Center Of Symmetry Research Articles

Liquid free boundary in vertical gap subject to modulated rotation

The effect of rotation velocity modulation on the equilibrium shape of the liquid-air interface in a vertical slot gap rotating around a horizontal axis is studied experimentally. The case is considered when the modulation frequency coincides with the rotation frequency. It is found that in this case, velocity modulation leads to a violation of the axial symmetry of the interface formed by the centrifugal force of inertia. The displacement of the center of symmetry of the interface increases linearly with the amplitude of the velocity modulation and decreases quadratically with the speed of rotation. It is shown that the detected phenomenon is explained by the averaged effect of an external gravitational field on a fluid in a rotating frame of reference.

Scour at a Submerged Square Pile in Various Flow Depths under Steady Flow

Local scour around submerged piles in currents are common in coastal and offshore engineering. This paper studies the influences of the submergence ratio (flow depth to pile height) on local scour around a square pile in steady flow. Submergence ratio ranging from 1–4, as well as two unsubmerged tests, were tested with a 10 × 10 square pile of 20 cm height. The three-dimensional profiles were measured to study the scour and deposition characteristics. Results show that the maximum scour depth was always at the upstream corner points rather than at the symmetry center point of the pile. The temporal maximum scour depth achieved its equilibrium sate in less than 4 h for each test. The equilibrium scour depths at the upstream corner points were independent of the submergence ratio when the latter was larger than 1.5. These findings give meaningful reference to the numerical simulations and local scour depth protections in the submerged pile cases deeper than which the flow depth does not affect the equilibrium scour depth.

An equivalent damage model to fretting fatigue initiation life considering wear

A new damage constitutive model is developed to predict the fretting initiation fatigue, taking the damage accumulation caused by wear into account. Instead of moving mesh technique, wear effect is considered by equivalent damage, which deceases the calculation cost and reflects characteristics of damage accumulation. It is found that wear accelerates the nucleation in the slip zone, and contributes more effect under low stress amplitude. Effect of friction coefficient on initiation life is greater than that of normal pressure, and the initiation crack location is far away from the center of symmetry due to large friction coefficient and normal pressure.

Acoustic sorting of airborne particles by a phononic crystal waveguide

A two-dimensional phononic crystal linear defect waveguide is utilized for size-based sorting of millimeter-sized solid particles in the air through acoustic radiation force. The waveguide channels ultrasonic waves at 20 kHz, as calculated through Finite-Element Method simulations. Spherical solid particles released from rest at the top of the vertically aligned waveguide experience the combined effect of the acoustic radiation, gravity, and drag forces. When the particles are released from the symmetry plane of the waveguide, they follow straight paths where the ones with radii smaller than a threshold value are trapped at the waveguide nodal planes, whereas larger particles are let pass through. This requires input sound pressure levels between 173 dB and 177 dB. Moreover, such particles can also be differentiated with respect to density. Alternatively, the release of particles with a slight offset from the symmetry center induces unbalanced acoustic radiation potential, and thus uneven radiation force, resulting in the initiation of horizontal displacement whose extent depends on particle radius. Thus, both simulation results and experimental findings suggest that this scheme can be employed in size-based particle separation. Sorting of spherical glass particles with 0.5 mm and 1.0 mm radii are experimentally demonstrated for low ultrasonic transducer acoustic power output up to 90 W. The proposed approach can be utilized in applications where contact-free separation of airborne particles is required.

Efficient algorithm for simulating particles in true quasiperiodic environments

We introduce an algorithm based on generalized dual method (GDM) to efficiently study the dynamics of a particle in quasiperiodic environments without the need to use periodic approximations or to save the information of the vertices that make up the quasiperiodic lattice. We show that the computation time and the memory required to find the tile in which a particle is located as a function of the distance R to the center of symmetry remains constant in our algorithm, while using the GDM directly both quantities go like R 2. This allows us to perform realistic simulations with low consumption of computational resources. The algorithm can be used to study any quasiperiodic lattice that can be produced by the cut-and-project method. Using this algorithm, we have calculated the free path length distribution in quasiperiodic Lorentz gases reproducing previous results and for systems with high symmetries at the Boltzmann–Grad limit. We have found for the Boltzmann–Grad limit, that the distribution of free paths depends on the rank r of the quasiperiodic system and not on its symmetry. The distribution as a function of the free path length l appears to be a combination of exponential decay and a power-law behavior. The latter seems to become important only for probabilities less than , showing an exponential decaying free-path length distribution for r → ∞, similar to what is observed in disordered systems.

