Table of Contents
Textures and Microstructures
Volume 23, Issue 3, Pages 185-199

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

MIFI (Moscow Engineering Physical Institute), Kashirskoe Shosse 31, Moscow 115409, Russia

Received 11 November 1993; Accepted 28 September 1994

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.


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.