Lectures on Topological Fluid Mechanics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Topological Fluid Mechanics write by Mitchell A. Berger. This book was released on 2009-05-05. Lectures on Topological Fluid Mechanics available in PDF, EPUB and Kindle. 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.
Lectures on Topological Fluid Mechanics
Lectures on Topological Fluid Mechanics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Topological Fluid Mechanics write by Mitchell A. Berger. This book was released on 2009-05-28. Lectures on Topological Fluid Mechanics available in PDF, EPUB and Kindle. 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.
Introductory Lectures on Knot Theory
Introductory Lectures on Knot Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introductory Lectures on Knot Theory write by Louis H. Kauffman. This book was released on 2012. Introductory Lectures on Knot Theory available in PDF, EPUB and Kindle. More recently, Khovanov introduced link homology as a generalization of the Jones polynomial to homology of chain complexes and Ozsvath and Szabo developed Heegaard-Floer homology, that lifts the Alexander polynomial. These two significantly different theories are closely related and the dependencies are the object of intensive study. These ideas mark the beginning of a new era in knot theory that includes relationships with four-dimensional problems and the creation of new forms of algebraic topology relevant to knot theory. The theory of skein modules is an older development also having its roots in Jones discovery. Another significant and related development is the theory of virtual knots originated independently by Kauffman and by Goussarov Polyak and Viro in the '90s. All these topics and their relationships are the subject of the survey papers in this book.
The Navier-Stokes Problem in the 21st Century
The Navier-Stokes Problem in the 21st Century - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Navier-Stokes Problem in the 21st Century write by Pierre Gilles Lemarie-Rieusset. This book was released on 2023-12-11. The Navier-Stokes Problem in the 21st Century available in PDF, EPUB and Kindle. Praise for the first edition “The author is an outstanding expert in harmonic analysis who has made important contributions. The book contains rigorous proofs of a number of the latest results in the field. I strongly recommend the book to postgraduate students and researchers working on challenging problems of harmonic analysis and mathematical theory of Navier-Stokes equations." —Gregory Seregin, St Hildas College, Oxford University “"This is a great book on the mathematical aspects of the fundamental equations of hydrodynamics, the incompressible Navier-Stokes equations. It covers many important topics and recent results and gives the reader a very good idea about where the theory stands at present.” —Vladimir Sverak, University of Minnesota The complete resolution of the Navier–Stokes equation—one of the Clay Millennium Prize Problems—remains an important open challenge in partial differential equations (PDEs) research despite substantial studies on turbulence and three-dimensional fluids. The Navier–Stokes Problem in the 21st Century, Second Edition continues to provide a self-contained guide to the role of harmonic analysis in the PDEs of fluid mechanics, now revised to include fresh examples, theorems, results, and references that have become relevant since the first edition published in 2016.
Introduction to Vortex Filaments in Equilibrium
Introduction to Vortex Filaments in Equilibrium - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Vortex Filaments in Equilibrium write by Timothy D. Andersen. This book was released on 2014-10-09. Introduction to Vortex Filaments in Equilibrium available in PDF, EPUB and Kindle. This book presents fundamental concepts and seminal results to the study of vortex filaments in equilibrium. It also presents new discoveries in quasi-2D vortex structures with applications to geophysical fluid dynamics and magnetohydrodynamics in plasmas. It fills a gap in the vortex statistics literature by simplifying the mathematical introduction to this complex topic, covering numerical methods, and exploring a wide range of applications with numerous examples. The authors have produced an introduction that is clear and easy to read, leading the reader step-by-step into this topical area. Alongside the theoretical concepts and mathematical formulations, interesting applications are discussed. This combination makes the text useful for students and researchers in mathematics and physics.
