The seminal 1970 Moscow thesis of Grigoriy A. Margulis, published for the first time. Entitled "On Some Aspects of the Theory of Anosov Systems", it uses ergodic theoretic techniques to study the distribution of periodic orbits of Anosov flows. The thesis introduces the "Margulis measure" and uses it to obtain a precise asymptotic formula for counting periodic orbits. This has an immediate application to counting closed geodesics on negatively curved manifolds. The thesis also contains asymptotic formulas for the number of lattice points on universal coverings  of compact manifolds of negative curvature. The thesis is complemented by a survey by Richard Sharp, discussing more recent developments in the theory of periodic orbits for hyperbolic flows, including the results obtained in the light of Dolgopyat's breakthroughs on bounding transfer operators and rates of mixing.

The book is concerned with mathematical modelling of supersonic and hyper sonic flows about bodies. Permanent interest in this topic is stimulated, first of all, by aviation and aerospace engineering. The designing of aircraft and space vehicles requires a more precise prediction of the aerodynamic and heat transfer characteristics. Together with broadening of the flight condition range, this makes it necessary to take into account a number of gas dynamic and physical effects caused by rarefaction, viscous-inviscid interaction, separation, various physical and chemical processes induced by gas heating in the intensive bow shock wave. The flow field around a body moving at supersonic speed can be divided into three parts, namely, shock layer, near wake including base flow, and far wake. The shock layer flow is bounded by the bow shock wave and the front and lat eral parts of the body surface. A conventional approach to calculation of shock layer flows consists in a successive solution of the inviscid gas and boundary layer equations. When the afore-mentioned effects become important, implementation of these models meets difficulties or even becomes impossible. In this case, one has to use a more general approach based on the viscous shock layer concept."

Social network analysis increasingly bridges the discovery of patterns in diverse areas of study as more data becomes available and complex. Yet the construction of huge networks from large data often requires entirely different approaches for analysis including; graph theory, statistics, machine learning and data mining. This work covers frontier studies on social network analysis and mining from different perspectives such as social network sites, financial data, e-mails, forums, academic research funds, XML technology, blog content, community detection and clique finding, prediction of user's- behavior, privacy in social network analysis, mobility from spatio-temporal point of view, agent technology and political parties in parliament. These topics will be of interest to researchers and practitioners from different disciplines including, but not limited to, social sciences and engineering.

This volume, whose contributors include leading researchers in their field, covers a wide range of topics surrounding Integrable Systems, from theoretical developments to applications. Comprising a unique collection of research articles and surveys, the book aims to serve as a bridge between the various areas of Mathematics related to Integrable Systems and Mathematical Physics. Recommended for postgraduate students and early career researchers who aim to acquire knowledge in this area in preparation for further research, this book is also suitable for established researchers aiming to get up to speed with recent developments in the area, and may very well be used as a guide for further study.

This book gathers outstanding papers on numerical modeling in Civil Engineering (Volume 1) as part of the 2-volume proceedings of the 4th International Conference on Numerical Modeling in Engineering (NME 2021), which was held in Ghent, Belgium, on 24-25 August 2021. The overall objective of the conference was to bring together international scientists and engineers in academia and industry from fields related to advanced numerical techniques, such as the finite element method (FEM), boundary element method (BEM), isogeometric analysis (IGA), etc., and their applications to a wide range of engineering disciplines. This volume covers numerical simulations with industrial civil engineering applications such as bridges and dams, cyclic loading, fluid dynamics, structural mechanics, geotechnical engineering, thermal analysis, reinforced concrete structures, steel structures, and composite structures.

