Subtended Angle Research Articles

Guidance using bearing-only measurements with three beacons in the plane

This paper proposes a bearing-only measurement based guidance algorithm for a mobile agent to navigate in a two-dimensional plane. Based on the bearing vectors and the subtended angles related to three stationary beacons, the proposed algorithm allows the agent to reach its desired location. We show that the agent reaches its desired location globally asymptotically based on Lyapunov stability theory. Under some assumptions, the agent is also proved to reach the desired location exponentially based on Lyapunov's indirect method. Simulations and actual experimental tests on quadrotor system are also provided to verify the effectiveness of the proposed algorithm in outdoor environment.

Crystal structure of 2-(thio-phen-3-yl)ethyl pyrene-1-carboxyl-ate.

In the title compound, C23H16O2S, the thio­phene group is rotationally disordered into two fractions almost parallel to each other, with occupation factors of 0.523 (7) and 0.477 (7), and subtending dihedral angles of 10.5 (5) and 9.3 (5)°, respectively, to the thio­phene group. The mol­ecules are held together by weak C—H⋯O and C—H⋯π hydrogen bonds, producing a laminar arrangement, which are further connected in a perpendicular fashion by S⋯π contacts [S⋯centroid = 3.539 (8) and 3.497 (8) Å]. In spite of the presence of the entended pyrene group, the structure does not present any parallel π–π stacking inter­actions. The structure was refined as an inversion twin.

Deriving an Optimum Mapping Function for the SKA-Shaped Offset Gregorian Reflectors

Of primary importance for a radio telescope is its receiving sensitivity. The offset Gregorian reflector antennas, as used for the Square Kilometer Array (SKA) radio telescope, can be shaped to make efficient use of the reflector’s aperture and thus to maximize sensitivity for a given sidelobe level. The shape of the reflector is controlled by a mapping function. This paper presents a method to derive the optimum mapping function given a selected set of single pixel feeds. In this case, the feeds were optimized for a geometrically similar classical conic section (unshaped) reflector system. Realistic performance results are given for reflector systems with various subreflector sizes, extensions, and subtended angles.

Flow Characteristic Study in a Configuration of Sudden Expansion with Central Restriction and Fence – Viewed as an Annular Flow Dump Combustor

In this paper, a numerical study on flow characteristics in configurations of sudden expansion with central restriction and fence viewed as annular flow dump combustor has been carried out for Reynolds number (Re) ranging from 50 to 200, percentage of central restriction (CR) from 10% to 40% and aspect ratio (AR) from 2 to 6 with a fixed fence subtended angle (FSA) of 10 degree and with a fixed distance of fence from throat respectively. The effect of each variable on streamline contour and velocity profile has been studied in detail. Results have been compared with the configuration of sudden expansion with central restriction only. From the study it is concluded that the configuration of sudden expansion with central restriction and fence with higher flow Reynolds number, higher central restriction and higher aspect ratio offers more benefit in terms of the mixing possibility compared to the case of sudden expansion with central restriction only.

곡선 강박스 거더의 휨-뒤틀림 응력비에 따른 중간 다이아프램 간격

Although distortions of horizontally curved box girder are more susceptible than which of the straight girder due to curvature effect, current domestic design standards does not present spacing of intermediate diaphragms for the curved box girder. In this study, parametric studies for straight and curved box girder considering distortional warping normal stresses based on linear finite element analysis were carried out. Single span curved girders were chosen for analysis based on current domestic bridge data with 1-6 of solid intermediate diaphragms, 0-30 degree of subtended angle, 30m and 60m of span length and 2-3m of flange width and web height. The adequate spacing of diaphragms for the box girder were suggested considering subtended angles and bending and distortional warping normal stress ratios with 5%, 10%, 15% and 20%. The analysis results were also compared to a current design standard and suggested spacing of diaphragm were evaluated.

