Perpendicular Symmetry Research Articles

In-Plane Design of Non-Circular Triangulated Tensile Spoke Wheels

This paper presents a new in-plane design of non-circular triangulated tensile spoke wheels with two perpendicular symmetry axes, like those used for roofing big sports stadiums, as well as a procedure to define such design. The proposed procedure describes how to define the in-plane shape and the necessary pre-stressing so that the outer ring behaves like a funicular polygon which has equal-length sides and is uniformly compressed. All in all, this procedure solves the problem of non-circularity of a triangulated spoke wheel by equalising the cross section sizing conditions of the outer ring to the sizing conditions that a circular structure would have.

Genomic incongruence accompanies the evolution of flower symmetry in Eudicots: a case study in the poppy family (Papaveraceae, Ranunculales).

Reconstructing evolutionary trajectories and transitions that have shaped floral diversity relies heavily on the phylogenetic framework on which traits are modelled. In this study, we focus on the angiosperm order Ranunculales, sister to all other eudicots, to unravel higher-level relationships, especially those tied to evolutionary transitions in flower symmetry within the family Papaveraceae. This family presents an astonishing array of floral diversity, with actinomorphic, disymmetric (two perpendicular symmetry axes), and zygomorphic flowers. We generated nuclear and plastid datasets using the Angiosperms353 universal probe set for target capture sequencing (of 353 single-copy nuclear ortholog genes), together with publicly available transcriptome and plastome data mined from open-access online repositories. We relied on the fossil record of the order Ranunculales to date our phylogenies and to establish a timeline of events. Our phylogenomic workflow shows that nuclear-plastid incongruence accompanies topological uncertainties in Ranunculales. A cocktail of incomplete lineage sorting, post-hybridization introgression, and extinction following rapid speciation most likely explain the observed knots in the topology. These knots coincide with major floral symmetry transitions and thus obscure the order of evolutionary events.

Large effective length and high efficiency by embedding L-shaped radiating blocks in subwavelength grating slot waveguide

Integrated optical antennas featuring large effective lengths and high radiation efficiency (RE) are essential to chip-scale light detection and ranging technology. However, there are challenges in simultaneously achieving both large effective length and high RE in silicon photonics platforms with high refractive index contrast. For traditional silicon waveguide grating antennas based on silicon photonics, the RE is relatively low and the antenna effective lengths are constrained to several hundred micrometers because of the high refractive index contrast. In this article, an embedded grating waveguide antenna which is L-shaped radiating blocks embedded in the slot gap of a silicon subwavelength grating slot waveguide is proposed and investigated numerically. Simulation results indicate the antenna’s effective length is above 4.25 mm, and the far-field divergence angle is near 0.0197°. Using L-shaped radiation blocks can break the diffraction’s perpendicular symmetry and increase the antenna’s RE to near 0.75 at 1550 nm compared to traditional design. Meanwhile, the antenna’s field-of-view reaches around 17.5° × 48.15° (θ× ϕ) to satisfy the needs of conventional optical phased arrays.

Orthotropic anisotropy: on contributions of elasticity parameters to a difference in quasi‐P‐wave‐squared velocities resulted from propagation in two orthogonal symmetry planes

ABSTRACTWe investigate the dependence of quasi P‐wave phase velocity propagating in orthotropic media on particular elasticity parameters. Specifically, due to mathematical facilitation, we consider the squared‐velocity difference, , resulted from propagation in two mutually perpendicular symmetry planes. In the context of the effective medium theory, may be viewed as a parameter evaluating the influence of cracks – embedded in the background medium – parallel to one or both aforementioned planes. Our investigation is both theoretical and numerical. Based on Christoffel's equations, we propose two accurate approximations of . Due to them, we interpret the aforementioned squared‐velocity difference as being twice more dependent on , than on . To describe the magnitude of the dependence, we consider the proportions between the partial derivatives of . Further, it occurs that is influenced by the ratio of vertically propagating quasi P‐wave to vertically propagating quasi S‐wave. Anomalously high might be caused by the low P/S ratio, which in turn can be an indicator of the presence of gas in natural fractures or aligned porosity. Also, we carry out numerical sensitivity study, according to which is approximately twice more dependent on than on , twice more sensitive to than to , and equally dependent on as on . The dependence on and can be neglected, especially for small phase angles. We verify the approximations and perform the sensitivity study, using eight examples of the elasticity tensors.