A Study on Integrity Testing for Platform-Pile Systems considering Wave Propagation

Platform-pile systems are typically used in bridge foundations and seaport structures. These systems are difficult to analyze using a conventional low-strain integrity test (LST) due to periodic oscillations. A staggered-grid finite-difference (SFD) method is proposed for a platform-pile system in soil and verified with ABAQUS and measured data. Different impact locations on the top surface of the platform and the lateral surface of the pile are analyzed, and parallel velocities are obtained at different locations. Choosing an appropriate impact location reduces the influence of the periodic oscillation signal; the impact locations at the center of symmetry are the best choices. At the same impact energy, the impact location should not be outside the cross section of the pile when the impact occurs on the top surface of the platform to achieve a meaningful damage signal. When the impact locations are on the lateral surface of the pile, the interferences are relatively small, and the damage vibration signal can be detected. The material and size of the hammer determine the impact duration and should be chosen to reduce the high-frequency influences and obtain reasonable data for analysis.

Spherically symmetric vacuum solutions and horizons in covariant f(T) gravity theory

In this paper we study properties that the vacuum must possess in the minimal extension to the teleparallel equivalent of general relativity (TEGR) where the action is supplemented with a quadratic torsion term. No assumption is made about the weakness of the quadratic term although in the weak-field regime the validity of our previously derived perturbative solution is confirmed. Regarding the exact nature of the vacuum, it is found that if the center of symmetry is to be regular, the mathematical conditions on the tetrad at the isotropy point mimic those of general relativity. With respect to horizons it is found that, under very mild assumptions, a smooth horizon cannot exist unless the quadratic torsion coupling, $\alpha$, vanishes, which is the TEGR limit (with the Schwarzschild tetrad as its solution). This analysis is then supplemented with computational work utilizing asymptotically Schwarzschild boundary data. It is verified that in no case studied does a smooth horizon form. For $\alpha > 0$ naked singularities occur which break down the equations of motion before a horizon can form. For $\alpha < 0$ there is a limited range of $\alpha$ where a vacuum horizon might exist but, if present, the horizon is singular. Therefore physically acceptable black hole horizons are problematic in the studied theory at least within the realm of vacuum static spherical symmetry. These results also imply that static spherical matter distributions generally must have extra restrictions on their spatial extent and stress-energy bounds so as to render the vacuum solution invalid in the singular region and make the solutions finite.

Curtain-type phase unwrapping algorithm

A curtain-type phase unwrapping algorithm is proposed. First, the 2 × 2 closed curve method is used to find out the residual point of the wrapped phase to form the residual template, and the Otsu threshold method is used to binary the modulation of the deformed pattern to form the shadow template. Second, the effective phases of up-down symmetrical points about the starting point are simultaneously unwrapped in turn until all the points in the column are completed. Third, the starting point is taken as the center of left-right symmetry, the effective phases of the nearest symmetric points are simultaneously unwrapped, and the corresponding columns are unwrapped in the same way as above. Fourth, in this way, the effective phases in the corresponding symmetric columns are successively unwrapped in the form of curtain opening until the whole phases are completely unwrapped. In the previous procedure, the shadow template and residual template guide the curtain-type phase unwrapping to avoid error diffusion. Finally, the 8-neighborhood mean algorithm and the cubic b-spline algorithm are employed to unwrap the phase values of residual points and shadow areas, respectively. The proposed method realizes the whole phase unwrapping without phase error diffusion. Experimental results show that the efficiency of the proposed method is 26% higher than that of the diamond algorithm, and its accuracy is significantly improved.

