A Descriptor System and Principles for Numbering Closed Boron Polyhedra with at Least One Rotational Symmetry Axis and One Symmetry Plane

1981 ◽  
Vol 20 (7) ◽  
pp. 2350-2352 ◽  
Author(s):  
James B. Casey ◽  
William J. Evans ◽  
Warren H. Powell
Keyword(s):  
Symmetry Axis ◽  
Rotational Symmetry ◽  
Symmetry Plane ◽  
Descriptor System

scholarly journals Nonlinear Optical Properties of Spheroidal Metallic Inclusions in a Dielectric Medium

2011 ◽  
Vol 2011 ◽  
pp. 1-9
Author(s):  
Bernard de Dormale ◽  
Vo-Van Truong
Keyword(s):  
Optical Properties ◽  
Nonlinear Optical ◽  
Symmetry Axis ◽  
Rotational Symmetry ◽  
Strong Dependence ◽  
Wavelength Region ◽  
Nonlinear Optical Properties ◽  
Linear Absorption ◽  
Direction Parallel ◽  
Depolarization Factor

A model for linear and nonlinear optical properties of a composite material consisting of spheroidal metal inclusions embedded in a host medium has been formulated using an effective medium approach. Both aligned and randomly oriented spheroids have been considered, and the results obtained showed a considerable difference between the two situations. Numerical calculations for metallic Au inclusions in a glass matrix have shown that the linear absorption in the case of aligned spheroids with their symmetry axis parallel to the z-axis is largely dependent on the depolarization factor, exhibiting an absorption in the vicinity of 500 nm when the depolarization factor in the direction parallel to the rotational symmetry axis is small. This structure shifts progressively to higher wavelengths when this depolarization factor is increased. In the case of randomly oriented spheroids, contributions from the different particle depolarization factors are present and prominent structures in the linear absorption appear in the long wavelength region, beyond 700 nm. Nonlinear optical properties for both aligned and randomly oriented spheroids also show a strong dependence on the depolarization factor and significant enhancements of these properties can be observed, suggesting possible tailoring of composite properties for various applications.

scholarly journals Pose Estimation of Sweet Pepper through Symmetry Axis Detection

Sensors ◽  
2018 ◽  
Vol 18 (9) ◽  
pp. 3083 ◽  
Author(s):  
Hao Li ◽  
Qibing Zhu ◽  
Min Huang ◽  
Ya Guo ◽  
Jianwei Qin
Keyword(s):  
Pose Estimation ◽  
Point Cloud ◽  
Fruits And Vegetables ◽  
Symmetry Axis ◽  
Symmetry Plane ◽  
Estimation Method ◽  
Sweet Pepper ◽  
Average Error ◽  
Simulated Test ◽  
Local Plane

The space pose of fruits is necessary for accurate detachment in automatic harvesting. This study presents a novel pose estimation method for sweet pepper detachment. In this method, the normal to the local plane at each point in the sweet-pepper point cloud was first calculated. The point cloud was separated by a number of candidate planes, and the scores of each plane were then separately calculated using the scoring strategy. The plane with the lowest score was selected as the symmetry plane of the point cloud. The symmetry axis could be finally calculated from the selected symmetry plane, and the pose of sweet pepper in the space was obtained using the symmetry axis. The performance of the proposed method was evaluated by simulated and sweet-pepper cloud dataset tests. In the simulated test, the average angle error between the calculated symmetry and real axes was approximately 6.5°. In the sweet-pepper cloud dataset test, the average error was approximately 7.4° when the peduncle was removed. When the peduncle of sweet pepper was complete, the average error was approximately 6.9°. These results suggested that the proposed method was suitable for pose estimation of sweet peppers and could be adjusted for use with other fruits and vegetables.

