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"This graduate textbook covers the basic formalism of supergravity, as well as a wide range of its modern applications, suitable for a focused first course. Assuming a working knowledge of quantum field theory, it gives Ph.D. students the tools they need to do research that uses supergravity"--
This book highlights the methods to engineer dissipative and magnetic nonlinear waves propagating in nonlinear systems. In the first part of the book, the authors present methodologically mathematical models of nonlinear waves propagating in one- and two-dimensional nonlinear transmission networks without/with dissipative elements. Based on these models, the authors investigate the generation and the transmission of nonlinear modulated waves, in general, and solitary waves, in particular, in networks under consideration. In the second part of the book, the authors develop basic theoretical results for the dynamics matter-wave and magnetic-wave solitons of nonlinear systems and of Bose¿Einstein condensates trapped in external potentials, combined with the time-modulated nonlinearity. The models treated here are based on one-, two-, and three-component non-autonomous Gross¿Pitaevskii equations. Based on the Heisenberg model of spin¿spin interactions, the authors also investigate the dynamics of magnetization in ferromagnet with or without spin-transfer torque. This research book is suitable for physicists, mathematicians, engineers, and graduate students in physics, mathematics, and network and information engineering.
These books provide a state-of-the-art treatment of mathematical theories of vibration. The first volume discusses numerical and semi-analytical methods to be used in solving various vibration problems. It is an invaluable guide for graduate and postgraduate students, teachers and researchers in various fields including applied mathematics, physics and engineering.
Tiden er en gåde. For at løse den tager fysiker Troels Harmark os med på en rejse tilbage til antikkens græske filosoffer, videre op gennem naturvidenskabens historie til bl.a. Newton og Einstein og helt ud til forskningsfronten i moderne fysik og de største spørgsmål som, hvordan universet blev til. Tiden oprandt ved universets fødsel, og vi lever stadig i tiden her 13,8 milliarder år senere. Vi har en krop, der ældes, og kan ikke forestille os vores liv uden tid – vi indordner os under den, og tænker, at den bevæger sig regelmæssigt, som visernes præcise vandring over døgnets timer på uret. Men fysikken beretter en anden historie – om tidens relativitet: at den går langsommere tæt ved Jordens overflade end på toppen af et bjerg, at tiden står stille på kanten af sorte huller, og at universet udvider sig uendeligt. Tidens gang skal findes imellem de to modpoler: at alt er tilfældigt og at alt er uafvendeligt. På sporet af tidens gåde handler om, hvordan det hele hænger sammen, og hvordan det kan være, at man regner med, at tiden en dag vil stoppe med at gå. Hvordan skal vi forstå tiden?
This book provides a solution to the problem with the energy concept. This problem manifests itself in the fact that physicists clearly diverge regarding the question of what energy is. Some define it but others state that we do not know what it is. Although this is a problem for physicists who need to explain the concept, it is not a problem for physics that can be solved by laboratory means. Penetrating into the origin of the notion of energy, this book offers a clear idea of what was discovered and what was invented to interpret the findings.Following the development of the concept, it provides an explanation of the trends in contemporary textbooks. The author's repetition, in his "History and Philosophy of Physics Laboratory", of Joule¿s famous experiment ¿ the paddle wheel experiment ¿ with a calorimeter as originally used by Joule and with a calorimeter as proposed in textbooks, is presented, yielding new insight into the phenomenon. Thus, science teachers andstudents will benefit from reading the book as well as historians, philosophers, students of the history and philosophy of science, and all who are interested in knowing about what it is that we call energy.
Unlocking the Mental Pathways to Mathematical Mastery Dive into the fascinating intersection of mind and math with "Psychology Behind Mathematics: The Comprehensive Guide." This book offers an unparalleled exploration into how psychological principles shape our understanding and capabilities in mathematics. It sheds light on the cognitive processes, learning strategies, and emotional factors that influence mathematical comprehension and problem-solving skills. By bridging the gap between abstract numerical concepts and tangible psychological insights, this guide promises to transform your approach to mathematics, making it more accessible, enjoyable, and profoundly rewarding. Without relying on images or illustrations to avoid copyright issues, the book meticulously presents complex ideas through vivid descriptions and compelling narratives, ensuring a rich and immersive learning experience. Whether you're a student struggling with numbers, a teacher seeking innovative teaching strategies, or simply a math enthusiast curious about the psychological aspects of this universal language, this book is your key to unlocking a deeper, more intuitive understanding of mathematics. It goes beyond traditional methods to present a holistic view of the mathematical mind, incorporating research findings, case studies, and practical exercises. "Psychology Behind Mathematics: The Comprehensive Guide" is not just a book; it's a journey into the heart of mathematics through the lens of psychology, promising to enlighten, inspire, and empower its readers.
