arXiv subjects

R. Oishi-Tomiyasu

Publications and source records attributed to R. Oishi-Tomiyasu.

3 recordsLinked to original sources

arXiv2024

Packing theory derived from phyllotaxis and products of linear forms 0

\textit{Parastichies} are spiral patterns observed in plants and numerical patterns generated using golden angle method. We generalize this method by using Markoff theory and the theory of product of linear forms, to obtain a theory for packing of Riemannian manifolds of general dimensions $n$ with a locally diagonalizable metric, including the Euclidean spaces. For example, packings in a plane with logarithmic spirals and in a 3D ball (3D analogue of the Vogel spiral) are newly obtained. Using this method, we prove that it is possible to generate almost uniformly distributed point sets on any real analytic Riemannian surfaces in a local sense. We also discuss how to extend the packing to the whole manifold in some special cases including the Vogel spiral. The packing density is bounded below by approximately 0.7 for surfaces and 0.38 for 3-manifolds under the most general assumption.

math.NT↗

arXiv2024

Ideas of lattice-basis reduction theory for error-stable Bravais lattice determination and ab-initio indexing

In ab-initio indexing, for a given diffraction/scattering pattern, the unit-cell parameters and the Miller indices assigned to reflections in the pattern are determined simultaneously. "Ab-initio" means a process performed without any good prior information on the crystal lattice. Newly developed ab-initio indexing software is frequently reported in crystallography. However, it is not widely recognized that use of a Bravais lattice determination method, which is tolerant to experimental errors, can simplify indexing algorithms and increase their success rates. One of the goals of this article is to collect information on the lattice-basis reduction theory and its applications. The main result is Bravais lattice determination algorithm for 2D lattices, along with a mathematical proof that it works even for parameters containing large observational errors. As in our error-stable algorithm for 3D lattices, it uses two lattice-basis reduction methods that seem to be optimal for different symmetries. In indexing, a method for error-stable unit-cell identification is also required to exclude duplicate solutions. We introduce several methods to measure the difference of unit cells known in crystallography and mathematics.

cond-mat.mtrl-sci↗

arXiv2020

Distribution rules of systematic absence and generalized de Wolff figure of merit applied to EBSD ab-initio indexing

For EBSD ab-initio indexing, a new method that adopts several methods originally invented for powder indexing, is reported. Distribution rules of systematic absence and error-stable Bravais lattice determination are used to eliminate negative influence of non-visible bands and erroneous information from visible bands. In addition, generalized versions of the de Wolff figures of merit are proposed as a new sorting criterion for the obtained unit-cell parameters, which can be used in both orientation determination and ab-initio indexing from Kikuchi patterns. Computational results show that the new figures of merit work well, similarly to the original de Wolff $M_n$. Ambiguity of indexing solutions is also pointed out, which happens in particular for low-symmetric cells, and may generate multiple distinct solutions even if very accurate positions of band center lines and the projection center are given.

cond-mat.mtrl-sci↗