arXiv subjects

Edward Bormashenko

Publications and source records attributed to Edward Bormashenko.

At least 19 recordsLinked to original sources

arXiv2024

Ramsey Approach to Quantum Mechanics

Ramsey theory enables re-shaping of the basic ideas of quantum mechanics. Quantum observables represented by linear Hermitian operators are seen as the vertices of a graph. Relations of commutation define the coloring of edges linking the vertices: if the operators commute, they are connected with a red link; if they do not commute, they are connected with a green link. Thus, a bi-colored complete Ramsey graph emerges. According to Ramsey's theorem, a complete bi-colored graph built of six vertices will inevitably contain at least one monochromatic triangle; in other words, the Ramsey number $ R(3,3) = 6 $. In our interpretation, this triangle represents the triad of observables that could or could not be established simultaneously in a given quantum system. The Ramsey approach to quantum mechanics is illustrated.

math-ph↗

arXiv2024

Voronoi Entropy and long-range order of 2D point sets

The Voronoi Entropy (VE) and the continuous measure of symmetry (CSM) characterize the orderliness of a set of points on a 2D plane. The Voronoi entropy is the Shannon entropy of the Voronoi tessellation of the plane into polygons, quantifying the diversity of polygons. The VE is widely used to study the self-assembly of colloidal, supramolecular, and other systems. The value of VE changes from S=0 for a completely ordered system, built of polygons with an equal number of sides, to S=1.690+/-0.001 for a random set of points. While the VE takes into account only neighboring polygons, covering the 2D plane imposes constraints on the number of polygons and the number of edges in polygons. Consequently, unlike the conventional Shannon Entropy, the VE captures some long-range order properties of the system. We calculate the VE for several hyperuniform sets of points and compare it with the values of exponents of collective density variables characterizing long-range correlations in the system. We show that the VE correlates with the latter up to a certain saturation level, after which the value of the VE falls to S=0, and we explain this phenomenon.

cond-mat.stat-mech↗

arXiv2024

Variational Principles of Physics and the Infinite Ramsey Theory

Application of the Ramsey Infinite Theorem to the variational principles of physics is discussed. According to the Ramsey Infinite Theorem,there exists the infinite, monochromatic chain of the pathways (clique), which are completely built from actual or virtual paths, connecting the intermediate states of the system.

physics.gen-ph↗

arXiv2023

Continuous Measure of Symmetry as a Dynamic Variable: a New Glance on the Three-Body Problem

The time evolution of the continuous measure symmetry for the system built of the three bodies interacting via the potential U(r)~1/r is reported. Gravitational and electrostatic interactions between the point bodies were addressed. In the case of the pure gravitational interaction the three-body-system deviated from its initial symmetrical location, described by the Lagrange equilateral triangle, comes to collapse, accompanied by the growth of the continuous measure of symmetry. When three point bodies interact via the Coulomb repulsive interaction, the time evolution of CMS is quite different. CMS calculated for all of studied initial configurations of the point charges and all of their charge-to-mass ratios always comes with time to its asymptotic value, evidencing the stabilization of the shape of the triangle, constituted by the interacting bodies.

physics.gen-ph↗

arXiv2023

Effects of Asymmetric Cooling and Surface Wettability on the Orientation of the Freezing Tip

Freezing of water droplets placed on the bare and superhydrophobic surfaces of polymer wedges are studied both experimentally and computationally. Two-dimensional numerical calculations of the transient temperature field in a chilled polymer wedge show that the direction of heat flux from the droplet through the thermal contact region with the wedge differs significantly from the normal to the wedge surface. This is the physical cause of the recently observed asymmetric cooling of the droplet. A novel approximate computational model is proposed that takes into account the variable area of the water freezing front in the droplet. This model gives a quantitative estimate of the faster freezing of the droplet on the bare surface. The obtained numerical results agree with the data of laboratory experiments. The velocity of the crystallization front and the droplet deformation including the so-called freezing tip formation are monitored in the experiment. The direction of the freezing cone axis appears to be noticeably different for the cases of bare and superhydrophobic wedge surfaces. This deviation is explained by the fact that the direction of the freezing cone axis is controlled by the local direction of the heat flux. For a hydrophobic wedge surface, the deviation of the freezing tip from the vertical is smaller, because the reduced thermal contact area reduces the influence of the heat flux direction at the wedge surface.