Static analysis and reanalysis of quasi-symmetric structure with symmetry components of the symmetry groups C3v and C1v

This work aims to discuss the static analysis and reanalysis of near-regular (quasi-symmetric) structures and to develop further the analysis of these structures based on the principle of general connect (coupling) and the group representation theory with symmetry groups C3v and C1v.During the analysis, only one-dimensional irreducible representations of different symmetry groups are taken into account, and we investigate the effect of these to the static analysis and to local modification method, as well.For these structures any general load can be decomposed into cyclic and asymmetric load, furthermore at most four symmetry components SSS, AAA (C3v) and S, A (C1v) (S – symmetric component, A – antimetric component) are used in this paper. The mentioned methods were applied for static analysis with two perpendicular symmetry planes; this paper examines the effect of three symmetry planes and considers the applicability in case of more-than-three symmetry planes for analysis.

Determination of loads in quasi-symmetric structure with symmetry components

This paper aims to describe the technique to analyse quasi-symmetric structures being subject to a general load. The paper introduces a general way of describing the symmetry properties of the structure, based on group representation theory (rectangular symmetry group C2v) and principle of general connect, and show how to simplify static structural analysis for quasi-symmetric structures with reflection symmetry only.Reflection symmetry is a main feature of the commercial vehicles, thus only this type of symmetry is considered. Naturally, there are a lot of parts in vehicle, where other symmetry types may occur. Two perpendicular symmetry planes are taken into account during examination. For these structures any general load can be split into symmetric and antimetric components, furthermore only four components SS, SA, AS and AA (S – symmetric component, A – antimetric component) are used in the paper during analysis. One part of these structures does not fulfil the geometrical and mechanical “perfect symmetry” requirements; therefore to extend the range of the analysis with using quasi-symmetry is required. This work distinguishes geometrical and mechanical quasi-symmetry, and takes bending moment only into consideration in the presented problems.

Oscillation of Confined Jets in Continuous Casting Mold Flow

AbstractIn continuous slab casting, the liquid steel is introduced into the mould via a submergered entry nozzle. This nozzle usually has two opposed orifices on its side walls, generating two diametrically opposed turbulent jets that are declined about 20° to the horizontal axis. These jets interact with the surrounding walls of the mould, which leads to an unstable flow situation and a self induced oscillation of the jets. Although both mould and nozzle geometry have two perpendicular symmetry planes, the oscillations are asymmetric. The fluid flow inside the mold is calculated with a 3D finite volume solver using turbulence models based on Reynolds‐averaging. The massflow of the jets and the mould extensions are varied, and the numerical results are partially compared with PIV‐measurements at a 1:1 scaled watermodel of the mould. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Ferromagnetic ordering in bis(benzene)chromium(+) Bis(4,5-dimethoxybenzene-1,2-dithiolato)nickel(-).

The compound bis(benzene)chromium(+) bis(4,5-dimethoxy-1,2-benzenedithiolato)nickel(-), [Cr(bz)(2)](+)[Ni(dmox)(2)](-), was prepared as well-defined crystals by a metathesis reaction. X-ray single-crystal structure confirms the expected symmetries of the cations (D6h) and anions (D2h). The Ni-S bond length is typical for a monoanionic bis(arene)-1,2-dithiolato nickel complex thus confirming the ascribed charges. The structure reveals interpenetrating cation and anion sublattices where all ions are well separated from other ions of the same charge and with almost perpendicular symmetry planes of cations and anions. Above ca. 10 K the compound is paramagnetic and follows the Curie-Weiss law for S = 1/2 on each ion with a Weiss temperature of 8.5 K. Magnetic susceptibility and magnetization studies reveal the transition to a ferromagnetically ordered phase at 3.4 K. The ferromagnetic interaction is likely to occur through short contacts between anion heteroatoms (O and Ni) and cation H atoms, forming a 2-D network. A third dimension is possible through somewhat longer interionic S-H contacts. The Curie-Weiss law behavior can be modeled for 1-D chains with a ferromagnetic interaction of J = 11.6 K.