Estimation of fracture parameters from reflection seismic data—Part II: Fractured models with orthorhombic symmetry

Geophysics ◽  
2000 ◽  
Vol 65 (6) ◽  
pp. 1803-1817 ◽  
Author(s):  
Andrey Bakulin ◽  
Vladimir Grechka ◽  
Ilya Tsvankin
Keyword(s):  
Symmetry Axis ◽  
Fractured Reservoirs ◽  
Symmetry Plane ◽  
P Wave ◽  
Single Fracture ◽  
Orthorhombic Symmetry ◽  
Weak Anisotropy ◽  
Horizontal Symmetry ◽  
Vertical Symmetry Plane ◽  
Vertical Fractures

Existing geophysical and geological data indicate that orthorhombic media with a horizontal symmetry plane should be rather common for naturally fractured reservoirs. Here, we consider two orthorhombic models: one that contains parallel vertical fractures embedded in a transversely isotropic background with a vertical symmetry axis (VTI medium) and the other formed by two orthogonal sets of rotationally invariant vertical fractures in a purely isotropic host rock. Using the linear‐slip theory, we obtain simple analytic expressions for the anisotropic coefficients of effective orthorhombic media. Under the assumptions of weak anisotropy of the background medium (for the first model) and small compliances of the fractures, all effective anisotropic parameters reduce to the sum of the background values and the parameters associated with each fracture set. For the model with a single fracture system, this result allows us to eliminate the influence of the VTI background by evaluating the differences between the anisotropic parameters defined in the vertical symmetry planes. Subsequently, the fracture weaknesses, which carry information about the density and content of the fracture network, can be estimated in the same way as for fracture‐induced transverse isotropy with a horizontal symmetry axis (HTI media) examined in our previous paper (part I). The parameter estimation procedure can be based on the azimuthally dependent reflection traveltimes and prestack amplitudes of P-waves alone if an estimate of the ratio of the P- and S-wave vertical velocities is available. It is beneficial, however, to combine P-wave data with the vertical traveltimes, NMO velocities, or AVO gradients of mode‐converted (PS) waves. In each vertical symmetry plane of the model with two orthogonal fracture sets, the anisotropic parameters are largely governed by the weaknesses of the fractures orthogonal to this plane. For weak anisotropy, the fracture sets are essentially decoupled, and their parameters can be estimated by means of two independently performed HTI inversions. The input data for this model must include the vertical velocities (or reflector depth) to resolve the anisotropic coefficients in each vertical symmetry plane rather than just their differences. We also discuss several criteria that can be used to distinguish between the models with one and two fracture sets. For example, the semimajor axis of the P-wave NMO ellipse and the polarization direction of the vertically traveling fast shear wave are always parallel to each other for a single system of fractures, but they may become orthogonal in the medium with two fracture sets.

DETERMINATION OF THE ELASTIC CONSTANTS OF ANISOTROPIC SOLIDS FROM GROUP VELOCITIES MEASURED IN SYMMETRY DIRECTIONS

1996 ◽  
Vol 10 (02) ◽  
pp. 235-246 ◽  
Author(s):  
KWANG YUL KIM ◽  
ARTHUR G. EVERY ◽  
WOLFGANG SACHSE
Keyword(s):  
Group Velocity ◽  
Elastic Constants ◽  
Symmetry Axis ◽  
Symmetry Plane ◽  
Orthorhombic Symmetry ◽  
Easy Method ◽  
Novel Method ◽  
Complete Set ◽  
Wave Normal

We present in this article a novel method of determining all three elastic constants of cubic crystals from a single broadband waveform propagating in the [001] direction. The method can be easily extended to media of orthorhombic symmetry whose symmetry plane quasitransverse (QT) group velocity sheet is folded across the symmetry axis. The usefulness of these formulas lies in providing a very convenient and easy method of determining all the elastic constants of a medium from the rays propagating in the principal symmetry directions of the medium. Particular emphasis is given to the so-called oblique-mode QT rays with group velocity lying along a symmetry axis but with wave normal lying away from that axis in a symmetry plane. Through the use of these oblique modes the need to make off-axis measurements to obtain a complete set of elastic constants is circumvented. Moreover, we describe a method of clarifying the ambiguity that arises; with which symmetry plane is the wave normal of an oblique-mode QT ray propagating in the symmetry axis associated. Further, we show how the effect of a finite rise time source can be corrected for in the determination of a mixed index elastic constant.

