Download or read book The Shock Development Problem written by Dēmētrēs Ch Christodulu and published by . This book was released on 2019 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph addresses the problem of the development of shocks in the context of the Eulerian equations of the mechanics of compressible fluids. The mathematical problem is that of an initial-boundary value problem for a nonlinear hyperbolic system of partial differential equations with a free boundary and singular initial conditions. The free boundary is the shock hypersurface and the boundary conditions are jump conditions relative to a prior solution, conditions following from the integral form of the mass, momentum and energy conservation laws. The prior solution is provided by the author's previous work which studies the maximal classical development of smooth initial data. New geometric and analytic methods are introduced to solve the problem. Geometry enters as the acoustical structure, a Lorentzian metric structure defined on the spacetime manifold by the fluid. This acoustical structure interacts with the background spacetime structure. Reformulating the equations as two coupled first order systems, the characteristic system, which is fully nonlinear, and the wave system, which is quasilinear, a complete regularization of the problem is achieved.Geometric methods also arise from the need to treat the free boundary. These methods involve the concepts of bi-variational stress and of variation fields. The main new analytic method arises from the need to handle the singular integrals appearing in the energy identities. Shocks being an ubiquitous phenomenon, occuring also in magnetohydrodynamics, nonlinear elasticity, and the electrodynamics of noninear media, the methods developed in this monograph are likely to be found relevant in these fields as well.
Download or read book Shock Formation in Small Data Solutions to 3D Quasilinear Wave Equations written by Jared Speck and published by American Mathematical Soc.. This book was released on 2016-12-07 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1848 James Challis showed that smooth solutions to the compressible Euler equations can become multivalued, thus signifying the onset of a shock singularity. Today it is known that, for many hyperbolic systems, such singularities often develop. However, most shock-formation results have been proved only in one spatial dimension. Serge Alinhac's groundbreaking work on wave equations in the late 1990s was the first to treat more than one spatial dimension. In 2007, for the compressible Euler equations in vorticity-free regions, Demetrios Christodoulou remarkably sharpened Alinhac's results and gave a complete description of shock formation. In this monograph, Christodoulou's framework is extended to two classes of wave equations in three spatial dimensions. It is shown that if the nonlinear terms fail to satisfy the null condition, then for small data, shocks are the only possible singularities that can develop. Moreover, the author exhibits an open set of small data whose solutions form a shock, and he provides a sharp description of the blow-up. These results yield a sharp converse of the fundamental result of Christodoulou and Klainerman, who showed that small-data solutions are global when the null condition is satisfied. Readers who master the material will have acquired tools on the cutting edge of PDEs, fluid mechanics, hyperbolic conservation laws, wave equations, and geometric analysis.
Download or read book Mathematical Problems of Classical Nonlinear Electromagnetic Theory written by Frederick Bloom and published by CRC Press. This book was released on 2020-11-29 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of some problems of current interest in the realm of classical nonlinear electromagnetic theory.
Download or read book The Mathematics of Shock Reflection Diffraction and von Neumann s Conjectures written by Gui-Qiang G Chen and published by Princeton University Press. This book was released on 2018-02-27 with total page 829 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a survey of recent developments in the analysis of shock reflection-diffraction, a detailed presentation of original mathematical proofs of von Neumann's conjectures for potential flow, and a collection of related results and new techniques in the analysis of partial differential equations (PDEs), as well as a set of fundamental open problems for further development. Shock waves are fundamental in nature. They are governed by the Euler equations or their variants, generally in the form of nonlinear conservation laws—PDEs of divergence form. When a shock hits an obstacle, shock reflection-diffraction configurations take shape. To understand the fundamental issues involved, such as the structure and transition criteria of different configuration patterns, it is essential to establish the global existence, regularity, and structural stability of shock reflection-diffraction solutions. This involves dealing with several core difficulties in the analysis of nonlinear PDEs—mixed type, free boundaries, and corner singularities—that also arise in fundamental problems in diverse areas such as continuum mechanics, differential geometry, mathematical physics, and materials science. Presenting recently developed approaches and techniques, which will be useful for solving problems with similar difficulties, this book opens up new research opportunities.
Download or read book The Shock and Vibration Bulletin written by and published by . This book was released on 1986 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Shock and Vibration Digest written by and published by . This book was released on 1986 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Shock Vibration and Associated Environments written by and published by . This book was released on 1963 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Mathematics of Shock Reflection Diffraction and von Neumann s Conjectures written by Gui-Qiang G Chen and published by Princeton University Press. This book was released on 2018-02-27 with total page 832 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a survey of recent developments in the analysis of shock reflection-diffraction, a detailed presentation of original mathematical proofs of von Neumann's conjectures for potential flow, and a collection of related results and new techniques in the analysis of partial differential equations (PDEs), as well as a set of fundamental open problems for further development. Shock waves are fundamental in nature. They are governed by the Euler equations or their variants, generally in the form of nonlinear conservation laws—PDEs of divergence form. When a shock hits an obstacle, shock reflection-diffraction configurations take shape. To understand the fundamental issues involved, such as the structure and transition criteria of different configuration patterns, it is essential to establish the global existence, regularity, and structural stability of shock reflection-diffraction solutions. This involves dealing with several core difficulties in the analysis of nonlinear PDEs—mixed type, free boundaries, and corner singularities—that also arise in fundamental problems in diverse areas such as continuum mechanics, differential geometry, mathematical physics, and materials science. Presenting recently developed approaches and techniques, which will be useful for solving problems with similar difficulties, this book opens up new research opportunities.
