Two examples of ray theories are the geometrical optics theory of light and semi-classical quantum mechanics. When applicable, ray theory is extremely powerful and it often provide surprisingly accurate quantitative results.

Author: Ferrucio Colombini

Publisher: Springer Science & Business Media

ISBN: 9781461220145

Category: Mathematics

Page: 366

View: 553

This book contains fourteen research papers which are expanded versions of conferences given at a meeting held in September 1996 in Cortona, Italy. The topics include blowup questions for quasilinear equations in two dimensions, time decay of waves in LP, uniqueness results for systems of conservation laws in one dimension, concentra tion effects for critical nonlinear wave equations, diffraction of nonlin ear waves, propagation of singularities in scattering theory, caustics for semi-linear oscillations. Other topics linked to microlocal analysis are Sobolev embedding theorems in Weyl-Hormander calculus, local solv ability for pseudodifferential equations, hypoellipticity for highly degen erate operators. The book also contains a result on uniqueness for the Cauchy problem under partial analyticity assumptions and an article on the regularity of solutions for characteristic initial-boundary value problems. On each topic listed above, one will find new results as well as a description of the state of the art. Various methods related to nonlinear geometrical optics are a transversal theme of several articles. Pseu dodifferential techniques are used to tackle classical PDE problems like Cauchy uniqueness. We are pleased to thank the speakers for their contributions to the meeting: Serge Alinhac, Mike Beals, Alberto Bressan, Jean-Yves Chemin, Christophe Cheverry, Daniele Del Santo, Nils Dencker, Patrick Gerard, Lars Hormander, John Hunter, Richard Melrose, Guy Metivier, Yoshinori Morimoto, and Tatsuo Nishitani. The meeting was made possible in part by the financial support of a European commission pro gram, "Human capital and mobility CHRX-CT94-044."

This volume contains 14 research papers, which cover various topics, including blowup questions for quasilinear equations in 2-D, uniqueness results for systems of conservation laws in 1-D, conservation effects for critical nonlinear wave ...

Author: Ferruccio Colombini

Publisher: Springer Science & Business Media

ISBN: 0817639586

Category: Mathematics

Page: 404

View: 398

This volume contains 14 research papers, which cover various topics, including blowup questions for quasilinear equations in 2-D, uniqueness results for systems of conservation laws in 1-D, conservation effects for critical nonlinear wave equations, diffraction of nonlinear waves, propagation of singularities in scattering theory, and caustics for semilinear oscillations. Other topics linked to microlocal analysis which are discussed are Sobolev spaces in Weyl-Hormander calculus, local solvability for pseudodifferential equations, and hypoellipticity for highly degenerate operators. A result for the Cauchy problem under partial analyticity assumptions and an article on the regularity of solutions for the characteristic initial boundary value problem are also included. Most of the papers contain detailed proofs which are accessible to graduate students and active researchers in connected areas

Bubbles, Scans and Geometric Flows Paul Baird, Ahmad El Soufi, Ali Fardoun, Rachid Regbaoui ... F. / Lerner , N. ( Eds . ) Geometrical Optics and Related Topics ( 1997 ) ISBN 0-8176-3958-6 PNLDE 31 : Cherkaev , A. / Kohn , R. ( Eds ...

Author: Paul Baird

Publisher: Springer Science & Business Media

ISBN: 3764324325

Category: Mathematics

Page: 176

View: 361

This volume has grown from a conference entitled Harmonic Maps, Minimal Sur faces and Geometric Flows which was held at the Universite de Bretagne Occi dentale from July 7th-12th, 2002, in the town of Brest in Brittany, France. We welcomed many distinguished mathematicians from around the world and a dy namic meeting took place, with many fruitful exchanges of ideas. In order to produce a work that would have lasting value to the mathematical community, the organisers decided to invite a small number of participants to write in-depth articles around a common theme. These articles provide a balance between introductory surveys and ones that present the newest results that lie at the frontiers of research. We thank these mathematicians, all experts in their field, for their contributions. Such meetings depend on the support of national organisations and the local community and we would like to thank the following: the Ministere de l'Education Nationale, Ministere des Affaires Etrangeres, Centre National de Recherche Sci en tifique (CNRS), Conseil Regional de Bretagne, Conseil General du Finistere, Com munaute Urbaine de Brest, Universite de Bretagne Occidentale (UBO), Faculte des Sciences de l'UBO, Laboratoire de Mathematiques de l'UBO and the Departement de Mathematiques de l'UBO. Their support was generous and ensured the success of the meeting. We would also like to thank the members of the scientific committee for their advice and for their participation in the conception and composition of this volume: Pierre Berard, Jean-Pierre Bourguignon, Frederic Helein, Seiki Nishikawa and Franz Pedit.