This thesis describes two groundbreaking measurements in the precision frontier at the LHC: the first ever differential measurement of the Z-associated single top quark (tZq) production, and the luminosity measurement using Z boson production rate for the first time in CMS. Observed only in 2018, the tZq process is of great importance in probing top quark electroweak couplings. These couplings are natural places for new phenomena to happen in the top quark sector of the standard model. Yet, they are the least explored directly. One has to obtain a firm understanding of the modeling of sensitive distributions to new top-Z interactions. The present analysis marks a major milestone in this long-term effort. All distributions relevant for new phenomena, and/or modeling of tZq, are studied in full depth using advanced Machine Learning techniques.The luminosity and its uncertainty contributes to every physics result of the experiment. The method minutely developed in this thesis provides a complementary measurement that results in a significant overall reduction of uncertainties.
Time, space and entanglement are the main characters in this book. Their nature is still a great mystery in physics and we study here the possibility that these three phenomena are closely connected, showing how entanglement can be at the basis of the emergence of time and space within closed quantum systems. We revisit and extend the Page and Wootters theory that was originally introduced in order to describe the emergence of time through entanglement between subsystems in a globally static, quantum Universe. In the book, after providing a complete review of the salient aspects of the theory, we establish a connection with recent research on the foundations of statistical mechanics and we provide a new understanding of the thermalization process. Furthermore, we generalize the framework in order describe the spatial degree of freedom and we provide a model of 3+1 dimensional, quantum spacetime emerging from entanglement among different subsystems in a globally "timeless" and "positionless" Universe. Finally, via the Page and Wootters theory, the evolution of quantum clocks within a gravitational field is treated and a time dilation effect is obtained in agreement with the Schwarzschild solution.
In recent decades, twistor theory has grown into an irreplaceable tool for the study of scattering amplitudes in gauge theory and gravity. This book introduces the reader to cutting-edge advances in twistor theory and its applications to general relativity. The problem of graviton scattering in four dimensions is shown to be dual to dramatically simpler computations in a two-dimensional CFT known as a twistor sigma model. Twistor sigma models are the first step toward a holographic description of gravity in asymptotically flat space-times. They underpin the infinitely many asymptotic symmetries of flat space physics discovered in celestial holography, and extend them to exciting new arenas like curved space-times. They also yield intrinsically mathematical results in the field of hyperkähler manifolds. This volume will be of broad interest to students and researchers looking for an accessible entry point into twistor geometry, scattering amplitudes, and celestial holography. It will also provide an invaluable reference for specialists by bringing together results from a host of different disciplines.
This book provides an advanced introduction to extended theories of quantum field theory and algebraic topology, including Hamiltonian quantization associated with some geometrical constraints, symplectic embedding and Hamilton-Jacobi quantization and Becchi-Rouet-Stora-Tyutin (BRST) symmetry, as well as de Rham cohomology. This extended new edition offers a multifaced insight into phenomenology of particles such as baryons and photons, in terms of extended objects. In particular, in the second edition, the baryons are described in hypersphere soliton model, and the photon properties are additionally included in stringy photon model and in Dirac type relativistic quantum mechanics for a photon.It offers a critical overview of the research in this area and unifies the existing literatures, employing a consistent notation. Although the results presented apply in principle to all alternative quantization schemes, special emphasis is placed on the BRST quantization and its de Rham cohomology group which contribute to a deep understanding of constrained physical theories. The book describes how solitons and other models subject to constraints include rigorous treatments of the geometrical constraints which affect the predictions themselves. The book is intended for use by any graduate-level student with quantum field and relativity theories, and it also serves as a useful reference for those working in the field. An extensive bibliography guides the reader toward the source literature on particular topics.
This book gathers outstanding papers on numerical modeling in Mechanical Engineering (Volume 2) as part of the 2-volume proceedings of the 5th International Conference on Numerical Modeling in Engineering (NME 2021), which was held in Ghent, Belgium, on August 23-24, 2022. The overall objective of the conference was to bring together international scientists and engineers in academia and industry from fields related to advanced numerical techniques, such as the finite element method (FEM), boundary element method (BEM), isogeometric analysis (IGA), and their applications to a wide range of engineering disciplines. This book addresses numerical simulations of various mechanical and materials engineering industrial applications such as aerospace applications, acoustic analysis, bio-mechanical applications, contact problems and wear, heat transfer analysis, vibration and dynamics, transient analysis, nonlinear analysis, composite materials, polymers, metal alloys, fracture mechanics, fatigue of materials, creep, mechanical behavior, micro-structure, phase transformation, and crystal plasticity. The book is intended for academics, including graduate students and researchers, as well as industrial practitioners working in the numerical modeling in mechanical engineering topics.
