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At least 1,423 records · Page 79

Pseudo-Spectral Methods for the Laplace-Beltrami Equation and the Hodge Decomposition on Surfaces of Genus One

The inversion of the Laplace-Beltrami operator and the computation of the Hodge decomposition of a tangential vector field on smooth surfaces arise as computational tasks in many areas of science, from computer graphics to machine learning to computational physics. In this work, we present a high-order accurate pseudo-spectral approach, applicable to closed surfaces of genus one in three-dimensional space, with a view toward applications in plasma physics and fluid dynamics.

97 MATHEMATICS AND COMPUTING↗

Incorporating the Min-Max Mesh Optimization Method within the Target-Matrix Paradigm

The Target-Matrix Optimization Paradigm (TMOP) is a method for improving mesh quality via node movement. Through the use of appropriate pre-defined quality metrics and Target-matrices, TMOP provides the ability to define mesh quality in terms of element shape, volume, and edge orientation as a function of position within the mesh, thus facilitating high-level goals such as size-adapted meshing. The Paradigm is developed further in this paper by showing how it can be applied to the problem of improving the mesh in locations where the quality is the worst. Improving the worst quality portions of a mesh was investigated by Freitag, Amenta, and others, who showed that the problem can be formulated as a min-max optimization problem. The Target-paradigm is used to extend the previous work in two important respects. First, by using quality metrics from the Target-paradigm, quality can be user-specified via Target-matrices instead of the quality definition being hard-wired into the quality metric. Second, by making use of the sample point concept in TMOP, one can extend min-max mesh optimization to non-simplicial element types such as quadrilaterals. Numerical experiments were performed to illustrate these extensions and to investigate their utility. A non-gradient solver known as the amoeba was used to numerically compute the optimal solutions. This derivative-free method, in conjunction with the use of barrier metrics from TMOP, enables the solution of the min-max problem without the use of explicit constraints to guarantee that the optimal mesh is non-inverted. The experiments showed that the use of Target-metrics in min-max with triangle (or tetrahedral) element meshes is able to effectively improve the worst quality elements in terms of shape or in terms of size+shape. The experiments also showed that the mesh min-max extension to quadrilateral element meshes can lead to acceptable meshes using barrier metrics from the Target-paradigm, provided that inter-element mesh smoothness is not important. Poor behavior was observed when using non-barrier Target-metrics in min-max with quadrilateral element meshes. For both simplicial and quadrilateral meshes, the min-sum method can be competitive with min-max, however.

97 MATHEMATICS AND COMPUTING↗

Simulation of crumpled sheets via alternating quasistatic and dynamic representations

In this work, we present a method for simulating the large-scale deformation and crumpling of thin, elastoplastic sheets. Motivated by the physical behavior of thin sheets during crumpling, two different formulations of the governing equations of motion are used: (1) a quasistatic formulation that effectively describes smooth deformations, and (2) a fully dynamic formulation that captures large changes in the sheet's velocity. The former is a differential-algebraic system of equations integrated implicitly in time, while the latter is a set of ordinary differential equations (ODEs) integrated explicitly. We adopt a hybrid integration scheme to adaptively alternate between the quasistatic and dynamic representations as appropriate. Further, we demonstrate the capacity of this method to effectively simulate a variety of crumpling phenomena. Finally, we show that statistical properties, notably the accumulation of creases under repeated loading, as well as the area distribution of facets, are consistent with experimental observations.

97 MATHEMATICS AND COMPUTING↗

A study on in situ growth of TaC whiskers in Al{sub 2}O{sub 3} matrix powder for ceramic cutting tools

