Mathematical Methods in Physics

Mathematical Methods in Physics PDF

Author: Philippe Blanchard

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 469

ISBN-13: 1461200490

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Physics has long been regarded as a wellspring of mathematical problems. Mathematical Methods in Physics is a self-contained presentation, driven by historic motivations, excellent examples, detailed proofs, and a focus on those parts of mathematics that are needed in more ambitious courses on quantum mechanics and classical and quantum field theory. Aimed primarily at a broad community of graduate students in mathematics, mathematical physics, physics and engineering, as well as researchers in these disciplines.

Variational Methods in Mathematical Physics

Variational Methods in Mathematical Physics PDF

Author: Philippe Blanchard

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 419

ISBN-13: 3642826989

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The first edition (in German) had the prevailing character of a textbook owing to the choice of material and the manner of its presentation. This second (translated, revised, and extended) edition, however, includes in its new parts considerably more recent and advanced results and thus goes partially beyond the textbook level. We should emphasize here that the primary intentions of this book are to provide (so far as possible given the restrictions of space) a selfcontained presentation of some modern developments in the direct methods of the cal culus of variations in applied mathematics and mathematical physics from a unified point of view and to link it to the traditional approach. These modern developments are, according to our background and interests: (i) Thomas-Fermi theory and related theories, and (ii) global systems of semilinear elliptic partial-differential equations and the existence of weak solutions and their regularity. Although the direct method in the calculus of variations can naturally be considered part of nonlinear functional analysis, we have not tried to present our material in this way. Some recent books on nonlinear functional analysis in this spirit are those by K. Deimling (Nonlinear Functional Analysis, Springer, Berlin Heidelberg 1985) and E. Zeidler (Nonlinear Functional Analysis and Its Applications, Vols. 1-4; Springer, New York 1986-1990).

Mathematical Physics 2000

Mathematical Physics 2000 PDF

Author: Athanassios Fokas

Publisher: World Scientific

Published: 2000-05-05

Total Pages: 336

ISBN-13: 1783261714

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Mathematical physics has made enormous strides over the past few decades, with the emergence of many new disciplines and with revolutionary advances in old disciplines. One of the especially interesting features is the link between developments in mathematical physics and in pure mathematics. Many of the exciting advances in mathematics owe their origin to mathematical physics — superstring theory, for example, has led to remarkable progress in geometry — while very pure mathematics, such as number theory, has found unexpected applications.The beginning of a new millennium is an appropriate time to survey the present state of the field and look forward to likely advances in the future. In this book, leading experts give personal views on their subjects and on the wider field of mathematical physics. The topics covered range widely over the whole field, from quantum field theory to turbulence, from the classical three-body problem to non-equilibrium statistical mechanics.

Variational Methods

Variational Methods PDF

Author: Michael Struwe

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 288

ISBN-13: 3662032120

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Hilbert's talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateau's problem by Douglas and Radò. The book gives a concise introduction to variational methods and presents an overview of areas of current research in this field. This new edition has been substantially enlarged, a new chapter on the Yamabe problem has been added and the references have been updated. All topics are illustrated by carefully chosen examples, representing the current state of the art in their field.

Variational Methods For Strongly Indefinite Problems

Variational Methods For Strongly Indefinite Problems PDF

Author: Yanheng Ding

Publisher: World Scientific

Published: 2007-07-30

Total Pages: 177

ISBN-13: 9814474509

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This unique book focuses on critical point theory for strongly indefinite functionals in order to deal with nonlinear variational problems in areas such as physics, mechanics and economics. With the original ingredients of Lipschitz partitions of unity of gage spaces (nonmetrizable spaces), Lipschitz normality, and sufficient conditions for the normality, as well as existence-uniqueness of flow of ODE on gage spaces, the book presents for the first time a deformation theory in locally convex topological vector spaces. It also offers satisfying variational settings for homoclinic-type solutions to Hamiltonian systems, Schrödinger equations, Dirac equations and diffusion systems, and describes recent developments in studying these problems. The concepts and methods used open up new topics worthy of in-depth exploration, and link the subject with other branches of mathematics, such as topology and geometry, providing a perspective for further studies in these areas. The analytical framework can be used to handle more infinite-dimensional Hamiltonian systems.

Nuclear Reactor Physics

Nuclear Reactor Physics PDF

Author: Weston M. Stacey

Publisher: John Wiley & Sons

Published: 2018-02-07

Total Pages: 766

ISBN-13: 352781230X

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The third, revised edition of this popular textbook and reference, which has been translated into Russian and Chinese, expands the comprehensive and balanced coverage of nuclear reactor physics to include recent advances in understanding of this topic. The first part of the book covers basic reactor physics, including, but not limited to nuclear reaction data, neutron diffusion theory, reactor criticality and dynamics, neutron energy distribution, fuel burnup, reactor types and reactor safety. The second part then deals with such physically and mathematically more advanced topics as neutron transport theory, neutron slowing down, resonance absorption, neutron thermalization, perturbation and variational methods, homogenization, nodal and synthesis methods, and space-time neutron dynamics. For ease of reference, the detailed appendices contain nuclear data, useful mathematical formulas, an overview of special functions as well as introductions to matrix algebra and Laplace transforms. With its focus on conveying the in-depth knowledge needed by advanced student and professional nuclear engineers, this text is ideal for use in numerous courses and for self-study by professionals in basic nuclear reactor physics, advanced nuclear reactor physics, neutron transport theory, nuclear reactor dynamics and stability, nuclear reactor fuel cycle physics and other important topics in the field of nuclear reactor physics.

Variational Principles of Continuum Mechanics

Variational Principles of Continuum Mechanics PDF

Author: Victor Berdichevsky

Publisher: Springer Science & Business Media

Published: 2009-09-18

Total Pages: 590

ISBN-13: 354088467X

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Thereareabout500booksonvariationalprinciples. Theyareconcernedmostlywith the mathematical aspects of the topic. The major goal of this book is to discuss the physical origin of the variational principles and the intrinsic interrelations between them. For example, the Gibbs principles appear not as the rst principles of the theory of thermodynamic equilibrium but as a consequence of the Einstein formula for thermodynamic uctuations. The mathematical issues are considered as long as they shed light on the physical outcomes and/or provide a useful technique for direct study of variational problems. Thebookisacompletelyrewrittenversionoftheauthor’smonographVariational Principles of Continuum Mechanics which appeared in Russian in 1983. I have been postponing the English translation because I wished to include the variational pr- ciples of irreversible processes in the new edition. Reaching an understanding of this subject took longer than I expected. In its nal form, this book covers all aspects of the story. The part concerned with irreversible processes is tiny, but it determines the accents put on all the results presented. The other new issues included in the book are: entropy of microstructure, variational principles of vortex line dynamics, va- ational principles and integration in functional spaces, some stochastic variational problems, variational principle for probability densities of local elds in composites with random structure, variational theory of turbulence; these topics have not been covered previously in monographic literature.

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