Isogeometric Analysis is a groundbreaking computational approach that promises the possibility of integrating the finite element method into conventional spline-based CAD design tools. It thus bridges the gap between numerical analysis and geometry, and moreover it allows to tackle new cutting edge applications at the frontiers of research in science and engineering. This proceedings volume contains a selection of outstanding research papers presented at the second International Workshop on Isogeometric Analysis and Applications, held at Annweiler, Germany, in April 2014.

Asymptotic methods are of great importance for practical applications, especially in dealing with boundary value problems for small stochastic perturbations. This book deals with nonlinear dynamical systems perturbed by noise. It addresses problems in which noise leads to qualitative changes, escape from the attraction domain, or extinction in population dynamics. The most likely exit point and expected escape time are determined with singular perturbation methods for the corresponding Fokker-Planck equation. The authors indicate how their techniques relate to the Ito calculus applied to the Langevin equation. The book will be useful to researchers and graduate students.

Constructibility and complexity play central roles in recent research in computer science, mathematics and physics. For example, scientists are investigating the complexity of computer programs, constructive proofs in mathematics and the randomness of physical processes. But there are different approaches to the explication of these concepts. This volume presents important research on the state of this discussion, especially as it refers to quantum mechanics. This foundational debate' in computer science, mathematics and physics was already fully developed in 1930 in the Vienna Circle. A special section is devoted to its real founder Hans Hahn, referring to his contribution to the history and philosophy of science. The documentation section presents articles on the early Philipp Frank and on the Vienna Circle in exile. Reviews cover important recent literature on logical empiricism and related topics.

This work tackles the problems of understanding how energy is transmitted and distributed in power-grids as well as in determining how robust this transmission and distribution is when modifications to the grid or power occur. The most important outcome is the derivation of explicit relationships between the structure of the grid, the optimal transmission and distribution of energy, and the grid's collective behavior (namely, the synchronous generation of power). These relationships are extremely relevant for the design of resilient power-grid models. To allow the reader to apply these results to other complex systems, the thesis includes a review of relevant aspects of network theory, spectral theory, and novel analytical calculations to predict the existence and stability of periodic collective behavior in complex networks of phase oscillators, which constitute a paradigmatic model for many complex systems.

Many books have been written on the history of quantum mechanics. So far as I am aware, however, this is the first to incorporate the results of the large amount of detailed scholarly research completed by professional historians of physics over the past fifteen years. It is also, I believe, the first since Max Jammer's pioneering study of fifteen years ago to attempt a genuine 'history' as opposed to a mere technical report or popular or semi-popular account. My aims in making this attempt have been to satisfy the needs of historians of science and, more especially, to promote a serious interest in the history of science among phYSicists and physics students. Since the creation of quantum mechanics was inevitably a technical process conducted through the medium of technical language it has been impossible to avoid the introduction of a large amount of such language. Some acquaintance with quantum mechanics, corresponding to that obtained through an undergraduate physics course, has accordingly been assumed. I have tried to ensure, however, that such an acquaintance should be sufficient as well as necessary, and even someone with only the most basic grounding in physics should be able with judicious skip ping, to get through the book. The technical details are essential to the dialogue, but the plot proceeds and can, I hope, be understood on a non technical level."

Ya. B. Zeldovich was most assuredly one of the greatest physicists and cosmologists of the 20th century. This volume presents reminiscences about this exemplary academician, providing biographical and historical insights from the friends, students, and colleagues who knew him best. They outline Zeldovich's life and achievements, from his early days in chemical physics through his groundbreaking work in combustion and detonation, his role in the development of Soviet nuclear and thermonuclear weapons, and his contributions to nuclear and elementary particle physics, to his later years in cosmology and astrophysics. Zeldovich: Reminiscences not only pays homage to an outstanding scientist and his accomplishments. It also offers incisive commentary on Soviet science and the impact that Zeldovich had on future generations, in the former Soviet Union and throughout the international physics community.

This provocative and critical work addresses the question of why scientific realists and positivists consider experimental physics to be a natural and empirical science. Taking insights from contemporary science studies, continental philosophy, and the history of physics, this book describes and analyses the metaphysical presuppositions that underwrite the technological use of experimental apparatus and instruments to explore, model, and understand nature. By revealing this metaphysical foundation, the author questions whether experimental physics is a natural and empirical science at all.

In philosophy as in ordinary life, cause and effect are twin pillars on which much of our thought seems based. But almost a century ago, Bertrand Russell declared that modern physics leaves these pillars without foundations. Russell's revolutionary conclusion was that "the law of causality is a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm."
Russell's famous challenge remains unanswered. Despite dramatic advances in physics, the intervening century has taken us no closer to an explanation of how to find a place for causation in a world of the kind that physics reveals. In particular, we still have no satisfactory account of the directionality of causation -- the difference between cause and effect, and the fact that causes typically precede their effects. In this important collection of new essays, 13 leading scholars revisit Russell's revolution, in search of reconciliation.
The connecting theme in these essays is that to reconcile causation with physics, we need to put ourselves in the picture: we need to think about why creatures in our situation should present their world in causal terms.

