A method of plane geometry primitive presentation
NASA Astrophysics Data System (ADS)
Jiao, Anbo; Luo, Haibo; Chang, Zheng; Hui, Bin
2014-11-01
Point feature and line feature are basic elements in object feature sets, and they play an important role in object matching and recognition. On one hand, point feature is sensitive to noise; on the other hand, there are usually a huge number of point features in an image, which makes it complex for matching. Line feature includes straight line segment and curve. One difficulty in straight line segment matching is the uncertainty of endpoint location, the other is straight line segment fracture problem or short straight line segments joined to form long straight line segment. While for the curve, in addition to the above problems, there is another difficulty in how to quantitatively describe the shape difference between curves. Due to the problems of point feature and line feature, the robustness and accuracy of target description will be affected; in this case, a method of plane geometry primitive presentation is proposed to describe the significant structure of an object. Firstly, two types of primitives are constructed, they are intersecting line primitive and blob primitive. Secondly, a line segment detector (LSD) is applied to detect line segment, and then intersecting line primitive is extracted. Finally, robustness and accuracy of the plane geometry primitive presentation method is studied. This method has a good ability to obtain structural information of the object, even if there is rotation or scale change of the object in the image. Experimental results verify the robustness and accuracy of this method.
Geometry of state space in plane Couette flow
NASA Astrophysics Data System (ADS)
Cvitanović, P.; Gibson, J. F.
A large conceptual gap separates the theory of low-dimensional chaotic dynamics from the infinite-dimensional nonlinear dynamics of turbulence. Recent advances in experimental imaging, computational methods, and dynamical systems theory suggest a way to bridge this gap in our understanding of turbulence. Recent discoveries show that recurrent coherent structures observed in wall-bounded shear flows (such as pipes and plane Couette flow) result from close passes to weakly unstable invariant solutions of the Navier-Stokes equations. These 3D, fully nonlinear solutions (equilibria, traveling waves, and periodic orbits) structure the state space of turbulent flows and provide a skeleton for analyzing their dynamics. We calculate a hierarchy of invariant solutions for plane Couette, a canonical wall-bounded shear flow. These solutions reveal organization in the flow's turbulent dynamics and can be used to predict directly from the fundamental equations physical quantities such as bulk flow rate and mean wall drag. All results and the code that generates them are disseminated through through our group's open-source CFD software and solution database Channelflow.org and the collaborative e-book ChaosBook.org.
Wei, Q.; Dalvit, D. A. R.; Lombardo, F. C.; Mazzitelli, F. D.; Onofrio, R.
2010-05-15
We report on measurements performed on an apparatus aimed to study the Casimir force in the cylinder-plane configuration. The electrostatic calibrations evidence anomalous behaviors in the dependence of the electrostatic force and the minimizing potential upon distance. We discuss analogies and differences of these anomalies with respect to those already observed in the sphere-plane configuration. At the smallest explored distances we observe frequency shifts of non-Coulombian nature preventing the measurement of the Casimir force in the same range. We also report on measurements performed in the parallel-plane configuration, showing that the dependence on distance of the minimizing potential, if present at all, is milder than in the sphere-plane or cylinder-plane geometries. General considerations on the interplay between the distance-dependent minimizing potential and the precision of Casimir force measurements in the range relevant to detect the thermal corrections for all geometries are finally reported.
Validating Phasing and Geometry of Large Focal Plane Arrays
NASA Technical Reports Server (NTRS)
Standley, Shaun P.; Gautier, Thomas N.; Caldwell, Douglas A.; Rabbette, Maura
2011-01-01
The Kepler Mission is designed to survey our region of the Milky Way galaxy to discover hundreds of Earth-sized and smaller planets in or near the habitable zone. The Kepler photometer is an array of 42 CCDs (charge-coupled devices) in the focal plane of a 95-cm Schmidt camera onboard the Kepler spacecraft. Each 50x25-mm CCD has 2,200 x 1,024 pixels. The CCDs accumulate photons and are read out every six seconds to prevent saturation. The data is integrated for 30 minutes, and then the pixel data is transferred to onboard storage. The data is subsequently encoded and transmitted to the ground. During End-to-End Information System (EEIS) testing of the Kepler Mission System (KMS), there was a need to verify that the pixels requested by the science team operationally were correctly collected, encoded, compressed, stored, and transmitted by the FS, and subsequently received, decoded, uncompressed, and displayed by the Ground Segment (GS) without the outputs of any CCD modules being flipped, mirrored, or otherwise corrupted during the extensive FS and GS processing. This would normally be done by projecting an image on the focal plane array (FPA), collecting the data in a flight-like way, and making a comparison between the original data and the data reconstructed by the science data system. Projecting a focused image onto the FPA through the telescope would normally involve using a collimator suspended over the telescope opening. There were several problems with this approach: the collimation equipment is elaborate and expensive; as conceived, it could only illuminate a limited section of the FPA (.25 percent) during a given test; the telescope cover would have to be deployed during testing to allow the image to be projected into the telescope; the equipment was bulky and difficult to situate in temperature-controlled environments; and given all the above, test setup, execution, and repeatability were significant concerns. Instead of using this complicated approach of
ERIC Educational Resources Information Center
Koyuncu, Ilhan; Akyuz, Didem; Cakiroglu, Erdinc
2015-01-01
This study aims to investigate plane geometry problem-solving strategies of prospective mathematics teachers using dynamic geometry software (DGS) and paper-and-pencil (PPB) environments after receiving an instruction with GeoGebra (GGB). Four plane geometry problems were used in a multiple case study design to understand the solution strategies…
Multigroup Time-Independent Neutron Transport Code System for Plane or Spherical Geometry.
1986-12-01
Version 00 PALLAS-PL/SP solves multigroup time-independent one-dimensional neutron transport problems in plane or spherical geometry. The problems solved are subject to a variety of boundary conditions or a distributed source. General anisotropic scattering problems are treated for solving deep-penetration problems in which angle-dependent neutron spectra are calculated in detail.
High School Plane Geometry Through Transformations: An Exploratory Study. Final Report.
ERIC Educational Resources Information Center
Olson, Alton T.
The plans for a field test of teaching tenth grade plane geometry through transformations is described. Text and homework materials have been written, and teachers have been trained. Eight intact classes are now being taught utilizing the materials. Data to be collected will include: (1) teacher descriptions of the course via questionnaire; (2)…
The orthogonal planes split of quaternions and its relation to quaternion geometry of rotations
NASA Astrophysics Data System (ADS)
Hitzer, Eckhard
2015-04-01
Recently the general orthogonal planes split with respect to any two pure unit quaternions f,g ∈ H, f2 = g2 = -1, including the case f = g, has proved extremely useful for the construction and geometric interpretation of general classes of double-kernel quaternion Fourier transformations (QFT) [7]. Applications include color image processing, where the orthogonal planes split with f = g = the grayline, naturally splits a pure quaternionic three-dimensional color signal into luminance and chrominance components. Yet it is found independently in the quaternion geometry of rotations [3], that the pure quaternion units f, g and the analysis planes, which they define, play a key role in the geometry of rotations, and the geometrical interpretation of integrals related to the spherical Radon transform of probability density functions of unit quaternions, as relevant for texture analysis in crystallography. In our contribution we further investigate these connections.
Effect of Bubbles on Liquid Nitrogen Breakdown in Plane-Plane Electrode Geometry From 100-250 kPa
Sauers, Isidor; James, David Randy; Tuncer, Enis; Polyzos, Georgios; Pace, Marshall O
2011-01-01
Liquid nitrogen (LN(2)) is used as the cryogen and dielectric for many high temperature superconducting, high voltage applications. When a quench in the superconductor occurs, bubbles are generated which can affect the dielectric breakdown properties of the LN(2). Experiments were performed using plane-plane electrode geometry where bubbles were introduced into the gap through a pinhole in the ground electrode. Bubbles were generated using one or more kapton heaters producing heater powers up to 30 W. Pressure was varied from 100-250 kPa. Breakdown strength was found to be relatively constant up to a given heater power and pressure at which the breakdown strength drops to a low value depending on the pressure. After the drop the breakdown strength continues to drop gradually at higher heater power. This is particularly illustrated at 100 kPa. After the drop in breakdown strength the breakdown is believed to be due to the formation of a vapor bridge. Also the heater power at which the breakdown strength changes from that of LN(2) to that of gaseous nitrogen increases with increasing pressure. The data can provide design constraints for high temperature superconducting fault current limiters (FCLs) so that the formation of a vapor bridge can be suppressed or avoided.
NASA Astrophysics Data System (ADS)
Martinetti, Pierre; Tomassini, Luca
2013-10-01
We study the metric aspect of the Moyal plane from Connes' noncommutative geometry point of view. First, we compute Connes' spectral distance associated with the natural isometric action of on the algebra of the Moyal plane . We show that the distance between any state of and any of its translated states is precisely the amplitude of the translation. As a consequence, we obtain the spectral distance between coherent states of the quantum harmonic oscillator as the Euclidean distance on the plane. We investigate the classical limit, showing that the set of coherent states equipped with Connes' spectral distance tends towards the Euclidean plane as the parameter of deformation goes to zero. The extension of these results to the action of the symplectic group is also discussed, with particular emphasis on the orbits of coherent states under rotations. Second, we compute the spectral distance in the double Moyal plane, intended as the product of (the minimal unitization of) by . We show that on the set of states obtained by translation of an arbitrary state of , this distance is given by the Pythagoras theorem. On the way, we prove some Pythagoras inequalities for the product of arbitrary unital and non-degenerate spectral triples. Applied to the Doplicher- Fredenhagen-Roberts model of quantum spacetime [DFR], these two theorems show that Connes' spectral distance and the DFR quantum length coincide on the set of states of optimal localization.
Studies of Low-Current Back-Discharge in Point-Plane Geometry with Dielectric Layer
Jaworek, Anatol; Rajch, Eryk; Krupa, Andrzej; Czech, Tadeusz; Lackowski, Marcin
2006-01-15
The paper presents results of spectroscopic investigations of back-discharges generated in the point-plane electrode geometry in ambient air at atmospheric pressure, with the plane electrode covered with a dielectric layer. Fly ash from an electrostatic precipitator of a coal-fired power plant was used as the dielectric layer in these investigations. The discharges for positive and negative polarities of the needle electrode were studied by measuring optical emission spectra at two regions of the discharge: near the needle electrode and dielectric layer surface. The visual forms of the discharge were recorded and correlated with the current-voltage characteristics and optical emission spectra. The back-arc discharge was of particular interest in these studies due to its detrimental effects it causes in electrostatic precipitators.
Models to relate wafer geometry measurements to in-plane distortion of wafers
NASA Astrophysics Data System (ADS)
Turner, Kevin T.; Vukkadala, Pradeep; Sinha, Jaydeep K.
2016-04-01
Achieving satisfactory overlay is increasingly challenging as feature sizes are reduced and allowable overlay budgets shrink to several nanometers and below. Overlay errors induced by wafer processing, such as film deposition and etching, constitute a meaningful fraction of overlay budgets. Wafer geometry measurements provide the opportunity to quantify stress-induced distortions at the wafer level and provide information that can be used in a feedback mode to alter wafer processing or in a feed-forward mode to set wafer-specific corrections in the lithography tool. In order for such feed-forward schemes based on wafer geometry to be realized, there is a need for mechanics models that relate in-plane distortion of a chucked wafer to the out-of-plane distortion of a wafer in a free state. Here, a simple analytical model is presented that shows the stress-induced component of overlay is correlated to a corrected local wafer slope metric for a wide range of cases. The analytical model is validated via finite element (FE) simulations of wafers with nonuniform stress distributions. Furthermore, FE modeling is used here to examine the effect of the spatial wavelength of stress variation on the connection between slope and the wafer stress-induced component of overlay.
RMT focal plane sensitivity to seismic network geometry and faulting style
NASA Astrophysics Data System (ADS)
Johnson, Kendra L.; Hayes, Gavin P.; Herrmann, Robert B.; Benz, Harley M.; McNamara, Dan E.; Bergman, Eric
2016-07-01
Modern tectonic studies often use regional moment tensors (RMTs) to interpret the seismotectonic framework of an earthquake or earthquake sequence; however, despite extensive use, little existing work addresses RMT parameter uncertainty. Here, we quantify how network geometry and faulting style affect RMT sensitivity. We examine how data-model fits change with fault plane geometry (strike and dip) for varying station configurations. We calculate the relative data fit for incrementally varying geometries about a best-fitting solution, applying our workflow to real and synthetic seismograms for both real and hypothetical station distributions and earthquakes. Initially, we conduct purely observational tests, computing RMTs from synthetic seismograms for hypothetical earthquakes and a series of well-behaved network geometries. We then incorporate real data and station distributions from the International Maule Aftershock Deployment (IMAD), which recorded aftershocks of the 2010 MW 8.8 Maule earthquake, and a set of regional stations capturing the ongoing earthquake sequence in Oklahoma and southern Kansas. We consider RMTs computed under three scenarios: (1) real seismic records selected for high data quality; (2) synthetic seismic records with noise computed for the observed source-station pairings and (3) synthetic seismic records with noise computed for all possible station-source pairings. To assess RMT sensitivity for each test, we observe the `fit falloff', which portrays how relative fit changes when strike or dip varies incrementally; we then derive the ranges of acceptable strikes and dips by identifying the span of solutions with relative fits larger than 90 per cent of the best fit. For the azimuthally incomplete IMAD network, Scenario 3 best constrains fault geometry, with average ranges of 45° and 31° for strike and dip, respectively. In Oklahoma, Scenario 3 best constrains fault dip with an average range of 46°; however, strike is best constrained by
NASA Astrophysics Data System (ADS)
Taran, Yu V.; Balagurov, A. M.; Sheverev, S. G.; Schreiber, J.; Korsunsky, A. M.; Vorster, W. J. J.; Bomas, H.; Stoeberl, C.
2008-03-01
Fatigue and fracture under multiaxial stresses are among the most important current research topics aimed at ensuring improved reliability of industrial components. An ex situ in-plane biaxial low cycle fatigued sample of cruciform geometry from austenitic stainless steel AISI 321 H was investigated on the FSD stress-diffractometer at the IBR-2 pulsed nuclear reactor by using the neutron strain scanner and the uniaxial stress rig. The phase composition of fatigued material was determined and the residual macrostresses and phase microstresses were measured. To the best of our knowledge, no neutron diffraction investigations of materials subjected to biaxial loading have been previously carried out. The first results of the neutron diffraction experiment are presented and discussed.
Matrix Riccati equation formulation for radiative transfer in a plane-parallel geometry
NASA Astrophysics Data System (ADS)
Chang, Hung-Wen; Wu, Tso-Lun
1997-01-01
In this paper, we formulate the radiative transfer problem as an initial value problem via a pair of nonlinear matrix differential equations (matrix Riccati equations or MREs) which describe the reflection ( R) and transmission ( T) matrices of the specific intensities in a plane-parallel geometry. One first computes R and T matrices of some small but finite layer thickness (equivalent optical thickness 0959-7174/7/1/009/img1) and then repetitively applies the doubling method to the reflection and transmission matrices 0959-7174/7/1/009/img2 and 0959-7174/7/1/009/img3 until reaching the desired layer thickness. The initial matrices 0959-7174/7/1/009/img4 and 0959-7174/7/1/009/img5 can be computed quite accurately by either of the following methods: multiple-order, multiple-scattering approximation, iterative method or fourth-order Runge - Kutta techniques. In addition, the reflection coefficient matrix of a semi-infinite medium satisfies an algebraic matrix equation which can be solved repetitively by a matrix method. MREs offer an alternative way of solving plane-parallel radiative transport problems. This method requires only elementary matrix operations (addition, multiplication and inversion). For vector and/or beam-wave radiative transfer problems, large matrices are required to describe the physics adequately, and the MRE method provides a significant reduction in computer memory and computation time.
