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Spatial prediction of crystalline defects observed in molecular dynamic simulations of plastic damage

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  • Geoffrey Colin L. Peterson
  • Dong Li
  • Brian J. Reich
  • Donald Brenner

Abstract

Molecular dynamic computer simulation is an essential tool in materials science to study atomic properties of materials in extreme environments and guide development of new materials. We propose a statistical analysis to emulate simulation output with the ultimate goal of efficiently approximating the computationally intensive simulation. We compare several spatial regression approaches including conditional autoregression (CAR), discrete wavelets transform (DWT), and principle components analysis (PCA). The methods are applied to simulation of copper atoms with twin wall and dislocation loop defects, under varying tilt tension angles. We find that CAR and DWT yield accurate results but fail to capture extreme defects, yet PCA better captures defect structure.

Suggested Citation

  • Geoffrey Colin L. Peterson & Dong Li & Brian J. Reich & Donald Brenner, 2017. "Spatial prediction of crystalline defects observed in molecular dynamic simulations of plastic damage," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(10), pages 1761-1784, July.
    • Handle: RePEc:taf:japsta:v:44:y:2017:i:10:p:1761-1784
    DOI: 10.1080/02664763.2016.1221915
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    References listed on IDEAS

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    1. Crainiceanu, Ciprian M. & Staicu, Ana-Maria & Di, Chong-Zhi, 2009. "Generalized Multilevel Functional Regression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1550-1561.
    2. Lee, Seonjoo & Shen, Haipeng & Truong, Young & Lewis, Mechelle & Huang, Xuemei, 2011. "Independent Component Analysis Involving Autocorrelated Sources With an Application to Functional Magnetic Resonance Imaging," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1009-1024.
    3. Jeffrey S. Morris & Raymond J. Carroll, 2006. "Wavelet‐based functional mixed models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 179-199, April.
    4. Dayanand Naik & Shantha Rao, 2001. "Analysis of multivariate repeated measures data with a Kronecker product structured covariance matrix," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(1), pages 91-105.
    5. Lin Zhang & Veerabhadran Baladandayuthapani & Hongxiao Zhu & Keith A. Baggerly & Tadeusz Majewski & Bogdan A. Czerniak & Jeffrey S. Morris, 2016. "Functional CAR Models for Large Spatially Correlated Functional Datasets," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 772-786, April.
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