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: 6828

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.

Essentials of Multiphase Flow in Porous Media

Author: George F. Pinder,William G. Gray

Publisher: John Wiley & Sons

ISBN: 0470380799

Category: Technology & Engineering

Page: 374

View: 1774

Learn the fundamental concepts that underlie the physics of multiphase flow and transport in porous media with the information in Essentials of Multiphase Flow in Porous Media, which demonstrates the mathematical-physical ways to express and address multiphase flow problems. Find a logical, step-by-step introduction to everything from the simple concepts to the advanced equations useful for addressing real-world problems like infiltration, groundwater contamination, and movement of non-aqueous phase liquids. Discover and apply the governing equations for application to these and other problems in light of the physics that influence system behavior.

The Method of Volume Averaging

Author: S. Whitaker

Publisher: Springer Science & Business Media

ISBN: 9401733899

Category: Science

Page: 210

View: 5804

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: 6478

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.

Theory of Critical Phenomena in Finite-Size Systems

Scaling and Quantum Effects

Author: Jordan G Brankov,Daniel M Danchev,Nicholai S Tonchev

Publisher: World Scientific

ISBN: 9814494569

Category: Science

Page: 460

View: 7878

The aim of this book is to familiarise the reader with the rich collection of ideas, methods and results available in the theory of critical phenomena in systems with confined geometry. The existence of universal features of the finite-size effects arising due to highly correlated classical or quantum fluctuations is explained by the finite-size scaling theory. This theory (1) offers an interpretation of experimental results on finite-size effects in real systems; (2) gives the most reliable tool for extrapolation to the thermodynamic limit of data obtained by computer simulations; (3) reveals the intimate mechanism of how the critical singularities build up in the thermodynamic limit; and (4) can be fruitfully used to explain the low-temperature behaviour of quantum critical systems. The exposition is given in a self-contained form which presumes the reader's knowledge only in the framework of standard courses on the theory of phase transitions and critical phenomena. The instructive role of simple models, both classical and quantum, is demonstrated by putting the accent on the derivation of rigorous and exact analytical results. Contents:Overview of Critical Phenomena in Bulk SystemsThe Approximating Hamiltonian MethodExactly Solved ModelsFinite-Size Scaling at CriticalityLong-Range InteractionsModified Finite-Size ScalingBoundary EffectsFinite-Size Scaling at First Order TransitionsLimit Gibbs States and Finite-Size ScalingBulk Quantum SystemsThe Casimir EffectSurvey of Results on the Casimir Effect Readership: Graduate students and researchers in theoretical and condensed matter physics. Keywords:Phase Transition;Critical Phenomena;Finite Size Scaling;Quantum Phase TransitionsReviews: “… this book offers a careful survey of finite-size scaling near bulk phase transitions …” Journal of Statistical Physics “The book is a very comprehensive and detailed account of this field … I have found the final section on the Casimir effect particularly interesting. It is very well written and detailed … I recommend it to serious students of critical phenomena and condensed matter, but those who already have the basic knowledge of the theory of phase transitions.” Contemporary Physics

Mathematical and Physical Fundamentals of Climate Change

Author: Zhihua Zhang,John C. Moore

Publisher: Elsevier

ISBN: 0128005831

Category: Science

Page: 494

View: 7738

Mathematical and Physical Fundamentals of Climate Change is the first book to provide an overview of the math and physics necessary for scientists to understand and apply atmospheric and oceanic models to climate research. The book begins with basic mathematics then leads on to specific applications in atmospheric and ocean dynamics, such as fluid dynamics, atmospheric dynamics, oceanic dynamics, and glaciers and sea level rise. Mathematical and Physical Fundamentals of Climate Change provides a solid foundation in math and physics with which to understand global warming, natural climate variations, and climate models. This book informs the future users of climate models and the decision-makers of tomorrow by providing the depth they need. Developed from a course that the authors teach at Beijing Normal University, the material has been extensively class-tested and contains online resources, such as presentation files, lecture notes, solutions to problems and MATLab codes. Includes MatLab and Fortran programs that allow readers to create their own models Provides case studies to show how the math is applied to climate research Online resources include presentation files, lecture notes, and solutions to problems in book for use in classroom or self-study

Scaling of Differential Equations

Author: Hans Petter Langtangen,Geir K. Pedersen

Publisher: Springer

ISBN: 3319327267

Category: Mathematics

Page: 138

View: 1556

The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics. The text is easily accessible and example-driven. The first part on ODEs fits even a lower undergraduate level, while the most advanced multiphysics fluid mechanics examples target the graduate level. The scientific literature is full of scaled models, but in most of the cases, the scales are just stated without thorough mathematical reasoning. This book explains how the scales are found mathematically. This book will be a valuable read for anyone doing numerical simulations based on ordinary or partial differential equations.

Stochastic Processes in Magnetic Resonance

Author: Dan Gamliel,Haim Levanon

Publisher: World Scientific

ISBN: 9789810222277

Category: Science

Page: 335

View: 7294

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.

Transportation Systems Analysis

Models and Applications

Author: Ennio Cascetta

Publisher: Springer Science & Business Media

ISBN: 0387758577

Category: Business & Economics

Page: 742

View: 2321

"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.

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: 4976

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.

Selected Papers on Probability and Statistics

Author: N.A

Publisher: American Mathematical Soc.

ISBN: 0821848216

Category: Mathematics

Page: 231

View: 5754

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.

Horizons in Physical Geography

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

Publisher: Rowman & Littlefield

ISBN: 9780389207528

Category: Science

Page: 395

View: 8355

'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.'

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: 662

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: 7909

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.

Mathematical Tools for Physicists

Author: Michael Grinfeld

Publisher: John Wiley & Sons

ISBN: 3527684271

Category: Science

Page: 632

View: 8750

The new edition is significantly updated and expanded. This unique collection of review articles, ranging from fundamental concepts up to latest applications, contains individual contributions written by renowned experts in the relevant fields. Much attention is paid to ensuring fast access to the information, with each carefully reviewed article featuring cross-referencing, references to the most relevant publications in the field, and suggestions for further reading, both introductory as well as more specialized. While the chapters on group theory, integral transforms, Monte Carlo methods, numerical analysis, perturbation theory, and special functions are thoroughly rewritten, completely new content includes sections on commutative algebra, computational algebraic topology, differential geometry, dynamical systems, functional analysis, graph and network theory, PDEs of mathematical physics, probability theory, stochastic differential equations, and variational methods.

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: 9618

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.

Dynamics of Galaxies

Author: Giuseppe Bertin

Publisher: Cambridge University Press

ISBN: 9780521478557

Category: Science

Page: 414

View: 4869

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

Vibrations and Stability

Advanced Theory, Analysis, and Tools

Author: Jon Juel Thomsen

Publisher: Springer Science & Business Media

ISBN: 9783540401407

Category: Mathematics

Page: 404

View: 9775

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.