As our title suggests, there are two aspects in the subject of this book. The first is the mathematical investigation of the dynamics of infinite systems of in teracting particles and the description of the time evolution of their states. The second is the rigorous derivation of kinetic equations starting from the results of the aforementioned investigation. As is well known, statistical mechanics started in the last century with some papers written by Maxwell and Boltzmann. Although some of their statements seemed statistically obvious, we must prove that they do not contradict what me chanics predicts. In some cases, in particular for equilibrium states, it turns out that mechanics easily provides the required justification. However things are not so easy, if we take a step forward and consider a gas is not in equilibrium, as is, e.g., the case for air around a flying vehicle. Questions of this kind have been asked since the dawn of the kinetic theory of gases, especially when certain results appeared to lead to paradoxical conclu sions. Today this matter is rather well understood and a rigorous kinetic theory is emerging. The importance of these developments stems not only from the need of providing a careful foundation of such a basic physical theory, but also to exhibit a prototype of a mathematical construct central to the theory of non-equilibrium phenomena of macroscopic size."

Class-tested textbook that shows readers how to solve physical problems and deal with their underlying theoretical concepts while using Mathematica to derive numeric and symbolic solutions.

Delivers dozens of fully interactive examples for learning and implementation, constants and formulae can readily be altered and adapted for the user 's purposes.

New edition offers enlarged two-volume format suitable to courses in mechanics and electrodynamics, while offering dozens of new examples and a more rewarding interactive learning environment.

CD-ROM presents the entire text contents and interactive examples in Mathematica

Notebooks for problem solving and learning.

The purpose of this monograph is to show that, in the radiation regime, there exists a Hamiltonian description of the dynamics of a massless scalar field, as well as of the dynamics of the gravitational field. The authors construct such a framework extending the previous work of Kijowski and Tulczyjew. They start by reviewing some elementary facts concerning Hamiltonian dynamical systems and then describe the geometric Hamiltonian framework, adequate for both the usual asymptotically flat-at-spatial-infinity regime and for the radiation regime. The text then gives a detailed description of the application of the new formalism to the case of the massless scalar field. Finally, the formalism is applied to the case of Einstein gravity. The Hamiltonian role of the Trautman--Bondi mass is exhibited. A Hamiltonian definition of angular momentum at null infinity is derived and analysed.

The subject of the book is the development of physics in the 18th century centered upon the fundamental contributions of Leonhard Euler to physics and mathematics. This is the first book devoted to Euler as a physicist. Classical mechanics are reconstructed in terms of the program initiated by Euler in 1736 and its completion over the following decades until 1760. The book examines how Euler coordinated his progress in mathematics with his progress in physics.

The main classes of inverse problems for equations of mathematical physics and their numerical solution methods are considered in this book which is intended for graduate students and experts in applied mathematics, computational mathematics, and mathematical modelling.

The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

This book provides an overview of many of the dramatic recent developments in the fields of astronomy, cosmology and fundamental physics. Topics include observations of the structure in the cosmic background radiation, evidence for an accelerating Universe, the extraordinary concordance in the fundamental parameters of the Universe coming from these and other diverse observations, the search for dark matter candidates, evidence for neutrino oscillations, space experiments on fundamental physics, and discoveries of extrasolar planets. This book will be useful for researchers and graduate students who wish to have a broad overview of the current developments in these fields.

The Poincare Seminar is held twice a year at the Institut Henri Poincare in Paris. This volume contains the lectures of the 2002 seminars. The main topic of the first one was the vacuum energy, in particular the Casimir effect and the nature of the cosmological constant. The second one concentrated on renormalization, giving a comprehensive account of its mathematical structure and applications to high energy physics, statistical mechanics and classical mechanics.
Students will find excellent introductions to the subjects with further lectures leading to the frontiers of experimental and theoretical research, scientists will profit from contributions by outstanding experts."

This book discusses the latest advances in algorithms for symbolic summation, factorization, symbolic-numeric linear algebra and linear functional equations. It presents a collection of papers on original research topics from the Waterloo Workshop on Computer Algebra (WWCA-2016), a satellite workshop of the International Symposium on Symbolic and Algebraic Computation (ISSAC'2016), which was held at Wilfrid Laurier University (Waterloo, Ontario, Canada) on July 23-24, 2016. This workshop and the resulting book celebrate the 70th birthday of Sergei Abramov (Dorodnicyn Computing Centre of the Russian Academy of Sciences, Moscow), whose highly regarded and inspirational contributions to symbolic methods have become a crucial benchmark of computer algebra and have been broadly adopted by many Computer Algebra systems.

