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Author: Charles Loewner
Publisher:
ISBN:
Category : Compressibility
Languages : en
Pages : 72
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Author: Charles Loewner
Publisher:
ISBN:
Category : Compressibility
Languages : en
Pages : 72
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Author: Stanford University. Applied Mathematics and Statistics Laboratory
Publisher:
ISBN:
Category :
Languages : en
Pages : 36
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Author: A. Majda
Publisher: Springer Science & Business Media
ISBN: 1461211166
Category : Science
Languages : en
Pages : 167
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Conservation laws arise from the modeling of physical processes through the following three steps: 1) The appropriate physical balance laws are derived for m-phy- t cal quantities, ul""'~ with u = (ul' ... ,u ) and u(x,t) defined m for x = (xl""'~) E RN (N = 1,2, or 3), t > 0 and with the values m u(x,t) lying in an open subset, G, of R , the state space. The state space G arises because physical quantities such as the density or total energy should always be positive; thus the values of u are often con strained to an open set G. 2) The flux functions appearing in these balance laws are idealized through prescribed nonlinear functions, F.(u), mapping G into J j = 1, ..• ,N while source terms are defined by S(u,x,t) with S a given smooth function of these arguments with values in Rm. In parti- lar, the detailed microscopic effects of diffusion and dissipation are ignored. 3) A generalized version of the principle of virtual work is applied (see Antman [1]). The formal result of applying the three steps (1)-(3) is that the m physical quantities u define a weak solution of an m x m system of conservation laws, o I + N(Wt'u + r W ·F.(u) + W·S(u,x,t))dxdt (1.1) R xR j=l Xj J for all W E C~(RN x R+), W(x,t) E Rm.
Author: A. Majda
Publisher: Springer
ISBN: 9780387960371
Category : Science
Languages : en
Pages : 172
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Book Description
Conservation laws arise from the modeling of physical processes through the following three steps: 1) The appropriate physical balance laws are derived for m-phy- t cal quantities, ul""'~ with u = (ul' ... ,u ) and u(x,t) defined m for x = (xl""'~) E RN (N = 1,2, or 3), t > 0 and with the values m u(x,t) lying in an open subset, G, of R , the state space. The state space G arises because physical quantities such as the density or total energy should always be positive; thus the values of u are often con strained to an open set G. 2) The flux functions appearing in these balance laws are idealized through prescribed nonlinear functions, F.(u), mapping G into J j = 1, ..• ,N while source terms are defined by S(u,x,t) with S a given smooth function of these arguments with values in Rm. In parti- lar, the detailed microscopic effects of diffusion and dissipation are ignored. 3) A generalized version of the principle of virtual work is applied (see Antman [1]). The formal result of applying the three steps (1)-(3) is that the m physical quantities u define a weak solution of an m x m system of conservation laws, o I + N(Wt'u + r W ·F.(u) + W·S(u,x,t))dxdt (1.1) R xR j=l Xj J for all W E C~(RN x R+), W(x,t) E Rm.
Author: Alexander Vasil'ev
Publisher: Springer Science & Business Media
ISBN: 331901806X
Category : Mathematics
Languages : en
Pages : 364
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Book Description
This volume highlights the main results of the research performed within the network “Harmonic and Complex Analysis and its Applications” (HCAA), which was a five-year (2007–2012) European Science Foundation Programme intended to explore and to strengthen the bridge between two scientific communities: analysts with broad backgrounds in complex and harmonic analysis and mathematical physics, and specialists in physics and applied sciences. It coordinated actions for advancing harmonic and complex analysis and for expanding its application to challenging scientific problems. Particular topics considered by this Programme included conformal and quasiconformal mappings, potential theory, Banach spaces of analytic functions and their applications to the problems of fluid mechanics, conformal field theory, Hamiltonian and Lagrangian mechanics, and signal processing. This book is a collection of surveys written as a result of activities of the Programme and will be interesting and useful for professionals and novices in analysis and mathematical physics, as well as for graduate students. Browsing the volume, the reader will undoubtedly notice that, as the scope of the Programme is rather broad, there are many interrelations between the various contributions, which can be regarded as different facets of a common theme.
