Papers
- Lazar, E.A., Lu, J., Rycroft, C.H., and Schwartz, D., "Voronoi topology in two dimensions: theory, algorithms, and applications", arXiv, (submitted).
- Worlitzer, V.M., Ariel, G., and Lazar, E.A., "Pair correlation function based on Voronoi topology", arXiv, Phys. Rev. E 108:064115, 2023.
- Askenazi, E.M., Lazar, E.A., and Grinberg, I., "Identification of high-reliability regions of machine learning predictions based on materials chemistry", J. Chem. Inf. Model., 2023.
- Lu, J., Lazar, E.A., and Rycroft, C.H., "An extension to VORO++ for multithreaded computation of Voronoi cells", arXiv, Comput. Phys. Commun. 291:108832, 2023.
- Forrest, R.M., Lazar, E.A., Goel, S., and Bean, J.J., "Quantifying the differences in properties between polycrystals containing planar and curved grain boundaries", Nanofabrication 7, 11-23, 2022.
- Lazar, E.A., Lu, J., and Rycroft, C.H., "Voronoi cell analysis: The shapes of particle systems", arXiv, Am. J. Phys. 90:469, 2022.
- Lazar, E.A. and Shoan, A. "Voronoi chains, blocks, and clusters in perturbed square lattices", arXiv, J. Stat. Mech. 103204, 2020.
- Lazar, E.A., Mason, J.K., MacPherson, R.D. and Srolovitz, D.J., "Distribution of Topological Types in Grain-Growth Microstructures", arXiv, Phys. Rev. Lett. 125:015501, 2020.
- Yoon, T.J., Lazar, E.A., Ha, M.Y., Lee, W.B., and Lee, Y-W., "Topological extension of the isomorph theory based on the Shannon entropy", arXiv, Phys. Rev. E. 100:012118, 2019.
- Yoon, T.J., Lazar, E.A., Ha, M.Y., Lee, W.B., and Lee, Y-W., "Topological generalization of the rigid-nonrigid transition in soft-sphere and hard-sphere fluids", arXiv, Phys. Rev. E. 99:052603, 2019.
- Yoon, T.J., Ha, M.Y., Lazar, E.A., Lee, W.B., and Lee, Y-W., "Topological Characterization of Rigid-Nonrigid Transition across the Frenkel Line", arXiv, J. Phys. Chem. Lett. 9:6524, 2018.
- Lazar, E.A. "VoroTop: Voronoi Cell Topology Visualization and Analysis Toolkit", arXiv, Model. Simul. Mater. Sci. Eng. 26:1, 2017.
- Lazar, E.A. and Srolovitz, D.J. "Topological Analysis of Local Structure in Atomic Systems", preprint, chapter in Statistical Methods for Materials Science: The Data Science of Microstructure Characterization, CRC Press 2019.
- Lutz, F.H., Mason, J.K., Lazar, E.A., and MacPherson, R.D. "Roundness of Grains in Cellular Microstructures", arXiv, Phys. Rev. E. 96:023001, 2017.
- Lazar, E.A. "Classifying Structure in Two-Dimensional Point Sets via Voronoi Topology", unpublished notes.
- Lazar, E.A. and Pemantle, R. "Coarsening in one dimension: invariant and asymptotic states", arXiv, Israel J. Math. 221:1, 2017.
- Leipold, H., Lazar, E.A., Brakke, K.A., and Srolovitz, D.J. "Statistical Topology of Perturbed Two-Dimensional Lattices", arXiv, J. Stat. Mech. P043103, 2016.
- Landweber, P.S., Lazar, E.A., Patel, N. "On fiber diameters of continuous maps", arXiv, Amer. Math. Monthly 123:4, 2016 (see also "A Surprise For Big-Data Analytics").
- Lazar, E.A., Han, J. and Srolovitz, D.J. "A Topological Framework for Local Structure Analysis in Condensed Matter", arXiv, Proc. Natl. Acad. Sci. 112:E5769, 2015.
- Mason, J.K., Lazar, E.A., MacPherson, R.D. and Srolovitz, D.J. "Geometric and topological properties of the canonical grain growth microstructure", arXiv, Phys. Rev. E. 92:063308, 2015.
- Wang, R., Lazar, E.A., Park, H., Millis, A.J., Marianetti, C.A. "Selectively Localized Wannier Functions", arXiv, Phys. Rev. B. 90:165125, 2014.
- Hilhorst, H.J., Lazar, E.A. "Many-faced cells and many-edged faces in 3D Poisson-Voronoi tessellations", arXiv, J. Stat. Mech. 10:P10021, 2014.
- Keller, T., Cutler, B., Lazar, E.A., Yauney, G., Lewis, D.J. "Comparative Grain Topology", Acta Materialia, 66:414, 2014.
