Dealing with the computer simulation of thermodynamic properties of many-body condensed-matter systems that use random numbers generated by a computer, this book describes the theoretical background of several variants of Monte Carlo methods. The result is a systematic course allowing newcomers to perform these simulations for themselves and to analyze their results. This third edition has been updated and expanded by a new chapter on important recent developments in the Monte Carlo methodology.
The second edition of Non-Perturbative Methods in Two-Dimensional Quantum Field Theory is an extensively revised version, involving major changes and additions. Although much of the material is special to two dimensions, the techniques used should prove helpful also in the development of techniques applicable in higher dimensions. In particular, the last three chapters of the book will be of direct interest to researchers wanting to work in the field of conformal field theory and strings.This book is intended for students working for their PhD degree and post-doctoral researchers wishing to acquaint themselves with the non-perturbative aspects of quantum field theory.
Our aim in this book is to present and enlarge upon those aspects of parallel computing that are needed by practitioners of computational science. Today al most all classical sciences, such as mathematics, physics, chemistry and biology, employ numerical methods to help gain insight into nature. In addition to the traditional numerical methods, such as matrix inversions and the like, a whole new field of computational techniques has come to assume central importance, namely the numerical simulation methods. These methods are much less fully developed than those which are usually taught in a standard numerical math ematics course. However, they form a whole new set of tools for research in the physical sciences and are applicable to a very wide range of problems. At the same time there have been not only enormous strides forward in the speed and capability of computers but also dramatic new developments in computer architecture, and particularly in parallel computers. These improvements offer exciting prospects for computer studies of physical systems, and it is the new techniques and methods connected with such computer simulations that we seek to present in this book, particularly in the light of the possibilities opened up by parallel computers. It is clearly not possible at this early stage to write a definitive book on simulation methods and parallel computing.
Boltzmann's formula S = In(W(E) defines the microcanonical ensemble. The usual textbooks on statistical mechanics start with the microensemble but rather quickly switch to the canonical ensemble introduced by Gibbs. This has the main advantage of easier analytical calculations, but there is a price to pay -- for example, phase transitions can only be defined in the thermodynamic limit of infinite system size. The question how phase transitions show up from systems with, say, 100 particles with an increasing number towards the bulk can only be answered when one finds a way to define and classify phase transitions in small systems. This is all possible within Boltzmann's original definition of the microcanonical ensemble. Starting from Boltzmann's formula, the book formulates the microcanonical thermodynamics entirely within the frame of mechanics. This way the thermodynamic limit is avoided and the formalism applies to small as well to other nonextensive systems like gravitational ones. Phasetransitions of first order, continuous transitions, critical lines and multicritical points can be unambiguously defined by the curvature of the entropy S(E, N). Special attention is given to the fragmentation of nuclei and atomic clusters as a peculiar phase transition of small systems controlled, among others, by angular momentum. The dependence of the liquid-gas transition of small atomic clusters under prescribed pressure is treated. Thus the analogue to the bulk transition can be studied. New insights into the many facets of the many-body physics of the critical point are presented. The book also describes the microcanonical statistics of the collapse of a self-gravitating system under large angular momentum.
This classic of modern theoretical physics is the first and only comprehensive treatment of the superfluid phases of helium 3, a crucial aspect of condensed matter physics with applications to many other fields. The self-contained approach explores ideas, concepts, and theoretical results, emphasizing symmetries and the consequences of their spontaneous breakdown. 1990 edition.
Computational methods pertaining to many branches of science, such as physics, physical chemistry and biology, are presented. The text is primarily intended for third-year undergraduate or first-year graduate students. However, active researchers wanting to learn about the new techniques of computational science should also benefit from reading the book. It treats all major methods, including the powerful molecular dynamics method, Brownian dynamics and the Monte-Carlo method. All methods are treated equally from a theroetical point of view. In each case the underlying theory is presented and then practical algorithms are displayed, giving the reader the opportunity to apply these methods directly. For this purpose exercises are included. The book also features complete program listings ready for application.
Johann Christoph Blumhardt (1805-1880) was a pastoral counselor and theologian of hope. His theology and pastoral approach, shaped as they were by the awakening in his congregation and numerous incidents of faith healing, provoked earnest and lively debate, and the controversy continues today. Ising's work mines the original sources, the product of an interaction with Blumhardt's life and work that goes back many years. He has drawn a portrait that explores the shadows as well as its bright side. Readers are invited to enter fully into the nineteenth century, Blumhardt's century, yet are constantly reminded that the problems of that day have lost none of their currency within the altered mental horizons of today.
Local approaches to fatigue assessment are used to predict the structural durability of welded joints, to optimise their design and to evaluate unforeseen joint failures. This standard work provides a systematic survey of the principles and practical applications of the various methods. It covers the hot spot structural stress approach to fatigue in general, the notch stress and notch strain approach to crack initiation and the fracture mechanics approach to crack propagation. Seam-welded and spot-welded joints in structural steels and aluminium alloys are also considered.This completely reworked second edition takes into account the tremendous progress in understanding and applying local approaches which has been achieved in the last decade. It is a standard reference for designers, structural analysts and testing engineers who are responsible for the fatigue-resistant in-service behaviour of welded structures.
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