Hayes, G.P.; Wald, D.J.
2009-01-01
A key step in many earthquake source inversions requires knowledge of the geometry of the fault surface on which the earthquake occurred. Our knowledge of this surface is often uncertain, however, and as a result fault geometry misinterpretation can map into significant error in the final temporal and spatial slip patterns of these inversions. Relying solely on an initial hypocentre and CMT mechanism can be problematic when establishing rupture characteristics needed for rapid tsunami and ground shaking estimates. Here, we attempt to improve the quality of fast finite-fault inversion results by combining several independent and complementary data sets to more accurately constrain the geometry of the seismic rupture plane of subducting slabs. Unlike previous analyses aimed at defining the general form of the plate interface, we require mechanisms and locations of the seismicity considered in our inversions to be consistent with their occurrence on the plate interface, by limiting events to those with well-constrained depths and with CMT solutions indicative of shallow-dip thrust faulting. We construct probability density functions about each location based on formal assumptions of their depth uncertainty and use these constraints to solve for the ‘most-likely’ fault plane. Examples are shown for the trench in the source region of the Mw 8.6 Southern Sumatra earthquake of March 2005, and for the Northern Chile Trench in the source region of the November 2007 Antofagasta earthquake. We also show examples using only the historic catalogues in regions without recent great earthquakes, such as the Japan and Kamchatka Trenches. In most cases, this method produces a fault plane that is more consistent with all of the data available than is the plane implied by the initial hypocentre and CMT mechanism. Using the aggregated data sets, we have developed an algorithm to rapidly determine more accurate initial fault plane geometries for source inversions of future
A Comparison of Two Methods of Teaching Selected Topics in Plane Analytic Geometry.
ERIC Educational Resources Information Center
Bundrick, Charles Michael
Reported are the results of a study to determine if there is a difference in learning as measured by an achievement test between high school students who study plane analytic geometric topics via a vector approach and those who study the same topics via a traditional approach. Secondary objectives concerned the transfer to further topics in solid…
Turtle Escapes the Plane: Some Advanced Turtle Geometry. Artificial Intelligence Memo Number 348.
ERIC Educational Resources Information Center
diSessa, Andy
The LOGO Turtles, originally developed at the Massachusetts Institute of Technology Artificial Intelligence Laboratory for teaching concepts in elementary geometry to primary-age children, can also be used in teaching higher-level mathematics. In the exercises described here, the turtle was programed to traverse curved surfaces. Both geometric and…
Lombardini, Manuel; Deiterding, Ralf
2010-01-01
This paper presents the use of a dynamically adaptive mesh refinement strategy for the simulations of shock-driven turbulent mixing. Large-eddy simulations are necessary due the high Reynolds number turbulent regime. In this approach, the large scales are simulated directly and small scales at which the viscous dissipation occurs are modeled. A low-numerical centered finite-difference scheme is used in turbulent flow regions while a shock-capturing method is employed to capture shocks. Three-dimensional parallel simulations of the Richtmyer-Meshkov instability performed in plane and converging geometries are described.
Ziętek, Zbigniew; Starczewski, Kamil; Sulikowski, Tadeusz; Iwan-Ziętek, Iza; Żukowski, Maciej; Kamiński, Marek; Ziętek-Czeszak, Angelika
2015-01-01
Background A new look at the topography of the lumbar triangle becomes a challenge for modern anesthesia. The aim of this study was to redefine the topography of the lumbar triangle for transverse abdominis plane block. Material/Methods We explored 74 lumbar regions in 37 preserved cadavers (17 F and 20 M). Results The lumbar triangle was identified in 66 (89%) out of all explored cadavers’ lumbar regions. The predominant triangle was the acute-angled shaped. It was identified in 39 (59%) out of all explored lumbar regions. The second type of dissected triangles had the obtuse-angled shaped. Most triangles of acute-angled shaped and obtuse-angled shaped (36) had medium surface (range from 3 cm2 to 6 cm2), which accounted for 55% of all dissected lumbar triangles. The mean surface of the lumbar triangle was 3.6±2.2 cm2. Based on other measurements, we demonstrated that the majority of the lumbar triangles (62 triangles) were beyond the posterior axillary line. Conclusions According to the obtained results, the randomized searching for lumbar triangle should be limited to the area situated beyond of the posterior axillary line. The region situated anteriorly to the midaxillary line was defined in the study as the critical area for finding the lumbar triangle. Outcomes from the study revealed that the size and the location of the lumbar triangle as the gate for the transverse abdominal plane block may be responsible for difficulties encountered by anesthetists. Thus, establishing the area with the highest probability of localization of the lumbar triangle can improve both safety and efficiency of transversus abdominis plane block. PMID:26714659
Investigation of flaw geometry and loading effects on plane strain fracture in metallic structures
NASA Technical Reports Server (NTRS)
Hall, L. R.; Finger, R. W.
1971-01-01
The effects on fracture and flaw growth of weld-induced residual stresses, combined bending and tension stresses, and stress fields adjacent to circular holes in 2219-T87 aluminum and 5AI-2.5Sn(ELI) titanium alloys were evaluated. Static fracture tests were conducted in liquid nitrogen; fatigue tests were performed in room air, liquid nitrogen, and liquid hydrogen. Evaluation of results was based on linear elastic fracture mechanics concepts and was directed to improving existing methods of estimating minimum fracture strength and fatigue lives for pressurized structure in spacecraft and booster systems. Effects of specimen design in plane-strain fracture toughness testing were investigated. Four different specimen types were tested in room air, liquid nitrogen and liquid hydrogen environments using the aluminum and titanium alloys. Interferometry and holograph were used to measure crack-opening displacements in surface-flawed plexiglass test specimens. Comparisons were made between stress intensities calculated using displacement measurements, and approximate analytical solutions.
NASA Astrophysics Data System (ADS)
Radu, Ion; Bartnikas, Raymond; Wertheimer, Michael
2002-10-01
We present an experimental and theoretical modeling study of "dielectric barrier discharges" (DBD) at atmospheric pressure in a needle-plane configuration. Synchronous, Ultra High Speed Imaging (UHSI, using a Princeton Instruments PI-MAX 512RB Digital ICCD Camera System) and real-time dual detection (optical-electrical) diagnostics have been carried out in a flow of He. A phase-resolved synchronizing circuit was used to trigger the ICCD camera's shutter for durations varying from 2 ns up to 100 ms. All diagnostics, including the PI-MAX images, could be precisely synchronized and processed on a PC computer. The high voltage electrode was a steel needle with a sharp point of precisely-machined radius, while a thin (1.6 mm) ceramic (Al2O3) plate with a metallized bottom surface was used as the ground electrode. Three different situations have been studied, namely (i) the bare Al2O3, and with an ultra-thin coatings of (ii) graphite (a semiconductor) or (iii) metal, the latter two at floating potential. The purpose of these experiments was to investigate possible effects of surface charging on the discharge behavior [1]. The axial [y(t)] and radial [x(t)] time evolutions of the discharge have been measured by UHSI, plotted, and found to differ very significantly among cases (i) to (iii). In the needle-plane configuration (like in the plane-plane case), the DBD is characterized by a single pulse per half-period of the applied voltage. A two-dimensional model of the needle-plane discharge, based upon the continuity equations for electrons, ions, excited particles, and the Poisson equation, is developed; it assumes a low degree of ionization, so that the transport coefficients of the gas are uniquely determined by the local electric field [2]. In order to determine the electric field and the electrical potential in the (hyperboloidal) needle-plane geometry, the finite element method is used. We have found excellent agreement between measured and calculated [y(t)] and [x
Development of a Plane Strain Tensile Geometry to Assess Shear Fracture in Dual Phase Steels
NASA Astrophysics Data System (ADS)
Taylor, M. D.; Matlock, D. K.; De Moor, E.; Speer, J. G.
2014-10-01
A geometrically modified sample capable of generating a triaxial stress state when tested on a standard uniaxial tensile frame was developed to replicate shear fractures observed during stretch bend tests and industrial sheet stamping operations. Seven commercially produced dual phase (DP) steels were tested using the geometrically modified sample, and the modified sample successfully produced shear fractures on a unique shear plane for all steels. For each steel, void densities were determined, based on metallographic analyses, as a function of imposed displacement. Microstructural properties of ferrite and martensite grain size, martensite volume fraction (MVF), retained austenite content, Vickers hardness, average nanoindentation hardness, average ferrite and martensite constituent hardness, and tensile properties were obtained in order to evaluate potential correlations with void data. A linear correlation was observed between Vickers hardness and the average nanoindentation hardness, verifying the ability of nanoindentation to produce data consistent with more traditional hardness measurement techniques. A linear relationship was observed between the number of voids present at 90% failure displacement and the martensite/ferrite hardness ratio, indicating that a decrease in relative hardness difference in a microstructure can suppress void formation, and potentially extend formability limits. The void population appeared independent of MVF, grain size, and tensile properties suggesting that constituent hardness may be a dominant parameter when considering suppression of void nucleation in DP steels.
Numerical solutions of matrix Riccati equations for radiative transfer in a plane-parallel geometry
NASA Astrophysics Data System (ADS)
Chang, Hung-Wen; Wu, Tso-Lun
1997-01-01
In this paper, we conduct numerical experiments with matrix Riccati equations (MREs) which describe the reflection ( R) and transmission ( T) matrices of the specific intensities in a layer containing randomly distributed scattering particles. The theoretical formulation of MREs is discussed in our previous paper where we show that R and T for a thick layer can be efficiently computed by successively doubling R and T matrices for a thin layer (with small optical thickness 0959-7174/7/1/010/img1). We can compute 0959-7174/7/1/010/img2 and 0959-7174/7/1/010/img3 very accurately using either a fourth-order Runge - Kutta scheme or the fourth-order iterative solution. The differences between these results and those computed by the eigenmode expansion technique (EMET) are very small (< 0.1%). Although the MRE formulation cannot be extended to handle the inhomogeneous term (source term) in the differential equation, we show that the force term can be reformulated as an equivalent boundary condition which is consistent with MRE methods. MRE methods offer an alternative way of solving plane-parallel radiative transport problems. For large problems that do not fit into computer memory, the MRE method provides a significant reduction in computer memory and computational time.
Design of a 1 DOF MEMS motion stage for a parallel plane geometry rheometer
Kim, Yong-Sik; Dagalakis, Nicholas G.; Ferraris, Chiara; Avramov-Zamurovic, Svetlana
2016-01-01
Rotational rheometers are used to measure paste properties, but the test would take too long to be useful for quality control (QC) on the job site. In this paper, a new type of rheometer is proposed based on a one degree of freedom (DOF) micro-electro-mechanical systems (MEMS)-based motion stage. Preliminary data will be presented to show the capability of the system to measure the viscoelastic properties of a paste. The parallel plate geometry rheometer consists of two plates, which move relative to each other to apply a strain to the material to be tested. From the stress measured and the strain applied, the rheological characteristics of the material can be calculated. The new device consists of an electrothermal actuator and a motion plate. For the rheological measurements, the device is designed to generate the shear stress up to 60 Pa and maintain its stiffness to less than 44 N/m. With these features, the device uses a square plate of 1.5 mm x 1.5 mm to provide enough area for a few micro-liter level volumes. The motion of the square plate is monitored by a capacitive sensor at the end of the oscillating plate which has a resolution of 1.06 μm. When a reference cementitious paste, Standard Reference Material (SRM)-2492, is placed between the oscillating plate of the presented motion stage and a fixed plate, the reduction in the displacement of the oscillating plate is monitored showing that the presented motion stage is reasonably designed to detect the response of the reference cementitious paste. PMID:27088006
Hayes, G.P.; Wald, D.J.; Keranen, K.
2009-01-01
Ongoing developments in earthquake source inversions incorporate nonplanar fault geometries as inputs to the inversion process, improving previous approaches that relied solely on planar fault surfaces. This evolution motivates advancing the existing framework for constraining fault geometry, particularly in subduction zones where plate boundary surfaces that host highly hazardous earthquakes are clearly nonplanar. Here, we improve upon the existing framework for the constraint of the seismic rupture plane of subduction interfaces by incorporating active seismic and seafloor sediment thickness data with existing independent data sets and inverting for the most probable nonplanar subduction geometry. Constraining the rupture interface a priori with independent geological and seismological information reduces the uncertainty in the derived earthquake source inversion parameters over models that rely on simpler assumptions, such as the moment tensor inferred fault plane. Examples are shown for a number of wellconstrained global locations. We expand the coverage of previous analyses to a more uniform global data set and show that even in areas of sparse data this approach is able to accurately constrain the approximate subduction geometry, particularly when aided with the addition of data from local active seismic surveys. In addition, we show an example of the integration of many two-dimensional profiles into a threedimensional surface for the Sunda subduction zone and introduce the development of a new global threedimensional subduction interface model: Slab1.0. ?? 2009 by the American Geophysical Union.
NASA Astrophysics Data System (ADS)
Maruyama, R.; Bigault, T.; Wildes, A. R.; Dewhurst, C. D.; Soyama, K.; Courtois, P.
2016-05-01
The in-plane magnetic structure of a layered system with a polycrystalline grain size less than the ferromagnetic exchange length was investigated using polarized neutron off-specular scattering and grazing incidence small angle scattering measurements to gain insight into the mechanism that controls the magnetic properties which are different from the bulk. These complementary measurements with different length scales and the data analysis based on the distorted wave Born approximation revealed the lateral correlation on a length scale of sub- μm due to the fluctuating orientation of the magnetization in the layer. The obtained in-plane magnetic structure is consistent with the random anisotropy model, i.e. competition between the exchange interactions between neighboring spins and the local magnetocrystalline anisotropy.
NASA Astrophysics Data System (ADS)
Nazareth, Daryl P.
Three-dimensional (3D) vessel trees can provide useful visual and quantitative information during interventional procedures. To calculate the 3D vasculature and improve these measurements, we have developed methods for the determination of geometric parameters from single-plane and biplane projection images. Our single-plane technique provides an accurate estimation of the magnification and orientation of objects of known dimensions in vessels by comparing measurements in the images with those in simulated images of modeled objects. Our biplane technique calculates the transformation relating the imaging systems (i.e., the rotation matrix R and the translation vector t) and requires only the identification of approximately corresponding vessel regions in the two images. Initial estimates of R and t are refined using an optimization method. The objective function to be minimized is based on the amount of overlap of corresponding vessel regions in the two images. The 3D vasculature is then obtained from the optimal R and t using triangulation. The accuracy of the 3D vasculature calculations may be further improved when a calibration object, such as a stent, is present in the vasculature and the biplane images, if the required user-indicated points in the stent are highly accurate. We have modified the above biplane technique to incorporate information provided by the stent, by including three additional terms in the objective function. These techniques were evaluated using simulated and phantom images. The single-plane technique provided accuracies of 1% in magnification and 2 degrees in orientation. The biplane technique provided accuracies of 1% and 1 degree, respectively, which was reduced to 0.3% and 0.5 degrees in simulations when a calibration object was present. The results of the biplane technique applied to the phantom indicated that inaccuracies in user indication of the calibration object may propagate into the errors in the 3D vessel tree reconstruction
Dowthwaite, Jodi N.; Rosenbaum, Paula F.; Scerpella, Tamara A.
