Abacs approximating the product-moment correlation for both explicit and implicit selection are presented. These abacs give accuracy to within .01 of the corresponding analytic estimate.

We discuss our current research focus on photovoltaic (PV) informatics, which is dedicated to functionality enhancement of solar materials through data management and data mining-aided, integrated computational materials engineering (ICME) for rapid screening and identification of multi-scale processing/structure/property/performance relationships. Our current PV informatics research ranges from transparent conducting oxides (TCO) to solar absorber materials. As a test bed, we report on examples of our current data management system for PV research and advanced data mining to improve the performance of solar cells such as CuInxGa1-xSe2 (CIGS) aiming at low-cost and high-rate processes. For the PV data management, we show recent developments of a strategy for data modeling, collection and aggregation methods, and construction of data interfaces, which enable proper archiving and data handling for data mining. For scientific data mining, the value of high-dimensional visualizations and non-linear dimensionality reduction is demonstrated to quantitatively assess how process conditions or properties are interconnected in the context of the development of Al-doped ZnO (AZO) thin films as the TCO layers for CIGS devices. Such relationships between processing and property of TCOs lead to optimal process design toward enhanced performance of CIGS cells/devices.

The purpose of this paper is to accelerate the pace of material discovery processes by systematically visualizing the huge search space that conventionally needs to be explored. To this end, we demonstrate not only the use of empirical- or crystal chemistry-based physical intuition for decision-making, but also to utilize knowledge-based data mining methodologies in the context of finding p-type delafossite transparent conducting oxides (TCOs). We report on examples using high-dimensional visualizations such as radial visualization combined with machine learning algorithms such as k-nearest neighbor algorithm (k-NN) to better define and visualize the search space (i.e. structure maps) of functional materials design. The vital role of search space generated from these approaches is discussed in the context of crystal chemistry of delafossite crystal structure.

Most theoretical and computational studies of turbulence in Navier—Stokes fluids and/or guiding-centre plasmas have been carried out in the presence of spatially periodic boundary conditions. In view of the frequently reproduced result that two-dimensional and/or MHD decaying turbulence leads to structures comparable in length scale to a box dimension, it is natural to ask if periodic boundary conditions are an adequate representation of any physical situation. Here, we study, computationally, the decay of two-dimensional turbulence in a Navier—Stokes fluid or guiding-centre plasma in the presence of circular no-slip rigid walls. The method is wholly spectral, and relies on a Galerkin approximation by a set of functions that obey two boundary conditions at the wall radius (analogues of the Chandrasekhar— Reid functions). It is possible to explore Reynolds numbers up to the order of 1250, based on an RMS velocity and a box radius. It is found that decaying turbulence is altered significantly by the no-slip boundaries. First, strong boundary layers serve as sources of vorticity and enstrophy and enhance the early-time energy decay rate, for a given Reynolds number, well above the periodic boundary condition values. More importantly, angular momentum turns out to be an even more slowly decaying ideal invariant than energy, and to a considerable extent governs the dynamics of the decay. Angular momentum must be taken into account, for example, in order to achieve quantitative agreeement with the predicition of maximum entropy, or ‘most probable’, states. These are predicitions of conditions that are established after several eddy turnover times but before the energy has decayed away. Angular momentum will cascade to lower azimuthal mode numbers, even if absent there initially, and the angular momentum modal spectrum is eventually dominated by the lowest mode available. When no initial angular momentum is present, no behaviour that suggests the likelihood of inverse cascades is observed.