Graphical abstract: In situ growth of TaC whiskers (TaC{sub w}) was synthesized in an α-Al{sub 2}O{sub 3} matrix powder via a carbothermal reduction technique. The whiskers were 0.2–0.5 μm in diameter and 5–15 μm in length; they were straight and had smooth surfaces. Highlights: ► In situ growth of TaC whiskers was synthesized in an α-Al{sub 2}O{sub 3} matrix powder. ► The wet mixing method and 1450 °C were suitable for whiskers growth. ► The growth of TaC whiskers is not influenced by the Al{sub 2}O{sub 3} powder. ► The major impurities were TaC particles, nickel and unreacted carbon. -- Abstract: In situ growth of tantalum carbide (TaC) whiskers was synthesized in an α-Al{sub 2}O{sub 3} matrix powder via a carbothermal reduction technique within a temperature range of 1350–1500 °C in an argon atmosphere. The starting materials consisted of Ta{sub 2}O{sub 5}, C, Ni and NaCl powders. Different mixing methods and various reaction temperatures were employed. Most of the prepared whiskers were 0.2–0.5 μm in diameter and 5–15 μm in length. The reaction temperature of 1400–1450 °C was suitable for the growth of TaC whiskers and a wet mixing method was beneficial to increase the whisker yield. Some of the whiskers exhibited the needle shape while others exhibited the screw shape. The growth mechanism of the whiskers was a complex mechanism involving a helical screw dislocation mechanism and a vapor–liquid–solid process. No obvious influences of the Al{sub 2}O{sub 3} matrix powder on the growth of TaC whiskers were found and the major impurities in the obtained powder were TaC particles, nickel and unreacted carbon.

36 MATERIALS SCIENCE↗

Epitaxial Atomic Layer Deposition of Sn-Doped Indium Oxide

Coherently strained, epitaxial Sn-doped In2O3 (ITO) thin films were fabricated at temperatures as low as 250 degrees C using atomic layer deposition (ALD) on (001)-, (011)-, and (111)-oriented single-crystal Y-stabilized ZrO2 (YSZ) substrates. Resultant films possess cube-on-cube epitaxial relationships with the underlying YSZ substrates and are smooth, highly conductive, and optically transparent. This epitaxial ALD approach is favorable compared to many conventional growth techniques as it is a large-scale synthesis method that does not necessitate the use of high temperatures or ultrahigh vacuum. These films may prove valuable as a conductive growth template in areas where high-quality crystalline thin film substrates are important, such as solar energy materials, light-emitting diodes, or wide bandgap semiconductors. Furthermore, we discuss the applicability of this ALD system as an excellent model system for the study of ALD surface chemistry, nucleation, and film growth.

Emery, Jonathan D.↗

Nanopatterning and tuning of optical taper antenna apex for tip-enhanced Raman scattering performance

This paper focuses on finding optimal electrochemical conditions from linear sweep voltammetry analysis for preparing highly reproducible tip-enhanced Raman scattering (TERS) conical gold tips with dc-pulsed voltage etching. Special attention is given to the reproducibility of tip apex shapes with different etchant mixtures. We show that the fractional Brownian motion model enables a mathematical description of the decaying current kinetics during the whole etching process up to the cutoff event. Further progress in preparation of highly reproducible smooth and sharp tip apexes is related to the effect of an additive, such as isopropanol, to aqueous acids. A finite-difference time-domain method based near-field analysis provides evidence that TERS performance depends critically on tip orientation relative to a highly focused laser beam. A TERS based criterion for recognizing gold tips able to couple/decouple optical near- and far-fields is proposed.

36 MATERIALS SCIENCE↗

Accurate pointing of tungsten welding electrodes

Thoriated-tungsten is pointed accurately and quickly by using sodium nitrite. Point produced is smooth and no effort is necessary to hold the tungsten rod concentric. The chemically produced point can be used several times longer than ground points. This method reduces time and cost of preparing tungsten electrodes.

Ziegelmeier, P.↗

Implicit determination of multispectral scanner data variation over extended areas.

Description of a method by which variations in aerial multispectral scanner data can be accounted for when there is insufficient ground truth information. The data are suitably filtered and smoothed along the flight line, and the reduced results are presented in a form such that the investigator can readily determine the preprocessing that should be used and the spatial extent to which it should be applied. An algorithm is developed for the detection of cloud-shadowed areas.

Kriegler, F. J.↗

A simulator evaluation of the use of spoilers on a light aircraft

A fixed-base flight simulator was used to evaluate wing spoilers for longitudinal flight path control on a modified Cessna Cardinal aircraft. Spoilers which generated the proper pitching moment to maintain aircraft trim C sub L constant could be used as an effective descent rate control. More than 100 simulated ILS approaches were flown by evaluation pilots using both conventional methods and spoiler descent rate control. Three spoiler control schemes were evaluated during the ILS approaches. Using the spoilers for control, instrument approaches could be flown smoothly and precisely with constant airspeed and pitch attitude. While the spoilers could adequately control ILS approaches, a spoiler system with greater authority would be desirable for use in visual approaches.