2011-01-01
Lumbar spine geometry, density and indices of bone strength were assessed relative to menarche status, using artistic gymnastics exposure during growth as a model of mechanical loading. Paired posteroanterior (PA) and supine lateral (LAT) DXA scans of L3 for 114 females (60 ex/gymnasts and 54 non-gymnasts) yielded output for comparison of paired (PALAT) versus standard PA and LAT outcomes. BMC, areal BMD, vertebral body dimensions, bone mineral apparent density (BMAD), axial compressive strength (IBS) and a fracture risk index were evaluated, modeling vertebral body geometry as an ellipsoid cylinder. Two-factor ANCOVA tested statistical effects of gymnastic exposure, menarche status and their interaction, adjusting for age and height as appropriate. Compared to non-gymnasts, ex/gymnasts exhibited greater PABMD, PABMC, PAWIDTH, PA CROSS-SECTIONAL AREA (CSA), PAVOLUME, LATBMD, LATBMAD, PALATCSA and PALATIBS (p<0.05). Non-gymnasts exhibited greater LATDEPTH/PAWIDTH, LATBMC/PABMC, LATVHEIGHT, LATAREA and Fracture Risk Index. Using ellipsoid vertebral geometric models, no significant differences were detected for PA or PALAT BMAD. In contrast, cuboid model results (Carter 1992) suggested erroneous ex/gymnast PABMAD advantages, resulting from invalid assumptions of proportional variation in linear skeletal dimensions. Gymnastic exposure was associated with shorter, wider vertebral bodies, yielding greater axial compressive strength and lower fracture risk, despite no BMAD advantage. Our results suggest the importance of plane-specific vertebral geometric adaptation to mechanical loading during growth. Paired scan output provides a more accurate assessment of this adaptation than PA or LAT plane scans alone. PMID:21839871
NASA Astrophysics Data System (ADS)
Kong, Dali; Zhang, Keke; Schubert, Gerald
2016-10-01
Unlike the even gravitational coefficients of Jupiter that are caused by both the rotational distortion and the equatorially symmetric zonal winds, the odd jovian gravitational coefficients are directly linked to the depth of the equatorially antisymmetric zonal winds. Accurate estimation of the wind-induced odd coefficients and comparison with measurements of those coefficients would be key to understanding the structure of the zonal winds in the deep interior of Jupiter. We consider two problems in connection with the jovian odd gravitational coefficients. In the first problem, we show, by solving the governing equations for the northern hemisphere of Jupiter subject to an appropriate condition at the equatorial plane, that the effect of non-spherical geometry makes an insignificant contribution to the lowermost-order odd gravitational coefficients. In the second problem, we investigate the effect of the equatorial smoothing used to avoid the discontinuity in the winds across the equatorial plane when the thermal wind equation is adopted to compute the odd gravitational coefficients. We reveal that, because of the dominant effect of the equatorial smoothing, the odd gravitational coefficients so obtained for deep zonal winds do not reflect physically realistic dynamics taking place in the deep interior of Jupiter.
NASA Astrophysics Data System (ADS)
Salvatore, A.; Savatore, G.; Vincenza, M.
2006-12-01
Since the beginning of 2001 Mt. Etna seismic activity revealed a change in the dynamic conditions acting on the volcano revealed by moderate-high levels of seismicity mainly restricted to the eastern flank of the edifice. The 2001-2006 period has been characterized by the 2001, 2002-2003 and 2004-2005 eruptive episodes and by a marked eastward displacement of the eastern flank. Hypocenters of eastern flank seismicity have been relocated applying two different techniques: the double- difference approach of Waldhauser and Ellsworth (2000) and a multiplets technique that use a cross-spectrum method based on that discussed by Fremont and Malone (1987). For the last technique we also investigated the presence of possible multiplet events measuring the waveform similarity with a cross-correlation function. The two approach give as very similar results furnishing high-precision locations of ca. 90 earthquakes distributed along some structure oriented ca. NE-SW and NW-SE; these alignments are in agreement with fault plane solutions (FPSs) calculated for all the events. This approach has allowed us to define: a) geometry of some depth structures of the eastern flank that have no surface evidences. b) the complex dynamic of these structure that may give new elements to the scientific debate about the causes of the large deformative effects measured on the eastern flank of the edifice. Frèmont, M.J., Malone, S.D., 1987. High precision relative locations of earthquake at Mount St. Helens, Washington. J. Geophy. Res., 92, 10223-10236. Waldhauser F. and W.L. Ellsworth, 2000 A double-difference earthquake location algorithm: Method and application to the northern Hayward fault, Bull. Seism. Soc. Am., 90, 1353-1368.
Euclidean Geometry via Programming.
ERIC Educational Resources Information Center
Filimonov, Rossen; Kreith, Kurt
1992-01-01
Describes the Plane Geometry System computer software developed at the Educational Computer Systems laboratory in Sofia, Bulgaria. The system enables students to use the concept of "algorithm" to correspond to the process of "deductive proof" in the development of plane geometry. Provides an example of the software's capability and compares it to…
NASA Astrophysics Data System (ADS)
Bordag, M.; Nikolaev, V.
2010-03-01
We consider the vacuum energy for a configuration of a sphere in front of a plane, both obeying the conductor boundary condition, at small separation. For the separation becoming small we derive the first next-to-leading order of the asymptotic expansion in the separation-to-radius ratio ɛ. This correction is of order ɛ. Opposite to the scalar cases it contains also contributions proportional to logarithms in first and second order, ɛlnɛ and ɛ(lnɛ)2. We compare this result with the available findings of numerical and experimental approaches.
Beaumont, A.; Leroy, J.; Crunteanu, A.
2014-04-21
Electrically activated metal-insulator transition (MIT) in vanadium dioxide (VO{sub 2}) is widely studied from both fundamental and practical points of view. It can give valuable insights on the currently controversial phase transition mechanism in this material and, at the same time, allows the development of original MIT-based electronic devices. Electrically triggered insulator-metal transitions are demonstrated in novel out-of-plane, metal-oxide-metal type devices integrating a VO{sub 2} thin film, upon applying moderate threshold voltages. It is shown that the current-voltage characteristics of such devices present clear negative differential resistance effects supporting the onset of continuous, current-driven phase oscillations across the vanadium dioxide material. The frequencies of these self-sustained oscillations are ranging from 90 to 300 kHz and they may be tuned by adjusting the injected current. A phenomenological model of the device and its command circuit is developed, and allows to extract the analytical expressions of the oscillation frequencies and to simulate the electrical oscillatory phenomena developed across the VO{sub 2} material. Such out-of-plane devices may further contribute to the general understanding of the driving mechanism in metal-insulator transition materials and devices, a prerequisite to promising applications in high speed/high frequency networks of oscillatory or resistive memories circuits.
NASA Astrophysics Data System (ADS)
Beaumont, A.; Leroy, J.; Orlianges, J.-C.; Crunteanu, A.
2014-04-01
Electrically activated metal-insulator transition (MIT) in vanadium dioxide (VO2) is widely studied from both fundamental and practical points of view. It can give valuable insights on the currently controversial phase transition mechanism in this material and, at the same time, allows the development of original MIT-based electronic devices. Electrically triggered insulator-metal transitions are demonstrated in novel out-of-plane, metal-oxide-metal type devices integrating a VO2 thin film, upon applying moderate threshold voltages. It is shown that the current-voltage characteristics of such devices present clear negative differential resistance effects supporting the onset of continuous, current-driven phase oscillations across the vanadium dioxide material. The frequencies of these self-sustained oscillations are ranging from 90 to 300 kHz and they may be tuned by adjusting the injected current. A phenomenological model of the device and its command circuit is developed, and allows to extract the analytical expressions of the oscillation frequencies and to simulate the electrical oscillatory phenomena developed across the VO2 material. Such out-of-plane devices may further contribute to the general understanding of the driving mechanism in metal-insulator transition materials and devices, a prerequisite to promising applications in high speed/high frequency networks of oscillatory or resistive memories circuits.
Flanders, D J; Rawlins, D J; Shaw, P J; Lloyd, C W
1990-04-01
To investigate the spatial relationship between the nucleus and the cortical division site, epidermal cells were selected in which the separation between these two areas is large. Avoiding enzyme treatment and air drying, Datura stramonium cells were labeled with antitubulin antibodies and the three-dimensional aspect of the cytoskeletons was reconstructed using computer-aided optical sectioning. In vacuolated cells preparing for division, the nucleus migrates into the center of the cell, suspended by transvacuolar strands. These strands are now shown to contain continuous bundles of microtubules which bridge the nucleus to the cortex. These nucleus-radiating microtubules adopt different configurations in cells of different shape. In elongated cells with more or less parallel side walls, oblique strands radiating from the nucleus to the long side walls are presumably unstable, for they are progressively realigned into a transverse disc (the phragmosome) as broad, cortical, preprophase bands (PPBs) become tighter. The phragmosome and the PPB are both known predictors of the division plane and our observations indicate that they align simultaneously in elongated epidermal cells. These observations suggest another hypothesis: that the PPB may contain microtubules polymerized from the nuclear surface. In elongated cells, the majority of the radiating microtubules, therefore, come to anchor the nucleus in the transverse plane, consistent with the observed tendency of such cells to divide perpendicular to the long axis. In nonrectangular isodiametric epidermal cells, which approximate regular hexagons in section, the radial microtubular strands emanating from the nucleus tend to remain associated with the middle of each subtending cell wall. The strands are not reorganized into a single dominant transverse bar, but remain as a starlike array until mitosis. PPBs in these cells are not as tight; they may only be a sparse accumulation of microtubules, even forming along non
NASA Astrophysics Data System (ADS)
Andreev, Pavel A.; Kuz'menkov, L. S.
2016-01-01
Applying the separated spin evolution quantum hydrodynamics to the two-dimensional electron gas in plane samples and nanotubes located in external magnetic fields we have found a novel type of waves in the electron gas which is called spin-electron acoustic wave. A separate spin-up and spin-down electrons' evolution reveals the replacement of the Langmuir wave by a pair of hybrid waves. One of the two hybrid waves is a modified Langmuir wave. Another hybrid wave is a spin-electron acoustic wave. We studied the dispersion of these waves in two-dimensional structures of electrons. We also considered the dependence of dispersion properties on spin polarization of electrons in an external magnetic field.
NASA Astrophysics Data System (ADS)
Rabal, A. M.; Ferrero, A.; Campos, J.; Fontecha, J. L.; Pons, A.; Rubiño, A. M.; Corróns, A.
2012-06-01
This paper presents the description and the characterization of the gonio-spectrophotometer GEFE (the acronym for 'Gonio-EspectroFotómetro Español'). This device has been designed and built for the low-uncertainty absolute measurement of the bidirectional reflectance distribution function (BRDF). It comprises a fixed, collimated and uniform light source, a six-axis robot-arm to rotate the sample and a spectroradiometer that may revolve around the sample to be able to vary the source-to-detector angular separation. This gonio-spectrophotometer makes it possible to perform spectral measurements in the visible range, both inside and outside the incidence plane, as well as measurements in retroreflection conditions. This fully automated system is able to measure autonomously a sample's complete spectral BRDF (comprising around 1000 different angular configurations) in less than 4 h.
Schilling, G D.; Andrade, Francisco J.; Barnes, James H.; Sperline, Roger P.; Denton, M BONNER.; Barinaga, Charles J.; Koppenaal, David W.; Hieftje, Gary M.
2006-07-01
A second-generation Faraday-strip array detector has been coupled to an inductively coupled plasma Mattauch- Herzog geometry mass spectrograph, thereby offering simultaneous acquisition of a range of mass-to-charge ratios. The second-generation device incorporates narrower, more closely spaced collectors than the earlier system. Furthermore, the new camera can acquire signal on all collectors at a frequency greater than 2 kHz and has the ability to independently adjust the gain level of each collector. Each collector can also be reset independently. With these improvements, limits of detection in the hundreds of picograms per liter for metals in solution have been obtained. Some additional features, such as a broader linear dynamic range (over 7 orders of magnitude), greater resolving power (up to 600), and improved isotope ratio accuracy were attained. In addition, isotope ratio precision as low as 0.018% RSD was achieved.
The Method of Centroids in Plane Geometry.
ERIC Educational Resources Information Center
Pinker, Aron
1980-01-01
Archimedes viewed the method of centroids as a valuable tool for intuitive discoveries. This article presents several uses of this technique and discusses how the method of centroids could be used in secondary schools. (Author/MK)
ERIC Educational Resources Information Center
KLIER, KATHERINE M.
PRESENTED IS A FUSED COURSE IN PLANE, SOLID, AND COORDINATE GEOMETRY. ELEMENTARY SET THEORY, LOGIC, AND THE PRINCIPLE OF SEPARATION PROVIDE UNIFYING THREADS THROUGHOUT THE TEXT. THE TWO CURRICULUM GUIDES HAVE BEEN PREPARED FOR USE WITH TWO DIFFERENT TEXTS. EITHER CURRICULUM GUIDE MAY BE USED DEPENDING UPON THE CHOICE OF THE TEACHER AND THE NEEDS…
Analogy and Dynamic Geometry System Used to Introduce Three-Dimensional Geometry
ERIC Educational Resources Information Center
Mammana, M. F.; Micale, B.; Pennisi, M.
2012-01-01
We present a sequence of classroom activities on Euclidean geometry, both plane and space geometry, used to make three dimensional geometry more catchy and simple. The activity consists of a guided research activity that leads the students to discover unexpected properties of two apparently distant geometrical entities, quadrilaterals and…
ERIC Educational Resources Information Center
Desseyn, H. O.; And Others
1985-01-01
Compares linear-nonlinear and planar-nonplanar geometry through the valence-shell electron pairs repulsion (V.S.E.P.R.), Mulliken-Walsh, and electrostatic force theories. Indicates that although the V.S.E.P.R. theory has more advantages for elementary courses, an explanation of the best features of the different theories offers students a better…
Geometry, Student's Text, Part II, Unit 14.
