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Classical Mechanics by Christopher W. Kulp; Vasilis PagonisClassical Mechanics: A Computational Approach with Examples using Python and Mathematica provides a unique, contemporary introduction to classical mechanics, with a focus on computational methods. In addition to providing clear and thorough coverage of key topics, this textbook includes integrated instructions and treatments of computation. Full of pedagogy, it contains both analytical and computational example problems within the body of each chapter. The example problems teach readers both analytical methods and how to use computer algebra systems and computer programming to solve problems in classical mechanics. End-of-chapter problems allow students to hone their skills in problem solving with and without the use of a computer. The methods presented in this book can then be used by students when solving problems in other fields both within and outside of physics. It is an ideal textbook for undergraduate students in physics, mathematics, and engineering studying classical mechanics. Features: Gives readers the "big picture" of classical mechanics and the importance of computation in the solution of problems in physics Numerous example problems using both analytical and computational methods, as well as explanations as to how and why specific techniques were used Online resources containing specific example codes to help students learn computational methods and write their own algorithms A solutions manual is available via the Routledge Instructor Hub and extra code is available via the Support Material tab
Dynamics by Pieter Moree (Editor); Anke Pohl (Editor); L'ubomir Snoha (Editor); Tom Ward (Editor)This volume contains the proceedings of the conference Dynamics: Topology and Numbers, held from July 2-6, 2018, at the Max Planck Institute for Mathematics, Bonn, Germany. The papers cover diverse fields of mathematics with a unifying theme of relation to dynamical systems. These include arithmetic geometry, flat geometry, complex dynamics, graph theory, relations to number theory, and topological dynamics. The volume is dedicated to the memory of Sergiy Kolyada and also contains some personal accounts of his life and mathematics.
Tycho Brahe and the Measure of the Heavens by John Robert ChristiansonThe Danish aristocrat and astronomer Tycho Brahe personified the inventive vitality of Renaissance life in the sixteenth century. Brahe lost his nose in a student duel, wrote Latin poetry, and built one of the most astonishing villas of the late Renaissance, while virtually inventing team research and establishing the fundamental rules of empirical science. His observatory at Uraniborg functioned as a satellite to Hamlet's castle of Kronborg until Tycho abandoned it to end his days at the court of the Holy Roman Emperor Rudolf II in Prague. This illustrated biography presents a new and dynamic view of Tycho's life, reassessing his gradual separation of astrology from astronomy and his key relationships with Johannes Kepler, his sister Sophie, and his kinsmen at the court of King Frederick II.
Analytic Trends in Mathematical Physics by Houssam M. A. Abdul Rahman; Robert Sims; Amanda YoungThis volume contains the proceedings of the Arizona School of Analysis and Mathematical Physics, held from March 5-9, 2018, at the University of Arizona, Tucson, Arizona. A main goal of this school was to introduce graduate students and postdocs to exciting topics of current research that are both influenced by physical intuition and require the use of cutting-edge mathematics. The articles in this volume reflect recent progress and innovative techniques developed within mathematical physics. Two works investigate spectral gaps of quantum spin systems. Specifically, Abdul-Rahman, Lemm, Lucia, Nachtergaele, and Young consider decorated AKLT models, and Lemm demonstrates a finite-size criterion for $D$-dimensional models. Bachmann, De Roeck, and Fraas summarize a recent proof of the adiabatic theorem, while Bachmann, Bols, De Roeck, and Fraas discuss linear response for interacting Hall insulators. Models on general graphs are the topic of the articles by Fischbacher, on higher spin XXZ, and by Latushkin and Sukhtaiev, on an index theorem for Schrodinger operators. Probabilistic applications are the focus of the articles by DeMuse and Yin, on exponential random graphs, by Saenz, on KPZ universality, and by Stolz, on disordered quantum spin chains. In all, the diversity represented here is a testament to the enthusiasm this rich field of mathematical physics generates.
Formulations of General Relativity by Kirill KrasnovThis monograph describes the different formulations of Einstein's General Theory of Relativity. Unlike traditional treatments, Cartan's geometry of fibre bundles and differential forms is placed at the forefront, and a detailed review of the relevant differential geometry is presented. Particular emphasis is given to general relativity in 4D space-time, in which the concepts of chirality and self-duality begin to play a key role. Associated chiral formulations are catalogued, and shown to lead to many practical simplifications. The book develops the chiral gravitational perturbation theory, in which the spinor formalism plays a central role. The book also presents in detail the twistor description of gravity, as well as its generalisation based on geometry of 3-forms in seven dimensions. Giving valuable insight into the very nature of gravity, this book joins our highly prestigious Cambridge Monographs in Mathematical Physics series. It will interest graduate students and researchers in the fields of theoretical physics and differential geometry.
