This volume reflects the state of the art of numerical simulation of transitional and turbulent flows and provides an active forum for discussion of recent developments in simulation techniques and understanding of flow physics. Following the tradition of earlier DLES workshops, these papers address numerous theoretical and physical aspects of transitional and turbulent flows. At an applied level it contributes to the solution of problems related to energy production, transportation, magneto-hydrodynamics and the environment. A special session is devoted to quality issues of LES. The ninth Workshop on 'Direct and Large-Eddy Simulation' (DLES-9) was held in Dresden, April 3-5, 2013, organized by the Institute of Fluid Mechanics at Technische Universitat Dresden. This book is of interest to scientists and engineers, both at an early level in their career and at more senior levels.

When we use science to describe and understand the world around us, we are in essence grasping nature through symmetry. Emphasizing the concepts, this book leads the reader coherently and comprehensively into the fertile field of symmetry and its applications. Among the most important applications considered are the fundamental forces of nature and the Universe. Written by a renowned expert, this book will convince all interested readers of the importance of symmetry in science.

This is an up to date exposition of nonlinear phenomena in random and inhomogeneous media which provides recent results on the combined effects of nonlinearity and inhomogeneity, including random inhomogeneity. Topics covered include recent developments within such popular areas as nonlinear photonic crystals, inhomogeneous optical fibres (dispersion management), discrete nonlinear lattices, discrete breathers, Bose-Einstein condensates, ultra-short optical pulse, Josephson lattices, various types of inhomogeneous waveguides and nonlinear quantization.

Due to the rapid expansion of the frontiers of physics and engineering, the demand for higher-level mathematics is increasing yearly. This book is designed to provide accessible knowledge of higher-level mathematics demanded in contemporary physics and engineering. Rigorous mathematical structures of important subjects in these fields are fully covered, which will be helpful for readers to become acquainted with certain abstract mathematical concepts. The selected topics are:

- Real analysis, Complex analysis, Functional analysis, Lebesgue integration theory, Fourier analysis, Laplace analysis, Wavelet analysis, Differential equations, and Tensor analysis.

This book is essentially self-contained, and assumes only standard undergraduate preparation such as elementary calculus and linear algebra. It is thus well suited for graduate students in physics and engineering who are interested in theoretical backgrounds of their own fields. Further, it will also be useful for mathematics students who want to understand how certain abstract concepts in mathematics are applied in a practical situation. The readers will not only acquire basic knowledge toward higher-level mathematics, but also imbibe mathematical skills necessary for contemporary studies of their own fields.

In August/September 1999, a group of 68 physicists from 48 laboratories in 17 countries met in Erice, Italy, to participate in the 37th Course of the International School of Subnuclear Physics. This volume constitutes the proceedings of that meeting. It focuses on the basic unity of fundamental physics at both the theoretical and the experimental level.

Methods of global analysis and stochastic analysis are most often applied in mathematical physics as separate entities, thus forming important directions in the field. However, while combination of the two subject areas is rare, it is fundamental for the consideration of a broader class of problems.

This book develops methods of Global Analysis and Stochastic Analysis such that their combination allows one to have a more or less common treatment for areas of mathematical physics that traditionally are considered as divergent and requiring different methods of investigation.

Global and Stochastic Analysis with Applications to Mathematical Physics covers branches of mathematics that are currently absent in monograph form. Through the demonstration of new topics of investigation and results, both in traditional and more recent problems, this book offers a fresh perspective on ordinary and stochastic differential equations and inclusions (in particular, given in terms of Nelson's mean derivatives) on linear spaces and manifolds. Topics covered include classical mechanics on non-linear configuration spaces, problems of statistical and quantum physics, and hydrodynamics.

A self-contained book that provides a large amount of preliminary material and recent results which will serve to be a useful introduction to the subject and a valuable resource for further research. It will appeal to researchers, graduate and PhD students working in global analysis, stochastic analysis and mathematical physics.