University Physics with Modern Physics, Technology Update, Thirteenth Edition continues to set the benchmark for clarity and rigor combined with effective teaching and research-based innovation. The Thirteenth Edition Technology Update contains QR codes throughout the textbook, enabling students to use their smartphone or tablet to instantly watch interactive videos about relevant demonstrations or problem-solving strategies. University Physics is known for its uniquely broad, deep, and thoughtful set of worked examples-key tools for developing both physical understanding and problem-solving skills. The Thirteenth Edition revises all the Examples and Problem-solving Strategies to be more concise and direct while maintaining the Twelfth Edition's consistent, structured approach and strong focus on modeling as well as math. To help students tackle challenging as well as routine problems, the Thirteenth Edition adds Bridging Problems to each chapter, which pose a difficult, multiconcept problem and provide a skeleton solution guide in the form of questions and hints. The text's rich problem sets-developed and refined over six decades-are upgraded to include larger numbers of problems that are biomedically oriented or require calculus. The problem-set revision is driven by detailed student-performance data gathered nationally through MasteringPhysics (R), making it possible to fine-tune the reliability, effectiveness, and difficulty of individual problems. Complementing the clear and accessible text, the figures use a simple graphic style that focuses on the physics. They also incorporate explanatory annotations-a technique demonstrated to enhance learning. This package consists of: University Physics with Modern Physics Technology Update, Volume 1 (Chapters 1-20), Thirteenth Edition

Modern Physics, Second Edition provides a clear, precise, and contemporary introduction to the theory, experiment, and applications of modern physics. Ideal for both physics majors and engineers, this eagerly awaited second edition puts the modern back into modern physics courses. Pedagogical features throughout the text focus the reader on the core concepts and theories while offering optional, more advanced sections, examples, and cutting-edge applications to suit a variety of students and courses. Critically acclaimed for his lucid style, in the second edition, Randy Harris applies the same insights into recent developments in physics, engineering, and technology.

Written as a textbook, A First Course in Functional Analysis is an introduction to basic functional analysis and operator theory, with an emphasis on Hilbert space methods. The aim of this book is to introduce the basic notions of functional analysis and operator theory without requiring the student to have taken a course in measure theory as a prerequisite. It is written and structured the way a course would be designed, with an emphasis on clarity and logical development alongside real applications in analysis. The background required for a student taking this course is minimal; basic linear algebra, calculus up to Riemann integration, and some acquaintance with topological and metric spaces.

Numerical methods are playing an ever-increasing role in physics and engineering. This is especially true after the recent explosion of computing power on the desk-top. This book is aimed at helping the user to make intelligent use of this power tool. Each method is introduced through realistic examples and actual computer programs. The explanations provide the background for making a choice between similar approaches and the knowledge to explore the network for the appropriate existing codes. Tedious proofs and derivations, on the other hand, are delegated to references. Examples of uncoventional methods are also given to stimulate readers in exploring new ways of solving problems.

To protect the Earth, China has launched its target of peaking carbon dioxide emissions by 2030, and achieving carbon neutrality by 2060 , which greatly encourages the use and development of renewable energy. Supercritical CO2 power cycle is a promising technology and the radial inflow turbine is the most important component of it, whose design and optimisation are considered as great challenges. This book introduces simulation tools and methods for supercritical CO2 radial inflow turbine, including a high fidelity quasi-one-dimensional design procedure, a non-ideal compressible fluid dynamics Riemann solver within open-source CFD software OpenFOAM framework, and a multi-objective Nelder-Mead geometry optimiser. Enhanced one-dimensional loss models are presented for providing a new insight towards the preliminary design of the supercritical CO2 radial inflow turbine. Since the flow phenomena within the blade channels are complex, involving fluid flow, shock wave transmission and boundary layer separation, only employing the ideal gas model is inadequate to predict the performance of the turbine. Thus, a non-ideal compressible fluid dynamics Riemann solver based on OpenFOAM library is developed. This book addresses the issues related to the turbine design and blade optimization and provides leading techniques. Hence, this book is of great value for the readers working on the supercritical CO2 radial inflow turbine and understanding the knowledge of CFD and turbomachinery.

This textbook describes rules and procedures for the use of Differential Operators (DO) in Ordinary Differential Equations (ODE). The book provides a detailed theoretical and numerical description of ODE. It presents a large variety of ODE and the chosen groups are used to solve a host of physical problems. Solving these problems is of interest primarily to students of science, such as physics, engineering, biology and chemistry. Scientists are greatly assisted by using the DO obeying several simple algebraic rules. The book describes these rules and, to help the reader, the vocabulary and the definitions used throughout the text are provided. A thorough description of the relatively straightforward methodology for solving ODE is given. The book provides solutions to a large number of associated problems. ODE that are integrable, or those that have one of the two variables missing in any explicit form are also treated with solved problems. The physics and applicable mathematics are explained and many associated problems are analyzed and solved in detail. Numerical solutions are analyzed and the level of exactness obtained under various approximations is discussed in detail.

