity theory commonly considered in seismology.

Download or read book Waves And Rays In Elastic Continua Fourth Edition written by Michael A Slawinski and published by World Scientific. This book was released on 2020-09-24 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: Seismology, as a branch of mathematical physics, is an active subject of both research and development. Its reliance on computational and technological advances continuously motivates the developments of its underlying theory. The fourth edition of Waves and Rays in Elastic Continua responds to these needs.The book is both a research reference and a textbook. Its careful and explanatory style, which includes numerous exercises with detailed solutions, makes it an excellent textbook for the senior undergraduate and graduate courses, as well as for an independent study. Used in its entirety, the book could serve as a sole textbook for a year-long course in quantitative seismology. Its parts, however, are designed to be used independently for shorter courses with different emphases. The book is not limited to quantitive seismology; it can serve as a textbook for courses in mathematical physics or applied mathematics.

Download or read book Nonlinear Periodic Waves and Their Modulations written by Anatoli? Mikha?lovich Kamchatnov and published by World Scientific. This book was released on 2000 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the mathematical theory of nonlinear waves and solitons has made great progress, its applications to concrete physical problems are rather poor, especially when compared with the classical theory of linear dispersive waves and nonlinear fluid motion. The Whitham method, which describes the combining action of the dispersive and nonlinear effects as modulations of periodic waves, is not widely used by applied mathematicians and physicists, though it provides a direct and natural way to treat various problems in nonlinear wave theory. Therefore it is topical to describe recent developments of the Whitham theory in a clear and simple form suitable for applications in various branches of physics.This book develops the techniques of the theory of nonlinear periodic waves at elementary level and in great pedagogical detail. It provides an introduction to a Whitham's theory of modulation in a form suitable for applications. The exposition is based on a thorough analysis of representative examples taken from fluid mechanics, nonlinear optics and plasma physics rather than on the formulation and study of a mathematical theory. Much attention is paid to physical motivations of the mathematical methods developed in the book. The main applications considered include the theory of collisionless shock waves in dispersive systems and the nonlinear theory of soliton formation in modulationally unstable systems. Exercises are provided to amplify the discussion of important topics such as singular perturbation theory, Riemann invariants, the finite gap integration method, and Whitham equations and their solutions.

Download or read book Seismic Waves and Rays in Elastic Media written by Michael A. Slawinski and published by Elsevier. This book was released on 2003 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book seeks to explore seismic phenomena in elastic media and emphasizes the interdependence of mathematical formulation and physical meaning. The purpose of this title - which is intended for senior undergraduate and graduate students as well as scientists interested in quantitative seismology - is to use aspects of continuum mechanics, wave theory and ray theory to describe phenomena resulting from the propagation of waves. The book is divided into three parts: Elastic continua, Waves and rays, and Variational formulation of rays. In Part I, continuum mechanics are used to describe the material through which seismic waves propagate, and to formulate a system of equations to study the behaviour of such material. In Part II, these equations are used to identify the types of body waves propagating in elastic continua as well as to express their velocities and displacements in terms of the properties of these continua. To solve the equations of motion in anisotropic inhomogeneous continua, the high-frequency approximation is used and establishes the concept of a ray. In Part III, it is shown that in elastic continua a ray is tantamount to a trajectory along which a seismic signal propagates in accordance with the variational principle of stationary travel time.

