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Arnold diffusion, which concerns the appearance of chaos in classical mechanics, is one of the most important problems in the fields of dynamical systems and mathematical physics. Since it was discovered by Vladimir Arnold in 1963, it has attracted the efforts of some of the most prominent researchers in mathematics. The question is whether a typical perturbation of a particular system will result in chaotic or unstable dynamical phenomena. This book provides the first complete proof of Arnold diffusion, demonstrating that that there is topological instability for typical perturbations of five-dimensional integrable systems (two and a half degrees of freedom). This proof realizes a plan John Mather announced in 2003 but was unable to complete before his death. The book follows Mather's strategy but emphasizes a more Hamiltonian approach, tying together normal forms theory, hyperbolic theory, Mather theory, and weak KAM theory. Offering a complete, clean, and modern explanation of the steps involved in the proof, and a clear account of background material, the book is designed to be accessible to students as well as researchers. The result is a critical contribution to mathematical physics and dynamical systems, especially Hamiltonian systems.

Studies of stars and stellar populations, and the discovery and characterization of exoplanets, are being revolutionized by new satellite and telescope observations of unprecedented quality and scope. Some of the most significant advances have been in the field of asteroseismology, the study of stars by observation of their oscillations. This book gives a comprehensive technical introduction to this discipline. It not only helps students and researchers learn about asteroseismology; it also serves as an essential instruction manual for those entering the field. The book presents readers with the foundational techniques used in the analysis and interpretation of asteroseismic data on cool stars that show solar-like oscillations. The techniques have been refined, and in some cases developed, to analyze asteroseismic data collected by the NASA Kepler mission. Topics range from the analysis of time-series observations to extract seismic data for stars to the use of those data to determine global and internal properties of the stars. Reading lists and problem sets are provided, and data necessary for the problem sets are available online.

Modern cosmology began a century ago with Albert Einstein's general theory of relativity and his notion of a homogenous, philosophically satisfying cosmos. This book is the story of how generations of scientists built on these thoughts and many new measurements to arrive at a well-tested physical theory of the structure and evolution of our expanding universe. This book offers an unparalleled personal perspective on how the field developed. The author was at the forefront of many of the greatest discoveries of the past century, making fundamental contributions to our understanding of the presence of helium and microwave radiation from the hot big bang, the measures of the distribution and motion of ordinary matter, and the new kind of dark matter that allows us to make sense of these results. Taking readers from the field's beginnings, the book describes how scientists working in independent directions found themselves converging on a theory of cosmic evolution interesting enough to warrant the rigorous testing it passes so well. The book explores the major advances—some inspired by remarkable insights or perhaps just lucky guesses—as well as the wrong turns taken and the roads not explored. It shares recollections from major players in this story and provides a rare, inside look at how natural science is really done. The book also emphasizes where the present theory is incomplete, suggesting exciting directions for continuing research.

This book provides a comprehensive, self-contained introduction to one of the most exciting frontiers in astrophysics today: the quest to understand how the oldest and most distant galaxies in our universe first formed. Until now, most research on this question has been theoretical, but the next few years will bring about a new generation of large telescopes that promise to supply a flood of data about the infant universe during its first billion years after the big bang. This book bridges the gap between theory and observation. It is an invaluable reference for students and researchers on early galaxies. The book starts from basic physical principles before moving on to more advanced material. Topics include the gravitational growth of structure, the intergalactic medium, the formation and evolution of the first stars and black holes, feedback and galaxy evolution, reionization, 21-cm cosmology, and more.

First published in 1922 and based on lectures delivered in May 1921, Albert Einstein's The Meaning of Relativity offered an overview and explanation of the then new and controversial theory of relativity. The work would go on to become a monumental classic, printed in numerous editions and translations worldwide. Now, this book introduces Einstein's masterpiece to new audiences. The volume contains Einstein's insightful text, accompanied by important historical materials and commentary looking at the origins and development of general relativity. The book provides fresh, original perspectives, placing Einstein's achievements into a broader context for all readers. It tells the rich story behind the early reception, spread, and consequences of Einstein's ideas during the formative years of general relativity in the late 1910s and 1920s. Relativity's meaning changed radically throughout the nascent years of its development, and the book describes in detail the transformation of Einstein's work from the esoteric pursuit of one individual communicating with a handful of colleagues into the preoccupation of a growing community of physicists, astronomers, mathematicians, and philosophers. The book quotes extensively from Einstein's correspondence and reproduces historical documents such as newspaper articles and letters. Inserts are featured in the main text giving concise explanations of basic concepts, and short biographical notes and photographs of some of Einstein's contemporaries are included. The first-ever English translations of two of Einstein's popular Princeton lectures are featured at the book's end.

