Investigating the micromechanics of polycrystalline materials using high-energy X-ray diffraction

Quantifying the state of materials and understanding their micromechanical behavior are ever more important for designing and building efficient, high-performance machines. High-energy synchrotron radiation is an attractive nondestructive tool for investigating the state and the micromechanical behavior of polycrystalline structural alloys. In this discussion, two high energy X-ray experimental techniques that are available at Sector 1 of the Advanced Photon Source will be presented. Wide angle X-ray scattering (WAXS) technique is used to measure orientation dependent quantities such as crystallographic texture or stress orientation distribution function. High-energy diffraction microscopy (HEDM) technique is a suite of experiments where orientation, strain, and position of individual grains in a polycrystalline sample can be measured

kk-positivity and Schmidt number under orthogonal group symmetries

In this paper, we study $k$-positivity and Schmidt number under standard orthogonal group symmetries. The Schmidt number is a widely used measure of quantum entanglement in quantum information theory. First of all, we exhibit a complete characterization of all $k$-positive orthogonally covariant maps. This generalizes the earlier results in [Tom85]. Then, we optimize some averaging techniques to establish duality relations between orthogonally covariant maps and orthogonally invariant operators. This new framework enables us to effectively compute the Schmidt numbers of all orthogonally invariant quantum states

Generalized gravity model for human migration

The gravity model (GM) analogous to Newton's law of universal gravitation has successfully described the flow between different spatial regions, such as human migration, traffic flows, international economic trades, etc. This simple but powerful approach relies only on the 'mass' factor represented by the scale of the regions and the 'geometrical' factor represented by the geographical distance. However, when the population has a subpopulation structure distinguished by different attributes, the estimation of the flow solely from the coarse-grained geographical factors in the GM causes the loss of differential geographical information for each attribute. To exploit the full information contained in the geographical information of subpopulation structure, we generalize the GM for population flow by explicitly harnessing the subpopulation properties characterized by both attributes and geography. As a concrete example, we examine the marriage patterns between the bride and the groom clans of Korea in the past. By exploiting more refined geographical and clan information, our generalized GM properly describes the real data, a part of which could not be explained by the conventional GM. Therefore, we would like to emphasize the necessity of using our generalized version of the GM, when the information on such nongeographical subpopulation structures is available.Comment: 14 pages, 6 figures, 2 table