Groupoid of orientational variants

Groupoid of orientational variants.

Daughter crystals in orientation relationship with a parent crystal are called variants. They can be created by a structural phase transition (Landau or reconstructive), by twinning or by precipitation. Internal and external classes of transformations defined from the point groups of the parent and daughter phases and from a transformation matrix allow the orientations of the distinct variants ...

The Monodromy Groupoid of a Lie Groupoid

R esum e: Nous d emontrons que, sous des circomstances g en erales, l'union disjoint des couvertes universales des etoiles d'un groupo de de Lie admet le structure d'un groupo de de Lie auquel que le projection a une propri et e de monodromie sur les extensions des morphismes emousse. Ca compl etes une conte d etailles des r esultats annonc es par J. Pradines. Introduction The notion of monodro...

GenOVa: a computer program to generate orientational variants

A computer program called GenOVa, written in Python, calculates the orientational variants, the operators (special types of misorientations between variants) and the composition table associated with a groupoid structure. The variants can be represented by three-dimensional shapes or by pole figures.

Groupoid of Equational Proofs

An equational presentation P = h ; V; E i induces a graph G P of terms and equations, while proof gures in P induces an -algebra A P on groupoids. Although the construction of A P is quite syntactic, it is not free over G P . In order to make the meaning of freeness precise, we introduce a notion of -graph, and show that A P is freely generated by the -graph G P induced by P . Incidentally, thi...

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