Lectures On Phase Field
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Lectures On Phase Field
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Author : Ingo Steinbach
language : en
Publisher: Springer Nature
Release Date : 2023-04-23
Lectures On Phase Field written by Ingo Steinbach and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-23 with Technology & Engineering categories.
This open access textbook fills a gap, in that it introduces readers to the theory and applications of the Phase-Field technique. Phase Field, over the years, has emerged as a standard tool for materials research, just as the Finite-Element technique has in structure mechanics. Whereas the few existing textbooks on this topic are intended for advanced readers, this one is made accessible to the widest possible audience, through an engaging, lecture format. The content grows out of a course the authors teach for graduate students at Ruhr-University Bochum. Even readers who may, at first, have no clue at all what a “Phase Field” is and for what it is used, are invited on a journey from general physics of thermodynamics and wave mechanics, through applications in all fields of materials science, up to the central questions of physical being. On this journey all the necessary techniques are detailed, mostly formulated in a mathematical language easily understood by engineers and natural scientists.
Multiphysics Phase Field Fracture
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Author : Thomas Wick
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-10-12
Multiphysics Phase Field Fracture written by Thomas Wick and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-12 with Mathematics categories.
This monograph is centered on mathematical modeling, innovative numerical algorithms and adaptive concepts to deal with fracture phenomena in multiphysics. State-of-the-art phase-field fracture models are complemented with prototype explanations and rigorous numerical analysis. These developments are embedded into a carefully designed balance between scientific computing aspects and numerical modeling of nonstationary coupled variational inequality systems. Therein, a focus is on nonlinear solvers, goal-oriented error estimation, predictor-corrector adaptivity, and interface conditions. Engineering applications show the potential for tackling practical problems within the fields of solid mechanics, porous media, and fluidstructure interaction.
Lectures On Matrix Field Theory
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Author : Badis Ydri
language : en
Publisher: Springer
Release Date : 2016-11-22
Lectures On Matrix Field Theory written by Badis Ydri and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-22 with Science categories.
These lecture notes provide a systematic introduction to matrix models of quantum field theories with non-commutative and fuzzy geometries. The book initially focuses on the matrix formulation of non-commutative and fuzzy spaces, followed by a description of the non-perturbative treatment of the corresponding field theories. As an example, the phase structure of non-commutative phi-four theory is treated in great detail, with a separate chapter on the multitrace approach. The last chapter offers a general introduction to non-commutative gauge theories, while two appendices round out the text. Primarily written as a self-study guide for postgraduate students – with the aim of pedagogically introducing them to key analytical and numerical tools, as well as useful physical models in applications – these lecture notes will also benefit experienced researchers by providing a reference guide to the fundamentals of non-commutative field theory with an emphasis on matrix models and fuzzy geometries.
Lectures Of Sidney Coleman On Quantum Field Theory Foreword By David Kaiser
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Author : Bryan Gin-ge Chen
language : en
Publisher: World Scientific Publishing
Release Date : 2018-11-08
Lectures Of Sidney Coleman On Quantum Field Theory Foreword By David Kaiser written by Bryan Gin-ge Chen and has been published by World Scientific Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-08 with Science categories.
'Sidney Coleman was the master teacher of quantum field theory. All of us who knew him became his students and disciples. Sidney’s legendary course remains fresh and bracing, because he chose his topics with a sure feel for the essential, and treated them with elegant economy.'Frank WilczekNobel Laureate in Physics 2004Sidney Coleman was a physicist's physicist. He is largely unknown outside of the theoretical physics community, and known only by reputation to the younger generation. He was an unusually effective teacher, famed for his wit, his insight and his encyclopedic knowledge of the field to which he made many important contributions. There are many first-rate quantum field theory books (the venerable Bjorken and Drell, the more modern Itzykson and Zuber, the now-standard Peskin and Schroeder, and the recent Zee), but the immediacy of Prof. Coleman's approach and his ability to present an argument simply without sacrificing rigor makes his book easy to read and ideal for the student. Part of the motivation in producing this book is to pass on the work of this outstanding physicist to later generations, a record of his teaching that he was too busy to leave himself.
Itep Lectures In Particle Physics And Field Theory
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Author : Mikhail A. Shifman
language : en
Publisher: World Scientific
Release Date : 1999
Itep Lectures In Particle Physics And Field Theory written by Mikhail A. Shifman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Science categories.
For almost two decades Prof. Shifman, a clear and pedagogical expositor, has been giving review lectures on frontier topics in theoretical high energy physics. This two-volume book is a collection of some of the best of those lectures. The lectures written in the 1980's and early 1990's have been revised and updated specifically for this publication. The lectures in this book are intended for beginners - graduate students and young researchers - who are about to delve into the intricacies of the theory. They were used by the author in his course ';Advanced Modern Field Theory and Its Applications';, given in the academic year 1994/95 at the University of Minnesota.A wide range of key topics is covered. In Volume 1, the first two chapters are devoted to quantum chromodynamics as the theory of hadrons. The author gives an in-depth discussion of a variety ofpowerful methods based on Wilson's operator product expansion. Chapter 3 (written together with V Novikov, A Vainshtein, and V Zakharov) is the most systematic and pedagogical presentation of instantons in the gauge theories one can find in the literature. Chapter 4 introduces supersymmetry. Chapter 5, concluding this volume, reviews the fascinating dynamics of supersymmetric gauge theories in the strong coupling regime. Chapter 6, which opens Volume 2, is a culmination of the supersymmetric theme. It gives a state-of-the-art description of the breakthrough developments in supersymmetric gauge theories. It has been written specifically for this book by A Vainshtein and the author. Chapter 7 is designed as a primer of two-dimensional conformal field theory, which constitutes the basis of modern string theory. Chapter 8, the last, presents remarkable new findings in quantum mechanics. Every chapter contains exercises and a list of recommended literature.Prof. Shifman has been an active participant and significant contributor in the development of the ideas presented in this book. This accounts for the historical remarks and digressions interspersed in the book, enhancing its pedagogical role. The book will serve as a comprehensive reference and textbook for all graduate students and researchers interested in modern particle physics. It will also be a useful guide for lecturers.
