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This accessible new text introduces the theoretical concepts and tools essential for graduate-level courses on the physics of materials in condensed matter physics, physical chemistry, materials science and engineering, and chemical engineering. Topics covered range from fundamentals such as crystal periodicity and symmetry, and derivation of single-particle equations, to modern additions including graphene, two-dimensional solids, carbon nanotubes, topological states, and Hall physics. Advanced topics such as phonon interactions with phonons, photons and electrons, and magnetism, are presented in an accessible way, and a set of appendices reviewing crucial fundamental physics and mathematical tools makes this text suitable for students from a range of backgrounds. Students will benefit from the emphasis on translating theory into practice, with worked examples explaining experimental observations, applications illustrating how theoretical concepts can be applied to real research problems, and 242 informative full color illustrations. End-of chapter exercises are included for homework and self-study, with solutions and lecture slides for instructors available online.
This volume gathers selected contributions from the participants of the Banff International Research Station (BIRS) workshop Coupled Mathematical Models for Physical and Biological Nanoscale Systems and their Applications, who explore various aspects of the analysis, modeling and applications of nanoscale systems, with a particular focus on low dimensional nanostructures and coupled mathematical models for their description. Due to the vastness, novelty and complexity of the interfaces between mathematical modeling and nanoscience and nanotechnology, many important areas in these disciplines remain largely unexplored. In their efforts to move forward, multidisciplinary research communities have come to a clear understanding that, along with experimental techniques, mathematical modeling and analysis have become crucial to the study, development and application of systems at the nanoscale. The conference, held at BIRS in autumn 2016, brought together experts from three different communities working in fields where coupled mathematical models for nanoscale and biosystems are especially relevant: mathematicians, physicists (both theorists and experimentalists), and computational scientists, including those dealing with biological nanostructures. Its objectives: summarize the state-of-the-art; identify and prioritize critical problems of major importance that require solutions; analyze existing methodologies; and explore promising approaches to addressing the challenges identified. The contributions offer up-to-date introductions to a range of topics in nano and biosystems, identify important challenges, assess current methodologies and explore promising approaches. As such, this book will benefit researchers in applied mathematics, as well as physicists and biologists interested in coupled mathematical models and their analysis for physical and biological nanoscale systems that concern applications in biotechnology and medicine, quantum information processing and optoelectronics.
An emerging theme in computational materials science is that of multiscale modelling. While the definition of 'multiscale modelling' is still developing as new applications appear, a broad interpretation includes efforts to exploit insights arising either from distinct methodologies or from the attempt to incorporate multiple mechanisms into the same modelling paradigm. Though multiple scale models are not new, the topic has recently taken on a new sense of urgency, due to the recognition that brute force computational approaches often fall short of allowing for direct simulation of both the characteristic structures and temporal processes found in real materials. As a result, a number of approaches are now finding favor in which ideas borrowed from modelling paradigms are unified to produce more powerful techniques. This book, first published in 1999, brings together experts to both exchange ideas on how to link methodologies at different length scales, and to outline the most promising future approaches. Topics include: modelling dislocation properties and behavior; defect dynamics and microstructural evolution; crystal defects and interfaces and noncrystalline and nanocrystalline materials.
This graduate textbook designed for students in physics, chemistry and materials science provides a modern treatment of the theory of solids dealing with the physics of electron and phonon states in crystals and how they determine the structure and properties of solids. The first part of the book deals with electrons and atoms in a crystal, and the second part extends the discussion to defects in crystals and to structures without crystalline symmetry. There are numerous exercises throughout and appendices to provide the necessary background.
Significant advances have been made towards understanding the properties of materials through theoretical approaches. These approaches are based either on first-principles quantum mechanical formulations or semi-empirical formulations, and have benefitted from increases in computational power. The advent of parallel computing has propelled the theoretical approaches to a new level of realism in modelling physical systems of interest. The theoretical methods and simulation techniques that are cur- rently under development are certain to become powerful tools in understanding, exploring and predicting the properties of existing and novel materials. This book discusses critically current developments in computations and simulational approaches specifically aimed at addressing real materials problems, with an emphasis on parallel computing and shows the most successful applications of computational and simulational work to date. Topics include: advances in computational methods; parallel algorithms and applications; fracture, brittle/ductile behavior and large-scale defects; thermodynamic stability of materials; surfaces and interfaces of materials; and complex materials simulations.
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