Lectures on Phase Field


Book Description

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.




Lectures On Phase Transitions And The Renormalization Group


Book Description

Covering the elementary aspects of the physics of phases transitions and the renormalization group, this popular book is widely used both for core graduate statistical mechanics courses as well as for more specialized courses. Emphasizing understanding and clarity rather than technical manipulation, these lectures de-mystify the subject and show precisely "how things work." Goldenfeld keeps in mind a reader who wants to understand why things are done, what the results are, and what in principle can go wrong. The book reaches both experimentalists and theorists, students and even active researchers, and assumes only a prior knowledge of statistical mechanics at the introductory graduate level.Advanced, never-before-printed topics on the applications of renormalization group far from equilibrium and to partial differential equations add to the uniqueness of this book.




Phase of the Field Trip Lectureson


Book Description

This book is, more or less, the script of a lecture series entitled "Phase-Field Theory and Application," which I give at Ruhr University Bochum (RUB) in my department Scale-bridging Thermodynamic and Kinetic Simulation (STKS). It strongly rests on my personal experience during many years in academic and applied research with a special focus on "phase field." The idea is to combine a very brief presentation of the materials-related mechanisms alongside the theoretical background of the phasefield theory and, last but not least, to introduce numerical solutions. The lecture series is designed for graduate students and newcomers to phase-field theory. There are many aspects of phase field that will only be covered briefly in this script. At my university, we are continuing this lecture series with an advanced course in the format of a discussion seminar. We hope that we can continue with this in a second volume of the book. The 12-lecture course, as held at RUB, is condensed to seven lectures in this book. An eighth lecture, "Quantum Phase Field," is added here that I do only in the advanced course: Just free your mind and enjoy! Exercises are recommended at the end of each lecture, and suggestions for further reading are given. Examples are added where appropriate. A short introduction to the phase-field code OpenPhase academic [1] is added as a "tutorial" with two examples as a beginning to your own research.




Lectures on Phase Transitions


Book Description

This book treats the problem of phase transitions, emphasizing the generality and universality of the methods and models used. The course is basically concentrated on the problems of vacuum degeneration in macroscopic systems and a fundamental concept of quasiaverages by Bogolubov playing a special role in the theory of phase transitions and critical phenomena. An analysis of the connection between phase transition and spontaneous symmetry breaking in a macroscopic system allows a unique description of both first- and second-order phase transitions.The unique features of this book are: (i) a unique approach of describing first ? as well as second-order phase transitions, based on the Bogolubov concept of quasi-averages.(ii) a detailed presentation of the material and at the same time a review of modern problems.(iii) a general character of developed ideas that could be applied to various particular systems of condensed matter physics, nuclear physics and high-energy physics.




Statistical Mechanics of Lattice Systems


Book Description

A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.




Lectures in Modern Analysis and Applications II


Book Description

This lecture series was presented by a consortium of universities in conjunction with the U.S. Air Force Office of Scientific Research during the period 1967-1969 in Washington, D.C. and at the University of Maryland. The series of lectures was devoted to active basic areas of contemporary analysis which is important in or shows potential in real-world applications. Each lecture presents a survey and critical review of aspects of the specific area addressed, with emphasis on new results, open problems, and applications. This volume contains six lectures in the series; subsequent lectures will also be published.







Field Theoretic Method in Phase Transformations


Book Description

The main subject of the book is the continuum, field theoretic method of study of phase transformations in material systems. The method, also known as "phase field", allows one to analyze different stages of transformations on the unified platform. It has received significant attention in the materials science community recently due to many successes in solving or illuminating important problems. The book will address fundamentals of the method starting from the classical theories of phase transitions, the most important theoretical and computational results, and some of the most advanced recent applications.




Quantum Field Theory and the Standard Model


Book Description

A modern introduction to quantum field theory for graduates, providing intuitive, physical explanations supported by real-world applications and homework problems.




Lectures on Field Theory and Topology


Book Description

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.