Lattice Sums Then And Now

Author : Jonathan M. Borwein
Publisher : Unknown
Page : 128 pages
File Size : 51,5 Mb
Release : 2013
Category : Electronic books
ISBN : 1107425158

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Lattice Sums Then and Now by Jonathan M. Borwein Pdf

"The study of lattice sums began when early investigators wanted to go from mechanical properties of crystals to the properties of the atoms and ions from which they were built (the literature of Madelung's constant). A parallel literature was built around the optical properties of regular lattices of atoms (initiated by Lord Rayleigh, Lorentz and Lorenz). For over a century many famous scientists and mathematicians have delved into the properties of lattices, sometimes unwittingly duplicating the work of their predecessors. Here, at last, is a comprehensive overview of the substantial body of knowledge that exists on lattice sums and their applications. The authors also provide commentaries on open questions, and explain modern techniques which simplify the task of finding new results in this fascinating and ongoing field. Lattice sums in one, two, three, four and higher dimensions are covered"--

Author : J. M. Borwein,M. L. Glasser,R. C. McPhedran,J. G. Wan,I. J. Zucker
Publisher : Cambridge University Press
Page : 391 pages
File Size : 48,7 Mb
Release : 2013-09-05
Category : Mathematics
ISBN : 9781107039902

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Lattice Sums Then and Now by J. M. Borwein,M. L. Glasser,R. C. McPhedran,J. G. Wan,I. J. Zucker Pdf

This comprehensive overview of lattice sums is long overdue for a topic that is important in diverse areas of science.

Author : Professor Jonathan Borwein,M L Glasser,R C McPhedran,Jonathan M. Borwein,I J Zucker,J G Wan
Publisher : Unknown
Page : 390 pages
File Size : 45,8 Mb
Release : 2014-05-14
Category : Lattice theory
ISBN : 1107417309

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Lattice Sums Then and Now by Professor Jonathan Borwein,M L Glasser,R C McPhedran,Jonathan M. Borwein,I J Zucker,J G Wan Pdf

This comprehensive overview of lattice sums is long overdue for a topic that is important in diverse areas of science.

Author : Eric Cancès,Gero Friesecke
Publisher : Springer Nature
Page : 595 pages
File Size : 43,8 Mb
Release : 2023-07-18
Category : Mathematics
ISBN : 9783031223402

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Density Functional Theory by Eric Cancès,Gero Friesecke Pdf

Density functional theory (DFT) provides the most widely used models for simulating molecules and materials based on the fundamental laws of quantum mechanics. It plays a central role in a huge spectrum of applications in chemistry, physics, and materials science.Quantum mechanics describes a system of N interacting particles in the physical 3-dimensional space by a partial differential equation in 3N spatial variables. The standard numerical methods thus incur an exponential increase of computational effort with N, a phenomenon known as the curse of dimensionality; in practice these methods already fail beyond N=2. DFT overcomes this problem by 1) reformulating the N-body problem involving functions of 3N variables in terms of the density, a function of 3 variables, 2) approximating it by a pioneering hybrid approach which keeps important ab initio contributions and re-models the remainder in a data-driven way. This book intends to be an accessible, yet state-of-art text on DFT for graduate students and researchers in applied and computational mathematics, physics, chemistry, and materials science. It introduces and reviews the main models of DFT, covering their derivation and mathematical properties, numerical treatment, and applications.

Author : George E. Andrews,Frank Garvan
Publisher : Springer
Page : 736 pages
File Size : 55,5 Mb
Release : 2018-02-01
Category : Mathematics
ISBN : 9783319683768

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Analytic Number Theory, Modular Forms and q-Hypergeometric Series by George E. Andrews,Frank Garvan Pdf

Gathered from the 2016 Gainesville Number Theory Conference honoring Krishna Alladi on his 60th birthday, these proceedings present recent research in number theory. Extensive and detailed, this volume features 40 articles by leading researchers on topics in analytic number theory, probabilistic number theory, irrationality and transcendence, Diophantine analysis, partitions, basic hypergeometric series, and modular forms. Readers will also find detailed discussions of several aspects of the path-breaking work of Srinivasa Ramanujan and its influence on current research. Many of the papers were motivated by Alladi's own research on partitions and q-series as well as his earlier work in number theory. Alladi is well known for his contributions in number theory and mathematics. His research interests include combinatorics, discrete mathematics, sieve methods, probabilistic and analytic number theory, Diophantine approximations, partitions and q-series identities. Graduate students and researchers will find this volume a valuable resource on new developments in various aspects of number theory.

