Lectures On Topological Fluid Mechanics

Author : Mitchell A. Berger,Renzo L. Ricca,Louis H. Kauffman,Boris Khesin,H. Keith Moffatt,De Witt Sumners
Publisher : Springer
Page : 223 pages
File Size : 42,7 Mb
Release : 2009-05-28
Category : Science
ISBN : 9783642008375

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Lectures on Topological Fluid Mechanics by Mitchell A. Berger,Renzo L. Ricca,Louis H. Kauffman,Boris Khesin,H. Keith Moffatt,De Witt Sumners Pdf

Helmholtz's seminal paper on vortex motion (1858) marks the beginning of what is now called topological fluid mechanics.After 150 years of work, the field has grown considerably. In the last several decades unexpected developments have given topological fluid mechanics new impetus, benefiting from the impressive progress in knot theory and geometric topology on the one hand, and in mathematical and computational fluid dynamics on the other. This volume contains a wide-ranging collection of up-to-date, valuable research papers written by some of the most eminent experts in the field. Topics range from fundamental aspects of mathematical fluid mechanics, including topological vortex dynamics and magnetohydrodynamics, integrability issues, Hamiltonian structures and singularity formation, to DNA tangles and knotted DNAs in sedimentation. A substantial introductory chapter on knots and links, covering elements of modern braid theory and knot polynomials, as well as more advanced topics in knot classification, provides an invaluable addition to this material.

Author : Mitchell A. Berger,Louis H. Kauffman,Boris Khesin,H. Keith Moffatt,De Witt Sumners
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 49,5 Mb
Release : 2009-05-05
Category : Mathematics
ISBN : 9783642008368

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Lectures on Topological Fluid Mechanics by Mitchell A. Berger,Louis H. Kauffman,Boris Khesin,H. Keith Moffatt,De Witt Sumners Pdf

This volume contains a wide-ranging collection of valuable research papers written by some of the most eminent experts in the field. Topics range from fundamental aspects of mathematical fluid mechanics to DNA tangles and knotted DNAs in sedimentation.

Author : Marvin Shinbrot
Publisher : Courier Corporation
Page : 242 pages
File Size : 40,5 Mb
Release : 2013-05-13
Category : Science
ISBN : 9780486267968

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Lectures on Fluid Mechanics by Marvin Shinbrot Pdf

A readable and user-friendly introduction to fluid mechanics, this high-level text is geared toward advanced undergraduates and graduate students. Topics include a derivation of the equations of fluid motion from statistical mechanics, classical theory, and a portion of the modern mathematical theory of viscous, incompressible fluids, with considerable attention to the Navier-Stokes equations. 1973 edition.

Author : Roman Jackiw
Publisher : Springer Science & Business Media
Page : 121 pages
File Size : 54,8 Mb
Release : 2013-03-09
Category : Science
ISBN : 9781475736656

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Lectures on Fluid Dynamics by Roman Jackiw Pdf

Explains the motivation and reviewing the classical theory in a new form; Discusses conservation laws and Euler equations; For one-dimensional cases, the models presented are completely integrable

Author : Karl Gustafson
Publisher : World Scientific
Page : 180 pages
File Size : 50,8 Mb
Release : 1997-12-18
Category : Science
ISBN : 9789814497138

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Lectures On Computational Fluid Dynamics, Mathematical Physics And Linear Algebra by Karl Gustafson Pdf

This book, an outgrowth of the author's distinguished lecture series in Japan in 1995, identifies and describes current results and issues in certain areas of computational fluid dynamics, mathematical physics, and linear algebra. Notable among these are the author's new notion of numerical rotational release for the understanding of correct solution capture when modelling time-dependent higher Reynolds number incompressible flows, the author's fundamental new perspective of wavelets seen as stochastic processes, and the author's new theory of antieigenvalues which has created an entirely new view of iterative methods in computational linear algebra.

Author : Sydney Goldstein
Publisher : American Mathematical Society(RI)
Page : 336 pages
File Size : 49,7 Mb
Release : 1960
Category : Science
ISBN : UCSD:31822011312873

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Lectures on Fluid Mechanics by Sydney Goldstein Pdf

Author : Guillaume Ovarlez,Sarah Hormozi
Publisher : Springer
Page : 259 pages
File Size : 51,8 Mb
Release : 2018-06-26
Category : Technology & Engineering
ISBN : 9783319894386

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Lectures on Visco-Plastic Fluid Mechanics by Guillaume Ovarlez,Sarah Hormozi Pdf

The book is designed for advanced graduate students as well as postdoctoral researchers across several disciplines (e.g., mathematics, physics and engineering), as it provides them with tools and techniques that are essential in performing research on the flow problems of visco-plastic fluids. The following topics are treated: analysis of classical visco-plastic fluid models mathematical modeling of flows of visco-plastic fluids computing flows of visco-plastic fluids rheology of visco-plastic fluids and visco-plastic suspensions application of visco-plastic fluids in engineering sciences complex flows of visco-plastic fluids.