Drawing on advanced probability theory, Ambit Stochastics is used to model stochastic processes which depend on both time and space. This monograph, the first on the subject, provides a reference for this burgeoning field, complete with the applications that have driven its development. Unique to Ambit Stochastics are ambit sets, which allow the delimitation of space-time to a zone of interest, and ambit fields, which are particularly well-adapted to modelling stochastic volatility or intermittency. These attributes lend themselves notably to applications in the statistical theory of turbulence and financial econometrics. In addition to the theory and applications of Ambit Stochastics, the book also contains new theory on the simulation of ambit fields and a comprehensive stochastic integration theory for Volterra processes in a non-semimartingale context. Written by pioneers in the subject, this book will appeal to researchers and graduate students interested in empirical stochastic modelling.

This volume is a textbook for a year-long graduate level course in All research universities have applied mathematics for scientists and engineers. such a course, which could be taught in different departments, such as mathematics, physics, or engineering. I volunteered to teach this course when I realized that my own research students did not learn much in this course at my university. Then I learned that the available textbooks were too introduc tory. While teaching this course without an assigned text, I wrote up my lecture notes and gave them to the students. This textbook is a result of that endeavor. When I took this course many, many, years ago, the primary references were the two volumes of P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953). The present text returns the contents to a similar level, although the syllabus is quite different than given in this venerable pair of books."

This book gives an analysis of Hertz's posthumously published Principles of Mechanics in its philosophical, physical and mathematical context. In a period of heated debates about the true foundation of physical sciences, Hertz's book was conceived and highly regarded as an original and rigorous foundation for a mechanistic research program. Insisting that a law-like account of nature would require hypothetical unobservables, Hertz viewed physical theories as (mental) images of the world rather than the true design behind the phenomena. This paved the way for the modern conception of a model. Rejecting the concept of force as a coherent basic notion of physics he built his mechanics on hidden masses (the ether) and rigid connections, and formulated it as a new differential geometric language. Recently many philosophers have studied Hertz's image theory and historians of physics have discussed his forceless mechanics. The present book shows how these aspects, as well as the hitherto overlooked mathematical aspects, form an integrated whole which is closely connected to the mechanistic world view of the time and which is a natural continuation of Hertz's earlier research on electromagnetism. Therefore it is also a case study of the strong interactions between philosophy, physics and mathematics. Moreover, the book presents an analysis of the genesis of many of the central elements of Hertz's mechanics based on his manuscripts and drafts. Hertz's research program was cut short by the advent of relativity theory but its image theory influenced many philosophers as well as some physicists and mathematicians and its geometric form had a lasting influence on advanced expositions of mechanics.

This work presents a Clean Quantum Theory of the Electron, based on Dirac's equation. Clean in the sense of a complete mathematical explanation of the well known paradoxes of Dirac's theory, and a connection to classical theory, including the motion of a magnetic moment (spin) in the given field, all for a charged particle (of spin 1/2) moving in a given electromagnetic field. This theory is relativistically covariant, and it may be regarded as a mathematically consistent quantum-mechanical generalization of the classical motion of such a particle, a la Newton and Einstein. Normally, our fields are time-independent, but also discussed is the time-dependent case, where slightly different features prevail. A Schroedinger particle, such as a light quantum, experiences a very different (time-dependent) Precise Predictablity of Observables. An attempt is made to compare both cases.

