This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory.
This book presents a multidisciplinary perspective on chance, with contributions from distinguished researchers in the areas of biology, cognitive neuroscience, economics, genetics, general history, law, linguistics, logic, mathematical physics, statistics, theology and philosophy. The individual chapters are bound together by a general introduction followed by an opening chapter that surveys 2500 years of linguistic, philosophical, and scientific reflections on chance, coincidence, fortune, randomness, luck and related concepts. A main conclusion that can be drawn is that, even after all this time, we still cannot be sure whether chance is a truly fundamental and irreducible phenomenon, in that certain events are simply uncaused and could have been otherwise, or whether it is always simply a reflection of our ignorance. Other challenges that emerge from this book include a better understanding of the contextuality and perspectival character of chance (including its scale-dependence), and the curious fact that, throughout history (including contemporary science), chance has been used both as an explanation and as a hallmark of the absence of explanation. As such, this book challenges the reader to think about chance in a new way and to come to grips with this endlessly fascinating phenomenon.
Instabilities are present in all natural fluids from rivers to atmospheres. This book considers the physical processes that generate instability. Part I describes the normal mode instabilities most important in geophysical applications, including convection, shear instability and baroclinic instability. Classical analytical approaches are covered, while also emphasising numerical methods, mechanisms such as internal wave resonance, and simple `rules of thumb' that permit assessment of instability quickly and intuitively. Part II introduces the cutting edge: nonmodal instabilities, the relationship between instability and turbulence, self-organised criticality, and advanced numerical techniques. Featuring numerous exercises and projects, the book is ideal for advanced students and researchers wishing to understand flow instability and apply it to their own research. It can be used to teach courses in oceanography, atmospheric science, coastal engineering, applied mathematics and environmental science. Exercise solutions and MATLAB® examples are provided online. Also available as Open Access on Cambridge Core.
This open access book focuses on processing, modeling, and visualization of anisotropy information, which are often addressed by employing sophisticated mathematical constructs such as tensors and other higher-order descriptors. It also discusses adaptations of such constructs to problems encountered in seemingly dissimilar areas of medical imaging, physical sciences, and engineering. Featuring original research contributions as well as insightful reviews for scientists interested in handling anisotropy information, it covers topics such as pertinent geometric and algebraic properties of tensors and tensor fields, challenges faced in processing and visualizing different types of data, statistical techniques for data processing, and specific applications like mapping white-matter fiber tracts in the brain. The book helps readers grasp the current challenges in the field and provides information on the techniques devised to address them. Further, it facilitates the transfer of knowledge between different disciplines in order to advance the research frontiers in these areas. This multidisciplinary book presents, in part, the outcomes of the seventh in a series of Dagstuhl seminars devoted to visualization and processing of tensor fields and higher-order descriptors, which was held in Dagstuhl, Germany, on October 28–November 2, 2018.
This revised textbook motivates and illustrates the techniques of applied probability by applications in electrical engineering and computer science (EECS). The author presents information processing and communication systems that use algorithms based on probabilistic models and techniques, including web searches, digital links, speech recognition, GPS, route planning, recommendation systems, classification, and estimation. He then explains how these applications work and, along the way, provides the readers with the understanding of the key concepts and methods of applied probability. Python labs enable the readers to experiment and consolidate their understanding. The book includes homework, solutions, and Jupyter notebooks. This edition includes new topics such as Boosting, Multi-armed bandits, statistical tests, social networks, queuing networks, and neural networks. The companion website now has many examples of Python demos and also Python labs used in Berkeley. Showcases techniques of applied probability with applications in EE and CS; Presents all topics with concrete applications so students see the relevance of the theory; Illustrates methods with Jupyter notebooks that use widgets to enable the users to modify parameters.
Many leading experts contribute to this follow-up to An Introduction to Reservoir Simulation using MATLAB/GNU Octave: User Guide for the MATLAB Reservoir Simulation Toolbox (MRST). It introduces more advanced functionality that has been recently added to the open-source MRST software. It is however a self-contained introduction to a variety of modern numerical methods for simulating multiphase flow in porous media, with applications to geothermal energy, chemical enhanced oil recovery (EOR), flow in fractured and unconventional reservoirs, and in the unsaturated zone. The reader will learn how to implement new models and algorithms in a robust, efficient manner. A large number of numerical examples are included, all fully equipped with code and data so that the reader can reproduce the results and use them as a starting point for their own work. Like the original textbook, this book will prove invaluable for researchers, professionals and advanced students using reservoir simulation methods. This title is available as Open Access on Cambridge Core.
This open access book serves as textbook on the physics of the radiation belts surrounding the Earth. Discovered in 1958 the famous Van Allen Radiation belts were among the first scientific discoveries of the Space Age. Throughout the following decades the belts have been under intensive investigation motivated by the risks of radiation hazards they expose to electronics and humans on spacecraft in the Earth’s inner magnetosphere. This textbook teaches the field from basic theory of particles and plasmas to observations which culminated in the highly successful Van Allen Probes Mission of NASA in 2012-2019. Using numerous data examples the authors explain the relevant concepts and theoretical background of the extremely complex radiation belt region, with the emphasis on giving a comprehensive and coherent understanding of physical processes affecting the dynamics of the belts. The target audience are doctoral students and young researchers who wish to learn about the physical processes underlying the acceleration, transport and loss of the radiation belt particles in the perspective of the state-of-the-art observations.