Based on research on the links between deep brain stimulation and its applications in the field of psychiatry, the history of techniques is of great importance in this book in order to understand the scope of the fields of application of electricity in brain sciences. The concepts of brain electricity, stimulation, measurement and therapy are further developed to identify lines of convergence, ruptures and conceptual perspectives for a materialistic understanding of human nature that emerged during the 18th century. In an epistemological posture, at the crossroads of the concepts of epistemes, as stated by Foucault, and phenomenotechnics, as conceived by Bachelard, the analyses focus on the technical content of the theories while inscribing them in the language and specificities of each era.

General relativity ranks among the most accurately tested fundamental theories in all of physics. Deficiencies in mathematical and conceptual understanding still exist, hampering further progress. This book collects surveys by experts in mathematical relativity writing about the current status of, and problems in, their fields. There are four contributions for each of the following mathematical areas: differential geometry and differential topology, analytical methods and differential equations, and numerical methods.

In this introductory text, Dr. Birdi demonstrates experimental methods and analyses of fractal dimensions in natural processes. In addition to a general overview, he discusses in detail problems in the fields of chemistry, geochemistry, and biophysics. Both students and professionals with a minimum of mathematics or physical science training will learn to find and model shapes and patterns from their own everyday observations.

Miniaturization has revolutionized human affairs by making possible inexpensive integrated electronic circuits comprised of devices and wires with sub-micrometer dimensions. These integrated circuits are now ubiquitous, controlling everything from our automobiles to our toasters. Continued miniaturization, beyond sub-micrometer dimensions, seems likely. And so we are compelled to explore science and technology on a new, yet smaller scale: the nanometer scale. This volume is a survey of the machinery and science of the nanometer scale. Its twenty-two contributing authors, drawn from many different disciplines including atomic physics, microelectronics, polymer chemistry, and bio-physics, delineate the course of current research and articulate a vision for the development of the nanometer frontiers in electronics, mechanics, chemistry, magnetics, materials, and biology. They reveal a world thirty years hence where motors are smaller than the diameter of a human hair; where single-celled organisms are programmed to fabricate materials with nanometer precision; where single atoms are used for computation, and where quantum chaos is the norm. Aimed at the level of comprehension of at least a junior- or senior-level undergraduate science (biology, chemistry, physics, or engineering) student, the book provides a survey of developments within the breadth of the nanotechnology field. The book is thus intended for both students and researchers in tunneling microscopy, polymer chemistry, bio-physics, atomic physics, electrical engineering, mechanical engineering, materials science, condensed matter physics, biology, lithography, and chaos. Mathematical derivations have been minimized, but not eliminted. The book contains many illustrations, some in color.

The Student's Study Guide summarizes the essential information in each chapter and provides additional problems for the student to solve, reinforcing the text's emphasis on problem-solving strategies and student misconceptions. Student's Study Guide for University Physics with Modern Physics, Volume 1 (Chapters 1-20)

Written in an accessible and informal style, this textbook is designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors. The book has its origins in a series of lecture courses given by the authors, all internationally known mathematicians and renowned expositors. The introduction by Nigel Hitchin addresses the meaning of integrability: how do we recognize an integrable system? His own contribution then develops connections with algebraic geometry, and includes an introduction to Riemann surfaces, sheaves, and line bundles.

One of the most enduring elements in theoretical physics has been group theory. GROUP 24: Physical and Mathematical Aspects of Symmetries provides an important selection of informative articles describing recent advances in the field. The applications of group theory presented in this book deal not only with the traditional fields of physics, but also include such disciplines as chemistry and biology.
Awarded the Wigner Medal and the Weyl Prize, respectively, H.J. Lipkin and E. Frenkel begin the volume with their contributions. Plenary session contributions are represented by 18 longer articles, followed by nearly 200 shorter articles. The book also presents coherent states, wavelets, and applications and quantum group theory and integrable systems in two separate sections.
As a record of an international meeting devoted to the physical and mathematical aspects of group theory, GROUP 24: Physical and Mathematical Aspects of Symmetries constitutes an essential reference for all researchers interested in various current developments related to the important concept of symmetry.

The motion of a particle in a random potential in two or more dimensions is chaotic, and the trajectories in deterministically chaotic systems are effectively random. It is therefore no surprise that there are links between the quantum properties of disordered systems and those of simple chaotic systems. The question is, how deep do the connec tions go? And to what extent do the mathematical techniques designed to understand one problem lead to new insights into the other? The canonical problem in the theory of disordered mesoscopic systems is that of a particle moving in a random array of scatterers. The aim is to calculate the statistical properties of, for example, the quantum energy levels, wavefunctions, and conductance fluctuations by averaging over different arrays; that is, by averaging over an ensemble of different realizations of the random potential. In some regimes, corresponding to energy scales that are large compared to the mean level spacing, this can be done using diagrammatic perturbation theory. In others, where the discreteness of the quantum spectrum becomes important, such an approach fails. A more powerful method, devel oped by Efetov, involves representing correlation functions in terms of a supersymmetric nonlinear sigma-model. This applies over a wider range of energy scales, covering both the perturbative and non-perturbative regimes. It was proved using this method that energy level correlations in disordered systems coincide with those of random matrix theory when the dimensionless conductance tends to infinity."

