Triangular Corner Research Articles

Subduction Initiation at the Corner of Small Oceanic Basins

AbstractIn Southeast Asia, emerging subduction zones often appear to begin at the corners of small oceanic basins, which have a triangular‐indenter continent–ocean boundary geometry. To investigate the influence of a triangular corner on subduction initiation, we performed a series of three‐dimensional numerical simulations with varying corner angles and base lengths. The results show that the apex of the corner constitutes the initial location of subduction, irrespective of the angle or the extent of the corner. Smaller angle corners are more likely to facilitate subduction initiation. At the same time, wide acute angle corners are difficult to form. Our findings suggest that triangular corner structures may facilitate subduction initiation in smaller basins; however, the role such corners in subduction initiation is limited in larger basins. Our results emphasize the importance of accounting for the three‐dimensional geometry of a subduction zone when examining its subduction dynamics and geological features.

Reducing Uncertainty Using Placement and Regrasp Planning on a Triangular Corner Fixture

This paper presented a regrasp planning method to eliminate grasp uncertainty while considering the geometric constraints of a fixture. The method automatically finds the Stable Placement Poses (SPPs) of an object on a Triangular Corner Fixture (TCF), elevates the object from its SPPs to dropping poses and finds the Deterministic Dropping Poses (DDPs), builds regrasp graphs by using the SPP-DDP pairs and their associated grasp configurations, and searches the graph to find regrasp motion sequences for precise assembly. Since the SPPs and their associated regrasps are constrained by the TCF’s geometry and have high precision, the final object poses regrasped via it has low uncertainty and can be directly used for assembly by position control. In the experimental section, we study the performance of analytical and learning-based methods for estimating the DDPs of different objects and quantitatively examine the proposed method’s ability to suppress uncertainty using assembly tasks like peg-in-hole insertion and sheathing tubes, aligning holes, mounting bearing housings, etc. The results demonstrate the method’s robustness and efficacy. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In production lines, robots interact with peripheral devices to improve efficiency and reduce uncertainty. In this work, we focus on a particular peripheral device – a Triangular Corner Fixture (TCF) made by three inclined and mutually perpendicular plates. We study using the TCF to improve manipulation precision. The inclined plates of the TCF form a gravity bucket that holds dropped objects in stable states under gravity. In a real scenario, a robot picks up an object and releases it above the TCF. The released object will reach a stable state on the TCF. Then, the robot regrasps and moves the stabilized object to the target pose with reduced uncertainty. Using the method proposed in this paper, a robot can automatically finish the above procedure by finding all the object’s stable states in the TCF, planning grasp configurations, invalidating infeasible states and grasps, building regrasp graphs and searching the graph to find a regrasp motion sequence that moves the object to a goal pose with high precision for assembly. In industrial applications, the proposed method has the potential to improve the flexibility of robotic systems for high-precision tasks. In the research fields, it may promote the research on sensorless manipulation and extrinsic manipulation, and push forward the studies in robotic regrasp.

Experience in deploying radar corner reflectors for InSAR monitoring

This work aims to analyze the effectiveness of corner reflectors deployment designed in various for InSAR monitoring by the Sentinel-1 satellite. Method. The accuracy of determining the spatial movements of the surface by the InSAR method in the places where the corner reflectors are deployed depends on their size, as well as the signal-to-clutter ratio on the radar images. Therefore, it is necessary to assess the backscattering intensity on radar images for the selected territory before installing the corner reflector. In places where corner reflectors are to be deployed, an increase in backscatter should be at least 10 dB. The orientation of the corner reflectors was performed based on Sentinel-1 satellite orbit parameters, which were obtained from the Heavens Above web resource. The analysis of the backscatter intensity time series on radar images was carried out using the online platform EO Browser. Results. The effectiveness of deployment and monitoring of trihedral triangular corner reflectors measuring 0.5 m and 1 m was studied. The research results made it possible to generalize the experience of deploying temporary corner reflectors and use them to design reflector structures for permanent monitoring using radar sensing. The maximum autonomy and constant value of the effective scattering area of the triangular corner reflector is ensured thanks to the equipped protective screen that prevents atmospheric precipitation from entering the reflector. Unlike three-sided corner reflectors, which are oriented to the ascending or descending orbit of the satellite, the circular four-sided corner reflector provides an increase in the intensity of backscatter on radar images taken from different orbits and different satellites. The circular quadrilateral reflector, which was deployed for continuous monitoring, is characterized as a universal reflector for all possible sensors that will conduct radar imaging. Scientific novelty and practical significance are in the confirmation of the effectiveness of the use of ground corner reflectors to increase the intensity of backscattering on radar images. Tested and improved designs of reflectors can be used when creating a network for constant monitoring, which will ensure millimeter accuracy in determining the spatial movements of the earth's surface and engineering structures by the InSAR method.