From Classical Mechanics to Quantum Field Theory, a Tutorial by Elisa Ercolessi; Valter Moretti; Manuel AsoreyThis book collects an extended version of the lectures delivered by the authors at the Fall Workshop on Geometry and Physics in the years 2014, 2015, 2016.It aims at introducing advanced graduate and PhD students, as well as young researchers, to current research in mathematics and physics. In particular, it fills the gap between the more physical-oriented and the more mathematical-oriented literature on quantum theory. It introduces various approaches to methods of quantization, along with their impact on modern mathematical methods.
Quasi-Periodic Standing Wave Solutions of Gravity-Capillary Water Waves by Massimiliano Berti; Riccardo MontaltoThe authors prove the existence and the linear stability of small amplitude time quasi-periodic standing wave solutions (i.e. periodic and even in the space variable $x$) of a 2-dimensional ocean with infinite depth under the action of gravity and surface tension. Such an existence result is obtained for all the values of the surface tension belonging to a Borel set of asymptotically full Lebesgue measure.
The Cosmic Spacetime by Fulvio MeliaThe growth of cosmology into a precision science represents one of the most remarkable stories of the past century. Much has been written chronicling this development, but rarely has any of it focused on the most critical element of this work-the cosmic spacetime itself. Addressing this lacuna is the principal focus of this book, documenting the growing body of evidence compelling us-not only to use this famous solution to Einstein's equations in order to refine the current paradigm, but-to probe its foundation at a much deeper level. Its excursion from the smallest to largest possible scales insightfully reveals an emerging link between the Universe we behold and the established tenets of our most fundamental physical theories. Key Features: Uncovers the critical link between the Local Flatness Theorem in general relativity and the symmetries informing the spacetime's metric coefficients Develops a physical explanation for some of the most unpalatable coincidences in cosmology Provides a sober assessment of the horizon problems precluding our full understanding of the early Universe Reveals a possible explanation for the origin of rest-mass energy in Einstein's theory In spite of its technical layout, this book does not shy away from introducing the principal players who have made the most enduring contributions to this field. Anyone with a graduate level foundation in physics and astronomy will be able to easily follow its contents.
Introduction to Effective Field Theory by Cliff P. BurgessUsing examples from across the sub-disciplines of physics, this introduction shows why effective field theories are the language in which physical laws are written. The tools of effective field theory are demonstrated using worked examples from areas including particle, nuclear, atomic, condensed matter and gravitational physics. To bring the subject within reach of scientists with a wide variety of backgrounds and interests, there are clear physical explanations, rigorous derivations, and extensive appendices on background material, such as quantum field theory. Starting from undergraduate-level quantum mechanics, the book gets to state-of-the-art calculations using both relativistic and nonrelativistic few-body and many-body examples, and numerous end-of-chapter problems derive classic results not covered in the main text. Graduate students and researchers in particle physics, condensed matter physics, nuclear physics, string theory, and mathematical physics more generally, will find this book ideal for both self-study and for organized courses on effective field theory.
Cosmic Pinwheels by Ronald J. ButaThe main goal of the book is to introduce the reader to the world of spiral galaxies, how spirals were discovered, what they represent from a physical point of view, and what people have learned about the universe and the nature of galaxies in general from the study of spirals. Topics include early discoveries of nebulae, the island universe concept, the structure of spirals as seen both visually with telescopes and in images obtained with different filters, the role of spirals in the discovery of interstellar dust and dark matter, the different kinds of spiral galaxies and the importance of bars and rings, how different non-spiral galaxy types such as elliptical galaxies and S0 galaxies connect to spirals, and how spirals have contributed to our understanding of star formation and evolution, galaxy formation and evolution, the cosmological distance scale, and the universal expansion. The Milky Way as a spiral galaxy is also discussed.The book is profusely illustrated and not only a discourse on the spirals, but is also a personal reminiscence based on the author's studies of spiral galaxies over the past 45 years.
Global Spacetime Structure by J. B. ManchakThis exploration of the global structure of spacetime within the context of general relativity examines the causal and singular structures of spacetime, revealing some of the curious possibilities that are compatible with the theory, such as 'time travel' and 'holes' of various types. Investigations into the epistemic and modal structures of spacetime highlight the difficulties in ruling out such possibilities, unlikely as they may seem at first. The upshot seems to be that what counts as a 'physically reasonable' spacetime structure in modern physics is far from clear.
Pointless by R. W. BoyerThis book examines how major interpretations of quantum theory are progressing toward a more unified understanding and experience of nature. It offers subtle insights to address core issues of wave-particle duality, the measurement problem, the mind/body problem, determinism/indeterminism/free will, and the nature of consciousness. It draws from physics, consciousness studies, and 'ancient Vedic science' to outline a new holistic interpretation of quantum theory. Accessible and thought-provoking, it will be profoundly integrating for scholars and researchers in science and technology, in philosophy, and also in South Asian studies.