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At the time of its publication this classic text, co-written by the Nobel Laureate Max Born, represented the definitive account of the subject and in many ways it still does. The book begins with a general discussion of the statistical mechanics of ideal lattices, leading to the electric polarizability and to the scattering of light. It then provides detailed discussions of long lattice waves, thermal properties, and optical properties. ... Read more

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THE ORIGIN OF THE BORN-OPPENHEIMER APPROACH
This is not only the first, but still one of the best, explicit formulation of the Born-Oppenheimer approach, which stands as the basis for most of the quantum chemistry. ... Read more

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This two-volume work provides a comprehensive study of the statistical mechanics of lattice models. It introduces the reader to the main areas in statistical mechanics and the theory of phase transitions. The development is built on a firm mathematical and physical basis. Volume 1 contains an account of mean-field and cluster variation methods successfully used in many applications in solid-state physics and theoretical chemistry as well as an account of exact results for the Ising and six-vertex models and those derivable by transformation methods. Volume 2 includes extensive treatments of scaling theory, algebraic and real-space renormalization group methods and the eight-vertex model. It also includes an account of series methods and a treatment of dimer assemblies. ... Read more

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This two-volume work provides a comprehensive study of the statistical mechanics of lattice models. It introduces readers to the main topics and the theory of phase transitions, building on a firm mathematical and physical basis. Volume 1 contains an account of mean-field and cluster variation methods successfully used in many applications in solid-state physics and theoretical chemistry, as well as an account of exact results for the Ising and six-vertex models and those derivable by transformation methods. ... Read more

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Information content and programming semantics are just two of the applications of the mathematical concepts of order, continuity and domains. This authoritative and comprehensive account of the subject will be an essential handbook for all those working in the area. An extensive index and bibliography make this an ideal sourcebook for all those working in domain theory. ... Read more

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This book has evolved from a set of lecture notes of a course on orthomodular lattices given at the University of Ulm.Most concepts are developed from their very first notions, but in some instances basic set theory and Hilbert space theory may be needed.The text is in general independent of the exercises and supplementary remarks.The book can be used for a general lecture on orthomodular lattices and also for seminars on special geometrical or logical topics. As the first monograph in the field it makes the widely spread results on orthomodular lattices more easily accessible for researchers. ... Read more

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Wonderful ideas for garden lattice vignette quilts-- garden scenes framed with lattice stripping for a whimsical touch. Let your imagination run wild!! Detailed instructions for strip framing and cut-fabric applique. Many beautiful, full-color photographs. A delightful book for the dedicated quilter's collection!! ... Read more

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Garden Lattice quilts
Another book by Eleanor Burns with clear step by step instructions for even the inexperienced quilter. Eleanor Burns books are exceptional. I am new to quilting and have several of her books in my quilting library.

Lattice in your salad?
Sure its just another book by Eleanor Burns, but her technique for laying out the project and speed piecing is world renound.

I can't say i've done any of her quilts in 1 day, but i've gotten pretty-darned far! Maybe she gets help. :-)

I love her books and patterns because they are typically very easy to understand! ... Read more

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Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new and promising methods for the numerical solution of nonlinear partial differential equations. The book provides an introduction for graduate students and researchers. Working knowledge of calculus is required and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellular automata are outlined in Chapter 2. The properties of various LGCA and special coding techniques are discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessary theoretical background for LGCA and LBM. The properties of lattice Boltzmann models and a method for their construction are presented in Chapter 5. ... Read more

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often inspiring, but not self-contained
This book is extremely well structured -as apparent from its table of contents. It describes and motivates the evolution from cellular automata to lattice-gas cellular automata to lattice Boltzmann schemes. It tells its story in a very brief yet lucid way. The text points to valuable references for further reading or for further explanation.