Quick Quality Assessment and Radiometric Calibration of C-SAR/01 Satellite Using Flexible Automatic Corner Reflector

C-SAR/01, the successor of China’s Gaofen-3 Satellite, which launched on 23 November 2021, is the first synthetic aperture radar (SAR) satellite to be launched in China’s civil space infrastructure plan and has served as an invaluable data resource. Radiometric calibration and validation are prerequisites for the quantitative application of SAR data. In this study, the radiometric calibration experiments of C-SAR/01 data of the ultra-fine strip (UFS) and fine strip I (FSI) modes were conducted applying flexible automatic triangular trihedral corner reflectors deployed in Xilinhot SAR satellite calibration and validation site. Accordingly, the image quality and radiometric calibration accuracy were evaluated. The results show that the spatial resolution, peak sidelobe ratio, and integrated sidelobe ratio of UFS and FSI mode data of C-SAR/01 are better than those of the design indexes, and the calibration results from the integral method are more stable than those from the peak method. Furthermore, the standard deviation of the calibration constant for UFS mode data is 0.234 dB, with the relative and absolute calibration accuracies obtained as 0.233 and 0.532 dB, respectively, whereas the standard deviation calibration constant for FSI mode data is 0.198 dB, with its relative and absolute calibration accuracies evaluated as 0.199 and 0.333 dB, respectively.

On the Efficacy of Compact Radar Transponders for InSAR Geodesy: Results of Multiyear Field Tests

Compact and low-cost radar transponders are an attractive alternative to corner reflectors (CR) for SAR interferometric (InSAR) deformation monitoring, datum connection, and geodetic data integration. Recently, such transponders have become commercially available for C-band sensors, which poses relevant questions on their characteristics in terms of radiometric, geometric, and phase stability. Especially for extended time series and for high-precision geodetic applications, the impact of secular or seasonal effects, such as variations in temperature and humidity, has yet to be proven. Here we address these challenges using a multitude of short baseline experiments with four transponders and six corner reflectors deployed at test sites in the Netherlands and Slovakia. Combined together, we analyzed 980 transponder measurements in Sentinel-1 time series to a maximum extent of 21 months. We find an average Radar Cross Section (RCS) of over 42 dBm2 within a range of up to 15 degrees of elevation misalignment, which is comparable to a triangular trihedral corner reflector with a leg length of 2.0 m. Its RCS shows temporal variations of 0.3--0.7~dBm2 (standard deviation) which is partially correlated with surface temperature changes. The precision of the InSAR phase double-differences over short baselines between a transponder and a stable reference corner reflectors is found to be 0.5-1.2 mm (one sigma). We observe a correlation with surface temperature, leading to seasonal variations of up to +/-3 mm, which should be modeled and corrected for in high precision InSAR applications. For precise SAR positioning, we observe antenna-specific constant internal electronic delays of 1.2-2.1 m in slant-range, i.e., within the range resolution of the Sentinel-1 Interferometric Wide Swath (IW) product, with a temporal variability of less than 20~cm. Comparing similar transponders from the same series, we observe distinct differences in performance. Our main conclusion is that these characteristics are favorable for a wide range of geodetic applications. For particular demanding applications, individual calibration of single devices is strongly recommended.

