Author: Story

Publisher: iUniverse

ISBN: 0595339212

Category: Mathematics

Page: 168

View: 4330

Introduction to Differential Geometry with applications to Navier-Stokes Dynamics is an invaluable manuscript for anyone who wants to understand and use exterior calculus and differential geometry, the modern approach to calculus and geometry. Author Troy Story makes use of over thirty years of research experience to provide a smooth transition from conventional calculus to exterior calculus and differential geometry, assuming only a knowledge of conventional calculus. Introduction to Differential Geometry with applications to Navier-Stokes Dynamics includes the topics: Geometry, Exterior calculus, Homology and co-homology, Applications of differential geometry and exterior calculus to: Hamiltonian mechanics, geometric optics, irreversible thermodynamics, black hole dynamics, electromagnetism, classical string fields, and Navier-Stokes dynamics.
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Będlewo, Poland, October 2013

Author: Jacek Banasiak,Adam Bobrowski,Mirosław Lachowicz

Publisher: Springer

ISBN: 3319121456

Category: Mathematics

Page: 337

View: 2180

Many results, both from semi group theory itself and from the applied sciences, are phrased in discipline-specific languages and hence are hardly known to a broader community. This volume contains a selection of lectures presented at a conference that was organised as a forum for all mathematicians using semi group theory to learn what is happening outside their own field of research. The collection will help to establish a number of new links between various sub-disciplines of semigroup theory, stochastic processes, differential equations and the applied fields. The theory of semigroups of operators is a well-developed branch of functional analysis. Its foundations were laid at the beginning of the 20th century, while the fundamental generation theorem of Hille and Yosida dates back to the forties. The theory was, from the very beginning, designed as a universal language for partial differential equations and stochastic processes, but at the same time it started to live as an independent branch of operator theory. Nowadays, it still has the same distinctive flavour: it develops rapidly by posing new ‘internal’ questions and in answering them, discovering new methods that can be used in applications. On the other hand, it is influenced by questions from PDEs and stochastic processes as well as from applied sciences such as mathematical biology and optimal control, and thus it continually gathers a new momentum. Researchers and postgraduate students working in operator theory, partial differential equations, probability and stochastic processes, analytical methods in biology and other natural sciences, optimization and optimal control will find this volume useful.
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A Classification of Flows and Exact Solutions

Author: P. G. Drazin,N. Riley

Publisher: Cambridge University Press

ISBN: 9780521681629

Category: Mathematics

Page: 196

View: 4062

This 2006 book details exact solutions to the Navier-Stokes equations for senior undergraduates and graduates or research reference.
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Author: Vladimir D. Liseikin

Publisher: Springer Science & Business Media

ISBN: 3540342362

Category: Science

Page: 294

View: 5933

The process of breaking up a physical domain into smaller sub-domains, known as meshing, facilitates the numerical solution of partial differential equations used to simulate physical systems. In an updated and expanded Second Edition, this monograph gives a detailed treatment based on the numerical solution of inverted Beltramian and diffusion equations with respect to monitor metrics for generating both structured and unstructured grids in domains and on surfaces.
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Author: Tian Ma,Shouhong Wang

Publisher: American Mathematical Soc.

ISBN: 0821836935

Category: Mathematics

Page: 234

View: 8386

This book presents a geometric theory for incompressible flow and its applications to fluid dynamics. The main objective is to study the stability and transitions of the structure of incompressible flows, and applications to fluid dynamics and geophysical fluid dynamics. The development of the theory and its applications has gone well beyond the original motivation, which was the study of oceanic dynamics. One such development is a rigorous theory for boundary layer separation of incompressible fluid flows. This study of incompressible flows has two major parts, which are interconnected. The first is the development of a global geometric theory of divergence-free fields on general two-dimensional compact manifolds. The second is the study of the structure of velocity fields for two-dimensional incompressible fluid flows governed by the Navier-Stokes equations or the Euler equations. Motivated by the study of problems in geophysical fluid dynamics, the program of research in this book seeks to develop a new mathematical theory, maintaining close links to physics along the way. In return, the theory is applied to physical problems, with more problems yet to be explored.
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Author: James C. Robinson,José L. Rodrigo,Witold Sadowski,Alejandro Vidal-López

