Phase-Field Methods in Materials Science and Engineering

An innovative treatment of mathematical methods for a multidisciplinary audience Clearly and elegantly presented, Mathematical Methods in Science and Engineering provides a coherent treatment of mathematical methods, bringing advanced mathematical tools to a multidisciplinary audience. The growing interest in interdisciplinary studies has brought scientists from many disciplines such as physics, mathematics, chemistry, biology, economics, and finance together, which has increased the demand for courses in upper-level mathematical techniques. This book succeeds in not only being tuned in to the existing practical needs of this multidisciplinary audience, but also plays a role in the development of new interdisciplinary science by introducing new techniques to students and researchers. Mathematical Methods in Science and Engineering's modular structure affords instructors enough flexibility to use this book for several different advanced undergraduate and graduate level courses. Each chapter serves as a review of its subject and can be read independently, thus it also serves as a valuable reference and refresher for scientists and beginning researchers. There are a growing number of research areas in applied sciences, such as earthquakes, rupture, financial markets, and crashes, that employ the techniques of fractional calculus and path integrals. The book's two unique chapters on these subjects, written in a style that makes these advanced techniques accessible to a multidisciplinary audience, are an indispensable tool for researchers and instructors who want to add something new to their compulsory courses. Mathematical Methods in Science and Engineering includes: * Comprehensive chapters on coordinates and tensors and on continuous groups and their representations * An emphasis on physical motivation and the multidisciplinary nature of the methods discussed * A coherent treatment of carefully selected topics in a style that makes advanced mathematical tools accessible to a multidisciplinary audience * Exercises at the end of every chapter and plentiful examples throughout the book Mathematical Methods in Science and Engineering is not only appropriate as a text for advanced undergraduate and graduate physics programs, but is also appropriate for engineering science and mechanical engineering departments due to its unique chapter coverage and easily accessible style. Readers are expected to be familiar with topics typically covered in the first three years of science and engineering undergraduate programs. Thoroughly class-tested, this book has been used in classes by more than 1,000 students over the past eighteen years.

A Practical, Interdisciplinary Guide to Advanced Mathematical Methods for Scientists and Engineers Mathematical Methods in Science and Engineering, Second Edition, provides students and scientists with a detailed mathematical reference for advanced analysis and computational methodologies. Making complex tools accessible, this invaluable resource is designed for both the classroom and the practitioners; the modular format allows flexibility of coverage, while the text itself is formatted to provide essential information without detailed study. Highly practical discussion focuses on the “how-to” aspect of each topic presented, yet provides enough theory to reinforce central processes and mechanisms. Recent growing interest in interdisciplinary studies has brought scientists together from physics, chemistry, biology, economy, and finance to expand advanced mathematical methods beyond theoretical physics. This book is written with this multi-disciplinary group in mind, emphasizing practical solutions for diverse applications and the development of a new interdisciplinary science. Revised and expanded for increased utility, this new Second Edition: Includes over 60 new sections and subsections more useful to a multidisciplinary audience Contains new examples, new figures, new problems, and more fluid arguments Presents a detailed discussion on the most frequently encountered special functions in science and engineering Provides a systematic treatment of special functions in terms of the Sturm-Liouville theory Approaches second-order differential equations of physics and engineering from the factorization perspective Includes extensive discussion of coordinate transformations and tensors, complex analysis, fractional calculus, integral transforms, Green's functions, path integrals, and more Extensively reworked to provide increased utility to a broader audience, this book provides a self-contained three-semester course for curriculum, self-study, or reference. As more scientific disciplines begin to lean more heavily on advanced mathematical analysis, this resource will prove to be an invaluable addition to any bookshelf.

An authoritative introduction to the science and engineering of bioinspired materials Bioinspired Materials Science and Engineering offers a comprehensive view of the science and engineering of bioinspired materials and includes a discussion of biofabrication approaches and applications of bioinspired materials as they are fed back to nature in the guise of biomaterials. The authors also review some biological compounds and shows how they can be useful in the engineering of bioinspired materials. With contributions from noted experts in the field, this comprehensive resource considers biofabrication, biomacromolecules, and biomaterials. The authors illustrate the bioinspiration process from materials design and conception to application of bioinspired materials. In addition, the text presents the multidisciplinary aspect of the concept, and contains a typical example of how knowledge is acquired from nature, and how in turn this information contributes to biological sciences, with an accent on biomedical applications. This important resource: Offers an introduction to the science and engineering principles for the development of bioinspired materials Includes a summary of recent developments on biotemplated formation of inorganic materials using natural templates Illustrates the fabrication of 3D-tumor invasion models and their potential application in drug assessments Explores electroactive hydrogels based on natural polymers Contains information on turning mechanical properties of protein hydrogels for biomedical applications Written for chemists, biologists, physicists, and engineers, Bioinspired Materials Science and Engineering contains an indispensible resource for an understanding of bioinspired materials science and engineering.