Author : Anonim
Publisher : Popov, Institut Fresnel
Page : 431 pages
File Size : 52,7 Mb
Release : 2024-05-02
Category : Electronic
ISBN : 9782853998604

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Gratings: Theory and Numeric Applications by Anonim Pdf

Author : Habib Ammari,Brian Fitzpatrick,Hyeonbae Kang,Matias Ruiz,Sanghyeon Yu,Hai Zhang
Publisher : American Mathematical Soc.
Page : 509 pages
File Size : 55,6 Mb
Release : 2018-10-15
Category : Photonics
ISBN : 9781470448004

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Mathematical and Computational Methods in Photonics and Phononics by Habib Ammari,Brian Fitzpatrick,Hyeonbae Kang,Matias Ruiz,Sanghyeon Yu,Hai Zhang Pdf

The fields of photonics and phononics encompass the fundamental science of light and sound propagation and interactions in complex structures, as well as its technological applications. This book reviews new and fundamental mathematical tools, computational approaches, and inversion and optimal design methods to address challenging problems in photonics and phononics. An emphasis is placed on analyzing sub-wavelength resonators, super-focusing and super-resolution of electromagnetic and acoustic waves, photonic and phononic crystals, electromagnetic cloaking, and electromagnetic and elastic metamaterials and metasurfaces. Throughout this book, the authors demonstrate the power of layer potential techniques for solving challenging problems in photonics and phononics when they are combined with asymptotic analysis. This book might be of interest to researchers and graduate students working in the fields of applied and computational mathematics, partial differential equations, electromagnetic theory, elasticity, integral equations, and inverse and optimal design problems in photonics and phononics.

Author : David H. Bailey,Jonathan M. Borwein
Publisher : Springer
Page : 507 pages
File Size : 43,6 Mb
Release : 2016-07-19
Category : Mathematics
ISBN : 9783319323770

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Pi: The Next Generation by David H. Bailey,Jonathan M. Borwein Pdf

This book contains a compendium of 25 papers published since the 1970s dealing with pi and associated topics of mathematics and computer science. The collection begins with a Foreword by Bruce Berndt. Each contribution is preceded by a brief summary of its content as well as a short key word list indicating how the content relates to others in the collection. The volume includes articles on actual computations of pi, articles on mathematical questions related to pi (e.g., “Is pi normal?”), articles presenting new and often amazing techniques for computing digits of pi (e.g., the “BBP” algorithm for pi, which permits one to compute an arbitrary binary digit of pi without needing to compute any of the digits that came before), papers presenting important fundamental mathematical results relating to pi, and papers presenting new, high-tech techniques for analyzing pi (i.e., new graphical techniques that permit one to visually see if pi and other numbers are “normal”). This volume is a companion to Pi: A Source Book whose third edition released in 2004. The present collection begins with 2 papers from 1976, published by Eugene Salamin and Richard Brent, which describe “quadratically convergent” algorithms for pi and other basic mathematical functions, derived from some mathematical work of Gauss. Bailey and Borwein hold that these two papers constitute the beginning of the modern era of computational mathematics. This time period (1970s) also corresponds with the introduction of high-performance computer systems (supercomputers), which since that time have increased relentlessly in power, by approximately a factor of 100,000,000, advancing roughly at the same rate as Moore’s Law of semiconductor technology. This book may be of interest to a wide range of mathematical readers; some articles cover more advanced research questions suitable for active researchers in the field, but several are highly accessible to undergraduate mathematics students.

