Lectures On Phase Field
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Lectures on Phase Field
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
Author: Thomas Wick
language: en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date: 2020-10-12
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
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.