Free vibration analysis of moderately thick functionally graded open shells with general boundary conditions

This paper presents the free vibration analysis of functionally graded open shells including cylindrical, conical and spherical ones with arbitrary subtended angle and general boundary conditions. The material properties of the open shells have continuous and smooth variation in the thickness direction based on general four-parameter power-law distributions in terms of volume fractions of the constituents. The formulation is derived by the modified Fourier series in conjunction with Rayleigh–Ritz method according to the first-order shear deformation shell theory. The modified Fourier series is expressed in the form of the linear superposition of a double cosine series and auxiliary functions which are introduced to ensure and accelerate the convergence of the series representations. The comprehensive investigations concerning the convergence and accuracy of the present method are performed by a number of numerical tests and comparisons. Some new results of FGM open shells with elastic restraints are presented. Parametric studies are carried out for FGM open shells with respect to the boundary conditions, material profiles and geometrical parameters.

Exact Ligand Solid Angles.

Steric demands of a ligand can be quantified by the area occluded by the ligand on the surface of an encompassing sphere centered at the metal atom. When viewed as solid spheres illuminated by the metal center, the ligand atoms generally cast a very complicated collective shadow onto the encompassing sphere, causing mathematical difficulties in computing the subtended solid angle. Herein, an exact, analytic solution to the ligand solid angle integration problem is presented based on a line integral around the multisegmented perimeter of the ligand shadow. The solution, which is valid for any ligand bound to any metal center, provides an excellent method for analyzing geometric structures from quantum chemical computations or X-ray crystallography. Over 275 structures of various metals bound to diverse mono- and multidentate ligands were optimized using B3LYP density functional theory to exhibit exact solid angle (Ω°) computations. Among the intriguing Ω° solutions, Pd(xantphos) and ferrocene exhibit holes in their ligand shadows, and Fe(EDTA)(2-) has a surprisingly simple shadow defined by only four arcs, despite having a multitude of overlaps among individual shadow cones.

(4-Fluorophenyl)thiourea–1,10-phenanthroline (1/1)

Refluxing a mixture of 1,10-phenanthroline, (4-fluoro­phen­yl)thio­urea and cadmium(II) chloride did not produce the expected mixed-ligand complex but formed a co-crystal of the two ligands, C12H8N2·C7H7FN2S. The asymmetric unit consists of two pairs of the co-crystal mol­ecules. In each (4-fluoro­phen­yl)thio­urea mol­ecule, the planes of the N2CS thio­urea units are almost perpendicular to the corresponding fluoro­benzene rings, subtending angles of 76.53 (7) and 85.25 (7)°. In the crystal, N—H⋯N and N—H⋯S hydrogen bonds form inversion dimers from the co-crystal pairs. A weak π–π inter­action between the phenanthroline rings [centroid–centroid distance = 3.7430 (15)Å] is also observed.

파형 복부판이 수평 곡선 I형 거더의 극한 거동에 미치는 영향

In this study, the effects of corrugated webs on the ultimate behavior of horizontally curved I-shaped girders are investigated. Because of the geometric characteristics of corrugated plates, corrugated webs can be used for enhancing torsional and warping stiffness of plate girders. Many researches have been conducted to study the effects of corrugated webs on the ultimate behavior of straight girders. But, the studies of the ultimate behavior of horizontally curved girders with corrugated webs, which generally show out-of plane behavior manly, have been rarely performed so far. By performing inelastic-nonlinear analysis, the ultimate behavior of curved girders with corrugated webs is studied in this paper. Laterally unsupported length and subtended angle of girders, and length of height of corrugation of webs are considered as the geometric parameters which would be expected to affect the ultimate behavior. By this analytical study with considering the geometric parameters, the changes of ultimate behavior and load carrying capacity of curved girders with corrugated webs are investigated. Also, the effects of corrugated webs on the increase of load carrying capacity for curved girders are studied with comparing to the capacity of general curved girders with flat webs. According to the analytical results, corrugated webs can be used to increase the ultimate load carrying capacity of curved girders, because of their high torsional and warping stiffness. But, it is also indicated that they may decrease the load carrying capacity of curved girders which have relatively small subtended angle or initial curvature, because of an accordion effect.