Crystal structure of bis-(ammonium) bis-[penta-aqua-(di-methyl-formamide)-zinc(II)] deca-vanadate tetra-hydrate.

The crystalline product (NH4)2[Zn(C3H7NO)(H2O)5]2[V10O28]·4H2O was success-fully isolated from an H2O/DMF solvent combination by evaporation at ambient temperature. The salt crystallizes in the P21/n space group. Imidazole, initially used in the synthesis but not present in the product, and DMF solvent appear to affect the synthesis and crystallization as structural-directing agents. In the title compound, the complex cation [Zn(H2O)5(DMF)]2+ acts as a counter-ion without being directly coordinated to the deca-vanadate anion. An extensive framework of hydrogen bonds integrates the whole architecture as evidenced by X-ray crystallography. The polyoxometalate [V10O28]6- lies on a center of symmetry while the complex cation [Zn(H2O)5(DMF)]2+ links three adjacent anions through a set of 2+2+3 hydrogen bonds.

Dislocation Equilibrium Positions on Either Side of a Grain Boundary

Abstract The equilibrium positions of two edge dislocations located on either side of a grain boundary have been determined when a disclination dipole is lying in the boundary. It is found that a configuration where the dislocations are distributed symmetrically with respect to the center of symmetry of the grain boundary is selected. This configuration depends on the disclination strength and the dislocation distance from the boundary.

Synthesis and structure of vanadium (IV) single-stranded dihelicate involving multi-ring nitrogen-heterocyclic ligand

1 The single stranded-helicate Vanadium(IV) complex [V2O2Cl4(L)(H2O)2] (1) involving heterocyclic bis-bidentate ligand viz. 3,3/-dipyridine-2-yl-[1.1/]bi[imidazo[1,5-a]pyridineyl] (L) with biological relevance is prepared and characterized by X-ray diffraction analysis. The compound lacks molecular center of symmetry where coordination environments around V(1) and V(2) centres are distorted octahedral (V···V# separation of 5.827 Å). Structure of the compound in the solid state structure shows anion−π interactions, classical and Carene-H---anion non-classical H-bonding interactions. These interactions play significant roles in shaping the extended structure of this molecule.

Rotation induced symmetry change of friction coefficient of water on graphene/h-BN heterostructures

The graphene/h-BN heterostructure provides a promising device for biomedical applications and biosensor. However, the friction characteristics of water on graphene/h-BN are still elusive. By means of molecular dynamics simulations, we investigated the friction coefficient of water on both sides of graphene/h-BN heterostructures under various rotation angle, which shows a non-monotonic but symmetrical variation with relative interlayer angle. Despite that friction coefficient of h-BN surface is larger than that of graphene, as the rotation angle increases, the friction coefficient of water on both sides of the graphene/h-BN heterostructure exhibits the same “M”-shaped curve. The center of symmetry of the curve is at the rotation angle of 30°; the friction coefficient is the largest when the rotation angle is 10° and 50°. It was found that graphene/h-BN heterostructure is a device whose friction coefficient is different on both sides and can be adjusted by twisting the relative interlayer angle. These results could be demonstrated by the van der Waals interaction and different pattern of free energy landscape. These findings provide detailed insights into the mechanism of the friction property of water at nanoscale, which would facilitate feasible applications of graphene/h-BN heterostructure in biosensor and biomedicine.

Non-Sinusoidal Waves in a Metamaterial, Specified as a Nonlinear Elastic Lattice with a Center of Symmetry

It is proposed a mathematical model of a metamaterial which is represented as a nonlinear elastic two-mass chain with a center of symmetry. The model was continualized. The conditions for the formation of non-sinusoidal strain waves are analyzed.

Crystal structures of N-[4-(tri-fluoro-meth-yl)phen-yl]benzamide and N-(4-meth-oxy-phen-yl)benz-amide at 173 K: a study of the energetics of conformational changes due to crystal packing.

