Fixed-orientation equilateral triangle matching of point sets

Given a point set P and a class C of geometric objects, G(C)(P) is a geometric graph with vertex set P such that any two vertices p and q are adjacent if and only if there is some C is an element of C containing both p and q but no other points from P. We study G(del)(P) graphs where del is the class of downward equilateral triangles (i.e., equilateral triangles with one of their sides parallel to the x-axis and the corner opposite to this side below that side). For point sets in general position, these graphs have been shown to be equivalent to half-Theta(6) graphs and TD-Delaunay graphs. The main result in our paper is that for point sets P in general position, G(del)(P) always contains a matching of size at least vertical bar P vertical bar-1/3] and this bound is tight. We also give some structural properties of G(star)(P) graphs, where is the class which contains both upward and downward equilateral triangles. We show that for point sets in general position, the block cut point graph of G(star)(P) is simply a path. Through the equivalence of G(star)(P) graphs with Theta(6) graphs, we also derive that any Theta(6) graph can have at most 5n-11 edges, for point sets in general position. (C) 2013 Elsevier B.V. All rights reserved.

Orientation dependent mechanical properties of commercially pure (cp) titanium

The present investigation is an attempt at correlating the crystallographic orientation and mechanical properties of hexagonal commercially pure titanium (cp-titanium). Annealed cp-titanium sheets are subjected to tensile deformation along the rolling direction, along 45 degrees to the rolling direction and along 90 degrees to the rolling direction respectively. Crystallographic textures and mechanical properties of these cp-titanium samples are investigated in the present study. The hardness of different grains/orientations is estimated through nanoindentation, grain average misorientation, orientation estimated elastic stiffness and Taylor factor measurements. It is observed that the hardness of the grains close to basal orientation is higher compared to non-basal orientations. It is further observed that the estimated bulk mechanical properties of cp-titanium have a direct relationship with the volume fraction of basal grains/orientations. (C) 2014 Elsevier Inc All rights reserved.

Effect of Nb orientation and deformation on the growth of Nb3Sn intermetallic superconductor by bronze technique

The growth of Nb3Sn by bronze technique on single crystals and deformed Nb is studied. The grain boundary diffusion-controlled growth rate is found to be higher for Nb-(0 1 3) than Nb-(0 1 1) because of smaller grain size of Nb3Sn. The difference in grain size is explained with the help of surface energies leading to different nucleation barrier. Significantly finer grains and higher growth rate of the product phase is found for rolled Nb because of available defects acting as potential nucleation sites.