Novel Corner-Reflector Array Application in Essential Infrastructure Monitoring

High precision monitoring of infrastructure using artificial reflectors is possible with freely available Sentinel-1 data, but large reflectors are needed. We find that a triangular trihedral corner reflector should typically have at least 1 m inner leg length. As such large reflectors are often not feasible for use in urban areas for essential infrastructure monitoring, we designed a multiple corner-reflector array to replace a single corner reflector with an inner leg length of 1 m. In this case, we use four reflectors where each of them is a truncated triangular trihedral with an inner leg length of 0.33 m. We measured InSAR amplitude, phase and coherence of this reflector array with various configurations of alignments of the array. We find that as long as great care is taken in the relative positioning of the four corner reflectors, so that they constructively interfere, each horizontal or vertical configuration provides the expected amplitude, coherence and phase stability. Applications of multiple small corner reflectors in urban areas range from essential infrastructure monitoring (e.g bridges, overpasses, tunnel constructions), through assessment of structural health of buildings, to monitoring highway and railway embankments. We show that the multiple corner array works when placed in a single InSAR resolution cell, but depending on the application, the number and projection of corner reflectors can be varied, as long as sufficient signal-to-clutter ratio is achieved in the area of interest.

ABSOLUTE LOCALIZATION OF CORNER REFLECTORS WITH TERRASAR-X SPOTLIGHT IMAGES

Abstract. Synthetic aperture radar, capable of imaging the Earth surface from space in nearly all-weather conditions and high spatial resolution, has shown its outstanding capability for a variety of ground mapping applications. With well-controlled orbits of the new generation SAR satellites, high accuracy absolute localization with multiple SAR images has been demonstrated and become one of the hot spots with increasing attention. In this paper, high-resolution Spotlight-mode TerraSAR-X images acquired from the single orbit track were applied to 3D absolute positioning of three triangular trihedral corner reflectors. In order to overcome the limitation imposed by the acquisitions with very short baselines, a height constraint was introduced and the sub-meter accuracy was derived after carefully compensating for the known error sources, such as atmospheric delays and solid earth tide shifts.

Corrugated Box Compression Strength Enhancement

In this study, 5x5x12 single-wall RSC corrugated boxes were strengthened to increase their compression strength using four different methods; horizontal brace, diagonal brace, L-shape corner post, and triangular corner stiffener. All braces are of 2-inch width. Horizontal Brace : Compression strength increased by 9% when the unsupported box height was reduced from 12 inches to 3 inches. Diagonal Brace : Compression strength increased by 8% and 14% for single and double braces, respectively. L-Shape Corner Post : Compression strength increased by 29% and 38% for exterior and interior posts, respectively. Triangular Corner Stiffener : Compression strength increased by 36% when the stiffener depth increased from 0 inch to 9 inches. The interior corner post method was the most effective and most practical.

Modelling small ventilated corner baffles for box culvert barrel

During the last decades, concerns regarding the ecological impact of standard culverts have led to some design evolution. The installation of baffles along the culvert barrel yields smaller velocities and larger water depths in the barrel, potentially more suitable for upstream fish passage, albeit with a decrease in discharge capacity. Small triangular corner baffles were proposed to facilitate the upstream passage of small-body-mass fish, without compromising the discharge capacity of the culvert at design flow. Although fish benefited from low velocity regions for resting and sheltering, a small fraction of small-body-mass fish were observed to become disoriented by the adverse effect of flow reversal regions in the wake of plain baffles. This study presents the hydrodynamic testing of small ventilated triangular corner baffles for standard box culverts. The baffle ventilation was introduced to reduce the impact of negative wake behind the baffles. Two designs were tested: a baffle with three holes and a brush baffle. Detailed modelling in a near-full-scale culvert barrel showed that the ventilated corner baffles created a smaller negative wake region. A lesser negative velocity magnitude was observed behind the ventilated baffles, in comparison to plain baffles, for the same flow rate, baffle height and spacing. With ventilated corner baffles, the longitudinal distribution of low-velocity zone was more uniform, yielding a better longitudinal connectivity for upstream passage, compared to plain baffles. A comparison between various boundary treatments suggested however that the requirements for continuous, sizeable low positive velocity zone suitable to small-bodied fish might be better fulfilled with an asymmetrically roughened culvert barrel than with triangular baffles, even with ventilation.