Three-Dimensional Vibration Analysis of Twisted Cylinder With Sectorial Cross Section

The three-dimensional (3D) free vibration of twisted cylinders with sectorial cross section or a radial crack through the height of the cylinder is studied by means of the Chebyshev–Ritz method. The analysis is based on the three-dimensional small strain linear elasticity theory. A simple coordinate transformation is applied to map the twisted cylindrical domain into a normal cylindrical domain. The product of a triplicate Chebyshev polynomial series along with properly defined boundary functions is selected as the admissible functions. An eigenvalue matrix equation can be conveniently derived through a minimization process by the Rayleigh–Ritz method. The boundary functions are devised in such a way that the geometric boundary conditions of the cylinder are automatically satisfied. The excellent property of Chebyshev polynomial series ensures robustness and rapid convergence of the numerical computations. The present study provides a full vibration spectrum for thick twisted cylinders with sectorial cross section, which could not be determined by 1D or 2D models. Highly accurate results presented for the first time are systematically produced, which can serve as a benchmark to calibrate other numerical solutions for twisted cylinders with sectorial cross section. The effects of height-to-radius ratio and twist angle on frequency parameters of cylinders with different subtended angles in the sectorial cross section are discussed in detail.

Understanding the Pincer - The Importance of Reference Plane Orientation on Acetabular Rim Evaluation

Objectives:Femoroacetabular impingement (FAI) is a common cause of young adult hip pain. FAI can result from an acetabular-sided bony lesion, or “pincer” lesion. A pincer lesion is defined as an area of linear contact between the acetabular rim and the femoral head-neck junction due to general or focal acetabular overcoverage. Three dimensional (3D) analysis of the acetabular rim morphology is essential to understand etiology and aciculate diagnosis of the of the pincer type FAI. A few studies have measured 3D geometry of the acetabular rim; in which the acetabular rim is described as a deviation from a reference plane. Therefore, the definition of the reference plane is critical to determine the acetabular rim geometry. The purpose of this study was to use 3D Computed Tomography (CT) modeling to evaluate the impact of varied acetabular orientation reference planes on the interpretation of acetabular rim abnormalities, with the goal to determine the ideal reference plane for future study use.Methods:3D CT modeling was performed on five hip joints of patients who underwent hip arthroscopy with acetabular trimming for a presumed pincer lesion. These models were exported into point-cloud models. An acetabular 3D model was automatically created within 10 mm from the femoral head surface (Fig. 1A, B). The acetabular articular surface and rim were separated with a threshold of 5 mm, which provided an acetabular rim model with a band width of 5 mm (Fig. 1C). A local coordinate system was defined with the acetabular notch midpoint being 6 o’clock. A best-fit plane of the acetabular rim was determined by the least square method using two different acetabular rim models: 1) a model excluding the acetabular notch (plane A) and 2) a model excluding the acetabular notch and superior region from 10:30 to 3:00 (3:00 being anterior) (plane B). The acetabular rim model was transformed into a cylindrical coordinate system with an axis determined by a normal vector of the plane. The final acetabular rim model consisting of 120 points with 3° increments was created by searching the outermost points of the rim. The acetabular center was determined using best-fit sphere of the articular surface model. A reference plane including the center point was determined with orientations determined by normal vectors of the acetabular rim planes (Fig. 1C, yellow line). The 3D geometry of the rim was described by subtended angles from the normal vector of the reference plane.Results:Three distinct peaks were noted at anteroinferior (AI), anterosuperior (AP) and posteroinferior (PI) regions (Fig. 2 A, B). While the AI and PI peaks measured with the plane A were higher than that measured with plane B, the AP peak measured with plane A was lower than that measured with plane B (Fig. 2C). The angle between the normal vectors of plane A and B was 13.7±3.5°.Conclusion:The findings demonstrate that the orientation of the reference plane is critical to the 3D measurement of the acetabular rim. Since bony prominence in the anterosuperior region has been considered as the pathogenesis of the impingement, the reference plane including this region may cause underestimation of the bony lesion. An appropriate determination of the reference plane is crucial for evaluation of the bony lesion in the pincer FAI patient.

