The Weierstrass Elliptic Function And Applications In Classical And Quantum Mechanics
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The Weierstrass Elliptic Function And Applications In Classical And Quantum Mechanics
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Author : Georgios Pastras
language : en
Publisher: Springer Nature
Release Date : 2020-10-31
The Weierstrass Elliptic Function And Applications In Classical And Quantum Mechanics written by Georgios Pastras and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-31 with Science categories.
The field of elliptic functions, apart from its own mathematical beauty, has many applications in physics in a variety of topics, such as string theory or integrable systems. This book, which focuses on the Weierstrass theory of elliptic functions, aims at senior undergraduate and junior graduate students in physics or applied mathematics. Supplemented by problems and solutions, it provides a fast, but thorough introduction to the mathematical theory and presents some important applications in classical and quantum mechanics. Elementary applications, such as the simple pendulum, help the readers develop physical intuition on the behavior of the Weierstrass elliptic and related functions, whereas more Interesting and advanced examples, like the n=1 Lamé problem-a periodic potential with an exactly solvable band structure, are also presented.
Gravitational Optics In Curved Spacetimes Contrasting Newtonian And Relativistic Perspectives
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Author : Bernard Lavenda
language : en
Publisher: Deep Science Publishing
Release Date : 2025-05-26
Gravitational Optics In Curved Spacetimes Contrasting Newtonian And Relativistic Perspectives written by Bernard Lavenda and has been published by Deep Science Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-26 with Science categories.
This book offers a critical appraisal of where we stand on a formulation of a theory of gravitation. Newtonian theory is reformulated in the general form of conics and their relation to aberrancy. Conics are to planetary orbits what Cassini ovals are to binaries. The transition from a Bernoulli lemniscate to Cassini ovals is discussed in terms the instability criteria of Roche lobes, and their fission. When the second derivative of the curve is no longer constant, the Newton inverse law does not apply and new central forces appear which can be derived from the radius of aberrancy, just as the inverse-square law follows from the radius of curvature. The logarithmic spiral becomes periodic in velocity space, and a new Hubble law appears between acceleration and velocity. This has the effect of decreasing the decay rate of accelerations so that they can explain the flat rotational curvatures oberserved in spiral galaxies. Numerical relativity has reduced its conception of general relativity to a Le Sage- type theory thereby making it refutable.
Introduction To Lagrangian Mechanics An 2nd Edition
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Author : Alain J Brizard
language : en
Publisher: World Scientific Publishing Company
Release Date : 2014-11-28
Introduction To Lagrangian Mechanics An 2nd Edition written by Alain J Brizard and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-28 with Science categories.
An Introduction to Lagrangian Mechanics begins with a proper historical perspective on the Lagrangian method by presenting Fermat's Principle of Least Time (as an introduction to the Calculus of Variations) as well as the principles of Maupertuis, Jacobi, and d'Alembert that preceded Hamilton's formulation of the Principle of Least Action, from which the Euler-Lagrange equations of motion are derived. Other additional topics not traditionally presented in undergraduate textbooks include the treatment of constraint forces in Lagrangian Mechanics; Routh's procedure for Lagrangian systems with symmetries; the art of numerical analysis for physical systems; variational formulations for several continuous Lagrangian systems; an introduction to elliptic functions with applications in Classical Mechanics; and Noncanonical Hamiltonian Mechanics and perturbation theory.The Second Edition includes a larger selection of examples and problems (with hints) in each chapter and continues the strong emphasis of the First Edition on the development and application of mathematical methods (mostly calculus) to the solution of problems in Classical Mechanics.New material has been added to most chapters. For example, a new derivation of the Noether theorem for discrete Lagrangian systems is given and a modified Rutherford scattering problem is solved exactly to show that the total scattering cross section associated with a confined potential (i.e., which vanishes beyond a certain radius) yields the hard-sphere result. The Frenet-Serret formulas for the Coriolis-corrected projectile motion are presented, where the Frenet-Serret torsion is shown to be directly related to the Coriolis deflection, and a new treatment of the sleeping-top problem is given.
Nist Handbook Of Mathematical Functions Hardback And Cd Rom
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Author : Frank W. J. Olver
language : en
Publisher: Cambridge University Press
Release Date : 2010-05-17
Nist Handbook Of Mathematical Functions Hardback And Cd Rom written by Frank W. J. Olver and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-17 with Mathematics categories.
The new standard reference on mathematical functions, replacing the classic but outdated handbook from Abramowitz and Stegun. Includes PDF version.
The Maths Book
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Author : DK
language : en
Publisher: Dorling Kindersley Ltd
Release Date : 2019-09-05
The Maths Book written by DK and has been published by Dorling Kindersley Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-05 with Mathematics categories.