The Centre de recherches mathCmatiques (CRM) was created in 1968 by the Universite de Montreal to promote research in the mathematical sci- ences. It is now a national institute that hosts several groups, holds special theme years, summer schools, workshops, postdoctoral program. The focus of its scientific activities ranges from pure to applied mathematics, and includes satistics, theoretical computer science, mathematical methods in biology and life sciences, and mathematical and theoretical physics. The CRM also promotes collaboration between mathematicians and industry. It is subsidized by the Natural Sciences and Engineering Research Council of Canada, the Fonds FCAR od the Province of Quebec, the Canadian Institute for Advanced Research and has private endowments. Current ac- tivities, fellowships, and annual reports can be found on the CRM web page at http://www . CRM. UMontreal. CAl. The CRM Series in Mathematical Physics will publish monographs, lec- ture notes, and proceedings base on research pursued and events held at the Centre de recherches mathematiques. Yvan Saint-Aubin Montreal Preface The subject of this three-week school was the explicit integration, that is, analytical as opposed to numerical, of all kinds of nonlinear differential equations (ordinary differential, partial differential, finite difference). The result of such integration is ideally the "general solution," but there are numerous physical systems for which only a particular solution is accessible, for instance the solitary wave of the equation of Kuramoto and Sivashinsky in turbulence.

This text is the proceedings volume of a NATO Advanced Research Workshop, held in Eliat, Israel, April 5th-8th, 2000. It brings together interdisciplinary contributions ranging from applied mathematics, theoretical physics, quantum chemistry and molecular biology, all addressing different facets of the problem to connect the many scales of the computer simulation of many systems of interest in chemistry - polymetric materials, biological molecules, clusters, surface and interface structure. Emphasis is placed on the multigrid technique and its applications, ranging from electronic structure calculations to the statistical mechanics of polymers.

This volume presents modern trends in the area of symmetries and their applications based on contributions from the workshop "Lie Theory and Its Applications in Physics", held near Varna, Bulgaria, in June 2015. Traditionally, Lie theory is a tool to build mathematical models for physical systems.Recently, the trend has been towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are employed in their widest sense, embracing representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators (PDO), special functions, and others. Furthermore, the necessary tools from functional analysis are included.

Theoretical and Computational Chemistry research has made unparalleled advancements in understanding every expanding area of science and technology. This volume presents the state-of-the-art research and progress made by eminent researchers in the area of theoretical computational chemistry and physics. The title mirrors the name of the annual international conference "Conference on Current Trends on Computational Chemistry" (CCTCC) which has become a popular discussion ground for eminent Theoretical and Computational Chemists and has been honored by the presence of several Nobel Laureates. Practical Aspects of Computational Chemistry III is aimed at theoretical and computational chemists, physical chemists, material scientists and those who are eager to apply computational chemistry methods to problems of chemical and physical importance. The book is a valuable resource for undergraduate, graduate and PhD students as well as established researchers.

Summarizing all the latest trends and recent topics in one handy volume, this book covers everything needed for a solid understanding of photochromic materials. Following a general introduction to organic photochromic materials, the authors move on to discuss not only the underlying theory but also the properties of such materials. After a selection of pplications, they look at the latest achievements in traditional solution-phase applications, including photochromic-based molecular logic operations and memory, optically modulated supramolecular system and sensors, as well as light-tunable chemical reactions. The book then describes the hotspot areas of photo-switchable surfaces and nanomaterials, photochromic-based luminescence/electronic devices and bulk materials together with light-regulated biological and bio-chemical systems. The authors conclude with a focus on current industrial applications and the future outlook for these materials. Written with both senior researchers and entrants to the field in mind.

This monograph is mostly devoted to the problem of the geome- trizing of Lagrangians which depend on higher order accelerations. It naturally prolongs the theme of the monograph "The Geometry of La- grange spaces: Theory and Applications", written together with M. Anastasiei and published by Kluwer Academic Publishers in 1994. The existence of Lagrangians of order k > 1 has been contemplated by mechanicists and physicists for a long time. Einstein had grasped their presence in connection with the Brownian motion. They are also present in relativistic theories based on metrics which depend on speeds and accelerations of particles or in the Hamiltonian formulation of non- linear systems given by Korteweg-de Vries equations. There resulted from here the methods to be adopted in their theoretical treatment. One is based on the variational problem involving the integral action of the Lagrangian. A second one is derived from the axioms of Analytical Mechanics involving the Poincare-Cartan forms. The geometrical methods based on the study of the geometries of higher order could invigorate the whole theory. This is the way adopted by us in defining and studying the Lagrange spaces of higher order. The problems raised by the geometrization of Lagrangians of order k > 1 investigated by many scholars: Ch. Ehresmann, P. Libermann, J. Pommaret; J.T. Synge, M. Crampin, P. Saunders; G.S. Asanov, P.Aringazin; I. Kolar, D. Krupka; M. de Leon, W. Sarlet, P. Cantrjin, H. Rund, W.M. Tulczyjew, A. Kawaguchi, K. Yano, K. Kondo, D.

