Singularities in Fluids, Plasmas and Optics, Russel Caflisch; George C. Papanicolaou

Автор: Vladimir Arnold
Название: Singularities of Caustics and Wave Fronts
ISBN: 0792310381 ISBN-13(EAN): 9780792310389
Издательство: Springer
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Описание: One service mathematics has rendered the 'Et moi, ... ) si j'avait su comment en revenir, human race. It has put common sense back je n'y serais point aile.' Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. ErieT. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com- puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Автор: Zi Cai Li
Название: Combined Methods for Elliptic Equations with Singularities, Interfaces and Infinities
ISBN: 1461333407 ISBN-13(EAN): 9781461333401
Издательство: Springer
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Описание: The combined methods have many advantages over single methods: high accuracy of solutions, less CPU time, less computer storage, easy coupling with singularities as well as the complicated boundary conditions. Since coupling techniques are essential to combinations, various matching strategies among different methods are carefully discussed.

Автор: Iouri Egorov; Bert-Wolfgang Schulze
Название: Pseudo-Differential Operators, Singularities, Applications
ISBN: 3034898207 ISBN-13(EAN): 9783034898201
Издательство: Springer
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Описание: Pseudo-differential operators belong to the most powerful tools in the analysis of partial differential equations. Basic achievements in the early sixties have initiated a completely new understanding of many old and important problems in analy- sis and mathematical physics. The standard calculus of pseudo-differential and Fourier integral operators may today be considered as classical. The development has been continuous since the early days of the first essential applications to ellip- ticity, index theory, parametrices and propagation of singularities for non-elliptic operators, boundary-value problems, and spectral theory. The basic ideas of the calculus go back to Giraud, Calderon, Zygmund, Mikhlin, Agranovich, Dynin, Vishik, Eskin, and Maslov. Subsequent progress was greatly stimulated by the classical works of Kohn, Nirenberg and Hormander. In recent years there developed a new vital interest in the ideas of micro- local analysis in connection with analogous fields of applications over spaces with singularities, e.g. conical points, edges, corners, and higher singularities. The index theory for manifolds with singularities became an enormous challenge for analysists to invent an adequate concept of ellipticity, based on corresponding symbolic structures. Note that index theory was another source of ideas for the later development of the theory of pseudo-differential operators. Let us mention, in particular, the fundamental contributions by Gelfand, Atiyah, Singer, and Bott.

Автор: Martin Golubitsky; David G. Schaeffer
Название: Singularities and Groups in Bifurcation Theory
ISBN: 1461295335 ISBN-13(EAN): 9781461295334
Издательство: Springer
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Описание: This book has been written in a frankly partisian spirit-we believe that singularity theory offers an extremely useful approach to bifurcation prob- lems and we hope to convert the reader to this view.

Название: Shocks, singularities and oscillations in nonlinear optics and fluid mechanics
ISBN: 3319520415 ISBN-13(EAN): 9783319520414
Издательство: Springer
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Описание: The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 14-18, 2015.

Автор: Golubitsky, Schaffer,
Название: Singularities and groups in bifurcation theory
ISBN: 0387966528 ISBN-13(EAN): 9780387966526
Издательство: Springer
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Описание: Preface.- Contents of Vol. I.- Introduction.- Group Theoretic Preliminaries.- Symmetry-Breaking in Steady-State Bifurcation.- Case Study 4: The Planar BГ©nard Problem.- Equivariant Normal Forms.- Equivariant Unfolding Theory.- Case Study 5: The Traction Problem for Mooney-Rivlin Material.- Symmetry-Breaking in Hopf Bifurcation.- Hopf Bifurcation with 0(2) Symmetry.- Further Examples of Hopf Bifurcation with Symmetry.- Mode Interactions.- Mode Interactions with 0(2) Symmetry.- Case Study 6: The Taylor-Couette System.- Bibliography.- Index.

Автор: Lars Garding
Название: Singularities in Linear Wave Propagation
ISBN: 354018001X ISBN-13(EAN): 9783540180012
Издательство: Springer
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Описание: Includes lecture notes stemming from a course given at the Nankai Institute for Mathematics, Tianjin, in 1986 that center on the construction of parametrices for fundamental solutions of hyperbolic differential and pseudodifferential operators.

Автор: David Massey
Название: Le Cycles and Hypersurface Singularities
ISBN: 3540603956 ISBN-13(EAN): 9783540603955
Издательство: Springer
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Описание: This text describes and gives applications of an important new tool in the study of complex analytic hypersurface singularities: the Le cycles of the hypersurface.

Автор: D. Durban; J.R. Pearson
Название: IUTAM Symposium on Non-Linear Singularities in Deformation and Flow
ISBN: 9401059918 ISBN-13(EAN): 9789401059916
Издательство: Springer
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Описание: Proceedings of the IUTAM Symposium held in Haifa, Israel, 17-21 March 1997

Автор: Jeffrey Rauch; Michael Taylor
Название: Singularities and Oscillations
ISBN: 0387982000 ISBN-13(EAN): 9780387982007
Издательство: Springer
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Описание: This volume contains a multiplicity of approaches brought to bear on problems varying from the formation of caustics and the propagation of waves at a boundary, to the examination of viscous boundary layers.

Автор: K. Bajer; H.K. Moffatt
Название: Tubes, Sheets and Singularities in Fluid Dynamics
ISBN: 9401739536 ISBN-13(EAN): 9789401739535
Издательство: Springer
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Описание: Modern experiments and numerical simulations show that the long-known coherent structures in turbulence take the form of elongated vortex tubes and vortex sheets.

Автор: Zi Cai Li
Название: Combined Methods for Elliptic Equations with Singularities, Interfaces and Infinities
ISBN: 0792350847 ISBN-13(EAN): 9780792350842
Издательство: Springer
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Описание: Sets out to answer two important questions: Which numerical methods may be combined together? And how can different numerical methods be matched together? This book presents a number of useful combinations, for instance, the combination of various FEMs, the combinations of FEM-FDM, REM-FEM and RGM-FDM.