Flutter of functionally graded open conical shell panels subjected to supersonic air flow

In this article, analysis of supersonic flutter of functionally graded open conical shell panels with clamped and simply supported edges is presented. The aeroelastic stability problem is formulated based on first-order shear deformation theory as well as classical shell theory and solved using Galerkin method. The effects of the volume fractions of constituent materials, the semi-vertex and subtended angles, thickness, and length on the flutter of the functionally graded conical shell panel are investigated. It is shown that the discrepancies between the results of the present classical shell theory and first-order shear deformation theory for the critical aerodynamic pressure are generally greater than those for the frequencies.

Jumping mechanisms in jumping plant lice (Hemiptera, Sternorrhyncha, Psyllidae)

Jumping mechanisms and performance were analysed in three species of psyllids (Hemiptera, Sternorrhyncha) that ranged from 2 to 4 mm in body length and from 0.7 to 2.8 mg in mass. Jumping was propelled by rapid movements of the short hind legs, which were only 10-20% longer than the other legs and 61-77% of body length. Power was provided by large thoracic muscles that depressed the trochantera so that the two hind legs moved in parallel planes on either side of the body. These movements accelerated the body to take-off in 0.9 ms in the smallest psyllid and 1.7 ms in the largest, but in all species imparted a rapid forward rotation so that at take-off the head pointed downwards, subtending angles of approximately -60 deg relative to the ground. The front legs thus supported the body just before take-off and either lost contact with the ground at the same time as, or even after, the hind legs. In the best jumps from the horizontal, take-off velocity reached 2.7 m s(-1) and the trajectory was steep at 62-80 deg. Once airborne, the body spun rapidly at rates of up to 336 Hz in the pitch plane. In many jumps, the wings did not open to provide stabilisation, but some jumps led directly to sustained flight. In their best jumps, the smallest species experienced a force of 637 g. The largest species had an energy requirement of 13 μJ, a power output of 13 mW and exerted a force of nearly 10 mN. In a rare jumping strategy seen in only two of 211 jumps analysed, the femoro-tibial joints extended further and resulted in the head pointing upwards at take-off and the spin rate being greatly reduced.

DUST AROUND R CORONAE BOREALIS STARS. I.SPITZER/INFRARED SPECTROGRAPH OBSERVATIONS

Spitzer/IRS spectra from 5 to 37 um for a complete sample of 31 R Coronae Borealis stars (RCBs) are presented. These spectra are combined with optical and near-infrared photometry of each RCB at maximum light to compile a spectral energy distribution (SED). The SEDs are fitted with blackbody flux distributions and estimates made of the ratio of the infrared flux from circumstellar dust to the flux emitted by the star. Comparisons for 29 of the 31 stars are made with the IRAS fluxes from three decades earlier: Spitzer and IRAS fluxes at 12 um and 25 um are essentially equal for all but a minority of the sample. For this minority, the IRAS to Spitzer flux ratio exceeds a factor of three. The outliers are suggested to be stars where formation of a dust cloud or dust puff is a rare event. A single puff ejected prior to the IRAS observations may have been reobserved by Spitzer as a cooler puff at a greater distance from the RCB. RCBs which experience more frequent optical declines have, in general, a circumstellar environment containing puffs subtending a larger solid angle at the star and a quasi-constant infrared flux. Yet, the estimated subtended solid angles and the blackbody temperatures of the dust show a systematic evolution to lower solid angles and cooler temperatures in the interval between IRAS and Spitzer. Dust emission by these RCBs and those in the LMC is similar in terms of total 24 um luminosity and [8.0]-[24.0] color index.