Author : H.K. Moffatt,G.M. Zaslavsky,P. Comte,M. Tabor
Publisher : Springer
Page : 606 pages
File Size : 40,7 Mb
Release : 2014-03-14
Category : Science
ISBN : 9401735514

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Topological Aspects of the Dynamics of Fluids and Plasmas by H.K. Moffatt,G.M. Zaslavsky,P. Comte,M. Tabor Pdf

This volume contains papers arising out of the program of the Institute for Theoretical Physics (ITP) of the University of California at Santa Bar bara, August-December 1991, on the subject "Topological Fluid Dynamics". The first group of papers cover the lectures on Knot Theory, Relaxation un der Topological Constraints, Kinematics of Stretching, and Fast Dynamo Theory presented at the initial Pedagogical Workshop of the program. The remaining papers were presented at the subsequent NATO Advanced Re search Workshop or were written during the course of the program. We wish to acknowledge the support of the NATO Science Committee in making this workshop possible. The scope of "Topological Fluid Dynamics" was defined by an earlier Symposium of the International Union of Theoretical and Applied Mechan ics (IUTAM) held in Cambridge, England in August, 1989, the Proceedings of which were published (Eds. H.K. Moffatt and A. Tsinober) by Cambridge University Press in 1990. The proposal to hold an ITP program on this sub ject emerged from that Symposium, and we are grateful to John Greene and Charlie Kennel at whose encouragement the original proposal was formu lated. Topological fluid dynamics covers a range of problems, particularly those involving vortex tubes and/or magnetic flux tubes in nearly ideal fluids, for which topological structures can be identified and to some extent quantified.

Author : Renzo L. Ricca
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 43,9 Mb
Release : 2001-11-30
Category : Science
ISBN : 1402002076

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An Introduction to the Geometry and Topology of Fluid Flows by Renzo L. Ricca Pdf

Leading experts present a unique, invaluable introduction to the study of the geometry and typology of fluid flows. From basic motions on curves and surfaces to the recent developments in knots and links, the reader is gradually led to explore the fascinating world of geometric and topological fluid mechanics. Geodesics and chaotic orbits, magnetic knots and vortex links, continual flows and singularities become alive with more than 160 figures and examples. In the opening article, H. K. Moffatt sets the pace, proposing eight outstanding problems for the 21st century. The book goes on to provide concepts and techniques for tackling these and many other interesting open problems.

Author : Alfio Quarteroni
Publisher : Springer Science & Business Media
Page : 264 pages
File Size : 42,8 Mb
Release : 2009-12-24
Category : Mathematics
ISBN : 9788847011229

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MATHKNOW by Alfio Quarteroni Pdf

Mathematics forms bridges between knowledge, tradition, and contemporary life. The continuous development and growth of its many branches, both classical and modern, permeates and fertilizes all aspects of applied science and technology, and so has a vital impact on our modern society. The book will focus on these aspects and will benefit from the contribution of several world-famous scientists from mathematics and related sciences, such as: Ralph Abraham, Andrew Crumey, Peter Markowich, Claudio Procesi, Clive Ruggles, Ismail Serageldin, Amin Shokrollahi, Tobias Wallisser.

Author : Giovanni Paolo Galdi,John Groves Heywood,Rolf Rannacher
Publisher : Birkhauser
Page : 293 pages
File Size : 53,6 Mb
Release : 2000
Category : Science
ISBN : 0817664149

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Fundamental Directions in Mathematical Fluid Mechanics by Giovanni Paolo Galdi,John Groves Heywood,Rolf Rannacher Pdf

Author : Tai-Peng Tsai
Publisher : American Mathematical Soc.
Page : 224 pages
File Size : 52,7 Mb
Release : 2018-08-09
Category : Fluid dynamics
ISBN : 9781470430962

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Lectures on Navier-Stokes Equations by Tai-Peng Tsai Pdf

This book is a graduate text on the incompressible Navier-Stokes system, which is of fundamental importance in mathematical fluid mechanics as well as in engineering applications. The goal is to give a rapid exposition on the existence, uniqueness, and regularity of its solutions, with a focus on the regularity problem. To fit into a one-year course for students who have already mastered the basics of PDE theory, many auxiliary results have been described with references but without proofs, and several topics were omitted. Most chapters end with a selection of problems for the reader. After an introduction and a careful study of weak, strong, and mild solutions, the reader is introduced to partial regularity. The coverage of boundary value problems, self-similar solutions, the uniform L3 class including the celebrated Escauriaza-Seregin-Šverák Theorem, and axisymmetric flows in later chapters are unique features of this book that are less explored in other texts. The book can serve as a textbook for a course, as a self-study source for people who already know some PDE theory and wish to learn more about Navier-Stokes equations, or as a reference for some of the important recent developments in the area.