Download or read book Securing Development in an Unstable World written by François Bourguignon and published by World Bank Publications. This book was released on 2006-01-01 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Annual World Bank Conference on Development Economics (ABCDE) brings together the world's finest development thinkers to present their perspectives and ideas. In recent years, a parallel, second conference has been held in Europe with the same goal of expanding the flow of ideas between thinkers, practitioners, and policymakers in the field of international development. This title presents selected papers from the seventh annual ABCDE - Europe meetings, held May 2005 in Amsterdam, the Netherlands.
Download or read book Bureau of Ships Journal written by and published by . This book was released on 1956 with total page 1250 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book National Resources Development Report written by United States. National Resources Planning Board and published by . This book was released on 1942 with total page 1136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Theory of Shocks COVID 19 and Normative Fundamentals for Policy Responses written by Pilipenko, Olga Ivanovna and published by IGI Global. This book was released on 2021-03-18 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The phenomenon of shocks is often mentioned in relation to economic crises but rarely studied. This gap in research has resulted in shocks being poorly understood, with no fundamental explanation of their inciting conditions. It is a system-forming problem that cannot be investigated without dynamic ideas about the economy, but an incomplete understanding of this event leaves economic systems vulnerable to collapse. Theory of Shocks, COVID-19, and Normative Fundamentals for Policy Responses is an essential publication that explores the factors that cause economic shocks and the mechanisms of their implementation. The book serves as a resource for the development of policy-oriented frameworks for achieving and maintaining national and international strategies to properly manage future global shocks. Featuring coverage of a wide range of topics including dialectics, self-evolvement, and structural relationships, this book is ideally designed for economists, executives, managers, entrepreneurs, academicians, students, and researchers in the areas of finance, macroeconomics, economic theory, and risk assessment.
Download or read book High Pressure Shock Compression of Solids VI written by Yasuyuki Horie and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Both experimental and theoretical investigations make it clear that mesoscale materials, that is, materials at scales intermediate between atomic and bulk matter, do not always behave in ways predicted by conventional theories of shock compression. At these scales, shock waves interact with local material properties and microstructure to produce a hierarchy of dissipative structures such as inelastic deformation fields, randomly distributed lattice defects, and residual stresses. A macroscopically steady planar shock wave is neither plane nor steady at the mesoscale. The chapters in this book examine the assumptions underlying our understanding of shock phenomena and present new measurements, calculations, and theories that challenge these assumptions. They address such questions as: - What are the experimental data on mesoscale effects of shocks, and what are the implications? - Can one formulate new mesoscale theories of shock dynamics? - How would new mesoscale theories affect our understanding of shock-induced phase transitions or fracture? - What new computational models will be needed for investigating mesoscale shocks?
Download or read book Report of NRL Progress written by Naval Research Laboratory (U.S.) and published by . This book was released on 1967 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book ICASE LaRC Workshop on Benchmark Problems in Computational Aeroacoustics CAA written by Jay C. Hardin and published by . This book was released on 1995 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Supply Shock written by Brian Czech and published by New Society Publishers. This book was released on 2013-04-26 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: Politicians, economists, and Wall Street would have us believe that limitless economic expansion is the Holy Grail, and that there is no conflict between growing the economy and protecting the environment. Supply Shock debunks these widely accepted myths and demonstrates that we are in fact navigating the end of the era of economic growth, and that the only sustainable alternative is the development of a steady state economy. Starting with a refreshingly accessible, comprehensive critique of economic growth, the author engages readers in an enormous topic that affects everyone in every country. Publisher's Weekly favorably compared Czech to Carl Sagan for popularizing their difficult subjects; Supply Shock shows why. Czech presents a compelling alternative to growth based on keen scientific, economic, and political insights including: The "trophic theory of money" The overlooked source of technological progress that prevents us from reconciling growth and environmental protection Bold yet practical policies for establishing a steady state economy. Supply Shock leaves no doubt that the biggest idea of the 20th century – economic growth – has become the biggest problem of the 21st. Required reading for anyone concerned about the world our children and grandchildren will inherit, this landmark work lays a solid foundation for a new economic model, perhaps in time for preventing global catastrophes; certainly in time for lessening the damages.
Download or read book Smart Modeling for Engineering Systems written by Igor B. Petrov and published by Springer. This book was released on 2019-01-08 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights the work of several world-class researchers on smart modeling of complex systems. The contributions are grouped into the four main categories listed below. · Numerical schemes construction for the solution of partial differential equations. · Numerical methods in continuum media mechanics problems. · Mathematical modeling in aerodynamics, plasma physics, deformable body mechanics, and geological hydrocarbon exploration. · Mathematical modeling in medical applications. The book offers a valuable resource for theoreticians and application scientists and engineers, as well as postgraduate students, in the fields of computational methods, numerical experiments, parallel algorithms, deformable solid bodies, seismic stability, seismic prospecting, migration, elastic and acoustic wave investigation, gas dynamics, astrophysics, aerodynamics, fluid dynamics, turbulent flows, hypersonic flows, detonation waves, composite materials, fracture mechanics, melting of metals, mathematical economics, medicine, and biology.