ERIC Educational Resources Information Center
Allen, Frank B.; And Others
Unit 14 in the SMSG secondary school mathematics series is a student text covering the following topics in geometry: areas of polygonal regions, similarity, circles and spheres, characterization of sets, constructions, areas of circles and sectors, volumes of solids, and plane coordinate geometry. Appendices cover Eratosthenes' measurement of the…
The Geometry of the Universe: Part 2
ERIC Educational Resources Information Center
Francis, Stephanie
2009-01-01
Hyperbolic geometry occurs on hyperbolic planes--the most commonly cited one being a saddle shape. In this article, the author explores negative hyperbolic curvature, and provides a detailed description of how she constructed two hyperbolic paraboloids. Hyperbolic geometry occurs on surfaces that have negative curvature. (Contains 11 figures and 4…
Berry, Edward A.; Walker, F. Ann
2009-01-01
Early investigation of the EPR spectra of bis-histidine-coordinated membrane-bound ferriheme proteins led to the description of a spectral signal that had only one resolved feature. These became known as “highly anisotropic low-spin” (HALS) or “large gmax” ferriheme centers. Extensive work with small-molecule model heme complexes showed that this spectroscopic signature occurs in bis-imidazole ferrihemes in which the planes of the imidazole ligands are nearly perpendicular, Δϕ = 57–90°. In the last decade protein crystallographic studies have revealed the atomic structures of a number of examples of bis-histidine heme proteins. A frequent characteristic of these large gmax ferrihemes in membrane-bound proteins is the occurrence of the heme within a four-helix bundle with a left-handed twist. The histidine ligands occur at the same level on two diametrically opposed helices of the bundle. These ligands have the same side chain conformation and ligate heme iron on the bundle axis, resulting in a quasi-2-fold symmetric structure. The two non-ligand-bearing helices also obey this symmetry, and have a conserved small residue, usually glycine, where the edge of the heme ring makes contact with the helix backbones. In many cases this small residue is preceded by a threonine or serine residue whose side chain hydroxyl oxygen acts as a hydrogen-bond acceptor from the Nδ1 atom of the heme-ligating histidine. The Δϕ angle is thus determined by the common histidine side-chain conformation and the crossing angle of the ligand-bearing helices, in some cases constrained by H-bonds to the Ser/Thr residues on the non-ligand-bearing helices. PMID:18418633
Horizons and plane waves: A review
Hubeny, Veronika E.; Rangamani, Mukund
2003-11-06
We review the attempts to construct black hole/string solutions in asymptotically plane wave spacetimes. First, we demonstrate that geometries admitting a covariantly constant null Killing vector cannot admit event horizons, which implies that pp-waves can't describe black holes. However, relaxing the symmetry requirements allows us to generate solutions which do possess regular event horizons while retaining the requisite asymptotic properties. In particular, we present two solution generating techniques and use them to construct asymptotically plane wave black string/brane geometries.
Advanced approaches to focal plane integration
NASA Astrophysics Data System (ADS)
Nelson, R. D.; Smith, E. C., Jr.
1980-01-01
Both visible and infrared focal plane assemblies have common architectural driving parameters which guide their design approaches. The key drivers for advanced focal plane assemblies (FPA) are: the detector type and performance required; the number of detector chips; the packaging density; and the geometry. The impact of these drivers is seen to determine the engineering compromises necessary to establish FPA design approach. Several new designs are discussed which show a range of applications from single detector assemblies to monolithic detector chips with on-chip signal processing. The main objective of many advanced designs is to integrate the focal plane components in order to reduce power and reduce the number of interconnections.
Correa, Diego H.; Silva, Guillermo A.
2008-07-28
We discuss how geometrical and topological aspects of certain (1/2)-BPS type IIB geometries are captured by their dual operators in N = 4 Super Yang-Mills theory. The type IIB solutions are characterized by arbitrary droplet pictures in a plane and we consider, in particular, axially symmetric droplets. The 1-loop anomalous dimension of the dual gauge theory operators probed with single traces is described by some bosonic lattice Hamiltonians. These Hamiltonians are shown to encode the topology of the droplets. In appropriate BMN limits, the Hamiltonians spectrum reproduces the spectrum of near-BPS string excitations propagating along each of the individual edges of the droplet. We also study semiclassical regimes for the Hamiltonians. For droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents.
Orbit propagation in Minkowskian geometry
NASA Astrophysics Data System (ADS)
Roa, Javier; Peláez, Jesús
2015-09-01
The geometry of hyperbolic orbits suggests that Minkowskian geometry, and not Euclidean, may provide the most adequate description of the motion. This idea is explored in order to derive a new regularized formulation for propagating arbitrarily perturbed hyperbolic orbits. The mathematical foundations underlying Minkowski space-time are exploited to describe hyperbolic orbits. Hypercomplex numbers are introduced to define the rotations, vectors, and metrics in the problem: the evolution of the eccentricity vector is described on the Minkowski plane in terms of hyperbolic numbers, and the orbital plane is described on the inertial reference using quaternions. A set of eight orbital elements is introduced, namely a time-element, the components of the eccentricity vector in , the semimajor axis, and the components of the quaternion defining the orbital plane. The resulting formulation provides a deep insight into the geometry of hyperbolic orbits. The performance of the formulation in long-term propagations is studied. The orbits of four hyperbolic comets are integrated and the accuracy of the solution is compared to other regularized formulations. The resulting formulation improves the stability of the integration process and it is not affected by the perihelion passage. It provides a level of accuracy that may not be reached by the compared formulations, at the cost of increasing the computational time.
NASA Technical Reports Server (NTRS)
Wagner, Herbert
1948-01-01
The present report deals with the processes accompanying the planing of a planing boat or a seaplane on water . The study is largely based upon theoretical investigations; mathematical problems and proofs are not discussed. To analyze theoreticaly actual planing processes, giving due consideration to all aspects of the problem, is probably not possible. The theories therefore treat various simple limiting cases, which in their entirety give a picture of the planing processes and enable the interpretation of the experimental results. The discussion is concerned with the stationary planing attitude: the boat planes at a constant speed V on an originally smooth surface.
Out of plane analysis for composite structures
NASA Technical Reports Server (NTRS)
Paul, P. C.; Saff, C. R.; Sanger, Kenneth B.; Mahler, M. A.; Kan, Han Pin; Kautz, Edward F.
1990-01-01
Simple two dimensional analysis techniques were developed to aid in the design of strong joints for integrally stiffened/bonded composite structures subjected to out of plane loads. It was found that most out of plane failures were due to induced stresses arising from rapid changes in load path direction or geometry, induced stresses due to changes in geometry caused by buckling, or direct stresses produced by fuel pressure or bearing loads. While the analysis techniques were developed to address a great variety of out of plane loading conditions, they were primarily derived to address the conditions described above. The methods were developed and verified using existing element test data. The methods were demonstrated using the data from a test failure of a high strain wingbox that was designed, built, and tested under a previous program. Subsequently, a set of design guidelines were assembled to assist in the design of safe, strong integral composite structures using the analysis techniques developed.
Axes, planes and tubes, or the geometry of embryogenesis.
Brauckmann, Sabine
2011-12-01
The paper presents selected figures of chick embryogenesis as depicted in the classic studies of Caspar Friedrich Wolff (1734-1794), Christian Heinrich Pander (1794-1865) and Karl Ernst von Baer (1792-1786). My main objective here is (1) to demonstrate how the imagery of Wolff, Pander and Baer attempted to project an image of a 3-dimensional rotating body into static figures on paper by means of linear contours, and (2) to ponder on the efficacy and pervasiveness of dots, lines and arrows for depicting embryogenesis. PMID:22035710
Axes, planes and tubes, or the geometry of embryogenesis.
Brauckmann, Sabine
2011-12-01
The paper presents selected figures of chick embryogenesis as depicted in the classic studies of Caspar Friedrich Wolff (1734-1794), Christian Heinrich Pander (1794-1865) and Karl Ernst von Baer (1792-1786). My main objective here is (1) to demonstrate how the imagery of Wolff, Pander and Baer attempted to project an image of a 3-dimensional rotating body into static figures on paper by means of linear contours, and (2) to ponder on the efficacy and pervasiveness of dots, lines and arrows for depicting embryogenesis.
Plane Transformations in a Complex Setting I: Homotheties-Translations
ERIC Educational Resources Information Center
Dana-Picard, T.
2006-01-01
A previous note described how complex numbers can be used for elementary analytic geometry in the plane, describing lines, circles and their intersections using complex Cartesian equations. In the present note, a description of elementary plane transformations, namely homotheties and translations, their group structure and their operations on…
Hyperbolic geometry for colour metrics.
Farup, Ivar
2014-05-19
It is well established from both colour difference and colour order perpectives that the colour space cannot be Euclidean. In spite of this, most colour spaces still in use today are Euclidean, and the best Euclidean colour metrics are performing comparably to state-of-the-art non-Euclidean metrics. In this paper, it is shown that a transformation from Euclidean to hyperbolic geometry (i.e., constant negative curvature) for the chromatic plane can significantly improve the performance of Euclidean colour metrics to the point where they are statistically significantly better than state-of-the-art non-Euclidean metrics on standard data sets. The resulting hyperbolic geometry nicely models both qualitatively and quantitatively the hue super-importance phenomenon observed in colour order systems.
Point-to-plane and plane-to-plane electrostatic charge injection atomization for insulating liquids
NASA Astrophysics Data System (ADS)
Malkawi, Ghazi
An electrostatic charge injection atomizer was fabricated and used to introduce and study the electrostatic charge injection atomization methods for highly viscous vegetable oils and high conductivity low viscosity aviation fuel, JP8. The total, spray and leakage currents and spray breakup characteristics for these liquids were investigated and compared with Diesel fuel data. Jet breakup and spray atomization mechanism showed differences for vegetable oils and lower viscosity hydrocarbon fuels. For vegetable oils, a bending/spinning instability phenomenon was observed similar to the phenomenon found in liquid jets of high viscosity polymer solutions. The spray tip lengths and cone angles were presented qualitatively and quantitatively and correlated with the appropriate empirical formulas. The different stages of the breakup mechanisms for such oils, as a function of specific charges and flow rates, were discussed. In order to make this method of atomization more suitable for practical use in high flow rate applications, a blunt face electrode (plane-to-plane) was used as the charge emitter in place of a single pointed electrode (point-to-plane). This allowed the use of a multi-orifice emitter that maintained a specific charge with the flow rate increase which could not be achieved with the needle electrode. The effect of the nozzle geometry, liquid physical properties and applied bulk flow on the spray charge, total charge, maximum critical spray specific charge and electrical efficiency compared with the needle point-to-plane atomizer results was presented. Our investigation revealed that the electrical efficiency of the atomizer is dominated by the charge forced convection rate rather than charge transport by ion motilities and liquid motion by the electric field. As a result of the electric coulomb forces between the electrified jets, the multi-orifice atomizer provided a unique means of dispersing the fuel in a hollow cone with wide angles making the new
ERIC Educational Resources Information Center
Cukier, Mimi; Asdourian, Tony; Thakker, Anand
2012-01-01
Geometry provides a natural window into what it is like to do mathematics. In the world of geometry, playful experimentation is often more fruitful than following a procedure, and logic plus a few axioms can open new worlds. Nonetheless, teaching a geometry course in a way that combines both rigor and play can be difficult. Many geometry courses…
Experiments with Planing Surfaces
NASA Technical Reports Server (NTRS)
Sottorf, W
1934-01-01
A previous report discusses the experimental program of a systematic exploration of all questions connected with the planing problem as well as the first fundamental results of the investigation of a flat planing surface. The present report is limited to the conversion of the model test data to full scale.
Conley, A.
1994-12-31
A classical problem in fluid dynamics is the study of the stability of plane Couette flow. This flow experimentally sustains turbulence for Reynolds numbers greater than 1440 {+-} 40. (The Reynolds number is based on channel width and wall velocity difference). Since plane Couette flow is linearly stable for all Reynolds numbers, obtaining non-trivial mathematical solutions to the plane Couette flow equations is difficult. However, M. Nagata finds a non-trivial number solution of the plane Couette flow equations at low Reynolds number. We confirm these solutions. We compute the minimum Reynolds number at which they exist. We study their stability. We also study the effect of a Coriolis force on plane Poiseuille flow.
Taxicab Conics: An Exploration into the World of Taxicab Geometry.
ERIC Educational Resources Information Center
Natsoulas, Anthula
1989-01-01
Gives definitions of taxicab geometry and the MacDraw format for graphing. In the world of taxicab geometry, movement through the plane is along horizontal and vertical paths. Describes specific application to conic sections, including circle, ellipse, parabola, and hyperbola. Lists five references. (YP)
Fourier plane imaging microscopy
Dominguez, Daniel Peralta, Luis Grave de; Alharbi, Nouf; Alhusain, Mdhaoui; Bernussi, Ayrton A.
2014-09-14
We show how the image of an unresolved photonic crystal can be reconstructed using a single Fourier plane (FP) image obtained with a second camera that was added to a traditional compound microscope. We discuss how Fourier plane imaging microscopy is an application of a remarkable property of the obtained FP images: they contain more information about the photonic crystals than the images recorded by the camera commonly placed at the real plane of the microscope. We argue that the experimental results support the hypothesis that surface waves, contributing to enhanced resolution abilities, were optically excited in the studied photonic crystals.
Combinatorial Geometry Printer Plotting.
1987-01-05
Picture generates plots of two-dimensional slices through the three-dimensional geometry described by the combinatorial geometry (CG) package used in such codes as MORSE and QAD-CG. These plots are printed on a standard line printer.
Fixed sagittal plane imbalance.
Savage, Jason W; Patel, Alpesh A
2014-12-01
Study Design Literature review. Objective To discuss the evaluation and management of fixed sagittal plane imbalance. Methods A comprehensive literature review was performed on the preoperative evaluation of patients with sagittal plane malalignment, as well as the surgical strategies to address sagittal plane deformity. Results Sagittal plane imbalance is often caused by de novo scoliosis or iatrogenic flat back deformity. Understanding the etiology and magnitude of sagittal malalignment is crucial in realignment planning. Objective parameters have been developed to guide surgeons in determining how much correction is needed to achieve favorable outcomes. Currently, the goals of surgery are to restore a sagittal vertical axis < 5 cm, pelvic tilt < 20 degrees, and lumbar lordosis equal to pelvic incidence ± 9 degrees. Conclusion Sagittal plane malalignment is an increasingly recognized cause of pain and disability. Treatment of sagittal plane imbalance varies according to the etiology, location, and severity of the deformity. Fixed sagittal malalignment often requires complex reconstructive procedures that include osteotomy correction. Reestablishing harmonious spinopelvic alignment is associated with significant improvement in health-related quality-of-life outcome measures and patient satisfaction.
ERIC Educational Resources Information Center
McDonald, Nathaniel J.
2001-01-01
Chronicles a teacher's first year teaching geometry at the Hershey Montessori Farm School in Huntsburg, Ohio. Instructional methods relied on Euclid primary readings and combined pure abstract logic with practical applications of geometry on the land. The course included geometry background imparted by Montessori elementary materials as well as…
2. VIEW SOUTH, INCLINE PLANE CAR, INCLINE PLANE TRACK, UPPER ...
2. VIEW SOUTH, INCLINE PLANE CAR, INCLINE PLANE TRACK, UPPER STATION. - Monongahela Incline Plane, Connecting North side of Grandview Avenue at Wyoming Street with West Carson Street near Smithfield Street, Pittsburgh, Allegheny County, PA
Axial Plane Optical Microscopy
Li, Tongcang; Ota, Sadao; Kim, Jeongmin; Wong, Zi Jing; Wang, Yuan; Yin, Xiaobo; Zhang, Xiang
2014-01-01
We present axial plane optical microscopy (APOM) that can, in contrast to conventional microscopy, directly image a sample's cross-section parallel to the optical axis of an objective lens without scanning. APOM combined with conventional microscopy simultaneously provides two orthogonal images of a 3D sample. More importantly, APOM uses only a single lens near the sample to achieve selective-plane illumination microscopy, as we demonstrated by three-dimensional (3D) imaging of fluorescent pollens and brain slices. This technique allows fast, high-contrast, and convenient 3D imaging of structures that are hundreds of microns beneath the surfaces of large biological tissues. PMID:25434770
Lampton, Michael L.; Kim, A.; Akerlof, C.W.; Aldering, G.; Amanullah, R.; Astier, P.; Barrelet, E.; Bebek, C.; Bergstrom, L.; Berkovitz, J.; Bernstein, G.; Bester, M.; Bonissent, A.; Bower, C.; Carithers Jr., W.C.; Commins, E.D.; Day, C.; Deustua, S.E.; DiGennaro,R.; Ealet, A.; Ellis, R.S.; Eriksson, M.; Fruchter, A.; Genat, J.-F.; Goldhaber, G.; Goobar, A.; Groom, D.; Harris, S.E.; Harvey, P.R.; Heetderks, H.D.; Holland, S.E.; Huterer, D.; Karcher, A.; Kolbe, W.; Krieger, B.; Lafever, R.; Lamoureux, J.; Levi, M.E.; Levin, D.S.; Linder,E.V.; Loken, S.C.; Malina, R.; Massey, R.; McKay, T.; McKee, S.P.; Miquel, R.; Mortsell, E.; Mostek, N.; Mufson, S.; Musser, J.; Nugent, P.; Oluseyi, H.; Pain, R.; Palaio, N.; Pankow, D.; Perlmutter, S.; Pratt, R.; Prieto, E.; Refregier, A.; Rhodes, J.; Robinson, K.; Roe, N.; Sholl, M.; Schubnell, M.; Smadja, G.; Smoot, G.; Spadafora, A.; Tarle, G.; Tomasch,A.; von der Lippe, H.; Vincent, R.; Walder, J.-P.; Wang, G.