Optical Second-Harmonic Generation in Benzophenone

Introduction Versatile and efficient sources of blue light are of fundamental importance for various applications including optical data storage [1,2], ophthalmologic or other medical techniques [3], and laser displays [4 to 6]. In spite of the rapid development of blue laser diodes [7,8] and concurrent physical principles like optical upconversion[9], the optical second-harmonic generation [10] (SHG) still is one of the most important methods to achieve intense coherent blue light with a good optical beam quality [11]. From symmetry aspects, SHG is only possible in crystals belonging to one of the 20 point groups which lack a center of symmetry [12]. Furthermore, to meet phase matching aspects in homogeneous crystals, refractive indices for the fundamental and the generated harmonic wavelength must be of identical size [13,14], optical birefringence is necessary. Here we discuss the properties of benzophenone (C 13 H 10 O), an organic crystal, which excellently meets the described conditions. Crystal Properties Crystals of benzophenone can be grown from the melt (melting point approximately 48°C) [15]. The crystal structure is orthorhombic with point symmetry 222. This forces the material to be optically biaxial with the axes of the indicatrix fixed to the three mutually perpendicular symmetry axes of the crystal. Theoretical studies revealed - due to the conjugated bonds - a good second order nonlinear optical polarizability [16]. Optical Absorption For optical applications in general - and especially for SHG - the material considered must be transparent in the wavelength region of interest. Measurements of the optical absorption in benzophenone show a region of excellent transparency spanning from 390 to 1700 nm. Depending on light polarization - parallel or perpendicular to the crystallographic c-axis - two typical spectra are found. The experimental results are sketched in Fig. 1.

Point symmetries in the Hartree-Fock approach. I. Densities, shapes, and currents

Three mutually perpendicular symmetry axes of the second order, inversion, and time reversal can be used to construct a double point group denoted by ${D}_{2h}^{\mathrm{TD}}.$ Properties of this group are analyzed in relation to the symmetry and symmetry-breaking effects within the mean-field (Hartree-Fock) theories, both in even and odd fermion systems. We enumerate space symmetries of local one-body densities, and symmetries of electromagnetic moments, that appear when some or all of the ${D}_{2h}^{\mathrm{TD}}$ elements represent self-consistent mean-field symmetries.

Point symmetries in the Hartree-Fock approach. II. Symmetry-breaking schemes

We analyze breaking of symmetries that belong to the double point group D2h(TD) (three mutually perpendicular symmetry axes of the second order, inversion, and time reversal). Subgroup structure of the D2h(TD) group indicates that there can be as much as 28 physically different, broken-symmetry mean-field schemes --- starting with solutions obeying all the symmetries of the D2h(TD) group, through 26 generic schemes in which only a non-trivial subgroup of D2h(TD) is conserved, down to solutions that break all of the D2h(TD) symmetries. Choices of single-particle bases and the corresponding structures of single-particle hermitian operators are discussed for several subgroups of D2h(TD).

Dynamics of HI photodissociation in the A band absorption via H-atom Doppler spectroscopy

The dynamics of HI photodissociation following absorption in the A band (200 to 300 nm) was investigated by Doppler spectroscopy at the Lyman α transition of the H-atom photofragments. Measurements of both the branching ratios for the formation of spin-orbit excited I(2P1/2) and ground state I(2P3/2) atoms and the angular distributions of the recoil velocity for these two photofragment channels were obtained at nine photolysis wavelengths between 212.5 and 266 nm. These results show that ground state products result from a transition of perpendicular symmetry (ΔΩ=1), while the excited state atoms are produced from a parallel transition (ΔΩ=0). These experimental results, in combination with total absorption cross section data obtained prior to the present study, have enabled a calculation of the potential curves for the dissociative excited states. The outcome of the calculation was found to be in good qualitative agreement with the model of HI electronic structure originally suggested by Mulliken.

D2h-symmetric nuclear shapes of higher multipolarities

Nuclear surfaces having three mutually perpendicular symmetry planes (D2h symmetry) are parametrized in terms of Oh-covariant deformation parameters. A method is presented how all the deformation parameters can be made dependent on the quadrupole deformation through arbitrary scalar functions. Specific results for multipolarity λ=6 are cited by way of example.

