Continuous Symmetry Measure vs Voronoi Entropy of Droplet Clusters

Mark Frenkel; Alexander A. Fedorets; Leonid A. Dombrovsky; Michael Nosonovsky; Irina Legchenkova; Edward Bormashenko

doi:10.1021/acs.jpcc.0c10384

Continuous Symmetry Measure vs Voronoi Entropy of Droplet Clusters

Mark Frenkel, Alexander A. Fedorets, Leonid A. Dombrovsky, Michael Nosonovsky, Irina Legchenkova, Edward Bormashenko

Department of Chemical Engineering

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

Symmetry and orderliness of two-dimensional (2D) levitating microdroplet clusters are quantified with the Voronoi entropy (VE) and the continuous symmetry measure (CSM). The time evolution of both VE and CSM is investigated. To compare the correlation between the two measures of orderliness, the Pearson correlation coefficient (PCC) was calculated. The maximum correlation between the VE and CSM was found for clusters containing the number of droplets enabling the formation of hexagons, i.e., droplet clusters possessing 6-fold symmetry. In other cases, the maxima and minima of the VE and CSM are not always well correlated; moreover, in certain cases, maxima of the CSM may correspond to the minima of the VE. Symmetry and orderliness of 2D patterns could not be quantified with a single mathematical measure.

Original language	English
Pages (from-to)	2431-2436
Number of pages	6
Journal	Journal of Physical Chemistry C
Volume	125
Issue number	4
DOIs	https://doi.org/10.1021/acs.jpcc.0c10384
State	Published - 4 Feb 2021

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abstract = "Symmetry and orderliness of two-dimensional (2D) levitating microdroplet clusters are quantified with the Voronoi entropy (VE) and the continuous symmetry measure (CSM). The time evolution of both VE and CSM is investigated. To compare the correlation between the two measures of orderliness, the Pearson correlation coefficient (PCC) was calculated. The maximum correlation between the VE and CSM was found for clusters containing the number of droplets enabling the formation of hexagons, i.e., droplet clusters possessing 6-fold symmetry. In other cases, the maxima and minima of the VE and CSM are not always well correlated; moreover, in certain cases, maxima of the CSM may correspond to the minima of the VE. Symmetry and orderliness of 2D patterns could not be quantified with a single mathematical measure.",

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T1 - Continuous Symmetry Measure vs Voronoi Entropy of Droplet Clusters

AU - Frenkel, Mark

AU - Fedorets, Alexander A.

AU - Dombrovsky, Leonid A.

AU - Nosonovsky, Michael

AU - Legchenkova, Irina

AU - Bormashenko, Edward

PY - 2021/2/4

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AB - Symmetry and orderliness of two-dimensional (2D) levitating microdroplet clusters are quantified with the Voronoi entropy (VE) and the continuous symmetry measure (CSM). The time evolution of both VE and CSM is investigated. To compare the correlation between the two measures of orderliness, the Pearson correlation coefficient (PCC) was calculated. The maximum correlation between the VE and CSM was found for clusters containing the number of droplets enabling the formation of hexagons, i.e., droplet clusters possessing 6-fold symmetry. In other cases, the maxima and minima of the VE and CSM are not always well correlated; moreover, in certain cases, maxima of the CSM may correspond to the minima of the VE. Symmetry and orderliness of 2D patterns could not be quantified with a single mathematical measure.

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Continuous Symmetry Measure vs Voronoi Entropy of Droplet Clusters

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