Demagnetizing Factors of the General Ellipsoid
TL;DR: In this paper, the demagnetizing factors of ellipsoids of three different axes are presented, along with supplementary formulas which cover a large number of special cases of ellipses.
Abstract: Charts and tables of the demagnetizing factors of prolate and oblate spheroids are readily available; however, demagnetizing factors of ellipsoids of three different axes are incompletely tabulated and laborious to calculate. This article presents charts and tables which make possible easy determination of the demagnetizing factor for any principal axis of an ellipsoid of any shape. Formulas for the demagnetizing factors of the general ellipsoid are included together with supplementary formulas which cover a large number of special cases.
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TL;DR: In this paper, it is shown that to answer several questions of physical or engineering interest, it is necessary to know only the relatively simple elastic field inside the ellipsoid.
Abstract: It is supposed that a region within an isotropic elastic solid undergoes a spontaneous change of form which, if the surrounding material were absent, would be some prescribed homogeneous deformation. Because of the presence of the surrounding material stresses will be present both inside and outside the region. The resulting elastic field may be found very simply with the help of a sequence of imaginary cutting, straining and welding operations. In particular, if the region is an ellipsoid the strain inside it is uniform and may be expressed in terms of tabulated elliptic integrals. In this case a further problem may be solved. An ellipsoidal region in an infinite medium has elastic constants different from those of the rest of the material; how does the presence of this inhomogeneity disturb an applied stress-field uniform at large distances? It is shown that to answer several questions of physical or engineering interest it is necessary to know only the relatively simple elastic field inside the ellipsoid.
11,784 citations
Cites background from "Demagnetizing Factors of the Genera..."
...For the prolate spheroid (b — c<a) we have 2nac2 fa /«2_ , 4 = ^ 2 _ c2) | \ c \ c2 — cosh-1-}, c (3*16) and the remaining quantities may be determined similarly. f Osborn (1945) has given curves for these quantities as functions of b/a and c/a....
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01 Jan 2011TL;DR: In this article, the authors present basic tools for elasticity and Hooke's law, effective media, granular media, flow and diffusion, and fluid effects on wave propagation for wave propagation.
Abstract: Preface 1. Basic tools 2. Elasticity and Hooke's law 3. Seismic wave propagation 4. Effective media 5. Granular media 6. Fluid effects on wave propagation 7. Empirical relations 8. Flow and diffusion 9. Electrical properties Appendices.
2,007 citations
09 Jan 2020
TL;DR: The third edition of the reference book as discussed by the authors has been thoroughly updated while retaining its comprehensive coverage of the fundamental theory, concepts, and laboratory results, and highlights applications in unconventional reservoirs, including water, hydrocarbons, gases, minerals, rocks, ice, magma and methane hydrates.
Abstract: Responding to the latest developments in rock physics research, this popular reference book has been thoroughly updated while retaining its comprehensive coverage of the fundamental theory, concepts, and laboratory results. It brings together the vast literature from the field to address the relationships between geophysical observations and the underlying physical properties of Earth materials - including water, hydrocarbons, gases, minerals, rocks, ice, magma and methane hydrates. This third edition includes expanded coverage of topics such as effective medium models, viscoelasticity, attenuation, anisotropy, electrical-elastic cross relations, and highlights applications in unconventional reservoirs. Appendices have been enhanced with new materials and properties, while worked examples (supplemented by online datasets and MATLAB® codes) enable readers to implement the workflows and models in practice. This significantly revised edition will continue to be the go-to reference for students and researchers interested in rock physics, near-surface geophysics, seismology, and professionals in the oil and gas industries.
1,387 citations
TL;DR: An analytic expression for the magnetometric demagnetizing factors of the general rectangular prism is given in this paper, with special emphasis on the particular case of a square cross section.
Abstract: An analytic expression is given for the magnetometric demagnetizing factors of the general rectangular prism, with special emphasis on the particular case of a square cross section. It is argued that this demagnetizing factor should be used in numerical computations that assume such prisms, when comparing the results with the theoretical study of ellipsoids.
1,067 citations