Symmetry Axis Research Articles

DETERMINATION OF THE UPPER LIMIT OF THE LOAD-LOADING CAPACITY OF BENDING REINFORCED METAL-COMPOSITE RING PLATES IN CONTACT WITH A LIQUID INCOMPRESSIBLE MEDIUM 1. PROBLEM FORMULATION AND CALCULATION METHOD

The problem of determining the load-bearing capacity of a bendable reinforced annular plate resting on an incompressible liquid base is considered. The internal opening of the structure is closed with a continuous, absolutely rigid insert. The connection between the insert and the plate can be rigid or hinged. The structure is supported on the outer edge, and it is possible to move the support in the vertical direction, for example in the case of a movable jamming. In the limiting state, liquid flow from one front surface of the plate to another surface is not allowed. The materials of the components of the composition are isotropic and rigid-plastic, having the same yield limits in tension and compression. Plastic flow in the phases of the composition is associated with piecewise linear yield criteria (such as the Tresk's or Ishlinsky - Ivlev's yield conditions). The limit state of such a composite plate is described within the framework of the classical theory of transverse bending. Reinforcement structures have axial and radial symmetry. Two reinforcement options are considered: laying two families of fibers along radially symmetrical spiral trajectories and reinforcement in the radial and circumferential directions. The rein-forcing fibers are assumed to be continuous and have constant cross sections along their length, which gives rise to significant heterogeneity of the structures under consideration in the radial direction. The plastic flow of a metal-composition is calculated using a structural model that takes into account the presence of a plane stress state in all substructural elements. Structural formulas have been written that make it possible to determine the coordinates of corner points on piecewise linear yield curves of the compositions under consideration, taking into account their dependence on non-uniform reinforcement parameters: angles and densities. An extremal principle has been formulated that makes it possible to obtain an upper (kinematic) estimate of the maximum load for this type of structure. The formulated problem is discretized along the polar radius. Nodal values of the sagging speed and mechanical energy dissipation were used as unknown grid functions. A numerical algorithm for solving the formulated discretized problem has been developed, based on the application of the simplex method of linear programming theory.

Coexistence of topological node surface and Dirac fermions in phonon-mediated superconductor YB2C2.

The interaction between nontrivial topology and superconductivity in condensed matter physics has attracted tremendous research interest as it could give rise to exotic phenomena. Herein, based on first-principles calculations, we investigate the electronic structures, mechanical properties, topological properties, dynamic stability, electron-phonon coupling (EPC), and superconducting properties of the synthesized real material YB2C2. It is a tetragonal structure with P4/mbm symmetry and exhibits excellent stability. The calculated electronic band structures reveal that a zero-dimension (0D) Dirac point and two-dimensional (2D) nodal surface coexist near the Fermi level. A spin-orbit coupling (SOC) Dirac point with the topological Fermi arc is observed on the (001) surface. These nodal surfaces are protected by a two-fold screw axis and time-reversal symmetry. Based on the Bardeen-Cooper-Schrieffer theory, the superconducting transition temperature (Tc) in the range 1.25-4.45 K with different Coulomb repulsion constant μ* for YB2C2 is estimated to be consistent with previous experimental results. In addition, the EPC is mainly from the coupling between the dx2-y2 and dz2 orbitals of the Y atom and low-energy phonon modes. The presence of superconductivity and nontrivial topological surface state in YB2C2 suggests that it may be a candidate material for topological superconductors.

Induction Motor Vibrations Caused by Mechanical and Magnetic Rotor Eccentricity

Vibration reduction of induction motors is a significant problem that requires effective models for the effects of mechanical and electromagnetic unbalanced forces. This article presents a mathematical model of dynamics for induction motors with rotor mass eccentricity and static and dynamic magnetic eccentricity. The model allows for the influence of the gyroscopic torque of the rotor and considers the elastic-damping characteristics of each of the stator supports and their location. The model has eight degrees of freedom, which makes it possible to simulate transverse and axial vibrations of various designs’ rotors and housings of induction motors. The results of modeling the dynamics for a three-phase squirrel cage induction motor with 11 kW capacity agreed with those obtained by other authors. Simultaneously, new results were also obtained within the research. The simulation results showed that the static magnetic eccentricity causes the appearance of additional critical speed of the motor, and its value decreases in proportion to the growth of the number of pole pairs. The change of the moment of inertia of the motor at a mismatch of the main axis of symmetry of the stator and the rotor axis of rotation allowed for obtaining an actual frequency spectrum of free oscillations, including the rotational motion of the stator. Since the actual static magnetic eccentricity can additionally increase at operating frequencies due to the increase of bearing clearance caused by dynamic unbalanced load, it should be considered in the analysis of unbalanced magnetic pull. The angle of static magnetic eccentricity significantly affects the magnitude of radial vibrations. This feature should also be considered when selecting the locations of balancing weights during the rotor balancing procedure.

