Introduction To Vortex Filaments In Equilibrium
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| Author | : Timothy D. Andersen |
| Publisher | : Springer |
| Total Pages | : 146 |
| Release | : 2014-10-09 |
| Genre | : Computers |
| ISBN | : 1493919385 |
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.
| Author | : Jacob Bedrossian |
| Publisher | : American Mathematical Society |
| Total Pages | : 235 |
| Release | : 2022-09-22 |
| Genre | : Mathematics |
| ISBN | : 1470471787 |
The aim of this book is to provide beginning graduate students who completed the first two semesters of graduate-level analysis and PDE courses with a first exposure to the mathematical analysis of the incompressible Euler and Navier-Stokes equations. The book gives a concise introduction to the fundamental results in the well-posedness theory of these PDEs, leaving aside some of the technical challenges presented by bounded domains or by intricate functional spaces. Chapters 1 and 2 cover the fundamentals of the Euler theory: derivation, Eulerian and Lagrangian perspectives, vorticity, special solutions, existence theory for smooth solutions, and blowup criteria. Chapters 3, 4, and 5 cover the fundamentals of the Navier-Stokes theory: derivation, special solutions, existence theory for strong solutions, Leray theory of weak solutions, weak-strong uniqueness, existence theory of mild solutions, and Prodi-Serrin regularity criteria. Chapter 6 provides a short guide to the must-read topics, including active research directions, for an advanced graduate student working in incompressible fluids. It may be used as a roadmap for a topics course in a subsequent semester. The appendix recalls basic results from real, harmonic, and functional analysis. Each chapter concludes with exercises, making the text suitable for a one-semester graduate course. Prerequisites to this book are the first two semesters of graduate-level analysis and PDE courses.
| Author | : Alexandre J. Chorin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 181 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 1441987282 |
This book provides an introduction to the theory of turbulence in fluids based on the representation of the flow by means of its vorticity field. It has long been understood that, at least in the case of incompressible flow, the vorticity representation is natural and physically transparent, yet the development of a theory of turbulence in this representation has been slow. The pioneering work of Onsager and of Joyce and Montgomery on the statistical mechanics of two-dimensional vortex systems has only recently been put on a firm mathematical footing, and the three-dimensional theory remains in parts speculative and even controversial. The first three chapters of the book contain a reasonably standard intro duction to homogeneous turbulence (the simplest case); a quick review of fluid mechanics is followed by a summary of the appropriate Fourier theory (more detailed than is customary in fluid mechanics) and by a summary of Kolmogorov's theory of the inertial range, slanted so as to dovetail with later vortex-based arguments. The possibility that the inertial spectrum is an equilibrium spectrum is raised.
| Author | : S. V. Alekseenko |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 505 |
| Release | : 2007-08-29 |
| Genre | : Technology & Engineering |
| ISBN | : 3540733760 |
This book presents comprehensive and authoritative coverage of the wide field of concentrated vortices observed in nature and technique. The methods for research of their kinematics and dynamics are considered. Special attention is paid to the flows with helical symmetry. The authors have described models of vortex structures used for interpretation of experimental data which serve as a ground for development of theoretical and numerical approaches to vortex investigation.
| Author | : 肖兰 |
| Publisher | : 清华大学出版社有限公司 |
| Total Pages | : 190 |
| Release | : 2005 |
| Genre | : Fluid mechanics |
| ISBN | : 9787302102045 |
| Author | : C.F. Barenghi |
| Publisher | : Springer |
| Total Pages | : 459 |
| Release | : 2008-01-11 |
| Genre | : Technology & Engineering |
| ISBN | : 3540455426 |
This book springs from the programme Quantized Vortex Dynamics and Sup- ?uid Turbulence held at the Isaac Newton Institute for Mathematical Sciences (University of Cambridge) in August 2000. What motivated the programme was the recognition that two recent developments have moved the study of qu- tized vorticity, traditionally carried out within the low-temperature physics and condensed-matter physics communities, into a new era. The ?rst development is the increasing contact with classical ?uid dynamics and its ideas and methods. For example, some current experiments with - lium II now deal with very classical issues, such as the measurement of velocity spectra and turbulence decay rates. The evidence from these experiments and many others is that super?uid turbulence and classical turbulence share many features. The challenge is now to explain these similarities and explore the time scales and length scales over which they hold true. The observed classical aspects have also attracted attention to the role played by the ?ow of the normal ?uid, which was somewhat neglected in the past because of the lack of direct ?ow visualization. Increased computing power is also making it possible to study the coupled motion of super?uid vortices and normal ?uids. Another contact with classical physics arises through the interest in the study of super?uid vortex - connections. Reconnections have been studied for some time in the contexts of classical ?uid dynamics and magneto-hydrodynamics (MHD), and it is useful to learn from the experience acquired in other ?elds.
| Author | : James Hiroshi Akao |
| Publisher | : |
| Total Pages | : 412 |
| Release | : 1994 |
| Genre | : |
| ISBN | : |
| Author | : Diana V. Shopova |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 367 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 146154727X |
This volume contains a collection of review articles that are extended versions of invited lectures given at the First Pamporovo Winter Workshop on Cooperative Phe nomena in Condensed Matter held in villa "Orlitza" (7th-15th March 1998, Pamporovo Ski Resort, Bulgaria). Selected research works reported at the Workshop have been published in the Journal of Physical Studies - a new International Journal for research papers in experimental and theoretical physics (Lviv University, Lviv, Ukraine). These reviews are supposed to be status reports and present new insights gained from the rapidly developing research of outstanding problems in condensed matter physics such as structural properties and phase transitions in fullerene crystals, super conductivity ofstrongly interacting electrons in copper oxides, spin polarized Fermi liq uids, chaotic vortex filaments in superfluid turbulent Helium-II, desorption induced by electronic transitions in ionic compounds, fluctuation phenomena in superconductors, and quantum critical phenomena in low dimensional magnets and quantum liquids. We have set the material according to the alphabetic order of authors' names although the high temperature superconductivity seems to be the hard kernel in condensed matter physics. The authors have taken care to present the recent advances in their research in a form which is readable and useful not only to experts in the respective field, but also to young scientists. That is why the lectures include a comprehensive introduction to the matter and also an extended discussion of methodical details.
| Author | : Andrew J. Majda |
| Publisher | : Cambridge University Press |
| Total Pages | : 562 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 9780521639484 |
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.
| Author | : Paul K. Newton |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 430 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 146849290X |
This text is an introduction to current research on the N- vortex problem of fluid mechanics. It describes the Hamiltonian aspects of vortex dynamics as an entry point into the rather large literature on the topic, with exercises at the end of each chapter.