Positioning the Caudal Septum During Primary Repair of Unilateral Cleft Lip

Since 1995, the senior surgeon has straightened the deviated anterocaudal septum in all infants undergoing primary repair of unilateral complete cleft lip/palate. A retrospective assessment was done on 17 patients who did not have septal correction and 17 patients who did have septal correction at the time of nasolabial repair. Operative reports were reviewed, and secondary procedures on the nose were documented.Posterior-anterior cephalograms were used to measure septal deviation from the midline, angle of septal deviation, and width of the inferior turbinate on the noncleft side. The angle subtended by the superior and inferior segments of the cartilaginous septum was measured at the point of maximal septal deviation. The uncorrected group had a mean maximal septal deviation from the midline of 5.8 mm compared with 4.1 mm in the corrected group (P < 0.01). The uncorrected group had a mean width of the contralateral inferior turbinate of 12.7 mm compared with 10.2 mm in the corrected group (P < 0.01). The uncorrected group had a mean subtended angle of 137.8 degrees compared with 147.9 degrees in the corrected group (P < 0.01). Positioning the anterior caudal septum during primary repair of unilateral complete cleft lip results in less septal deviation and a smaller contralateral turbinate as documented by posteroanterior cephalometry in adolescence.

Why large-head metal-on-metal hip replacements are painful

Large-head metal-on-metal total hip replacement has a failure rate of almost 8% at five years, three times the revision rate of conventional hip replacement. Unexplained pain remains a feature of this type of arthroplasty. All designs of the femoral component of large-head metal-on-metal total hip replacements share a unique characteristic: a subtended angle of 120° defining the proportion of a sphere that the head represents. Using MRI, we measured the contact area of the iliopsoas tendon on the femoral head in sagittal reconstruction of 20 hips of patients with symptomatic femoroacetabular impingement. We also measured the articular extent of the femoral head on 40 normal hips and ten with cam-type deformities. Finally, we performed virtual hip resurfacing on normal and cam-type hips, avoiding overhang of the metal rim inferomedially. The articular surface of the femoral head has a subtended angle of 120° anteriorly and posteriorly, but only 100° medially. Virtual surgery in a normally shaped femoral head showed a 20° skirt of metal protruding medially where iliopsoas articulates. The excessive extent of the large-diameter femoral components may cause iliopsoas impingement independently of the acetabular component. This may be the cause of postoperative pain with these implants.

역량스펙트럼을 이용한 곡선교의 내진성능평가에 대한 비탄성요구스펙트럼의 영향

역량스펙트럼방법은 구조물의 내진성능을 평가하는 도구로서 점점 더 이용 빈도가 증가하고 있다. 강도감소계수는 역량스펙트럼방법에서 정의하는 비탄성요구스펙트럼을 생성하기 위해 사용되며 다양한 강도감소계수 공식들이 제안되고 있다. 이 연구는 강도감소계수의 공식이 비탄성요구스펙트럼의 형상에 미치는 영향과 아울러 교량의 지진응답변위에 미치는 영향을 평가하였다. 연구 목적에 따라, 기존에 제안된 몇 가지 강도감소계수 공식들이 조사되고, 예제연구를 통하여 분석되었다. 서로 다른 원호각을 갖는 곡선교를 선정하여 서로 다른 강도감소계수 공식을 적용하여 역량스펙트럼방법으로 교각의 변위를 평가하였다. 역량스펙트럼의 결과를 검증할 목적으로 비선형시간이력해석도 함께 수행되었다. 연구결과에 의하면, 역량스펙트럼방법은 더 큰 원호각을 갖는 교량일수록 실제보다 더 큰 교각의 변위를 산출한다. 비탄성요구스펙트럼을 작성하는 많은 방법이 제안되어 있음에도 불구하고, 각 방법들이 산출하는 교각의 비탄성변위응답은 큰 차이가 없다. The capacity spectrum method(CSM) has been more frequently used as a tool to evaluate the seismic capacity of the structure. Many formulas of strength reduction factors(SRF) have been proposed and adopted to generate the inelastic demand spectrum for the CSM. This study evaluates the impacts of the type of the SRF on the inelastic demand spectrum and finally on the seismic response displacement of curved bridge. For the purpose, the several existing formulas of SRFs were comparatively investigated through the case study. Curved bridges with different subtended angles were selected and the displacements of the bridge piers were estimated by using the different formulas of SRFs. Nonlinear time history analyses were also performed for the validation purpose of the CSM results. According to study results, the CSM may generate the larger displacement responses than the actual behaviors for the curved bridge with larger subtended angles. Though many methods have been suggested to generate the inelastic demand spectrum for CSM, they might not give noticeable differences in inelastic displacement of the bridge pier.

