Mathematical Tools for Changing Scale in the Analysis of Physical Systems

Author: William G. Gray,Anton Leijnse,Randall L. Kolar,Cheryl A. Blain

Publisher: CRC Press

ISBN: 9780849389344

Category: Mathematics

Page: 256

View: 6648

Mathematical Tools for Changing Scale in the Analysis of Physical Systems presents a new systematic approach to changing the spatial scale of the differential equations describing science and engineering problems. It defines vectors, tensors, and differential operators in arbitrary orthogonal coordinate systems without resorting to conceptually difficult Riemmann-Christoffel tensor and contravariant and covariant base vectors. It reveals the usefulness of generalized functions for indicating curvilineal, surficial, or spatial regions of integration and for transforming among these integration regions. These powerful mathematical tools are harnessed to provide 128 theorems in tabular format (most not previously available in the literature) that transform time-derivative and del operators of a function at one scale to the corresponding operators acting on the function at a larger scale. Mathematical Tools for Changing Scale in the Analysis of Physical Systems also provides sample applications of the theorems to obtain continuum balance relations for arbitrary surfaces, multiphase systems, and problems of reduced dimensionality. The mathematical techniques and tabulated theorems ensure the book will be an invaluable analysis tool for practitioners and researchers studying balance equations for systems encountered in the fields of hydraulics, hydrology, porous media physics, structural analysis, chemical transport, heat transfer, and continuum mechanics.

The Method of Volume Averaging

Author: S. Whitaker

Publisher: Springer Science & Business Media

ISBN: 9401733899

Category: Science

Page: 210

View: 8472

Multiphase systems dominate nearly every area of science and technology, and the method of volume averaging provides a rigorous foundation for the analysis of these systems. The development is based on classical continuum physics, and it provides both the spatially smoothed equations and a method of predicting the effective transport coefficients that appear in those equations. The text is based on a ten-week graduate course that has been taught for more than 20 years at the University of California at Davis and at other universities around the world. Problems dealing with both the theoretical foundations and the applications are included with each chapter, and detailed solutions for all problems are available from the author. The course has attracted participants from chemical engineering, mechanical engineering, civil engineering, hydrologic science, mathematics, chemistry and physics.

A Guided Tour of Mathematical Methods for the Physical Sciences

Author: Roel Snieder,Kasper van Wijk

Publisher: Cambridge University Press

ISBN: 131624086X

Category: Science

Page: N.A

View: 8159

Mathematical methods are essential tools for all physical scientists. This book provides a comprehensive tour of the mathematical knowledge and techniques that are needed by students across the physical sciences. In contrast to more traditional textbooks, all the material is presented in the form of exercises. Within these exercises, basic mathematical theory and its applications in the physical sciences are well integrated. In this way, the mathematical insights that readers acquire are driven by their physical-science insight. This third edition has been completely revised: new material has been added to most chapters, and two completely new chapters on probability and statistics and on inverse problems have been added. This guided tour of mathematical techniques is instructive, applied, and fun. This book is targeted for all students of the physical sciences. It can serve as a stand-alone text, or as a source of exercises and examples to complement other textbooks.

Selected Papers on Probability and Statistics

Author: N.A

Publisher: American Mathematical Soc.

ISBN: 0821848216

Category: Mathematics

Page: 231

View: 7977

This volume contains translations of papers that originally appeared in the Japanese journal Sugaku. The papers range over a variety of topics in probability theory, statistics, and applications. This volume is suitable for graduate students and research mathematicians interested in probability and statistics.

Climate Change Science

An Analysis of Some Key Questions

Author: National Research Council,Division on Earth and Life Studies,Committee on the Science of Climate Change

Publisher: National Academies Press

ISBN: 9780309183352

Category: Science

Page: 42

View: 780

The warming of the Earth has been the subject of intense debate and concern for many scientists, policy-makers, and citizens for at least the past decade. Climate Change Science: An Analysis of Some Key Questions, a new report by a committee of the National Research Council, characterizes the global warming trend over the last 100 years, and examines what may be in store for the 21st century and the extent to which warming may be attributable to human activity.

Transportation Systems Analysis

Models and Applications

Author: Ennio Cascetta

Publisher: Springer Science & Business Media

ISBN: 0387758577

Category: Business & Economics

Page: 742

View: 9017

"This book provides a rigorous and comprehensive coverage of transportation models and planning methods and is a must-have to anyone in the transportation community, including students, teachers, and practitioners." Moshe Ben-Akiva, Massachusetts Institute of Technology.

Horizons in Physical Geography

Author: M. J. Clark,Kenneth John Gregory,Angela M. Gurnell

Publisher: Rowman & Littlefield

ISBN: 9780389207528

Category: Science

Page: 395

View: 5766

'The authority of the contributors, the quality of production, and the bibliographic notes are first-rate. It is essential for basic earth science collections, and for any college library that supports geography or geology.'