The intersection of probability and physics has been a rich and explosive area of growth in the past two decades, specifically covering such subjects as percolation theory, random walks, interacting particle systems, and various topics related to statistical mechanics. In the last several years, substantial progress has been made in a number of directions: fluctuations of 2-dimensional growth processes, Wulf constructions in higher dimensions for percolation, Potts and Ising models, classification of random walks in random environments, the introduction of the stochastic Loewner equation, the rigorous proof of intersection exponents for planar Brownian motion, and finally the proof of conformal invariance for critical percolation on the triangular lattice. This volume consists of a collection of invited articles, written by some of the most distinguished probabilists in the above-mentioned areas, most of whom were personally responsible for advances in the various subfields of probability. All of the articles are an outgrowth of the Fourth Brazilian School of Probability, held in Mambucaba, Brazil, August 2000. Contributors: K. Alexander * J.M. AzaAs * J. van den Berg * T. Bodineau * F. Camia * N. Cancrini * G. Grimmett * P. Hiemer * A.E. Holroyd * H. Kesten * G.F. Lawler * T.M. Liggett * J. Lorinczi * F. Martinelli * C. M. Newman * J. Quastel * C.-E. Pfister * M. PrAhofer * C. Roberto * O. Schramm * V. Sidoravicius * H. Spohn * A. Toom * B. TA3th * D. Ueltschi * W. Werner * M. Wschebor * M. WA1/4thrich Graduate students and researchers in probability theory and math physics will find this book a useful reference.

Equivariant cohomology on smooth manifolds is the subject of this book which is part of a collection of volumes edited by J. Bruning and V.W. Guillemin. The point of departure are two relatively short but very remarkable papers be Henry Cartan, published in 1950 in the Proceedings of the "Colloque de Topologie." These papers are reproduced here, together with a modern introduction to the subject, written by two of the leading experts in the field. This "introduction" comes as a textbook of its own, though, presenting the first full treatment of equivariant cohomology in the de Rahm setting. The well known topological approach is linked with the differential form aspect through the equivariant de Rahm theorem. The systematic use of supersymmetry simplifies considerably the ensuing development of the basic technical tools which are then applied to a variety of subjects, leading up to the localization theorems and other very recent results."

Electron Paramagnetic Resonance (EPR) Volume 17 highlights major developments in this area reported up to the end of 1999, with results being set into the context of earlier work and presented as a set of critical yet coherent overviews. The topics covered describe contrasting types of application, ranging from biological areas such as EPR and ENDOR studies of metalloproteins and evidence of free-radical reactions in biology and medically-related systems, to experimental developments and applications involving EPR imaging, the use of very high fields, and time-resolved methods. Critical reviews of applications involving bacterial photosynthesis, spin-labelling and spin-probes studies of self-assembled systems, and organometallic chemistry are also included. As EPR continues to find new applications in virtually all areas of modern science, including physics, chemistry, biology and materials science, this series caters not only for experts in the field, but also those wishing to gain a general overview of EPR applications in a given area. Specialist Periodical Reports provide systematic and detailed review coverage in major areas of chemical research. Compiled by teams of leading authorities in the relevant subject areas, the series creates a unique service for the active research chemist, with regular, in-depth accounts of progress in particular fields of chemistry. Subject coverage within different volumes of a given title is similar and publication is on an annual or biennial basis.

Mankind has a fascination with measurement. Down the centuries we have produced a plethora of incompatible and duplicatory systems for measuring everything from the width of an Egyptian pyramid to the concentration of radioactivity near a nuclear reactor and the value of the fine structure constant. With the introduction first of the metric system and of its successor the Système International d'Unités (SI), the scientific community has established a standard method of measurement based on only seven core units. The Encyclopaedia of Scientific Units, Weights and Measures converts the huge variety of units from all over the world in every period of recorded history into units of the SI. Featuring: - An A - Z of conversion tables for over 10,000 units of measurements. - Tables of the fundamental constants of nature with their units. - Listings of professional societies, and national standardization bodies for easy reference. - An extensive bibliography detailing further reading on the multifarious aspects of measurement and its units. This huge work is simply a "must have" for any reference library frequented by scientists of any discipline or by those with historical interests in units of measurement such as archaeologists.

