Orthogonal Surfaces Research Articles

Piezoelectrically operated MEMS corner cube retroreflector for optical communications

A bulk-micromachined corner cube retroreflector (CCR) was designed and fabricated for free-space optical communications with ultra-low voltage operation and negligible power consumption. The proposed CCR was comprised of a bulk-micromachined vertical mirror which has two mutually orthogonal reflective surfaces and a horizontal mirror with piezoelectric actuator. The fabricated vertical and horizontal mirrors have sizes of 300 µm × 300 µm and 150 µm × 150 µm, respectively. The vertical mirror was fabricated using a double silicon-on-insulator wafer and the anisotropic wet etching of a (1 1 0) silicon wafer. The horizontal mirror was comprised of two supporting and one actuating lead zirconate titanate (PZT) cantilevers. The supporting cantilevers were utilized for the accurate angular alignment of the mirror by balancing and isolating the residual stresses occurring in the PZT cantilevers. The bottom-actuated mirror exhibited an angular displacement of 1.37° at an applied voltage of 5 V. The fabricated CCR exhibited a good angular misalignment of less than 0.35° and switching characteristics with an off-to-on-state transition of 163 µs and on-to-off-state transition of 276 µs at a rectangular input voltage and switching frequency of 10 V and 1 kHz, respectively. The fabricated CCR also exhibited a cutoff frequency of 2.5 kHz and could be digitally modulated up to about 5 kb s−1.

Reflection characteristics of a composite planar AMC surface

This study investigates the reflection characteristics of a composite Artificial Magnetic Conductor (AMC) surface consisting of multiple orthogonal gradient AMC surfaces arranged in a two-dimensional periodic pattern. The gradient AMC surface in this study consists of square metal patches of variable size printed on a grounded dielectric substrate. Due to the orthogonal placement of the gradient AMC surface, the incident energy of a plane wave normally incident on the composite AMC surface will be reflected into four major lobes away from the impinging direction. To achieve a systematical design, a simple formula based on array antenna theory was developed to determine the reflection pattern of the gradient AMC surface illuminated by a normal incident plane wave. A time-domain full-wave simulation was also carried out to calculate the electromagnetic fields in the structure and the far-field patterns. The scattering patterns of the structure were measured in an electromagnetic anechoic chamber. Results confirm the design principle and procedures in this research. Since such a composite AMC surface can be easily fabricated using the standard printed circuit board technique without via-hole process, it may have potential applications in beam-steering and radar cross section reduction.

Low Temperature Sensitization on the Orthogonal Surfaces of Prior Deformed AISI 304LN and Aged at 673 K to 873 K (400 °C to 600 °C)

This study investigates the sensitization behavior of AISI 304LN deformed previously by cold rolling (CR) to 5 pct to 25 pct reduction in thickness and aged at 673 K to 873 K (400 °C to 600 °C). The emphasis was on revealing the degree of sensitization (DOS) resulting from low-temperature sensitization (LTS) on the orthogonal surfaces and correlation thereof with the changes in various metallurgical properties caused by cold rolling. It was found that the DOS differs among the orthogonal surfaces such as the rolling surface (RS), transverse surface (TS), and cross transverse surface (CTS). RS showed lower DOS compared with CTS and TS. The differences in the DOS were attributed to the combined effect of deformation-induced martensite (DIM), grain size, and slip band formation. A deformation of 5 pct was critical to the susceptibility of AISI 304LN to intergranular (IGC) and transgranular corrosion (TGC). The sensitization kinetics was slow or saturated leading to desensitization beyond 5pct deformations at 773 K (500 °C) and 873 K (600 °C). It was, however, uniformly accelerated over 5 to 25 pct deformation when aged at 673 K (400 °C).

