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| Author | : Y.V. Stupochenko |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 404 |
| Release | : 2012-12-06 |
| Genre | : Technology & Engineering |
| ISBN | : 3642482465 |
| Author | : E. V. Stupochenko |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 1967 |
| Genre | : |
| ISBN | : 9780387037271 |
| Author | : E. V. Stupočenko |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 1967 |
| Genre | : |
| ISBN | : |
| Author | : Joel Smoller |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 650 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461208734 |
For this edition, a number of typographical errors and minor slip-ups have been corrected. In addition, following the persistent encouragement of Olga Oleinik, I have added a new chapter, Chapter 25, which I titled "Recent Results." This chapter is divided into four sections, and in these I have discussed what I consider to be some of the important developments which have come about since the writing of the first edition. Section I deals with reaction-diffusion equations, and in it are described both the work of C. Jones, on the stability of the travelling wave for the Fitz-Hugh-Nagumo equations, and symmetry-breaking bifurcations. Section II deals with some recent results in shock-wave theory. The main topics considered are L. Tartar's notion of compensated compactness, together with its application to pairs of conservation laws, and T.-P. Liu's work on the stability of viscous profiles for shock waves. In the next section, Conley's connection index and connection matrix are described; these general notions are useful in con structing travelling waves for systems of nonlinear equations. The final sec tion, Section IV, is devoted to the very recent results of C. Jones and R. Gardner, whereby they construct a general theory enabling them to locate the point spectrum of a wide class of linear operators which arise in stability problems for travelling waves. Their theory is general enough to be applica ble to many interesting reaction-diffusion systems.
| Author | : Lee Davison |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 439 |
| Release | : 2008-04-24 |
| Genre | : Science |
| ISBN | : 3540745696 |
My intent in writing this book is to present an introduction to the thermo- chanical theory required to conduct research and pursue applications of shock physics in solid materials. Emphasis is on the range of moderate compression that can be produced by high-velocity impact or detonation of chemical exp- sives and in which elastoplastic responses are observed and simple equations of state are applicable. In the interest of simplicity, the presentation is restricted to plane waves producing uniaxial deformation. Although applications often - volve complex multidimensional deformation fields it is necessary to begin with the simpler case. This is also the most important case because it is the usual setting of experimental research. The presentation is also restricted to theories of material response that are simple enough to permit illustrative problems to be solved with minimal recourse to numerical analysis. The discussions are set in the context of established continuum-mechanical principles. I have endeavored to define the quantities encountered with some care and to provide equations in several convenient forms and in a way that lends itself to easy reference. Thermodynamic analysis plays an important role in continuum mechanics, and I have included a presentation of aspects of this subject that are particularly relevant to shock physics. The notation adopted is that conventional in expositions of modern continuum mechanics, insofar as possible, and variables are explained as they are encountered. Those experienced in shock physics may find some of the notation unconventional.
| Author | : Heinrich Freistühler |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 527 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461201934 |
In the field known as "the mathematical theory of shock waves," very exciting and unexpected developments have occurred in the last few years. Joel Smoller and Blake Temple have established classes of shock wave solutions to the Einstein Euler equations of general relativity; indeed, the mathematical and physical con sequences of these examples constitute a whole new area of research. The stability theory of "viscous" shock waves has received a new, geometric perspective due to the work of Kevin Zumbrun and collaborators, which offers a spectral approach to systems. Due to the intersection of point and essential spectrum, such an ap proach had for a long time seemed out of reach. The stability problem for "in viscid" shock waves has been given a novel, clear and concise treatment by Guy Metivier and coworkers through the use of paradifferential calculus. The L 1 semi group theory for systems of conservation laws, itself still a recent development, has been considerably condensed by the introduction of new distance functionals through Tai-Ping Liu and collaborators; these functionals compare solutions to different data by direct reference to their wave structure. The fundamental prop erties of systems with relaxation have found a systematic description through the papers of Wen-An Yong; for shock waves, this means a first general theorem on the existence of corresponding profiles. The five articles of this book reflect the above developments.
