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Mathematical Modeling of the Orientation Distribution Function by the Vector Method of Quantitative Texture Analysis
Author(s) -
Schaeben H.
Publication year - 1984
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221230204
Subject(s) - uniqueness , orientation (vector space) , function (biology) , computer science , distribution (mathematics) , texture (cosmology) , distribution function , deformation (meteorology) , numerical analysis , algorithm , mathematical analysis , mathematics , geometry , artificial intelligence , image (mathematics) , geology , physics , oceanography , quantum mechanics , evolutionary biology , biology
In contrast to metallurgy, where quantitative methods of texture analysis are frequently used to check for certain types of preferred orientations as generated by well‐defined processes of production, in geosciences the same methods are applied in order to reconstruct the history of deformation the sample has undergone. More detailed, the reproduced orientation distribution function (ODF) should be translated back in terms of deformation processes, which match with the entire geological situation. Within this concept, problems of the uniqueness of the reproduced ODF become essential. As the vector method provides certain advantages in comparison to the harmonic method for applications of texture analysis in geosciences, the numerical procedure of solution involved in it is mathematically analysed with special emphasis laid on problems concerning the non‐uniqueness of the solution provided by the vector method in its original form. Finally, the problem is mathematically restated in a well‐posed form, which leads to both, an improved solution and numerical algorithm.