Приготовление растворов различной концентрации

When preparing treatment solutions of fertilizers and pesticides for technological processes, one should mix liquids taking into account the precise dosing of components. However, the existing designs of dosing and mixing devices do not provide qualitative dosing. Moreover, a sharp increase of fraction quantity may result in a hydraulic impact. To eliminate these disadvantages, based on analytical research of available designs and patent search results, the authors worked out a mixer for preparing solutions of various concentrations. The device is also capable of changing the ratio of components in the process of operation. The device provides smooth change of preparation concentrations due to the design of dosing valves forming square-shaped ports with a changing configuration. The port plates move relative to each other both horizontally and vertically. The proposed device smoothly changes the concentration of the solution, thereby providing for more accurate dosing. It was experimentally found that a smoother change in the flow rate of treatment liquid according to the solution concentration is observed at a distance from the axes of symmetry of the dosing device disks to the rotation axis of the distribution ports, equal to 0.04 to 0.1 m. The deviation of the actual treatment liquid flow rate from the calculated one does not exceed 5%. The integration of the developed mixer into the systems of fertigation units, sprayers and other specialized machines will ensure better quality of the fine irrigation of plants, seeds, and soil.

МОДЕЛЬ ПРОГНОЗИРОВАНИЯ РЕСУРСА УПРОЧНЕННЫХ МОЛОТКОВ КОРМОДРОБИЛЬНЫХ МАШИН

During operation, the working parts (hammers) of hammertype feed-crushing machines are subjected to intense wear. The maximum wear of the working edge of the hammer is considered to be wear up to the main axis of symmetry. To reduce wear and increase the service life of the hammer, a technology of combined hardening of the working edge of the hammer with a hard alloy plate using iron-carbon solder is proposed. This work is based on theoretical substantiations and experimental processing of production tests of hardened hammers. (Research purpose) The research purpose is searching for the regularities of the wear process of hardened hammers from operating time during the operation of the feed crushing machine. (Materials and methods) The design and technological parameters and mechanical properties of the materials of the hardened hammer were substantiated. Methods of processing the results of production tests based on mathematical statistics and reliability theory, comparative methods of analysis of hardened and serial hammers were presented. (Results and discussion) The results of studies of experimental hardened hammers were presented, in which the mechanical strength and the magnitude of the diffusion zone of the soldered connection of a hard alloy with the material of the hammer and the iron-carbon solder used in this case were determined. We carried out a theoretical analysis of the dependence of hammer wear on operating time and constructed a mathematical model for predicting the life of a hardened hammer. It was determined as a result of theoretical studies that with the combined hardening of the working edge of the hammer of the feed-crushing machine with a hard alloy VK8 using iron-carbon solder, the maximum operating time increases by 2.76 times. (Conclusions) The results of theoretical studies and production tests prove that the resource of hardened hammers has increased 3.5 times compared to serial ones. The constructed mathematical model for predicting the life of hardened hammers accurately reflects the results of experimental values of the dependence of hammer wear on operating time.

The influence of orthopedic rapid maxillary expansion on the deviation of the nasal septum.