cond-mat.soft↗

arXiv2022

Ramsey Theory and Geometry of Closed Loops

We apply the Ramsey theory to the analysis of geometrical properties of closed contours. Consider a set of six points placed on a closed contour. The straight lines connecting these points are y_ik (x)={\alpha}_ik x+\b{eta}_ik (i,k=1...6), {\alpha}_ik is not equal to 0. We color the edges connecting the points for which {\alpha}_ik>0 holds with red, and the edges for which {\alpha}_ik<0 with green with red. At least one monochromic triangle should necessarily appear within the curve (according to the Ramsey number R(3,3)=6). This result is immediately applicable for the analysis of dynamical billiards. The second theorem emerges from the combination of the Jordan curve and Ramsey theorem. The closed curve is considered. We connect the points located within the same region with green links and the points placed within the different regions with red links. In this case, transitivity/intransitivity of the relations between the points should be considered. Ramsey constructions arising from the differential geometry of closed contours are discussed.

math.DS↗

arXiv2022

Measurement of Magnetic Susceptibility of Diamagnetic Liquids Exploiting the Moses Effect

A novel comparative technique enabling measurement of the magnetic susceptibility of diamagnetic liquids with the "Moses effect" is presented. The technique is based on the experimental establishment of the deformation of the liquid/vapor interface by a steady magnetic field. The deformation of the liquid surface by a modest magnetic field $(B\sim 0.60T)$ is measured with an optical technique. The surface tension of the liquid is taken into account. The magnetic susceptibilities of the investigated liquids (Ethanol and Glycerol) were calculated from the maximal slope of the liquid/air interface. The suggested approach yields an accuracy on the order of about $0.4-0.6\%$ and hence is superior to previous methods which used the \textquotedblleft Moses effect\textquotedblright\ for the same purpose.

physics.app-ph↗

arXiv2021

Metamaterials Demonstrating Negative Thermal Capacity

One-dimensional chain of core-shell pairs connected by ideal springs enables design of the metamaterial demonstrating the negative effective density and negative specific thermal capacity. We assume that the molar thermal capacity of the reported metamaterial is governed by the Dulong-Petit law in its high temperature limit. The specific thermal capacity depends on the density of the metamaterial; thus, it is expected to be negative, when the effective density of the chain is negative. The range of the frequencies enabling the effect of the negative thermal capacity is established. Dependence of the effective thermal capacity on the exciting frequency for various core/shell mass ratios is elucidated. The effective thermal capacity becomes negative in the vicinity of the local resonance frequency {\omega}_0 in the situation when the frequency {\omega} approaches {\omega}_0 from above. The effect of the negative effective thermal capacity is expected in metals in the vicinity of the plasma frequency. The effect of the viscous dissipation on the effective thermal capacity is addressed.

physics.gen-ph↗

arXiv2021

A hierarchical levitating cluster containing transforming small aggregates of water droplets

A new type of a levitating droplet clusters composed of often transforming small aggregates of water droplets is described for the first time. Unlike earlier observed droplet clusters controlled by aerodynamic forces, which formed either an ordered hexagonal structure or a chain structure, the cluster under consideration has a hierarchical organization. Small groups of closely spaced or packed droplets with interactions controlled by the electrostatic force are combined into larger structures controlled by aerodynamic forces. Since charged droplets in the nucleus of the cluster do not have dynamically stable configurations, droplet aggregates keep continuously restructuring. However, droplets with lower charge in external layers of the cluster form a stable hexagonal structure.

physics.chem-ph↗

arXiv2021

Thermophoretic Levitation of Solid Particles at Atmospheric Pressure

Separation and transportation of small particles are important processes in various applications such as the food and pharmaceutical industries. Although mechanical, chemical or electrical methods can provide possible solutions, operational or environmental constraints may require alternative methods. Spreading and levitation of clusters (aggregates) of fumed silica nanoparticles placed under atmospheric pressure on a hot plate is reported. In a closed chamber, the particles started to spread horizontally at the threshold temperature of $T_c^*=403 \pm 1$K. The powder spreading in the chamber continued until the temperature-dependent saturation value $r_{sat} (T)$, which grew linearly with the temperature. Open space experiments clearly demonstrated levitation of the powder clouds. The onset of levitation in the open space corresponded to the minimal threshold temperature of $T_o^*=373 \pm 1$K. Qualitative physical analysis of the observed phenomena is suggested. The effect of levitation is explained by the lifting thermo-phoretic force emerging in the Knudsen layer of air on the heater surface. The levitation of the powder under atmospheric pressure becomes possible due to the combination of low adhesion of the fluorinated fumed silica clusters built of nanoparticles to the substrate, relatively low density of the particles and clusters, and their high specific surface area. Ordering of the aggregates of nanoparticles within the levitating powder cloud was quantified with Voronoi diagrams.