Light Scattering of Rough Orthogonal Anisotropic Surfaces with Secondary Most Probable Slope Distributions

We study the light scattering of an orthogonal anisotropic rough surface with secondary most probable slope distribution. It is found that the scattered intensity profiles have obvious secondary maxima, and in the direction perpendicular to the plane of incidence, the secondary maxima are oriented in a curve on the observation plane, which is called the orientation curve. By numerical calculation of the scattering wave fields with the height data of the sample, it is validated that the secondary maxima are induced by the side face element, which constitutes the prismoid structure of the anisotropic surface. We derive the equation of the quadratic orientation curve. Experimentally, we construct the system for light scattering measurement using a CCD. The scattered intensity profiles are extracted from the images at different angles of incidence along the orientation curves. The experimental results conform to the theory.

Signature of a three-dimensional photonic band gap observed on silicon inverse woodpile photonic crystals

We have studied the reflectivity of CMOS-compatible three-dimensional silicon inverse woodpile photonic crystals at near-infrared frequencies. Polarization-resolved reflectivity spectra were obtained from two orthogonal crystal surfaces using an objective with a high numerical aperture. The spectra reveal broad peaks with maximum reflectivity of $67%$ that are independent of the spatial position on the crystals. The spectrally overlapping reflectivity peaks for all directions and polarizations form the signature of a broad photonic band gap with a relative bandwidth up to $16%$. This signature is supported with stop gaps in plane-wave band-structure calculations and with the frequency region of the expected band gap.

Market Prices of Orthogonal Risk and Risk Aversion in Complete Stochastic Volatility Models: Theoretical and Empirical

Considering a production economy with an arbitrary von-Neumann Morgenstern utility, this paper derives a general equilibrium relationship between the market prices of risks and market risk aversion under a continuous time stochastic volatility model completed by liquidly traded options. Empirical market price of orthogonal risk and risk aversion surfaces as well as their time series are obtained from traded option prices. It is found that implied risk aversion exhibits a smiling pattern across strikes and highly correlates with regular macrofinance variables.

A characterization of Weingarten surfaces in hyperbolic 3-space

We study 2-dimensional submanifolds of the space \({\mathbb{L}}({\mathbb{H}}^{3})\) of oriented geodesics of hyperbolic 3-space, endowed with the canonical neutral Kähler structure. Such a surface is Lagrangian iff there exists a surface in ℍ3 orthogonal to the geodesics of Σ.We prove that the induced metric on a Lagrangian surface in \({\mathbb{L}}({\mathbb{H}}^{3})\) has zero Gauss curvature iff the orthogonal surfaces in ℍ3 are Weingarten: the eigenvalues of the second fundamental form are functionally related. We then classify the totally null surfaces in \({\mathbb{L}}({\mathbb{H}}^{3})\) and recover the well-known holomorphic constructions of flat and CMC 1 surfaces in ℍ3.

Determination of Easy Magnetization Axis of Mordenite Zeolite

Abstract The easy-magnetization axis of mordenite zeolite was determined using commercially available mordenite powder. The well-dispersed suspension of the powder was consolidated by slip casting in a 12-T static magnetic field. The thick bulk deposit was cut into a dice in order to investigate the XRD patterns from the mutually orthogonal surfaces of the consolidated mordenite compacts, the normal lines of which surfaces were parallel and perpendicular to the applied magnetic field. The easy-magnetization axis of mordenite was determined to be the b axis based on the XRD measurements.

MR Harmonic Phase surface for tracking cardiac motion

Purpose Quantitative analysis of left ventricle motion can be performed by tracking the tag surfaces motion, where the intersection of orthogonal tag surfaces resolves the 3D motion of the heart tissue. Although, previous work was done to construct tag surfaces between image slices, it was restricted to the specific tag lines and not between them. The reconstruction of the tag surfaces, based on their harmonic phase value, enables an accurate tracking of 3D motion of the cardiac tissue, which will enable an objective and accurate assessment of cardiac function.

