ARTICLE | doi:10.20944/preprints202003.0418.v1
Subject: Physical Sciences, Condensed Matter Physics Keywords: metamaterials; negative effective mass; plasma oscillations; low frequency plasmons
Online: 29 March 2020 (03:39:01 CEST)
We report the negative effective mass metamaterials based on the electro-mechanical coupling exploiting plasma oscillations of a free electron gas. The negative mass appears as a result of vibration of a metallic particle with a frequency of ω which is close the frequency of the plasma oscillations of the electron gas m_2 relatively to the ionic lattice m_1. The plasma oscillations are represented with the elastic spring k_2=ω_p^2 m_2, where ω_p is the plasma frequency. Thus, the metallic particle vibrated with the external frequency ω is described by the effective mass m_eff=m_1+(m_2 ω_p^2)/(ω_p^2-ω^2 ) , which is negative when the frequency ω approaches ω_p from above. The idea is exemplified with two conducting metals, namely Au and Li.
Subject: Chemistry And Materials Science, Materials Science And Technology Keywords: metamaterials; negative effective mass; plasma oscillations; low frequency plasmons; optical and acoustical branches.
Online: 21 July 2020 (13:38:18 CEST)
We report the negative effective mass metamaterials based on the electro-mechanical coupling exploiting plasma oscillations of a free electron gas. The negative mass appears as a result of vibration of a metallic particle with a frequency of ω which is close to the frequency of the plasma oscillations of the electron gas m_2 relatively to the ionic lattice m_1. The plasma oscillations are represented with the elastic spring k_2=ω_p^2 m_2, where ω_p is the plasma frequency. Thus, the metallic particle vibrated with the external frequency ω is described by the effective mass m_eff=m_1+(m_2 ω_p^2)/(ω_p^2-ω^2 ) , which is negative when the frequency ω approaches ω_p from above. The idea is exemplified with two conducting metals, namely Au and Li embedded into various matrices. The one-dimensional lattice built of the identical metallic micro-elements m_eff connected by ideal springs k_1 representing various media such as polydimethylsiloxane and soda-lime glass is treated. The optical and acoustical branches of longitudinal modes propagating through the lattice are elucidated for various ratios ω_1/ω_p . The 1D lattice built of the thin metallic wires giving rise to the low frequency plasmons is treated. The possibility of the anti-resonant propagation, strengthening the effect of the negative mass occurring under = p = 1 is addressed.
ARTICLE | doi:10.20944/preprints201904.0336.v1
Subject: Computer Science And Mathematics, Mathematics Keywords: Voronoi entropy; Voronoi tessellation; symmetry; ordering; Shannon measure of information
Online: 30 April 2019 (11:51:44 CEST)
Voronoi entropy for the random patterns and patterns demonstrating various elements of symmetry are calculated. The symmetric patterns are characterized by the values of the Voronoi entropy very close to those inherent to random ones. This contradicts the idea that the Voronoi entropy quantifies the ordering of the seed points, constituting the pattern. The extension of the Shannon-like formula embracing symmetric patterns is suggested. Analysis of Voronoi diagrams enables revealing of the elements of symmetry of the pattern.
ARTICLE | doi:10.20944/preprints202009.0616.v1
Subject: Physical Sciences, Condensed Matter Physics Keywords: interfacial crystallization; liquid marble, hydrophobic particle; superhydrophobic surface; coffee-stain effect.
Online: 25 September 2020 (15:30:00 CEST)
We report interfacial crystallization in droplets of saline solutions placed on superhydrophobic surfaces and liquid marbles filled with the saline. Evaporation of saline droplets deposited on superhydrophobic surface resulted in the formation of cup-shaped millimeter-scaled residues. The formation of the cup-like deposit is reasonably explained within the framework of the theory of the coffee-stain effect, namely, the rate of heterogeneous crystallization along the contact line of the droplet is many times higher than in the droplet bulk. Crystallization within evaporated saline marbles, coated with lycopodium particles, depends strongly on the evaporation rate. Rapidly evaporated saline marbles yielded dented shells built of a mixture of colloidal particles and NaCl crystals. We relate the formation of these shells to the interfacial crystallization promoted by hydrophobic particles coating the marbles, accompanied with the upward convection flows supplying the saline to the particles, serving as the centers of interfacial crystallization. Convective flows prevail over the diffusion mass transport for the saline marbles heated from below.