2002-07-29
The proposed SuperNova/Acceleration Probe (SNAP) mission will have a two-meter class telescope delivering diffraction-limited images to an instrumented 0.7 square-degree field sensitive in the visible and near-infrared wavelength regime. We describe the requirements for the instrument suite and the evolution of the focal plane design to the present concept in which all the instrumentation--visible and near-infrared imagers, spectrograph, and star guiders--share one common focal plane.
Axial Plane Optical Microscopy
NASA Astrophysics Data System (ADS)
Li, Tongcang; Ota, Sadao; Kim, Jeongmin; Wong, Zi Jing; Wang, Yuan; Yin, Xiaobo; Zhang, Xiang
2014-12-01
We present axial plane optical microscopy (APOM) that can, in contrast to conventional microscopy, directly image a sample's cross-section parallel to the optical axis of an objective lens without scanning. APOM combined with conventional microscopy simultaneously provides two orthogonal images of a 3D sample. More importantly, APOM uses only a single lens near the sample to achieve selective-plane illumination microscopy, as we demonstrated by three-dimensional (3D) imaging of fluorescent pollens and brain slices. This technique allows fast, high-contrast, and convenient 3D imaging of structures that are hundreds of microns beneath the surfaces of large biological tissues.
Blackfolds, plane waves and minimal surfaces
NASA Astrophysics Data System (ADS)
Armas, Jay; Blau, Matthias
2015-07-01
Minimal surfaces in Euclidean space provide examples of possible non-compact horizon geometries and topologies in asymptotically flat space-time. On the other hand, the existence of limiting surfaces in the space-time provides a simple mechanism for making these configurations compact. Limiting surfaces appear naturally in a given space-time by making minimal surfaces rotate but they are also inherent to plane wave or de Sitter space-times in which case minimal surfaces can be static and compact. We use the blackfold approach in order to scan for possible black hole horizon geometries and topologies in asymptotically flat, plane wave and de Sitter space-times. In the process we uncover several new configurations, such as black helicoids and catenoids, some of which have an asymptotically flat counterpart. In particular, we find that the ultraspinning regime of singly-spinning Myers-Perry black holes, described in terms of the simplest minimal surface (the plane), can be obtained as a limit of a black helicoid, suggesting that these two families of black holes are connected. We also show that minimal surfaces embedded in spheres rather than Euclidean space can be used to construct static compact horizons in asymptotically de Sitter space-times.
Colliding plane waves in F(R)=RN gravity
NASA Astrophysics Data System (ADS)
Tahamtan, T.; Halilsoy, M.; Habib Mazharimousavi, S.
2016-10-01
We identify a region of a specific F( R)= R N gravity solution without external sources which is isometric to the spacetime of colliding plane waves (CPW). The analogy renders construction and collision of plane waves in F( R)= R N gravity possible. The geometry of the interaction region is equivalent to the Reissner-Nordström (RN) one, however there is no Einstein-Maxwell (EM) source --this is made possible by using the model of RN gravity and the parameter N>1 creates the source. For N=1, we naturally recover the plane waves (and their collision) in Einstein's theory.
ERIC Educational Resources Information Center
Lyublinskaya, Irina; Funsch, Dan
2012-01-01
Several interactive geometry software packages are available today to secondary school teachers. An example is The Geometer's Sketchpad[R] (GSP), also known as Dynamic Geometry[R] software, developed by Key Curriculum Press. This numeric based technology has been widely adopted in the last twenty years, and a vast amount of creativity has been…
Frolov, Vadim A; Escalada, Artur; Akimov, Sergey A; Shnyrova, Anna V
2015-01-01
Cellular membranes define the functional geometry of intracellular space. Formation of new membrane compartments and maintenance of complex organelles require division and disconnection of cellular membranes, a process termed membrane fission. Peripheral membrane proteins generally control membrane remodeling during fission. Local membrane stresses, reflecting molecular geometry of membrane-interacting parts of these proteins, sum up to produce the key membrane geometries of fission: the saddle-shaped neck and hour-glass hemifission intermediate. Here, we review the fundamental principles behind the translation of molecular geometry into membrane shape and topology during fission. We emphasize the central role the membrane insertion of specialized protein domains plays in orchestrating fission in vitro and in cells. We further compare individual to synergistic action of the membrane insertion during fission mediated by individual protein species, proteins complexes or membrane domains. Finally, we describe how local geometry of fission intermediates defines the functional design of the protein complexes catalyzing fission of cellular membranes. PMID:25062896
Carbon nanotube plane fastener
NASA Astrophysics Data System (ADS)
Hirahara, Kaori; Ajioka, Shoichi; Nakayama, Yoshikazu
2011-12-01
We report a feature of carbon nanotubes (CNTs) that arises when the surfaces of two vertically-aligned CNT brushes are pressed together. Adhesion between the CNTs creates a plane fastener-like device. Observations from scanning electron microscopy and measurements of adhesion properties indicate a device-dependence on CNT density and shape near the tip region. Among other applications, such fasteners have the potential to attach small components onto micron-sized electronic devices.
Modelling the Landing of a Plane in a Calculus Lab
ERIC Educational Resources Information Center
Morante, Antonio; Vallejo, Jose A.
2012-01-01
We exhibit a simple model of a plane landing that involves only basic concepts of differential calculus, so it is suitable for a first-year calculus lab. We use the computer algebra system Maxima and the interactive geometry software GeoGebra to do the computations and graphics. (Contains 5 figures and 1 note.)
Glide planes symmetry in the organization of some sulfide structures
NASA Astrophysics Data System (ADS)
Borisov, S. V.; Magarill, S. A.; Pervukhina, N. V.
2016-03-01
The role of glide planes in the organization of structures is shown based on a crystallographic analysis of the monoclinic structures of TlAs3S5 and Tl2(As,Sb)3S13 sulfides. In the first structure, cations and anions form systems (with identical geometries) of two face-centered sublattices, linked by the c plane, with the effect of unified "two-dimensional" (2D) ordering. The second structure, exhibiting signs of order-disorder (OD) type, is interpreted as a superposition of two noncentrosymmetric components with independent cation and anion sublattices, which, however, also form a regular 2D order due to the n plane. The stabilizing role of Tl cations in the geometry of cation matrices is indicated.
Noncommutative Geometry and Physics
Connes, Alain
2006-11-03
In this very short essay we shall describe a 'spectral' point of view on geometry which allows to start taking into account the lessons from both renormalization and of general relativity. We shall first do that for renormalization and explain in rough outline the content of our recent collaborations with Dirk Kreimer and Matilde Marcolli leading to the universal Galois symmetry of renormalizable quantum field theories provided by the renormalization group in its cosmic Galois group incarnation. As far as general relativity is concerned, since the functional integral cannot be treated in the traditional perturbative manner, it relies heavily as a 'sum over geometries' on the chosen paradigm of geometric space. This will give us the occasion to discuss, in the light of noncommutative geometry, the issue of 'observables' in gravity and our joint work with Ali Chamseddine on the spectral action, with a first attempt to write down a functional integral on the space of noncommutative geometries.
ERIC Educational Resources Information Center
Chern, Shiing-Shen
1990-01-01
Discussed are the major historical developments of geometry. Euclid, Descartes, Klein's Erlanger Program, Gaus and Riemann, globalization, topology, Elie Cartan, and an application to molecular biology are included as topics. (KR)
Proof in Transformation Geometry
ERIC Educational Resources Information Center
Bell, A. W.
1971-01-01
The first of three articles showing how inductively-obtained results in transformation geometry may be organized into a deductive system. This article discusses two approaches to enlargement (dilatation), one using coordinates and the other using synthetic methods. (MM)
ERIC Educational Resources Information Center
Emenaker, Charles E.
1999-01-01
Describes a sixth-grade interdisciplinary geometry unit based on Charles Dickens's "A Christmas Carol". Focuses on finding area, volume, and perimeter, and working with estimation, decimals, and fractions in the context of making gingerbread houses. (ASK)
Induced geometry from disformal transformation
NASA Astrophysics Data System (ADS)
Yuan, Fang-Fang; Huang, Peng
2015-05-01
In this note, we use the disformal transformation to induce a geometry from the manifold which is originally Riemannian. The new geometry obtained here can be considered as a generalization of Weyl integrable geometry. Based on these results, we further propose a geometry which is naturally a generalization of Weyl geometry.
Software Geometry in Simulations
NASA Astrophysics Data System (ADS)
Alion, Tyler; Viren, Brett; Junk, Tom
2015-04-01
The Long Baseline Neutrino Experiment (LBNE) involves many detectors. The experiment's near detector (ND) facility, may ultimately involve several detectors. The far detector (FD) will be significantly larger than any other Liquid Argon (LAr) detector yet constructed; many prototype detectors are being constructed and studied to motivate a plethora of proposed FD designs. Whether it be a constructed prototype or a proposed ND/FD design, every design must be simulated and analyzed. This presents a considerable challenge to LBNE software experts; each detector geometry must be described to the simulation software in an efficient way which allows for multiple authors to easily collaborate. Furthermore, different geometry versions must be tracked throughout their use. We present a framework called General Geometry Description (GGD), written and developed by LBNE software collaborators for managing software to generate geometries. Though GGD is flexible enough to be used by any experiment working with detectors, we present it's first use in generating Geometry Description Markup Language (GDML) files to interface with LArSoft, a framework of detector simulations, event reconstruction, and data analyses written for all LAr technology users at Fermilab. Brett is the other of the framework discussed here, the General Geometry Description (GGD).
2005-01-01
The Common Geometry Module (CGM) is a code library which provides geometry functionality used for mesh generation and other applications. This functionality includes that commonly found in solid modeling engines, like geometry creation, query and modification; CGM also includes capabilities not commonly found in solid modeling engines, like geometry decomposition tools and support for shared material interfaces. CGM is built upon the ACIS solid modeling engine, but also includes geometry capability developed beside and onmore » top of ACIS. CGM can be used as-is to provide geometry functionality for codes needing this capability. However, CGM can also be extended using derived classes in C++, allowing the geometric model to serve as the basis for other applications, for example mesh generation. CGM is supported on Sun Solaris, SGI, HP, IBM, DEC, Linux and Windows NT platforms. CGM also indudes support for loading ACIS models on parallel computers, using MPI-based communication. Future plans for CGM are to port it to different solid modeling engines, including Pro/Engineer or SolidWorks. CGM is being released into the public domain under an LGPL license; the ACIS-based engine is available to ACIS licensees on request.« less
Asymmetric magnetic reconnection with out-of-plane shear flows in a two dimensional hybrid model
Wang, Lin; Wang, Xiao-Gang; Wang, Xian-Qu; Liu, Yue
2015-05-15
Effects of out-of-plane shear flows on asymmetric magnetic reconnect are investigated in a two-dimensional (2D) hybrid model with an initial Harris sheet equilibrium. It is found that the out-of-plane flow with an in-plane shear can significantly change the asymmetric reconnection process as well as the related geometry. The magnetic flux, out-of-plane magnetic field, in-plane flow vorticity, plasma density, and the reconnection rate are discussed in detail. The results are in comparison with the cases without the shear flows to further understand the effect.
ERIC Educational Resources Information Center
Sampson, Gloria
1999-01-01
Currently, the language sciences place together four different forms of mental activity on one plane of language, which results in confusion. This paper presents arguments from metaphysics, hermeneutics, and semiotics to demonstrate that there are actually three planes of language (a biologically-based information processing plane, a literal…
NASA Technical Reports Server (NTRS)
Zahm, A F
1924-01-01
This report gives the description and the use of a specially designed aerodynamic plane table. For the accurate and expeditious geometrical measurement of models in an aerodynamic laboratory, and for miscellaneous truing operations, there is frequent need for a specially equipped plan table. For example, one may have to measure truly to 0.001 inch the offsets of an airfoil at many parts of its surface. Or the offsets of a strut, airship hull, or other carefully formed figure may require exact calipering. Again, a complete airplane model may have to be adjusted for correct incidence at all parts of its surfaces or verified in those parts for conformance to specifications. Such work, if but occasional, may be done on a planing or milling machine; but if frequent, justifies the provision of a special table. For this reason it was found desirable in 1918 to make the table described in this report and to equip it with such gauges and measures as the work should require.
Hackel, L.A.; Hermann, M.R.; Dane, C.B.; Tiszauer, D.H.
1995-12-12
A solid state laser is frequency tripled to 0.3 {micro}m. A small portion of the laser is split off and generates a Stokes seed in a low power oscillator. The low power output passes through a mask with the appropriate hole pattern. Meanwhile, the bulk of the laser output is focused into a larger stimulated Brillouin scattering (SBS) amplifier. The low power beam is directed through the same cell in the opposite direction. The majority of the amplification takes place at the focus which is the fourier transform plane of the mask image. The small holes occupy large area at the focus and thus are preferentially amplified. The amplified output is now imaged onto the multichip module where the holes are drilled. Because of the fourier plane amplifier, only about 1/10th the power of a competitive system is needed. This concept allows less expensive masks to be used in the process and requires much less laser power. 1 fig.
Hackel, Lloyd A.; Hermann, Mark R.; Dane, C. Brent; Tiszauer, Detlev H.
1995-01-01
A solid state laser is frequency tripled to 0.3 .mu.m. A small portion of the laser is split off and generates a Stokes seed in a low power oscillator. The low power output passes through a mask with the appropriate hole pattern. Meanwhile, the bulk of the laser output is focused into a larger stimulated Brillouin scattering (SBS) amplifier. The low power beam is directed through the same cell in the opposite direction. The majority of the amplification takes place at the focus which is the fourier transform plane of the mask image. The small holes occupy large area at the focus and thus are preferentially amplified. The amplified output is now imaged onto the multichip module where the holes are drilled. Because of the fourier plane amplifier, only .about.1/10th the power of a competitive system is needed. This concept allows less expensive masks to be used in the process and requires much less laser power.
Local geometry of isoscalar surfaces.