Inverse Solution of Soil-Water Transport Model Parameters Using Response Surface Methodology

<emph italic=no/>Soil hydraulic properties influence crop yield, soil fertility, and soil water status. While the laboratory or direct methods of measuring hydraulic properties are accurate, they are expensive, time consuming, and may not represent in-situ properties. On the other hand, model-based inverse solution procedures or indirect methods of estimating soil hydraulic conductivity (K) relate primary model variables such as volumetric water content (<emph>θ</emph>) and soil water suction (<emph>ψ</emph>) to K and the soil-water characteristic curve. In this study, an inverse solution technique was developed to determine saturated soil hydraulic conductivity (K<emph subscript=yes>s</emph>, cm h<emph superscript=yes>-1</emph>) and plant conductance to water uptake (C, m<emph superscript=yes>-1</emph> min<emph superscript=yes>-1</emph>) under field conditions using a 1-D water transport model. The soil water content data (<emph>θ</emph>) were measured at 12 locations and at several depths at each location within the root zone in two different alfalfa checks using access tubes (each 1.5 m deep) and a neutron moisture probe. The inverse solution process utilized the measured soil moisture conditions in the alfalfa checks between two successive irrigations. In this study, the soil water retention curve was assumed to be of the form described by van Genuchten. The water contents at upper (0.225 m) and lower (1.2 m) depths provided the boundary conditions (BCs) needed for the model. The water content readings immediately following the irrigation event (i.e., t = 0) were used as the initial condition (IC). The model was solved to develop third-order orthogonal response surfaces over a range of model parameters (K<emph subscript=yes>s</emph> and C). Moreover, a multiple linear regression technique was used to empirically relate experimental <emph>θ</emph> to the depth and time of measurements. The response surface solutions were then optimized against the empirical surface to seek the optimum values of K<emph subscript=yes>s</emph> and C. The parameters estimated by the inverse solution technique were found to be unique and robust, and they predicted experimentally observed soil water data very well (R<emph superscript=yes>2</emph> > 0.95 and slope = 1:1 for most of the cases). These parameters, known from the inverse solution technique, were used to estimate the amount of deep percolation beyond the root zone depth for all cases.

Mapping mesoscale heterogeneity in the plastic deformation of a copper single crystal

Part of a ‘multiscale characterization’ study of heterogeneous deformation patterns in metals is reported. A copper single crystal was oriented for single slip in the (111)[] slip system and tested to ∼10% strain in roughly uniaxial compression. The macroscopic strain field was monitored during the test by optical ‘image correlation’. The strain field was measured on orthogonal surfaces, one of which (the x-face) was oriented perpendicular to [] and contained the [] direction of the preferred slip system. The macroscopic strain developed in an inhomogeneous pattern of broad, crossed shear bands in the x-face. One, the primary band, lay parallel to (111). The second, the ‘conjugate’ band, was oriented perpendicular to (111) with an overall () habit that contains no common slip plane of the fcc crystal. The mesoscopic deformation pattern was explored with selected area diffraction, using a focused synchrotron radiation polychromatic beam with a resolution of 1–3 µm. Areas within the primary, conjugate and mixed (primary + conjugate) strain regions of the x-face were identified and mapped for their orientation, excess defect density and shear stress. The mesoscopic defect structure was concentrated in broad, somewhat irregular primary bands that lay nominally parallel to (111) in an almost periodic distribution with a period of about 30 µm. These primary bands were dominant even in the region of conjugate strain. There were also broad conjugate defect bands, almost precisely perpendicular to the primary bands, which tended to bridge primary bands and terminate at them. The residual shear stresses were large (ranging to well above 500 MPa) and strongly correlated with the primary shear bands; interband stresses were small. The maximum resolved shear stresses within the primary bands were oriented out of the plane of the bands, and, hence, could not recover the dislocation structure in the bands. The maximum resolved shear stresses in the interband regions lay predominantly in {111} planes. The results are compared to the mesoscopic defect patterns found in Cu in etch pit studies done some decades ago, which also revealed a mesoscopic dislocation structure made up of orthogonal bands.

