Voronoi Tessellations and the Shannon Entropy of the Pentagonal Tilings.

We used the complete set of convex pentagons to enable 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.

From Chaos to Ordering: New Studies in the Shannon Entropy of 2D Patterns.

Properties of the Voronoi tessellations arising from random 2D distribution points are reported. We applied an iterative procedure to the Voronoi diagrams generated by a set of points randomly placed on the plane. The procedure implied dividing the edges of Voronoi cells into equal or random parts.

Robust icephobic coating based on the spiky fluorinated AlO particles.

Omniphobic and icephobic twin-scale surfaces based on the "urchin"-like fluorinated AlO particles are presented. Combined effect of hierarchical topography and fluorination supplied to the surfaces omniphobic and icephobic properties. The study of the stability of the Cassie wetting state is reported.

Osmotic evolution of composite liquid marbles.

Hypothesis: We hypothesized that the reported evolution (growth) of composite water marbles filled with saline water and coated with lycopodium dispersed in a thin layer of silicone oil is due to the osmotic mass transfer. The hypothesis is supported by the semi-empirical model of osmotic growth of small liquid marbles floating on distilled water.

Experiments: Saline composite, silicone oil-coated marbles floating on distilled water grew with time; whereas, composite marbles filled with distilled water floating on aqueous solutions of NaCl lost mass with time and shrunk.

Directional Droplet Transport Mediated by Circular Groove Arrays. Part II: Theory of Effect.

In the first part of this research, we reported the experimental study of the drop impact on the superhydrophobic circular groove arrays, which resulted in a directional droplet transport. In the second part, we further explored the influence of the Weber number (), ridge height (), and the deviation distance () between the impacting point and the center of curvature on the lateral offset distance (Δ) of bouncing drops. The suggested theoretical analysis is in reasonable agreement with the experimental observations.

Directional Droplet Transport Mediated by Circular Groove Arrays. Part I: Experimental Findings.

Directional transport of liquid droplets is crucial for various applications including water harvesting, anti-icing, and condensation heat transfer. Here, bouncing of water droplets with patterned superhydrophobic surfaces composed of circular equidistant grooves was studied. The directional transport of droplets toward the pole of the grooves was observed.

Negative Effective Mass in Plasmonic Systems II: Elucidating the Optical and Acoustical Branches of Vibrations and the Possibility of Anti-Resonance Propagation.

We report the negative effective mass metamaterials based on the electro-mechanical coupling exploiting plasma oscillations of free electron gas. The negative mass appears as a result of the vibration of a metallic particle with a frequency which is close to the frequency of the plasma oscillations of the electron gas m2, relative to the ionic lattice m1. The plasma oscillations are represented with the elastic spring constant k2=ωp2m2, where ωp is the plasma frequency.

Study of wetting of the animal retinas by Water and organic liquids and its Implications for ophthalmology.

Interfacial properties of the animal retinas are reported. Wetting of the retina-retinal pigment epithelium-choroid-sclera tissues of cow, sheep, and pig eyes by water, silicone and castor oil was explored experimentally. Both water and silicone oils demonstrated complete wetting of the retina, regardless of the viscosity of the silicone oil, whereas the castor oil demonstrated a partial wetting regime.

Manufacture and properties of composite liquid marbles.

Hypothesis: Liquid marbles are non-stick droplets coated with colloidal usually hydrophobic particles. We suggest that "composite" liquid marbles, i.e.

Negative Effective Mass in Plasmonic Systems.

We report the negative effective mass (density) metamaterials based on the electro-mechanical coupling exploiting plasma oscillations of a free electron gas. The negative mass appears as a result of the vibration of a metallic particle with a frequency of , which is close the frequency of the plasma oscillations of the electron gas m 2 relative 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.

Faceted and Circular Droplet Spreading on Hierarchical Superhydrophobic Surfaces.

Bouncing of water droplets on the post-built superhydrophobic surfaces was studied. The topography of the surfaces was constituted by PDMS conical posts decorated with ZnO nanoparticles. Droplet impact on surface topographies built of posts with varied configuration and separation was studied under different Weber numbers.

Self-Arranged Levitating Droplet Clusters: A Reversible Transition from Hexagonal to Chain Structure.

Water microdroplets condense over locally heated water-vapor interfaces and levitate in an ascending vapor-air flow forming self-assembled ordered monolayer clusters. The droplets do not coalesce due to complex aerodynamic interactions between them. The droplet cluster formation is governed by the condensation/evaporation balance and by coupling of heat flux and vapor flow with aerodynamic forces.

Mini-Generator of Electrical Power Exploiting the Marangoni Flow Inspired Self-Propulsion.

The mini-generator of electrical energy exploiting Marangoni soluto-capillary flows is reported. The interfacial flows are created by molecules of camphor emitted by the "camphor engines" placed on floating polymer rotors bearing permanent magnets. Camphor molecules adsorbed by the water/vapor interface decrease its surface tension and create the stresses resulting in the rotation of the system.

Symmetry and Shannon Measure of Ordering: Paradoxes of Voronoi Tessellation.

The Voronoi entropy for random patterns and patterns demonstrating various elements of symmetry was calculated. The symmetric patterns were characterized by the values of the Voronoi entropy being 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.

Is the Voronoi Entropy a True Entropy? Comments on "Entropy, Shannon's Measure of Information and Boltzmann's H-Theorem", 2017, , 48.

The goal of this comment note is to express our considerations about the recent paper by A. Ben Naim ( , , 48). We strongly support the distinguishing between the Shannon measure of information and the thermodynamic entropy, suggested in the paper.

Characterization of Self-Assembled 2D Patterns with Voronoi Entropy.

The Voronoi entropy is a mathematical tool for quantitative characterization of the orderliness of points distributed on a surface. The tool is useful to study various surface self-assembly processes. We provide the historical background, from Kepler and Descartes to our days, and discuss topological properties of the Voronoi tessellation, upon which the entropy concept is based, and its scaling properties, known as the Lewis and Aboav-Weaire laws.

Self-Propulsion of Water-Supported Liquid Marbles Filled with Sulfuric Acid.

Self-propulsion of liquid marbles filled with sulfuric acid and coated with hydrophobic fluorosilica powder on a water surface is reported. The prolonged self-propulsion of marbles occurs over a couple of minutes with a typical velocity of the center of mass of the marble being [Formula: see text]. The shell of the marble is not uniform, resulting in the asymmetric absorption of water by a marble, giving rise to the nonuniform thermal field within its volume.

Toward an Understanding of Magnetic Displacement of Floating Diamagnetic Bodies, I: Experimental Findings.

Diamagnetic objects (polymer and metallic plates and spheres, ceramic beads, and liquid marbles), floating on water, and a variety of organic liquids may be driven by a steady magnetic field of 0.1 T, registered at the water-vapor surface. Diamagnetic bodies are attracted to the magnet, when the apparent contact angle at the solid/liquid interface is obtuse and repelled from the magnet, when the angle is acute.