Dopazo, César; Martín, Jesús; Hierro, Juan
2007-11-01
An inert dynamically passive scalar in a constant density fluid forced by a statistically homogeneous field of turbulence has been investigated using the results of a 256(3) grid direct numerical simulation. Mixing characteristics are characterized in terms of either principal curvatures or mean and Gauss curvatures. The most probable small-scale scalar geometries are flat and tilelike isosurfaces. Preliminary correlations between flow and scalar small-scale structures associate highly curved saddle points with large-strain regions and elliptic points with vorticity-dominated zones. The concavity of the scalar profiles along the isosurface normal coordinate xn correlates well with negative mean curvatures, Gauss curvatures displaying any sign, which correspond to scalar minima, tiles, or saddle points; on the other hand, convexity along xn is associated with positive mean curvatures, Gauss curvatures ranging from negative to positive signs, featuring maxima, tiles, or saddle points; inflection points along xn correlate well with small values of the mean curvature and zero or negative values of kg, corresponding to plane isosurfaces or saddle points with curvatures of equal and opposite signs. Small values of the scalar gradient are associated with elliptic points, either concave or convex (kg>0) , for both concave and convex scalar profiles along xn. Large values of the scalar gradient (or, equivalently, scalar fluctuation dissipation rates) are generally connected with small values of the Gauss curvature (either flat or moderate-curvature tilelike local geometries), with both concave and convex scalar profiles along xn equally probable. Vortical local flow structures correlate well with small and moderate values of the scalar gradient, while strain-dominated regions are associated with large values. PMID:18233765
NASA Technical Reports Server (NTRS)
1999-01-01
Excerpt from the NASA Connect show 'Plane Weather' This clip explains how our weather occurs, and why Solar radiation is responsible. Weather affects our daily lives. The elements of weather: rain, wind, fog, ice and snow affect the operation and flight of an airplane. In this program, NASA and FAA researchers will introduce students to math, science, and weather; demonstrate how these elements influence flight; and show how NASA and FAA research is used to limit the effects of these elements on flight. Students will examine: the tools, techniques, and technologies used by engineers and scientists to detect these and other climatological factors affecting aircraft in flight. The lesson and classroom experiment will involve students in the scientific process and emphasizing problem solving, measurement, and reasoning skills.
NASA Technical Reports Server (NTRS)
1999-01-01
Excerpt from the NASA Connect show 'Plane Weather' This clip explains what high and low pressure weather systems are, and how they form. Weather affects our daily lives. The elements of weather: rain, wind, fog, ice and snow affect the operation and flight of an airplane. In this program, NASA and FAA researchers will introduce students to math, science, and weather; demonstrate how these elements influence flight; and show how NASA and FAA research is used to limit the effects of these elements on flight. Students will examine: the tools, techniques, and technologies used by engineers and scientists to detect these and other climatological factors affecting aircraft in flight. The lesson and classroom experiment will involve students in the scientific process and emphasizing problem solving, measurement, and reasoning skills.
NASA Technical Reports Server (NTRS)
1999-01-01
Excerpt from the NASA Connect show 'Plane Weather' This clip explains what high and low pressure weather systems are, and how these affect weather patterns. Weather affects our daily lives. The elements of weather: rain, wind, fog, ice and snow affect the operation and flight of an airplane. In this program, NASA and FAA researchers will introduce students to math, science, and weather; demonstrate how these elements influence flight; and show how NASA and FAA research is used to limit the effects of these elements on flight. Students will examine: the tools, techniques, and technologies used by engineers and scientists to detect these and other climatological factors affecting aircraft in flight. The lesson and classroom experiment will involve students in the scientific process and emphasizing problem solving, measurement, and reasoning skills.
Geometry of Miura-folded metamaterials
Schenk, Mark; Guest, Simon D.
2013-01-01
This paper describes two folded metamaterials based on the Miura-ori fold pattern. The structural mechanics of these metamaterials are dominated by the kinematics of the folding, which only depends on the geometry and therefore is scale-independent. First, a folded shell structure is introduced, where the fold pattern provides a negative Poisson’s ratio for in-plane deformations and a positive Poisson’s ratio for out-of-plane bending. Second, a cellular metamaterial is described based on a stacking of individual folded layers, where the folding kinematics are compatible between layers. Additional freedom in the design of the metamaterial can be achieved by varying the fold pattern within each layer. PMID:23401549
NASA Astrophysics Data System (ADS)
Ochiai, T.; Nacher, J. C.
2011-09-01
Recently, the application of geometry and conformal mappings to artificial materials (metamaterials) has attracted the attention in various research communities. These materials, characterized by a unique man-made structure, have unusual optical properties, which materials found in nature do not exhibit. By applying the geometry and conformal mappings theory to metamaterial science, it may be possible to realize so-called "Harry Potter cloaking device". Although such a device is still in the science fiction realm, several works have shown that by using such metamaterials it may be possible to control the direction of the electromagnetic field at will. We could then make an object hidden inside of a cloaking device. Here, we will explain how to design invisibility device using differential geometry and conformal mappings.
2011-01-01
Cells are highly complex and orderly machines, with defined shapes and a startling variety of internal organizations. Complex geometry is a feature of both free-living unicellular organisms and cells inside multicellular animals. Where does the geometry of a cell come from? Many of the same questions that arise in developmental biology can also be asked of cells, but in most cases we do not know the answers. How much of cellular organization is dictated by global cell polarity cues as opposed to local interactions between cellular components? Does cellular structure persist across cell generations? What is the relationship between cell geometry and tissue organization? What ensures that intracellular structures are scaled to the overall size of the cell? Cell biology is only now beginning to come to grips with these questions. PMID:21880160
The Prints: A Picture Book for Pre-Formal Geometry
ERIC Educational Resources Information Center
Skoumpourdi, Chrysanthi; Mpakopoulou, Ifigenia
2011-01-01
A pre-test questionnaire was conducted in a kindergarten and it showed that, although the children were able to give various examples of objects, from their everyday lives, that are similar to solid shapes, the examples they gave for plane figures were also tangible objects. Since it is suggested that geometry instruction has to begin early,…
Secondary School Advanced Mathematics, Chapter 3, Formal Geometry. Student's Text.
ERIC Educational Resources Information Center
Stanford Univ., CA. School Mathematics Study Group.
This text is the second of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. This volume is devoted to a rigorous development of theorems in plane geometry from 22…
Students Discovering Spherical Geometry Using Dynamic Geometry Software
ERIC Educational Resources Information Center
Guven, Bulent; Karatas, Ilhan
2009-01-01
Dynamic geometry software (DGS) such as Cabri and Geometers' Sketchpad has been regularly used worldwide for teaching and learning Euclidean geometry for a long time. The DGS with its inductive nature allows students to learn Euclidean geometry via explorations. However, with respect to non-Euclidean geometries, do we need to introduce them to…
Computational synthetic geometry
Sturmfels, B. )
1988-01-01
This book deals with methods for realizing abstract geometric objects in concrete vector spaces. It considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It appears that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems, a variety of symbolic algorithms are discussed, and the methods are applied to obtain mathematical results on convex polytopes, projective configurations and the combinatories of Grassmann varieties.
Current-induced in-plane superconducting transition in intrinsic Josephson junctions
NASA Astrophysics Data System (ADS)
You, L. X.; Yurgens, A.; Winkler, D.; Torstensson, M.; Kajiki, K.; Tanaka, I.
2006-05-01
In stacks of intrinsic Josephson junctions (IJJs) with lateral sizes of several microns, the current is non-uniform in many cases. In certain geometries a significant part of the current flows along the superconducting planes and can reach the critical value. The current-driven superconductivity breakdown within a single Cu2O4 plane can be seen as an extra branch structure of the c-axis current-voltage characteristics. This allows us to deduce the sheet critical current of a single Cu2O4 plane in different measurement configurations. The conditions for the observation of such a current-induced transition in different IJJ geometries are discussed.
SAR imagery in non-Cartesian geometries
NASA Astrophysics Data System (ADS)
Dendal, Didier
1995-11-01
The subject of the reported work is the improvement of geometrical models for a SAR scanning in pushbroom, spotlight, scansar or bistatic imaging modes. This research has been motivated by the planetary cornerstone mission of ESA's long term program for European Space Science ('rendezvous' with a comet, and fly-bys of asteroids). In this specific context, the synthetic aperture radar is destined for an important role, but the rules and standard backgrounds of the Cartesian geometry are no longer justified. Several new techniques are proposed to handle with an optimal precision the data relative to celestial bodies with a complex geometry (coherent and non-coherent imagery). On the basis of a mathematical rigor (singleness of solutions, convergence of processes, biunivocity of transformations and generalizations), a lot of scenarios are discussed with key relations established (plane and spherical models, bodies with a symmetry of revolution and general bodies, specific sensor(s) trajectories as fly-bys or flight into orbit with the possibility of an approaching probe). The four methods developed are the tomographic analogy of radar principles (only known, previously, in the usual case of a straight line flight at constant altitude over a plane surface) and Hilbertian techniques for a direct adaptation to the scanned surface geometry, an automated autofocusing which enhances the contrast resulting from a Cartesian reconstruction and the coordinates transformation where the real space is converted into a fictitious space where Cartesian algorithms are fully rigorous. Beyond the fact that an interpolation step is often unavoidable, the major conclusion of the research is that all the prospected techniques are complementary and that the choice between the methods has to be made according to geometry, objectives and time requirements (reconstruction on board or not). In particular, coordinates transformation techniques are worthy of commendation in the case of plane
Bradley, F L
2001-01-01
The derivation of the trigonometric equations necessary to calculate gantry, floor and collimator settings for a treatment plane at an angle phi to the transverse plane of the patient has been described previously. The derivation of a second set of equations to facilitate treatment in a plane at an angle phi to the coronal plane has also been described previously. This work reinterprets the geometry of inclined volumes and shows that essentially only one set of equations is required to determine the settings for treatment planes at an angle phi to either the transverse or coronal planes of the patient.
Advanced geometries and regimes
Bulanov, S. S.; Bulanov, S. V.; Turchetti, G.; Limpouch, J.; Klimo, O.; Psikal, J.; Margarone, D.; Korn, G.
2013-07-26
We review and discuss different schemes of laser ion acceleration as well as advanced target geometries in connection with the development of the laser-driven proton source for hadron therapy of oncological diseases, which is a part of the ELIMED project.
Spacetime and Euclidean geometry
NASA Astrophysics Data System (ADS)
Brill, Dieter; Jacobson, Ted
2006-04-01
Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem.
ERIC Educational Resources Information Center
Cooper, Brett D.; Barger, Rita
2009-01-01
The many connections between music and mathematics are well known. The length of a plucked string determines its tone, the time signature of a piece of music is a ratio, and note durations are measured in fractions. One connection commonly overlooked is that between music and geometry--specifically, geometric transformations, including…
ERIC Educational Resources Information Center
Hartz, Viggo
1981-01-01
Allowing students to use a polystyrene cutter to fashion their own three-dimensional models is suggested as a means of allowing individuals to experience problems and develop ideas related to solid geometry. A list of ideas that can lead to mathematical discovery is provided. (MP)
Teaching Geometry with Tangrams.
ERIC Educational Resources Information Center
Russell, Dorothy S.; Bologna, Elaine M.
1982-01-01
Geometry is viewed as the most neglected area of the elementary school mathematics curriculum. Tangram activities provide numerous worthwhile mathematical experiences for children. A method of constructing tangrams through paper folding is followed by suggested spatial visualization, measurement, and additional activities. (MP)
Sliding vane geometry turbines
Sun, Harold Huimin; Zhang, Jizhong; Hu, Liangjun; Hanna, Dave R
2014-12-30
Various systems and methods are described for a variable geometry turbine. In one example, a turbine nozzle comprises a central axis and a nozzle vane. The nozzle vane includes a stationary vane and a sliding vane. The sliding vane is positioned to slide in a direction substantially tangent to an inner circumference of the turbine nozzle and in contact with the stationary vane.
ERIC Educational Resources Information Center
MacKeown, P. K.
1984-01-01
Clarifies two concepts of gravity--those of a fictitious force and those of how space and time may have geometry. Reviews the position of Newton's theory of gravity in the context of special relativity and considers why gravity (as distinct from electromagnetics) lends itself to Einstein's revolutionary interpretation. (JN)
ERIC Educational Resources Information Center
Martin, John
2010-01-01
The cycloid has been called the Helen of Geometry, not only because of its beautiful properties but also because of the quarrels it provoked between famous mathematicians of the 17th century. This article surveys the history of the cycloid and its importance in the development of the calculus.
Atiyah, Michael; Dijkgraaf, Robbert; Hitchin, Nigel
2010-01-01
We review the remarkably fruitful interactions between mathematics and quantum physics in the past decades, pointing out some general trends and highlighting several examples, such as the counting of curves in algebraic geometry, invariants of knots and four-dimensional topology. PMID:20123740
ERIC Educational Resources Information Center
Case, Christine L.
1991-01-01
Presented is an activity in which students make models of viruses, which allows them to visualize the shape of these microorganisms. Included are some background on viruses, the biology and geometry of viruses, directions for building viruses, a comparison of cells and viruses, and questions for students. (KR)
NASA Astrophysics Data System (ADS)
Prástaro, Agostino
2008-02-01
Following our previous results on this subject [R.P. Agarwal, A. Prástaro, Geometry of PDE's. III(I): Webs on PDE's and integral bordism groups. The general theory, Adv. Math. Sci. Appl. 17 (2007) 239-266; R.P. Agarwal, A. Prástaro, Geometry of PDE's. III(II): Webs on PDE's and integral bordism groups. Applications to Riemannian geometry PDE's, Adv. Math. Sci. Appl. 17 (2007) 267-285; A. Prástaro, Geometry of PDE's and Mechanics, World Scientific, Singapore, 1996; A. Prástaro, Quantum and integral (co)bordism in partial differential equations, Acta Appl. Math. (5) (3) (1998) 243-302; A. Prástaro, (Co)bordism groups in PDE's, Acta Appl. Math. 59 (2) (1999) 111-201; A. Prástaro, Quantized Partial Differential Equations, World Scientific Publishing Co, Singapore, 2004, 500 pp.; A. Prástaro, Geometry of PDE's. I: Integral bordism groups in PDE's, J. Math. Anal. Appl. 319 (2006) 547-566; A. Prástaro, Geometry of PDE's. II: Variational PDE's and integral bordism groups, J. Math. Anal. Appl. 321 (2006) 930-948; A. Prástaro, Th.M. Rassias, Ulam stability in geometry of PDE's, Nonlinear Funct. Anal. Appl. 8 (2) (2003) 259-278; I. Stakgold, Boundary Value Problems of Mathematical Physics, I, The MacMillan Company, New York, 1967; I. Stakgold, Boundary Value Problems of Mathematical Physics, II, Collier-MacMillan, Canada, Ltd, Toronto, Ontario, 1968], integral bordism groups of the Navier-Stokes equation are calculated for smooth, singular and weak solutions, respectively. Then a characterization of global solutions is made on this ground. Enough conditions to assure existence of global smooth solutions are given and related to nullity of integral characteristic numbers of the boundaries. Stability of global solutions are related to some characteristic numbers of the space-like Cauchy dataE Global solutions of variational problems constrained by (NS) are classified by means of suitable integral bordism groups too.
An introduction to Minkowski geometries
NASA Astrophysics Data System (ADS)
Farnsworth, David L.
2016-07-01
The fundamental ideas of Minkowski geometries are presented. Learning about Minkowski geometries can sharpen our students' understanding of concepts such as distance measurement. Many of its ideas are important and accessible to undergraduate students. Following a brief overview, distance and orthogonality in Minkowski geometries are thoroughly discussed and many illustrative examples and applications are supplied. Suggestions for further study of these geometries are given. Indeed, Minkowski geometries are an excellent source of topics for undergraduate research and independent study.
ERIC Educational Resources Information Center
Stanford Univ., CA. School Mathematics Study Group.
