Elementary Fluid Dynamics

Author: D. J. Acheson

Publisher: Clarendon Press

ISBN: 0191059390

Category: Mathematics

Page: 408

View: 1906

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The study of the dynamics of fluids is a central theme of modern applied mathematics. It is used to model a vast range of physical phenomena and plays a vital role in science and engineering. This textbook provides a clear introduction to both the theory and application of fluid dynamics, and will be suitable for all undergraduates coming to the subject for the first time. Prerequisites are few: a basic knowledge of vector calculus, complex analysis, and simple methods for solving differential equations are all that is needed. Throughout, numerous exercises (with hints and answers) illustrate the main ideas and serve to consolidate the reader's understanding of the subject. The book's wide scope (including inviscid and viscous flows, waves in fluids, boundary layer flow, and instability in flow) and frequent references to experiments and the history of the subject, ensures that this book provides a comprehensive and absorbing introduction to the mathematical study of fluid behaviour.

Physical Fluid Dynamics

Author: D. J. Tritton

Publisher: Springer Science & Business Media

ISBN: 9400999925

Category: Science

Page: 362

View: 8174

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To classify a book as 'experimental' rather than 'theoretical' or as 'pure' rather than 'applied' is liable to imply umeal distinctions. Nevertheless, some Classification is necessary to teIl the potential reader whether the book is for him. In this spirit, this book may be said to treat fluid dynamies as a branch of physics, rather than as a branch of applied mathematics or of engineering. I have often heard expressions of the need for such a book, and certainly I have feIt it in my own teaching. I have written it primariIy for students of physics and of physics-based applied science, aIthough I hope others may find it useful. The book differs from existing 'fundamental' books in placing much greater emphasis on what we know through laboratory experiments and their physical interpretation and less on the mathe matieal formalism. It differs from existing 'applied' books in that the choice of topics has been made for the insight they give into the behaviour of fluids in motion rather than for their practical importance. There are differences also from many existing books on fluid dynamics in the branches treated, reflecting to some extent shifts of interest in reeent years. In particular, geophysical and astrophysical applications have prompted important fundamental developments in topics such as conveetion, stratified flow, and the dynamics of rotating fluids. These developments have hitherto been reflected in the contents of textbooks only to a limited extent.

An Introduction to Theoretical Fluid Mechanics

Author: Stephen Childress

Publisher: American Mathematical Soc.

ISBN: 0821848887

Category: Science

Page: 201

View: 2539

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This book gives an overview of classical topics in fluid dynamics, focusing on the kinematics and dynamics of incompressible inviscid and Newtonian viscous fluids, but also including some material on compressible flow. The topics are chosen to illustrate the mathematical methods of classical fluid dynamics. The book is intended to prepare the reader for more advanced topics of current research interest.

Worlds of Flow

A History of Hydrodynamics from the Bernoullis to Prandtl

Author: Olivier Darrigol

Publisher: Oxford University Press

ISBN: 9780198568438

Category: Mathematics

Page: 356

View: 3283

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This book provides the first fully-fledged history of hydrodynamics, including lively accounts of the concrete problems of hydraulics, navigation, blood circulation, meteorology, and aeronautics that motivated the main conceptual innovations. Richly illustrated, technically competent, and philosophically sensitive, it should attract a broad audience and become a standard reference for any one interested in fluid mechanics.

Waves in Fluids

Author: James Lighthill

Publisher: Cambridge University Press

ISBN: 9780521010450

Category: Mathematics

Page: 504

View: 1657

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This comprehensive text describes the science of waves in fluids.

Physics of Continuous Matter

Exotic and Everyday Phenomena in the Macroscopic World

Author: B. Lautrup

Publisher: CRC Press

ISBN: 9780750307529

Category: Science

Page: 624

View: 8919

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Offering a modern approach to this most classical of subjects, Physics of Continuous Matter is first and foremost an introduction to the basic concepts and phenomenology of continuous systems, and the derivations of the equations of continuum mechanics from Newtonian mechanics. Although many examples, particularly in the earlier chapters, are taken from geophysics and astrophysics, the author places the emphasis frimly on generic methods and applications. Each chapter begins with a ‘soft’ introduction, placing the discussion within an everyday context, and the level of difficulty then rises steadily, a pattern which is reflected throughout the text as a whole. The necessary mathematical tools are developed in parallel with the physics on a ‘need-to-know’ basis, an approach that avoids lengthy mathematical preliminaries.