Using small triangular baffles to facilitate upstream fish passage in standard box culverts

A culvert is a covered channel to pass streams and floodwaters through an embankment. The ecological impact of culverts has been recognised, in particular in terms of stream connectivity, but existing guidelines lead often to un-economical culvert design. Herein, a small triangular corner baffle system was tested physically in a near-full-scale fish-friendly facility of a box culvert barrel. Experiments were repeated with several configurations to characterise the flow properties for a range of less-than-design flows, baffle sizes and spacings. In presence of triangular corner baffles, the flow was asymmetrical, owing to the wake behind each baffle. The presence of triangular corner baffles had a moderate effect on the flow resistance and discharge capacity, albeit the data indicated the combined effect of relative baffle height and spacing on the friction factor. With triangular baffles, the surface area of slow velocity regions increased by a factor of two to three. Such low velocity regions are preferential swimming zones for fish, beneficial to small-bodied fish passage. Testing with small-bodied fish showed that fish preferred to swim upstream in slow-velocity regions, typically next to the sidewalls and in the left corner where the triangular baffles were located. The presence of small triangular baffles facilitated substantially the upstream passage of small fish, including in terms of endurance, compared to a smooth un-baffled box culvert barrel, when the baffle size was comparable to the fish length. The present findings highlighted the importance of physical modelling at near full-scale for the development of fish-friendly culvert designs.

Ground-Based Differential Interferometric Radar Monitoring of Unstable Mountain Blocks in a Coastal Environment

In this paper, we present the results of eight years of continuous monitoring with a ground-based, interferometric, real-aperture radar of two unstable mountain blocks at Tafjord on the western coast of Norway. A real-time, interferometric, ground-based radar has the capability to provide high accuracy range measurements by using the phase of the transmitted signal, thus achieving sub-millimeter accuracy when a sufficient signal-to-noise level is present. The main challenge with long term monitoring is the variations in radio refractivity caused by changes in the atmosphere. The range variations caused by refractive changes in the atmosphere are corrected using meteorological data. We use triangular corner reflectors as references to improve the signal-to-clutter ratio and improve the accuracy of the measurements. We have also shown that by using differential interferometry, a significant part of the variation caused by radio refractivity variations is removed. The overall reduction in path length variation when using differential interferometry varies from 27 to 164 times depending on the radar-to-reflector path length. The measurements reveal cyclic seasonal variations, which are coherent with air temperature. The results show that radar measurements are as accurate as data from in situ instruments like extensometers and crack meters, making it possible to monitor inaccessible areas. The total measured displacement is between 1.2 mm and 4.7 mm for the two monitored mountain blocks.

On the Design of Radar Corner Reflectors for Deformation Monitoring in Multi-Frequency InSAR

Trihedral corner reflectors are being increasingly used as point targets in deformation monitoring studies using interferometric synthetic aperture radar (InSAR) techniques. The frequency and size dependence of the corner reflector Radar Cross Section (RCS) means that no single design can perform equally in all the possible imaging modes and radar frequencies available on the currently orbiting Synthetic Aperture Radar (SAR) satellites. Therefore, either a corner reflector design tailored to a specific data type or a compromise design for multiple data types is required. In this paper, I outline the practical and theoretical considerations that need to be made when designing appropriate radar targets, with a focus on supporting multi-frequency SAR data. These considerations are tested by performing field experiments on targets of different size using SAR images from TerraSAR-X, COSMO-SkyMed and RADARSAT-2. Phase noise behaviour in SAR images can be estimated by measuring the Signal-to-Clutter ratio (SCR) in individual SAR images. The measured SCR of a point target is dependent on its RCS performance and the influence of clutter near to the deployed target. The SCR is used as a metric to estimate the expected InSAR displacement error incurred by the design of each target and to validate these observations against theoretical expectations. I find that triangular trihedral corner reflectors as small as 1 m in dimension can achieve a displacement error magnitude of a tenth of a millimetre or less in medium-resolution X-band data. Much larger corner reflectors (2.5 m or greater) are required to achieve the same displacement error magnitude in medium-resolution C-band data. Compromise designs should aim to satisfy the requirements of the lowest SAR frequency to be used, providing that these targets will not saturate the sensor of the highest frequency to be used. Finally, accurate boresight alignment of the corner reflector can be critical to the overall target performance. Alignment accuracies better than 4° in azimuth and elevation will incur a minimal impact on the displacement error in X and C-band data.