The first chapter, Perpendiculars and Parallels (II), of the ninth unit in this SMSG series includes a discussion of the properties of triangles, circles and perpendiculars, parallels in space, perpendicular lines and planes, and parallel planes. The next chapter, on coordinate geometry, covers distance; midpoints; algebraic descriptions of…
Detecting Translation Errors in CAD Surfaces and Preparing Geometries for Mesh Generation
Petersson, N Anders; Chand, K K
2001-08-27
The authors have developed tools for the efficient preparation of CAD geometries for mesh generation. Geometries are read from IGES files and then maintained in a boundary-representation consisting of a patchwork of trimmed and untrimmed surfaces. Gross errors in the geometry can be identified and removed automatically while a user interface is provided for manipulating the geometry (such as correcting invalid trimming curves or removing unwanted details). Modifying the geometry by adding or deleting surfaces and/or sectioning it by arbitrary planes (e.g. symmetry planes) is also supported. These tools are used for robust and accurate geometry models for initial mesh generation and will be applied to in situ mesh generation requirements of moving and adaptive grid simulations.
Stability characteristics of a conical aerospace plane concept
NASA Technical Reports Server (NTRS)
Hahne, David E.; Luckring, James M.; Covell, Peter F.; Phillips, W. Pelham; Gatlin, Gregory M.
1989-01-01
Data on stability characteristics of a conical aerospace plane concept were collected for a number of model geometry variations and test conditions, using several NASA-Langley wind tunnels spanning Mach range 0.1-6. The baseline configuration of this plane concept incorporated a 5-deg cone forebody, a 75.96-deg delta wing, a 16-deg leading-edge sweep deployable canard, and a centerline vertical tail. The key results pertinent to stability considerations about all three axes of the model are presented together with data on the effect of the canard on pitch stability, the effect of vertical tail on lateral-directional stability, and the effect of forebody geometry on yaw asymmetries. The experimental stability data are compared with the results from an engineering predictive code.
Nebeck, H.E.
1986-08-01
The MAZE mesh generator represents an arbitrary two dimensional region of space as an ordered collection of quadrilateral elements. Each element is defined by its four corner points (nodes) and an integer material number. Models are created by subdividing the region(s) of interest into one or more PARTS and specifying the element distribution in each part. Then, parts can be merged together to form the meshed representation of the entire region. Applying boundary conditions and describing material properties completes the model construction process. This activity takes place in three distinct phases: phase I-define geometry, subdivide regions into elements; phase II-refine geometry, establish interface and boundary conditions; phase III-describe material properties. This work presents explanations and examples of the phase I commands, along with an overview of the MAZE mesh generation process.
Cylindrical geometry hall thruster
Raitses, Yevgeny; Fisch, Nathaniel J.
2002-01-01
An apparatus and method for thrusting plasma, utilizing a Hall thruster with a cylindrical geometry, wherein ions are accelerated in substantially the axial direction. The apparatus is suitable for operation at low power. It employs small size thruster components, including a ceramic channel, with the center pole piece of the conventional annular design thruster eliminated or greatly reduced. Efficient operation is accomplished through magnetic fields with a substantial radial component. The propellant gas is ionized at an optimal location in the thruster. A further improvement is accomplished by segmented electrodes, which produce localized voltage drops within the thruster at optimally prescribed locations. The apparatus differs from a conventional Hall thruster, which has an annular geometry, not well suited to scaling to small size, because the small size for an annular design has a great deal of surface area relative to the volume.
Inflation from quantum geometry.
Bojowald, Martin
2002-12-23
Quantum geometry predicts that a universe evolves through an inflationary phase at small volume before exiting gracefully into a standard Friedmann phase. This does not require the introduction of additional matter fields with ad hoc potentials; rather, it occurs because of a quantum gravity modification of the kinetic part of ordinary matter Hamiltonians. An application of the same mechanism can explain why the present day cosmological acceleration is so tiny.
NASA Astrophysics Data System (ADS)
Bengtsson, Ingemar; Zyczkowski, Karol
2007-12-01
Preface; 1. Convexity, colours and statistics; 2. Geometry of probability distributions; 3. Much ado about spheres; 4. Complex projective spaces; 5. Outline of quantum mechanics; 6. Coherent states and group actions; 7. The stellar representation; 8. The space of density matrices; 9. Purification of mixed quantum states; 10. Quantum operations; 11. Duality: maps versus states; 12. Density matrices and entropies; 13. Distinguishability measures; 14. Monotone metrics and measures; 15. Quantum entanglement; Epilogue; Appendices; References; Index.
Freezing in confined geometries
NASA Technical Reports Server (NTRS)
Sokol, P. E.; Ma, W. J.; Herwig, K. W.; Snow, W. M.; Wang, Y.; Koplik, Joel; Banavar, Jayanth R.
1992-01-01
Results of detailed structural studies, using elastic neutron scattering, of the freezing of liquid O2 and D2 in porous vycor glass, are presented. The experimental studies have been complemented by computer simulations of the dynamics of freezing of a Lennard-Jones liquid in narrow channels bounded by molecular walls. Results point to a new simple physical interpretation of freezing in confined geometries.
Integral geometry and holography
Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel; Sully, James
2015-10-27
We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS_{3}/CFT_{2} correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulk curve. We explain how basic geometric concepts -- points, distances and angles -- are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS_{3} whose kinematic space is two-dimensional de Sitter space.
Integral geometry and holography
Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel; Sully, James
2015-10-27
We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS3/CFT2 correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulkmore » curve. We explain how basic geometric concepts -- points, distances and angles -- are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS3 whose kinematic space is two-dimensional de Sitter space.« less
Emergent Complex Network Geometry
NASA Astrophysics Data System (ADS)
Wu, Zhihao; Menichetti, Giulia; Rahmede, Christoph; Bianconi, Ginestra
2015-05-01
Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant for routing problems, inference and data mining. In real growing networks, topological, structural and geometrical properties emerge spontaneously from their dynamical rules. Nevertheless we still miss a model in which networks develop an emergent complex geometry. Here we show that a single two parameter network model, the growing geometrical network, can generate complex network geometries with non-trivial distribution of curvatures, combining exponential growth and small-world properties with finite spectral dimensionality. In one limit, the non-equilibrium dynamical rules of these networks can generate scale-free networks with clustering and communities, in another limit planar random geometries with non-trivial modularity. Finally we find that these properties of the geometrical growing networks are present in a large set of real networks describing biological, social and technological systems.
Anti-Selfdual Connections on the Quantum Projective Plane: Monopoles
NASA Astrophysics Data System (ADS)
D'Andrea, Francesco; Landi, Giovanni
2010-08-01
We present several results on the geometry of the quantum projective plane. They include: explicit generators for the K-theory and the K-homology; a real calculus with a Hodge star operator; anti-selfdual connections on line bundles with explicit computation of the corresponding ‘classical’ characteristic classes (via Fredholm modules); complete diagonalization of gauged Laplacians on these line bundles; ‘quantum’ characteristic classes via equivariant K-theory and q-indices.
Geometry of solar coronal rays
NASA Astrophysics Data System (ADS)
Filippov, B. P.; Martsenyuk, O. V.; Platov, Yu. V.; Den, O. E.
2016-02-01
Coronal helmet streamers are the most prominent large-scale elements of the solar corona observed in white light during total solar eclipses. The base of the streamer is an arcade of loops located above a global polarity inversion line. At an altitude of 1-2 solar radii above the limb, the apices of the arches sharpen, forming cusp structures, above which narrow coronal rays are observed. Lyot coronagraphs, especially those on-board spacecrafts flying beyond the Earth's atmosphere, enable us to observe the corona continuously and at large distances. At distances of several solar radii, the streamers take the form of fairly narrow spokes that diverge radially from the Sun. This radial direction displays a continuous expansion of the corona into the surrounding space, and the formation of the solar wind. However, the solar magnetic field and solar rotation complicate the situation. The rotation curves radial streams into spiral ones, similar to water streams flowing from rotating tubes. The influence of the magnetic field is more complex and multifarious. A thorough study of coronal ray geometries shows that rays are frequently not radial and not straight. Coronal streamers frequently display a curvature whose direction in the meridional plane depends on the phase of the solar cycle. It is evident that this curvature is related to the geometry of the global solar magnetic field, which depends on the cycle phase. Equatorward deviations of coronal streamers at solar minima and poleward deviations at solar maxima can be interpreted as the effects of changes in the general topology of the global solar magnetic field. There are sporadic temporal changes in the coronal rays shape caused by remote coronal mass ejections (CMEs) propagating through the corona. This is also a manifestation of the influence of the magnetic field on plasma flows. The motion of a large-scale flux rope associated with a CME away from the Sun creates changes in the structure of surrounding field
Measuring Space-Time Geometry over the Ages
Stebbins, Albert; /Fermilab
2012-05-01
Theorists are often told to express things in the 'observational plane'. One can do this for space-time geometry, considering 'visual' observations of matter in our universe by a single observer over time, with no assumptions about isometries, initial conditions, nor any particular relation between matter and geometry, such as Einstein's equations. Using observables as coordinates naturally leads to a parametrization of space-time geometry in terms of other observables, which in turn prescribes an observational program to measure the geometry. Under the assumption of vorticity-free matter flow we describe this observational program, which includes measurements of gravitational lensing, proper motion, and redshift drift. Only 15% of the curvature information can be extracted without long time baseline observations, and this increases to 35% with observations that will take decades. The rest would likely require centuries of observations. The formalism developed is exact, non-perturbative, and more general than the usual cosmological analysis.
Twin plane re-entrant mechanism for catalytic nanowire growth.
Gamalski, Andrew D; Voorhees, Peter W; Ducati, Caterina; Sharma, Renu; Hofmann, Stephan
2014-03-12
A twin-plane based nanowire growth mechanism is established using Au catalyzed Ge nanowire growth as a model system. Video-rate lattice-resolved environmental transmission electron microscopy shows a convex, V-shaped liquid catalyst-nanowire growth interface for a ⟨112⟩ growth direction that is composed of two Ge {111} planes that meet at a twin boundary. Unlike bulk crystals, the nanowire geometry allows steady-state growth with a single twin boundary at the nanowire center. We suggest that the nucleation barrier at the twin-plane re-entrant groove is effectively reduced by the line energy, and hence the twin acts as a preferential nucleation site that dictates the lateral step flow cycle which constitutes nanowire growth.
Geometry for the Secondary School
ERIC Educational Resources Information Center
Moalem, D.
1977-01-01
A sequential but non-axiomatic high school geometry course which includes Euclidean, transformation, and analytic geometry and vectors and matrices, and emphasizes the invariance property of transformations, is outlined. Sample problems, solutions, and comments are included. (MN)
Navigating solid medical images by pencils of sectioning planes
NASA Astrophysics Data System (ADS)
Bookstein, Fred L.; Athey, Brian D.; Green, William D. K.; Wetzel, Arthur W.
2000-10-01
Beyond their involvement in ordinary surface rendering, the boundaries of organs in medical images have differential properties that make them quite useful for quantitative understanding. In particular, their geometry affords a framework for navigating the original solid, representing its R3 contents quite flexibility as multiple pseudovolumes R2 x T, where T is ar eal-valued parameter standing for screen time. A navigation is a smoothly parameterized series of image sections characterized by normal direction, centerpoint, scale and orientation. Such filmstrips represent a radical generalization of conventional medical image dynamics. The lances encountered in these navigations can be represented by constructs from classic differential geometry. Sequences of plane sections can be formalized as continuous pencils of planes, sets of cardinality (infinity) 1 that are sometimes explicitly characterized by a real-value parameter and sometimes defined implicitly as the intersection (curve of common elements) of a pair of bundles of (infinity) 2 planes. An example of the first type of navigation is the pencil of planes through the tangent line at one point of a curve; of the second type, the cone of planes through a point tangent to a surface. The further enhancements of centering, orienting, and rescaling in the medical context are intended to leave landmark points or boundary intersections invariant on the screen. Edgewarp, a publicly available software package, allows free play with pencils of planes like these as they section one single enormous medical data resource, the Visible Human data sets from the National Library of Medicine. This paper argues the relative merits of such visualizations over conventional surface-rendered flybys for understanding and communication of associated anatomical knowledge.
Computer-Aided Geometry Modeling
NASA Technical Reports Server (NTRS)
Shoosmith, J. N. (Compiler); Fulton, R. E. (Compiler)
1984-01-01
Techniques in computer-aided geometry modeling and their application are addressed. Mathematical modeling, solid geometry models, management of geometric data, development of geometry standards, and interactive and graphic procedures are discussed. The applications include aeronautical and aerospace structures design, fluid flow modeling, and gas turbine design.
Teaching of Geometry in Bulgaria
ERIC Educational Resources Information Center
Bankov, Kiril
2013-01-01
Geometry plays an important role in the school mathematics curriculum all around the world. Teaching of geometry varies a lot (Hoyls, Foxman, & Kuchemann, 2001). Many countries revise the objectives, the content, and the approaches to the geometry in school. Studies of the processes show that there are not common trends of these changes…
NASA Astrophysics Data System (ADS)
Bengtsson, Ingemar; Zyczkowski, Karol
2006-05-01
Quantum information theory is at the frontiers of physics, mathematics and information science, offering a variety of solutions that are impossible using classical theory. This book provides an introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory. After a gentle introduction to the necessary mathematics the authors describe the geometry of quantum state spaces. Focusing on finite dimensional Hilbert spaces, they discuss the statistical distance measures and entropies used in quantum theory. The final part of the book is devoted to quantum entanglement - a non-intuitive phenomenon discovered by Schrödinger, which has become a key resource for quantum computation. This richly-illustrated book is useful to a broad audience of graduates and researchers interested in quantum information theory. Exercises follow each chapter, with hints and answers supplied. The first book to focus on the geometry of quantum states Stresses the similarities and differences between classical and quantum theory Uses a non-technical style and numerous figures to make the book accessible to non-specialists
National Aerospace Plane (NASP) program
NASA Technical Reports Server (NTRS)
1990-01-01
Artists concept of the X-30 aerospace plane flying through Earth's atmosphere on its way to low-Earth orbit. the experimental concept is part of the National Aero-Space Plane Program. The X-30 is planned to demonstrate the technology for airbreathing space launch and hypersonic cruise vehicles. Photograph and caption published in Winds of Change, 75th Anniversary NASA publication (page 117), by James Schultz.
Ionization coefficient approach to modeling breakdown in nonuniform geometries.
Warne, Larry Kevin; Jorgenson, Roy Eberhardt; Nicolaysen, Scott D.
2003-11-01
This report summarizes the work on breakdown modeling in nonuniform geometries by the ionization coefficient approach. Included are: (1) fits to primary and secondary ionization coefficients used in the modeling; (2) analytical test cases for sphere-to-sphere, wire-to-wire, corner, coaxial, and rod-to-plane geometries; a compilation of experimental data with source references; comparisons between code results, test case results, and experimental data. A simple criterion is proposed to differentiate between corona and spark. The effect of a dielectric surface on avalanche growth is examined by means of Monte Carlo simulations. The presence of a clean dry surface does not appear to enhance growth.
The solar system's invariable plane
NASA Astrophysics Data System (ADS)
Souami, D.; Souchay, J.