Nasal septal deviation (NSD) is one of the most common abnormalities impacting the maxillofacial development of children. Herein, we investigated the impact of orthopedic rapid maxillary expansion (RME) on the nasomaxillary complex and NSD in pediatric patients. The study sample consisted of a total of 40 patients divided into two groups. The experimental group included 26 patients (13 females and 13 males) with skeletal maxillary transversal constriction and NSD greater than 1 mm, while the control group comprised 14 patients (6 females and 8 males) with skeletal maxillary transversal constriction but no NSD. All the patients were treated for approximately 15 days with the tooth-tissue born RME device. The activation procedure was to turn the transversal Hyrax screw a quarter turn, twice a day. After that, the device was left in place for a period of five months to facilitate passive retention. Radiographic analysis was performed on posteroanterior (PA) cephalometric radiographs taken at pre-expansion (T1) and post-expansion (T2). The data were evaluated using the Mann-Whitney U and Wilcoxon Sign tests. The experimental group showed a statistically significant decrease (p < 0.05) in the distance from the axis of symmetry to middle of nasal septum (SNM-mid) and to inferior part of the nasal septum (SNI-mid) measurements, indicating a reduction in NSD. Additionally, both experimental and control groups showed a statistically significant increase (p < 0.05) in maxillofacial measurements, including the distance between the nose length (X-SNM and SNM-SNAC), width of the nasal cavity (Pir L-R), basal maxillary width (Mx L-R), vestibular cuspid of upper first molars (CVM + L-R) and lower first molars (CVM-L-R). Based on the study findings, RME was considered effective in achieving craniofacial improvement in pediatric patients with NSD, which positively impacted their healthy growth and development. The improvement in the nasomaxillary complex was similar between genders.

Фрески придела святителя Николая Мирликийского в соборе Рождества Богородицы Ферапонтова монастыря: принципы визуализации житийного цикла

The Cathedral of the Nativity of the Virgin of the Ferapontov Monastery houses the life of St. Nicholas of Myra, consisting of 12 episodes, the earliest one among Russian murals. The cathedral was painted by the artel of the Muscovite painter Dionisy in 1502. The frescoes of St. Nicholas chapel (actually, a sacristy) with the central image of the Saint, located in the conch of the altar apse, have attracted much attention. Researchers did not fail to notice the expressiveness and psychological characterisation of the face of St. Nicholas in the central image. The combination of the themes of the Theotokos and St. Nicholas in the Ferapontov Cathedral was a manifestation not only of the Byzantine tradition but also of the idea of spe-cial closeness of St. Nicholas to the Mother of God characteristic for the Russian religiosity. The iconographic program of Cathedral’s sanctuary with the image of John the Baptist and the consecration of the sacristy to St. Nicholas, was unusual for the Russian tradition, but echoed mosaic decorations of side apses with a similar dedication in the Cathedral of the Assumption of the Virgin in Daphne (circa 1100). The custom of having a side church in the sacristy was widely spread in Byzantium and was also adopted in Medieval Russia. When examining the frescoes of St. Nicholas chapel, scientists did not pay sufficient attention to the principles of placement and order of scenes running in the space of the apse in two tiers, but not in a chron-ological order. In this regard, a hypothesis was formulated about the influence of the hagiog-raphic icons of St. Nicholas on the spatial composition of the paintings in St. Nicholas chapel. This paper discusses both strong and weak sides of this hypothesis with a purpose to further the study of the problem. When studying the location of the episodes of the cycle, we found that a few scenes were placed relative to each other in a similar manner. In addition, it turned out that the main principle governing the placement of the episodes was the principle of pair-ing. Within the pair, scenes and images were selected in accordance with iconographic simi-larity or a thematic relation. The axis of symmetry of the apse was of crucial importance. The compositions were distributed in the space of the sacristy with visual and semantic balance relative to this axis. The very principle of the spatial design, where thematically related scenes were placed opposite to each other endowed the entire composition with completeness and integrity, being quite different from a linear historical narrative with a more primitive visual conception.

Hierarchical self-assembly of Au-nanoparticles into filaments: evolution and break.

