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Author: Vladimir I. Arnold Publisher: Springer Nature ISBN: 3030742784 Category : Mathematics Languages : en Pages : 455
Book Description
The first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. The book is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry.
Author: Vladimir I. Arnold Publisher: Springer Nature ISBN: 3030742784 Category : Mathematics Languages : en Pages : 455
Book Description
The first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. The book is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry.
Author: Vladimir I. Arnold Publisher: Springer Science & Business Media ISBN: 0387225897 Category : Mathematics Languages : en Pages : 376
Book Description
The first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. The book is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry.
Author: Vladimir I. Arnold Publisher: Springer Science & Business Media ISBN: 038794947X Category : Mathematics Languages : en Pages : 385
Book Description
The first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. The book is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry.
Author: V.K. Andreev Publisher: Springer Science & Business Media ISBN: 9780792352150 Category : Mathematics Languages : en Pages : 966
Book Description
It was long ago that group analysis of differential equations became a powerful tool for studying nonlinear equations and boundary value problems. This analysis was especially fruitful in application to the basic equations of mechanics and physics because the invariance principles are already involved in their derivation. It is in no way a coincidence that the equations of hydrodynamics served as the first object for applying the new ideas and methods of group analysis which were developed by 1. V. Ovsyannikov and his school. The authors rank themselves as disciples of the school. The present monograph deals mainly with group-theoretic classification of the equations of hydrodynamics in the presence of planar and rotational symmetry and also with construction of exact solutions and their physical interpretation. It is worth noting that the concept of exact solution to a differential equation is not defined rigorously; different authors understand it in different ways. The concept of exact solution expands along with the progress of mathematics (solu tions in elementary functions, in quadratures, and in special functions; solutions in the form of convergent series with effectively computable terms; solutions whose searching reduces to integrating ordinary differential equations; etc. ). We consider it justifiable to enrich the set of exact solutions with rank one and rank two in variant and partially invariant solutions to the equations of hydrodynamics.
Author: Viktor Grigorʹevich Zvi︠a︡gin Publisher: de Gruyter ISBN: Category : Mathematics Languages : en Pages : 252
Book Description
"In the present book a method for solving evolutionary problems is described. The outline of this method is as follows. The initial-boundary value problem is considered as an operator equation which naturally corresponds to the underlying problem. The involved operator often does not possess good properties, therefore certain approximations of this equation are considered, which result e.g. from smoothing of nonlinear terms. One then studies the solvability of this approximating equation in spaces with better topological properties. For this purpose, one applies the technique of the Leray-Schauder topological degree or its generalizations. The approximating equation has natural properties, which allows to apply various approximating methods for the analysis of this equation. The last step of the method is the passage to the limit in the approximating equation as the approximation parameters tend to zero, and here the solutions of the approximating equation converge to a solution of the original equation (usually in a weaker topology)." "In particular, this method turns out to be useful for those problems of non-Newtonian hydrodynamics where it is hard or impossible to express the deviatoric stress tensor via the velocity vector function explicitly. Here this method is used for the investigation of some models for motion of viscoelastic media. The book contains preliminary material from rheology which is required for understanding the models under consideration."--BOOK JACKET.
Author: Jorgen Fredsoe Publisher: World Scientific ISBN: 981449805X Category : Languages : en Pages : 550
Book Description
This book discusses the subject of wave/current flow around a cylinder, the forces induced on the cylinder by the flow, and the vibration pattern of slender structures in a marine environment.The primary aim of the book is to describe the flow pattern and the resulting load which develops when waves or current meet a cylinder. Attention is paid to the special case of a circular cylinder. The development in the forces is related to the various flow patterns and is discussed in detail. Regular as well as irregular waves are considered, and special cases like wall proximities (pipelines) are also investigated.The book is intended for MSc students with some experience in basic fluid mechanics and for PhD students.
Author: Vladimir Gordin Publisher: CRC Press ISBN: 9789056991647 Category : Mathematics Languages : en Pages : 846
Book Description
The material provides an historical background to forecasting developments as well as introducing recent advances. The book will be of interest to both mathematicians and physicians, the topics covered include equations of dynamical meteorology, first integrals, non-linear stability, well-posedness of boundary problems, non-smooth solutions, parameters and free oscillations, meteorological data processing, methods of approximation and interpolation and numerical methods for forecast modelling.
Author: Vladimir I. Arnold Publisher: Springer Science & Business Media ISBN: 9783540206149 Category : Mathematics Languages : en Pages : 664
Book Description
Vladimir Arnold is one of the most outstanding mathematicians of our time Many of these problems are at the front line of current research
Author: Renzo L. Ricca Publisher: Springer Science & Business Media ISBN: 9781402002076 Category : Science Languages : en Pages : 364
Book Description
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: Renzo L. Ricca Publisher: Springer Science & Business Media ISBN: 9401004463 Category : Science Languages : en Pages : 346
Book Description
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: Vladimir I. Arnold
Author: Vladimir I. Arnold
Author: Vladimir I. Arnold
Author: Vladimir I. Arnold
Author: V.K. Andreev
Author: Viktor Grigorʹevich Zvi︠a︡gin
Author: Jorgen Fredsoe
Author: Vladimir Gordin
Author: Vladimir I. Arnold
Author: Renzo L. Ricca
Author: Renzo L. Ricca