L. HöRMANDER, On the uniqueness of the Cauchy problem under partial analyticity assumptions, in Geometrical Optics and Related Topics, F. Colombini and N. Lerner (eds.), Birkhäuser, 1997. M.A, HORN, Implications of sharp trace ...

Author: Chrisopher B. Croke

Publisher: Springer Science & Business Media

ISBN: 9781468493757

Category: Mathematics

Page: 330

View: 448

This IMA Volume in Mathematics and its Applications GEOMETRIC METHODS IN INVERSE PROBLEMS AND PDE CONTROL contains a selection of articles presented at 2001 IMA Summer Program with the same title. We would like to thank Christopher B. Croke (University of Penn sylva nia), Irena Lasiecka (University of Virginia), Gunther Uhlmann (University of Washington), and Michael S. Vogelius (Rutgers University) for their ex cellent work as organizers of the two-week summer workshop and for editing the volume. We also take this opportunity to thank the National Science Founda tion for their support of the IMA. Series Editors Douglas N. Arnold, Director of the IMA Fadil Santosa, Deputy Director of the IMA v PREFACE This volume contains a selected number of articles based on lectures delivered at the IMA 2001 Summer Program on "Geometric Methods in Inverse Problems and PDE Control. " The focus of this program was some common techniques used in the study of inverse coefficient problems and control problems for partial differential equations, with particular emphasis on their strong relation to fundamental problems of geometry. Inverse coef ficient problems for partial differential equations arise in many application areas, for instance in medical imaging, nondestructive testing, and geophys ical prospecting. Control problems involving partial differential equations may arise from the need to optimize a given performance criterion, e. g. , to dampen out undesirable vibrations of a structure , or more generally, to obtain a prescribed behaviour of the dynamics.

This is the essence of the phenomena discovered in [14]; one of the problems we have investigated is to make explicit ... We established the following preliminary result, suggested by an analogy with geometrical optics, and proved by ...

Author: Robert Everist Greene

Publisher: American Mathematical Soc.

ISBN: 9780821814956

Category: Mathematics

Page: 655

View: 443

The second of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1). Among the subjects of Part 2 are gauge theory, symplectic geometry, complex ge

The geometrical optics description of amplitude fluctuations is primarily of historical interest and one is referred to ... Problems are included at the end of each chapter to develop additional insights and to explore related topics.

Author: Albert D. Wheelon

Publisher: Cambridge University Press

ISBN: 9781139430531

Category: Science

Page: 455

View: 210

Electromagnetic Scintillation describes the phase and amplitude fluctuations imposed on signals that travel through the atmosphere. The volumes that make up Electromagnetic Scintillation will provide a modern reference and comprehensive tutorial, treating both optical and microwave propagation and integrating measurements and predictions at each step of the development. This first volume deals with phase and angle-of-arrival measurement errors, accurately described by geometrical optics. It will be followed by a further volume examining weak scattering. In this book, measured properties of tropospheric and ionospheric irregularities are reviewed first. Electromagnetic fluctuations induced by these irregularities are then estimated for a wide range of applications. The book will be of interest to those working in the resolution of astronomical interferometers and large single-aperture telescopes, as well as synthetic aperture radars and laser pointing/tracking systems. It is also directly relevant to those working in laser metrology, GPS location accuracy, and terrestrial and satellite communications.

Author: I︠U︡riĭ Aleksandrovich Kravt︠s︡ovPublish On: 1990-09-10

( By these we mean books either dealing with physical problems [ 1.24-30 ] or discussing generalizations of the ray method [ 1.21,31 ] ; the relevant mathematical fundamentals were presented in ( 1.2 , 18 , 19,32 ] ) .

