The power engineering domain is facing huge challenges, with an increasing interest in intermittent renewable energies which are imposing major technical limitations. Operating ever closer to their limits, the industry-standard AC power grids are subject to instabilities. This book presents an insight into DC grid systems, offering interesting issues to well controlled power grids, in contrast to current AC systems which provide the simplest and most economic connection method for short distances.

Topics of complex system physics and their interdisciplinary applications to different problems in seismology, biology, economy, sociology, energy and nanotechnology are covered in this new work from renowned experts in their fields. Inparticular, contributed papers contain original results on network science, earthquake dynamics, econophysics, sociophysics, nanoscience and biological physics. Most of the papers use interdisciplinary approaches based on statistical physics, quantum physics and other topics of complex system physics.Papers on econophysics and sociophysics are focussed on societal aspects of physics such as, opinion dynamics, public debates and financial and economic stability. This work will be of interest to statistical physicists, economists, biologists, seismologists and all scientists working in interdisciplinary topics of complexity."

Our knowledge of objects of complex and potential analysis has been enhanced recently by ideas and constructions of theoretical and mathematical physics, such as quantum field theory, nonlinear hydrodynamics, material science. These are some of the themes of this refereed collection of papers, which grew out of the first conference of the European Science Foundation Networking Programme 'Harmonic and Complex Analysis and Applications' held in Norway 2007.

This textbook provides an introduction to representations of general -algebras by unbounded operators on Hilbert space, a topic that naturally arises in quantum mechanics but has so far only been properly treated in advanced monographs aimed at researchers. The book covers both the general theory of unbounded representation theory on Hilbert space as well as representations of important special classes of -algebra, such as the Weyl algebra and enveloping algebras associated to unitary representations of Lie groups. A broad scope of topics are treated in book form for the first time, including group graded -algebras, the transition probability of states, Archimedean quadratic modules, noncommutative Positivstellensatze, induced representations, well-behaved representations and representations on rigged modules. Making advanced material accessible to graduate students, this book will appeal to students and researchers interested in advanced functional analysis and mathematical physics, and with many exercises it can be used for courses on the representation theory of Lie groups and its application to quantum physics. A rich selection of material and bibliographic notes also make it a valuable reference.

The Shaggy Steed is an unassuming figure from Irish folklore who reveals himself as an inspiring teacher of the forces hidden in the universe. This book celebrates an unassuming bit of physics that also turns out to be an inspiring teacher. The two-body problem - the motion of two bodies bound by the inverse-square force of gravity and electricity - is the Shaggy Steed of physics, guiding the reader to an understanding of both the forces and the mathematical beauty hidden in the physical world.

This book surveys the physics of small clusters of particles undergoing vibrations, with applications in nuclear physics and the physics and chemistry of atomic clusters. The book begins with a survey of the experimental information on collective vibrations in atoms, metal clusters and nuclei. Next, the book goes on to develop theoretical tools to understand these findings. Special emphasis is placed on the Rayleigh-Ritz principle, the use of sum rules, and the quantum mechanics of mean field theory, known as 'RPA'. The important vibrational modes observed in the different systems are then discussed, including the dipole mode of oscillation (important in both nuclei and metal clusters), surface modes of higher polarity, and the compressional mode. In the last two chapters mechanisms for the damping of vibrational modes and the effects of excitation energy on the modes are described.

Introduction to Mathematical Modeling helps students master the processes used by scientists and engineers to model real-world problems, including the challenges posed by space exploration, climate change, energy sustainability, chaotic dynamical systems and random processes. Primarily intended for students with a working knowledge of calculus but minimal training in computer programming in a first course on modeling, the more advanced topics in the book are also useful for advanced undergraduate and graduate students seeking to get to grips with the analytical, numerical, and visual aspects of mathematical modeling, as well as the approximations and abstractions needed for the creation of a viable model.

Professor Atiyah is one of the greatest living mathematicians and is well known throughout the mathematical world. He is a recipient of the Fields Medal, the mathematical equivalent of the Nobel Prize, and is still at the peak of his career. His huge number of published papers, focusing on the areas of algebraic geometry and topology, have here been collected into six volumes, divided thematically for easy reference by individuals interested in a particular subject.
This sixth volume in Michael Atiyah's collected works contains a selection of his publications since 1987, including his work on skyrmions, "Atiyah's axioms" for topological quantum field theories, monopoles, knots, K-theory, equivariant problems, point particles, and M-theory.

