Vortex Equations
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| Author | : Etienne Sandier |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 327 |
| Release | : 2008-05-14 |
| Genre | : Mathematics |
| ISBN | : 0817645500 |
This book presents the mathematical study of vortices of the two-dimensional Ginzburg-Landau model, an important phenomenological model used to describe superconductivity. The vortices, identified as quantized amounts of vorticity of the superconducting current localized near points, are the objects of many observational and experimental studies, both past and present. The Ginzburg-Landau functionals considered include both the model cases with and without a magnetic field. The book acts a guide to the various branches of Ginzburg-Landau studies, provides context for the study of vortices, and presents a list of open problems in the field.
| Author | : Christopher R. Anderson |
| Publisher | : Springer |
| Total Pages | : 150 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540460349 |
| Author | : Robert C. Costen |
| Publisher | : |
| Total Pages | : 76 |
| Release | : 1970 |
| Genre | : Winds |
| ISBN | : |
A new equation is derived for the motion of vorticity in a general fluid, including the effects of viscosity, compressibility, nonhomogeneity, and nonconservative forces. The equation holds, in particular, for vortices which may not move with the fluid. A linearized form of this equation is applied to tornado cyclones and to the twin tornado of April 11, 1965, near Elkhart, Indiana. It is shown that the displacement of tornado cyclones to the right of the mean tropospheric winds may be accounted for by the upward efflux of fluid from the cyclone into the jet stream. Also, the retarded revolution rate of the twin tornado may be due in part to an attractive "buoyancy" force acting on the partially rarefied cores of the pair.
| Author | : Georges-Henri Cottet |
| Publisher | : Cambridge University Press |
| Total Pages | : 0 |
| Release | : 2008-04-24 |
| Genre | : Science |
| ISBN | : 9780521061704 |
Vortex methods have matured in recent years, offering an interesting alternative to finite difference and spectral methods for high resolution numerical solutions of the Navier Stokes equations. In the past three decades, research into the numerical analysis aspects of vortex methods has provided a solid mathematical background for understanding the accuracy and stability of the method. At the same time vortex methods retain their appealing physical character, which was the motivation for their introduction. This book presents and analyzes vortex methods as a tool for the direct numerical simulation of impressible viscous flows. It will interest graduate students and researchers in numerical analysis and fluid mechanics and also serve as an ideal textbook for courses in fluid dynamics.
| Author | : Ivan K. Lifanov |
| Publisher | : VSP |
| Total Pages | : 494 |
| Release | : 1996 |
| Genre | : Mathematics |
| ISBN | : 9789067642071 |
This monograph is divided into five parts and opens with elements of the theory of singular integral equation solutions in the class of absolutely integrable and non-integrable functions. The second part deals with elements of potential theory for the Helmholtz equation, especially with the reduction of Dirichlet and Neumann problems for Laplace and Helmholtz equations to singular integral equations. Part three contains methods of calculation for different one-dimensional and two-dimensional singular integrals. In this part, quadrature formulas of discrete vortex pair type in the plane case and closed vortex frame type in the spatial case for singular integrals are described for the first time. These quadrature formulas are applied to numerical solutions of singular integral equations of the 1st and 2nd kind with constant and variable coefficients, in part four of the book. Finally, discrete mathematical models of some problems in aerodynamics, electrodynamics and elasticity theory are given.
| Author | : Karl E. Gustafson |
| Publisher | : SIAM |
| Total Pages | : 226 |
| Release | : 1991-01-01 |
| Genre | : Science |
| ISBN | : 0898712580 |
Vortex methods have emerged as a new class of powerful numerical techniques to analyze and compute vortex motion. This book addresses the theoretical, numerical, computational, and physical aspects of vortex methods and vortex motion.
| 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 | : Alexandre J. Chorin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 176 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1468403648 |
Mathematical Introduction to Fluid Mechanics presents some selected highlights of currently interesting topics in fluid mechanics in a compact form, as well as providing a concise and appealing exposition of the basic theory of fluid mechanics. The first chapter contains an elementary derivation of the equations, and the concept of vorticity is introduced. The second chapter contains a discussion of potential flow, vortex motion, and boundary layers. A construction of boundary layers using vortex sheets and random walks is presented. Chapter 3 contains an analysis of one-dimensional gas flow from a mildly modern point of view. Weak solution, Riemann problems, Glimm's scheme, and combustion waves are covered.
| Author | : David E. Loper |
| Publisher | : Cambridge University Press |
| Total Pages | : 521 |
| Release | : 2017-10-26 |
| Genre | : Science |
| ISBN | : 1107186196 |
This book is a unified presentation of waves and flows occurring in the atmosphere, oceans, rivers, volcanoes and the mantle, for graduate students and researchers.
| Author | : Boris N. Apanasov |
| Publisher | : Walter de Gruyter |
| Total Pages | : 361 |
| Release | : 2011-06-24 |
| Genre | : Mathematics |
| ISBN | : 3110805057 |
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
