Methods of Nonlinear Analysis

A self-contained introduction to magnetohydrodynamics (MHD), with emphasis on nonlinear processes. Chapters 2 to 4 outline the conventional aspects of MHD theory, magnetostatic equilibrium and linear stability theory, which form a natural basis for the topics in the subsequent chapters. The main part, chapters 5 to 7, presents nonlinear theory, starting with the evolutions and saturations of individual ideas and resistive instabilities, continuing with a detailed analysis of magnetic reconnection, and concluding with the most complex nonlinear behaviour, that of MHD turbulence. The last chapters describe three important applications of the theory: disruptive processes in tokamaks, MHD effects in reversed-field pinches, and solar flares. In the presentation the focus is more on physical mechanisms than on special formalisms. The book is essential reading for researchers and graduate students interested in MHD processes both in laboratory and in astrophysical plasmas.

This 1997 work explores the role of probabilistic methods for solving combinatorial problems. These methods not only provide the means of efficiently using such notions as characteristic and generating functions, the moment method and so on but also let us use the powerful technique of limit theorems. The basic objects under investigation are nonnegative matrices, partitions and mappings of finite sets, with special emphasis on permutations and graphs, and equivalence classes specified on sequences of finite length consisting of elements of partially ordered sets; these specify the probabilistic setting of Sachkov's general combinatorial scheme. The author pays special attention to using probabilistic methods to obtain asymptotic formulae that are difficult to derive using combinatorial methods. This was an important book, describing many ideas not previously available in English; the author has taken the chance to rewrite parts of the text and refresh the references where appropriate.

A practical guide for multivariate statistical techniques-- now updated and revised In recent years, innovations in computer technology and statistical methodologies have dramatically altered the lan

Describes and illustrates various modeling techniques which are applicable to the area of EMC and includes material previously available only in international reports or other hard-to-obtain reference

Electrical Engineering/Electromagnetics Methods for Electromagnetic Field Analysis A volume in the IEEE Series on Electromagnetic Wave Theory Donald G. Dudley, Series Editor . a gigantic platter of fo

This major, two-volume work is devoted to the methods of the spectral theory of operators and the important role they play in infinite-dimensional analysis and its applications. Central to this stu

Social network analysis is used widely in the social and behavioral sciences, as well as in economics, marketing, and industrial engineering. The social network perspective focuses on relationships among social entities and is an important addition to standard social and behavioral research, which is primarily concerned with attributes of the social units. Social Network Analysis: Methods and Applications reviews and discusses methods for the analysis of social networks with a focus on applications of these methods to many substantive examples. It is a reference book that can be used by those who want a comprehensive review of network methods, or by researchers who have gathered network data and want to find the most appropriate method by which to analyze it. It is also intended for use as a textbook as it is the first book to provide comprehensive coverage of the methodology and applications of the field.

Systematically builds a sequence of increasingly complex ecological models of two or three interacting populations and classifies them with methods from bifurcation theory. The main topics include: th

The dynamics of physical, chemical, biological, or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. In this book the perspectives generated by analytical, topological and computational methods, and interplays between them, are developed in a variety of contexts. This book is a comprehensive introduction to this field, suited to a broad readership, and reflecting a wide range of applications. Some of the concepts considered are: topological equivalence; embeddings; dimensions and fractals; Poincaré maps and map-dynamics; empirical computational sciences vis-á-vis mathematics; Ulam's synergetics; Turing's instability and dissipative structures; chaos; dynamic entropies; Lorenz and Rossler models; predator-prey and replicator models; FPU and KAM phenomena; solitons and nonsolitons; coupled maps and patt

The dynamics of physical, chemical, biological or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. In this book and its companion volume, Perspectives of nonlinear dynamics, volume 1, the perspectives generated by analytical, topological and computational methods, and interplays between them, are developed in a variety of contexts. The presentation and style is intended to stimulate the reader's imagination to apply these methods to a host of problems and situations. The text is complemented by copious references, extensive historical and bibliographical notes, exercises and examples, and appendices giving more details of some mathematical ideas. Each chapter includes an extensive section commentary on the exercises and their solution. Graduate students and research workers in physics, applied mathem

The use of social structure as a defining concept has produced a large body of creative speculations, insights, and intuitions about social life. In its broad-ranging examination of the kind of data t

Contains 26 edited papers (from the symposium held Nov. 1990, Boston, Mass.) discussing the methodology of applying nondestructive characterizing techniques to newly developed materials. The technique

This book deals with advanced fluid flow methods for design and analysis of engineering systems. Panel methods employing surface distributions of source and vortex singularities based on the solution of boundary integral equations have been extensively used for modelling external and internal aerodynamic flows. Part 1 describes the surface vorticity method and illustrates applications of this technique over a wide range of engineering problems in aerodynamics and turbo-machines, including lifting aerofoils and cascades, mixed-flow and rotating cascades for fans, pumps or turbines, meridional flows in turbo-machines, flow past axisymmetric bodies, ducts and ducted propellers or fans. Part 2 extends surface vorticity modelling to the fairly new CFM field of vortex dynamics or vortex cloud theory, including foundation chapters on convection and viscous diffusion by the random walk technique. Vortex cloud methods are developed, again from first principles, to deal with shear layers, bounda

Details the basic theory of polynomial and fractional representation methods for algebraic analysis and synthesis of linear multivariable control systems. It also serves as a self-contained treatise o

Presents methods for determining the secondary and tertiary structure of proteins. The issues covered here involve theoretical/empirical approaches for predicting protein structure; a review using pro

This is the second of a five-volume exposition of the main principles of nonlinear functional analysis and its applications to the natural sciences, economics, and numerical analysis. The presentation

This is the second of a five-volume exposition of the main principles of nonlinear functional analysis and its applications to the natural sciences, economics, and numerical analysis. The presentation

The volume is oriented to applications in continuum mechanics and deals with the numerical simulation of the behavior of continuous media by augmented Lagrangian and operator-splitting methods (couple

The standard work on laboratory analysis of musts and wines, fully updated to cover modern procedures and practice. This second edition contains new material on the use of HPLC, GC, and mass spectrome

Nonlinear programming provides an excellent opportunity to explore an interesting variety of pure and solidly applicable mathematics, numerical analysis, and computing. This text develops some of the

Meta-Analysis shows concisely, yet comprehensively, how to apply statistical methods to achieve a literature review of a common research domain. It demonstrates the use of combined tests an

The main purpose of this book is to address the statistical issues for integrating independent studies. There exist a number of papers and books that discuss the mechanics of collecting, coding, and p

Structural Sensitivity in Econometric Models Edwin Kuh, John W. Neese and Peter Hollinger Provides a pathbreaking assessment of the worth of linear dynamic systems methods for probing the behavior of

Describes various commonly used methods of initial factoring and factor rotation. In addition to a full discussion of exploratory factor analysis, confirmatory factor analysis and various methods of

This volume will serve several purposes: to provide an introduction for graduate students not previously acquainted with the material, to serve as a reference for mathematical physicists already worki

Completely revised and updated, Chemical Analysis: Second Edition is an essential introduction to a wide range of analytical techniques and instruments. Assuming little in the way of prior knowledge,