Download or read book Methods of Wave Theory in Dispersive Media written by Mikhail Viktorovich Kuzelev and published by World Scientific. This book was released on 2010 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ch. 1. Linear harmonic waves in dispersive systems. Initial-value problem and problem with an external source. 1. Harmonic waves in dispersive systems. 2. Initial-value problem. Eigenmode method. 3. Characteristic function of the state vector. Dispersion operator. 4. Laplace transform method -- ch. 2. A case study of linear waves in dispersive media. 5. Transverse electromagnetic waves in an isotropic dielectric. 6. Longitudinal electrostatic waves in a cold isotropic plasma. Collisional dissipation of plasma waves. 7. Transverse electromagnetic waves in a cold isotropic plasma. Dissipation of transverse waves in a plasma. 8. Electromagnetic waves in metals. 9. Electromagnetic waves in a waveguide with an isotropic dielectric. 10. Longitudinal waves in a hot isotropic plasma. Electron diffusion in a plasma. 11. Longitudinal waves in an isotropic degenerate plasma. Waves in a quantum plasma. 12. Ion acoustic waves in a nonisothermal plasma. Ambipolar diffusion. 13. Electromagnetic waves in a waveguide with an anisotropic plasma in a strong external magnetic field. 14. Electromagnetic waves propagating in a magnetized electron plasma along a magnetic field. 15. Electrostatic waves propagating in a magnetized electron plasma at an angle to a magnetic field. 16. Magnetohydrodynamic waves in a conducting fluid. 17. Acoustic waves in crystals. 18. Longitudinal electrostatic waves in a one-dimensional electron beam. 19. Beam instability in a plasma. 20. Instability of a current-carrying plasma -- ch. 3. Linear waves in coupled media. Slow amplitude method. 21. Coupled oscillator representation and slow amplitude method. 22. Beam-plasma system in the coupled oscillator representation. 23. Basic equations of microwave electronics. 24. Resonant Buneman instability in a current-carrying plasma in the coupled oscillator representation. 25. Dispersion function and wave absorption in dissipative systems. 26. Some effects in the interaction between waves in coupled systems. 27. Waves and their interaction in periodic structures -- ch. 4. Nonharmonic waves in dispersive media. 28. General solution to the initial-value problem. 29. Quasi-harmonic approximation. Group velocity. 30. Pulse spreading in equilibrium dispersive media. 31. Stationary-phase method. 32. Some problems for wave equations with a source -- ch. 5. Nonharmonic waves in nonequilibrium media. 33. Pulse propagation in nonequilibrium media. 34. Stationary-phase method for complex frequencies. 35. Quasi-harmonic approximation in the theory of interaction of electron beams with slowing-down media -- ch. 6. Theory of instabilities. 36. Convective and absolute instabilities. First criterion for the type of instability. 37. Saddle-point method. Second criterion for the type of instability. 38. Third Criterion for the type of instability. 39. Type of beam instability in the interaction with a slowed wave of zero group velocity in a medium. 40. Calculation of the Green's functions of unstable systems -- ch. 7. Hamiltonian method in the theory of electromagnetic radiation in dispersive media. 41. Equations for the excitation of transverse electromagnetic field oscillators. 42. Dipole radiation. 43. Radiation from a moving dipole - undulator radiation. 44. Cyclotron radiation. 45. Cherenkov effect. Anomalous and normal doppler effects. 46. Application of the Hamiltonian method to the problem of the excitation of longitudinal waves

Download or read book Waves And Rays In Elastic Continua written by Michael A Slawinski and published by World Scientific Publishing Company. This book was released on 2010-09-09 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book — which is the second, and significantly extended, edition of the textbook originally published by Elsevier Science — emphasizes the interdependence of mathematical formulation and physical meaning in the description of seismic phenomena. Herein, we use aspects of continuum mechanics, wave theory and ray theory to explain phenomena resulting from the propagation of seismic waves.The book is divided into three main sections: Elastic Continua, Waves and Rays and Variational Formulation of Rays. There is also a fourth part, which consists of appendices.In Elastic Continua, we use continuum mechanics to describe the material through which seismic waves propagate, and to formulate a system of equations to study the behaviour of such a material. In Waves and Rays, we use these equations to identify the types of body waves propagating in elastic continua as well as to express their velocities and displacements in terms of the properties of these continua. To solve the equations of motion in anisotropic inhomogeneous continua, we invoke the concept of a ray. In Variational Formulation of Rays, we show that, in elastic continua, a ray is tantamount to a trajectory along which a seismic signal propagates in accordance with the variational principle of stationary traveltime. Consequently, many seismic problems in elastic continua can be conveniently formulated and solved using the calculus of variations. In the Appendices, we describe two mathematical concepts that are used in the book; namely, homogeneity of a function and Legendre's transformation. This section also contains a list of symbols.