We compare the assembly of individual Au nanoparticles in a vacuum and between two Au(111) surfaces via classical molecular dynamics on a timescale of 100 ns. In a vacuum, the assembly of three nanoparticles used as seeds, initially showing decahedral, truncated octahedral and icosahedral shapes with a diameter of 1.5-1.7 nm, evolves into a spherical object with about 10-12 layers and a gyration radius ∼2.5-2.8 nm. In a vacuum, 42% show just one 5-fold symmetry axis, 33% adopt a defected icosahedral arrangement, and 25% lose all 5-fold symmetry and display a face-centred-cubic shape with several parallel stacking faults. We model a constrained version of the same assembly that takes place between two Au(111) surfaces. During the dynamics, the two Au(111) surfaces are kept fixed at distances of 55 Å, 55.5 Å, 56 Å, and 56.5 Å. The latter distance accommodates 24 Au layers with no strain, while the others correspond to nominal strains of 1.5%, 2.4%, and 3.3%, respectively. In the constrained assembly, each individual seed tends to reorganize into a layered configuration, but the filament may break. The probability of breaking the assembled nanofilament depends on the individual morphology of the seeds. It is more likely to break at the decahedron/icosahedron interface, whilst it is more likely to layer with respect to the (111) orientation when a truncated octahedron sits between the decahedron and the icosahedron. We further observe that nanofilaments between surfaces at 56 Å have a >90% probability of breaking, which decreases to 8% when the surfaces are 55 Å apart. We attribute the dramatic change in probability of breaking to the peculiar decahedron/icosahedron interface and the higher average atomic strain in the nanofilaments. This in silico experiment can shed light on the understanding and control of the formation of metallic nanowires and nanoparticle-assembled networks, which find applications in next-generation electronic devices, such as resistive random access memories and neuromorphic devices.

Разрывное конически симметричное течение идеальной несжимаемой жидкости

The Euler equations are considered in spherical coordinates to describe the steady flow of an ideal incompressible fluid. An exact conically symmetric solution based on the source/sink and strong conic discontinuity with an apex in zero of the coordinate system is obtained. The northern region of the flow is situated in the finite vicinity of the symmetry axis, i.e., within a discontinuity cone, where the solution is regular and vortex-free. On the other side of the discontinuity, the flow adjoins the permeable equator plane. In this region, the flow is vortex-like, and its properties are determined by a density jump. The fluid flowing through the discontinuity is governed by the increase of entropy principle. The thermal field corresponding to the flow is presented. It shows that the spatial heterogeneity of temperature results from the interaction between the azimuth vorticity component and the meridional velocity component. A strong discontinuity cone angle is revealed to be a significant parameter of the problem. A comparative analysis of the source and sink properties is performed. The considered flows qualitatively differ in terms of pressure and velocity behavior.

Расчетно-экспериментальное исследование закрученного кольцевого потока

In the course of work on the energy perfection of thermal control systems for spacecraft with a twophase circuit, the issue of partial regeneration of thermal energy into electrical energy in a low-speed turbogenerator is considered, part of the design work requires computational modeling during the transport of swirling flows in the axial direction from the external input to the input plane into the impeller, which determines the need for theoretical and experimental elaboration of the problem. The paper considers transformations of equations for changing the amount of fluid motion in boundary conditions of an axial annular channel with fixed cylindrical surfaces. Assuming the symmetry axis of the flows using the integral form of writing the continuity equation, the relations are obtained in the form of two differential equations with expressed derivatives along the channel axis for the total pressure p* and the circumferential velocity constant Cu = UR (const — at the integration step). The equation forms the basis of the algorithm of integration in finite differences supplemented by a system of service equations describing the friction stress, thermodynamic parameters, etc. Test calculations are carried out using real parameters, the results are analyzed.

X-Ray Polarized View of the Accretion Geometry in the X-Ray Binary Circinus X-1

Cir X-1 is a neutron star X-ray binary characterized by strong variations in flux during its eccentric ∼16.6 day orbit. There are also strong variations in the spectral state, and it has historically shown both atoll and Z state properties. We observed the source with the Imaging X-ray Polarimetry Explorer during two orbital segments, 6 days apart, for a total of 263 ks. We find an X-ray polarization degree in these segments of 1.6% ± 0.3% and 1.4% ± 0.3% at polarization angles of 37° ± 5° and −12° ± 7°, respectively. Thus, we observed a rotation of the polarization angle by 49° ± 8° along the orbit. Because variations of accretion flow, and then of the hardness ratio, are expected during the orbit, we also studied the polarization binned in hardness ratio and found the polarization angle differing by 67° ± 11° between the lowest and highest values of the hardness ratio. We discuss possible interpretations of this result that could indicate a possible misalignment between the symmetry axes of the accretion disk and the Comptonizing region caused by the misalignment of the neutron star’s angular momentum with respect to the orbital one.