Computational Modeling in Biological Fluid Dynamics

Author: Lisa J. Fauci,Shay Gueron,Institute of Mathematics and Its Applications

Publisher: Springer Science & Business Media

ISBN: 9780387952338

Category: Mathematics

Page: 238

View: 9132

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This volume contains invited and refereed papers based upon presentations given in the IMA workshop on Computational Modeling in Biological Fluid Dynamics during January of 1999, which was part of the year-long program "Mathematics in Biology." This workshop brought together biologists, zoologists, engineers, and mathematicians working on a variety of issues in biological fluid dynamics. A unifying theme in biological fluid dynamics is the interaction of elastic boundaries with a surrounding fluid. These moving boundary problems, coupled with the equations of incompressible, viscuous fluid dynamics, pose formidable challenges to the computational scientist. In this volume, a variety of computational methods are presented, both in general terms and within the context of applications including ciliary beating, blood flow, and insect flight. Our hope is that this collection will allow others to become aware of and interested in the exciting accomplishments and challenges uncovered during this workshop.

An Introduction to Fluid Dynamics

Author: G. K. Batchelor

Publisher: Cambridge University Press

ISBN: 9780521663960

Category: Mathematics

Page: 615

View: 8995

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First published in 1967, Professor Batchelor's classic text on fluid dynamics is still one of the foremost texts in the subject. The careful presentation of the underlying theories of fluids is still timely and applicable, even in these days of almost limitless computer power. This re-issue should ensure that a new generation of graduate students see the elegance of Professor Batchelor's presentation.

Statistical Physics

Statics, Dynamics and Renormalization

Author: Leo P Kadanoff

Publisher: World Scientific Publishing Company

ISBN: 981310290X

Category: Science

Page: 500

View: 1820

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The material presented in this invaluable textbook has been tested in two courses. One of these is a graduate-level survey of statistical physics; the other, a rather personal perspective on critical behavior. Thus, this book defines a progression starting at the book-learning part of graduate education and ending in the midst of topics at the research level. To supplement the research-level side the book includes some research papers. Several of these are classics in the field, including a suite of six works on self-organized criticality and complexity, a pair on diffusion-limited aggregation, some papers on correlations near critical points, a few of the basic sources on the development of the real-space renormalization group, and several papers on magnetic behavior in a plain geometry. In addition, the author has included a few of his own papers.

Theory and Computation of Hydrodynamic Stability

Author: W. O. Criminale,T. L. Jackson,Ronald Douglas Joslin

Publisher: Cambridge University Press

ISBN: 9780521632003

Category: Mathematics

Page: 441

View: 3413

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Graduate text/reference with exercises, computer code on basic topic in fluid dynamics.

Essential Mathematical Biology

Author: Nicholas F. Britton

Publisher: Springer Science & Business Media

ISBN: 1447100492

Category: Mathematics

Page: 335

View: 2697

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This self-contained introduction to the fast-growing field of Mathematical Biology is written for students with a mathematical background. It sets the subject in a historical context and guides the reader towards questions of current research interest. A broad range of topics is covered including: Population dynamics, Infectious diseases, Population genetics and evolution, Dispersal, Molecular and cellular biology, Pattern formation, and Cancer modelling. Particular attention is paid to situations where the simple assumptions of homogenity made in early models break down and the process of mathematical modelling is seen in action.

Physical Hydrodynamics

Author: Etienne Guyon,Jean-Pierre Hulin,Catalin D. Mitescu,Luc Petit

Publisher: Oxford University Press

ISBN: 0198702442

Category: Science

Page: 544

View: 3351

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This second edition of Physical Hydrodynamics is a deeply enriched version of a classical textbook on fluid dynamics. It retains the same pedagogical spirit, based on the authors' experience of teaching university students in the physical sciences, and emphasizes an experimental (inductive) approach rather than the more formal approach found in many textbooks in the field. Today the field is more widely open to other experimental sciences: materials,environmental, life, and earth sciences, as well as the engineering sciences. Representative examples from these fields have been included where possible, while retaining a general presentation in each case.

Elementary Fluid Mechanics

Author: Tsutomu Kambe

Publisher: World Scientific

ISBN: 9812564160

Category: Science

Page: 386

View: 3598

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This textbook describes the fundamental ?physical? aspects of fluid flows for beginners of fluid mechanics in physics, mathematics and engineering, from the point of view of modern physics.It also emphasizes the dynamical aspects of fluid motions rather than the static aspects, illustrating vortex motions, waves, geophysical flows, chaos and turbulence. Beginning with the fundamental concepts of the nature of flows and the properties of fluids, the book presents fundamental conservation equations of mass, momentum and energy, and the equations of motion for both inviscid and viscous fluids.In addition to the fundamentals, this book also covers water waves and sound waves, vortex motions, geophysical flows, nonlinear instability, chaos, and turbulence. Furthermore, it includes the chapters on superfluids and the gauge theory of fluid flows.The material in the book emerged from the lecture notes for an intensive course on Elementary Fluid Mechanics for both undergraduate and postgraduate students of theoretical physics given in 2003 and 2004 at the Nankai Institute of Mathematics (Tianjin) in China. Hence, each chapter may be presented separately as a single lecture.

