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Author: Anatoliy Malyarenko
Publisher: Cambridge University Press
Published: 2019
Total Pages: 313
ISBN-13: 1108429858
DOWNLOAD EBOOKPresents a complete description of homogenous and isotropic tensor-valued random fields, including the problems of continuum physics, mathematical tools and applications.
Author: François Willot
Publisher: Springer Nature
Published:
Total Pages: 284
ISBN-13: 3031586654
DOWNLOAD EBOOKAuthor: Patrizia Trovalusci
Publisher: Springer
Published: 2015-10-17
Total Pages: 135
ISBN-13: 3319214942
DOWNLOAD EBOOKThe book presents a series of concise papers by researchers specialized in various fields of continuum and computational mechanics and of material science. The focus is on principles and strategies for multiscale modeling and simulation of complex heterogeneous materials, with periodic or random microstructure, subjected to various types of mechanical, thermal, chemical loadings and environmental effects. A wide overview of complex behavior of materials (plasticity, damage, fracture, growth, etc.) is provided. Among various approaches, attention is given to advanced non-classical continua modeling which, provided by constitutive characterization for the internal and external actions (in particular boundary conditions), is a very powerful frame for the gross mechanical description of complex material behaviors, able to circumvent the restrictions of classical coarse–graining multiscale approaches.
Author: Anatoliy Malyarenko
Publisher: Springer Nature
Published: 2020-11-05
Total Pages: 106
ISBN-13: 3030600645
DOWNLOAD EBOOKRandom fields are a necessity when formulating stochastic continuum theories. In this book, a theory of random piezoelectric and piezomagnetic materials is developed. First, elements of the continuum mechanics of electromagnetic solids are presented. Then the relevant linear governing equations are introduced, written in terms of either a displacement approach or a stress approach, along with linear variational principles. On this basis, a statistical description of second-order (statistically) homogeneous and isotropic rank-3 tensor-valued random fields is given. With a group-theoretic foundation, correlation functions and their spectral counterparts are obtained in terms of stochastic integrals with respect to certain random measures for the fields that belong to orthotropic, tetragonal, and cubic crystal systems. The target audience will primarily comprise researchers and graduate students in theoretical mechanics, statistical physics, and probability.
Author: Sergei Silvestrov
Publisher: Springer
Published: 2018-12-05
Total Pages: 482
ISBN-13: 3030028259
DOWNLOAD EBOOKThis book highlights the latest advances in stochastic processes, probability theory, mathematical statistics, engineering mathematics and algebraic structures, focusing on mathematical models, structures, concepts, problems and computational methods and algorithms important in modern technology, engineering and natural sciences applications. It comprises selected, high-quality, refereed contributions from various large research communities in modern stochastic processes, algebraic structures and their interplay and applications. The chapters cover both theory and applications, illustrated by numerous figures, schemes, algorithms, tables and research results to help readers understand the material and develop new mathematical methods, concepts and computing applications in the future. Presenting new methods and results, reviews of cutting-edge research, and open problems and directions for future research, the book serves as a source of inspiration for a broad spectrum of researchers and research students in probability theory and mathematical statistics, applied algebraic structures, applied mathematics and other areas of mathematics and applications of mathematics. The book is based on selected contributions presented at the International Conference on “Stochastic Processes and Algebraic Structures – From Theory Towards Applications” (SPAS2017) to mark Professor Dmitrii Silvestrov’s 70th birthday and his 50 years of fruitful service to mathematics, education and international cooperation, which was held at Mälardalen University in Västerås and Stockholm University, Sweden, in October 2017.
Author: Francesco Bajardi
Publisher: Cambridge University Press
Published: 2022-11-30
Total Pages: 451
ISBN-13: 1009208748
DOWNLOAD EBOOKThis volume summarizes the many modified theories of gravity and shows how to select physically viable models using symmetry principles.
Author: Stephen W. Hawking
Publisher: Cambridge University Press
Published: 2023-02-16
Total Pages: 414
ISBN-13: 1009253182
DOWNLOAD EBOOKFirst published in 1973, this influential work discusses Einstein's General Theory of Relativity to show how two of its predictions arise: first, that the ultimate fate of many massive stars is to undergo gravitational collapse to form 'black holes'; and second, that there was a singularity in the past at the beginning of the universe. Starting with a precise formulation of the theory, including the necessary differential geometry, the authors discuss the significance of space-time curvature and examine the properties of a number of exact solutions of Einstein's field equations. They develop the theory of the causal structure of a general space-time, and use it to prove a number of theorems establishing the inevitability of singularities under certain conditions. A Foreword contributed by Abhay Ashtekar and a new Preface from George Ellis help put the volume into context of the developments in the field over the past fifty years.
Author: Bei-Lok B. Hu
Publisher: Cambridge University Press
Published: 2020-03-05
Total Pages: 615
ISBN-13: 0521193575
DOWNLOAD EBOOKAn overview of semi-classical gravity theory and stochastic gravity as theories of quantum gravity in curved space-time.
Author: Kirill Krasnov
Publisher: Cambridge University Press
Published: 2020-11-26
Total Pages: 391
ISBN-13: 1108689604
DOWNLOAD EBOOKThis monograph describes the different formulations of Einstein's General Theory of Relativity. Unlike traditional treatments, Cartan's geometry of fibre bundles and differential forms is placed at the forefront, and a detailed review of the relevant differential geometry is presented. Particular emphasis is given to general relativity in 4D space-time, in which the concepts of chirality and self-duality begin to play a key role. Associated chiral formulations are catalogued, and shown to lead to many practical simplifications. The book develops the chiral gravitational perturbation theory, in which the spinor formalism plays a central role. The book also presents in detail the twistor description of gravity, as well as its generalisation based on geometry of 3-forms in seven dimensions. Giving valuable insight into the very nature of gravity, this book joins our highly prestigious Cambridge Monographs in Mathematical Physics series. It will interest graduate students and researchers in the fields of theoretical physics and differential geometry.
Author: Luca Lusanna
Publisher: Cambridge University Press
Published: 2019-07-04
Total Pages: 339
ISBN-13: 110857419X
DOWNLOAD EBOOKInterpreting general relativity relies on a proper description of non-inertial frames and Dirac observables. This book describes global non-inertial frames in special and general relativity. The first part covers special relativity and Minkowski space time, before covering general relativity, globally hyperbolic Einstein space-time, and the application of the 3+1 splitting method to general relativity. The author uses a Hamiltonian description and the Dirac–Bergmann theory of constraints to show that the transition between one non-inertial frame and another is a gauge transformation, extra variables describing the frame are gauge variables, and the measureable matter quantities are gauge invariant Dirac observables. Point particles, fluids and fields are also discussed, including how to treat the problems of relative times in the description of relativistic bound states, and the problem of relativistic centre of mass. Providing a detailed description of mathematical methods, the book is perfect for theoretical physicists, researchers and students working in special and general relativity.
