Author : Jeffrey Groah
Publisher : Springer Science & Business Media
Page : 157 pages
File Size : 37,7 MB
Release : 2007-04-03
Category : Mathematics
ISBN : 0387446028
This monograph presents a self contained mathematical treatment of the initial value problem for shock wave solutions of the Einstein equations in General Relativity. It has a clearly outlined goal: proving a certain local existence theorem. Concluding remarks are added and commentary is provided throughout. The author is a well regarded expert in this area.
Author : Jeffrey Groah
Publisher : Springer
Page : 0 pages
File Size : 40,48 MB
Release : 2006-11-30
Category : Mathematics
ISBN : 9780387350738
This monograph presents a self contained mathematical treatment of the initial value problem for shock wave solutions of the Einstein equations in General Relativity. It has a clearly outlined goal: proving a certain local existence theorem. Concluding remarks are added and commentary is provided throughout. The author is a well regarded expert in this area.
Author : Moritz Andreas Reintjes
Publisher :
Page : pages
File Size : 44,71 MB
Release : 2011
Category :
ISBN : 9781267240712
We show that the regularity of the gravitational metric tensor cannot be lifted from C(0,1) to C(1,1) by any C(1,1) coordinate transformation in a neighborhood of a point of shock wave interaction in General Relativity, without forcing the determinant of the metric tensor to vanish at the point of interaction. This is in contrast to Israel's Theorem which states that such coordinate transformations always exist in a neighborhood of a point on a smooth single shock surface. The results thus imply that points of shock wave interaction represent a new kind of singularity in spacetime, singularities that make perfectly good sense physically, that can form from the evolution of smooth initial data, but at which the spacetime is not locally Minkowskian under any coordinate transformation. In particular, at such singularities, delta function sources in the second derivatives of the gravitational metric tensor exist in all coordinate systems, but due to cancelation, the curvature tensor remains uniformly bounded.
Author :
Publisher :
Page : 846 pages
File Size : 30,44 MB
Release : 2001
Category : Shock waves
ISBN :
Author : Konstantinos Kontis
Publisher : Springer
Page : 408 pages
File Size : 46,35 MB
Release : 2018-03-28
Category : Technology & Engineering
ISBN : 3319731807
This edited monograph contains the proceedings of the International Shock Interaction Symposium, which emerged as an heir to both the Mach Reflection and Shock Vortex Interaction Symposia. These scientific biannual meetings provide an ideal platform to expose new developments and discuss recent challenges in the field of shock wave interaction phenomena. The goal of the symposia is to offer a forum for international interaction between young and established scientists in the field of shock and blast wave interaction phenomena. The target audience of this book comprises primarily researchers and experts in the field of shock waves, but the book may also be beneficial for young scientists and graduate students alike.
Author : Heinrich Freistühler
Publisher : Springer Science & Business Media
Page : 527 pages
File Size : 24,53 MB
Release : 2012-12-06
Category : 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 : R. S. Srivastava
Publisher : Springer Science & Business Media
Page : 329 pages
File Size : 10,53 MB
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9401110867
One of the great twentieth-century achievements in the mechanics of fluids was the full elucidation of the physics of shock waves and the later comprehensive development of understanding of how shock waves propagate (i) through otherwise undisturbed fluid and (ii) in interaction either with solid bodies or with independently generated fluid flows. The interaction problems (ii) were soon found to raise some very special difficulties (beginning with the common formation of "Mach stems" in shock-wave reflection) yet they also turned out to possess enormous scientific interest as well as being highly important in practical applications. For all these reasons the appearance of this book on "Interaction of Shock Waves" by one of the world's major contributors to knowledge in that field is most particularly to be welcomed. It covers all those approaches to the subject which have been found fruitful, and most satisfactorily goes into comprehensive detail about each. At last the important achievements of the leading research workers, experimental as well as theoretical, on shockwave interaction problems are brought together in a single convenient and well written volume. I warmly congratulate the author and the publisher on having performed, for the benefit of everyone interested in the mechanics of fluids, this immensely valuable service.
Author : André Balogh
Publisher : Springer Science & Business Media
Page : 503 pages
File Size : 41,66 MB
Release : 2013-01-04
Category : Science
ISBN : 1461460999
The present book provides a contemporary systematic treatment of shock waves in high-temperature collisionless plasmas as are encountered in near Earth space and in Astrophysics. It consists of two parts. Part I develops the complete theory of shocks in dilute hot plasmas under the assumption of absence of collisions among the charged particles when the interaction is mediated solely by the self-consistent electromagnetic fields. Such shocks are naturally magnetised implying that the magnetic field plays an important role in their evolution and dynamics. This part treats subcritical shocks which dissipate flow energy by generating anomalous resistance or viscosity. The main emphasis is, however, on super-critical shocks where the anomalous dissipation is insufficient to retard the upstream flow. These shocks, depending on the direction of the upstream magnetic field, are distinguished as quasi-perpendicular and quasi-parallel shocks which exhibit different behaviours, reflecting particles back upstream and generating high electromagnetic wave intensities. Particle acceleration and turbulence at such shocks become possible and important. Part II treats planetary bow shocks and the famous Heliospheric Termination shock as examples of two applications of the theory developed in part I.
Author : Kazuyoshi Takayama
Publisher : Springer Nature
Page : 237 pages
File Size : 21,42 MB
Release : 2022-06-07
Category : Science
ISBN : 303090735X
The book contains 12 chapters written by well-known shock wave researchers from seven different countries. Each researcher provides a brief description of his main research interests and results, thereby providing the readers with an excellent view of shock wave research conducted in the past fifty years. It also provides hints as to what still needs further investigation. It will be an excellent guide for young researchers entering the field of shock wave phenomena. Among the described investigations are the following topics: Blast wave interaction with a body when the body is in the area of interference of two blast waves moving in different directions; equation of state for water based on the shock Hugoniot data; Mach waves occurring over a backward facing edge in supersonic flow; shock waves in dusty gas; shock wave interaction with various bodies; three shock interactions.
Author : Christopher E. Glass
Publisher :
Page : 28 pages
File Size : 30,84 MB
Release : 1999
Category : Fluid dynamics
ISBN :
CFD numerical simulations of low-density shock-wave interactions for an incident shock impinging on a cylinder have been performed. Flow-field density gradient and surface pressure and heating define the type of interference pattern and corresponding perturbations. The maximum pressure and heat transfer level and location of various interaction types are presented. A time-accurate solution of the Type IV interference is employed to demonstrate the establishment and the steadiness of the low-density flow interaction.