Vibrations and Stability

Advanced Theory, Analysis, and Tools

Author: Jon Juel Thomsen

Publisher: Springer Science & Business Media

ISBN: 9783540401407

Category: Mathematics

Page: 404

View: 9145

Lucidly uniting classical and modern topics of advanced vibration analysis, this text provides students with a background in elementary vibrations, especially with tools necessary for understanding and analyzing more complex dynamical phenomena that can be encountered in engineering and scientific practice. It progresses steadily from linear vibration theory over levels of nonlinearity to bifurcation analysis, global dynamics and chaotic vibrations. Readers gain analytical skills with simple models, learn to recognize nonlinear phenomena, and employ advanced tools such as perturbation analysis and bifurcation analysis. Enriching theory with relevant examples from real systems, this book meets the increasing interest in non-linear dynamics in engineering, applied mathematics, and physics. This edition includes a new chapter on the useful effects of fast vibrations and many new exercise problems.

Stochastic Processes in Magnetic Resonance

Author: Dan Gamliel,Haim Levanon

Publisher: World Scientific

ISBN: 9789810222277

Category: Science

Page: 335

View: 3932

This book describes methods for calculating magnetic resonance spectra which are observed in the presence of random processes. The emphasis is on the stochastic Liouville equation (SLE), developed mainly by Kubo and applied to magnetic resonance mostly by J H Freed and his co-workers. Following an introduction to the use of density matrices in magnetic resonance, a unified treatment of Bloch-Redfield relaxation theory and chemical exchange theory is presented. The SLE formalism is then developed and compared to the other relaxation theories. Methods for solving the SLE are explained in detail, and its application to a variety of problems in electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR) is studied. In addition, experimental aspects relevant to the applications are discussed. Mathematical background material is given in appendices.

Progress in Computational Physics Volume 3: Novel Trends in Lattice-Boltzmann Methods

Author: Matthias Ehrhardt

Publisher: Bentham Science Publishers

ISBN: 160805716X

Category: Science

Page: 275

View: 9541

Progress in Computational Physics is an e-book series devoted to recent research trends in computational physics. It contains chapters contributed by outstanding experts of modeling of physical problems. The series focuses on interdisciplinary computational perspectives of current physical challenges, new numerical techniques for the solution of mathematical wave equations and describes certain real-world applications. With the help of powerful computers and sophisticated methods of numerical mathematics it is possible to simulate many ultramodern devices, e.g. photonic crystals structures, semiconductor nanostructures or fuel cell stacks devices, thus preventing expensive and longstanding design and optimization in the laboratories. In this book series, research manuscripts are shortened as single chapters and focus on one hot topic per volume. Engineers, physicists, meteorologists, etc. and applied mathematicians can benefit from the series content. Readers will get a deep and active insight into state-of-the art modeling and simulation techniques of ultra-modern devices and problems. The third volume - Novel Trends in Lattice Boltzmann Methods - Reactive Flow, Physicochemical Transport and Fluid-Structure Interaction - contains 10 chapters devoted to mathematical analysis of different issues related to the lattice Boltzmann methods, advanced numerical techniques for physico-chemical flows, fluid structure interaction and practical applications of these phenomena to real world problems.

Quantitative Measure for Discrete Event Supervisory Control

Author: Asok Ray,Vir V. Phoha,Shashi Phoha

Publisher: Springer Science & Business Media

ISBN: 9780387239033

Category: Computers

Page: 264

View: 2795

Supervisory Control Theory (SCT) provides a tool to model and control human-engineered complex systems, such as computer networks, World Wide Web, identification and spread of malicious executables, and command, control, communication, and information systems. Although there are some excellent monographs and books on SCT to control and diagnose discrete-event systems, there is a need for a research monograph that provides a coherent quantitative treatment of SCT theory for decision and control of complex systems. This new monograph will assimilate many new concepts that have been recently reported or are in the process of being reported in open literature. The major objectives here are to present a) a quantitative approach, supported by a formal theory, for discrete-event decision and control of human-engineered complex systems; and b) a set of applications to emerging technological areas such as control of software systems, malicious executables, and complex engineering systems. The monograph will provide the necessary background materials in automata theory and languages for supervisory control. It will introduce a new paradigm of language measure to quantitatively compare the performance of different automata models of a physical system. A novel feature of this approach is to generate discrete-event robust optimal decision and control algorithms for both military and commercial systems.

Dynamics of Galaxies

Author: Giuseppe Bertin

Publisher: Cambridge University Press

ISBN: 9780521478557

Category: Science

Page: 414

View: 4488

A complete and self-contained introduction to modern galactic dynamics for graduate students.