The Standard Model is the most comprehensive physical theory ever developed. This textbook conveys the basic elements of the Standard Model using elementary concepts, without the theoretical rigor found in most other texts on this subject. It contains examples of basic experiments, allowing readers to see how measurements and theory interplay in the development of physics. The author examines leptons, hadrons and quarks, before presenting the dynamics and the surprising properties of the charges of the different forces. The textbook concludes with a brief discussion on the discoveries of physics beyond the Standard Model, and its connections with cosmology. Quantitative examples are given, and the reader is guided through the necessary calculations. Each chapter ends in the exercises, and solutions to some problems are included in the book. Complete solutions are available to instructors at www.cambridge.org/9781107406094.
This book contains select papers on mathematical analysis and modeling, discrete mathematics, fuzzy sets, and soft computing. All the papers were presented at the international conference on FIM28-SCMSPS20 virtually held at Sri Sivasubramaniya Nadar (SSN) College of Engineering, Chennai, India, and Stella Maris College (Autonomous), Chennai, from November 23-27, 2020. The conference was jointly held with the support of the Forum for Interdisciplinary Mathematics. Both the invited articles and submitted papers were broadly grouped under three heads: Part 1 on analysis and modeling (six chapters), Part 2 on discrete mathematics and applications (six chapters), and Part 3 on fuzzy sets and soft computing (three chapters).
This book is a re-assessment of the structure and reach of symmetry, by an interdisciplinary group of specialists from the arts, humanities, and sciences at Oxford University. This book aims to open up the scope of interdisciplinary work in the study of symmetry and is intended for scholars of any background.
The book concerns with solving about 650 ordinary and partial differential equations. Each equation has at least one solution and each solution has at least one coloured graph. The coloured graphs reveal different features of the solutions. Some graphs are dynamical as for Clairaut differential equations. Thus, one can study the general and the singular solutions. All the equations are solved by Mathematica. The first chapter contains mathematical notions and results that are used later through the book. Thus, the book is self-contained that is an advantage for the reader. The ordinary differential equations are treated in Chapters 2 to 4, while the partial differential equations are discussed in Chapters 5 to 10. The book is useful for undergraduate and graduate students, for researchers in engineering, physics, chemistry, and others. Chapter 9 treats parabolic partial differential equations while Chapter 10 treats third and higher order nonlinear partial differential equations, both with modern methods. Chapter 10 discusses the Korteweg-de Vries, Dodd-Bullough-Mikhailov, Tzitzeica-Dodd-Bullough, Benjamin, Kadomtsev-Petviashvili, Sawada-Kotera, and Kaup-Kupershmidt equations.
This book focuses on nonextensive statistical mechanics, a current generalization of Boltzmann-Gibbs (BG) statistical mechanics.Conceived nearly 150 years ago by Maxwell, Boltzmann and Gibbs, the BG theory, one of the greatest monuments of contemporary physics, exhibits many impressive successes in physics, chemistry, mathematics, and computational sciences. Presently, several thousands of publications by scientists around the world have been dedicated to its nonextensive generalization. A variety of applications have emerged in complex systems and its mathematical grounding is by now well advanced.Since the first edition release thirteen years ago, there has been a vast amount of new results in the field, all of which have been incorporated in this comprehensive second edition. Heavily revised and updated with new sections and figures, the second edition remains the go-to text on the subject.A pedagogical introduction to the BG theory concepts and their generalizations ¿ nonlinear dynamics, extensivity of the nonadditive entropy, global correlations, generalization of the standard CLT¿s, complex networks, among others ¿ is presented in this book, as well as a selection of paradigmatic applications in various sciences together with diversified experimental verifications of some of its predictions. Introduction to Nonextensive Statistical Mechanics is suitable for students and researchers with an interest in complex systems and statistical physics.
This book presents improved numerical techniques and applied computer-aided simulations as a part of emerging trends in mechatronics in all areas related to complex fluids, with particular focus on using a combination of modeling, theory, and simulation to study systems that are complex due to the rheology of fluids (i.e., ceramic pastes, polymer solutions and melts, colloidal suspensions, emulsions, foams, micro-/nanofluids, etc.) and multiphysics phenomena in which the interactions of various effects (thermal, chemical, electric, magnetic, or mechanical) lead to complex dynamics. The areas of applications span materials processing, manufacturing, and biology.
