Quantification of ordering in active light driven colloids

Frenkel, Mark; Arya, Pooja; Bormashenko, Edward; Santer, Svetlana

doi:10.1016/j.jcis.2020.10.053

Cited by 13 publications

(17 citation statements)

References 38 publications

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“…Various quantitative measures were introduced in order to quantify "order" in physical systems in mathematical objects. One of the most popular (but not the only) of measures of ordering in 2D sets of points are the Voronoi entropy [4][5][6][7][8][9][10][11][12][13][39][40][41] and the recently introduced and developed continuous measure of symmetry, breaking the binary (YES/NO) approach to symmetry [19][20][21][22][23][24][25][26][27][28][29]. We posed the following question: are the Voronoi entropy and continuous measure of symmetry (which both quantify "ordering" in 2D sets of points) necessarily correlated?…”

Section: Discussionmentioning

confidence: 99%

“…where P i is the portion of the polygons possessing n edges in a given Voronoi diagram (also called the coordination number of the polygon) and i is the total number of polygon types with different number of edges [4][5][6][7][8][9][10][11][12][13]. The summation in Equation ( 1) is performed from i = 3 (the smallest possible polygon-a triangle) to the largest coordination number of the polygon, e.g., for a hexagon, the largest value of i is 6.…”

Section: Voronoi Entropy and The Continuous Symmetry Measure Of The Set Of Pointsmentioning

confidence: 99%

“…How can the orderliness of this pattern be quantified? There exist various pathways of quantifying an order in 2D patterns, including calculation of the Voronoi entropy [4][5][6][7][8][9][10][11][12][13], and use of the Minkowski functionals [14,15] and correlation functions [16]. The Voronoi tessellation was already known to Rene Descartes in the 17th century [5].…”

Section: Introductionmentioning

confidence: 99%

“…Descartes proved that the distribution of matter in the Universe is characterized by vortices that are centered at fixed stars, using these tessellations [5,13]. The idea was developed by Georgy Voronoi in 1908 [4], and it was broadly implemented for quantifying the ordering inherent for 2D patterns [6][7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

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Voronoi Entropy vs. Continuous Measure of Symmetry of the Penrose Tiling: Part I. Analysis of the Voronoi Diagrams

et al. 2021

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A continuous measure of symmetry and the Voronoi entropy of 2D patterns representing Voronoi diagrams emerging from the Penrose tiling were calculated. A given Penrose tiling gives rise to a diversity of the Voronoi diagrams when the centers, vertices, and the centers of the edges of the Penrose rhombs are taken as the seed points (or nuclei). Voronoi diagrams keep the initial symmetry group of the Penrose tiling. We demonstrate that the continuous symmetry measure and the Voronoi entropy of the studied sets of points, generated by the Penrose tiling, do not necessarily correlate. Voronoi diagrams emerging from the centers of the edges of the Penrose rhombs, considered nuclei, deny the hypothesis that the continuous measure of symmetry and the Voronoi entropy are always correlated. The Voronoi entropy of this kind of tiling built of asymmetric convex quadrangles equals zero, whereas the continuous measure of symmetry of this pattern is high. Voronoi diagrams generate new types of Penrose tiling, which are different from the classical Penrose tessellation.

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Section: Discussionmentioning

confidence: 99%

Section: Voronoi Entropy and The Continuous Symmetry Measure Of The Set Of Pointsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Voronoi Entropy vs. Continuous Measure of Symmetry of the Penrose Tiling: Part I. Analysis of the Voronoi Diagrams

et al. 2021

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“…In the present paper we introduce the alternative measure of the symmetry of 2D patterns, namely the informational measure of symmetry (ISM) and apply the suggested measure for the analysis of the patterns generated by the P3 Penrose tiling. We compare the informational measure of symmetry with the Voronoi entropy (denoted S vor ) [23][24][25][26][27][28][29][30][31][32][33][34][35] and the continuous measure of symmetry [14][15][16][17][18][19][20][21][22] calculated for the patterns generated by the Penrose tessellation P3, presented in Figure 1.…”

Section: Introductionmentioning

confidence: 99%

Informational Measure of Symmetry vs. Voronoi Entropy and Continuous Measure of Entropy of the Penrose Tiling. Part II of the “Voronoi Entropy vs. Continuous Measure of Symmetry of the Penrose Tiling”

et al. 2021

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The notion of the informational measure of symmetry is introduced according to: Hsym(G)=−∑i=1kP(Gi)lnP(Gi), where P(Gi) is the probability of appearance of the symmetry operation Gi within the given 2D pattern. Hsym(G) is interpreted as an averaged uncertainty in the presence of symmetry elements from the group G in the given pattern. The informational measure of symmetry of the “ideal” pattern built of identical equilateral triangles is established as Hsym(D3)= 1.792. The informational measure of symmetry of the random, completely disordered pattern is zero, Hsym=0. The informational measure of symmetry is calculated for the patterns generated by the P3 Penrose tessellation. The informational measure of symmetry does not correlate with either the Voronoi entropy of the studied patterns nor with the continuous measure of symmetry of the patterns. Quantification of the “ordering” in 2D patterns performed solely with the Voronoi entropy is misleading and erroneous.

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Versatile Microfluidics Separation of Colloids by Combining External Flow with Light‐Induced Chemical Activity

et al. 2023

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Separation of particles by size, morphology, or material identity is of paramount importance in fields such as filtration or bioanalytics. Up to now separation of particles distinguished solely by surface properties or bulk/surface morphology remains a very challenging process. Here a combination of pressure-driven microfluidic flow and local self-phoresis/ osmosis are proposed via the light-induced chemical activity of a photoactive azobenzene-surfactant solution. This process induces a vertical displacement of the sedimented particles, which depends on their size and surface properties . Consequently, different colloidal components experience different regions of the ambient microfluidic shear flow. Accordingly, a simple, versatile method for the separation of such can be achieved by elution times in a sense of particle chromatography. The concepts are illustrated via experimental studies, complemented by theoretical analysis, which include the separation of bulk-porous from bulk-compact colloidal particles and the separation of particles distinguished solely by slight differences in their surface physico-chemical properties.

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Quantification of ordering in active light driven colloids

Cited by 13 publications

References 38 publications

Voronoi Entropy vs. Continuous Measure of Symmetry of the Penrose Tiling: Part I. Analysis of the Voronoi Diagrams

Voronoi Entropy vs. Continuous Measure of Symmetry of the Penrose Tiling: Part I. Analysis of the Voronoi Diagrams

Informational Measure of Symmetry vs. Voronoi Entropy and Continuous Measure of Entropy of the Penrose Tiling. Part II of the “Voronoi Entropy vs. Continuous Measure of Symmetry of the Penrose Tiling”

Versatile Microfluidics Separation of Colloids by Combining External Flow with Light‐Induced Chemical Activity

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