Author : Dick Bedeaux,Jan Vlieger
Publisher : World Scientific
Page : 464 pages
File Size : 47,9 Mb
Release : 2004-07-19
Category : Technology & Engineering
ISBN : 9781783260744

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Optical Properties of Surfaces by Dick Bedeaux,Jan Vlieger Pdf

This invaluable book represents a substantial body of work describing the theory of the optical properties of thin island films and rough surfaces. In both cases the feature sizes are small compared to the wavelength of light. The approach is extremely rigorous and theoretically very thorough. The reflection, transmission and absorption of light are described. Computer programs that provide exact solutions for theoretical properties of thin island films are available, and this makes the book of great practical use. The early chapters present a comprehensive theoretical framework. In this new edition a chapter on reflection from gyrotropic media has been added. Contributions due to the gyrotropic nature of the interfacial layer are discussed. Contents:Excess Currents, Charge Densities and FieldMaxwell's Equations with Singular FieldsReflection and TransmissionIsland Films in the Low Coverage LimitSpheroidal Island Films in the Low Coverage LimitIsland Films for a Finite CoverageFilms of Truncated Spheres for a Low CoverageFilms of Truncated Spheroids in the Low Coverage LimitFilms of Truncated Spheres or Spheroids for Finite CoverageStratified LayersThe Wave Equation and Its General SolutionGeneral Linear Response Theory for SurfacesSurface RoughnessReflection of a Gyrotropic Medium Readership: Graduate students, academics, researchers and practitioners in optics, nano-optics and surface science. Key Features:An extremely rigorous theoretical descriptionFor thin films computer programs are available for obtaining the optical properties exactlyPresents optical properties of rough surfaces, including capillary waves and oxide layersProvides a new discussion on reflection from a gyrotropic surfaceDescribes reflection from a self-affine rough surfaceKeywords:Optical Properties of Surfaces;Reflection;Transmission;Ellipsometry;Thin Island Films;Rough Surfaces;Gyrotropic Surfaces;Symmetry Relations;Boundary Conditions;Interfacial Polarization and Magnetization

Author : Michael P. Marder
Publisher : John Wiley & Sons
Page : 985 pages
File Size : 43,6 Mb
Release : 2010-11-17
Category : Science
ISBN : 9780470949948

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Condensed Matter Physics by Michael P. Marder Pdf

Now updated—the leading single-volume introduction to solid state and soft condensed matter physics This Second Edition of the unified treatment of condensed matter physics keeps the best of the first, providing a basic foundation in the subject while addressing many recent discoveries. Comprehensive and authoritative, it consolidates the critical advances of the past fifty years, bringing together an exciting collection of new and classic topics, dozens of new figures, and new experimental data. This updated edition offers a thorough treatment of such basic topics as band theory, transport theory, and semiconductor physics, as well as more modern areas such as quasicrystals, dynamics of phase separation, granular materials, quantum dots, Berry phases, the quantum Hall effect, and Luttinger liquids. In addition to careful study of electron dynamics, electronics, and superconductivity, there is much material drawn from soft matter physics, including liquid crystals, polymers, and fluid dynamics. Provides frequent comparison of theory and experiment, both when they agree and when problems are still unsolved Incorporates many new images from experiments Provides end-of-chapter problems including computational exercises Includes more than fifty data tables and a detailed forty-page index Offers a solutions manual for instructors Featuring 370 figures and more than 1,000 recent and historically significant references, this volume serves as a valuable resource for graduate and undergraduate students in physics, physics professionals, engineers, applied mathematicians, materials scientists, and researchers in other fields who want to learn about the quantum and atomic underpinnings of materials science from a modern point of view.

Author : M. Hetenyi,W. G. Vincenti
Publisher : Springer Science & Business Media
Page : 445 pages
File Size : 44,6 Mb
Release : 2013-11-27
Category : Science
ISBN : 9783642856402

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Applied Mechanics by M. Hetenyi,W. G. Vincenti Pdf

This volume contains the Proceedings of the Twelfth International Congress of Applied Mechanics, held at Stanford University on August 26 to 31, 1968. The Congress was organized by the International Union of Theoretical and Applied Mechanics; members of the IUTAM Congress Committee and Bureau are listed under Congress Organization. The members of the Stanford Organizing Committee, which was responsible for the detailed organization of the Congress, are also given, as are the names of the sponsors and the industrial and educational organizations that contributed so generously to the financial support of the meeting. Those attending the Congress came from 32 countries and totaled 1337 persons, plus wives and children. A list of the registered participants is included in the volume. The technical sessions of the Congress comprised four General Lectures and 281 contributed papers, the latter being presented in groups of five simultaneous sessions. The final choice of the contributed papers was made on the basis of abstracts by an International Papers Commit tee of IUTAM consülting of G. K. BATCHELOR, E. BECKER, N. J. HOFF, and W. T. KOlTER.