Toeplitz and Toeplitz-related systems arise in a variety of applications in mathematics and engineering, especially in signal and image processing. This book deals primarily with iterative methods for solving Toeplitz and Toeplitz-related linear systems, discussing both the algorithms and their convergence theories. A basic knowledge of real analysis, elementary numerical analysis and linear algebra is assumed. The first part of the book (chapters one and two) gives a brief review of some terms and results in linear algebra and the conjugate gradient method, which are important topics for handling the mathematics later on in the book. The second part of the book (chapters three to seven) presents the theory of using iterative methods for solving Toeplitz and Toeplitz-related systems. The third part of the book (chapters eight to twelve) presents recent results from applying the use of iterative methods in different fields of applications, such as partial differential equations, signal and image processing, integral equations and queuing networks. These chapters provide research and application-oriented readers with a thorough understanding of using iterative methods, enabling them not only to apply these methods to the problems discussed but also to derive and analyze new methods for other types of problems and applications.

Demonstrating many fundamental concepts of physics and engineering through the working principles of popular science toys is inexpensive, quickly reaching the senses and inspiring a better learning. The systematic way of setting theoretical model equations for the toys provides a remarkable experience in constructing model equations for physical and engineering systems.Given that most science toys are based on the principles of physics, and to cater to the needs of graduate and master-level programme students in physics and engineering, the present book covers more than 40 wide ranging popular toys. For each toy various features are presented including history, construction, working principle, theoretical model, a solved problem and 5-10 exercises.A course on The Physics of Toys can be designed based on the proposed book to be taught as a full course at graduate and master-level and even to students who have never been exposed to physics. Further, the features of the toys covered in this book can be used to illustrate various concepts and principles in different branches of physics and engineering.

This book is a concise introduction to the key concepts of classical field theory for beginning graduate students and advanced undergraduate students who wish to study the unifying structures and physical insights provided by classical field theory without dealing with the additional complication of quantization. In that regard, there are many important aspects of field theory that can be understood without quantizing the fields. These include the action formulation, Galilean and relativistic invariance, traveling and standing waves, spin angular momentum, gauge invariance, subsidiary conditions, fluctuations, spinor and vector fields, conservation laws and symmetries, and the Higgs mechanism, all of which are often treated briefly in a course on quantum field theory.

This book provides a comprehensive analysis of time-fixed terminal rendezvous around the Earth using chemical propulsion. The book has two main objectives. The first is to derive the mathematics of relative motion in near-circular orbit when subjected to perturbations emanating from the oblateness of the Earth, third-body gravity, and atmospheric drag. The mathematics are suitable for quick trajectory prediction and the creation of computer codes and efficient software to solve impulsive maneuvers and fly rendezvous missions. The second objective of this book is to show how the relative motion theory is applied to the exact precision-integrated, long-duration, time-fixed terminal rendezvous problem around the oblate Earth for the general elliptic orbit case. The contents are both theoretical and applied, with long-lasting value for aerospace engineers, trajectory designers, professors of orbital mechanics, and students at the graduate level and above.

Encouraged to share his memories of Michael Faraday (1791 1867), John Hall Gladstone (1827 1902) published in 1872 this short work about his late friend's life and career. Faraday's successor as Fullerian Professor of Chemistry at the Royal Institution, Gladstone discusses how Faraday approached science, and the value of his discoveries. Offering informed insights into Faraday's character, Gladstone includes a number of extracts from personal letters. The work also includes a translation of part of the eulogy given by Jean-Baptiste Dumas at the Academie des Sciences, as well as an anonymous poem honouring Faraday and published in Punch shortly after his death. An appendix lists the numerous learned societies to which Faraday belonged. Also reissued in this series are The Life and Letters of Faraday (1870), compiled by Henry Bence Jones, and John Tyndall's Faraday as a Discoverer (1868)."

Learn how to think like a physicist from a Nobel laureate and "one of the greatest minds of the twentieth century" (New York Review of Books) with these six classic and beloved lessons It was Richard Feynman's outrageous and scintillating method of teaching that earned him legendary status among students and professors of physics. From 1961 to 1963, Feynman delivered a series of lectures at the California Institute of Technology that revolutionized the teaching of physics around the world. Six Easy Pieces, taken from these famous Lectures on Physics, represent the most accessible material from the series. In these classic lessons, Feynman introduces the general reader to the following topics: atoms, basic physics, energy, gravitation, quantum mechanics, and the relationship of physics to other topics. With his dazzling and inimitable wit, Feynman presents each discussion with a minimum of jargon. Filled with wonderful examples and clever illustrations, Six Easy Pieces is the ideal introduction to the fundamentals of physics by one of the most admired and accessible physicists of modern times. "If one book was all that could be passed on to the next generation of scientists it would undoubtedly have to be Six Easy Pieces."- John Gribbin, New Scientist

Originally published in 1938 by Cambridge University Press, The Evolution of Physics traces the development of ideas in physics, in a manner suitable for any reader. Written by famed physicist Albert Einstein and Leopold Infeld, this latest edition includes a new introduction from modern Einstein biographer, Walter Isaacson. Using this work to push his realist approach to physics in defiance of much of quantum mechanics, Einstein's The Evolution of Physics was published to great popularity and was featured in a Time magazine cover story. A classic work for any student of physics or lover of Albert Einstein, The Evolution of Physics can be enjoyed by any and should be celebrated by all.

