Computational Matter

This book is concerned with computing in materio: that is, unconventional computing performed by directly harnessing the physical properties of materials. It offers an overview of the field, covering four main areas of interest: theory, practice, applications and implications. Each chapter synthesizes current understanding by deliberately bringing together researchers across a collection of related research projects. The book is useful for graduate students, researchers in the field, and the general scientific reader who is interested in inherently interdisciplinary research at the intersections of computer science, biology, chemistry, physics, engineering and mathematics.

This book provides algorithms and ideas for computationalists. Subjects treated include low-level algorithms, bit wizardry, combinatorial generation, fast transforms like the Fourier transform, and fast arithmetic for both real numbers and finite fields. Various optimization techniques are described and the actual performance of many given implementations is examined. The focus is on material that does not usually appear in textbooks on algorithms. The implementations are done in C++ and the GP language, written for POSIX-compliant platforms such as the Linux and BSD operating systems.

Soft condensed matter physics relies on a fundamental understanding at the interface between physics, chemistry, biology, and engineering for a host of materials and circumstances that are related to, but outside, the traditional definition of condensed matter physics. Featuring contributions from leading researchers in the field, this book uniquely discusses both the contemporary experimental and computational manifestations of soft condensed matter systems. From particle tracking and image analysis, novel materials and computational methods, to confocal microscopy and bacterial assays, this book will equip the reader for collaborative and interdisciplinary research efforts relating to a range of modern problems in nonlinear and non-equilibrium systems. It will enable both graduate students and experienced researchers to supplement a more traditional understanding of thermodynamics and statistical systems with knowledge of the techniques used in contemporary investigations. Color versions of a selection of the figures are available at www.cambridge.org/9780521115902.

This book covers the essentials of Computational Science and gives tools and techniques to solve materials science problems using molecular dynamics (MD) and first-principles methods. The new edition expands upon the density functional theory (DFT) and how the original DFT has advanced to a more accurate level by GGA+U and hybrid-functional methods. It offers 14 new worked examples in the LAMMPS, Quantum Espresso, VASP and MedeA-VASP programs, including computation of stress-strain behavior of Si-CNT composite, mean-squared displacement (MSD) of ZrO2-Y2O3, band structure and phonon spectra of silicon, and Mo-S battery system. It discusses methods once considered too expensive but that are now cost-effective. New examples also include various post-processed results using VESTA, VMD, VTST, and MedeA.

Addressing graduate students and researchers, this book gives a very detailed theoretical and computational description of multiple scattering in solid matter. Particular emphasis is placed on solids with reduced dimensions, on full potential approaches and on relativistic treatments. For the first time approaches such as the screened Korringa-Kohn-Rostoker method are reviewed, considering all formal steps such as single-site scattering, structure constants and screening transformations, and also the numerical point of view. Furthermore, a very general approach is presented for solving the Poisson equation, needed within density functional theory in order to achieve self-consistency. Special chapters are devoted to the Coherent Potential Approximation and to the Embedded Cluster Method, used, for example, for describing nanostructured matter in real space. In a final chapter, physical properties related to the (single-particle) Green's function, such as magnetic anisotropies, interlayer exchange coupling, electric and magneto-optical transport and spin-waves, serve to illustrate the usefulness of the methods described.

Data, Matter, Design presents a comprehensive overview of current design processes that rely on the input of data and use of computational design strategies, and their relationship to an array of outputs. Technological changes, through the use of computational tools and processes, have radically altered and influenced our relationship to cities and the methods by which we design architecture, urban, and landscape systems. This book presents a wide range of curated projects and contributed texts by leading architects, urbanists, and designers that transform data as an abstraction, into spatial, experiential, and performative configurations within urban ecologies, emerging materials, robotic agents, adaptive fields, and virtual constructs. Richly illustrated with over 200 images, Data, Matter, Design is an essential read for students, academics, and professionals to evaluate and discuss how data in design methodologies and theoretical discourses have evolved in the last two decades and why processes of data collection, measurement, quantification, simulation, algorithmic control, and their integration into methods of reading and producing spatial conditions, are becoming vital in academic and industry practices.

This is the only book to cover the most recent developments in applied quantum theory and their use in modeling materials properties. It describes new approaches to modeling disordered alloys and focuses on those approaches that combine the most efficient quantum-level theories of random alloys with the most sophisticated numerical techniques. In doing so, it establishes a theoretical insight into the electronic structure of complex materials such as stainless steels, Hume-Rothery alloys and silicates.

Unlike existing texts, this book blends for the first time three topics in physics - symmetry, condensed matter physics and computational methods - into one pedagogical textbook. It includes new concepts in mathematical crystallography; experimental methods capitalizing on symmetry aspects; non-conventional applications such as Fourier crystallography, color groups, quasicrystals and incommensurate systems; as well as concepts and techniques behind the Landau theory of phase transitions. Adopting a computational approach to the application of group theoretical techniques to solving symmetry related problems, it dramatically alleviates the need for intensive calculations usually found in the presentation of symmetry. Writing computer programs helps the student achieve a firm understanding of the underlying concepts, and sample programs, based on Mathematica, are presented throughout the book. Containing over 150 exercises, this textbook is ideal for graduate students in condensed matter physics, materials science, and chemistry. Solutions and computer programs are available online at www.cambridge.org/9780521828451.

This textbook introduces modern techniques based on computer simulation to study materials science. It starts from first principles calculations enabling to calculate the physical and chemical properties by solving a many-body Schroedinger equation with Coulomb forces. For the exchange-correlation term, the local density approximation is usually applied. After the introduction of the first principles treatment, tight-binding and classical potential methods are briefly introduced to indicate how one can increase the number of atoms in the system. In the second half of the book, Monte Carlo simulation is discussed in detail. Problems and solutions are provided to facilitate understanding. Readers will gain sufficient knowledge to begin theoretical studies in modern materials research. This second edition includes a lot of recent theoretical techniques in materials research. With the computers power now available, it is possible to use these numerical techniques to study various physical and chemical properties of complex materials from first principles. The new edition also covers empirical methods, such as tight-binding and molecular dynamics.

Since the first edition sold out in less than a year, we now present the revised second edition of Mainzer's popular book. The theory of nonlinear complex systems has become a successful problem-solving approach in the natural sciences from laser physics, quantum chaos, and meteorology to computer simulations of cell growth in biology. It is now recognized that many of our social, ecological, and political problems are also of a global, complex, and nonlinear nature. And one of the most exciting contemporary topics is the idea that even the human mind is governed largely by the nonlinear dynamics of complex systems. In this wide-ranging but concise treatment, Prof. Mainzer discusses, in a nontechnical language, the common framework behind these endeavors. Emphasis is given to the evolution of new structures in natural and cultural systems and we see clearly how the new integrative approach can give insights not available from traditional reductionistic methods.