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
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.
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