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. For the sake of comparison, the motion of pure floating polystyrene particles was studied. Both kinds of the studied particles moved toward the magnet and stopped at the boundary of the near-surface well produced by the magnetic field. The Moses effect-driven motion of floating Janus particles was analyzed and investigated under different strengths of the magnetic field and salt concentrations. The study of the Janus particle displacement led to the development of a unified theoretical framework explaining the mechanism of the motion. This framework predicts that the motion of particles placed at an air-salt solution interface is not only dictated by magnetic energy but also intricately influenced by the interplay of factors, including the curvature of the interface caused by the static magnetic field, gravitational potential, and capillary forces. The orientation of the particles was observed. A qualitative explanation of the observed phenomena is suggested. The investigated process has potential for the self-assembly of particles placed at the liquid/air interface.

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. Here, we study the structure and behavior of such cold-stabilized droplet clusters with variable temperature. It has been established that as the temperature decreases, the role of aerodynamic forces decreases, while electrostatic forces, on the contrary, increase. We studied the behavior of droplet clusters at relatively low temperatures down to 28 °C. A chaotic motion of droplets and a phase transition were observed at the surface temperature of the water below a critical value of about Tmax = 35 ± 2 °C. The orderliness of the cluster was quantified with the Shannon/Voronoi entropy. Several stages of cluster evolution were observed and analyzed, and a mechanism of this phenomenon is discussed. An inverse phase transition in which cooling of the cluster decreases its orderliness is discussed. Frequencies of the droplets' oscillations coincide qualitatively with the frequency of the plasma oscillations within the cluster.

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. The Landauer principle is discussed in the context of fundamental physical limiting principles, such as the Abbe diffraction limit, the Margolus-Levitin limit, and the Bekenstein limit. Synthesis of the Landauer bound with the Abbe, Margolus-Levitin, and Bekenstein limits yields the minimal time of computation, which scales as τmin~hkBT. Decreasing the temperature of a thermal bath will decrease the energy consumption of a single computation, but in parallel, it will slow the computation. The Landauer principle bridges John Archibald Wheeler's "it from bit" paradigm and thermodynamics. Experimental verifications of the Landauer principle are surveyed. The interrelation between thermodynamic and logical irreversibility is addressed. Generalization of the Landauer principle to quantum and non-equilibrium systems is addressed. The Landauer principle represents the powerful heuristic principle bridging physics, information theory, and computer engineering.

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 tc as a function of the Weber number (We) was established; the scaling law tc = tc(We) was independent of the kind of powder and the type of solid substrate. The total contact time consists of spreading time and retraction time. It is weakly dependent on We and this is true for all kinds of studied powders and substrates. This observation hints to the surface tension/inertia spring model governing the impact. By contrast, the spreading time ts scales as [Formula: see text], n = 0.28 - 0.30 ± 0.002. We relate the origin of this scaling law to the viscous dissipation occurring within the spreading marbles. The retraction time tr grows weakly with the Weber number. The scaling law was changed at threshold values of We ≅ 15-20. It is reasonable to explain this change with the breaking of the Leidenfrost regime of spreading under high values of We.

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 ß-links, are considered. Shannon entropy is introduced according to the classical Shannon formula considering the fractions of monochromatic convex α-colored polygons with n α-sides or edges, and the fraction of monochromatic ß-colored convex polygons with m ß-sides in the given complete graph. The introduced Shannon entropy is insensitive to the exact shape of the polygons, but it is sensitive to the distribution of monochromatic polygons in a given complete graph. The introduced Shannon entropies Sα and Sß are interpreted as follows: Sα is interpreted as an average uncertainty to find the green α-polygon in the given graph; Sß is, in turn, an average uncertainty to find the red ß-polygon in the same graph. The re-shaping of the Ramsey theorem in terms of the Shannon entropy is suggested. Generalization for multi-colored complete graphs is proposed. Various measures quantifying the Shannon entropy of the entire complete bi-colored graphs are suggested. Physical interpretations of the suggested Shannon entropies are discussed.

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. 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.

Rotating Minimal Thermodynamic Systems.

Minimal rotating thermodynamic systems are addressed. Particle m 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. The procedure of recording turns out to be irreversible; it is impossible to return the particle to its initial state under rotation about the same axis. The same rotating double-well system exerted to the thermal noise is considered. A minimal rotating thermal engine built of the rotating chamber, movable partition, and the particle confined within the chamber is treated. Rotation of the system displaces the partition, thus enabling erasing of one bit information. Erasing of 1 bit of information is due to the inertia (centrifugal force) acting on the partition. Isothermal expansion of the "minimal gas" expectedly gives rise to the Landauer bound. Compression of the "gas" with the rotation around the same axis is impossible and demands the additional axis of rotation. The interrelation between the possibility of recording/erasing information and the symmetry of the system is considered.