Download or read book Theory of Seismic Imaging written by John A. Scales and published by Springer. This book was released on 1995-05-17 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Seismic imaging methods are currently used to produce images of the Earth's subsurface properties at diverse length scales, from high-resolution, near-surface environmental studies for oil and gas exploration to long-period images of the entire planet. This book presents the physical and mathematical basis of imaging algorithms in the context of controlled-source reflection seismology. The approach taken is motivated by physical optics and theoretical seismology. The theory is constantly put into practice via a graded sequence of computer exercises using the widely available SU (Seismic Unix) software package.

Download or read book Fundamental Aspects of Dislocation Theory written by John Arthur Simmons and published by . This book was released on 1970 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Noisy Pendulum written by M. Gitterman and published by World Scientific. This book was released on 2008 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the general description of the mathematical pendulum subject to constant torque, periodic and random forces. The latter appear in additive and multiplicative form with their possible correlation. For the underdamped pendulum driven by periodic forces, a new phenomenon OCo deterministic chaos OCo comes into play, and the common action of this chaos and the influence of noise are taken into account. The inverted position of the pendulum can be stabilized either by periodic or random oscillations of the suspension axis or by inserting a spring into a rigid rod, or by their combination. The pendulum is one of the simplest nonlinear models, which has many applications in physics, chemistry, biology, medicine, communications, economics and sociology. A wide group of researchers working in these fields, along with students and teachers, will benefit from this book.

Download or read book Introduction To Lagrangian Mechanics An 2nd Edition written by Alain J Brizard and published by World Scientific Publishing Company. This book was released on 2014-11-28 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Lagrangian Mechanics begins with a proper historical perspective on the Lagrangian method by presenting Fermat's Principle of Least Time (as an introduction to the Calculus of Variations) as well as the principles of Maupertuis, Jacobi, and d'Alembert that preceded Hamilton's formulation of the Principle of Least Action, from which the Euler-Lagrange equations of motion are derived. Other additional topics not traditionally presented in undergraduate textbooks include the treatment of constraint forces in Lagrangian Mechanics; Routh's procedure for Lagrangian systems with symmetries; the art of numerical analysis for physical systems; variational formulations for several continuous Lagrangian systems; an introduction to elliptic functions with applications in Classical Mechanics; and Noncanonical Hamiltonian Mechanics and perturbation theory.The Second Edition includes a larger selection of examples and problems (with hints) in each chapter and continues the strong emphasis of the First Edition on the development and application of mathematical methods (mostly calculus) to the solution of problems in Classical Mechanics.New material has been added to most chapters. For example, a new derivation of the Noether theorem for discrete Lagrangian systems is given and a modified Rutherford scattering problem is solved exactly to show that the total scattering cross section associated with a confined potential (i.e., which vanishes beyond a certain radius) yields the hard-sphere result. The Frenet-Serret formulas for the Coriolis-corrected projectile motion are presented, where the Frenet-Serret torsion is shown to be directly related to the Coriolis deflection, and a new treatment of the sleeping-top problem is given.

Download or read book Hamilton s Principle in Continuum Mechanics written by Anthony Bedford and published by Springer Nature. This book was released on 2021-12-14 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised, updated edition provides a comprehensive and rigorous description of the application of Hamilton’s principle to continuous media. To introduce terminology and initial concepts, it begins with what is called the first problem of the calculus of variations. For both historical and pedagogical reasons, it first discusses the application of the principle to systems of particles, including conservative and non-conservative systems and systems with constraints. The foundations of mechanics of continua are introduced in the context of inner product spaces. With this basis, the application of Hamilton’s principle to the classical theories of fluid and solid mechanics are covered. Then recent developments are described, including materials with microstructure, mixtures, and continua with singular surfaces.

