Numerical Determination of the Variation Width of Feasible ODFs | Zendy

Helmut Schaeben | Zendy

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Numerical Determination of the Variation Width of Feasible ODFs

Author(s) -

Helmut Schaeben

Publication year - 1992

Publication title -

texture stress and microstructure

Language(s) - English

Resource type - Journals

eISSN - 1687-5400

pISSN - 1687-5397

DOI - 10.1155/tsm.21.55

Subject(s) - projection (relational algebra) , set (abstract data type) , sequence (biology) , variation (astronomy) , orientation (vector space) , simple (philosophy) , mathematics , algorithm , mathematical analysis , mathematical optimization , computer science , geometry , physics , philosophy , epistemology , biology , astrophysics , genetics , programming language

Within all known methods of calculating a model orientation density (odf) from a given set of pole densities (pdfs) the set of all feasible odfs and in particular its associated variation width remained unaccessible up to now. Here, the variation width is mathematically well defined for the continuous and the discrete setting of the fundamental projection equation of texture goniometry. For the discrete case it is shown that it can be numerically determined by a sequence of optimization problems with extremely simple objective functions. The general solution is exemplified for the SANTA FE model data.

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