Author: Charles Loewner
Publisher:
ISBN:
Category : Mathematicians
Languages : en
Pages : 540
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Charles Loewner, Professor of Mathematics at Stanford University from 1950 until his death in 1968, was a Visiting Professor at the University of California at Berkeley on five separate occasions. During his 1955 visit to Berkeley he gave a course on continuous groups, and his lectures were reproduced in the form of mimeographed notes. Loewner planned to write a detailed book on continuous groups based on these lecture notes, but the project was still in the formative stage at the time of his death. Since the notes themselves have been out of print for several years, Professor Harley Flanders, Department of Mathematics, Tel Aviv University, and Professor Murray Protter, Department of Mathematics, University of California, Berkeley, have taken this opportunity to revise and correct the original fourteen lectures and make them available in permanent form.Loewner became interested in continuous groups--particularly with respect to possible applications in geometry and analysis--when he studied the three volume work on transformation groups by Sophus Lie. He managed to reconstruct a coherent development of the subject by synthesizing Lie's numerous illustrative examples, many of which appeared only as footnotes. The examples contained in this book are primarily geometric in character and reflect the unique way in which Loewner viewed each of the topics he treated.This book is part of the series "Mathematicians of Our Time, " edited by Professor Gian-Carlo Rota, Department of Mathematics, Massachusetts Institute of Technology."Contents: " Transformation Groups; Similarity; Representations of Groups; Combinations of Representations; Similarity and Reducibility; Representations of Cyclic Groups; Representations of Finite Abelian Groups; Representations of Finite Groups; Characters; Introduction to Differentiable Manifolds; Tensor Calculus on a Manifold; Quantities, Vectors, Tensors; Generation of Quantities by Differentiation; Commutator of Two Covariant Vector Fields; Hurwitz Integration on a Group Manifold; Representation of Compact Groups; Existence of Representations; Characters; Examples; Lie Groups; Infinitesimal Transformation on a Manifold; Infinitesimal Transformations on a Group; Examples; Geometry on the Group Space; Parallelism; First Fundamental Theorem of Lie Groups; Mayer-Lie Systems; The Sufficiency Proof; First Fundamental Theorem, Converse; Second Fundamental Theorem, Converse; Concept of Group Germ; Converse of the Third Fundamental Theorem; The Helmholtz-Lie Problem.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 542
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Author: Miloslav Feistauer
Publisher: Oxford University Press, USA
ISBN: 9780198505884
Category : Computers
Languages : en
Pages : 560
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Book Description
This book is concerned with mathematical and numerical methods for compressible flow. It aims to provide the reader with a sufficiently detailed and extensive, mathematically precise, but comprehensible guide, through a wide spectrum of mathematical and computational methods used in Computational Fluid Dynamics (CFD) for the numerical simulation of compressible flow. Up-to-date techniques applied in the numerical solution of inviscid as well as viscous compressible flow on unstructured meshes are explained, thus allowing the simulation of complex three-dimensional technically relevant problems. Among some of the methods addressed are finite volume methods using approximate Riemann solvers, finite element techniques, such as the streamline diffusion and the discontinuous Galerkin methods, and combined finite volume - finite element schemes. The book gives a complex insight into the numerics of compressible flow, covering the development of numerical schemes and their theoretical mathematical analysis, their verification on test problems and use in solving practical engineering problems. The book will be helpful to specialists coming into contact with CFD - pure and applied mathematicians, aerodynamists, engineers, physicists and natural scientists. It will also be suitable for advanced undergraduate, graduate and postgraduate students of mathematics and technical sciences.
Author:
Publisher:
ISBN:
Category : Electronic journals
Languages : en
Pages : 778
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Book Description
The American Journal of Mathematics publishes research papers and articles of broad appeal covering the major areas of contemporary mathematics.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 40
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