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 I and the linear system (string with length of L) of N elementary non-interacting magnets/spins µâ†’ is reported. The system of elementary magnets is supposed to be in the thermal equilibrium with the infinite thermal bath T. The entropic force at large distance from the current scales as Fmagnen~1r3, where r is the distance between the edge of the string and the current I, and kB is the Boltzmann constant; (r≫L is adopted). The entropic magnetic force is the repulsion force. The entropic magnetic force scales as Fmagnen~1T, which is unusual for entropic forces. The effect of "entropic pressure" is predicted for the situation when the source of the magnetic field is embedded into the continuous media, comprising elementary magnets/spins. Interrelation between bulk and entropy magnetic forces is analyzed. Entropy forces acting on the 1D string of elementary magnets that exposed the magnetic field produced by the magnetic dipole are addressed.

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. The dividing points were then used to construct the following Voronoi diagram. Repeating this procedure led to a surprising effect of the 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 can introduce order into an initially disordered system. At the same time, the Shannon (Voronoi) entropy showed a tendency to attain values that are typical for completely random patterns; thus, the Shannon (Voronoi) entropy does not distinguish the short-range ordering. The Shannon entropy and the continuous measure of symmetry of the patterns demonstrated the distinct asymptotic behavior, while approaching the close saturation values with the increase in the number of iteration steps. The Shannon entropy grew with the number of iterations, whereas the continuous measure of symmetry of the same patterns demonstrated the opposite asymptotic behavior. The Shannon (Voronoi) entropy is not an unambiguous measure of order in the 2D patterns. The more symmetrical patterns may demonstrate the higher values of the Shannon entropy.

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 (We), ridge height (H), and the deviation distance (r) between the impacting point and the center of curvature on the lateral offset distance (ΔL) of bouncing drops. The suggested theoretical analysis is in reasonable agreement with the experimental observations. We demonstrate that a Cassie-Wenzel wetting transition occurred within the microstructures of the relief under the threshold Weber number, for example, We ≅ 19-25, which switched the nature of drop bouncing. The dynamic pressure plays a decisive role in the directional droplet transport. The reported investigation may shed light on the solid-liquid interactions occurring on the patterned hierarchical surfaces and open up new opportunities for directional droplet transportation.

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 kBT (where kB is the Boltzmann's constant and T 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.e., the repulsing forces between hydrophobic particles and regions of molecules) in a water environment. Hydrophobic forces are entropic, and they are driven by a system's tendency to attain the maximum disordered state. On the other hand, in information systems, entropic forces are responsible for erasing information, if the energy barrier between two states of a switch is on the order of kBT, which is referred to as Landauer's principle. We treated hydrophobic interactions responsible for the self-assembly of viruses as an information-processing mechanism. We further showed a similarity of these submicron-scale processes with the self-assembly in colloidal crystals, droplet clusters, and liquid marbles.

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. Faceted spreading and retraction of droplets were observed. Square-, pentagon-, and hexagon-shaped droplets were registered. It was shown that the nature of droplet spreading depended on both the Weber number and the topography of the post arrays. Even bouncing under small Weber numbers We ≅ 6.5 resulted in the Cassie-Wenzel transitions, starting from the area adjacent to the axis of droplets, and the area exposed to the wetting transitions scaled as [Formula: see text]. During spreading, two main stages were recorded as the kinematic (inertial) stage and the viscous stage. The viscous stage, in turn, appeared as a consequence of two substages governed by various time scaling laws. The faceted triple line was observed for the Cassie-like retraction of droplets.

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. The impact of the Weber number, initial polar distance r, and geometrical parameters of the surface on the directional droplet bouncing was experimentally explored. The nature of bouncing was switched when the Weber numbers exceeded We ≅ 20-25. The rebouncing height was slightly dependent on the initial polar coordinate of the impact point for a fixed We, whereas it grew for We > 20. The weak dependence of the droplet spreading time on the Weber number was close to the dependence predicted by the Hertz bouncing, thus evidencing the negligible influence of viscosity in the process. Change in the scaling exponent describing the dependence of the normalized spreading time on the Weber number was registered for We ≅ 25. The universal dependence of the offset distance ΔL of the droplets on the Weber number ΔL/D0 ∼ We1.5 was established. The normalized offset distance decreased with the normalized initial polar distance as ΔL/D0 ∼ (r/S)-1, where D0 and S are the droplet diameter and groove width, respectively. This research may yield more insights into droplet bouncing on patterned surfaces and offer more options in directed droplet transportation.

Impact of Surfactants on the Formation and Properties of Droplet Clusters.