The main drawback is that -after all- it sometimes really are 'just' lecture notes in mathematics (being an aid mainly for those who follow the lectures). *Some* of the important derivations are very short and formal, with implicit mathematical shortcuts, and without giving any physical interpretation of the main formula's. In addition, once too often the reader is referred to the scientific literature -which is not always easily accessible. In other words: the book is not self-contained.

Nevertheless, I truly enjoyed reading the book from back to back, even though I had to work hard to get through some sections.

Computational Models of Physical Processes
This is an outstanding book for anyone concerned with computational models of real physical processes (digital mechanics or digital physics).It is accessible to anyone with a bachelor's degree in computer science,mathematics, engineering, or physics.It is also accessible to others witha few years of math courses.Lattice gasses and lattice boltzmann machinesare the natural extensions of cellular automata such as the game of life. ... Read more

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Quantum field theory describes basic physical phenomena over an extremely wide range of length or energy scales. Quantum fields exist in space and time, which can be approximated by a set of lattice points. This book presents a comprehensive and coherent account of the theory of quantum fields on a lattice, an essential technique for the study of the strong and electroweak nuclear interactions. After introductory chapters on scalar fields, gauge fields and fermion fields, the book studies quarks and gluons in QCD and fermions and bosons in the electroweak theory. The last chapter is devoted to numerical simulations algorithms that have been used in recent large-scale numerical simulations. The book will be valuable for graduate students and researchers in theoretical physics, elementary particle physics, and field theory, as well as non-perturbative approximations and numerical simulations of quantum field phenomena. ... Read more

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Quantum statistical mechanics plays a major role in many fields such as thermodynamics, plasma physics, solid-state physics, and the study of stellar structure. While the theory of quantum harmonic oscillators is relatively simple, the case of anharmonic oscillators, a mathematical model of a localized quantum particle, is more complex and challenging. Moreover, infinite systems of interacting quantum anharmonic oscillators possess interesting ordering properties with respect to quantum stabilization. This book presents a rigorous approach to the statistical mechanics of such systems, in particular with respect to their actions on a crystal lattice. The text is addressed to both mathematicians and physicists, especially those who are concerned with the rigorous mathematical background of their results and the kind of problems that arise in quantum statistical mechanics. The reader will find here a concise collection of facts, concepts, and tools relevant for the application of path integrals and other methods based on measure and integration theory to problems of quantum physics, in particular the latest results in the mathematical theory of quantum anharmonic crystals. The methods developed in the book are also applicable to other problems involving infinitely many variables, for example, in biology and economics. ... Read more

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This dissertation presents a systematic developmentof a new thermal lattice Boltzmann multiphase model. Unlike conventional CFD methods,the lattice Boltzmann equation (LBE) method is based on microscopic models and mesoscopickinetic equations in which the collective behavior of the particles in a system is used tosimulate the continuum mechanics of the system. Due to this kinetic nature, the LBE method has beenfound to be particularly useful in applications involving interfacial dynamics andcomplex boundaries, e.g. multiphase or multicomponent flows.Based on the SC model, a new and generalized latticeBoltzmann model for simulating thermal two-phase flow is described. In this model,the SC model is used to simulate the fluid dynamics. The temperature field is simulated usingthe passive-scalar approach, i.e. through modeling the density field of an extra component,which evolves according to the advectiondiffusion equation. By coupling the fluid dynamics andtemperature field through a suitably defined body force term, the thermal two-phaselattice Boltzmann model is obtained. ... Read more

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Trotz der Komplexität der Materie ist dieses Buch nicht mathematisch überfrachtet. Phänomenologische Ansätze aus der Strömungsmechanik und Thermodynamik werden mittels kinetischer Gastheorie einfach einsichtig erklärt und qualitativ hergeleitet. Der Autor leitet Gleichungen der Strömungsmechanik sowie Lösungsansätze für Strömungsprobleme konsequent ab und interpretiert ihre Gültigkeit. ... Read more

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This monograph identifies polytopes that are "combinatorially R1-embeddable", within interesting lists of polytopal graphs, i.e. such that corresponding polytopes are either prominent mathematically (regular partitions, root lattices, uniform polytopes and so on), or applicable in chemistry (fullerenes, polycycles, etc.). The embeddability, if any, provides applications to chemical graphs and, in the first case, it gives new combinatorial perspective to "R2-prominent" affine polytopal objects.

