Beyond Perturbation Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Beyond Perturbation book. This book definitely worth reading, it is an incredibly well-written.
Solving nonlinear problems is inherently difficult, and the stronger the nonlinearity, the more intractable solutions become. Analytic approximations often break down as nonlinearity becomes strong, and even perturbation approximations are valid only for problems with weak nonlinearity. This book introduces a powerful new analytic method for nonlinear problems-homotopy analysis-that remains valid even with strong nonlinearity. In Part I, the author starts with a very simple example, then presents the basic ideas, detailed procedures, and the advantages (and limitations) of homotopy analysis. Part II illustrates the application of homotopy analysis to many interesting nonlinear problems. These range from simple bifurcations of a nonlinear boundary-value problem to the Thomas-Fermi atom model, Volterra's population model, Von Karman swirling viscous flow, and nonlinear progressive waves in deep water. Although the homotopy analysis method has been verified in a number of prestigious journals, it has yet to be fully detailed in book form. Written by a pioneer in its development, Beyond Pertubation: Introduction to the Homotopy Analysis Method is your first opportunity to explore the details of this valuable new approach, add it to your analytic toolbox, and perhaps make contributions to some of the questions that remain open.
Solving nonlinear problems is inherently difficult, and the stronger the nonlinearity, the more intractable solutions become. Analytic approximations often break down as nonlinearity becomes strong, and even perturbation approximations are valid only for problems with weak nonlinearity. This book introduces a powerful new analytic method for
The Theory of the Quantum World by David Gross,Marc Henneaux,Alexander Sevrin Pdf
Ever since 1911, the Solvay Conferences have shaped modern physics. The 25th edition held in October 2011 in Brussels and chaired by David Gross continued this tradition and celebrated the first centennial of this illustrious series of conferences. The development and applications of quantum mechanics have always been the main threads in the history of the Solvay Conferences, hence the 25th Solvay conference gathered many of the leading figures working on a wide variety of profound problems in physics where quantum mechanical effects play a central role. The conference addressed some of the most pressing open questions in the field of physics. The proceedings contain the “rapporteur talks” which give a broad overview with unique insights by distinguished and renowned scientists. These lectures cover the seven sessions: “History and Reflections”, “Foundations of Quantum Mechanics and Quantum Computation”, “Control of Quantum Systems”, “Quantum Condensed Matter”, “Particles and Fields”, “Quantum Gravity and String Theory” and it ended with a general discussion attempting to arrive at a synthesis. In the Solvay tradition, the proceedings also include the prepared comments to the rapporteur talks. The discussions among the participants — some of which quite lively and involving dramatically divergent points of view — have been carefully edited and are reproduced in full. Contents:History and Reflections (M Henneaux, J Heilbron and M Gell-Mann)Foundations of Quantum Mechanics and Quantum Computation (A Aspect, A Leggett and J Preskill)Control of Quantum Systems (P Zoller, I Cirac and S Girvin)Quantum Condensed Matter (B Halperin and S Sachdev)Particles and Fields (H Georgi and F Wilczek)Quantum Gravity and String Theory (J Polchinski, J Maldacena and A Guth)General Discussion and Conclusions (D Gross, A Aspect, P Zoller, B Halperin, H Georgi and J Polchinski) Readership: Graduate students and researchers in physics. Keywords:Quantum Physics;Solvay ConferenceKey Features:Presents a broad overview of the role of quantum mechanics in contemporary physicsThe rapporteur talks, given by the leaders in the field, provide a beautiful review of the state of the art in each of the subfields discussedThe discussions — transcribed in full — provide a unique view on the thoughts of some of the most outstanding physicistsReviews: “This book does full justice to the great reputation of the Solvay Conferences. Some of the discussions are on the same topics as in the old days, many are new. It testifies that fundamental physics is still a thriving field of research.” Gerard 't Hooft Nobel Laureate “The 25th Solvay Conference had an ambitious theme: The theory of the quantum world, including foundations of quantum physics, cosmology, particle physics, condensed matter physics, quantum control and quantum simulations. It was exciting to see the strong connections between those different areas, and this excitement has been captured in these proceedings. This book documents that 100 years after the first Solvay Conference in Physics, quantum physics still poses puzzles and reveals surprises.” Wolfgang Ketterle Nobel Laureate “The 25th Solvay Conference of Physics was an extremely exciting event. It joined the tradition started by the original Solvay meetings at the beginning of the 20th century. A comprehensive overview of the status of Quantum Mechanics and its applications was presented by the world experts and the outstanding problems were discussed deeply. It is clear that this meeting will be as important and as influential as the previous Solvay meetings. The proceedings are an insightful reference about the broad range of topics that were discussed. Just like the previous proceedings, this will also be a document of historic significance.” Nathan Seiberg IAS Princeton “This was one of the most interesting meetings I attended in the last few years. I very much enjoyed being updated on current issues in particle physics, cosmology, and quantum gravity — topics that I wouldn't hear about in conferences that I typically attend. Nearly all talks were presented at an accessible level for the non-specialist, and the extended-discussion format was very informative.” David Wineland Nobel Laureate “Highly selected group of physicists, famous or very promising, were invited to assess recent advances and open problems.” RECENSIONI
Geometric Singular Perturbation Theory Beyond the Standard Form by Martin Wechselberger Pdf
This volume provides a comprehensive review of multiple-scale dynamical systems. Mathematical models of such multiple-scale systems are considered singular perturbation problems, and this volume focuses on the geometric approach known as Geometric Singular Perturbation Theory (GSPT). It is the first of its kind that introduces the GSPT in a coordinate-independent manner. This is motivated by specific examples of biochemical reaction networks, electronic circuit and mechanic oscillator models and advection-reaction-diffusion models, all with an inherent non-uniform scale splitting, which identifies these examples as singular perturbation problems beyond the standard form. The contents cover a general framework for this GSPT beyond the standard form including canard theory, concrete applications, and instructive qualitative models. It contains many illustrations and key pointers to the existing literature. The target audience are senior undergraduates, graduate students and researchers interested in using the GSPT toolbox in nonlinear science, either from a theoretical or an application point of view. Martin Wechselberger is Professor at the School of Mathematics & Statistics, University of Sydney, Australia. He received the J.D. Crawford Prize in 2017 by the Society for Industrial and Applied Mathematics (SIAM) for achievements in the field of dynamical systems with multiple time-scales.
Weakly Nonlocal Solitary Waves and Beyond-All-Orders Asymptotics by John P. Boyd Pdf
This is the first thorough examination of weakly nonlocal solitary waves, which are just as important in applications as their classical counterparts. The book describes a class of waves that radiate away from the core of the disturbance but are nevertheless very long-lived nonlinear disturbances.