Retaining its proven concept, the second edition of this ready reference specifically addresses the need of materials engineers for reliable, detailed information on modern material characterization methods. As such, it provides a systematic overview of the increasingly important field of characterization of engineering materials with the help of neutrons and synchrotron radiation. The first part introduces readers to the fundamentals of structure-property relationships in materials and the radiation sources suitable for materials characterization. The second part then focuses on such characterization techniques as diffraction and scattering methods, as well as direct imaging and tomography. The third part presents new and emerging methods of materials characterization in the field of 3D characterization techniques like three-dimensional X-ray diffraction microscopy. The fourth and final part is a collection of examples that demonstrate the application of the methods introduced in the first parts to problems in materials science. With thoroughly revised and updated chapters and now containing about 20% new material, this is the must-have, in-depth resource on this highly relevant topic.

Food Materials Science and Engineering covers a comprehensive range of topics in relation to food materials, their properties and characterisation techniques, thus offering a new approach to understanding food production and quality control. The opening chapter will define the scope and application of food materials science, explaining the relationship between raw material structure and processing and quality in the final product. Subsequent chapters will examine the structure of food materials and how they relate to quality, sensory perception, processing attributes and nutrient delivery. The authors also address applications of nanotechnology to food and packaging science. Methods of manufacturing food systems with improved shelf-life and quality attributes will be highlighted in the book.

A complete introduction to the multidisciplinary applications of mathematical methods In order to work with varying levels of engineering and physics research, it is important to have a firm understanding of key mathematical concepts such as advanced calculus, differential equations, complex analysis, and introductory mathematical physics. Essentials of Mathematical Methods in Science and Engineering provides a comprehensive introduction to these methods under one cover, outlining basic mathematical skills while also encouraging students and practitioners to develop new, interdisciplinary approaches to their research. The book begins with core topics from various branches of mathematics such as limits, integrals, and inverse functions. Subsequent chapters delve into the analytical tools that are commonly used in scientific and engineering studies, including vector analysis, generalized coordinates, determinants and matrices, linear algebra, complex numbers, complex analysis, and Fourier series. The author provides an extensive chapter on probability theory with applications to statistical mechanics and thermodynamics that complements the following chapter on information theory, which contains coverage of Shannon's theory, decision theory, game theory, and quantum information theory. A comprehensive list of references facilitates further exploration of these topics. Throughout the book, numerous examples and exercises reinforce the presented concepts and techniques. In addition, the book is in a modular format, so each chapter covers its subject thoroughly and can be read independently. This structure affords flexibility for individualizing courses and teaching. Providing a solid foundation and overview of the various mathematical methods and applications in multidisciplinary research, Essentials of Mathematical Methods in Science and Engineering is an excellent text for courses in physics, science, mathematics, and engineering at the upper-undergraduate and graduate levels. It also serves as a useful reference for scientists and engineers who would like a practical review of mathematical methods.

A comprehensive introduction to the multidisciplinary applications of mathematical methods, revised and updated The second edition of Essentials of Mathematical Methods in Science and Engineering offers an introduction to the key mathematical concepts of advanced calculus, differential equations, complex analysis, and introductory mathematical physics for students in engineering and physics research. The book’s approachable style is designed in a modular format with each chapter covering a subject thoroughly and thus can be read independently. This updated second edition includes two new and extensive chapters that cover practical linear algebra and applications of linear algebra as well as a computer file that includes Matlab codes. To enhance understanding of the material presented, the text contains a collection of exercises at the end of each chapter. The author offers a coherent treatment of the topics with a style that makes the essential mathematical skills easily accessible to a multidisciplinary audience. This important text: • Includes derivations with sufficient detail so that the reader can follow them without searching for results in other parts of the book • Puts the emphasis on the analytic techniques • Contains two new chapters that explore linear algebra and its applications • Includes Matlab codes that the readers can use to practice with the methods introduced in the book Written for students in science and engineering, this new edition of Essentials of Mathematical Methods in Science and Engineering maintains all the successful features of the first edition and includes new information.

Besides its coverage of the four important aspects of synchrotron sources, materials and material processes, measuring techniques, and applications, this ready reference presents both important method types: diffraction and tomography. Following an introduction, a general section leads on to methods, while further sections are devoted to emerging methods and industrial applications. In this way, the text provides new users of large-scale facilities with easy access to an understanding of both the methods and opportunities offered by different sources and instruments.

An Introduction to Materials Engineering and Science for Chemical and Materials Engineers provides a solid background in materials engineering and science for chemical and materials engineering students. This book: Organizes topics on two levels; by engineering subject area and by materials class. Incorporates instructional objectives, active-learning principles, design-oriented problems, and web-based information and visualization to provide a unique educational experience for the student. Provides a foundation for understanding the structure and properties of materials such as ceramics/glass, polymers, composites, bio-materials, as well as metals and alloys. Takes an integrated approach to the subject, rather than a «metals first» approach.

For engineering and scientific endeavors to progress there must be generally accepted ethical guidelines in place to which engineers and scientists must adhere. This book explores the various scientific and engineering disciplines, examining the potential for unethical behavior by professionals. Documented examples are presented to show where unethical behavior could have been halted before it became an issue. The authors also look to the future to see what is in store for professionals in the scientific and engineering disciplines and how the potential for unethical behavior can be negated.