The theory of complex functions is a strikingly beautiful and powerful area of mathematics. Some particularly fascinating examples are seemingly complicated integrals which are effortlessly computed after reshaping them into integrals along contours, as well as apparently difficult differential and integral equations, which can be elegantly solved using similar methods. To use them is sometimes routine but in many cases it borders on an art. The goal of the book is to introduce the reader to this beautiful area of mathematics and to teach him or her how to use these methods to solve a variety of problems ranging from computation of integrals to solving difficult integral equations. This is done with a help of numerous examples and problems with detailed solutions.

An account of Newton's life and work.

This book explains how standard micro-founded macroeconomics is misguided and proposes an alternative method based on statistical physics. The Great Recession following the bankruptcy of Lehman Brothers in September 2015 amply demonstrated that mainstream micro-founded macroeconomics was in trouble. The new approach advanced in this book reasonably explains important macro-problems such as employment, business cycles, growth, and inflation/deflation. The key concept is demand failures, which modern micro-founded macroeconomics has ignored. "It (Chapter 3) captures analytically a good part of the intuition that underlies the Keynesian economics of people like Tobin and me." Robert Solow, Emeritus Institute Professor of Economics, Massachusetts Institute of Technology, Nobel Laureate in Economics, 1987 "Professor Hiroshi Yoshikawa provides a unique synthesis of statistical physics and macro-economic theory in order to confront the dismal failure in economics and in finance to understand how an economy or a financial market works, given the heterogeneous decision making of many different individual interacting actors. Economics has failed in this regard with the naive and often misleading concept of "representative agents." The author presents many insights on the historical development, concepts, and errors made by the most illustrious economists in the past. This book should be essential readings for any economics students as well as academic researchers and policy makers, who should learn to bring back good-sense thinking in their impactful decisions." Didier Sornette, Professor on the Chair of Entrepreneurial Risks at the Swiss Federal Institute of Technology Zurich (ETH Zurich)

The book is devoted to recent developments in the theory of fractional calculus and its applications. Particular attention is paid to the applicability of this currently popular research field in various branches of pure and applied mathematics. In particular, the book focuses on the more recent results in mathematical physics, engineering applications, theoretical and applied physics as quantum mechanics, signal analysis, and in those relevant research fields where nonlinear dynamics occurs and several tools of nonlinear analysis are required. Dynamical processes and dynamical systems of fractional order attract researchers from many areas of sciences and technologies, ranging from mathematics and physics to computer science.

Over the course of a scientific career spanning more than fifty years, Alex Grossmann (1930-2019) made many important contributions to a wide range of areas including, among others, mathematics, numerical analysis, physics, genetics, and biology.  His lasting influence can be seen not only in his research and numerous publications, but also through the relationships he cultivated with his collaborators and students.  This edited volume features chapters written by some of these colleagues, as well as researchers whom Grossmann’s work and way of thinking has impacted in a decisive way.  Reflecting the diversity of his interests and their interdisciplinary nature, these chapters explore a variety of current topics in quantum mechanics, elementary particles, and theoretical physics; wavelets and mathematical analysis; and genomics and biology.  A scientific biography of Grossmann, along with a more personal biography written by his son, serve as an introduction.  Also included are the introduction to his PhD thesis and an unpublished paper coauthored by him.  Researchers working in any of the fields listed above will find this volume to be an insightful and informative work.

Help students to develop their knowledge and build essential skills with practical assessment guidance and plenty of support for the new mathematical requirements in this updated, all-in-one textbook for Years 1 and 2. Combining everything your students need to know for the Pearson Edexcel A level Physics specification, this revised textbook will: - Support practical assessment with practical skill summaries throughout. - Provide support for all 16 required practicals with detailed explanations, data and exam style questions for students to answer. - Build understanding and knowledge with a variety of questions to engage and challenge students throughout the course: prior knowledge, worked examples, 'Test yourself' and exam practice questions. - Aid mathematical understanding and application with worked examples of calculations and a dedicated 'Maths for Physics' chapter. - Develop understanding and enable self- and peer-assessment with free online access to 'Test yourself' answers.

