Applied Analysis of the Navier-Stokes Equations

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Author: Charles R. Doering,J. D. Gibbon

Publisher: Cambridge University Press

ISBN: 9780521445689

Category: Mathematics

Page: 217

View: 3986

The Navier-Stokes equations are a set of nonlinear partial differential equations that describe the fundamental dynamics of fluid motion. They are applied routinely to problems in engineering, geophysics, astrophysics, and atmospheric science. This book is an introductory physical and mathematical presentation of the Navier-Stokes equations, focusing on unresolved questions of the regularity of solutions in three spatial dimensions, and the relation of these issues to the physical phenomenon of turbulent fluid motion. The goal of the book is to present a mathematically rigorous investigation of the Navier-Stokes equations that is accessible to a broader audience than just the subfields of mathematics to which it has traditionally been restricted. Therefore, results and techniques from nonlinear functional analysis are introduced as needed with an eye toward communicating the essential ideas behind the rigorous analyses. This book is appropriate for graduate students in many areas of mathematics, physics, and engineering.

Recent Progress in the Theory of the Euler and Navier-Stokes Equations

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Author: James C. Robinson,José L. Rodrigo,Witold Sadowski,Alejandro Vidal-López

Publisher: Cambridge University Press

ISBN: 1107554977

Category: Mathematics

Page: 245

View: 759

Accessible summary of a wide range of active research topics written by leaders in their field, including exciting new results.

Handbook of Applications of Chaos Theory

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Author: Christos H. Skiadas,Charilaos Skiadas

Publisher: CRC Press

ISBN: 1466590440

Category: Mathematics

Page: 934

View: 6896

In addition to explaining and modeling unexplored phenomena in nature and society, chaos uses vital parts of nonlinear dynamical systems theory and established chaotic theory to open new frontiers and fields of study. Handbook of Applications of Chaos Theory covers the main parts of chaos theory along with various applications to diverse areas. Expert contributors from around the world show how chaos theory is used to model unexplored cases and stimulate new applications. Accessible to scientists, engineers, and practitioners in a variety of fields, the book discusses the intermittency route to chaos, evolutionary dynamics and deterministic chaos, and the transition to phase synchronization chaos. It presents important contributions on strange attractors, self-exciting and hidden attractors, stability theory, Lyapunov exponents, and chaotic analysis. It explores the state of the art of chaos in plasma physics, plasma harmonics, and overtone coupling. It also describes flows and turbulence, chaotic interference versus decoherence, and an application of microwave networks to the simulation of quantum graphs. The book proceeds to give a detailed presentation of the chaotic, rogue, and noisy optical dissipative solitons; parhelic-like circle and chaotic light scattering; and interesting forms of the hyperbolic prism, the Poincaré disc, and foams. It also covers numerous application areas, from the analysis of blood pressure data and clinical digital pathology to chaotic pattern recognition to economics to musical arts and research.

Geometric Theory of Incompressible Flows with Applications to Fluid Dynamics

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Author: Tian Ma,Shouhong Wang

Publisher: American Mathematical Soc.

ISBN: 0821836935

Category: Mathematics

Page: 234

View: 7596

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.

Hamiltonian Dynamical Systems and Applications

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Author: Walter Craig

Publisher: Springer Science & Business Media

ISBN: 1402069642

Category: Mathematics

Page: 441

View: 8944

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.

Nonlinearity

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematical analysis

Page: N.A

View: 5204

RAIRO.

Modélisation Mathématique Et Analyse Numérique : M2N.. Mathematical modelling and numerical analysis

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Author: EDP Sciences

Publisher: N.A

ISBN: N.A

Category: Numerical analysis

Page: N.A

View: 6479

Physical Review

Statistical physics, plasmas, fluids, and related interdisciplinary topics. E

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: Fluids

Page: N.A

View: 1011

Viscous Flow

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Author: H. Ockendon,J. R. Ockendon

Publisher: Cambridge University Press

ISBN: 9780521458818

Category: Mathematics

Page: 113

View: 834

Viscous flow crops up in many real-life situations such as aerodynamics and lubrication, and because of its universality it is a paradigm for the application of mathematics to the real world. This book is a coherent account of the ways in which mathematics can both give insight into viscous flow and suggest analogies and implications for other branches of applied mathematics. The authors place particular emphasis on the unification brought about by the use of asymptotic analysis and scaling properties and the use of everyday observations from the real world (especially industry) to illustrate the theory. The book is aimed at final-year undergraduate and beginning graduate students in applied mathematics, physics, and engineering courses on fluid flow.

Infinite-Dimensional Dynamical Systems

An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors

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Author: James C. Robinson

Publisher: Cambridge University Press

ISBN: 9780521635646

Category: Mathematics

Page: 461

View: 9018

This book treats the theory of global attractors, a recent development in the theory of partial differential equations, in a way that also includes much of the traditional elements of the subject. As such it gives a quick but directed introduction to some fundamental concepts, and by the end proceeds to current research problems. Since the subject is relatively new, this is the first book to attempt to treat these various topics in a unified and didactic way. It is intended to be suitable for first year graduate students.

Vorticity and Incompressible Flow

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Author: Andrew J. Majda,Andrea L. Bertozzi

Publisher: Cambridge University Press

ISBN: 9780521639484

Category: Mathematics

Page: 545

View: 8295

This book is a comprehensive introduction to the mathematical theory of vorticity and incompressible flow ranging from elementary introductory material to current research topics. While the contents center on mathematical theory, many parts of the book showcase the interaction between rigorous mathematical theory, numerical, asymptotic, and qualitative simplified modeling, and physical phenomena. The first half forms an introductory graduate course on vorticity and incompressible flow. The second half comprise a modern applied mathematics graduate course on the weak solution theory for incompressible flow.

An Introduction to Magnetohydrodynamics

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Author: P. A. Davidson

Publisher: Cambridge University Press

ISBN: 9780521794879

Category: Mathematics

Page: 431

View: 6087

This book is an introductory text on magnetohydrodynamics (MHD) - the study of the interaction of magnetic fields and conducting fluids.

Mathematical Models in the Applied Sciences

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Author: A. C. Fowler

Publisher: Cambridge University Press

ISBN: 9780521467032

Category: Mathematics

Page: 402

View: 6740

Presents a thorough grounding in the techniques of mathematical modelling, and proceeds to explore a range of classical and continuum models from an array of disciplines.

The Kinematics of Mixing

Stretching, Chaos, and Transport

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Author: J. M. Ottino

Publisher: Cambridge University Press

ISBN: 9780521368780

Category: Mathematics

Page: 364

View: 9431

In spite of its universality, mixing is poorly understood and generally speaking, mixing problems are attacked on a case-by-case basis. This is the first book to present a unified treatment of the mixing of fluids from a kinematical viewpoint. The author's aim is to provide a conceptually clear basis from which to launch analysis and to facilitate an understanding of the numerous mixing problems encountered in nature and technology. After presenting the necessary background in kinematics and fluid dynamics, Professor Ottino considers various examples of dealing with necessary background in dynamical systems and chaos. The book assumes little previous knowledge of fluid dynamics and dynamical systems and can be used as a textbook by final-year undergraduates, graduate students and researchers in applied mathematics, engineering science, geophysics and physics who have an interest in fluid dynamics, continuum mechanics and dynamical systems. It is profusely illustrated in colour, with many line diagrams and half-tones. Systems which illustrate the most important concepts, many exercises and examples are included.