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: 6658

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: 3488

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: 1315356546

Category: Mathematics

Page: 934

View: 4245

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.

Mathematical and Numerical Foundations of Turbulence Models and Applications

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Author: Tomás Chacón Rebollo,Roger Lewandowski

Publisher: Springer

ISBN: 1493904558

Category: Mathematics

Page: 517

View: 9868

With applications to climate, technology, and industry, the modeling and numerical simulation of turbulent flows are rich with history and modern relevance. The complexity of the problems that arise in the study of turbulence requires tools from various scientific disciplines, including mathematics, physics, engineering and computer science. Authored by two experts in the area with a long history of collaboration, this monograph provides a current, detailed look at several turbulence models from both the theoretical and numerical perspectives. The k-epsilon, large-eddy simulation and other models are rigorously derived and their performance is analyzed using benchmark simulations for real-world turbulent flows. Mathematical and Numerical Foundations of Turbulence Models and Applications is an ideal reference for students in applied mathematics and engineering, as well as researchers in mathematical and numerical fluid dynamics. It is also a valuable resource for advanced graduate students in fluid dynamics, engineers, physical oceanographers, meteorologists and climatologists.

Hamiltonian Dynamical Systems and Applications

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Author: Walter Craig

Publisher: Springer Science & Business Media

ISBN: 1402069642

Category: Mathematics

Page: 441

View: 7682

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: 3672

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

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