As a part of our study of the syntheses of aryl amides, the crystal structures of two benzamides were determined from single-crystal X-ray data at 173 K. Both crystal structures contain mol-ecular units as asymmetric units with no solvent in the unit cells. Crystal structure I, TFMP, is the result of the crystallization of N-[4-(tri-fluoro-meth-yl)phen-yl]benzamide, C14H10F3NO. Crystal structure II, MOP, is composed of N-(4-meth-oxy-phen-yl)benzamide, C14H13NO2, units. TFMP is triclinic, space group P , consisting of two mol-ecules in the unit cell related by the center of symmetry. MOP is monoclinic, space group P21/c, consisting of four mol-ecules in the unit cell. Both types of mol-ecules contain three planar regions; a phenyl ring, an amide planar region, and a para-substituted phenyl ring. The orientations of these planar regions within the asymmetric units are compared to their predicted orientations, in isolation, from DFT calculations. The aryl rings are tilted approximately 60° with respect to each other in both experimentally determined structures, as compared to 30° in the DFT results. These conformational changes result in more favorable environments for N-H⋯O hydrogen bonding and aryl ring π-stacking in the crystal structures. Inter-molecular inter-actions were examined by Hirshfeld surface analysis and qu-anti-fied by calculating mol-ecular inter-action energies. The results of this study demonstrate that both hydrogen bonding and dispersion are essential to the side-by-side stacking of mol-ecular units in these crystal structures. Weaker dispersion inter-actions along the axial directions of the mol-ecules reveal insight into the melting mechanisms of these crystals.

Poly[dipotassium [(μ6-2,2',2'',2'''-{[pyrazine-2,3,5,6-tetra-yltetra-kis-(methyl-ene)]tetra-kis-(sulfanedi-yl)}tetra-acetato)-disilver(I)] 5.2-hydrate

The reaction of AgNO3 with the ligand 2,2',2'',2'''-{[pyrazine-2,3,5,6-tetra-yltetra-kis-(methyl-ene)]tetra-kis-(sulfanedi-yl)}tetra-acetic acid in the presence of a potassium acetate buffer lead to the formation of a silver(I)-potassium-organic framework, poly[dipotassium [(μ6-2,2',2'',2'''-{[pyrazine-2,3,5,6-tetra-yltetra-kis(methyl-ene)]tetra-kis-(sulfanedi-yl)}tetra-acetato)-disilver(I)] 5.2-hydrate], {K2[Ag2(C16H16N2O8S4)]·5.2H2O} n , (I). The asymmetric unit is composed of half a binuclear silver complex located about a center of symmetry, a potassium cation and 2.6 disordered water mol-ecules. The whole binuclear silver complex is generated by inversion symmetry with the pyrazine ring being located about an inversion centre. The ligand coordinates in a bis-tetra-dentate manner. The binuclear silver complex anions are linked via bridging Ag⋯S⋯Ag zigzag bonds, forming a network lying parallel to the bc plane. The networks are linked by Ocarboxyl-ate⋯K +⋯Ocarboxyl-ate bridging bonds to form a framework. The disordered water mol-ecules are present near to the K+ cations.

Length scale formation in the Landau levels of quasicrystals

Exotic tiling patterns of quasicrystals have motivated extensive studies of quantum phenomena such as critical states and phasons. Nevertheless, the systematic understanding of the Landau levels of quasicrystals in the presence of the magnetic field has not been established yet. One of the main obstacles is the complication of the quasiperiodic tilings without periodic length scales, thus it has been thought that the system cannot possess any universal features of the Landau levels. In this paper, contrary to these assertions, we develop a generic theory of the Landau levels for quasicrystals. Focusing on the two dimensional quasicrystals with rotational symmetries, we highlight that quasiperiodic tilings induce anomalous Landau levels where electrons are localized near the rotational symmetry centers. Interestingly, the localization length of these Landau levels has a universal dependence on n for quasicrystals with n-fold rotational symmetry. Furthermore, macroscopically degenerate zero energy Landau levels are present due to the chiral symmetry of the rhombic tilings. In this case, each Landau level forms an independent island where electrons are trapped at given fields, but with field control, the interference between the islands gives rise to an abrupt change in the local density of states. Our work provide a general scheme to understand the electron localization behavior of the Landau levels in quasicrystals.

