This book starts with an introduction to quantitative texture analysis (QTA), which adopts conventions (active rotations, definition of Euler angles, Wigner D-functions) that conform to those of the present-day mathematics and physics literature. Basic concepts (e.g., orientation; orientation distribution function (ODF), orientation density function, and their relationship) are made precise through their mathematical definition. Parts II and III delve deeper into the mathematical foundations of QTA, where the important role played by group representations is emphasized. Part II includes one chapter on generalized QTA based on the orthogonal group, and Part III one on tensorial Fourier expansion of the ODF and tensorial texture coefficients. This work will appeal to students and practitioners who appreciate a precise presentation of QTA through a unifying mathematical language, and to researchers who are interested in applications of group representations to texture analysis. Previously published in the Journal of Elasticity, Volume 149, issues 1-2, April, 2022

Combining research methods from various areas of mathematics and physics, Probabilistic Models of Cosmic Backgrounds describes the isotropic random sections of certain fibre bundles and their applications to creating rigorous mathematical models of both discovered and hypothetical cosmic backgrounds. Previously scattered and hard-to-find mathematical and physical theories have been assembled from numerous textbooks, monographs, and research papers, and explained from different or even unexpected points of view. This consists of both classical and newly discovered results necessary for understanding a sophisticated problem of modelling cosmic backgrounds. The book contains a comprehensive description of mathematical and physical aspects of cosmic backgrounds with a clear focus on examples and explicit calculations. Its reader will bridge the gap of misunderstanding between the specialists in various theoretical and applied areas who speak different scientific languages. The audience of the book consists of scholars, students, and professional researchers. A scholar will find basic material for starting their own research. A student will use the book as supplementary material for various courses and modules. A professional mathematician will find a description of several physical phenomena at the rigorous mathematical level. A professional physicist will discover mathematical foundations for well-known physical theories.

Crystallographic texture or preferred orientation has long been known to strongly influence material properties. Historically, the means of obtaining such texture data has been though the use of x-ray or neutron diffraction for bulk texture measurements, or transmission electron microscopy or electron channeling for local crystallographic information. In recent years, we have seen the emergence of a new characterization technique for probing the microtexture of materials. This advance has come about primarily through the automated indexing of electron backscatter diffraction (EBSD) patterns. The first commercially available system was introduced in 1994, and since then of sales worldwide has been dramatic. This has accompanied widening the growth applicability in materials scienceproblems such as microtexture, phase identification, grain boundary character distribution, deformation microstructures, etc. and is evidence that this technique can, in some cases, replace more time-consuming transmission electron microscope (TEM) or x-ray diffraction investigations. The benefits lie in the fact that the spatial resolution on new field emission scanning electron microscopes (SEM) can approach 50 nm, but spatial extent can be as large a centimeter or greater with a computer controlled stage and montagingofthe images. Additional benefits include the relative ease and low costofattaching EBSD hardware to new or existing SEMs. Electron backscatter diffraction is also known as backscatter Kikuchi diffraction (BKD), or electron backscatter pattern technique (EBSP). Commercial names for the automation include Orientation Imaging Microscopy (OIMTM) and Automated Crystal Orientation Mapping (ACOM).

Reflecting emerging methods and the evolution of the field, Introduction to Texture Analysis: Macrotexture, Microtexture, and Orientation Mapping keeps mathematics to a minimum in covering both traditional macrotexture analysis and more advanced electron-microscopy-based microtexture analysis. The authors integrate the two techniques and address the subsequent need for a more detailed explanation of philosophy, practice, and analysis associated with texture analysis. The book illustrates approaches to orientation measurement and interpretation and elucidates the fundamental principles on which measurements are based. Thoroughly updated, this Third Edition of a best-seller is a rare introductory-level guide to texture analysis. Discusses terminology associated with orientations, texture, and their representation, as well as the diffraction of radiation, a phenomenon that is the basis for almost all texture analysis Covers data acquisition, as well as representation and evaluation related to the well-established methods of macrotexture analysis Updated to include experimental details of the latest transmission or scanning electron microscope-based techniques for microstructure analysis, including electron backscatter diffraction (EBSD) Describes how microtexture data are evaluated and represented and emphasizes the advances in orientation microscopy and mapping, and advanced issues concerning crystallographic aspects of interfaces and connectivity Offers new and innovative grain boundary descriptions and examples This book is an ideal tool to help readers in the materials sciences develop a working understanding of the practice and applications of texture.

Texture Analysis in Materials Science Mathematical Methods focuses on the methodologies, processes, techniques, and mathematical aids in the orientation distribution of crystallites. The manuscript first offers information on the orientation of individual crystallites and orientation distributions. Topics include properties and representations of rotations, orientation distance, and ambiguity of rotation as a consequence of crystal and specimen symmetry. The book also takes a look at expansion of orientation distribution functions in series of generalized spherical harmonics, fiber textures, and methods not based on the series expansion. The publication reviews special distribution functions, texture transformation, and system of programs for the texture analysis of sheets of cubic materials. The text also ponders on the estimation of errors, texture analysis, and physical properties of polycrystalline materials. Topics include comparison of experimental and recalculated pole figures; indetermination error for incomplete pole figures; and determination of the texture coefficients from anisotropie polycrystal properties. The manuscript is a dependable reference for readers interested in the use of mathematical aids in the orientation distribution of crystallites.

Through his voluminous and in?uential writings, editorial activities, organi- tional leadership, intellectual acumen, and strong sense of history, Clifford - brose Truesdell III (1919–2000) was the main architect for the renaissance of - tional continuum mechanics since the middle of the twentieth century. The present collection of 42 essays and research papers pays tribute to this man of mathematics, science, and natural philosophy as well as to his legacy. The ?rst ?ve essays by B. D. Coleman, E. Giusti, W. Noll, J. Serrin, and D. Speiser were texts of addresses given by their authors at the Meeting in memory of Clifford Truesdell, which was held in Pisa in November 2000. In these essays the reader will ?nd personal reminiscences of Clifford Truesdell the man and of some of his activities as scientist, author, editor, historian of exact sciences, and principal founding member of the Society for Natural Philosophy. The bulk of the collection comprises 37 research papers which bear witness to the Truesdellian legacy. These papers cover a wide range of topics; what ties them together is the rational spirit. Clifford Truesdell, in his address upon receipt of a Birkhoff Prize in 1978, put the essence of modern continuum mechanics succinctly as “conceptual analysis, analysis not in the sense of the technical term but in the root meaning: logical criticism, dissection, and creative scrutiny.

This book provides a comprehensive discussion of the Jahn-Teller Effect (JTE), focusing on the boson-fermion interaction. While current research is concerned with measuring and calculating ever more sophisticated and complex manifestations of the JT effect, the present volume takes away the epicycles of the theory and focuses on the symmetry dilemma at its core. When fermions and bosons meet, they get entangled and form a new dynamic reality. According to the rules of Molecular Symmetry, this reality is limited to a small set of patterns, with degeneracy cardinalities: 2, 3, 4, 5, and 6. The novelty of the book is that it adopts a unique mathematical technique, known as the Bargmann-Fock representation, and treats all degeneracies in detail. So far, this method was only applied to the simplest doublet case therefore its extension to the entire range of cases offers a new unified perspective. This volume will help the reader acquire a clear understanding of the JT effect, discover its universal mechanism and it will be a great tool for researchers and graduates working on this topic.