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The methods of quantum field theory underpin many conceptual advances in contemporary condensed matter physics and neighbouring fields. This book provides a praxis-oriented and pedagogical introduction to quantum field theory in many-particle physics, emphasizing the application of theory to real physical systems. This third edition is organized into two parts: the first half of the text presents a streamlined introduction, elevating readers to a level where they can engage with contemporary research literature, from the introduction of many-body techniques and functional integration to renormalization group methods, and the second half addresses a range of advanced topics including modern aspects of gauge theory, topological and relativistic quantum matter, and condensed matter physics out of thermal equilibrium. At all stages, the text seeks a balance between methodological aspects of quantum field theory and practical applications. Extended problems with worked solutions provide a bridge between formal theory and a research-oriented approach.
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Quantum field theory. --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics)
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This book presents fundamental theoretical and experimental studies of well-known scientists in solid mechanics, hydromechanics, aeromechanics, biomechanics, etc. These studies relate to contact and mixed problems of the theory of elasticity and viscoelasticity, tribology, fracture mechanics, electroelasticity, magnetoelasticity, as well as to the theory of anisotropic shells and plates and are aimed at application in various areas of engineering practice. The book is devoted to the 110th birthday of academician N.Kh. Arutunyan.
Continuum mechanics. --- Mechanics of continua --- Elasticity --- Mechanics, Analytic --- Field theory (Physics)
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This book studies using string-net models to accomplish a direct, purely two-dimensional, approach to correlators of two-dimensional rational conformal field theories. The authors obtain concise geometric expressions for the objects describing bulk and boundary fields in terms of idempotents in the cylinder category of the underlying modular fusion category, comprising more general classes of fields than is standard in the literature. Combining these idempotents with Frobenius graphs on the world sheet yields string nets that form a consistent system of correlators, i.e. a system of invariants under appropriate mapping class groups that are compatible with factorization. The authors extract operator products of field objects from specific correlators; the resulting operator products are natural algebraic expressions that make sense beyond semisimplicity. They also derive an Eckmann-Hilton relation internal to a braided category, thereby demonstrating the utility of string nets for understanding algebra in braided tensor categories. Finally, they introduce the notion of a universal correlator. This systematizes the treatment of situations in which different world sheets have the same correlator and allows for the definition of a more comprehensive mapping class group.
Quantum field theory. --- Particles (Nuclear physics) --- Elementary particles (Physics) --- High energy physics --- Nuclear particles --- Nucleons --- Nuclear physics --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics)
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This book in the advanced structured materials series provides first an introduction to the mircomechanics of fiber-reinforced laminae, which deals with the prediction of the macroscopic mechanical lamina properties based on the mechanical properties of the constituents, i.e., fibers and matrix. Composite materials, especially fiber-reinforced composites, are gaining increasing importance since they can overcome the limits of many structures based on classical metals. Particularly, the combination of a matrix with fibers provides far better properties than the constituents alone. Despite their importance, many engineering degree programs do not treat the mechanical behavior of this class of advanced structured materials in detail, at least on the bachelor’s degree level. Thus, some engineers are not able to thoroughly apply and introduce these modern engineering materials in their design process. The second part of this book provides a systematic and thorough introduction to the classical laminate theory based on the theory for plane elasticity elements and classical (shear-rigid) plate elements. The focus is on unidirectional lamina which can be described based on orthotropic constitutive equations and their composition to layered laminates. In addition to the elastic behavior, failure is investigated based on the maximum stress, maximum strain, Tsai-Hill, and the Tsai-Wu criteria. The introduced classical laminate theory provides a simplified stress analysis, and a subsequent failure analysis, without the solution of the system of coupled differential equations for the unknown displacements in the three coordinate directions. The book concludes with a short introduction to a calculation program, the so-called Composite Laminate Analysis Tool (CLAT), which allows the application of the classical laminate based on a sophisticated Python script.
