Spherical Harmonics In P Dimensions

Author: Costas Efthimiou
Publisher: World Scientific
ISBN: 981459671X
Size: 53.87 MB
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Spherical Harmonics In P Dimensions from the Author: Costas Efthimiou. The current book makes several useful topics from the theory of special functions, in particular the theory of spherical harmonics and Legendre polynomials in arbitrary dimensions, available to undergraduates studying physics or mathematics. With this audience in mind, nearly all details of the calculations and proofs are written out, and extensive background material is covered before exploring the main subject matter. Contents:Introduction and MotivationWorking in p DimensionsOrthogonal PolynomialsSpherical Harmonics in p DimensionsSolutions to Problems Readership: Undergraduate and graduate students in mathematical physics and differential equations. Key Features:Accessible to everyone (including undergraduate students who have some knowledge in mathematics)Presents a topic that, although well-studied, is not widely disseminated in booksSolutions to all end-of-chapter problems with all the necessary details are given in the final chapter of the bookKeywords:Spherical Harmonics;Special Functions;Mathematical Physics;Green's Functions;Legendre Polynomials

The Functions Of Mathematical Physics

Author: Harry Hochstadt
Publisher: Courier Corporation
ISBN: 0486168786
Size: 72.93 MB
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The Functions Of Mathematical Physics from the Author: Harry Hochstadt. Comprehensive text provides a detailed treatment of orthogonal polynomials, principal properties of the gamma function, hypergeometric functions, Legendre functions, confluent hypergeometric functions, and Hill's equation.

Sdma For Multipath Wireless Channels

Author: Igor P. Kovalyov
Publisher: Springer Science & Business Media
ISBN: 9783540402251
Size: 10.64 MB
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Sdma For Multipath Wireless Channels from the Author: Igor P. Kovalyov. Space Division Multiple Access (SDMA) is one of the most promising methods in solving the capacity problem of wireless communication systems. In addition to creating more efficient SDMA algorithms it is vital to determine and understand the theoretical limit of performance improvement. The greatest challenge is extending Shannon’s channel capacity equation to cover the wireless channels that use spatial signal processing. This book defines formulas which can be used to evaluate the limit capacity of multipath wireless channels in a particular receiving region with size limitation. It also contains charts with optimum numbers of space subchannels and limit capacities related to radio channel parameters. The book also investigates stochastic models for 2-D and 3-D multipath random radio channels. The non-ray method for building a stochastic model, based on spherical harmonics, is presented here for the first time.

Electrical Properties Of The Earth S Mantle

Publisher: BirkhÀuser
ISBN: 3034873735
Size: 55.12 MB
Format: PDF, Mobi
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Electrical Properties Of The Earth S Mantle from the Author: CAMPBELL. Table 1 Earth conductivity profiles Figure File Name Apx. Depth Remarks References 1. Global Models 1939-69 LAPR39 0--1250 global Sq, Dst LAHIRI and PRICE, 1939; PRICE, 1973 RIKI50 0--1400 misc. data sources RIKITAKE. 1950; 1966 MCD057 0--2900 LAPR39 + secular change McDoNALD, 1957 CANT60 100--600 see ECKHARDT et a!. , 1963 CANTWELL, 1960 YUKU65 380--1900 ring current YUKUTAKE, 1965 BANK69 0--1700 ring current BANKS, 1969; 1972 2. Global Models 1970--74 BFRS70 100--700 Sq, Dst 27-d variations BERDICHEVSKY et a!. , 1970; 1973 PRKR70 0--3200 rework BANKS, 1969, data PARKER, 1970 SCJA72 0--1000 pulsations, bays, Sq, Dst SCHMUCKER and JANKOWSKI, 1972 BANK72 230--1250 model summary BANKS, 1972 JADY74 0--2951 Sq, 27-d, annual variations JADY, 1974 FAR074 300--1500 with BFRS70 FAINBERG and ROTANOVA, 1974 SCHM74 0--1000 see HAAK, 1980 SCHMUCKER, 1974 DMRB77 0--1450 all available data DMITRIEV et al. , 1977 Global Models 1974-1983 3. PRKN74 60-430 Sq PARKINSON, 1974 DUCM80 0--2900 annual means DUCRUIX et a!. , 1980 ISIK80 320--2020 Sq, Dst, annual, solar cycle ISIKARA, 1980 ACMC81 0--2875 secular impulse ACACHE et a!. , 1980 ROKI82 350--1200 various methods ROKITYANSKY. 1982 JAPA83 0--1200 Dst JADY and PATERSON, 1983 4. Pacific Models LAUN74 0--500 near Calif. ; see DRURY, 1978 LAUNAY, 1975 LARSEN, 1975 LAHA75 0--800 Hawaii 7-1350 FILL80 NE Pacific FILLOUX, 1980 LAW and GREENHOUSE, LWGR81 0--200 Juan de Fuca 1981 0--250 Juan de Fuca OLDENBURG et a!. , 1984 OLJA84 OLCA84 0-250 near Calif. OLDENBURG et al. , 1984 OLNC84 0--250 N. cent. Pacific OLDENBURG et ai.