| Author | : Franz Hindelang |
| Publisher | : |
| Total Pages | : 44 |
| Release | : 1967 |
| Genre | : Carbon dioxide |
| ISBN | : |
The harmonic oscillator rigid-rotator model has been used to calculate the relaxation region behind a shock wave in carbon dioxide. Finite relaxation rates for the three different vibrational modes and two dissociation reactions are included. Models for the coupling between the vibrational relaxation and the dissociation process are based on the assumption that dissociation can proceed from any vibrational level with equal probability. Two different models for the vibrational excitation have been examined. Solutions have been obtained for the interdependent fluid-flow, chemical rate, and vibrational relaxation-rate equations incorporating estimated rate coefficients. Results are presented in the form of flow-field profiles for density, pressure, translational and vibrational temperatures, and species concentrations. The effects of vibrational excitation, vibration-dissociation coupling, and energy exchange between the vibrational modes are investigated. The effect of vibrational relaxation and vibration-dissociation coupling is much stronger in CO2 with three different vibrational modes than in diatomic gases with only a single mode. The results of this study show that the effect of coupled vibrational relaxation and dissociation can sometimes alter the flow-field profiles by a factor of 2 compared to similar calculations without such coupling. For vibrational relaxation the results indicate that the shock-wave profiles depend primarily on the rate at which the translational energy is fed into internal modes and not so strongly on the energy distribution among the modes.
| Author | : Tai-Ping Liu |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 437 |
| Release | : 2021-10-12 |
| Genre | : Education |
| ISBN | : 1470466252 |
This book presents the fundamentals of the shock wave theory. The first part of the book, Chapters 1 through 5, covers the basic elements of the shock wave theory by analyzing the scalar conservation laws. The main focus of the analysis is on the explicit solution behavior. This first part of the book requires only a course in multi-variable calculus, and can be used as a text for an undergraduate topics course. In the second part of the book, Chapters 6 through 9, this general theory is used to study systems of hyperbolic conservation laws. This is a most significant well-posedness theory for weak solutions of quasilinear evolutionary partial differential equations. The final part of the book, Chapters 10 through 14, returns to the original subject of the shock wave theory by focusing on specific physical models. Potentially interesting questions and research directions are also raised in these chapters. The book can serve as an introductory text for advanced undergraduate students and for graduate students in mathematics, engineering, and physical sciences. Each chapter ends with suggestions for further reading and exercises for students.
| Author | : G.I. Kanel' |
| Publisher | : CRC Press |
| Total Pages | : 225 |
| Release | : 2019-04-30 |
| Genre | : Science |
| ISBN | : 1000005275 |
Methods and the latest results of experimental studies of the strength properties, polymorphism and metastable states of materials and substances with extremely short durations of shock-wave action are presented. The author provides a comprehensive and theoretical description of specific features of the dynamics of elastoplastic shock compression waves in relaxing media. The presentation is preceded by a detailed description of the theoretical foundations of the method and a brief discussion of the basic methods of generating and diagnosing shock waves in solids. Key Selling Features: Addresses dynamic elastic-plastic response, spallation, and shock-induced phase transformation. Provides a centralized presentation of topics of interest to the shock physics community Presents new data on the mechanism and basic patterns of sub-microsecond polymorphic transformations and phase transitions. Investigates destruction waves in shock-compressed glasses. Analyzes the behavior of highly hard brittle materials under shock-wave loading and ways to diagnose fracture.
| Author | : Wallace Hayes |
| Publisher | : Elsevier |
| Total Pages | : 479 |
| Release | : 2012-12-02 |
| Genre | : Science |
| ISBN | : 0323147852 |
Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, Volume II presents interpretations of the physical basis of shockwaves and high-temperature hydrodynamic phenomena and gives practical guidance to those who work with these subjects in science and modern technology. This volume contains chapters discussing such topics as the shockwave structure in gases; physical and chemical kinetics in hydrodynamic processes; the radiative phenomena in shock waves and in strong explosions in the air; thermal waves and shockwaves in solids; and self-similar processes in gasdynamics. Physicists, engineers, researchers, and professors and students in the field of the physical sciences will find the book very educational.