The field of phase transitions and critical phenomena continues to be active in research, producing a steady stream of interesting and fruitful results. It has moved into a central place in condensed matter studies.
Statistical physics, and more specifically, the theory of transitions between states of matter, more or less defines what we know about 'everyday' matter and its transformations.
The major aim of this serial is to provide review articles that can serve as standard references for research workers in the field, and for graduate students and others wishing to obtain reliable information on important recent developments.

This updated edition is designed as a brief introduction to the fundamental particles that make up the matter in our universe. Numerous examples, figures, and simple explanations enable general readers and physics students to understand complex concepts related to the universe. Selected topics include atoms, quarks, accelerators, detectors, colliders, string theory, and more.

This volume begins with a description of Alladi Ramakrishnan's remarkable scientific career and his grand vision that led to the creation of The Institute of Mathematical Sciences (MATSCIENCE), in Madras (now Chennai), India, in 1962. The lists of his research publications, his PhD students, and other relevant facts relating to his eventful career are included. The inclusion of both research and survey articles by leading mathematicians, statisticians, and physicists who got to know Alladi Ramakrishnan over the years and admired his significant contributions to research and to the scientific profession, have been written and dedicated in this volume to Ramakrishnan's memory.

Density functional theory (DFT) is by now a well-established method for tackling the quantum mechanics of many-body systems. Originally applied to compute properties of atoms and simple molecules, DFT has quickly become a work horse for more complex applications in the chemical and materials sciences. The present set of lectures, spanning the whole range from basic principles to relativistic and time-dependent extensions of the theory, is the ideal introduction for graduate students or nonspecialist researchers wishing to familiarize themselves with both the basic and most advanced techniques in this field.

Mathematical physics has made enormous strides over the past few decades, with the emergence of many new disciplines and with revolutionary advances in old disciplines. One of the especially interesting features is the link between developments in mathematical physics and in pure mathematics. Many of the exciting advances in mathematics owe their origin to mathematical physics -- superstring theory, for example, has led to remarkable progress in geometry -- while very pure mathematics, such as number theory, has found unexpected applications.

The beginning of a new millennium is an appropriate time to survey the present state of the field and look forward to likely advances in the future. In this book, leading experts give personal views on their subjects and on the wider field of mathematical physics. The topics covered range widely over the whole field, from quantum field theory to turbulence, from the classical three-body problem to non-equilibrium statistical mechanics.

A Nobel Prize-winning physicist explains what happened at the very beginning of the universe, and how we know, in this popular science classic. Our universe has been growing for nearly 14 billion years. But almost everything about it, from the elements that forged stars, planets, and lifeforms, to the fundamental forces of physics, can be traced back to what happened in just the first three minutes of its life. In this book, Nobel Laureate Steven Weinberg describes in wonderful detail what happened in these first three minutes. It is an exhilarating journey that begins with the Planck Epoch - the earliest period of time in the history of the universe - and goes through Einstein's Theory of Relativity, the Hubble Red Shift, and the detection of the Cosmic Microwave Background. These incredible discoveries all form the foundation for what we now understand as the "standard model" of the origin of the universe. The First Three Minutes examines not only what this model looks like, but also tells the exciting story of the bold thinkers who put it together. Clearly and accessibly written, The First Three Minutes is a modern-day classic, an unsurpassed explanation of where it is we really come from.

This book presents the current knowledge about nonlinear localized travelling excitations in crystals. Excitations can be vibrational, electronic, magnetic or of many other types, in many different types of crystals, as silicates, semiconductors and metals. The book is dedicated to the British scientist FM Russell, recently turned 80. He found 50 years ago that a mineral mica muscovite was able to record elementary charged particles and much later that also some kind of localized excitations, he called them quodons, was also recorded. The tracks, therefore, provide a striking experimental evidence of quodons existence. The first chapter by him presents the state of knowledge in this topic. It is followed by about 18 chapters from world leaders in the field, reviewing different aspects, materials and methods including experiments, molecular dynamics and theory and also presenting the latest results. The last part includes a personal narration of FM Russell of the deciphering of the marks in mica. It provides a unique way to present the science in an accessible way and also illustrates the process of discovery in a scientist's mind.