Analytical and numerical solutions to some one-dimensional relativistic heat equations

Analytical and numerical solutions to a family of one-dimensional (nonlinear) relativistic heat equations in finite domains are presented. The analytical solutions correspond to steady state conditions in the absence of source terms and have been obtained as functions of the (absolute) temperature at one of the boundaries, a characteristic exponent, a Péclet number based on the speed of light and the heat flux, while the numerical ones correspond to an initial Gaussian temperature distribution, adiabatic boundary conditions and different values of the Péclet number and a characteristic exponent. It is shown that, for steady conditions, the difference between the (nondimensional) temperature of the relativistic heat equation and that corresponding to Fourier law is very large for large values of both the coefficient and the exponent of the nonlinearity that characterize the relativistic contribution to the heat flux, small values of the temperature at one of the boundaries and large heat fluxes. Travelling-wave solutions of the wave-front type are reported for odd values of the nonlinearity exponent in infinite domains and in the absence of source terms. For an initial Gaussian distribution, it is shown that the relativistic contribution to heat transfer results in the formation of two triangular corner regions where the temperature is equal to the initial one, and the formation of two temperature fronts that propagate towards the domain’s boundaries. The amplitude and steepness of these fronts increase whereas their width and speed decrease as the Péclet number is decreased. It is also shown that the effects of the characteristic exponent are small provided that its value is greater than about two, and that, in the absence of source terms, the temperature becomes uniform in space and constant in time for adiabatic boundary conditions. In the presence of source terms and for adiabatic boundary conditions, it is shown that, soon after the temperature fronts hit the boundaries, the temperature becomes uniform in space but may either increase or decrease with time until it reaches a stable fixed point of the source term. For a cubic source term that exhibits bistability, it is shown that the temperature tends to the attractor of lowest temperature.

Modified closing-opening wedge osteotomy for the treatment of sagittal malalignment in thoracolumbar fractures malunion

Background ContextMany techniques have been described for the surgical treatment of rigid posttraumatic thoracolumbar kyphosis, but none is well adapted to the modified shape of the wedged vertebra. PurposeThe study aimed to describe the modified closing-opening wedge osteotomy (MCOWO), a new osteotomy technique that adapts to the triangular shape of the wedged apical vertebra of the deformity. Study DesignA retrospective assessment of the degree of correction before and after the MCOWO was carried out. Patient SampleTen patients presenting rigid posttraumatic thoracolumbar kyphosis were enrolled in this study. Outcome MeasuresWe used preoperative and postoperative whole spine radiographs to assess the sagittal plane parameters, and computed tomography scan for measurement of the vertebral segment height at the osteotomy level, spinal cord length, aorta length, and fusion rate. MethodsTen patients underwent the MCOWO at T12 or L1. The procedure involves removing the postero-superior triangular corner of the wedged vertebra and transforming it to a shape similar to a trapezoid. ResultsThe patients' mean age was 36.6±7.5 years, the mean time between the fracture and the surgery was 12.2±5.6 months, and the mean follow-up was 30.6±5 months. In all patients, statistically significant improvement was observed in the sagittal plane after surgery. The thoracolumbar angle improved from 52±6° preoperatively to 7.1±5.7° at the last follow-up. Mean osteotomy angle was 38.1±2.6°, mean spinal cord shortening was 1.2±0.2 cm, and mean aorta lengthening was 2.3±0.4 cm. All the patients showed complete fusion at 2 years, and none required revision surgery. Two patients presented a temporary unilateral weakness that recovered completely within 3 months after the surgery. ConclusionsThe MCOWO is an interesting procedure for patients with posttraumatic thoracolumbar kyphosis. The modified osteotomy is adapted to the modified shape of the compressed vertebra. Spinal cord shortening and aorta lengthening were well tolerated in all patients.

