Introduction to Differential Geometry with Applications to Navier Stokes Dynamics

Author: Story
Publisher: iUniverse
ISBN: 9780595339211
Release Date: 2005
Genre: Mathematics

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.

The Navier Stokes Equations

Author: P. G. Drazin
Publisher: Cambridge University Press
ISBN: 0521681626
Release Date: 2006-05-25
Genre: Mathematics

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

Geometric Theory of Incompressible Flows with Applications to Fluid Dynamics

Author: Tian Ma
Publisher: American Mathematical Soc.
ISBN: 9780821836934
Release Date: 2005
Genre: Mathematics

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.

UC Santa Cruz

Author: University of California, Santa Cruz
ISBN: UCSC:32106020266075
Release Date: 2006

Fundamental Algorithms in Computational Fluid Dynamics

Author: Thomas H. Pulliam
Publisher: Springer Science & Business Media
ISBN: 9783319050539
Release Date: 2014-03-31
Genre: Technology & Engineering

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.

The Courant Friedrichs Lewy CFL Condition

Author: Carlos A. de Moura
Publisher: Springer Science & Business Media
ISBN: 9780817683948
Release Date: 2012-10-28
Genre: Mathematics

This volume comprises a carefully selected collection of articles emerging from and pertinent to the 2010 CFL-80 conference in Rio de Janeiro, celebrating the 80th anniversary of the Courant-Friedrichs-Lewy (CFL) condition. A major result in the field of numerical analysis, the CFL condition has influenced the research of many important mathematicians over the past eight decades, and this work is meant to take stock of its most important and current applications. The Courant–Friedrichs–Lewy (CFL) Condition: 80 Years After its Discovery will be of interest to practicing mathematicians, engineers, physicists, and graduate students who work with numerical methods.

Topics in Finite Elasticity

Author: Morton E. Gurtin
Publisher: SIAM
ISBN: 9780898711684
Release Date: 1981-09-01
Genre: Technology & Engineering

This monograph presents a derivation of the basic equations of the theory of finite elasticity.

Integer Programming

Author: Ellis L. Johnson
Publisher: SIAM
ISBN: 9780898711622
Release Date: 1980-01-01
Genre: Mathematics

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.

Large Deviations and Applications

Author: S. R. S. Varadhan
Publisher: SIAM
ISBN: 9780898711899
Release Date: 1984-01-31
Genre: Mathematics

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.

Geometric Analysis and Nonlinear Partial Differential Equations

Author: Stefan Hildebrandt
Publisher: Springer Science & Business Media
ISBN: 3540440518
Release Date: 2003
Genre: Mathematics

This well-organized and coherent collection of papers leads the reader to the frontiers of present research in the theory of nonlinear partial differential equations and the calculus of variations and offers insight into some exciting developments. In addition, most articles also provide an excellent introduction to their background, describing extensively as they do the history of those problems presented, as well as the state of the art and offer a well-chosen guide to the literature. Part I contains the contributions of geometric nature: From spectral theory on regular and singular spaces to regularity theory of solutions of variational problems. Part II consists of articles on partial differential equations which originate from problems in physics, biology and stochastics. They cover elliptic, hyperbolic and parabolic cases.

Dynamical Systems and Probabilistic Methods in Partial Differential Equations

Author: Percy Deift
Publisher: American Mathematical Soc.
ISBN: 0821897004
Release Date:
Genre: Mathematics

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.

Computing Handbook Third Edition

Author: Teofilo Gonzalez
Publisher: CRC Press
ISBN: 9781439898536
Release Date: 2014-05-07
Genre: Mathematics

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.

Raum Zeit Materie

Author: Hermann Weyl
Publisher: Springer-Verlag
ISBN: 9783662020449
Release Date: 2013-04-17
Genre: Science

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.