A Comprehensive Analysis of Hyperbolical Fluids in Modified Gravity.

This paper is devoted to understanding a few characteristics of static irrotational matter content that assumes hyperbolical symmetry. For this purpose, we use metric gravity to carry out our analysis. It is noticed that the matter distribution cannot fill the region close to the center of symmetry, thereby implying the existence of an empty core. Moreover, the evaluation of the effective energy density reveals that it is inevitably negative, which could have utmost relevance in understanding various quantum field events. To derive the structure scalars, we perform the orthogonal splitting of the Riemann tensor in this modified gravity. Few relationships among matter variables and both Tolman and Misner Sharp are determined. Through two generating functions, some hyperbolically symmetric cosmological models, as well as their physical interpretations, are studied. To delve deeply into the role of terms, the model of the less-complex relativistic system of Einstein gravity is presented.

Hyperbolically symmetric sources in [formula omitted] gravity

This paper studies the static fluid distributions admitting the hyperbolically symmetric structure by extending the work of Herrera et al. (2021) in f(R,T) gravity. The unavailability of the fluid distribution in the region which is close to the center of symmetry has been observed. A vacuum cavity can be used to depict this region around the center. The effective matter density emerges inevitably to be negative and this implies that the conceivable use of such fluids needs transcendental physical conditions when the significant quantum effects are observed. Furthermore, the Tolman mass, as well as an appropriate formulation of the mass function, are particularly computed. Along with this, we evaluated the structure scalars through the orthogonal splitting of the Riemann tensor in this modified gravity. Imposing the conditions of conformal flatness and stiff equation of state, we constructed several models for the less-complex systems. We also evaluated the generating functions to study the fluid distribution in this theory. A general hypothesis to attain precise solutions are also conferred through matter-curvature coupling.

Effects and mechanism of (Be/Mg/Ca) doping and point defects (VZn, Hi) on the p-type conductivity of ZnO: A first-principles study

A stable and reliable p-type ZnO semiconductor is difficult to obtain, because ZnO crystals have a hexagonal wurtzite structure, they have no center of symmetry, and the c-axis direction exhibits polarity. The preparation of ZnO materials by using growth techniques, such as metal–organic chemical vapor deposition or hydrogenated vapor phase epitaxy, will produce a large amount of H interstitial, that is difficult to remove. To solve this problem, we applied the generalized gradient approximation method and performed density functional theory in this work, to study the influences of Be/Mg/Ca single doping and the coexistence of Zn vacancies and H interstitial on the conductivity of ZnO. This study found that the formation energy of Zn34MHiO36 (M = Be/Mg/Ca) system is lower than that of the doped system the Zn34MO36 (M = Be/Mg/Ca), and the formation energy of Zn34BeHiO36 is the smallest. The hole mobility and conductivity of all the doped systems parallel to the c-axis direction are larger than those of the systems parallel to the a-axis direction. Among them, the hole mobility and conductivity of the Zn34CaHiO36 system are the largest. This study exerts a guiding effect on the design and preparation of new p-type ZnO conductive functional materials.

Crystal structure of N,N,N',N'-tetra-methyl-ethane-di-amine.

The title compound N,N,N',N'-tetra-methyl-ethanedi-amine, C6H16N2, is a bidentate amine ligand commonly used in organolithium chemistry for deaggregation. Crystals were grown at 243 K from n-pentane solution. The complete mol-ecule is generated by a crystallographic center of symmetry and the conformation of the di-amine is anti-periplanar. To investigate the inter-molecular inter-actions, a Hirshfeld surface analysis was performed. It showed that H⋯H (van der Waals) inter-actions dominate with a contact percentage of 92.3%.