Publisher: Cambridge University Press

ISBN: 131658934X

Category: Mathematics

Page: N.A

View: 3249

The rigorous mathematical theory of the Navier–Stokes and Euler equations has been a focus of intense activity in recent years. This volume, the product of a workshop in Venice in 2013, consolidates, surveys and further advances the study of these canonical equations. It consists of a number of reviews and a selection of more traditional research articles on topics that include classical solutions to the 2D Euler equation, modal dependency for the 3D Navier–Stokes equation, zero viscosity Boussinesq equations, global regularity and finite-time singularities, well-posedness for the diffusive Burgers equations, and probabilistic aspects of the Navier–Stokes equation. The result is an accessible summary of a wide range of active research topics written by leaders in their field, together with some exciting new results. The book serves both as a helpful overview for graduate students new to the area and as a useful resource for more established researchers.
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Author: University of California, Santa Cruz

Publisher: N.A

ISBN: N.A

Category:

Page: N.A

View: 9486

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Principles of Analysis and Design

Author: Stanley Middleman

Publisher: John Wiley & Sons Incorporated

ISBN: 9780471182092

Category: Technology & Engineering

Page: 513

View: 4501

This comprehensive text links abstract mathematics to engineering applications in order to provide a clear and thorough exploration of fluid dynamics. Focus is on the development of mathematical models of physical phenomena and the wide range of technologies available to students. Filled with examples and problems inspired by real engineering applications, this resource will not only teach, but motivate students to further emerge themselves in the field.
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1994 Summer Seminar on Dynamical Systems and Probabilistic Methods for Nonlinear Waves, June 20-July 1, 1994, MSRI, Berkeley, CA

Author: Percy Deift,C. D. Levermore,C. Eugene Wayne

Publisher: American Mathematical Soc.

ISBN: 9780821897003

Category: Mathematics

Page: 268

View: 9752

This volume contains some of the lectures presented in June 1994 during the AMS-SIAM Summer Seminar at the Mathematical Sciences Research Institute in Berkeley. The goal of the seminar was to introduce participants to as many interesting and active applications of dynamical systems and probabilistic methods to problems in applied mathematics as possible. As a result, this book covers a great deal of ground. Nevertheless, the pedagogical orientation of the lectures has been retained, and therefore the book will serve as an ideal introduction to these varied and interesting topics.
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Vorlesungen über Allgemeine Relativitätstheorie

Author: Hermann Weyl

Publisher: Springer-Verlag

ISBN: 3642989500

Category: Science

Page: 338

View: 8196

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.
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With Applications to Heat Transfer, Fluid Mechanics, and Solid Mechanics

Author: Junuthula Narasimha Reddy,J. N. Reddy

Publisher: Oxford University Press, USA

ISBN: 0199641757

Category: Science

Page: 687

View: 1030

The second edition of An Introduction to Nonlinear Finite Element Analysis offers an easy-to-understand treatment of nonlinear finite element analysis, which includes element development from mathematical models and numerical evaluation of the underlying physics. Additional explanations, examples, and problems have been added to all chapters. The book may be used as a textbook for an advanced course (after a first course) on the finite element method orthe first course on nonlinear finite element analysis. A solutions manual is available on request from the publisher to instructors who adopt the book as a textbook for a course.
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Author: Thomas H. Pulliam,David W. Zingg

Publisher: Springer Science & Business Media

ISBN: 3319050532

Category: Technology & Engineering

Page: 211

View: 4990

Intended as a textbook for courses in computational fluid dynamics at the senior undergraduate or graduate level, this book is a follow-up to the book Fundamentals of Computational Fluid Dynamics by the same authors, which was published in the series Scientific Computation in 2001. Whereas the earlier book concentrated on the analysis of numerical methods applied to model equations, this new book concentrates on algorithms for the numerical solution of the Euler and Navier-Stokes equations. It focuses on some classical algorithms as well as the underlying ideas based on the latest methods. A key feature of the book is the inclusion of programming exercises at the end of each chapter based on the numerical solution of the quasi-one-dimensional Euler equations and the shock-tube problem. These exercises can be included in the context of a typical course and sample solutions are provided in each chapter, so readers can confirm that they have coded the algorithms correctly.
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Author: Walter Craig