Orthogonal Surfaces and Their CP-Orders

Orthogonal surfaces are nice mathematical objects which have interesting connections to various fields, e.g., integer programming, monomial ideals and order dimension. While orthogonal surfaces in one or two dimensions are rather trivial already the three dimensional case has a rich structure with connections to Schnyder woods, planar graphs and three-polytopes. Our objective is to detect more of the structure of orthogonal surfaces in four and higher dimensions. In particular we are driven by the question which non-generic orthogonal surfaces have a polytopal structure. We review the state of knowledge of the three-dimensional situation. On that basis we introduce terminology for higher dimensional orthogonal surfaces and continue with the study of characteristic points and the cp-orders of orthogonal surfaces, i.e., the dominance orders on the characteristic points. In the generic case these orders are (almost) face lattices of polytopes. Examples show that in general cp-orders can lack key properties of face lattices. We investigate extra requirements which may help to have cp-orders which are face lattices. Finally, we turn the focus and ask for the realizability of polytopes on orthogonal surfaces. There are criteria which prevent large classes of simplicial polytopes from being realizable. On the other hand we identify some families of polytopes which can be realized on orthogonal surfaces.

Schnyder Woods and Orthogonal Surfaces

In this paper we study connections between planar graphs, Schnyder woods, and orthogonal surfaces. Schnyder woods and the face counting approach have important applications in graph drawing and the dimension theory of orders. Orthogonal surfaces explain connections between these seemingly unrelated notions. We use these connections for an intuitive proof of the Brightwell-Trotter Theorem which says, that the face lattice of a 3-polytope minus one face has order dimension three. Our proof yields a linear time algorithm for the construction of the three linear orders that realize the face lattice. Coplanar orthogonal surfaces are in correspondence with a large class of convex straight line drawings of 3-connected planar graphs. We show that Schnyder’s face counting approach with weighted faces can be used to construct all coplanar orthogonal surfaces and hence the corresponding drawings. Appropriate weights are computable in linear time.

Fitting a Two-Component Scattering Model to Polarimetric SAR Data From Forests

Two simple scattering mechanisms are fitted to polarimetric synthetic aperture radar (SAR) observations of forests. The mechanisms are canopy scatter from a reciprocal medium with azimuthal symmetry and a ground scatter term that can represent double-bounce scatter from a pair of orthogonal surfaces with different dielectric constants or Bragg scatter from a moderately rough surface, which is seen through a layer of vertically oriented scatterers. The model is shown to represent the behavior of polarimetric backscatter from a tropical forest and two temperate forest sites by applying it to data from the National Aeronautic and Space Agency/Jet Propulsion Laboratory's Airborne SAR (AIRSAR) system. Scattering contributions from the two basic scattering mechanisms are estimated for clusters of pixels in polarimetric SAR images. The solution involves the estimation of four parameters from four separate equations. This model fit approach is justified as a simplification of more complicated scattering models, which require many inputs to solve the forward scattering problem. The model is used to develop an understanding of the ground-trunk double-bounce scattering that is present in the data, which is seen to vary considerably as a function of incidence angle. Two parameters in the model fit appear to exhibit sensitivity to vegetation canopy structure, which is worth further exploration. Results from the model fit for the ground scattering term are compared with estimates from a forward model and shown to be in good agreement. The behavior of the scattering from the ground-trunk interaction is consistent with the presence of a pseudo-Brewster angle effect for the air-trunk scattering interface. If the Brewster angle is known, it is possible to directly estimate the real part of the dielectric constant of the trunks, a key variable in forward modeling of backscatter from forests. It is also shown how, with a priori knowledge of the forest height, an estimate for the attenuation coefficient of the canopy can be obtained directly from the multi-incidence-angle polarimetric observations. This attenuation coefficient is another key variable in forward models and is generally related to the canopy density.