Characterization of anisotropy in basin-scale subsurface using teleseismic receiver function analysis

Teleseismic receiver function (RF) analysis offers a passive-source analogue to detect impedance boundaries using the converted body waves generated by earthquakes. While the technique traditionally has targeted deep earth structures such as the Moho and transition zones, there is growing interest in assessing its applicability in basin-scale seismic characterization, ultimately aimed for onshore commercial integration as a cost-effective complement to existing active-source seismic surveys. Specifically, the conventional broadband seismometers used in global observational seismic experiments are not only logistically simple in terms of data acquisition, but they also record ground motions in three mutually orthogonal time series, enabling effective detection of shear waves and directional variations of observed signals. Here, we perform teleseismic RF analysis to detect shear-wave anisotropy and related symmetry axes orientations in a basin setting, using open-source seismic data recorded at 55 closely spaced seismic stations in the LaBarge Passive Seismic Experiment deployed in Wyoming between November 2008 and June 2009. We find that the strengths and geometry of the observed anisotropy are variable along the array. Significantly, not only can anisotropy effectively delineate subsurface fault interfaces, it can also substantiate and reveal additional interpretable signals that are otherwise disregarded. The estimated fast axes orientations compare favorably with the complex fracture systems documented in the region. Finally, we show that P-to-S amplitude variations with P incidence are systematic and modelable using existing computational tools, offering an opportunity to develop an analysis technique similar to amplitude variation with offset with the products of RF analysis.

Gas heating by nanosecond repetitively pulsed glow discharges applied to a methane–air flame

In this work, the thermal effect induced by non-equilibrium plasma produced by nanosecond repetitively pulsed (NRP) glow discharges applied across a lean premixed methane–air flame is investigated. The flame is laminar, stationary, and axis-symmetric. The discharges are applied on the symmetry axis of the flame, crossing the fresh reactants, flame front, and burned gases. The obtained plasma-assisted flame is stable and reproducible, allowing phase-locked averaged diagnostics. The thermal effect is investigated by acquiring spatially and temporally resolved temperature measurements in the plasma discharges using optical emission spectroscopy (OES) of the second positive system of nitrogen. The results show that for an applied voltage of 10 kV, NRP glow discharges increased the gas temperature by up to 130 K within 10 ns. However, this heating was location-dependent, i.e., high near the anode tip and not detectable 0.5 mm above the anode. It was also shown that reducing the applied voltage down to 9 kV caused this ultra-fast heating to disappear. On the other hand, the reactants near the anode tip had a constant temperature of 480 K, between discharges, while the reactants were injected at 293 K. The reason for this slow heating could be due to (1) heating by the flame which is pulled down to the anode when NRP discharges are applied, (2) slow gas heating induced by relaxation of vibrational excited states of nitrogen, or (3) post-discharge oxidation chemistry. Based on temperature measurements performed on NRP corona discharges, heating by the flame could be ruled out. Zero-dimensional numerical simulations’ results suggest that post-discharge oxidation chemistry can heat the gas by 110–130 K, indicating that this is an important heating mechanism. Further investigation will be necessary to assess the significance of the vibrational–translational relaxation of nitrogen.

Combining and segmenting geometric shapes into parts depending on symmetry type: Evidence from children and adults.

Symmetry is an important geometric feature that affects object segmentation into parts, though De Winter and Wagemans note that partly occluded objects can still be identified by the remaining visible parts. In two sets of experiments with children (n = 31, age 7-11, M = 8.8, SD = 1.4) and adults (n = 19, age 17-57, M = 30.4, SD = 12.6), we used 13 basic geometric figures distinguished by symmetry types to test how they are naturally segmented or combined and what the developmental impacts are on the segmentation and combination. In the first experiment, participants were asked to cut figures into two along a straight line; in the second experiment, participants had to create five sets of connected two-figure combinations where overlapping figures were allowed. The results confirmed the importance of the symmetry axis in both tasks. Other relevant criteria were dividing into half, maximal/minimal curvature, and use of edges or corners for reference. This study allows comparisons of the impact of symmetry type on the segmentation and combining of geometric figures and indicates developmental differences between children and adults.