Author : Josef Malek,Jindrich Necas,Mirko Rokyta
Publisher : Springer Science & Business Media
Page : 232 pages
File Size : 52,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642573088

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Advances in Mathematical Fluid Mechanics by Josef Malek,Jindrich Necas,Mirko Rokyta Pdf

This book consists of six survey contributions that are focused on several open problems of theoretical fluid mechanics both for incompressible and compressible fluids. The first article "Viscous flows in Besov spaces" by M area Cannone ad dresses the problem of global existence of a uniquely defined solution to the three-dimensional Navier-Stokes equations for incompressible fluids. Among others the following topics are intensively treated in this contribution: (i) the systematic description of the spaces of initial conditions for which there exists a unique local (in time) solution or a unique global solution for small data, (ii) the existence of forward self-similar solutions, (iii) the relation of these results to Leray's weak solutions and backward self-similar solutions, (iv) the extension of the results to further nonlinear evolutionary problems. Particular attention is paid to the critical spaces that are invariant under the self-similar transform. For sufficiently small Reynolds numbers, the conditional stability in the sense of Lyapunov is also studied. The article is endowed by interesting personal and historical comments and an exhaustive bibliography that gives the reader a complete picture about available literature. The papers "The dynamical system approach to the Navier-Stokes equa tions for compressible fluids" by Eduard Feireisl, and "Asymptotic problems and compressible-incompressible limits" by Nader Masmoudi are devoted to the global (in time) properties of solutions to the Navier-Stokes equa and three tions for compressible fluids. The global (in time) analysis of two dimensional motions of compressible fluids were left open for many years.

Author : Jaime Klapp,Abraham Medina Ovando
Publisher : Springer
Page : 473 pages
File Size : 53,5 Mb
Release : 2013-12-25
Category : Science
ISBN : 3319001175

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Experimental and Computational Fluid Mechanics by Jaime Klapp,Abraham Medina Ovando Pdf

This book collects invited lectures and selected contributions presented at the Enzo Levi and XVIII Annual Meeting of the Fluid Dynamic Division of the Mexican Physical Society in 2012. It is intended for fourth-year undergraduate and graduate students, and for scientists in the fields of physics, engineering and chemistry with an interest in Fluid Dynamics from experimental, theoretical and computational points of view. The invited lectures are introductory in nature and avoid the use of complicated mathematics. The other selected contributions are also suitable for fourth-year undergraduate and graduate students. The Fluid Dynamics applications include oceanography, multiphase flows, convection, diffusion, heat transfer, rheology, granular materials, viscous flows, porous media flows and astrophysics. The material presented in the book includes recent advances in experimental and computational fluid dynamics and is well-suited to both teaching and research.

Author : Ivan Zelinka,Ali Sanayei,Hector Zenil,Otto E. Rössler
Publisher : Springer Science & Business Media
Page : 290 pages
File Size : 41,5 Mb
Release : 2013-07-18
Category : Technology & Engineering
ISBN : 9783319002545

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How Nature Works by Ivan Zelinka,Ali Sanayei,Hector Zenil,Otto E. Rössler Pdf

This book is based on the outcome of the “2012 Interdisciplinary Symposium on Complex Systems” held at the island of Kos. The book consists of 12 selected papers of the symposium starting with a comprehensive overview and classification of complexity problems, continuing by chapters about complexity, its observation, modeling and its applications to solving various problems including real-life applications. More exactly, readers will have an encounter with the structural complexity of vortex flows, the use of chaotic dynamics within evolutionary algorithms, complexity in synthetic biology, types of complexity hidden inside evolutionary dynamics and possible controlling methods, complexity of rugged landscapes, and more. All selected papers represent innovative ideas, philosophical overviews and state-of-the-art discussions on aspects of complexity. The book will be useful as instructional material for senior undergraduate and entry-level graduate students in computer science, physics, applied mathematics and engineering-type work in the area of complexity. The book will also be valuable as a resource of knowledge for practitioners who want to apply complexity to solve real-life problems in their own challenging applications. The authors and editors hope that readers will be inspired to do their own experiments and simulations, based on information reported in this book, thereby moving beyond the scope of the book.