This book proposes and develops the equilibrium compound nucleus post-fission theory, a powerful tool for studying the fission process and making numerical calculations of post-fission nuclear data. It begins with a detailed historical background on fission theory and covers fundamental concepts, such as the Bohr-Wheeler formula and time dependent nuclear density functional theory.The authors explain the kinematics of heavy-ion collisions and develop a heavy-ion spherical optical model. They also present the theoretical methods for calculating the yield, kinetic energy distribution, and angular distribution of fission fragments in the initial state of fission. In addition, readers are provided with the method for calculating the prompt neutron and prompt gamma-ray data as well as the proportion of the isomeric state nucleus and independent yield from the initial yield of the fission fragments. Using the nuclear decay data of the fission products, a method for calculating thecumulative yield and decay heat of the fission fragments is also given. A fission delayed neutron simplification model is proposed and the theoretical method for calculating the total contribution of three fission channels to post-fission nuclear data is provided.This book concludes with a step-by-step guide on numerical calculations for post-fission nuclear data and a Fortran program for optimizing the best theoretical model parameters. It is ideal for both junior and senior researchers in nuclear physics, as well as graduate students who are interested learning about the subject. Given the current interest in post-fission and the tremendous experimental and theoretical efforts in studying it, this book serves as a timely and comprehensive resource for the nuclear physics community.
Originally published in 1977, this book presents an extended introduction to the theory of hadrons, the elementary particles which occur in the atomic nucleus. The main emphasis is on the theory of the complex angular momentum plane 'Regge theory', which has grown from Regge's demonstration in 1959 that it is useful to regard angular momentum as a complex variable when discussing solutions of the Schrodinger equation for non-relativistic potential scattering. This theory helps to classify the many different particles which have been discovered in recent years, to explain the forces between these particles and to predict the results of high-energy scattering experiments. Regge theory thus serves as a unifying concept drawing together many different features of high-energy physics. This monograph is intended primarily for research students just beginning to concern themselves with particle physics, but more experienced workers will also find much to interest them in this detailed survey of the basic ideas and results of Regge theory.
This book provides an alternative approach to time-independent perturbation theory in non-relativistic quantum mechanics. It allows easy application to any initial condition because it is based on an approximation to the evolution operator and may also be used on unitary evolution operators for the unperturbed Hamiltonian in the case where the eigenvalues cannot be found. This flexibility sets it apart from conventional perturbation theory. The matrix perturbation method also gives new theoretical insights; for example, it provides corrections to the energy and wave function in one operation. Another notable highlight is the facility to readily derive a general expression for the normalization constant at m-th order, a significant difference between the approach within and those already in the literature. Another unique aspect of the matrix perturbation method is that it can be extended directly to the Lindblad master equation. The first and second-order corrections are obtained for this equation and the method is generalized for higher orders. An alternative form of the Dyson series, in matrix form instead of integral form, is also obtained. Throughout the book, several benchmark examples and practical applications underscore the potential, accuracy and good performance of this novel approach. Moreover, the method's applicability extends to some specific time-dependent Hamiltonians. This book represents a valuable addition to the literature on perturbation theory in quantum mechanics and is accessible to students and researchers alike.
This book provides a concise and comprehensive introduction to several basic methods with more attention to their theoretical basis and applications in fluid dynamics. Furthermore, some new ideas are presented in this book, for example, a method to solve the transition matrix by difference operator transformation. For this method, the book gives the definition of Fourier integral transformation of translation operator, and proves the transition matrix equaling to the differential operator transformation, so that it is extended to general situations of explicit, implicit, multi-layer difference equations, etc. This flexible approach is also used in the differential part. In addition, the book also includes six types of equivalent stability definitions in two ways and deeply analyzes their errors, stabilities and convergences of the difference equations. What is more important, some new scientific contributions on lattice Boltzmann method (LBM) in recent years are presented in the book as well. The authors write the book combining their ten years teaching experience and research results and this book is intended for graduate students who are interested in the area of computational fluid dynamics (CFD). Authors list some new research achievements, such as simplified lattice Boltzmann method, the simplified lattice Boltzmann flux solver and discrete unified gas kinetic scheme, and expect that this new information could give readers possible further investigating ideas in their future research on CFD area.
This volume presents modern trends in the area of symmetries and their applications based on contributions to the Workshop "Lie Theory and Its Applications in Physics" held in Sofia, Bulgaria (on-line) in June 2021.Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is 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 meant in their widest sense, i.e., 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, special functions, and others. Furthermore, the necessary tools from functional analysis are included. This is a big interdisciplinary and interrelated field.The topics covered in this Volume are the most modern trends in the field of the Workshop: Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, Exceptional quantum algebra for the standard model of particle physics, Gauge Theories and Applications, Structures on Lie Groups and Lie Algebras.This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.
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