Quantifying order in breath figure patterns through Voronoi entropy.

In this study, we simulate breath figures that are evolving two-dimensional assemblies of droplets on a substrate. We focus on the Voronoi/Shannon entropy of these figures, which quantifies the order related to the coordination number of droplets. We show that the Voronoi entropy of the complete breath figure pattern converges to a value that is the one of a randomly distributed point system.

Inverse Phase Transition in Droplet Clusters Levitating over the Locally Heated Water Layer.

Self-assembled microdroplet clusters can levitate above a locally heated water surface. Normally, the temperature of droplets is in the range of 50-95 °C. However, it is possible to generate clusters at lower temperatures.

Motion and Orientation of Janus Spherical Particles at a Liquid-Air Interface Governed by the Moses Effect.

We investigated the motion of spherical polystyrene/polypyrrole-coated polystyrene Janus particles placed at an air/saline interface and driven by a permanent magnetic field of ca. 0.5 T.

Landauer Bound in the Context of Minimal Physical Principles: Meaning, Experimental Verification, Controversies and Perspectives.

The physical roots, interpretation, controversies, and precise meaning of the Landauer principle are surveyed. The Landauer principle is a physical principle defining the lower theoretical limit of energy consumption necessary for computation. It states that an irreversible change in information stored in a computer, such as merging two computational paths, dissipates a minimum amount of heat kBTln2 per a bit of information to its surroundings.

Fermat Principle, Ramsey Theory and Metamaterials.

Reinterpretation of the Fermat principle governing the propagation of light in media within the Ramsey theory is suggested. Complete bi-colored graphs corresponding to light propagation in media are considered. The vertices of the graphs correspond to the points in real physical space in which the light sources or sensors are placed.

Shannon Entropy of Ramsey Graphs with up to Six Vertices.

Shannon entropy quantifying bi-colored Ramsey complete graphs is introduced and calculated for complete graphs containing up to six vertices. Complete graphs in which vertices are connected with two types of links, labeled as α-links and -links, are considered. Shannon entropy is introduced according to the classical Shannon formula considering the fractions of monochromatic convex α-colored polygons with -sides or edges, and the fraction of monochromatic β-colored convex polygons with -sides in the given complete graph.

Apple-like Shape of Freezing Paraffin Wax Droplets and Its Origin.

Paraffin wax stores energy in the form of latent heat at a nearly constant temperature during melting and releases this energy during solidification. This effect is used in industrial energy storage. At the same time, the possible deformation of even small volumes of material as a result of phase change is insufficiently studied.

Universality of Scaling Laws Governing Contact and Spreading Time Spans of Bouncing Liquid Marbles and its Physical Origin.

The impact of liquid marbles coated with a diversity of hydrophobic powders with various solid substrates, including hydrophobic, hydrophilic, and superhydrophobic ones, was investigated. The contact time of the bouncing marbles was studied. Universal scaling behavior of the contact time as a function of the Weber number () was established; the scaling law = () was independent of the kind of powder and the type of solid substrate.

Ramsey theory and thermodynamics.

Re-shaping of thermodynamics with the graph theory and Ramsey theory is suggested. Maps built of thermodynamic states are addressed. Thermodynamic states may be attainable and non-attainable by the thermodynamic process in the system of constant mass.

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.

Interfacial crystallization in the polyhedral liquid marbles.

Hypothesis: We hypothesized that interfacial crystallization occurring within evaporated polyhedral liquid marbles may be controlled by hydrophilization of the polymer plates coating the marbles. The hypothesis was tested with polyhedral marbles coated with hydrophobized and cold plasma-hydrophilized PET (Polyethylene terephthalate) plates.

Experiments: Interfacial crystallization within polyhedral liquid marbles was investigated experimentally.

Hierarchical liquid marbles formed using floating hydrophobic powder and levitating water droplets.

Hypothesis: Liquid marbles i.e. droplets coated by hydrophobic particles may be formed not only on the solid substrates but also on the floating layers of hydrophobic powders such as fluorinated fumed silica or polytetrafluoroethylene.

