19,429 research outputs found

    Beyond the local approximation to exchange and correlation: the role of the Laplacian of the density in the energy density of Si

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    We model the exchange-correlation (XC) energy density of the Si crystal and atom as calculated by variational Monte Carlo (VMC) methods with a gradient analysis beyond the local density approximation (LDA). We find the Laplacian of the density to be an excellent predictor of the discrepancy between VMC and LDA energy densities in each system. A simple Laplacian-based correction to the LDA energy density is developed by means of a least square fit to the VMC XC energy density for the crystal, which fits the homogeneous electron gas and Si atom without further effort.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let

    Inflectional loci of scrolls

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    Let XāŠ‚PNX\subset \mathbb P^N be a scroll over a smooth curve CC and let \L=\mathcal O_{\mathbb P^N}(1)|_X denote the hyperplane bundle. The special geometry of XX implies that some sheaves related to the principal part bundles of \L are locally free. The inflectional loci of XX can be expressed in terms of these sheaves, leading to explicit formulas for the cohomology classes of the loci. The formulas imply that the only uninflected scrolls are the balanced rational normal scrolls.Comment: 9 pages, improved version. Accepted in Mathematische Zeitschrif
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