Zeitschrift Fur Naturforschung

Author: Max-Planck-Gesellschaft zur Förderung der Wissenschaften
Size: 55.90 MB
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Zeitschrift Fur Naturforschung from the Author: Max-Planck-Gesellschaft zur Förderung der Wissenschaften.

Fundamentals Of Amorphous Solids

Author: Zbigniew H. Stachurski
Publisher: John Wiley & Sons
ISBN: 3527682198
Size: 12.58 MB
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Fundamentals Of Amorphous Solids from the Author: Zbigniew H. Stachurski. Long awaited, this textbook fills the gap for convincing concepts to describe amorphous solids. Adopting a unique approach, the author develops a framework that lays the foundations for a theory of amorphousness. He unravels the scientific mysteries surrounding the topic, replacing rather vague notions of amorphous materials as disordered crystalline solids with the well-founded concept of ideal amorphous solids. A classification of amorphous materials into inorganic glasses, organic glasses, glassy metallic alloys, and thin films sets the scene for the development of the model of ideal amorphous solids, based on topology- and statistics-governed rules of three-dimensional sphere packing, which leads to structures with no short, mid or long-range order. This general model is then concretized to the description of specific compounds in the four fundamental classes of amorphous solids, as well as amorphous polyethylene and poly(methyl)methacrylate, emphasizing its versatility and descriptive power. Finally, he includes example applications to indicate the abundance of amorphous materials in modern-day technology, thus illustrating the importance of a better understanding of their structure and properties. Equally ideal as supplementary reading in courses on crystallography, mineralogy, solid state physics, and materials science where amorphous materials have played only a minor role until now.

Spherical Harmonics Methods For Thermal Radiation Transport

Author: Ryan G. McClarren
Size: 11.29 MB
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Spherical Harmonics Methods For Thermal Radiation Transport from the Author: Ryan G. McClarren. An implicit, spherical harmonic (Pn) method for solving thermal transport problems is developed. The method uses a high resolution Riemann solver to produce an upwinded discretization. The high resolution scheme introduces nonlinearities to the radiation transport operator to avoid the creation of artificial oscillations in the solution. By using a minmod limiter a quasi-linear approach to solving this nonlinear system of equations is developed. Through analysis and numerical results it is shown that the quasi-linear approach does suppress artificial oscillations and gives better than first order accuracy and is less computationally demanding than a fully nonlinear solve. The time integration methods considered are the backward Euler method and a high resolution time integration method. Also, reflecting boundary conditions for the Pn equations in three-dimensions are presented. It is shown that the standard Riemann solver is not robust in the diffusion limit. A fix is suggested that scales out the dissipation added by the Riemann solver as spatial cells become optically thick. The Green's function for the one-dimensional P 1 thermal transport equations with Cv ∝ T3 is derived. The Green's function is used to create the P1 solution to a common benchmark and to a problem of an infinite, pulsed line source. The implicit method was able to produce robust results to thermal transport problems in one and two dimensions. The implicit approach allowed the numerical method to take times steps on the longer material energy time scale rather than the speed of light time scale. In two dimensional problems the Pn solutions contained negative radiation energy densities. These negatives caused the material temperature to become negative as well. The free-streaming limit of the Pn equations is explored and it is shown why in transient problems in multiple-dimensions the Pn solutions can have negative energy densities.

Geoid And Its Geophysical Interpretations

Author: Mr. Petr Vanicek
Publisher: CRC Press
ISBN: 9780849342271
Size: 24.80 MB
Format: PDF
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Geoid And Its Geophysical Interpretations from the Author: Mr. Petr Vanicek. Geoid and its Geophysical Interpretations explains how an accurate geoid can be constructed and used for a variety of applied and theoretical geophysical purposes. The book discusses existing techniques for geoid computation, recently developed mathematical and computational tools designed for applications, and various interpretations. Principles and results are well illustrated. This book will be an excellent reference for geodesists, geophysicists, geophysical prospectors, oceanographers, and researchers and students in geophysics and geodesy.