ARTICLE | doi:10.20944/preprints202301.0307.v1
Subject: Computer Science And Mathematics, Mathematics Keywords: Archimedes Spiral; Voronoi tessellation; Voronoi entropy; surface patterns; aesthetic attraction; phyllotaxis; golden ratio.
Online: 17 January 2023 (10:07:18 CET)
Voronoi mosaics inspired by the seed points placed on the Archimedes Spirals are reported. Voronoi entropy was calculated for these patterns. Equidistant and non-equidistant patterns are treated. Voronoi mosaics built from a sells of equal size which are of a primary importance for decorative arts are reported. The pronounced prevalence of hexagons is inherent for the patterns with an equidistant and non-equidistant distribution of points, when the distance between the seed points is of the same order of magnitude as the distance between the turns of the spiral. Penta- and heptagonal “defected” cells appeared in the Voronoi diagrams due to the finite nature of the pattern. The ordered Voronoi tessellations demonstrating the Voronoi entropy larger than 1.71, reported for the random 2D distribution of points, were revealed. The dependence of the Voronoi entropy on the total number of the seed points located on the Archimedes Spirals is reported. Voronoi tessellations generated by the phyllotaxis-inspired patterns are addressed. The aesthetic attraction of the Voronoi mosaics arising from seed points placed on the Archimedes Spirals is discussed.
ARTICLE | doi:10.20944/preprints202212.0012.v1
Subject: Physical Sciences, Mathematical Physics Keywords: Shannon entropy; pentagonal tiling; Marjorie Rice tiling; Voronoi tessellation; iso-symmetrical transitions
Online: 1 December 2022 (06:42:44 CET)
We used the complete set of convex pentagons enabling filing the plane without any overlaps or gaps (including the Marjorie Rice tiles) as generators of Voronoi tessellations. Shannon entropy of the tessellations was calculated. Some of the basic mosaics are flexible and give rise to a diversity of Voronoi tessellations. The Shannon entropy of these tessellations varied in a broad range. Voronoi tessellation, emerging from the basic pentagonal tiling built from hexagons only, was revealed (the Shannon entropy of this tiling is zero). Decagons and hendecagon did not appear in the studied Voronoi diagrams. The most abundant Voronoi tessellations are built from three different kinds of polygons. The most widespread is the combination of pentagons, hexagons and heptagons. The most abundant polygons are pentagons and hexagons. No Voronoi tiling built only of pentagons was registered. Flexible basic pentagonal mosaics give rise to a diversity of Voronoi tessellations, which are characterized by the same symmetry group; however, the coordination number of the vertices is variable. These Voronoi tessellations may be useful for the interpretation of the iso-symmetrical phase transitions.
ARTICLE | doi:10.20944/preprints202109.0347.v1
Subject: Physical Sciences, Thermodynamics Keywords: informational measure of symmetry; 1D shapes; 2D shapes; fractal patterns; time evolution; symmetry; pattern
Online: 20 September 2021 (16:39:57 CEST)
Informational (Shannon) measures of symmetry are introduced and analyzed for the patterns built of 1D and 2D shapes. The informational measure of symmetry Hsym (G) characterizes the an averaged uncertainty in the presence of symmetry elements from the group G in a given pattern; whereas the Shannon-like measure of symmetry Ωsym (G) quantifies averaged uncertainty of appearance of shapes possessing in total n elements of symmetry belonging to group G in a given pattern. Hsym(G1)=Ωsym(G1)=0 for the patterns built of irregular, non-symmetric shapes. Both of informational measures of symmetry are intensive parameters of the pattern and do not depend on the number of shapes, their size and area of the pattern. They are also insensitive to the long-range order inherent for the pattern. Informational measures of symmetry of fractal patterns are addressed. The mixed patterns including curves and shapes are considered. Time evolution of the Shannon measures of symmetry is treated. The close-packed and dispersed 2D patterns are analyzed.