Author : Boris K. Vainshtein,Vladimir M. Fridkin,Vladimir L. Indenbom
Publisher : Springer Science & Business Media
Page : 539 pages
File Size : 42,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642572548

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Modern Crystallography 2 by Boris K. Vainshtein,Vladimir M. Fridkin,Vladimir L. Indenbom Pdf

The four-volume treatment Modern Crystallography presents an encyclopaedic exposition of problems concerning the structure of crystals, their growth and their properties. Structure of Crystals deals with crystal structures in inorganic and organic compounds, polymers, liquid crystals, biological crystals and macromolecules.

Author : Boris K. Vainshtein,Vladimir M. Friedkin,Vladimir L. Indenbom
Publisher : Springer Science & Business Media
Page : 538 pages
File Size : 47,6 Mb
Release : 2013-03-14
Category : Science
ISBN : 9783642975127

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Structure of Crystals by Boris K. Vainshtein,Vladimir M. Friedkin,Vladimir L. Indenbom Pdf

Modern Crystallography provides an encyclopedic exposition of the field in four volumes written by Russian scientists. Structures of Crystals considers the ideal and real atomic structure of crystals as well as their electronic structures, the fundamentals of chemical bonding between atoms, geometric representations in the theory of crystal structure and crystal chemistry, as well as lattice energy. The important classes of crystal structures in inorganic compounds as well as structure polymers, liquid crystals, biological crystals, and macromolecules are treated. This second edition is complemented by recent data on many types of crystal structures - fullerenes, high-temperature superconductors, minerals, liquid crystals, etc.

Author : Andrew T. Boothroyd
Publisher : Oxford University Press
Page : 509 pages
File Size : 55,6 Mb
Release : 2020-07-09
Category : Science
ISBN : 9780192607058

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Principles of Neutron Scattering from Condensed Matter by Andrew T. Boothroyd Pdf

Neutron scattering is arguably the most powerful technique available for looking inside materials and seeing what the atoms are doing. This textbook provides a comprehensive and up-to-date account of the many different ways neutrons are being used to investigate the behaviour of atoms and molecules in bulk matter. It is written in a pedagogical style, and includes many examples and exercises. Every year, thousands of experiments are performed at neutron scattering facilities around the world, exploring phenomena in physics, chemistry, materials science, as well as in interdisciplinary areas such as biology, materials engineering, and cultural heritage. This book fulfils a need for a modern and pedagogical treatment of the principles behind the various different neutron techniques, in order to provide scientists with the essential formal tools to design their experiments and interpret the results. The book will be of particular interest to researchers using neutrons to study the atomic-scale structure and dynamics in crystalline solids, simple liquids and molecular fluids by diffraction techniques, including small-angle scattering and reflectometry, and by spectroscopic methods, ranging from conventional techniques for inelastic and quasielastic scattering to neutron spin-echo and Compton scattering. A comprehensive treatment of magnetic neutron scattering is given, including the many and diverse applications of polarized neutrons.

Author : Michael de Podesta
Publisher : CRC Press
Page : 451 pages
File Size : 49,5 Mb
Release : 2020-05-18
Category : Science
ISBN : 9781482267822

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Understanding the Properties of Matter by Michael de Podesta Pdf

Understanding the Properties of Matter: 2nd Edition takes a unique phenomenological approach to the presentation of matter, materials, and solid-state physics. After an overview of basic ideas and a reminder of the importance of measurement, the author considers in turn gases, solids, liquids, and phase changes. For each topic, the focus is on "what happens." After a preliminary examination of data on the properties of matter, the author raises, then addresses a series of questions concerning the data. It is only in answering these questions that he adopts the theoretical approach to the properties of matter. This approach can reawaken in readers the fascination for the subject that inspired some of the greatest physicists of our age. Examples and extensive exercises reinforce the concepts. A supporting Web site furnishes for free download a plethora of additional materials, including: " Supplementary chapters on the band theory of solids and the magnetic properties of solids " Copies of all the data talbes used in the book, in PDF and spreadsheet formats " Enlarged copies of all figures " A simple molecular dynamics simulation " Animations uillustrating important featrues of key equations " Answers to the end-of-chapter exercises Understanding the Properties of Matter is an entertaining and innovative text accessible at the undergraduate level.