Download or read book Python API Development Fundamentals written by Jack Chan and published by Packt Publishing Ltd. This book was released on 2019-11-22 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learn all that’s needed to build a fully functional web application from scratch. Key FeaturesDelve deep into the principle behind RESTful APILearn how to build a scalable web application with the RESTful API architecture and Flask frameworkKnow what are the exact tools and methodology to test your applications and how to use themBook Description Python is a flexible language that can be used for much more than just script development. By knowing the Python RESTful APIs work, you can build a powerful backend for web applications and mobile applications using Python. You'll take your first steps by building a simple API and learning how the frontend web interface can communicate with the backend. You'll also learn how to serialize and deserialize objects using the marshmallow library. Then, you'll learn how to authenticate and authorize users using Flask-JWT. You'll also learn how to enhance your APIs by adding useful features, such as email, image upload, searching, and pagination. You'll wrap up the whole book by deploying your APIs to the cloud. By the end of this book, you'll have the confidence and skill to leverage the power of RESTful APIs and Python to build efficient web applications. What you will learnUnderstand the concept of a RESTful APIBuild a RESTful API using Flask and the Flask-Restful extensionManipulate a database using Flask-SQLAlchemy and Flask-MigrateSend out plaintext and HTML format emails using the Mailgun APIImplement a pagination function using Flask-SQLAlchemyUse caching to improve API performance and efficiently obtain the latest informationDeploy an application to Heroku and test it using PostmanWho this book is for This book is ideal for aspiring software developers who have a basic-to-intermediate knowledge of Python programming and who want to develop web applications using Python. Knowledge of how web applications work will be beneficial but is not essential.

Download or read book Free Boundary Problems in Continuum Mechanics written by Stanislav Nikolaevich Antont︠s︡ev and published by Springer Science & Business Media. This book was released on 1992 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some extremum and unilateral boundary value problems in viscous hydrodynamics.- On axisymmetric motion of the fluid with a free surface.- On the occurrence of singularities in axisymmetrical problems of hele-shaw type.- New asymptotic method for solving of mixed boundary value problems.- Some results on the thermistor problem.- New applications of energy methods to parabolic and elliptic free boundary problems.- A localized finite element method for nonlinear water wave problems.- Approximate method of investigation of normal oscillations of viscous incompressible liquid in container.- The classical Stefan problem as the limit case of the Stefan problem with a kinetic condition at the free boundary.- A mathematical model of oscillations energy dissipation of viscous liquid in a tank.- Existence of the classical solution of a two-phase multidimensional Stefan problem on any finite time interval.- Asymptotic theory of propagation of nonstationary surface and internal waves over uneven bottom.- Multiparametric problems of two-dimensional free boundary seepage.- Nonisothermal two-phase filtration in porous media.- Explicit solution of time-dependent free boundary problems.- Nonequilibrium phase transitions in frozen grounds.- System of variational inequalities arising in nonlinear diffusion with phase change.- Contact viscoelastoplastic problem for a beam.- Application of a finite-element method to two-dimensional contact problems.- Computations of a gas bubble motion in liquid.- Waves on the liquid-gas free surface in the presence of the acoustic field in gas.- Smooth bore in a two-layer fluid.- Numerical calculation of movable free and contact boundaries in problems of dynamic deformation of viscoelastic bodies.- On the canonical variables for two-dimensional vortex hydrodynamics of incompressible fluid.- About the method with regularization for solving the contact problem in elasticity.- Space evolution of tornado-like vortex core.- Optimal shape design for parabolic system and two-phase Stefan problem.- Incompressible fluid flows with free boundary and the methods for their research.- On the Stefan problems for the system of equations arising in the modelling of liquid-phase epitaxy processes.- Stefan problem with surface tension as a limit of the phase field model.- The modelization of transformation phase via the resolution of an inclusion problem with moving boundary.- To the problem of constructing weak solutions in dynamic elastoplasticity.- The justification of the conjugate conditions for the Euler's and Darcy's equations.- On an evolution problem of thermo-capillary convection.- Front tracking methods for one-dimensional moving boundary problems.- On Cauchy problem for long wave equations.- On fixed point (trial) methods for free boundary problems.- Nonlinear theory of dynamics of a viscous fluid with a free boundary in the process of a solid body wetting.

Download or read book Mathematics for Physics written by Michael Stone and published by Cambridge University Press. This book was released on 2009-07-09 with total page 821 pages. Available in PDF, EPUB and Kindle. Book excerpt: An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of physics – differential and integral equations, Fourier series and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and complex variables. The authors' exposition avoids excess rigor whilst explaining subtle but important points often glossed over in more elementary texts. The topics are illustrated at every stage by carefully chosen examples, exercises and problems drawn from realistic physics settings. These make it useful both as a textbook in advanced courses and for self-study. Password-protected solutions to the exercises are available to instructors at www.cambridge.org/9780521854030.