From the reviews: "A unique feature of this book is the nice blend of engineering vividness and mathematical rigour. [...] The authors are to be congratulated for their valuable contribution to the literature in the area of theoretical thermoelasticity and vibration of plates." Journal of Sound and Vibration

Over the course of his distinguished career, Nicolai Reshetikhin has made a number of groundbreaking contributions in several fields, including representation theory, integrable systems, and topology. The chapters in this volume - compiled on the occasion of his 60th birthday - are written by distinguished mathematicians and physicists and pay tribute to his many significant and lasting achievements. Covering the latest developments at the interface of noncommutative algebra, differential and algebraic geometry, and perspectives arising from physics, this volume explores topics such as the development of new and powerful knot invariants, new perspectives on enumerative geometry and string theory, and the introduction of cluster algebra and categorification techniques into a broad range of areas. Chapters will also cover novel applications of representation theory to random matrix theory, exactly solvable models in statistical mechanics, and integrable hierarchies. The recent progress in the mathematical and physicals aspects of deformation quantization and tensor categories is also addressed. Representation Theory, Mathematical Physics, and Integrable Systems will be of interest to a wide audience of mathematicians interested in these areas and the connections between them, ranging from graduate students to junior, mid-career, and senior researchers.

This textbook serves as an introduction to groups, rings, fields, vector and tensor spaces, algebras, topological spaces, differentiable manifolds and Lie groups --- mathematical structures which are foundational to modern theoretical physics. It is aimed primarily at undergraduate students in physics and mathematics with no previous background in these topics. Applications to physics --- such as the metric tensor of special relativity, the symplectic structures associated with Hamilton's equations and the Generalized Stokes's Theorem --- appear at appropriate places in the text. Worked examples, end-of-chapter problems (many with hints and some with answers) and guides to further reading make this an excellent book for self-study. Upon completing this book the reader will be well prepared to delve more deeply into advanced texts and specialized monographs in theoretical physics or mathematics.

This book collects a selection of papers presented at ELECTRIMACS 2019, the 13th international conference of the IMACS TC1 Committee, held in Salerno, Italy, on 21st-23rd May 2019. The conference papers deal with modelling, simulation, analysis, control, power management, design optimization, identification and diagnostics in electrical power engineering. The main application fields include electric machines and electromagnetic devices, power electronics, transportation systems, smart grids, electric and hybrid vehicles, renewable energy systems, energy storage, batteries, supercapacitors and fuel cells, and wireless power transfer. The contributions included in Volume 1 are particularly focused on electrical engineering simulation aspects and innovative applications.

This book discusses the impetus-based physics of the Jesuit natural philosopher and mathematician Honore Fabri (1608-1688), a senior representative of Jesuit scientists during the period between Galileo's death (1642) and Newton's Principia (1687). It shows how Fabri, while remaining loyal to a general Aristotelian outlook, managed to reinterpret the old concept of "impetus" in such a way as to assimilate into his physics building blocks of modern science, like Galileo's law of fall and Descartes' principle of inertia. This account of Fabri's theory is a novel one, since his physics is commonly considered as a dogmatic rejection of the New Science, not essentially different from the medieval impetus theory. This book shows how New Science principles were taught in Jesuit Colleges in the 1640s, thus depicting the sophisticated manner in which new ideas were settling within the lion's den of Catholic education.

Even though mathematics and physics have been related for centuries and this relation appears to be unproblematic, there are many questions still open: Is mathematics really necessary for physics, or could physics exist without mathematics? Should we think physically and then add the mathematics apt to formalise our physical intuition, or should we think mathematically and then interpret physically the obtained results? Do we get mathematical objects by abstraction from real objects, or vice versa? Why is mathematics effective into physics?

These are all relevant questions, whose answers are necessary to fully understand the status of physics, particularly of contemporary physics.

The aim of this book is to offer plausible answers to such questions through both historical analyses of relevant cases, and philosophical analyses of the relations between mathematics and physics.

First published in 1868, soon after the death of Michael Faraday (1791 1867), this short work assesses the discoveries made by a humble bookbinder who became one of the foremost scientific investigators of the nineteenth century. Eminently qualified, John Tyndall (1820 93), who received Faraday's support in taking up the professorship of natural philosophy at the Royal Institution in 1853, gives an informed appraisal of a remarkable scientific career. The protege of Sir Humphry Davy, Faraday went on to carry out pioneering work in the fields of electromagnetism, diamagnetism and electrolysis. Tyndall focuses here on Faraday's research, describing his influences and how he approached his investigations, although insights into his character are also incorporated: 'Underneath his sweetness and gentleness was the heat of a volcano.' Also reissued in this series are The Life and Letters of Faraday (1870), compiled by Henry Bence Jones, and John Hall Gladstone's Michael Faraday (1872)."