ARTICLE | doi:10.20944/preprints202109.0076.v1
Subject: Physical Sciences, Condensed Matter Physics Keywords: symmetry; informational measure; penrose tiling; Voronoi entropy; continuous symmetry measure; ordering
Online: 3 September 2021 (21:36:08 CEST)
The notion of the informational measure of symmetry is introduced according to: HsymG=-i=1kPGilnPGi, where PGi is the probability of appearance of the symmetry operation Gi within the given 2D pattern. HsymG 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 HsymD3=1.792. The informational measure of symmetry of the random, completely disordered pattern is zero, Hsym=0. Informational measure of symmetry is calculated for the patterns generated by the P3 Penrose tessellation. Informational measure of symmetry does not correlate neither with the Voronoi entropy of the studied patterns nor with the continuous measure of symmetry of the patterns.
ARTICLE | doi:10.20944/preprints202011.0590.v1
Subject: Chemistry And Materials Science, Surfaces, Coatings And Films Keywords: cold plasma; polyvinylchloride; wettability; hydrophilization; apparent contact angle; contact angle hysteresis; hydrophobic recovery.
Online: 23 November 2020 (14:31:54 CET)
Impact of the Corona, dielectric barrier discharge and low pressure radiofrequency air plasmas on the chemical composition and wettability of the medical grade polyvinylchloride was investigated. Corona plasma treatment exerted the most pronounced increase in the hydrophilization of polyvinylchloride. The specific energy of adhesion of the pristine and plasma treated PVC tubing is reported. The kinetics of hydrophobic recovery following the plasma treatment was explored. The time evolution of the apparent contact angle under the hydrophobic recovery is satisfactorily described by the exponential fitting. Energy-dispersive X-ray spectroscopy of the chemical composition of the near-surface layers of the plasma treated catheters revealed their oxidation. The effect of the hydrophobic recovery is hardly correlated with oxidation of the polymer surface, which is irreversible.
REVIEW | doi:10.20944/preprints202204.0252.v1
Subject: Physical Sciences, Thermodynamics Keywords: Voronoi tessellation; Voronoi entropy; random set of points; ordering; lamellae; spherulite; continuous measure of symmetry
Online: 27 April 2022 (08:29:01 CEST)
Properties of the Voronoi tessellations arising from the random 2D distribution points are reported. We applied the procedure of dividing the sides of Voronoi cells into equal or random parts to Voronoi diagrams generated by a set of randomly placed on the plane points. The dividing points were then used to construct the following Voronoi diagram. Repeating this procedure led to a surprising effect of positional ordering of Voronoi cells, reminiscent of the formation of lamellae and spherulites in linear semi-crystalline polymers and metallic glasses. Thus, we can conclude, that by applying even a simple set of rules to a random set of seeds we introduce order into an initially disordered system. At the same time, the Voronoi entropy showed a tendency to values typical for completely random patterns and did not distinguish the short-range ordering. The Voronoi entropy and the continuous measure of symmetry of the patterns demonstrated the distinct asymptotic behavior, while approaching the close saturation values with the increase of the number of the iteration steps. Voronoi entropy grew, with the number of iterations, whereas the continuous measure of symmetry of the same patterns demonstrated the opposite asymptotic behavior. The Voronoi entropy is not an unambiguous measure of order in the 2D patterns. The more symmetrical patterns may demonstrate the higher values of the Voronoi entropy.