This book provides readers with the skills they need to write computer codes that simulate convection, internal gravity waves, and magnetic field generation in the interiors and atmospheres of rotating planets and stars. Using a teaching method perfected in the classroom, the book begins by offering a step-by-step guide on how to design codes for simulating nonlinear time-dependent thermal convection in a 2D box using Fourier expansions in the horizontal direction and finite differences in the vertical direction. It then describes how to implement more efficient a nd accurate numerical methods and more realistic geometries in two and three dimensions. The third part of the book demonstrates how to incorporate more sophisticated physics, including the effects of magnetic field, density stratification, and rotation. The book features numerous exercises throughout, and is an ideal textbook for students and an essential resource for researchers. It explains how to create codes that simulate the internal dynamics of planets and stars, and builds on basic concepts and simple methods. The book shows how to improve the efficiency and accuracy of the numerical methods. It considers more relevant geometries and boundary conditions.

An instant landmark on its publication, this book remains the essential introduction to this vital area of research. Written by one of the world's most esteemed theoretical cosmologists, it provides an invaluable historical introduction to the subject, and an enduring overview of key methods, statistical measures, and techniques for dealing with cosmic evolution. With characteristic clarity and insight, the author focuses on the largest known structures — galaxy clusters — weighing the empirical evidence of the nature of clustering and the theories of how it evolves in an expanding universe. A must-have reference for students and researchers alike, this edition introduces a new generation of readers to a classic text in modern cosmology.

Quantum mechanics was still in its infancy in 1932 when the young John von Neumann, who would go on to become one of the greatest mathematicians of the twentieth century, published Mathematical Foundations of Quantum Mechanics—a revolutionary book that for the first time provided a rigorous mathematical framework for the new science. Robert Beyer's 1955 English translation, which von Neumann reviewed and approved, is cited more frequently today than ever before. But its many treasures and insights were too often obscured by the limitations of the way the text and equations were set on the page. This new edition of this classic work has been completely reset in TeX, making the text and equations far easier to read. The book has also seen the correction of a handful of typographic errors, revision of some sentences for clarity and readability, provision of an index for the first time, and prefatory remarks drawn from the writings of Léon Van Hove and Freeman Dyson have been added. The result brings new life to an essential work in theoretical physics and mathematics.

This book presents a dynamic new approach to the physics of enzymes and DNA from the perspective of materials science. Unified around the concept of molecular deformability—how proteins and DNA stretch, fold, and change shape—the book describes the complex molecules of life from the innovative perspective of materials properties and dynamics, in contrast to structural or purely chemical approaches. It covers a wealth of topics, including nonlinear deformability of enzymes and DNA; the chemo-dynamic cycle of enzymes; supra-molecular constructions with internal stress; nano-rheology and viscoelasticity; and chemical kinetics, Brownian motion, and barrier crossing. Essential reading for researchers in materials science, engineering, and nanotechnology, the book also describes the landmark experiments that have established the materials properties and energy landscape of large biological molecules. The book gives graduate students a working knowledge of model building in statistical mechanics, making it an essential resource for tomorrow's experimentalists in this cutting-edge field. In addition, mathematical methods are introduced in the bio-molecular context. The result is a generalized approach to mathematical problem solving that enables students to apply their findings more broadly.

This book is the essential introduction to this critical area of modern physics, written by a leading pioneer who has shaped the course of the field for decades. The book provides an authoritative overview of the field, showing how observation has combined with theory to establish the science of physical cosmology. The book presents the elements of physical cosmology, including the history of the discovery of the expanding universe; surveys the cosmological tests that measure the geometry of space-time, with a discussion of general relativity as the basis for these tests; and reviews the origin of galaxies and the large-scale structure of the universe. Now featuring the author's 2019 Nobel lecture, the book remains an indispensable reference for students and researchers alike.

This book explains the often counterintuitive physics of quantum mechanics, unlocking this key area of physics for students by enabling them to work through detailed applications of general concepts and ideas. The book states general principles first in terms of wave mechanics and then in the standard abstract linear space formalism. It offers a detailed discussion of measurement theory — an essential feature of quantum mechanics — and emphasizes the art of numerical estimates. Along the way, the book provides a wealth of physical examples together with numerous problems, some easy, some challenging, but all of them selected because they are physically interesting. The book is an essential resource for advanced undergraduates and beginning graduate students in physics.

This richly annotated facsimile edition of “The Foundation of General Relativity” introduces a new generation of readers to Albert Einstein's theory of gravitation. Written in 1915, this remarkable document is a watershed in the history of physics and an enduring testament to the elegance and precision of Einstein's thought. Presented here is a beautiful facsimile of Einstein's original handwritten manuscript, along with its English translation and an insightful page-by-page commentary that places the work in historical and scientific context. The concise introduction traces Einstein's intellectual odyssey from the special to the general theory of relativity, and the chapter “The Charm of a Manuscript” provides a delightful meditation on the varied afterlife of Einstein's text. The book also includes a biographical glossary of the figures discussed in the book, a comprehensive bibliography, suggestions for further reading, and numerous photos and illustrations throughout.