Finite Elements and Fast Iterative Solvers

With Applications in Incompressible Fluid Dynamics

Author: Howard C. Elman,David J. Silvester,Andrew J. Wathen

Publisher: Oxford University Press

ISBN: 0199678790

Category: Mathematics

Page: 479

View: 2127

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This book is a description of why and how to do Scientific Computing for fundamental models of fluid flow. It contains introduction, motivation, analysis, and algorithms and is closely tied to freely available MATLAB codes that implement the methods described. The focus is on finite element approximation methods and fast iterative solution methods for the consequent linear(ized) systems arising in important problems that model incompressible fluid flow. The problems addressed are the Poisson equation, Convection-Diffusion problem, Stokes problem and Navier-Stokes problem, including new material on time-dependent problems and models of multi-physics. The corresponding iterative algebra based on preconditioned Krylov subspace and multigrid techniques is for symmetric and positive definite, nonsymmetric positive definite, symmetric indefinite and nonsymmetric indefinite matrix systems respectively. For each problem and associated solvers there is a description of how to compute together with theoretical analysis that guides the choice of approaches and describes what happens in practice in the many illustrative numerical results throughout the book (computed with the freely downloadable IFISS software). All of the numerical results should be reproducible by readers who have access to MATLAB and there is considerable scope for experimentation in the "computational laboratory" provided by the software. Developments in the field since the first edition was published have been represented in three new chapters covering optimization with PDE constraints (Chapter 5); solution of unsteady Navier-Stokes equations (Chapter 10); solution of models of buoyancy-driven flow (Chapter 11). Each chapter has many theoretical problems and practical computer exercises that involve the use of the IFISS software. This book is suitable as an introduction to iterative linear solvers or more generally as a model of Scientific Computing at an advanced undergraduate or beginning graduate level.

The Calculus Story

A Mathematical Adventure

Author: David Acheson

Publisher: Oxford University Press

ISBN: 0192526715

Category: Mathematics

Page: 160

View: 7081

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Calculus is the key to much of modern science and engineering. It is the mathematical method for the analysis of things that change, and since in the natural world we are surrounded by change, the development of calculus was a huge breakthrough in the history of mathematics. But it is also something of a mathematical adventure, largely because of the way infinity enters at virtually every twist and turn... In The Calculus Story David Acheson presents a wide-ranging picture of calculus and its applications, from ancient Greece right up to the present day. Drawing on their original writings, he introduces the people who helped to build our understanding of calculus. With a step by step treatment, he demonstrates how to start doing calculus, from the very beginning.

Mathematical Foundations of Neuroscience

Author: G. Bard Ermentrout,David H. Terman

Publisher: Springer Science & Business Media

ISBN: 0387877088

Category: Mathematics

Page: 422

View: 3079

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This book applies methods from nonlinear dynamics to problems in neuroscience. It uses modern mathematical approaches to understand patterns of neuronal activity seen in experiments and models of neuronal behavior. The intended audience is researchers interested in applying mathematics to important problems in neuroscience, and neuroscientists who would like to understand how to create models, as well as the mathematical and computational methods for analyzing them. The authors take a very broad approach and use many different methods to solve and understand complex models of neurons and circuits. They explain and combine numerical, analytical, dynamical systems and perturbation methods to produce a modern approach to the types of model equations that arise in neuroscience. There are extensive chapters on the role of noise, multiple time scales and spatial interactions in generating complex activity patterns found in experiments. The early chapters require little more than basic calculus and some elementary differential equations and can form the core of a computational neuroscience course. Later chapters can be used as a basis for a graduate class and as a source for current research in mathematical neuroscience. The book contains a large number of illustrations, chapter summaries and hundreds of exercises which are motivated by issues that arise in biology, and involve both computation and analysis. Bard Ermentrout is Professor of Computational Biology and Professor of Mathematics at the University of Pittsburgh. David Terman is Professor of Mathematics at the Ohio State University.

The Quantum Theory of Light

Author: Rodney Loudon

Publisher: OUP Oxford

ISBN: 9780191589782

Category:

Page: 448

View: 2431

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This third edition, like its two predecessors, provides a detailed account of the basic theory needed to understand the properties of light and its interactions with atoms, in particular the many nonclassical effects that have now been observed in quantum-optical experiments. The earlier chapters describe the quantum mechanics of various optical processes, leading from the classical representation of the electromagnetic field to the quantum theory of light. The later chapters develop the theoretical descriptions of some of the key experiments in quantum optics. Over half of the material in this third edition is new. It includes topics that have come into prominence over the last two decades, such as the beamsplitter theory, squeezed light, two-photon interference, balanced homodyne detection, travelling-wave attenuation and amplification, quantum jumps, and the ranges of nonliner optical processes important in the generation of nonclassical light. The book is written as a textbook, with the treatment as a whole appropriate for graduate or postgraduate students, while earlier chapters are also suitable for final- year undergraduates. Over 100 problems help to intensify the understanding of the material presented.