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

Ariel University

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

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

All Science Journal Classification (ASJC) codes

Electronic, Optical and Magnetic Materials
General Energy
Physical and Theoretical Chemistry
Surfaces, Coatings and Films

Access to Document

10.1021/acs.jpcc.0c10384

Cite this

@article{3d1b6196c6344f1dac9ee50b6bc44393,

title = "Continuous Symmetry Measure vs Voronoi Entropy of Droplet Clusters",

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.",

author = "Mark Frenkel and Fedorets, \{Alexander A.\} and Dombrovsky, \{Leonid A.\} and Michael Nosonovsky and Irina Legchenkova and Edward Bormashenko",

note = "Publisher Copyright: {\textcopyright} 2021 American Chemical Society.",

year = "2021",

month = feb,

day = "4",

doi = "10.1021/acs.jpcc.0c10384",

language = "الإنجليزيّة",

volume = "125",

pages = "2431--2436",

journal = "Journal of Physical chemistry c",

issn = "1932-7447",

publisher = "American Chemical Society",

number = "4",

}

TY - JOUR

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

Y1 - 2021/2/4

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=85100626695&partnerID=8YFLogxK

U2 - 10.1021/acs.jpcc.0c10384

DO - 10.1021/acs.jpcc.0c10384

M3 - مقالة

SN - 1932-7447

VL - 125

SP - 2431

EP - 2436

JO - Journal of Physical chemistry c

JF - Journal of Physical chemistry c

IS - 4

ER -

Continuous Symmetry Measure vs Voronoi Entropy of Droplet Clusters

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this