cond-mat.soft↗

arXiv2020

Investigation of the Impact of Cold Plasma Treatment on the Wettability of Medical Grade Polyvinylchloride

The impact of the Corona, dielectric barrier discharge and low pressure radiofrequency air plasmas on the 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.

physics.med-ph↗

arXiv2020

What Is the 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 the different points of view. The concept of temperature turns out to be much more fundamental than it is conventionally thought. In particular, the temperature may be introduced for the systems built of "small" number of particles and particles in rest. The Kelvin temperature scale may be introduced into the 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 the temperature to the metrics of the configurational space describing the behavior of the system built from non-interacting particles is demonstrated. The Landauer principle asserts that the temperature of the system is the only physical value defining the energy cost of isothermal erasing of the single bit of information. The role of the temperature the cosmic microwave background in modern cosmology is discussed.

cond-mat.stat-mech↗

arXiv2020

Voronoi Diagrams Generated by the Archimedes Spiral

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 cells of equal size which are of 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. The aesthetic attraction of the Voronoi mosaics arising from seed points placed on the Archimedes Spirals is discussed.

math.HO↗

arXiv2020

Spiral Thermal Waves Generated by Self-Propelled Camphor Boats

Spiral thermal surface waves arising from self-propulsion of the camphor-driven objects are reported. Spiral thermal waves were registered for the dissolution and evaporation-guided self-propulsion. Soluto-capillarity is accompanied by thermo-capillarity under self-propulsion of camphor boats. The jump in the surface tension due to the soluto-capillarity is much larger than that due to the thermo-capillarity. The observed thermal effect is related to the adsorption of camphor molecules at the water/vapor interface. The observed spirals are shaped as Archimedean ones.

cond-mat.soft↗

arXiv2019

On relative contribution of electrostatic and aerodynamic effects to dynamics of a levitating droplet cluster

New experimental results and their physical analysis are presented to clarify the behavior of a relatively stable self-arranged droplet cluster levitating over the locally heated water surface. An external electric field of both opposite directions leads to a significant increase in the rate of a condensational growth of droplets in the cluster. The experimental data are used to estimate a small electrical charge of single droplets and the attraction force of polarized droplets to the water layer. It is confirmed that the interaction between the droplets is governed by aerodynamic forces.

physics.flu-dyn↗

arXiv2018

Drop-Wise and Film-Wise Water Condensation Processes Occurring on Metallic Micro-Scaled Surfaces

Water condensation was studied on silanized (superhydrophobic) and fluorinated (superoleophobic) micro-rough aluminum surfaces of the same topography. Condensation on superhydrophobic surfaces occurred via film-wise mechanism, whereas on superoleophobic surfaces it was drop-wise. The difference in the pathways of condensation was attributed to the various energy barriers separating the Cassie and Wenzel wetting states on the investigated surfaces. The higher barriers inherent for superoleophobic surfaces promoted the drop-wise condensation. Triple-stage kinetics of growth of droplets condensed on superoleophobic surfaces is reported and discussed.

physics.app-ph↗

arXiv2018

Co-occurrence of the Benford-like and Zipf Laws Arising from the Texts Representing Human and Artificial Languages

We demonstrate that large texts, representing human (English, Russian, Ukrainian) and artificial (C++, Java) languages, display quantitative patterns characterized by the Benford-like and Zipf laws. The frequency of a word following the Zipf law is inversely proportional to its rank, whereas the total numbers of a certain word appearing in the text generate the uneven Benford-like distribution of leading numbers. Excluding the most popular words essentially improves the correlation of actual textual data with the Zipfian distribution, whereas the Benford distribution of leading numbers (arising from the overall amount of a certain word) is insensitive to the same elimination procedure. The calculated values of the moduli of slopes of double logarithmical plots for artificial languages (C++, Java) are markedly larger than those for human ones.

cs.CL↗

arXiv2018

Wetting of Flat Gradient Surfaces

Gradient, chemically modified, flat surfaces enable directed transport of droplets. Calculation of apparent contact angles inherent for gradient surfaces is challenging even for atomically flat ones. Wetting of gradient, flat solid surfaces is treated within the variational approach, under which the contact line is free to move along the substrate. Transversality conditions of the variational problem give rise to the generalized Young equation valid for gradient solid surfaces. The apparent (equilibrium) contact angle of a droplet, placed on a gradient surface depends on the radius of the contact line and the values of derivatives of interfacial tensions. The linear approximation of the problem is considered. It is demonstrated that the contact angle hysteresis is inevitable on gradient surfaces. Electrowetting of gradient surfaces is discussed.

physics.flu-dyn↗