Truncated corner cubes with near-perfect retroreflection efficiency

By isolating a finite effective volume from a conventional triangular pyramid corner cube, we obtained truncated corner cube structures with greatly enhanced retroreflection efficiency. We explore an optimal truncated corner cube with near 100% retroreflection efficiency based on the expectation that the traveling paths of the optical rays can be localized in the finite effective volume of the structure, and, as a result, truncated corner cubes with perfect efficiency can be produced. As a case study, the retroreflection efficiency of a commercialized 3M truncated corner cube sample is evaluated. Furthermore, it is shown with numerical verification that a truncated corner cube array sheet with near-perfect retroreflection efficiency can be produced.

Development of n+-in-p large-area silicon microstrip sensors for very high radiation environments – ATLAS12 design and initial results

We have been developing a novel radiation-tolerant n+-in-p silicon microstrip sensor for very high radiation environments, aiming for application in the high luminosity large hadron collider. The sensors are fabricated in 6in., p-type, float-zone wafers, where large-area strip sensor designs are laid out together with a number of miniature sensors. Radiation tolerance has been studied with ATLAS07 sensors and with independent structures. The ATLAS07 design was developed into new ATLAS12 designs. The ATLAS12A large-area sensor is made towards an axial strip sensor and the ATLAS12M towards a stereo strip sensor. New features to the ATLAS12 sensors are two dicing lines: standard edge space of 910μm and slim edge space of 450μm, a gated punch-through protection structure, and connection of orphan strips in a triangular corner of stereo strips. We report the design of the ATLAS12 layouts and initial measurements of the leakage current after dicing and the resistivity of the wafers.

Mode I Stress Intensity Factors for triangular corner crack nearby intersecting of cylindrical holes

The paper deals with the Stress Intensity Factor assessment of cracks at the intersection of holes loaded by internal pressure. Triangular flaws are considered at the intersection of two holes inside a specific specimen. The research examines the influence of hole diameter ratio D1/D2 and the angle between their axes ?. Numerical analysis is performed to determine the Stress Intensity Factors (SIF) of mode I in many different geometric configurations. The actual shape of a real crack nucleated at the intersection of two cylindrical holes is subject to variable internal pressure and is usually geometrically complex. The Stress Intensity Factor changes along the crack contour and the crack shape development is controlled by its local value, e.g. during a fatigue loading. In general, the estimation of the Stress Intensity Factors of cracks with a complex shape is made by means of numerical methods since closed form solutions in literature are limited. However, in order to solve the problem of crack propagation more quickly, in the case of a crack corner at the intersection between two cylindrical holes, we can assume, in agreement with scientific literature, a symmetrical triangular crack shape and the Stress Intensity Factor are only calculated at the middle of the crack. Obviously, this is a strong approximation, but this allows a reduction in the computation effort for crack growth rate assessments and safety evaluation. In this paper, the weight function technique is used by integrating the actual stress field evaluated in the uncracked model. The method of the weight function is of general validity and the weight function is related to the displacement components close to the crack front, as proposed by Bueckner and Rice. From a computational point of view, the use of the three-dimensional weight function is complex and in scientific literature a weight function of general validity is not available. Nevertheless, thanks to the work conducted by Petroski and Achenbach, Shen and Glinka, an efficient generalised weight function has been adopted and then developed by Sha and Yang [9], which considers a series expansion of non-singular terms. In this way, the integration of the weight function, multiplied by a nominal stress, is made along a line and not in a two-dimensional domain. In this preliminary work, according to Herz et al., we consider a weight function with three terms by assuming a priori the coefficients of the second and third non-singular terms. This contribution is essentially an extension of a previous paper by Herz et al. They only considered the case of D1/D2=1 and ?=90° (Di are the diameters of the two cylindrical holes and a is the angle between their axis). Here, we extend the analysis to D1/D2 equal to 2, 4 and 8 with an ? of 60 and 45 degrees. With the aid of three-dimensional modelling, an accurate FE model of a triangular corner crack at different crack depths has been made. Subsequently, by using ANSYS finite element software, it is possible to employ the command KCAL that evaluates the Stress Intensity Factors in the middle of the crack. Subsequently, a comparison between numerical FE results and the analytical results, giving the values of the unknown coefficients of the weight function (the unknown coefficient is indicated in the paper as M1). As reported in the tables, the accuracy of the weight functions in SIF predictions is about 5% despite the strong simplification previously introduced in the model. This result is considerable because it is possible to determine the Stress Intensity Factor of a triangular shaped crack by a line integral of a stress profile in a model without considering the crack.