scholarly journals Modeling of quasicrystal lattices with a 4-fold symmetry axis

2018 ◽  
Vol 26 (2) ◽  
pp. 49-54
Author(s):  
O. V. Smolyakov
Keyword(s):  
Symmetry Axis ◽  
Flat Surface ◽  
Rotational Symmetry ◽  
Reciprocal Lattice ◽  
Lattice Points ◽  
Hypercubic Lattice ◽  
Indexing System ◽  
Icosahedral Quasicrystals ◽  
Quasiperiodic Structures ◽  
Projection Approach

The construction method of a quasilattice with a four-fold rotational symmetry axis is proposed. The described method is based on the recurrent generation of the initial group of lattice points, which are a set of vertices of a square. The aperiodic crystal reciprocal lattice modeling algorithm is analyzed. Used modeling technique is compared with conventional projection approach. The orthogonal basis of a four-dimensional hypercubic lattice is proposed. This lattice produces two-dimensional quasicrystal with a four-fold symmetry axis after it projection on a flat surface. It is shown that the indexation of diffraction pattern of similar quasiperiodic structures can be carry out using 3 integer indexes, which is analogous to the indexing system proposed by Cahn for application to icosahedral quasicrystals.

An improved magnetic prism design for a transmission electron microscope energy filter

1978 ◽  
Vol 36 (1) ◽  
pp. 40-41 ◽  
Author(s):  
John W. Andrew ◽  
F.P. Ottensmeyer ◽  
E. Martell
Keyword(s):  
Energy Resolution ◽  
Symmetry Plane ◽  
Fringe Field ◽  
Focal Distance ◽  
Electron Trajectories ◽  
Focusing Effect ◽  
Transmission Electron ◽  
Path Lengths ◽  
Electron Microscopes ◽  
Focusing Properties

Energy selecting electron microscopes of the Castaing-Henry prism-mirror-prism design suffer from a loss of image and energy resolution with increasing field of view. These effects can be qualitatively understood by examining the focusing properties of the prism shown in Fig. 1. A cone of electrons emerges from the entrance lens crossover A and impinges on the planar face of the prism. The task of the prism is to focus these electrons to a point B at a focal distance f2 from the side of the prism. Electrons traveling in the plane of the diagram (i.e., the symmetry plane of the prism) are focused toward point B due to the different path lengths of different electron trajectories in the triangularly shaped magnetic field. This is referred to as horizontal focusing; the better this focusing effect the better the energy resolution of the spectrometer. Electrons in a plane perpendicular to the diagram and containing the central ray of the incident cone are focused toward B by the curved fringe field of the prism.

Comparison of Calculated and Recorded Electron Energy-Loss Spectra of Aluminium and Carbon

1990 ◽  
Vol 48 (2) ◽  
pp. 64-65
Author(s):  
L. Reimer ◽  
R. Oelgeklaus
Keyword(s):  
Fourier Transform ◽  
Energy Loss ◽  
Electron Energy ◽  
Rotational Symmetry ◽  
Mean Free Path ◽  
Single Scattering ◽  
Specimen Thickness ◽  
Two Dimensional ◽  
Image Position ◽  
Electron Energy Loss

Quantitative electron energy-loss spectroscopy (EELS) needs a correction for the limited collection aperture α and a deconvolution of recorded spectra for eliminating the influence of multiple inelastic scattering. Reversely, it is of interest to calculate the influence of multiple scattering on EELS. The distribution f(w,θ,z) of scattered electrons as a function of energy loss w, scattering angle θ and reduced specimen thickness z=t/Λ (Λ=total mean-free-path) can either be recorded by angular-resolved EELS or calculated by a convolution of a normalized single-scattering function ϕ(w,θ). For rotational symmetry in angle (amorphous or polycrystalline specimens) this can be realised by the following sequence of operations :(1)where the two-dimensional distribution in angle is reduced to a one-dimensional function by a projection P, T is a two-dimensional Fourier transform in angle θ and energy loss w and the exponent -1 indicates a deprojection and inverse Fourier transform, respectively.

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