Learn about the most important mathematical ideas, theorems, and movements in The Maths Book. Part of the fascinating Big Ideas series, this book tackles tricky topics and themes in a simple and easy to follow format. Learn about Maths in this overview guide to the subject, great for novices looking to find out more and experts wishing to refresh their knowledge alike! The Maths Book brings a fresh and vibrant take on the topic through eye-catching graphics and diagrams to immerse yourself in. This captivating book will broaden your understanding of Maths, with: - More than 85 ideas and events key to the development of mathematics - Packed with facts, charts, timelines and graphs to help explain core concepts - A visual approach to big subjects with striking illustrations and graphics throughout - Easy to follow text makes topics accessible for people at any level of understanding The Maths Book is a captivating introduction to the world's most famous theorems, mathematicians and movements, aimed at adults with an interest in the subject and students wanting to gain more of an overview. Charting the development of maths around the world from Babylon to Bletchley Park, this book explains how maths help us understand everything from patterns in nature to artificial intelligence. Your Maths Questions, Simply Explained What is an imaginary number? Can two parallel lines ever meet? How can maths help us predict the future? This engaging overview explores answers to big questions like these and how they contribute to our understanding of maths. If you thought it was difficult to learn about topics like algebra and statistics, The Maths Book presents key information in an easy to follow layout. Learn about the history of maths, from ancient ideas such as magic squares and the abacus to modern cryptography, fractals, and the final proof of Fermat's Last Theorem. The Big Ideas Series With millions of copies sold worldwide, The Maths Book is part of the award-winning Big Ideas series from DK. The series uses striking graphics along with engaging writing, making big topics easy to understand. r to understand.
Classical And Quantum Nonlinear Integrable Systems
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Author : A Kundu
language : en
Publisher: CRC Press
Release Date : 2019-04-23
Classical And Quantum Nonlinear Integrable Systems written by A Kundu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-23 with Science categories.
Covering both classical and quantum models, nonlinear integrable systems are of considerable theoretical and practical interest, with applications over a wide range of topics, including water waves, pin models, nonlinear optics, correlated electron systems, plasma physics, and reaction-diffusion processes. Comprising one part on classical theories
Nonlinear Dynamics
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Author :
language : en
Publisher:
Release Date : 2005
Nonlinear Dynamics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Chaotic behavior in systems categories.
Journal Of Research Of The National Institute Of Standards And Technology
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Author :
language : en
Publisher:
Release Date : 2001
Journal Of Research Of The National Institute Of Standards And Technology written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Measurement categories.
Reports NIST research and development in the physical and engineering sciences in which the Institute is active. These include physics, chemistry, engineering, mathematics, and computer sciences. Emphasis on measurement methodology and the basic technology underlying standardization.
Low Dimensional Applications Of Quantum Field Theory
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Author : L. Baulieu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Low Dimensional Applications Of Quantum Field Theory written by L. Baulieu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Science categories.
The Cargese Summer School "Low Dimensional Applications of Quantum Field Theory" was held in July 1995. The School was dedicated to the memory of Claude Itzykson. This session focused on the recent progress in quantum field theory in two dimen sions with a particular emphasis on integrable models and applications of quantum field theory to condensed matter physics. A large fraction of the school was also devoted to a detailed review of the exciting developments in four dimensional super symmetric Yang-Mills theory. The diversity of the topics presented constitute, in our opinion, one of the most attractive features of these proceedings. Some contributions constitute a very thor ough introduction to their subject matter and should be helpful to advanced students in the field while others present entirely new research, not previously published, and should be of considerable interest to the specialist. There were in depth introductory lectures on the application of conformal field theory techniques to disordered systems, on the quantum Hall effect, on quantum in tegrable systems, on the thermodynamic Bethe Ansatz and on the new developments in supersymmetric gauges theories. The computation of the three point function of the Liouville model using conformal bootstrap methods was presented in detail.
A Nonlinear Progress To Modern Soliton Theory
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Author : Colin Rogers
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2022-12-06
A Nonlinear Progress To Modern Soliton Theory written by Colin Rogers and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-06 with Mathematics categories.
This book provides a historical account of the discovery in 1834 of a remarkable singular wave that was ultimately to lead to the development of modern soliton theory with its diverse physical applications. In terms of associated geometry, the classical work of Bäcklund and Bianchi and its consequences is recounted, notably with regard to nonlinear superposition principles, which later were shown to be generic to soliton systems and which provide the analytic description of complex multi-soliton interaction. Whereas the applications of modern soliton in certain areas of physics are well-documented, deep connections between soliton theory and nonlinear continuum mechanics have had a separate development. This book describes wide applications in such disparate areas as elastostatics, elastodynamics, superelasticity, shell theory, magnetohydrostatics and magnetohydrodynamics, and will appeal to research scientists and advanced students with an interest in integrable systems in nonlinear physics or continuum mechanics.