Texture, Stress, and Microstructure

Texture, Stress, and Microstructure / 1995 / Article

Open Access

Volume 23 |Article ID 709013 | https://doi.org/10.1155/TSM.23.185

T. I. Savyolova, "Calculation of Domains of Dependence for Pole Figures With an Ultrahyperbolic Differential Equation", Texture, Stress, and Microstructure, vol. 23, Article ID 709013, 15 pages, 1995. https://doi.org/10.1155/TSM.23.185

Calculation of Domains of Dependence for Pole Figures With an Ultrahyperbolic Differential Equation

Received11 Nov 1993
Accepted28 Sep 1994

Abstract

X-ray and neutron methods of texture investigation are used to get experimental pole figures (PF) of polcrystalline samples and geological materials (Bunge, 1982). Usually several PF are used, 1–4 for polycrystalline samples with cubic, hexagonal lattice symmetry (copper, iron, beryllium...), 6–19 for low-symmetry materials of geological samples (quartz, biotite...). Pole figures are the sum of solutions of two ultrahyperbolic equations (Savyolova, 1982). If the solutions of ultrahyperbolic equations are known in some domains we can determine them uniquely in other domains using the Asgeirsson's theorem (Courant, 1962) and their generalizations by ultra-Lorentz transformations. We get the domains of dependence of pole figures and the methods of continuations of solutions of ultrahyperbolic equations.

Copyright © 1995 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


More related articles

 PDF Download Citation Citation
 Order printed copiesOrder
Views25
Downloads0
Citations

We are committed to sharing findings related to COVID-19 as quickly as possible. We will be providing unlimited waivers of publication charges for accepted research articles as well as case reports and case series related to COVID-19. Review articles are excluded from this waiver policy. Sign up here as a reviewer to help fast-track new submissions.