This 2006 book presents the geometrical ideas of structure at the atomic level that are being developed and integrated into materials science. Emphasis is placed on the intuitive understanding of geometrical principles through illustrations not detailed computation. This book will appeal to those working in crystallography, solid-state science and materials science.
Selected peer-reviewed full text papers from the XVII International Scientific and Practical Conference "New Polymer Composite Materials" (NPCM 2021) Selected, peer-reviewed papers from the XVII International Scientific and Practical Conference "New Polymer Composite Materials" (NPCM 2021), July 5-10, 2021, Nalchik, Russian Federation
Advanced Lightweight Multifunctional Materials presents the current state-of-the-art on multifunctional materials research, focusing on different morphologies and their preparation and applications. The book emphasizes recent advances on these types of materials as well as their application. Chapters cover porous multifunctional materials, thermochromic and thermoelectric materials, shape memory materials, piezoelectric multifunctional materials, electrochromic and electrorheological, soft materials, magnetic and photochromic materials, and more. The book will be a valuable reference resource for academic researchers and industrial engineers working in the design and manufacture of multifunctional materials, composites and nanocomposites. - Provides detailed information on design, modeling and structural applications - Focuses on characteristics, processing, design and applications - Discusses the main types of lightweight multifunctional materials and processing techniques, as well as the physico-chemical insights that can lead to improved performance
Designers are becoming more directly involved in the fabrication process from the earliest stages of design. This book showcases the design and research work by some of the leading designers, makers and thinkers today. This highly illustrated text brings together a wealth of information and numerous examples from practice which will appeal to both students and practitioners.
The book is an innovative modern exposition of geometry, or rather, of geometries; it is the first textbook in which Felix Klein's Erlangen Program (the action of transformation groups) is systematically used as the basis for defining various geometries. The course of study presented is dedicated to the proposition that all geometries are created equal--although some, of course, remain more equal than others. The author concentrates on several of the more distinguished and beautiful ones, which include what he terms ``toy geometries'', the geometries of Platonic bodies, discrete geometries, and classical continuous geometries. The text is based on first-year semester course lectures delivered at the Independent University of Moscow in 2003 and 2006. It is by no means a formal algebraic or analytic treatment of geometric topics, but rather, a highly visual exposition containing upwards of 200 illustrations. The reader is expected to possess a familiarity with elementary Euclidean geometry, albeit those lacking this knowledge may refer to a compendium in Chapter 0. Per the author's predilection, the book contains very little regarding the axiomatic approach to geometry (save for a single chapter on the history of non-Euclidean geometry), but two Appendices provide a detailed treatment of Euclid's and Hilbert's axiomatics. Perhaps the most important aspect of this course is the problems, which appear at the end of each chapter and are supplemented with answers at the conclusion of the text. By analyzing and solving these problems, the reader will become capable of thinking and working geometrically, much more so than by simply learning the theory. Ultimately, the author makes the distinction between concrete mathematical objects called ``geometries'' and the singular ``geometry'', which he understands as a way of thinking about mathematics. Although the book does not address branches of mathematics and mathematical physics such as Riemannian and Kahler manifolds or, say, differentiable manifolds and conformal field theories, the ideology of category language and transformation groups on which the book is based prepares the reader for the study of, and eventually, research in these important and rapidly developing areas of contemporary mathematics.
Euclidean plane geometry is one of the oldest and most beautiful topics in mathematics. Instead of carefully building geometries from axiom sets, this book uses a wealth of methods to solve problems in Euclidean geometry. Many of these methods arose where existing techniques proved inadequate. In several cases, the new ideas used in solving specific problems later developed into independent areas of mathematics. This book is primarily a geometry textbook, but studying geometry in this way will also develop students' appreciation of the subject and of mathematics as a whole. For instance, despite the fact that the analytic method has been part of mathematics for four centuries, it is rarely a tool a student considers using when faced with a geometry problem. Methods for Euclidean Geometry explores the application of a broad range of mathematical topics to the solution of Euclidean problems.
The engineering of materials with advanced features is driving the research towards the design of innovative materials with high performances. New materials often deliver the best solution for structural applications, precisely contributing towards the finest combination of mechanical properties and low weight. The mimicking of nature's principles lead to a new class of structural materials including biomimetic composites, natural hierarchical materials and smart materials. Meanwhile, computational modeling approaches are the valuable tools complementary to experimental techniques and provide significant information at the microscopic level and explain the properties of materials and their very existence. The modeling also provides useful insights to possible strategies to design and fabricate materials with novel and improved properties. The book brings together these two fascinating areas and offers a comprehensive view of cutting-edge research on materials interfaces and technologies the engineering materials. The topics covered in this book are divided into 2 parts: Engineering of Materials, Characterizations & Applications and Computational Modeling of Materials. The chapters include the following: Mechanical and resistance behavior of structural glass beams Nanocrystalline metal carbides - microstructure characterization SMA-reinforced laminated glass panel Sustainable sugarcane bagasse cellulose for papermaking Electrospun scaffolds for cardiac tissue engineering Bio-inspired composites Density functional theory for studying extended systems First principles based approaches for modeling materials Computer aided materials design Computational materials for stochastic electromagnets Computational methods for thermal analysis of heterogeneous materials Modelling of resistive bilayer structures Modeling tunneling of superluminal photons through Brain Microtubules Computer aided surgical workflow modeling Displaced multiwavelets and splitting algorithms
Symmetry and Pattern in Projective Geometry is a self-contained study of projective geometry which compares and contrasts the analytic and axiomatic methods. The analytic approach is based on homogeneous coordinates, and brief introductions to Plücker coordinates and Grassmann coordinates are presented. This book looks carefully at linear, quadratic, cubic and quartic figures in two, three and higher dimensions. It deals at length with the extensions and consequences of basic theorems such as those of Pappus and Desargues. The emphasis throughout is on special configurations that have particularly interesting symmetry properties. The intricate and novel ideas of ‘Donald’ Coxeter, who is considered one of the great geometers of the twentieth century, are also discussed throughout the text. The book concludes with a useful analysis of finite geometries and a description of some of the remarkable configurations discovered by Coxeter. This book will be appreciated by mathematics students and those wishing to learn more about the subject of geometry. It makes accessible subjects and theorems which are often considered quite complicated and presents them in an easy-to-read and enjoyable manner.