The lists of polytopal graphs in the book come from broad areas of geometry, crystallography and graph theory. The book concentrates on such concise and, as much as possible, independent definitions. The scale-isometric embeddability — the main unifying question, to which those lists are subjected — is presented with the minimum of technicalities. ... Read more

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Number theory is one of the oldest and most appealing areas of mathematics. Computation has always played a role in number theory, a role which has increased dramatically in the last 20 or 30 years, both because of the advent of modern computers, and because of the discovery of surprising and powerful algorithms. As a consequence, algorithmic number theory has gradually emerged as an important and distinct field with connections to computer science and cryptography as well as other areas of mathematics. This text provides a comprehensive introduction to algorithmic number theory for beginning graduate students, written by the leading experts in the field. It includes several articles that cover the essential topics in this area, such as the fundamental algorithms of elementary number theory, lattice basis reduction, elliptic curves, algebraic number fields, and methods for factoring and primality proving.In addition, there are contributions pointing in broader directions, including cryptography, computational class field theory, zeta functions and L-series, discrete logarithm algorithms, and quantum computing. ... Read more

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This book is concerned primarily with the theory of Banach lattices and with linear operators defined on, or with values in, Banach lattices. More general classes of Riesz spaces are considered so long as this does not lead to more complicated constructions or proofs. The intentions for writing this book were twofold. First, there appeared in the literature many results completing the theory extensively. On the other hand, new techniques systematically applied here for the first time lead to surprisingly simple and short proofs of many results originally known as deep. These new methods are purely elementary: they directly yield the Banach lattice versions of theorems which then include the classical theorems in a trivial manner.In particular the book covers: Riesz spaces, normed Riesz spaces, C(K)-and Mspaces, Banach function spaces, Lpspaces, tensor products of Banach lattices, Grothendieck spaces; positive and regular operators, extensions of positive operators, disjointness-preserving operators, operators on L- and M-spaces, kernel operators, weakly compact operators and generalizations, Dunford-Pettis operators and spaces, irreducible operators; order continuity of norms, p-subadditive norms; spectral theory, order spectrum; embeddings of C; the Radon-Nikodym property; measures of non-compactness. This textbook on functional analysis, operator theory and measure theory is intended for advanced students and researchers. ... Read more

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Devoted to the problem of studying functions and equations in Boolean algebras, Post algebras, Heyting algebras, Stone algebras, and distributive lattices. For researchers and programmers. Softcover. ... Read more

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This book-and-software package supplies users with an interactive experience for nuclear visualization via a computer-graphical interface, similar in principle to the molecular visualizations already available in chemistry. Models of the Atomic Nucleus explains the nucleus in a way that makes nuclear physics as comprehensible as chemistry or cell biology. The book/software supplements virtually any of the current textbooks in nuclear physics by providing a means for 3D visual display of the diverse models of nuclear structure. For the first time, an easy-to-master software for scientific visualization of the nucleus makes this notoriously 'nonvisual' field become immediately ‘visible.’ After a review of the basics, the book explores and compares the competing models, and addresses how the lattice model best resolves remaining controversies. The appendix explains how to obtain the most from the software provided on extras.springer.com. This new edition has been updated completely and expanded to cover recent developments in low energy nuclear reactions (LENR), and to show how the fcc nucleon lattice explains both the asymmetric fragments produced by the fission of Uranium and the symmetric fragmens produced by the fission of Palladium. The associated software to visualize the models of atomic nuclei had been rewritten and updated to include all new developments. ... Read more