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.

Branched droplet clusters and the Kramers theorem.

Scaling laws inherent for polymer molecules are checked for the linear and branched chains constituting two-dimensional (2D) levitating microdroplet clusters condensed above the locally heated layer of water. We demonstrate that the dimensionless averaged end-to-end distance of the droplet chain r[over ¯] normalized by the averaged distance between centers of the adjacent droplets l[over ¯] scales as r[over ¯]/l[over ¯]∼n^{0.76}, where n is the number of links in the chain, which is close to the power exponent ¾, predicted for 2D polymer chains with excluded volume in the dilution limit.

Effect of asymmetric cooling of sessile droplets on orientation of the freezing tip.

Hypothesis: The shape of the "freezing tip" formed by the crystallization of water droplets demonstrated remarkable universality - no dependence on the cooling rate and physico-chemical properties of the substrate has been observed. At the same time, the spatial orientation of the freezing cone may be varied. We hypothesized that the orientation of the freezing tip is determined by the direction of heat flux at the base of the sessile droplet.

Magnetic Entropic Forces Emerging in the System of Elementary Magnets Exposed to the Magnetic Field.

A temperature dependent entropic force acting between the straight direct current and the linear system (string with length of ) of elementary non-interacting magnets/spins μ→ is reported. The system of elementary magnets is supposed to be in the thermal equilibrium with the infinite thermal bath . The entropic force at large distance from the current scales as Fmagnen~1r3, where is the distance between the edge of the string and the current , and kB is the Boltzmann constant; (r≫L is adopted).

Rotating Minimal Thermodynamic Systems.

Minimal rotating thermodynamic systems are addressed. Particle placed into the rotating symmetrical double-well potential (bowl), providing binary logical system is considered. The condition providing the transfer of the particle from one frictionless half-well to another, and, in this way, the possibility to record 1 bit of information is derived.

Topology of eeg wave fronts.

Whenever one attempts to comb a hairy ball flat, there will always be at least one tuft of hair at one point on the ball. This seemingly worthless sentence is an informal description of the hairy ball theorem, an invaluable mathematical weapon that has been proven useful to describe a variety of physical/biological processes/phenomena in terms of topology, rather than classical cause/effect relationships. In this paper we will focus on the electrical brain field-electroencephalogram (EEG).

Interfacial crystallization at the intersection of thermodynamic and geometry.

Interfacial crystallization appears as a crucial stage in the numeral natural phenomena and technological applications, such as industry of semi-conductors and manufacturing of nano-whiskers. Interfacial aspects of heterogeneous crystallization are surveyed. The review is focused on the interplay of thermodynamic and geometric aspects of the interfacial crystallization.

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.

Survival of Virus Particles in Water Droplets: Hydrophobic Forces and Landauer's Principle.

Many small biological objects, such as viruses, survive in a water environment and cannot remain active in dry air without condensation of water vapor. From a physical point of view, these objects belong to the mesoscale, where small thermal fluctuations with the characteristic kinetic energy of (where is the Boltzmann's constant and is the absolute temperature) play a significant role. The self-assembly of viruses, including protein folding and the formation of a protein capsid and lipid bilayer membrane, is controlled by hydrophobic forces (i.

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.

Informational Reinterpretation of the Mechanics Notions and Laws.

The informational re-interpretation of the basic laws of the mechanics exploiting the Landauer principle is suggested. When a physical body is in rest or it moves rectilinearly with the constant speed, zero information is transferred; thus, the informational affinity of the rest state and the rectilinear motion with a constant speed is established. Inertial forces may be involved in the erasure/recording of information.

Entropy, Information, and Symmetry; Ordered Is Symmetrical, II: System of Spins in the Magnetic Field.

The second part of this paper develops an approach suggested in , (1), 11; which relates ordering in physical systems to symmetrizing. Entropy is frequently interpreted as a quantitative measure of "chaos" or "disorder". However, the notions of "chaos" and "disorder" are vague and subjective, to a great extent.