Atomic structure and edge magnetism in MoS2+x parallelogram shaped platelets

The structural, electronic, and magnetic properties of MoS(2+x) parallelogram shaped platelets having m and n Mo atoms on the adjoining edges have been studied using first principles calculations and by varying m and n from 1 to 6. These platelets have 100% S coverage on two adjoining edges while 50% S coverage on the other two edges. The structural stability of the platelets increases with size but the highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) energy gap in general decreases. There is a triangular metallic corner at the intersection of 100% S covered edges of the platelets when m = n. On the other hand magnetism is observed on the 50% S covered edges of the platelets for the sizes greater than that of the (3,4) platelet. The magnetic moments mainly arise from the undercoordinated S(2c) atoms at the 50% S covered edges rather than from Mo atoms. The criteria for the existence of the magnetic moments on S(2c) atoms are suggested and the electronic structure of the platelets on the edges as well as inside is discussed.

대기 굴절률을 이용한 원형레일 기반 지상 SAR 자료의 대기보정

In this paper, an atmospheric effect of repetitive measurements of X-band (9.65 GHz) arc-rail type GB-SAR (ArcSAR) system was quantitatively analyzed. Four artificial triangular trihedral corner reflectors as stationary targets for getting stable back scattered signal during 43 hours continually. The results of the analysis showed that the phase of those stationary targets had changed maximum of 5 radian (12.4 mm) and total RMS error had was 1.62 radian (4 mm) during 65 repeated measuring time. The refractive index of air which was calculated using the temperature, humidity and pressure of atmosphere showed very close relationship with the phase difference. We could check the atmospheric correction was fulfilled by the correction of an atmospheric effect using refractive index during the selected 16 hours period showed that RMS error was dropped from 1.74 radian (4.3 mm) to 0.10 radian (0.24 mm).

Statistical Discriminants from Two-Dimensional Grids of Regional P/S Spectral Ratios

Abstract This paper describes a statistical methodology for earthquake/explosion discrimination using two-dimensional (2D) grids (frequency of S against frequency of P ) of regional P / S ratios. A method similar to that of scan statistics is developed by applying a counting rule on an N -length bitmap image of the 2D plots. An average density of bits is computed for explosions in the training set; it is assumed that each bitmap cell represents an independent sample taken from a Bernoulli process. A hypothesis test H 0 : explosion is designed, and a p value (a statistical measure) indicating the degree of membership of a new event to the explosion population is computed. A statistical method is presented that allows construction of p values under the null hypothesis that the event in question is an explosion. The field of view is the lower-right triangular corner plot for P / S ratios closely related to the high-frequency P to low-frequency S discriminant. The plot is converted to a bit map, and bits are summed and treated as a Bernoulli random variable. Using a set of calibration data, the background density of bits for explosions can be estimated and used to compute p values for new events. Importantly, the p values from the 2D P / S ratios can be naturally combined with other p values from other discriminants constructed under the same hypothesis to form a multivariate discriminant as in Anderson et al. (2007).