This book is based on the idea that Boltzmann-like modelling methods can be developed to design, with special attention to applied sciences, kinetic-type models which are called generalized kinetic models. In particular, these models appear in evolution equations for the statistical distribution over the physical state of each individual of a large population. The evolution is determined both by interactions among individuals and by external actions.

Considering that generalized kinetic models can play an important role in dealing with several interesting systems in applied sciences, the book provides a unified presentation of this topic with direct reference to modelling, mathematical statement of problems, qualitative and computational analysis, and applications. Models reported and proposed in the book refer to several fields of natural, applied and technological sciences. In particular, the following classes of models are discussed: population dynamics and socio-economic behaviours, models of aggregation and fragmentation phenomena, models of biology and immunology, traffic flow models, models of mixtures and particles undergoing classic and dissipative interactions.

NOW A MAJOR SERIES 'GENIUS' ON NATIONAL GEOGRAPHIC, PRODUCED BY RON HOWARD AND STARRING GEOFFREY RUSH Einstein is the great icon of our age: the kindly refugee from oppression whose wild halo of hair, twinkling eyes, engaging humanity and extraordinary brilliance made his face a symbol and his name a synonym for genius. He was a rebel and nonconformist from boyhood days. His character, creativity and imagination were related, and they drove both his life and his science. In this marvellously clear and accessible narrative, Walter Isaacson explains how his mind worked and the mysteries of the universe that he discovered. Einstein's success came from questioning conventional wisdom and marvelling at mysteries that struck others as mundane. This led him to embrace a worldview based on respect for free spirits and free individuals. All of which helped make Einstein into a rebel but with a reverence for the harmony of nature, one with just the right blend of imagination and wisdom to transform our understanding of the universe. This new biography, the first since all of Einstein's papers have become available, is the fullest picture yet of one of the key figures of the twentieth century. This is the first full biography of Albert Einstein since all of his papers have become available -- a fully realised portrait of this extraordinary human being, and great genius. Praise for EINSTEIN by Walter Isaacson:- 'YOU REALLY MUST READ THIS.' Sunday Times 'As pithy as Einstein himself.' New Scientist '[A] brilliant biography, rich with newly available archival material.' Literary Review 'Beautifully written, it renders the physics understandable.' Sunday Telegraph 'Isaacson is excellent at explaining the science. ' Daily Express

This book provides an elementary introduction to the ideas and methods of topology by the detailed study of certain topics. There are elegant but rigorous proofs of many of the basic theorems, and special attention is given to the results needed in the theory of functions.

This book presents a broad survey of models for critical and catastrophic phenomena in the geosciences, with strong emphasis on earthquakes. It assumes the perspective of statistical physics, which provides the theoretical frame for dealing with complex systems in general. This volume addresses graduate students wishing to specialize in the field and researchers working or interested in the field having a background in the physics, geosciences or applied mathematics.

Relationalism about space is a venerable doctrine that is enjoying renewed attention among philosophers and physicists. Relationalists deny that space is ontologically prior to matter and seek to ground all claims about the structure of space in facts about actual and possible configurations of matter. Thus, many relationalists maintain that to say that space is infinite is to say that certain sorts of infinite arrays of material points are possible (even if, in fact, the world contains only a finite amount of matter).
Gordon Belot investigates the distinctive notion of geometric possibility that relationalists rely upon. He examines the prospects for adapting to the geometric case the standard philosophical accounts of the related notion of physical possibility, with particular emphasis on Humean, primitivist, and necessitarian accounts of physical and geometric possibility. This contribution to the debate concerning the nature of space will be of interest not only to philosophers and metaphysicians concerned with space and time, but also to those interested in laws of nature, modal notions, or more general issues in ontology.