Subcycle Conservation Law in Strong-Field Ionization

Exploiting the infinite-order continuous dynamical rotational symmetry of circularly or elliptically polarized classical light pulses, we establish the conservation law between the angular momentum and energy in strong-field ionization that is applicable at the subcycle level. We illustrate the conservation law through the correlated spectrum of angular momentum and energy of photoelectrons, both at the tunnel exit and in the asymptotic region. Moreover, we propose a protocol based on electron vortices to directly visualize the existence of the subcycle conservation law. Our work paves the pathway toward a deeper understanding of fundamental light–matter interactions on the subcycle scale.

Pair correlations of the easy magnetisation axes of superparamagnetic nanoparticles in a ferrofluid/ferrocomposite.

The widespread use of magnetic nanoparticles in modern technologies and medical applications highlights the need for reliable theoretical models that can predict their physical properties. The pair correlation function of two randomly selected superparamagnetic nanoparticles in a ferrofluid/ferrocomposite is studied to depict the joint probability density of the easy magnetisation axes across the planes of parameters of major importance; these are the interaction of ferroparticles with an external magnetic field, the energy of magnetic anisotropy inside the superparamagnetic nanoparticle, and the interparticle magnetic dipole-dipole interaction. Assuming the rotational symmetry of the system, we come to the conclusion that the pair correlations of interest are dependent only on the polar angles, determining the inclinations of the ferroparticle easy axes from the direction of an external magnetic field. The dimer configuration, where two ferroparticles are in close contact along a magnetic field with their easy magnetisation axes aligned, is the most probable. This configuration becomes more pronounced with increasing anisotropy energy, dipolar coupling constant, and external magnetic field.

On rotation invariant integrable systems

The problem of finding the first integrals of the Newton equations in the $n$-dimensional Euclidean space is reduced to that of finding two integrals of motion on the Lie algebra $\mathrm{so}(4)$ which are invariant under $m\geq n-2$ rotation symmetry fields. As an example, we obtain several families of integrable and superintegrable systems with first, second, and fourth-degree integrals of motion in the momenta. The corresponding Hamilton-Jacobi equation does not admit separation variables in any of the known curvilinear orthogonal coordinate systems in the Euclidean space.

Transition mechanism of the coverage-dependent polymorphism of self-assembled melamine nanostructures on Au(111).

Molecular self-assembled films have recently attracted increasing attention within the field of nanotechnology as they offer a route to obtain new materials. However, careful selection of the molecular precursors and substrates, as well as exhaustive control of the system evolution is required to obtain the best possible outcome. The three-fold rotational symmetry of melamine molecules and their capability to form hydrogen bonds make them suitable candidates to synthesize this type of self-assembled network. In this work, we have studied the polymorphism of melamine nanostructures on Au(111) at room temperature. We find two coverage-dependent phases: a honeycomb structure (α-phase) for submonolayer coverage and a close-packed structure (β-phase) for full monolayer coverage. A combined scanning tunnel microscopy and density functional theory based-calculations study of the transition regime where both phases coexist allows describing the mechanism underlying this coverage driven phase transition in terms of the changes in the molecular lateral tension.

Visualizing localized nematic states in twisted double bilayer graphene.

Direct visualization of the states originating from electron-electron interactions is of great importance for engineering the surface and interfacial properties of graphene-based quantum materials. For instance, the rotational symmetry breaking or nematic phase inferred from spectroscopic imaging has confirmed the existence of correlated states in a wide range of moiré materials. Here, we study the atomic-scale spatial distributions and symmetry of wave functions in gate-tunable twisted double bilayer graphene by employing scanning tunneling microscopy/spectroscopy and continuum model calculations. A series of spectroscopic imaging analyses are used to identify dominant symmetry breaking of the emergent states. Interestingly, in non-integer hole fillings, a completely new localized electronic state with rotational symmetry breaking is observed on the left side of the valence flat band. The degree of anisotropy is found to increase from the conduction flat band through the valence flat band to the new state. Our results provide an essential microscopic insight into the flat band and its adjacent state for a full understanding of their electric field response in twisted graphene systems.

Visualization of steam with Venn diagrams

An understanding of STEM and STEAM and their visualization through Venn diagrams are presented. For the visualization of a Venn diagram of 5 groups, Grünbaum's idea with application of rotational symmetry of a curve is used. Several embodiments are described.