This collection of original articles and surveys, emerging from a 2011 conference in Bertinoro, Italy, addresses recent advances in linear and nonlinear aspects of the theory of partial differential equations (PDEs). Phase space analysis methods, also known as microlocal analysis, have continued to yield striking results over the past years and are now one of the main tools of investigation of PDEs. Their role in many applications to physics, including quantum and spectral theory, is equally important. Key topics addressed in this volume include: *general theory of pseudodifferential operators *Hardy-type inequalities *linear and non-linear hyperbolic equations and systems *Schroedinger equations *water-wave equations *Euler-Poisson systems *Navier-Stokes equations *heat and parabolic equations Various levels of graduate students, along with researchers in PDEs and related fields, will find this book to be an excellent resource. Contributors T. Alazard P.I. Naumkin J.-M. Bony F. Nicola N. Burq T. Nishitani C. Cazacu T. Okaji J.-Y. Chemin M. Paicu E. Cordero A. Parmeggiani R. Danchin V. Petkov I. Gallagher M. Reissig T. Gramchev L. Robbiano N. Hayashi L. Rodino J. Huang M. Ruzhanky D. Lannes J.-C. Saut F. Linares N. Visciglia P.B. Mucha P. Zhang C. Mullaert E. Zuazua T. Narazaki C. Zuily

The history of mechanics, and more particularly, the history of mechanics applied to constructions, constitutes a field of research that is relatively recent. This volume, together with the recent publication "Towards a History of Construction," is intended as an homage to the two eminent scholars who made a determinant contribution to the history of mechanics: Edoardo Benvenuto and Clifford Truesdell.

Chaotic Dynamics: Theory: Complexity, Control and Data Representation: Complexity and Unpredictable Scaling of Hierarchical Structures; R. Badii. Fractals, Multifractals, and Analyticity of Normal Forms: Multifractal Coding Measures in Dynamics; G. Mantica. Integrability, Painleve Property, and Singularity Analysis: Note on a Complex Eckhaus Equation; M.F. Jorgensen, et al.. Statistical Physics, Celestial Mechanics, and Cosmology: Phase Transitions Within the Fully Developed Regime; R. Kluiving. Chaotic Dynamics: Practice: Controlling Dynamical Systems: Feedback Control of Chaotic Systems; . Romeiras et al.. Semiconductors, Superconductors, Lasers, and Electronic Circuits: Chaotic Dynamics in Practice; E. Del Rio, et al . Biology, Chemistry, Atmospheric, and Magnetospheric Dynamics: Irregular Bursting in Model Neurones; J. Hyde. Hamiltonian Dynamics, Dissipative Dynamics, and Normal Forms. 30 additional articles. Index.

Econophysics research studies, which apply methods developed by physicists to solve problems in economics, enable you to deepen your understanding of what financial systems are and how they operate. Articles in this book identify and explain the statistical behavior of the underlying networks in trading, banking, and stock markets as well as other financial systems. Authors also debate the latest issues arising from these econophysics studies.

This volume, which brings together research presented at the IUTAM Symposium Intelligent Multibody Systems - Dynamics, Control, Simulation, held at Sozopol, Bulgaria, September 11-15, 2017, focuses on preliminary virtual simulation of the dynamics of motion, and analysis of loading of the devices and of their behaviour caused by the working conditions and natural phenomena. This requires up-to-date methods for dynamics analysis and simulation, novel methods for numerical solution of ODE and DAE, real-time simulation, passive, semi-passive and active control algorithms. Applied examples are mechatronic (intelligent) multibody systems, autonomous vehicles, space structures, structures exposed to external and seismic excitations, large flexible structures and wind generators, robots and bio-robots. The book covers the following subjects: -Novel methods in multibody system dynamics; -Real-time dynamics; -Dynamic models of passive and active mechatronic devices; -Vehicle dynamics and control; -Structural dynamics; -Deflection and vibration suppression; -Numerical integration of ODE and DAE for large scale and stiff multibody systems; -Model reduction of large-scale flexible systems. The book will be of interest for scientists and academicians, PhD students and engineers at universities and scientific institutes.