A levitating cluster of condensed microdroplets can form over the heated area of a water layer. The thermocapillary (TC) flow at the surface of the water layer combined with the convective flow in the layer often prevents a cluster's stability due to disturbances that it creates in the gas flow over the water surface. The TC flow can be suppressed by introducing small amounts of surfactants into the water layer. We conduct a systematic study of the effect of a surfactant on the cluster. We show experimentally that the introduction of the surfactant sodium laureth sulfate with concentrations of 0.05-0.5 g/L can suppress the TC convection. It is shown that the amount of surfactant does not affect the condensational growth of droplets and the structure of the cluster. In the absence of the surfactant, a ring-shaped cluster is formed, which is reported in this paper for the first time.

Clustering and self-organization in small-scale natural and artificial systems.

Physical properties of clusters, i.e. systems composed of a 'small' number of particles, are qualitatively different from those of infinite systems. The general approach to the problem of clustering is suggested. Clusters, as they are seen in the graphs theory, are discussed. Various physical mechanisms of clustering are reviewed. Dimensional properties of clusters are addressed. The dimensionality of clusters governs to a great extent their properties. Weakly and strongly coupled clusters are discussed. Hydrodynamic and capillary interactions giving rise to clusters formation are surveyed. Levitating droplet clusters, turbulent clusters and droplet clusters responsible for the breath-figures self-assembly are considered. Entropy factors influencing clustering are considered. Clustering in biological systems results in non-equilibrium multi-scale assembly, where at each scale, self-driven components come together by consuming energy in order to form the hierarchical structure. This article is part of the theme issue 'Bioinspired materials and surfaces for green science and technology (part 3)'.

Symmetry of small clusters of levitating water droplets.

Self-assembled clusters of condensed water microdroplets can levitate over a locally heated layer of water. Large clusters form hexagonally ordered (honeycomb) structures similar to colloidal crystals, while small (from one to several dozens of droplets) clusters possess special symmetry properties. Small clusters may demonstrate 4-fold, 5-fold, and 7-fold symmetry which is absent from large clusters and crystals. The symmetry properties of small cluster configurations are universal, i.e., they do not depend on the size of the droplets and details of the interactions between the droplets. The small cluster configurations may be compared with other types of symmetric objects in geometry.

What Is Temperature? Modern Outlook on the Concept of Temperature.

The meaning and evolution of the notion of "temperature" (which is a key concept for the condensed and gaseous matter theories) are addressed from different points of view. The concept of temperature has turned out to be much more fundamental than conventionally thought. In particular, the temperature may be introduced for systems built of a "small" number of particles and particles at rest. The Kelvin temperature scale may be introduced into quantum and relativistic physics due to the fact that the efficiency of the quantum and relativistic Carnot cycles coincides with that of the classical one. The relation of temperature with the metrics of the configurational space describing the behavior of systems built from non-interacting particles is demonstrated. The role of temperature in constituting inertia and gravity forces treated as entropy forces is addressed. The Landauer principle asserts that the temperature of a system is the only physical value defining the energy cost of the isothermal erasure of a single bit of information. The fundamental role of the temperature of the cosmic microwave background in modern cosmology is discussed. The range of problems and controversies related to the negative absolute temperature is treated.

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 Entropy 2020, 22(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. This leads to numerous misinterpretations of entropy. We propose that the disorder is viewed as an absence of symmetry and identify "ordering" with symmetrizing of a physical system; in other words, introducing the elements of symmetry into an initially disordered physical system. We explore the initially disordered system of elementary magnets exerted to the external magnetic field H → . Imposing symmetry restrictions diminishes the entropy of the system and decreases its temperature. The general case of the system of elementary magnets demonstrating j-fold symmetry is studied. The T j = T j interrelation takes place, where T and T j are the temperatures of non-symmetrized and j-fold-symmetrized systems of the magnets, correspondingly.

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. The analysis of the minimal Szilard thermal engine as seen from the noninertial frame of references is carried out. The Szilard single-particle minimal thermal engine undergoes isobaric expansion relative to accelerated frame of references, enabling the erasure of 1 bit of information. The energy ΔQ spent by the inertial force for the erasure of 1 bit of information is estimated as Δ Q ≅ 5 3 k B T ¯ , which is larger than the Landauer bound but qualitatively is close to it. The informational interpretation of the equivalence principle is proposed: the informational content of the inertial and gravitational masses is the same.

Pre-germination plasma treatment of seeds does not alter cotyledon DNA structure, nor phenotype and phenology of tomato and pepper plants.

The impact of cold radiofrequency plasma on CPDs formation, and the morphological and phenological development of tomato and pepper plants and fruits in greenhouse conditions was studied. Quality characteristics of fruits: total sugars, titratable acidity, pH and total solids were determined. Our results show that plasma treatment in the time ranges used for pre-sowing treatments, did not cause the formation of CPDs in the cotyledons, even when the testa was removed before treatment, as opposed to high UV radiation. In addition, plasma treatment did not have a negative effect on the morphology, phenology and quality parameters of plants and fruits that grew up from treated tomato and pepper seeds in the greenhouse.