Processes with long range correlations occur in a wide variety of fields ranging from physics and biology to economics and finance. This book, suitable for both graduate students and specialists, brings the reader up to date on this rapidly developing field. A distinguished group of experts have been brought together to provide a comprehensive and well-balanced account of basic notions and recent developments. The book is divided into two parts. The first part deals with theoretical developments in the area. The second part comprises chapters dealing primarily with three major areas of application: anomalous diffusion, economics and finance, and biology (especially neuroscience).

Designed to cover the fundamental concepts of digital signal processing, the book introduces topics such as discrete-time signals, the z-transform, frequency analysis, discrete and fast Fourier transforms, digital filters, FIR, statistical DSP, applications, and more. DSP has been applied in most disciplines ranging from engineering to telecommunications, and from astronomy to medical imaging. This book focuses on the fundamentals of DSP, namely on the representation of signals by mathematical models and on the processing of signals by discrete-time systems. Features Designed to cover the fundamental concepts of DSP Introduces topics such as discrete-time signals, the z-transform, frequency analysis, discrete and fast Fourier transforms, digital filters, FIR, statistical DSP, applications, and more Features a variety of exercises and a glossary

The present monograph provides a systematic and basicaIly self-eontained introduetion to a mathematieal framework eapable of ineOIporating those fundamental physical premises of general relativity and quantum meehanics which are not mutually ineonsistent, and which ean be therefore retained in the unifieation of these two fundamental areas of twentieth- eentury physics. Thus, its underlying thesis is that the equivalenee principle of classical general relativity remains true at the quantum level, where it has to be reeonciled, however, with the uneertainty principle. As will be discussed in the first as weIl as in the last chapter, eonventional methods based on classical geometries and on single Hilbert space frame- works for quantum meehanics have failed to aehieve such a reconciliation. On the other hand, foundational arguments suggest that new types of geometries should be introdueed. The geometries proposed and studied in this monograph are referred to as quantum geometries, sinee basic quantum principles are ineorporated into their strueture from the outset. The mathematical tools used in constructing these quantum geometries are drawn from functional analysis and fibre bundle theory, and in particular from Hilbert space the- ory, group representation theory, and modern formulations of differential geometry. The developed physical eoncepts have their roots in nonrelativistic and relativistic quantum me- chanics in Hilbert spaee, in classical general relativity and in quantum field theory for mas- sive and gauge fields.

In this third volume of his modern introduction to quantum field theory, Eberhard Zeidler examines the mathematical and physical aspects of gauge theory as a principle tool for describing the four fundamental forces which act in the universe: gravitative, electromagnetic, weak interaction and strong interaction.

Volume III concentrates on the "classical aspects "of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles." "This must be supplemented by the crucial, but elusive quantization procedure.

The book is arranged in four sections, devoted to realizing the universal principle "force equals curvature: "

Part I: The Euclidean Manifold as a Paradigm

Part II: Ariadne's Thread in Gauge Theory

Part III: Einstein's Theory of Special Relativity

Part IV: Ariadne's Thread in Cohomology

For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum.

"Quantum Field Theory" builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos).

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The 26th International Conference on the Physics of Semiconductors was held from 29 July to 2 August 2002 at the Edinburgh International Conference Centre. It is the premier meeting in the field of semiconductor physics and attracted over 1000 participants from leading academic, governmental and industrial institutions in some 50 countries around the world. Plenary and invited papers (34) have been printed in the paper volume, and all submitted papers (742) are included on the downloadable resources.These proceedings provide an international perspective on the latest research and a review of recent developments in semiconductor physics. Topics range from growth and properties of bulk semiconductors to the optical and transport properties of semiconductor nanostructures. There are 742 papers, mostly arranged in chapters on Bulk, dynamics, defects and impurities, growth (147); Heterostructures, quantum wells, superlattices - optical (138); Heterostructures, quantum wells, superlattices - transport (97); Quantum nanostructures - optical (120); Quantum nanostructures - transport (85); New materials and concepts (52); Novel devices (43); and Spin and magnetic effects (48). A number of trends were identified in setting up the overall programme of the conference. There were significant contributions from new directions of research such as nanostructures and one-dimensional physics; spin effects and ferromagnetism; and terahertz and subband physics. These complemented areas in which the conference has traditional strengths, such as defects and bulk materials; crystal growth; quantum transport; and optical properties.As a record of a conference that covers the whole range of semiconductor physics, this book is an essential reference for researchers working on semiconductor physics, device physics, materials science, chemistry, and electronic and electrical engineering.

This is the best seller in this market. It provides a comprehensive introduction to complex variable theory and its applications to current engineering problems. It is designed to make the fundamentals of the subject more easily accessible to students who have little inclination to wade through the rigors of the axiomatic approach. Modeled after standard calculus books-both in level of exposition and layout-it incorporates physical applications throughout the presentation, so that the mathematical methodology appears less sterile to engineering students.