Continuity and Change in the Development of Russell’s Philosophy

Author: P.J. Hager

Publisher: Springer Science & Business Media

ISBN: 9401108447

Category: Philosophy

Page: 200

View: 6500

The general view of Russell's work amongst philosophers has been that repeat edly, during his long and distinguished career, crucial changes of mind on fun damental points were significant enough to cause him to successively adopt a diversity of radically new philosophical positions. Thus Russell is seen to have embraced and then abandoned, amongst others, neo-Hegelianism, Platonic re alism, phenomenalism and logical atomism, before settling finally on a form of neutral monism that philosophers have generally found to be incredible. This view of Russell is captured in C. D. Broad's famous remark that "Mr. Russell pro duces a different system of philosophy every few years . . . " (Muirhead, 1924: 79). Reflecting this picture of Russell continually changing his position, books and papers on Russell's philosophy have typically belonged to one of two kinds. Either they have concentrated on particular periods of his thought that are taken to be especially significant, or, accepting the view of his successive conversion to dis tinctly different philosophical positions, they have provided some account of each of these supposedly disconnected periods of his thought. While much good work has been done on Russell's philosophy, this framework has had its limitations, the main one being that it conceals the basic continuity behind his thought.

Early Childhood Curriculum for All Learners

Integrating Play and Literacy Activities

Author: Ann M. Selmi,Raymond J. Gallagher,Eugenia R. Mora-Flores

Publisher: SAGE Publications

ISBN: 1483322556

Category: Education

Page: 504

View: 7190

Early Childhood Curriculum for All Learners: Integrating Play and Literacy Activities is designed to teach early childhood professionals about the latest research on play and early literacy and then to show them practical methods for adapting this research to everyday classroom practices that will encourage the development of learning skills. The authors link solid, play-based research to specific developmentally appropriate practices. By combining these two areas, the text demonstrates that academic learning and play activities are highly compatible, and that children can and do develop academic skills through play. In addition, the text focuses on socio-dramatic play, a recently acknowledged, essential aspect of child-initiated play interactions. It provides specific strategies that link these interactive behaviors with the early academic skills needed for the initial primary grades. Implementation of the information presented in this book will enable children to experience a richer transition into primary education classrooms.

Multi-scale Modelling for Structures and Composites

Author: G. Panasenko

Publisher: Springer Science & Business Media

ISBN: 9781402029813

Category: Mathematics

Page: 398

View: 8442

Rod structures are widely used in modern engineering. These are bars, beams, frames and trusses of structures, gridwork, network, framework and other constructions. Numerous applications of rod structures in civil engineering, aircraft and spacecraft confirm the importance of the topic. On the other hand the majority of books on structural mechanics use some simplifying hypotheses; these hypotheses do not allow to consider some important effects, for instance the boundary layer effects near the points of junction of rods. So the question concerning the limits of applicability of structural mechanics hypotheses and the possibilities of their refinement arise. In this connection the asymptotic analysis of equations of mathematical physics, the equations of elasticity in rod structures (without these hypotheses and simplifying assumptions being imposed) is undertaken in the present book. Moreover, a lot of modern structures are made of composite materials and therefore the material of the rods is not homogeneous. This inhomogeneity of the material can generate some unexpected effects. These effects are analysed in the present book. The methods of multi-scale modelling are presented in the book by the homogenization, multi-level asymptotic analysis and the domain decomposition. These methods give an access to a new class of hybrid models combining macroscopic description with "microscopic zooms". Major features are: Rigorous mathematical analysis of structures without hypotheses of the Kirchhoff-Love, Kirchhoff-Clebsch type Taking into consideration the inhomogeneity of the rods and plates New numerical algorithms decomposing a structure in 3D and 1D parts with some interface conditions between them.

Handbook of Research Methods in Social and Personality Psychology

Author: Harry T. Reis,Charles M. Judd

Publisher: Cambridge University Press

ISBN: 1139867369

Category: Psychology

Page: N.A

View: 6266

This indispensable sourcebook covers conceptual and practical issues in research design in the field of social and personality psychology. Key experts address specific methods and areas of research, contributing to a comprehensive overview of contemporary practice. This updated and expanded second edition offers current commentary on social and personality psychology, reflecting the rapid development of this dynamic area of research over the past decade. With the help of this up-to-date text, both seasoned and beginning social psychologists will be able to explore the various tools and methods available to them in their research as they craft experiments and imagine new methodological possibilities.

Dynamics, Games and Science I

DYNA 2008, in Honor of Maurício Peixoto and David Rand, University of Minho, Braga, Portugal, September 8-12, 2008

Author: Mauricio Matos Peixoto,Alberto Adrego Pinto,David A. Rand

Publisher: Springer Science & Business Media

ISBN: 9783642114564

Category: Mathematics

Page: 809

View: 9233

Dynamics, Games and Science I and II are a selection of surveys and research articles written by leading researchers in mathematics. The majority of the contributions are on dynamical systems and game theory, focusing either on fundamental and theoretical developments or on applications to modeling in biology, ecomonics, engineering, finances and psychology. The papers are based on talks given at the International Conference DYNA 2008, held in honor of Mauricio Peixoto and David Rand at the University of Braga, Portugal, on September 8-12, 2008. The aim of these volumes is to present cutting-edge research in these areas to encourage graduate students and researchers in mathematics and other fields to develop them further.

Practical Environmental Statistics and Data Analysis

Author: Yue Rong

Publisher: ILM Publications

ISBN: 1906799040

Category: NATURE

Page: 269

View: 7442

"Describes the application of statistical methods in different environmental fields, with an emphasis on how to solve real-world problems in complex systems"--Provided by publisher.