This book presents the mathematical study of vortices of the two-dimensional Ginzburg-Landau model, an important phenomenological model used to describe superconductivity. The vortices, identified as quantized amounts of vorticity of the superconducting current localized near points, are the objects of many observational and experimental studies, both past and present. The Ginzburg-Landau functionals considered include both the model cases with and without a magnetic field. The book acts a guide to the various branches of Ginzburg-Landau studies, provides context for the study of vortices, and presents a list of open problems in the field.

The spectacular culinary creations of modern cuisine are the stuff of countless articles and Instagram feeds. But to a scientist they are also perfect pedagogical explorations into the basic scientific principles of cooking. In Science and Cooking, Harvard professors Michael Brenner, Pia Soerensen and David Weitz bring the classroom to your kitchen to teach the physics and chemistry underlying every recipe. Science and Cooking answers questions such as why we knead bread, what determines the temperature at which we cook a steak or the how much time our chocolate chip cookies should spend in the oven, through fascinating lessons ranging from the role of pressure and boiling points in pecan praline to that of microbes in your coffee. With beautiful full-colour illustrations and recipes, hands-on experiments, and engaging introductions from world-renowned chefs Ferran Adria and Jose Andres, Science and Cooking will change the way readers approach both subjects-in their kitchens and beyond.

This book highlights two essential analyses of data collected during the LHCb experiment, based on the Large Hadron Collider at CERN. The first comprises the first observation and studies of matter-antimatter asymmetries in two three-body b-baryon decays, paving the way for more precise measurements of the relatively unknown decay properties of b-baryon decays. The second is an analysis of a charged B meson decay to three charged pions, where previously large matter-antimatter asymmetries were observed in a model-independent analysis. Here a model of the decay amplitude is constructed using the unitarity-conserving 'K-matrix' model for the scalar contributions, so as to gain an understanding of how the previously observed matter-antimatter asymmetries arise; further, the model's construction yields the most precise and comprehensive study of this decay mode to date.

Classical mechanics is a subject that is teeming with life. However, most of the interesting results are scattered around in the specialist literature, which means that potential readers may be somewhat discouraged by the effort required to obtain them. Addressing this situation, Hamiltonian Dynamical Systems includes some of the most significant papers in Hamiltonian dynamics published during the last 60 years. The book covers bifurcation of periodic orbits, the break-up of invariant tori, chaotic behavior in hyperbolic systems, and the intricacies of real systems that contain coexisting order and chaos. It begins with an introductory survey of the subjects to help readers appreciate the underlying themes that unite an apparently diverse collection of articles. The book concludes with a selection of papers on applications, including in celestial mechanics, plasma physics, chemistry, accelerator physics, fluid mechanics, and solid state mechanics, and contains an extensive bibliography. The book provides a worthy introduction to the subject for anyone with an undergraduate background in physics or mathematics, and an indispensable reference work for researchers and graduate students interested in any aspect of classical mechanics.

With exoplanets being discovered daily, Earth is still the only planet we know of that is home to creatures who seek a coherent explanation for the structure, origins, and fate of the universe, and of humanity s place within it. Today, science and religion are the two major cultural entities on our planet that share this goal of coherent understanding, though their interpretation of evidence differs dramatically. Many scientists look at the known universe and conclude we are here by chance. The renowned astronomer and historian of science Owen Gingerich looks at the same evidence along with the fact that the universe is comprehensible to our minds and sees it as proof for the planning and intentions of a Creator-God. He believes that the idea of a universe without God is an oxymoron, a self-contradiction. God s Planet" exposes the fallacy in thinking that science and religion can be kept apart.

Gingerich frames his argument around three questions: Was Copernicus right, in dethroning Earth from its place at the center of the universe? Was Darwin right, in placing humans securely in an evolving animal kingdom? And was Hoyle right, in identifying physical constants in nature that seem singularly tuned to allow the existence of intelligent life on planet Earth? Using these episodes from the history of science, Gingerich demonstrates that cultural attitudes, including religious or antireligious beliefs, play a significant role in what passes as scientific understanding. The more rigorous science becomes over time, the more clearly God s handiwork can be comprehended."