Treatise On Process Metallurgy
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Author : Roderick Guthrie
language : en
Publisher: Elsevier
Release Date : 2024-01-25
Treatise On Process Metallurgy written by Roderick Guthrie and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-25 with Technology & Engineering categories.
Treatise on Process Metallurgy: Volume One, Process Fundamentals provides academics with the fundamentals of the manufacturing of metallic materials, from raw materials into finished parts or products. In these fully updated volumes, coverage is expanded into four volumes, including Process Fundamentals, encompassing process fundamentals, structure and properties of matter; thermodynamic aspects of process metallurgy, and rate phenomena in process metallurgy; Processing Phenomena, encompassing interfacial phenomena in high temperature metallurgy, metallurgical process phenomena, and metallurgical process technology; Metallurgical Processes, encompassing mineral processing, aqueous processing, electrochemical material and energy processes, and iron and steel technology, non-ferrous process principles and production technologies, and more. The work distills the combined academic experience from the principal editor and the multidisciplinary four-member editorial board. - Provides the entire breadth of process metallurgy in a single work - Includes in-depth knowledge in all key areas of process metallurgy - Approaches the topic from an interdisciplinary perspective, providing broad range coverage on topics
Digital Materials
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Author : Marc Bernacki
language : en
Publisher: John Wiley & Sons
Release Date : 2024-10-31
Digital Materials written by Marc Bernacki and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-31 with Technology & Engineering categories.
Digital materials are integral to the modern design methods for industrial components and structures, allowing mechanical properties to be predicted from a description of the microstructure and behavior laws of the constituent parts. This book examines a wide range of material properties, from transport phenomena to the mechanics of materials and microstructure changes in physical metallurgy. The fundamental mechanisms of deformation, annealing and damage to materials involve complex atomic processes; these have been explored and studied by numerical simulations, such as molecular dynamics. In contrast to this minutely detailed approach, Digital Materials explores how these mechanisms can instead be integrated into an approach that considers the continuum of the physics and mechanics of materials at the mesoscopic scale. The book thus focuses on the mechanics of continuous media and the continuum thermodynamics of irreversible processes. The models displayed take the myriad properties of different materials into account, in particular their polycrystalline and/or composite natures; this becomes an intermediate step toward establishing effective laws for engineers in the processes of structure calculation and manufacturing.
Programming Phase Field Modeling
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Author : S. Bulent Biner
language : en
Publisher: Springer
Release Date : 2017-01-25
Programming Phase Field Modeling written by S. Bulent Biner and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-25 with Technology & Engineering categories.
This textbook provides a fast-track pathway to numerical implementation of phase-field modeling—a relatively new paradigm that has become the method of choice for modeling and simulation of microstructure evolution in materials. It serves as a cookbook for the phase-field method by presenting a collection of codes that act as foundations and templates for developing other models with more complexity. Programming Phase-Field Modeling uses the Matlab/Octave programming package, simpler and more compact than other high-level programming languages, providing ease of use to the widest audience. Particular attention is devoted to the computational efficiency and clarity during development of the codes, which allows the reader to easily make the connection between the mathematical formulism and the numerical implementation of phase-field models. The background materials provided in each case study also provide a forum for undergraduate level modeling-simulations courses as part of their curriculum.
Lectures On Random Interfaces
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Author : Tadahisa Funaki
language : en
Publisher: Springer
Release Date : 2016-12-27
Lectures On Random Interfaces written by Tadahisa Funaki and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-27 with Mathematics categories.
Interfaces are created to separate two distinct phases in a situation in which phase coexistence occurs. This book discusses randomly fluctuating interfaces in several different settings and from several points of view: discrete/continuum, microscopic/macroscopic, and static/dynamic theories. The following four topics in particular are dealt with in the book.Assuming that the interface is represented as a height function measured from a fixed-reference discretized hyperplane, the system is governed by the Hamiltonian of gradient of the height functions. This is a kind of effective interface model called ∇φ-interface model. The scaling limits are studied for Gaussian (or non-Gaussian) random fields with a pinning effect under a situation in which the rate functional of the corresponding large deviation principle has non-unique minimizers.Young diagrams determine decreasing interfaces, and their dynamics are introduced. The large-scale behavior of such dynamics is studied from the points of view of the hydrodynamic limit and non-equilibrium fluctuation theory. Vershik curves are derived in that limit.A sharp interface limit for the Allen–Cahn equation, that is, a reaction–diffusion equation with bistable reaction term, leads to a mean curvature flow for the interfaces. Its stochastic perturbation, sometimes called a time-dependent Ginzburg–Landau model, stochastic quantization, or dynamic P(φ)-model, is considered. Brief introductions to Brownian motions, martingales, and stochastic integrals are given in an infinite dimensional setting. The regularity property of solutions of stochastic PDEs (SPDEs) of a parabolic type with additive noises is also discussed.The Kardar–Parisi–Zhang (KPZ) equation , which describes a growing interface with fluctuation, recently has attracted much attention. This is an ill-posed SPDE and requires a renormalization. Especially its invariant measures are studied.
Lectures On Field Theory And Topology
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Author : Daniel S. Freed
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-08-23
Lectures On Field Theory And Topology written by Daniel S. Freed and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-23 with Mathematics categories.
These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.