Solutions of Ultrahyperbolic Differential Equations 2 × 2 and Their Application to the Description of Pole Figures
https://doi.org/10.56304/S2304487X21030056
Abstract
The theory of solving ultrahyperbolic differential equations is poorly developed, since it is believed that the problems associated with their solution do not occur in practice. However, it was found that in quantitative texture analysis, the pole figures measured experimentally by X-ray or neutron methods, depending on the choice of the crystallographic direction in R3, satisfy the ultrahyperbolic equation 2 × 2. Solutions of ultrahyperbolic differential equations combine the properties of both hyperbolic and elliptic equations. The direct application of solutions of ultrahyperbolic differential equations to the description of pole figures contains an additional complexity, which consists in the fact that a pole figure is the sum of solutions of two equations that depend on different independent variables. This is due to a special approach to the crystallographic directions in the X-ray experiment. In this paper, we analytically and numerically investigate the class of solutions of the ultrahyperbolic equations 2 × 2, and calculate some pole figures for them. The solutions found can be used as model functions for calculating experimental pole figures in quantitative texture analysis.
About the Authors
E. A. Fedotov
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
115409
Moscow
T. I. Savyolova
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
115409
Moscow
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Review
For citations:
Fedotov E.A., Savyolova T.I. Solutions of Ultrahyperbolic Differential Equations 2 × 2 and Their Application to the Description of Pole Figures. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2021;10(3):253-259. (In Russ.) https://doi.org/10.56304/S2304487X21030056
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