2,159 research outputs found
An Eulerian projection method for quasi-static elastoplasticity
A well-established numerical approach to solve the Navier--Stokes equations
for incompressible fluids is Chorin's projection method, whereby the fluid
velocity is explicitly updated, and then an elliptic problem for the pressure
is solved, which is used to orthogonally project the velocity field to maintain
the incompressibility constraint. In this paper, we develop a mathematical
correspondence between Newtonian fluids in the incompressible limit and
hypo-elastoplastic solids in the slow, quasi-static limit. Using this
correspondence, we formulate a new fixed-grid, Eulerian numerical method for
simulating quasi-static hypo-elastoplastic solids, whereby the stress is
explicitly updated, and then an elliptic problem for the velocity is solved,
which is used to orthogonally project the stress to maintain the
quasi-staticity constraint. We develop a finite-difference implementation of
the method and apply it to an elasto-viscoplastic model of a bulk metallic
glass based on the shear transformation zone theory. We show that in a
two-dimensional plane strain simple shear simulation, the method is in
quantitative agreement with an explicit method. Like the fluid projection
method, it is efficient and numerically robust, making it practical for a wide
variety of applications. We also demonstrate that the method can be extended to
simulate objects with evolving boundaries. We highlight a number of
correspondences between incompressible fluid mechanics and quasi-static
elastoplasticity, creating possibilities for translating other numerical
methods between the two classes of physical problems.Comment: 49 pages, 20 figure
Applying machine learning methods for characterization of hexagonal prisms from their 2D scattering patterns – an investigation using modelled scattering data
This document is the Accepted Manuscript version of the following article: Emmanuel Oluwatobi Salawu, Evelyn Hesse, Chris Stopford, Neil Davey, and Yi Sun, 'Applying machine learning methods for characterization of hexagonal prisms from their 2D scattering patterns – an investigation using modelled scattering data', Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 201, pp. 115-127, first published online 5 July 2017. Under embargo. Embargo end date: 5 July 2019. The Version of Record is available online at doi: https://doi.org/10.1016/j.jqsrt.2017.07.001. © 2017 Elsevier Ltd. All rights reserved.Better understanding and characterization of cloud particles, whose properties and distributions affect climate and weather, are essential for the understanding of present climate and climate change. Since imaging cloud probes have limitations of optical resolution, especially for small particles (with diameter < 25 μm), instruments like the Small Ice Detector (SID) probes, which capture high-resolution spatial light scattering patterns from individual particles down to 1 μm in size, have been developed. In this work, we have proposed a method using Machine Learning techniques to estimate simulated particles’ orientation-averaged projected sizes (PAD) and aspect ratio from their 2D scattering patterns. The two-dimensional light scattering patterns (2DLSP) of hexagonal prisms are computed using the Ray Tracing with Diffraction on Facets (RTDF) model. The 2DLSP cover the same angular range as the SID probes. We generated 2DLSP for 162 hexagonal prisms at 133 orientations for each. In a first step, the 2DLSP were transformed into rotation-invariant Zernike moments (ZMs), which are particularly suitable for analyses of pattern symmetry. Then we used ZMs, summed intensities, and root mean square contrast as inputs to the advanced Machine Learning methods. We created one random forests classifier for predicting prism orientation, 133 orientation-specific (OS) support vector classification models for predicting the prism aspect-ratios, 133 OS support vector regression models for estimating prism sizes, and another 133 OS Support Vector Regression (SVR) models for estimating the size PADs. We have achieved a high accuracy of 0.99 in predicting prism aspect ratios, and a low value of normalized mean square error of 0.004 for estimating the particle’s size and size PADs.Peer reviewe
Metallic Icosahedron Phase of Sodium at Terapascal Pressures
Alkali metals exhibit unexpected structures and electronic behavior at high
pressures. Compression of metallic sodium (Na) to 200 GPa leads to the
stability of a wide-band-gap insulator with the double hexagonal hP4 structure.
Post-hP4 structures remain unexplored, but they are important for addressing
the question of the pressure at which Na reverts to a metal. Here we report the
reentrant metallicity of Na at the very high pressure of 15.5 terapascal (TPa),
predicted using first-principles structure searching simulations. Na is
therefore insulating over the large pressure range of 0.2-15.5 TPa. Unusually,
Na adopts an oP8 structure at pressures of 117-125 GPa, and the same oP8
structure at 1.75-15.5 TPa. Metallization of Na occurs on formation of a stable
and striking body-centered cubic cI24 electride structure consisting of Na12
icosahedra, each housing at its center about one electron which is not
associated with any Na ions.Comment: 5 pages, 4 figures, PRL (2015
Gene selection algorithm by combining reliefF and mRMR
Background: Gene expression data usually contains a large number of genes, but a small number of samples. Feature selection for gene expression data aims at finding a set of genes that best discriminate biological samples of different types. In this paper, we present a two-stage selection algorithm by combining ReliefF and mRMR: In the first stage, ReliefF is applied to find a candidate gene set; In the second stage, mRMR method is applied to directly and explicitly reduce redundancy for selecting a compact yet effective gene subset from the candidate set. Results: We perform comprehensive experiments to compare the mRMR-ReliefF selection algorithm with ReliefF, mRMR and other feature selection methods using two classifiers as SVM and Naive Bayes, on seven different datasets. And we also provide all source codes and datasets for sharing with others. Conclusion: The experimental results show that the mRMR-ReliefF gene selection algorithm is very effective
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