1,4-Bis(2,2′:6′,2′′-terpyridin-4′-yl)benzene

The asymmetric unit of the title compound, C36H24N6, comprises a whole mol­ecule. Supra­molecular inter­actions between neighbouring mol­ecules are essentially π–π stacking inter­actions with small inter­planar distances [3.5140 (15) and 3.6041 (15) Å]. The central phenyl­ene ring is tilted with respect to the two pyridine substituents, subtending angles of 36.17 (11) and 34.95 (11)°. Three of the peripheral pyridine substituents are almost coplanar with the central pyridines [dihedral angles = 5.10 (12)-8.21 (12)°], but one subtends an angle of 24.86 (12)°.

Orientation of larval and juvenile horseshoe crabs Limulus polyphemus to visual cues: Effects of chemical odors

Abstract Adult horseshoe crabs Limulus polyphemus have long served as models for the study of vision in marine arthropods. Yet, little is known about the ability of early life history stages to detect and respond to visual cues. We examined the visually directed movements of larvae and first stage juveniles to horizons containing dark visual targets of different sizes. The study tested the hypotheses that (1) larval and juvenile crabs can detect and respond to visual targets and (2) the direction of orientation varies with the presence of chemical cues associated with settlement habitats. Orientation of larval and juvenile crabs to rectangles subtending angles from 30–330° was tested in a circular arena containing water that either lacked estuarine chemical cues (offshore water) or contained odors from aquatic vegetation or known predators. In the absence of chemical odors, larvae oriented toward and juveniles moved away from dark horizons subtending angles &gt; 60°. When placed in water containing chemical odors from potential nursery habitats, including the seagrasses Halodule wrightii and Syringodium filiforme, crabs reversed their direction of orientation relative to their responses in offshore water. Odors from two known predators, the mummichug Fundulus grandis and blue crab Callinectes sapidus, had no affect on the orientation of larvae. Yet, juveniles responded to both odors by moving toward the visual target. Results support the hypothesis that the visual orientation of larval and juvenile horseshoe crabs changes upon exposure to habitat and predator cues and that the direction of the response undergoes an ontogenetic shift following metamorphosis.

Measuring tree stem diameters using intensity profiles from ground-based scanning lidar from a fixed viewpoint

This paper presents a method for using the intensity of returns from a scanning light detection and ranging (lidar) system from a single viewing point to identify the location and measure the diameter of tree stems within a forest. Such instruments are being used for rapid forest inventory and to provide consistent supporting information for airborne lidars. The intensity transect across a tree stem is found to be consistent with a simple model parameterised by the range and diameter of the trunk. The stem diameter is calculated by fitting the model to transect data. The angular span of the stem can also be estimated by using a simple threshold where intensity values are tested against the expected intensity for a stem of given diameter. This is useful when data are insufficient to fit the model or the stem is partially obscured. The process of identifying tree positions and trunk diameters is fully automated and is shown to be successful in identifying a high proportion of trees, including some that are partially obscured from view. The range and bearing to trees are in excellent agreement with field data. Trunk angular span and diameter estimations are well correlated with field measurements at the plot scale. The accuracy of diameter estimation is found to decrease with range from the scanning position and is also reduced for stems subtending small angles (less than twice the scanning resolution) to the instrument. A method for adjusting survey results to compensate for trees missed due to obscuration from the scanning point and the use of angle count methods is found to improve basal area estimates and achieve agreement within 4% of field measurements.