Brainerd, C. H.↗

A radar image of Venus.

Radar scans of Venus have yielded a brightness map of a large portion of the surface. The bright area in the south (alpha) and the twin such areas in the north (beta and delta) were first discovered by spectral analysis of radar echos. When range-gating is also applied, their shapes are revealed, and they are seen to be roundish and about 1000 km across. Although radar brightness can be the result of either intrinsic reflectivity or surface roughness, polarization studies show these features to be rough (to the scale of the wavelength, 12.5 cm). Dark, circular areas can also be seen, many with bright central spots. The dark areas are probably smooth. The blurring of the equatorial strip is an artifact of the range-Doppler geometry; all resolution disappears at the equator. Another artifact of the method is the 'ghost', in the south, of the images of beta and delta. Such ghosts appear only at the eastern and western extremes of the map.

Goldstein, R. M.↗

Boundary-layer transition on a plate subjected to simultaneous spanwise and chordwise pressure gradients

The boundary-layer transition on a short plate was studied by means of the china-clay visual technique. The plate model was mounted in a wind tunnel so that it was subjected to small simultaneous spanwise and chordwise pressure gradients. Results of the experimental study, which was performed at three subsonic velocities, indicated that the transition pattern was appreciably curved in the spanwise direction but quite smooth and well behaved. Reasonable comparisons between predictions of transition and experiment were obtained from two finite-difference two-dimensional boundary-layer calculation methods which incorporated transition models based on the concept of a transition intermittency factor.

Boldman, D. R.↗

Multilevel techniques for nonelliptic problems

Multigrid and multilevel methods are extended to the solution of nonelliptic problems. A framework for analyzing these methods is established. A simple nonelliptic problem is given, and it is shown how a multilevel technique can be used for its solution. Emphasis is on smoothness properties of eigenvectors and attention is drawn to the possibility of conditioning the eigensystem so that eigenvectors have the desired smoothness properties.

Jespersen, D. C.↗

Thrust imbalance of solid rocket motor pairs on Space Shuttle flights

This analysis extends the investigation presented at the 17th Joint Propulsion Conference in 1981 to include fifteen sets of Space Shuttle flight data. The previous report dealt only with static test data and the first flight pair. The objective is to compare the authors' previous theoretical analysis of thrust imbalance with actual Space Shuttle performance. The theoretical prediction method, which involves a Monte Carlo technique, is reviewed briefly as are salient features of the flight instrumentation system and the statistical analysis. A scheme for smoothing flight data is discussed. The effects of changes in design parameters are discussed with special emphasis on the filament wound motor case being developed to replace the steel case. Good agreement between the predictions and the flight data is demonstrated.

Foster, W. A., Jr.↗

X-ray testing of the AXAF Technology Mirror Assembly (TMA) mirror

The X-ray performance of the Advanced X-ray Astrophysics Facility TMA in the 0.277-6.4-keV range. The precise figure and smooth surface originally specified (which were expected from the in-process optical and mechanical measurements) are verified. The paper primarily describes the test equipment and methods used and gives examples of the detailed on-axis and off-axis data.

Schwartz, D. A.↗

Multiplier-continuation algorthms for constrained optimization

Several path following algorithms based on the combination of three smooth penalty functions, the quadratic penalty for equality constraints and the quadratic loss and log barrier for inequality constraints, their modern counterparts, augmented Lagrangian or multiplier methods, sequential quadratic programming, and predictor-corrector continuation are described. In the first phase of this methodology, one minimizes the unconstrained or linearly constrained penalty function or augmented Lagrangian. A homotopy path generated from the functions is then followed to optimality using efficient predictor-corrector continuation methods. The continuation steps are asymptotic to those taken by sequential quadratic programming which can be used in the final steps. Numerical test results show the method to be efficient, robust, and a competitive alternative to sequential quadratic programming.