As telescopes, detectors, and computers grow ever more powerful, the volume of data at the disposal of astronomers and astrophysicists will enter the petabyte domain, providing accurate measurements for billions of celestial objects. This book provides a comprehensive and accessible introduction to the cutting-edge statistical methods needed to efficiently analyze complex data sets from astronomical surveys such as the Panoramic Survey Telescope and Rapid Response System, the Dark Energy Survey, and the upcoming Large Synoptic Survey Telescope. It serves as a practical handbook for graduate students and advanced undergraduates in physics and astronomy, and as an indispensable reference for researchers. The book presents a wealth of practical analysis problems, evaluates techniques for solving them, and explains how to use various approaches for different types and sizes of data sets. For all applications described in the book, Python code and example data sets are provided. The supporting data sets have been carefully selected from contemporary astronomical surveys (for example, the Sloan Digital Sky Survey) and are easy to download and use. The accompanying Python code is publicly available, well documented, and follows uniform coding standards. Together, the data sets and code enable readers to reproduce all the figures and examples, evaluate the methods, and adapt them to their own fields of interest.

In 1969, Princeton physicist Gerard O'Neill began looking outward to space colonies as the new frontier for humanity's expansion. A decade later, Eric Drexler turned his attention to the molecular world as the place where society's future needs could be met using self-replicating nanoscale machines. These modern utopians predicted that their technologies could transform society as humans mastered the ability to create new worlds, undertook atomic-scale engineering, and, if truly successful, overcame their own biological limits. This book tells the story of how these scientists and the communities they fostered imagined, designed, and popularized speculative technologies such as space colonies and nanotechnologies. The book traces how these visioneers blended countercultural ideals with hard science, entrepreneurship, libertarianism, and unbridled optimism about the future. It shows how they built networks that communicated their ideas to writers, politicians, and corporate leaders. But the visioneers were not immune to failure. O'Neill and Drexler faced difficulty funding their work and overcoming colleagues' skepticism, and saw their ideas co-opted and transformed. Ultimately, both men struggled to overcome stigma and ostracism as they tried to unshackle their visioneering from pejorative labels like “fringe” and “pseudoscience”? This book provides a balanced look at the successes and pitfalls they encountered. It exposes the dangers of promotion that can plague exploratory science. But above all, it highlights the importance of radical new ideas that inspire us to support cutting-edge research into tomorrow's technologies.

Gamma-ray bursts are the brightest—and, until recently, among the least understood—cosmic events in the universe. Discovered by chance during the Cold War, these evanescent high-energy explosions confounded astronomers for decades. But a rapid series of startling breakthroughs beginning in 1997 revealed that the majority of gamma-ray bursts are caused by the explosions of young and massive stars in the vast star-forming cauldrons of distant galaxies. New findings also point to very different origins for some events, serving to complicate but enrich our understanding of the exotic and violent universe. This book is an introduction to this fast-growing subject, written by an astrophysicist who is at the forefront of today's research into these incredible cosmic phenomena. The book gives readers a concise and accessible overview of gamma-ray bursts and the theoretical framework that physicists have developed to make sense of complex observations across the electromagnetic spectrum. The book traces the history of remarkable discoveries that led to our current understanding of gamma-ray bursts, and reveals the decisive role these phenomena could play in the grand pursuits of twenty-first century astrophysics, from studying gravity waves and unveiling the growth of stars and galaxies after the big bang to surmising the ultimate fate of the universe itself. This book is an essential primer to this exciting frontier of scientific inquiry, and a must-read for anyone seeking to keep pace with cutting-edge developments in physics today.

Emitting no radiation or any other kind of information, black holes mark the edge of the universe—both physically and in our scientific understanding. Yet astronomers have found clear evidence for the existence of black holes, employing the same tools and techniques used to explore other celestial objects. This book goes behind the theory and physics of black holes to describe how astronomers are observing these enigmatic objects and developing a remarkably detailed picture of what they look like and how they interact with their surroundings. Accessible to undergraduates and others with some knowledge of introductory college-level physics, this book presents the techniques used to identify and measure the mass and spin of celestial black holes. These key measurements demonstrate the existence of two kinds of black holes, those with masses a few times that of a typical star, and those with masses comparable to whole galaxies—supermassive black holes. The book provides a detailed account of the nature, formation, and growth of both kinds of black holes. The book also describes the possibility of observing theoretically predicted phenomena such as gravitational waves, wormholes, and Hawking radiation. A cutting-edge introduction to a subject that was once on the border between physics and science fiction, this book shows how black holes are becoming routine objects of empirical scientific study.