Publisher: Springer Science & Business Media

ISBN: 1402069642

Category: Mathematics

Page: 441

View: 3135

This volume is the collected and extended notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NATO Advanced Study Institute in Montreal in 2007. Many aspects of the modern theory of the subject were covered at this event, including low dimensional problems. Applications are also presented to several important areas of research, including problems in classical mechanics, continuum mechanics, and partial differential equations.
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Author: Jean-Paul Caltagirone

Publisher: John Wiley & Sons

ISBN: 1119058074

Category: Science

Page: 252

View: 6339

This book presents the fundamental principles of mechanics tore-establish the equations of Discrete Mechanics. It introducesphysics and thermodynamics associated to the physicalmodeling. The development and the complementarity of scienceslead to review today the old concepts that were the basis for thedevelopment of continuum mechanics. The differential geometry isused to review the conservation laws of mechanics. For instance,this formalism requires a different location of vector and scalarquantities in space. The equations of Discrete Mechanics form asystem of equations where the Helmholtz-Hodge decomposition playsan important role.
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Author: S. R. S. Varadhan

Publisher: SIAM

ISBN: 0898711894

Category: Mathematics

Page: 75

View: 3417

Many situations exist in which solutions to problems are represented as function space integrals. Such representations can be used to study the qualitative properties of the solutions and to evaluate them numerically using Monte Carlo methods. The emphasis in this book is on the behavior of solutions in special situations when certain parameters get large or small.
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Proceedings of the 25th Meeting of the Dutch Association for Numerical Fluid Mechanics

Author: Wesseling Pieter

Publisher: Springer-Verlag

ISBN: 332289729X

Category: Technology & Engineering

Page: 130

View: 8848

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Author: Morton E. Gurtin

Publisher: SIAM

ISBN: 0898711681

Category: Technology & Engineering

Page: 58

View: 4962

This monograph presents a derivation of the basic equations of the theory of finite elasticity.
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Facets, Subadditivity, and Duality for Group and Semi-group Problems

Author: Ellis L. Johnson

Publisher: SIAM

ISBN: 0898711622

Category: Mathematics

Page: 68

View: 4534

This monograph considers pure integer programming problems which concern packing, partitioning or covering. For this class of problems, an algorithmic framework using a duality approach is offered. Furthermore, the author proposes for the first time a general framework for both packing and covering problems characterizing the convex whole of integer solutions.
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Computer Science and Software Engineering

Author: Teofilo Gonzalez,Jorge Diaz-Herrera,Allen Tucker

Publisher: CRC Press

ISBN: 1439898537

Category: Mathematics

Page: 2326

View: 5821

Computing Handbook, Third Edition: Computer Science and Software Engineering mirrors the modern taxonomy of computer science and software engineering as described by the Association for Computing Machinery (ACM) and the IEEE Computer Society (IEEE-CS). Written by established leading experts and influential young researchers, the first volume of this popular handbook examines the elements involved in designing and implementing software, new areas in which computers are being used, and ways to solve computing problems. The book also explores our current understanding of software engineering and its effect on the practice of software development and the education of software professionals. Like the second volume, this first volume describes what occurs in research laboratories, educational institutions, and public and private organizations to advance the effective development and use of computers and computing in today’s world. Research-level survey articles provide deep insights into the computing discipline, enabling readers to understand the principles and practices that drive computing education, research, and development in the twenty-first century.
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Author: Wei-Ming Ni

Publisher: SIAM

ISBN: 1611971969

Category: Mathematics

Page: 110

View: 6502

Diffusion has been used extensively in many scientific disciplines to model a wide variety of phenomena. The Mathematics of Diffusion focuses on the qualitative properties of solutions to nonlinear elliptic and parabolic equations and systems in connection with domain geometry, various boundary conditions, the mechanism of different diffusion rates, and the interaction between diffusion and spatial heterogeneity. The book systematically explores the interplay between different diffusion rates from the viewpoint of pattern formation, particularly Turing's diffusion-driven instability in both homogeneous and heterogeneous environments, and the roles of random diffusion, directed movements and spatial heterogeneity in the classical Lotka–Volterra competition systems. Interspersed throughout the book are many simple, fundamental and important open problems for readers to investigate.
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