- Lazar, E.A., Mason, J.K., MacPherson, R.D. and Srolovitz, D.J. "Statistical topology of three-dimensional Poisson-Voronoi cells and cell boundary networks", arXiv, Phys. Rev. E. 88:063309, 2013.
- Mason, J.K., Lazar, E.A., MacPherson, R.D. and Srolovitz, D.J. "Statistical topology of cellular networks in two and three dimensions", Phys. Rev. E. 86:051128, 2012.
- Lazar, E.A., Mason, J.K., MacPherson, R.D. and Srolovitz, D.J. "Complete topology of cells, grains, and bubbles in three-dimensional microstructures", arXiv, Phys. Rev. Lett. 109:095505, 2012.
- Mason, J.K., Ehrenborg, R. and Lazar, E.A. "A geometric formulation of the Law of Aboav-Weaire in two and three dimensions", J. Phys. A 45:065001, 2012.
- Lazar, E.A., "The Evolution of Cellular Structures via Curvature Flow", Thesis, Princeton University, 2011.
- Lazar, E.A., Mason, J.K., MacPherson, R.D. and Srolovitz, D.J. "A more accurate three-dimensional grain growth algorithm", preprint, Acta Materialia, 59:6837, 2011.
- Lazar, E.A., MacPherson, R.D. and Srolovitz, D.J. "A more accurate two-dimensional grain growth algorithm", preprint, Acta Materialia, 58:364, 2010.
- Lazar, E.A. "Molecular Dynamic Studies in the Fracturing of Metals." Honors Thesis, Yeshiva University, 2005.
- Lazar, E.A. "A Visual Demonstration of the Fundamental Theorem of Calculus", unpublished, 2003.
Software
- VoroTop is a modern set of open-source tools for analyzing structure of spatial point sets in three dimensions. The power of this approach results from its coarse-graining of structural data in a natural configuration space, instead of in the image of this space under a continuous mapping, which has notable theoretical restrictions.
Coauthors and collaborators
Aaron Koolyk, Hebrew University
Amanda Redlich, UMass Lowell
Amir Shoan, Bar-Ilan University
Andrew Millis, Columbia University
Benjamin Matschke, Boston University
Chris Marianetti, Columbia University
Chris Rycroft , University of Wisconsin—Madison
Dan Lewis, Rensselaer Polytechnic Institute
David Srolovitz, The University of Hong Kong
Frank Lutz, Technische Universität Berlin
Gil Ariel, Bar Ilan University
Hannes Leipold, University of Southern California
Henk Hilhorst, Laboratoire de Physique Théorique
Jeremy Mason, University of California, Davis
Jian Han, City University of Hong Kong
Jiayin Lu, Harvard University
Jonathan Bean, University of Cambridge
Amanda Redlich, UMass Lowell
Amir Shoan, Bar-Ilan University
Andrew Millis, Columbia University
Benjamin Matschke, Boston University
Chris Marianetti, Columbia University
Chris Rycroft , University of Wisconsin—Madison
Dan Lewis, Rensselaer Polytechnic Institute
David Srolovitz, The University of Hong Kong
Frank Lutz, Technische Universität Berlin
Gil Ariel, Bar Ilan University
Hannes Leipold, University of Southern California
Henk Hilhorst, Laboratoire de Physique Théorique
Jeremy Mason, University of California, Davis
Jian Han, City University of Hong Kong
Jiayin Lu, Harvard University
Jonathan Bean, University of Cambridge
Ken Brakke, Susquehanna University
Min Young Ha, Seoul National University
Neel Patel, Instituto de Ciencias Matemáticas
Peter Landweber, Rutgers University
Richard Ehrenborg, University of Kentucky
Robert Forrest, University of Cambridge
Robert MacPherson, Institute for Advanced Study
Robin Pemantle, University of Pennsylvania
Runzhi Wang, Columbia University
Shlomo Ta'asan, Carnegie Mellon University
Tae Jun Yoon, Los Alamos National Laboratory
Trevor Keller, National Institute of Standards and Technology
Vasco Worlitzer, Bar Ilan University
Won Bo Lee, Seoul National University
Youn-Woo Lee, Seoul National University
Min Young Ha, Seoul National University
Neel Patel, Instituto de Ciencias Matemáticas
Peter Landweber, Rutgers University
Richard Ehrenborg, University of Kentucky
Robert Forrest, University of Cambridge
Robert MacPherson, Institute for Advanced Study
Robin Pemantle, University of Pennsylvania
Runzhi Wang, Columbia University
Shlomo Ta'asan, Carnegie Mellon University
Tae Jun Yoon, Los Alamos National Laboratory
Trevor Keller, National Institute of Standards and Technology
Vasco Worlitzer, Bar Ilan University
Won Bo Lee, Seoul National University
Youn-Woo Lee, Seoul National University