Author: I︠U︡riĭ Aleksandrovich Kravt︠s︡ov

Publisher: Springer

ISBN: UOM:39015019005324

Category: Science

Page: 338

View: 164

This monograph is concerned with the fundamentals of up-to-date geo metrical optics treated as an approximate method of wave theory. Geometrical optics has changed dramatically over the last two decades. Primarily, it has acquired a number of novel disciplines: space-time geo metrical optics, the quasi-isotropic approximation, the modern theory of caustics related to catastrophe theory, and perturbation techniques for rays, to name only a few. Another acquisition is the reliable boundaries of appli cability for geometrical optics, based upon the concept of the Fresnel volume for a ray. These recent additions to the field are the focus of dis cussion in the book. We did not attempt to separate study-oriented and illustrative material from that intended for professionals, but rather we spread it throughout the text to facilitate for the reader the mastering of this attractive, intuitively appealing and efficient ray method. In preparing the manuscript we used a set of lecture notes devised for All-Union Schools on Diffraction and Wave Propagation, published in Rus sian. Sections 2.1-4,6 and 10 result from joint efforts of both authors. The other material of the book we wrote separately. I contributed Sects. 2.5,9 and 3.17 and Chap.4; Yu.l. Orlov prepared the rest. Unfortunately, he could not take part in the preparation of the English edition, as he died in 1982 at the age of 41, on the verge of what would have been great achieve ments considering his strong and original talent.

Since, tosome extend, the behaviour of charged beams in the guiding structures shares analogies with geometrical optics, all the complex of problems related to charged beam transport is commonly referred to as charged beam optics.

Author: G Dattoli

Publisher: World Scientific

ISBN: 9789814506373

Category: Science

Page: 660

View: 996

Contents:Electron Beam OpticsSynchrotron Radiation: A Short DescriptionSynchrotron Radiation: Emission in Undulator MagnetsAccelerators with Radiative DumpingFree Electron Laser: An IntroductionFEL Pendulum EquationUndulator FEL DynamicsFEL Integral EquationMiscellaneous Considerations on the FEL Gain and the High-Gain LimitA Qualitative Description of Storage-Ring FEL Dynamics and Longitudinal Mode Coupling Readership: Laser physicists. keywords:Free Electron Laser;Laser;Linac;Microtron;Storage Ring;Synchrotron Radiation;Undulators;Wigglers;Bending Magnets;Coherent Radiation Sources;Beam Optics;Colson Equation;Electron Beam Transport;FEL Pendulum Equation;Gain Curve;High Gain Regime;Saturation;Small Gain Regime;Transport Channel;Magnetic Undulator

Author: AMS-IMS-SIAM Joint Summer Research Conference on Differential Geometric Methods in the Control of Partial Differential EquationsPublish On: 2000

L. Hörmander, On the uniqueness of the Cauchy problem under partial analyticity assumptions, in “Geometrical Optics and Related Topics” (F. Colombini and N. Lerner, Eds.), Birkhäuser, Boston, 1997. V. Isakov, Inverse Problem for Partial ...

Author: AMS-IMS-SIAM Joint Summer Research Conference on Differential Geometric Methods in the Control of Partial Differential Equations

Publisher: American Mathematical Soc.

ISBN: 9780821819272

Category: Mathematics

Page: 406

View: 985

This volume contains selected papers that were presented at the AMS-IMS-SIAM Joint Summer Research Conference on ""Differential Geometric Methods in the Control of Partial Differential Equations"", which was held at the University of Colorado in Boulder in June 1999. The aim of the conference was to explore the infusion of differential-geometric methods into the analysis of control theory of partial differential equations, particularly in the challenging case of variable coefficients, where the physical characteristics of the medium vary from point to point. While a mutually profitable link has been long established, for at least 30 years, between differential geometry and control of ordinary differential equations, a comparable relationship between differential geometry and control of partial differential equations (PDEs) is a new and promising topic.Very recent research, just prior to the Colorado conference, supported the expectation that differential geometric methods, when brought to bear on classes of PDE modelling and control problems with variable coefficients, will yield significant mathematical advances. The papers included in this volume - written by specialists in PDEs and control of PDEs as well as by geometers - collectively support the claim that the aims of the conference are being fulfilled. In particular, they endorse the belief that both subjects - differential geometry and control of PDEs - have much to gain by closer interaction with one another. Consequently, further research activities in this area are bound to grow.

This text features a careful treatment of flow lines and algebraic invariants in contact form geometry, a vast area of research connected to symplectic field theory, pseudo-holomorphic curves, and Gromov-Witten invariants (contact homology). In particular, it develops a novel algebraic tool in this field: rooted in the concept of critical points at infinity, the new algebraic invariants defined here are useful in the investigation of contact structures and Reeb vector fields. The book opens with a review of prior results and then proceeds through an examination of variational problems, non-Fredholm behavior, true and false critical points at infinity, and topological implications. An increasing convergence with regular and singular Yamabe-type problems is discussed, and the intersection between contact form and Riemannian geometry is emphasized. Rich in open problems and full, detailed proofs, this work lays the foundation for new avenues of study in contact form geometry and will benefit graduate students and researchers.