De Haas-Van alphen effect in Pd 2Si

A de Haas-van Alphen study of the disilicide Pd 2Si has been performed. The sample is rotated in two perpendicular symmetry planes. In the basal plane five frequency branches are observed, in the other plane only two. A Fermi surface geometry is deduced which is characterized by one large open sheet and several small pockets. This geometry is in reasonable agreement with a band structure calculation if in the latter the Fermi energy is slightly decreased.

De Haas-van Alphen effect in Pd2Si

A de Haas-van Alphen study of the disilicide Pd 2 Si has been performed. The sample is rotated in two perpendicular symmetry planes. In the basal plane five frequency branches are observed, in the other plane only two. A Fermi surface geometry is deduced which is characterized by one large open sheet and several small pockets. This geometry is in reasonable agreement with a band structure calculation if in the latter the Fermi energy is slightly decreased.

ASHRAE 93-77 Instantaneous and All-Day Tests of the Sunpak™ Evacuated-Tube Collector

The results of ASHRAE 93-77 instantaneous and all day tests for two Sunpak™ evacuated-tube collectors are presented and discussed in terms of a simple dynamic response model and a biaxial incidence angle modifier approximation. The dynamic model predicts, and experimental results confirm, a residence time type of response rather than the exponential response that is assumed to characterize most collectors. The anisotropic geometries of the two collectors require that their optical properties be described by an incidence angle modifier that depends on both solar altitude and azimuth in the tilted aperture plane. The test results support the idea that this dependence can be characterized with sufficient accuracy by a biaxial approximation which requires that incidence angle modifiers be measured in each of two mutually perpendicular symmetry planes of the collectors. The all-day measurements are compared with the results to be expected from the ASHRAE 93-77 instantaneous tests, and excellent agreement is obtained when the dynamic model is used to account for the time variations in insolation and inlet temperature. It is concluded that the two Sunpak™ evacuated-tube models can be characterized adequately within the scope of ASHRAE 93-77, but that measurements over and above those actually required by this standard are necessary for a complete characterization. In addition, it is recommended that these collectors be tested on a tracking mount because of their long response times. Such instantaneous test results, in combination with the dynamic model, can be used to predict daily and long-term performance under most conditions.

Rotation of an isolated triaxial ellipsoid suspended in slow viscous flow

A freely suspended triaxial ellipsoid, or particle with two perpendicular symmetry planes, orients in a creeping flow at a rate given by differential equations in the three Euler angles, derived here for simple shear flow. The parameters for a given particle are three components of Bretherton's tensor; observations along two directions in space suffice to determine these. Any ellipsoid's two axis ratios can be chosen with the second deviating from unity less than the square root of the first. Numerical integration shows that, in contrast to the orbits of Jeffery, the particle has no fixed period of rotation about the fluid's vorticity axis. The longest axis of a rod-like triaxial particle crosses the plane perpendicular to the fluid vorticity, a motion impossible for an axisymmetric particle. In typical graphs for a quarter rotation, times required and changes in orientation are shown. Lack of axial symmetry implies that a suspension of such particles can be more disoriented.

On pseudo-rotation in (AsCH3)5 and (AsCF3)5

Two internal rearrangement processes can be deduced from the temperature dependences of the 1H and 19F nuclear magnetic resonance (n.m.r.) spectra of the asymmetric puckered five-membered ring compounds (AsCH3)5, (AsCF3)5, and (PCF3)5. The first is a fast "butterfly" motion of the ring puckering which yields a time-averaged plane of symmetry perpendicular to the ring through the puckered atom. This motion could not be stopped in any of the three compounds by cooling, even to −130 °C in the case of (AsCF3)5. The second is a slow pseudo-rotation, or a rotation of the perpendicular symmetry plane around the ring yielding a time-averaged fivefold rotation axis. There is a choice between two mechanisms for this second rearrangement, either a "clickstop" process in which the puckering progresses around the ring by one position at a time, or a "pancake" process in which the puckering drops randomly into any one of the five ring positions from a planar transition state. This choice can be resolved for this cyclic permutation process by appeal to the n.m.r. lineshapes. The present data for (AsCH3)5 favor the "clickstop" mechanism in spite of a competing intermolecular process at elevated temperatures with other components in the system which are in equilibrium with the ring compound.