Lundberg, Bruce N.↗

A compressed marine data set for geomagnetic field modeling

Some 13 million scalar magnetic field data points that have been collected from the world's ocean areas reside in the collection of the National Geophysical Data Center. In order to derive a suitable data set for modeling the geomagnetic field of the earth, each ship track is divided into 220 km segments. The distribution of the reduced data in position, time and local time is discussed. The along-track filtering process described has proved to be an effective method of condensing large numbers of shipborne magnetic data into a manageable and meaningful data set for field modeling. This process also provides the benefits of smoothing short-wavelength crystal anomalies, discarding data recorded during magnetically noisy periods, and assigning reasonable error estimates to be utilized in the least squares modeling.

Langel, R. A.↗

SU-E-J-133: Autosegmentation of Linac CBCT: Improved Accuracy Via Penalized Likelihood Reconstruction

Purpose: To improve the quality of kV X-ray cone beam CT (CBCT) for use in radiotherapy delivery assessment and re-planning by using penalized likelihood (PL) iterative reconstruction and auto-segmentation accuracy of the resulting CBCTs as an image quality metric. Methods: Present filtered backprojection (FBP) CBCT reconstructions can be improved upon by PL reconstruction with image formation models and appropriate regularization constraints. We use two constraints: 1) image smoothing via an edge preserving filter, and 2) a constraint minimizing the differences between the reconstruction and a registered prior image. Reconstructions of prostate therapy CBCTs were computed with constraint 1 alone and with both constraints. The prior images were planning CTs(pCT) deformable-registered to the FBP reconstructions. Anatomy segmentations were done using atlas-based auto-segmentation (Elekta ADMIRE). Results: We observed small but consistent improvements in the Dice similarity coefficients of PL reconstructions over the FBP results, and additional small improvements with the added prior image constraint. For a CBCT with anatomy very similar in appearance to the pCT, we observed these changes in the Dice metric: +2.9% (prostate), +8.6% (rectum), −1.9% (bladder). For a second CBCT with a very different rectum configuration, we observed +0.8% (prostate), +8.9% (rectum), −1.2% (bladder). For a third case with significant lateral truncation of the field of view, we observed: +0.8% (prostate), +8.9% (rectum), −1.2% (bladder). Adding the prior image constraint raised Dice measures by about 1%. Conclusion: Efficient and practical adaptive radiotherapy requires accurate deformable registration and accurate anatomy delineation. We show here small and consistent patterns of improved contour accuracy using PL iterative reconstruction compared with FBP reconstruction. However, the modest extent of these results and the pattern of differences across CBCT cases suggest that significant further development will be required to make CBCT useful to adaptive radiotherapy.

60 APPLIED LIFE SCIENCES↗

Diffusion of Cd and Te adatoms on CdTe(111) surfaces: A computational study using density functional theory

CdTe is one of the most promising semiconductor for thin-film based solar cells. Here we report a computational study of Cd and Te adatom diffusion on the CdTe (111) A-type (Cd terminated) and B-type (Te terminated) surfaces and their migration paths. The atomic and electronic structure calculations are performed under the DFT formalism and climbing Nudge Elastic Band (cNEB) method has been applied to evaluate the potential barrier of the Te and Cd diffusion. In general the minimum energy site on the surface is labeled as A{sub a} site. In case of Te and Cd on B-type surface, the sub-surface site (a site just below the top surface) is very close in energy to the A site. This is responsible for the subsurface accumulation of adatoms and therefore, expected to influence the defect formation during growth. The diffusion process of adatoms is considered from A{sub a} (occupied) to A{sub a} (empty) site at the nearest distance. We have explored three possible migration paths for the adatom diffusion. The adatom surface interaction is highly dependent on the type of the surface. Typically, Te interaction with both type (5.2 eV for A-type and 3.8 eV for B-type) is stronger than Cd interactions(2.4 eV for B-type and 0.39 eV for A-type). Cd interaction with the A-type surface is very weak. The distinct behavior of the A-type and B-type surfaces perceived in our study explain the need of maintaining the A-type surface during growth for smooth and stoichiometric growth.

36 MATERIALS SCIENCE↗