New calibration technique for multiple-component stress wave force balances

The measurement of forces in hypervelocity expansion tubes is not possible using conventional techniques. The stress wave force balance technique can be applied in expansion tubes to measure forces despite the short test times involved. This article presents a new calibration technique for multiple-component stress wave force balances where an impulse response created using a load distribution is required and no orthogonal surfaces on the model exist. This new technique relies on the tensorial superposition of single-component impulse responses analogous to the vectorial superposition of the calibration loads. The example presented here is that of a scale model of the Mars Pathfinder, but the technique is applicable to any geometry and may be useful for cases where orthogonal loads cannot be applied.

CONFORMALLY FLAT HYPERSURFACES WITH CYCLIC GUICHARD NET

We classify the 3-dimensional conformally flat hypersurfaces with cyclic principal Guichard net. The orthogonal surfaces of the cyclic system turn out to be linear Weingarten surfaces in suitable ambient space forms and we provide explicit parametrizations for the conformally flat hypersurfaces.

0247 NEUROCOGNITIVE REHABILITATION –A FOUR-CASE PILOT STUDY

With the advent of probing systems and their integration with machining centers, coordinate metrology-based datum establishment is eliminating the need for precision hard-contact locators in many machining applications. Unfortunately, the coordinate data collected by these systems are often subject to noise in the form of random and biased errors of the workpiece datum features and measurement system. Consequently it is important to use datum-establishment algorithms that are insensitive to noise and that lead to the least measurable machined-feature error.This paper describes a simulation analysis that was carried out to evaluate the performance of three datum-establishment methods: 3–2–1, sequential least-squares (SQLS) and simultaneous least-squares (SMLS). The analysis involved the simulated drilling of three holes in a two set-up process. Simulated coordinate data were obtained from three planar, nominally orthogonal surfaces subject to perpendicularity errors and random roughness errors. Workpiece datum reference frames were fitted to this data using the three methods, the holes were drilled relative to these reference frames, and their position errors were computed relative to an ANSI-Y14.5M-defined reference frame.This analysis demonstrated that the SMLS method results in significantly less hole-position error [0.0173 mm average, 0.0146 mm standard deviation (SD)] than either the 3–2–1 method (0.0943 mm average, 0.0143 mm SD) or the SQLS method (0.0904 mm average, 0.0245 mm SD). This is despite the fact that the datum reference planes (ANSI Y14.5M) used to define these errors are defined sequentially relative to the extrema of the datum features, whereas the SMLS method defines the datum reference planes simultaneously with the purpose of minimizing fitting error.

402 主応力線グリッド生成システムの開発(計算力学と数値シミュレーション)

This paper presents a new algorithm to obtain principal stress trajectory grid. Grid points are calculated as the intersections of three mutually orthogonal isoplethic surfaces(two mutually orthogonal contour lines in 2D domain)of direction functions which are evaluated from the result of FEM. The contour lines cannot be obtained, when the pattern of trajectories is not topologically equivalent to an orthogonal grid. This problem with 2D pattern is solved by partitioning the triangular mesh with a line passing through the singular point where the maximum shear stress reaches the minimum value.

Dipole de-excitation near orthogonal conductor surfaces

A dipole active emitter radiating, not in free space, but within a homogeneous dielectric near the intersection line of two orthogonal planar conductors bounding the dielectric displays novel emission characteristics. This situation is shown here to give rise to superradiance and subradiance phenomena that are highly sensitive to the dipole orientation (controllable optically), and to the proximity of the emitter to the intersection line. The theory is developed using non-relativistic quantum electrodynamics where the fields are second quantised in terms of modes satisfying the electromagnetic boundary conditions at the conductor surfaces and the interaction Hamiltonian between the emitter and the quantised fields is the familiar form Hint=−μ·D/ε0, where μ is the dipole moment vector and D is the quantised electric displacement field. The variations of the emission rate with position are displayed for different dipole orientations and the implications of the results for the possibility of using this physical environment for the realisation of scalable architectures for quantum information processing are pointed out.

Curvature lines on orthogonal surfaces of R3 and Joachimsthal Theorem

In this paper is studied, as a complement of Joachimsthal theorem, the behavior of curvature lines near a principal cycle common to two orthogonal surfaces.