Continuum mechanics. --- Composite materials. --- Continuum Mechanics. --- Composites. --- Composites (Materials) --- Multiphase materials --- Reinforced solids --- Solids, Reinforced --- Two phase materials --- Materials --- Mechanics of continua --- Elasticity --- Mechanics, Analytic --- Field theory (Physics)
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This textbook on Continuum Mechanics presents 9 chapters. Chapters 1 and 2 are devoted to Tensor Algebra and Tensor Analysis. Part I of the book includes the next 3 chapters. All the content here is valid for both solid and fluid materials. At the end of Part I, the reader should be able to set up in local spatial/material form, the fundamental governing equations and inequalities for a Continuum Mechanics problem. Part II of the book, Chapters 6 to 10, is devoted to presenting some nonlinear constitutive models for Nonlinear Solid Mechanics, including Finite Deformation Hyperelasticity, Finite Deformation Plasticity, Finite Deformation Coupled Thermoplasticity, and Finite Deformation Contact Mechanics. The constitutive equations are derived within a thermodynamically consistent framework. Finite deformation elastoplasticity models are based on a multiplicative decomposition of the deformation gradient and the notion of an intermediate configuration. Different formulations based on the intermediate configuration, the current or spatial configuration, and the material configuration are considered. The last chapter is devoted to Variational Methods in Solid Mechanics, a fundamental topic in Computational Mechanics. The book may be used as a textbook for an advanced Master’s course on Nonlinear Continuum Mechanics for graduate students in Civil, Mechanical or Aerospace Engineering, Applied Mathematics, or Applied Physics, with an interest in Continuum Mechanics and Computational Mechanics.
Continuum mechanics. --- Nonlinear mechanics. --- Mechanics, Nonlinear --- Mechanics, Analytic --- Mechanics of continua --- Elasticity --- Field theory (Physics) --- Mechanics, Applied. --- Engineering Mechanics. --- Continuum Mechanics. --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics
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This book gathers a selection of peer-reviewed papers presented at the 3rd International Conference on Experimental and Computational Mechanics in Engineering (ICECME 2021), held as a virtual conference and organized by Universitas Syiah Kuala, Banda Aceh, Indonesia, on October 11–12, 2021. This book, prepared by international scientists and engineers, covers the latest advances in computational mechanics, metallurgy and material science, energy systems, manufacturing processing systems, industrial and system engineering, biomechanics, artificial intelligence, micro-/nano-engineering, micro-electro-mechanical system, machine learning, mechatronics, and engineering design. This book is intended for academics, including graduate students and researchers, as well as industrial practitioners working in the areas of experimental and computational mechanics.
Mechanics, Applied. --- Mechanics, Applied --- Mathematical models. --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Continuum mechanics. --- Mathematics --- Engineering Mechanics. --- Continuum Mechanics. --- Computational Mathematics and Numerical Analysis. --- Data processing. --- Mechanics of continua --- Elasticity --- Mechanics, Analytic --- Field theory (Physics)
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Bringing together the key ideas from nonequilibrium statistical mechanics and powerful methodology from quantum field theory, this 2008 book captures the essence of nonequilibrium quantum field theory. Beginning with the foundational aspects of the theory, the book presents important concepts and useful techniques, discusses issues of basic interest, and shows how thermal field, linear response, kinetic theories and hydrodynamics emerge. It also illustrates how these concepts are applied to research topics including nonequilibrium phase transitions, thermalization in relativistic heavy ion collisions, the nonequilibrium dynamics of Bose-Einstein condensation, and the generation of structures from quantum fluctuations in the early Universe. This self-contained book is a valuable reference for graduate students and researchers in particle physics, gravitation, cosmology, atomic-optical and condensed matter physics. It has been reissued as an Open Access publication on Cambridge Core.
Quantum field theory. --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Many-body problem. --- Nonequilibrium statistical mechanics. --- Mécanique statistique hors d'équilibre. --- Problème des N corps. --- Théorie quantique des champs.
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In this book, well-known scientists discuss modern aspects of generalized continua, in order to better understand modern materials and advanced structures. They possess complicated internal structure, and it requires the development of new approaches to model such structures and new effects caused by it. This book combines fundamental contributions in honor of Victor Eremeyev and his 60th birthday.
Continuum mechanics. --- Mechanics, Applied. --- Solids. --- Mathematics—Data processing. --- Continuum Mechanics. --- Solid Mechanics. --- Computational Science and Engineering. --- Solid state physics --- Transparent solids --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Mechanics of continua --- Elasticity --- Mechanics, Analytic --- Field theory (Physics)
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