2012-07-01
Context. The dynamics of solar system objects, such as dwarf planets and asteroids, has become a well-established field of celestial mechanics in the past thirty years, owing to the improvements that have been made in observational techniques and numerical studies. In general, the ecliptic is taken as the reference plane in these studies, although there is no dynamical reason for doing so. In contrast, the invariable plane as originally defined by Laplace, seems to be a far more natural choice. In this context, the latest study of this plane dates back to Burkhardt. Aims: We define and determine the orientation of the invariable plane of the solar system with respect to both the ICRF and the equinox-ecliptic of J2000.0, and evaluate the accuracy of our determination. Methods: Using the long-term numerical ephemerides DE405, DE406, and INPOP10a over their entire available time span, we computed the total angular momentum of the solar system, as well as the individual contribution to it made by each of the planets, the dwarf planets Pluto and Ceres, and the two asteroids Pallas and Vesta. We then deduced the orientation of the invariable plane from these ephemerides. Results: We update the previous results on the determination of the orientation of the invariable plane with more accurate data, and a more complete analysis of the problem, taking into account the effect of the dwarf planet (1) Ceres as well as two of the biggest asteroids, (4) Vesta and (2) Pallas. We show that the inclusion of these last three bodies significantly improves the accuracy of determination of the invariable plane, whose orientation over a 100 y interval does not vary more than 0.1 mas in inclination, and 0.3 mas in longitude of the ascending node. Moreover, we determine the individual contributions of each body to the total angular momentum of the solar system, as well as the inclination and longitude of the node with respect to this latter plane. Conclusions: Owing to the high accuracy
Evaluation of a cone beam computed tomography geometry for image guided small animal irradiation.
Yang, Yidong; Armour, Michael; Wang, Ken Kang-Hsin; Gandhi, Nishant; Iordachita, Iulian; Siewerdsen, Jeffrey; Wong, John
2015-07-01
The conventional imaging geometry for small animal cone beam computed tomography (CBCT) is that a detector panel rotates around the head-to-tail axis of an imaged animal ('tubular' geometry). Another unusual but possible imaging geometry is that the detector panel rotates around the anterior-to-posterior axis of the animal ('pancake' geometry). The small animal radiation research platform developed at Johns Hopkins University employs the pancake geometry where a prone-positioned animal is rotated horizontally between an x-ray source and detector panel. This study is to assess the CBCT image quality in the pancake geometry and investigate potential methods for improvement. We compared CBCT images acquired in the pancake geometry with those acquired in the tubular geometry when the phantom/animal was placed upright simulating the conventional CBCT geometry. Results showed signal-to-noise and contrast-to-noise ratios in the pancake geometry were reduced in comparison to the tubular geometry at the same dose level. But the overall spatial resolution within the transverse plane of the imaged cylinder/animal was better in the pancake geometry. A modest exposure increase to two folds in the pancake geometry can improve image quality to a level close to the tubular geometry. Image quality can also be improved by inclining the animal, which reduces streak artifacts caused by bony structures. The major factor resulting in the inferior image quality in the pancake geometry is the elevated beam attenuation along the long axis of the phantom/animal and consequently increased scatter-to-primary ratio in that orientation. Not withstanding, the image quality in the pancake-geometry CBCT is adequate to support image guided animal positioning, while providing unique advantages of non-coplanar and multiple mice irradiation. This study also provides useful knowledge about the image quality in the two very different imaging geometries, i.e. pancake and tubular geometry, respectively.
Evaluation of a cone beam computed tomography geometry for image guided small animal irradiation
NASA Astrophysics Data System (ADS)
Yang, Yidong; Armour, Michael; Kang-Hsin Wang, Ken; Gandhi, Nishant; Iordachita, Iulian; Siewerdsen, Jeffrey; Wong, John
2015-07-01
The conventional imaging geometry for small animal cone beam computed tomography (CBCT) is that a detector panel rotates around the head-to-tail axis of an imaged animal (‘tubular’ geometry). Another unusual but possible imaging geometry is that the detector panel rotates around the anterior-to-posterior axis of the animal (‘pancake’ geometry). The small animal radiation research platform developed at Johns Hopkins University employs the pancake geometry where a prone-positioned animal is rotated horizontally between an x-ray source and detector panel. This study is to assess the CBCT image quality in the pancake geometry and investigate potential methods for improvement. We compared CBCT images acquired in the pancake geometry with those acquired in the tubular geometry when the phantom/animal was placed upright simulating the conventional CBCT geometry. Results showed signal-to-noise and contrast-to-noise ratios in the pancake geometry were reduced in comparison to the tubular geometry at the same dose level. But the overall spatial resolution within the transverse plane of the imaged cylinder/animal was better in the pancake geometry. A modest exposure increase to two folds in the pancake geometry can improve image quality to a level close to the tubular geometry. Image quality can also be improved by inclining the animal, which reduces streak artifacts caused by bony structures. The major factor resulting in the inferior image quality in the pancake geometry is the elevated beam attenuation along the long axis of the phantom/animal and consequently increased scatter-to-primary ratio in that orientation. Not withstanding, the image quality in the pancake-geometry CBCT is adequate to support image guided animal positioning, while providing unique advantages of non-coplanar and multiple mice irradiation. This study also provides useful knowledge about the image quality in the two very different imaging geometries, i.e. pancake and tubular geometry
Critique of information geometry
Skilling, John
2014-12-05
As applied to probability, information geometry fails because probability distributions do not form a metric space. Probability theory rests on a compelling foundation of elementary symmetries, which also support information (aka minus entropy, Kullback-Leibler) H(p;q) as the unique measure of divergence from source probability distribution q to destination p. Because the only compatible connective H is from≠to asymmetric, H(p;q)≠H(q;p), there can be no compatible geometrical distance (which would necessarily be from=to symmetric). Hence there is no distance relationship compatible with the structure of probability theory. Metrics g and densities sqrt(det(g)) interpreted as prior probabilities follow from the definition of distance, and must fail likewise. Various metrics and corresponding priors have been proposed, Fisher's being the most popular, but all must behave unacceptably. This is illustrated with simple counter-examples.
Optically defined mechanical geometry
NASA Astrophysics Data System (ADS)
Barasheed, Abeer Z.; Müller, Tina; Sankey, Jack C.
2016-05-01
In the field of optomechanics, radiation forces have provided a particularly high level of control over the frequency and dissipation of mechanical elements. Here we propose a class of optomechanical systems in which light exerts a similarly profound influence over two other fundamental parameters: geometry and mass. By applying an optical trap to one lattice site of an extended phononic crystal, we show it is possible to create a tunable, localized mechanical mode. Owing to light's simultaneous and constructive coupling with the structure's continuum of modes, we estimate that a trap power at the level of a single intracavity photon should be capable of producing a significant effect within a realistic, chip-scale device.
Magnetism in curved geometries
NASA Astrophysics Data System (ADS)
Streubel, Robert; Fischer, Peter; Kronast, Florian; Kravchuk, Volodymyr P.; Sheka, Denis D.; Gaididei, Yuri; Schmidt, Oliver G.; Makarov, Denys
2016-09-01
Extending planar two-dimensional structures into the three-dimensional space has become a general trend in multiple disciplines, including electronics, photonics, plasmonics and magnetics. This approach provides means to modify conventional or to launch novel functionalities by tailoring the geometry of an object, e.g. its local curvature. In a generic electronic system, curvature results in the appearance of scalar and vector geometric potentials inducing anisotropic and chiral effects. In the specific case of magnetism, even in the simplest case of a curved anisotropic Heisenberg magnet, the curvilinear geometry manifests two exchange-driven interactions, namely effective anisotropy and antisymmetric exchange, i.e. Dzyaloshinskii–Moriya-like interaction. As a consequence, a family of novel curvature-driven effects emerges, which includes magnetochiral effects and topologically induced magnetization patterning, resulting in theoretically predicted unlimited domain wall velocities, chirality symmetry breaking and Cherenkov-like effects for magnons. The broad range of altered physical properties makes these curved architectures appealing in view of fundamental research on e.g. skyrmionic systems, magnonic crystals or exotic spin configurations. In addition to these rich physics, the application potential of three-dimensionally shaped objects is currently being explored as magnetic field sensorics for magnetofluidic applications, spin-wave filters, advanced magneto-encephalography devices for diagnosis of epilepsy or for energy-efficient racetrack memory devices. These recent developments ranging from theoretical predictions over fabrication of three-dimensionally curved magnetic thin films, hollow cylinders or wires, to their characterization using integral means as well as the development of advanced tomography approaches are in the focus of this review.
Magnetism in curved geometries
NASA Astrophysics Data System (ADS)
Streubel, Robert; Fischer, Peter; Kronast, Florian; Kravchuk, Volodymyr P.; Sheka, Denis D.; Gaididei, Yuri; Schmidt, Oliver G.; Makarov, Denys
2016-09-01
Extending planar two-dimensional structures into the three-dimensional space has become a general trend in multiple disciplines, including electronics, photonics, plasmonics and magnetics. This approach provides means to modify conventional or to launch novel functionalities by tailoring the geometry of an object, e.g. its local curvature. In a generic electronic system, curvature results in the appearance of scalar and vector geometric potentials inducing anisotropic and chiral effects. In the specific case of magnetism, even in the simplest case of a curved anisotropic Heisenberg magnet, the curvilinear geometry manifests two exchange-driven interactions, namely effective anisotropy and antisymmetric exchange, i.e. Dzyaloshinskii-Moriya-like interaction. As a consequence, a family of novel curvature-driven effects emerges, which includes magnetochiral effects and topologically induced magnetization patterning, resulting in theoretically predicted unlimited domain wall velocities, chirality symmetry breaking and Cherenkov-like effects for magnons. The broad range of altered physical properties makes these curved architectures appealing in view of fundamental research on e.g. skyrmionic systems, magnonic crystals or exotic spin configurations. In addition to these rich physics, the application potential of three-dimensionally shaped objects is currently being explored as magnetic field sensorics for magnetofluidic applications, spin-wave filters, advanced magneto-encephalography devices for diagnosis of epilepsy or for energy-efficient racetrack memory devices. These recent developments ranging from theoretical predictions over fabrication of three-dimensionally curved magnetic thin films, hollow cylinders or wires, to their characterization using integral means as well as the development of advanced tomography approaches are in the focus of this review.
Helicoidal plane of dental occlusion.
Osborn, J W
1982-03-01
A helicoidal plane of postcanine occlusion has been patchily reported in many recent and fossil dentitions of man, and has been suggested as a taxonomic marker distinguishing between the dentitions of Homo and Australopithecines. The present paper describes the helicoidal plane in 19 out of 23 modern human (probably Indian) worn dentitions, in both gracile and robust Australopithecines and in extant anthropoids. It is suggested that tooth wear converts the plane of occlusion present in little-worn teeth, the Monson curve, into a helicoidal plane when 1) the diet is more abrasive, 2) the enamel is thinner and less abrasion resistant, and 3) a longer time separates the eruption of the three molar teeth in a jaw quadrant. A model demonstrates that during the power stroke of a chewing cycle the working side molars move in much the same direction whether the molar occlusal plan follows a Monson curve or a helicoidal plane. The difference is that in the former case the three molars work at the same time while in the latter case they work in sequence from anterior to posterior, thereby concentrating force on one tooth at a time. Because the occlusal plane changes during the life of individuals consuming an abrasive diet, the condition of most anthropoids and hominids, it is argued that the Monson curve has functional significance not because of its influence on occlusal relations and/or jaw movement but because the molar teeth are embedded in bone roughly perpendicular to it, a direction which resists tilting of the teeth during mastication. It is concluded that the helicoidal plane probably has little if any value as a taxonomic marker.
The Laplace Planes of Uranus and Pluto
NASA Technical Reports Server (NTRS)
Dobrovolskis, Anthony R.
1993-01-01
Satellite orbits close to an oblate planet precess about its equatorial plane, while distant satellites precess around the plane of the planet's heliocentric orbit. In between, satellites in nearly circular orbits precess about a warped intermediate surface called the Laplace 'plane.' Herein we derive general formulas for locating the Laplace plane. Because Uranus and Pluto have high obliquities, their Laplace planes are severely warped. We present maps of these Laplace planes, of interest in telescopic searches for new satellites. The Laplace plane of the Solar System as a whole is similarly distorted, but comets in the inner Oort cloud precess too slowly to sense the Laplace plane.
Numerical shadow and geometry of quantum states
NASA Astrophysics Data System (ADS)
Dunkl, Charles F.; Gawron, Piotr; Holbrook, John A.; Miszczak, Jarosław A.; Puchała, Zbigniew; Życzkowski, Karol
2011-08-01
The totality of normalized density matrices of dimension N forms a convex set {\\cal Q}_N in { R}^{N^2-1}. Working with the flat geometry induced by the Hilbert-Schmidt distance, we consider images of orthogonal projections of {\\cal Q}_N onto a two-plane and show that they are similar to the numerical ranges of matrices of dimension N. For a matrix A of dimension N, one defines its numerical shadow as a probability distribution supported on its numerical range W(A), induced by the unitarily invariant Fubini-Study measure on the complex projective manifold { C}P^{N-1}. We define generalized, mixed-state shadows of A and demonstrate their usefulness to analyse the structure of the set of quantum states and unitary dynamics therein.
Geometry and mechanics of thin growing bilayers.
Pezzulla, Matteo; Smith, Gabriel P; Nardinocchi, Paola; Holmes, Douglas P
2016-05-11
We investigate how thin sheets of arbitrary shapes morph under the isotropic in-plane expansion of their top surface, which may represent several stimuli such as nonuniform heating, local swelling and differential growth. Inspired by geometry, an analytical model is presented that rationalizes how the shape of the disk influences morphing, from the initial spherical bending to the final isometric limit. We introduce a new measure of slenderness that describes a sheet in terms of both thickness and plate shape. We find that the mean curvature of the isometric state is three fourths the natural curvature, which we verify by numerics and experiments. We finally investigate the emergence of a preferred direction of bending in the isometric state, guided by numerical analyses. The scalability of our model suggests that it is suitable to describe the morphing of sheets spanning several orders of magnitude.
Geometry and mechanics of thin growing bilayers.
Pezzulla, Matteo; Smith, Gabriel P; Nardinocchi, Paola; Holmes, Douglas P
2016-05-11
We investigate how thin sheets of arbitrary shapes morph under the isotropic in-plane expansion of their top surface, which may represent several stimuli such as nonuniform heating, local swelling and differential growth. Inspired by geometry, an analytical model is presented that rationalizes how the shape of the disk influences morphing, from the initial spherical bending to the final isometric limit. We introduce a new measure of slenderness that describes a sheet in terms of both thickness and plate shape. We find that the mean curvature of the isometric state is three fourths the natural curvature, which we verify by numerics and experiments. We finally investigate the emergence of a preferred direction of bending in the isometric state, guided by numerical analyses. The scalability of our model suggests that it is suitable to describe the morphing of sheets spanning several orders of magnitude. PMID:27098344
Interactive design of hypersonic waverider geometries
NASA Technical Reports Server (NTRS)
Center, K. B.; Sobieczky, H.; Dougherty, F. C.
1991-01-01
The paper deals with an inverse design code utilizing the method of oscillating cones; the code integrated into an interactive graphics software package allows manipulation of both the exit-plane shock profile and leading edge of the vehicle. Another interactive feature of the system is the ability to vary freestream conditions and reevaluate the governing conditions. The development of the oscillating cones is shown on five classes each of which is chosen to demonstrate an aspect of improved design flexibility over previous studies. Results are evaluated using a robust flow solver, insuring that the shock shapes specified in the design process are recovered. It is pointed out that the expanded range of waverider geometries that may be generated using the oscillating cones technique may provide insight into visually oriented optimization parameters such as volumetric efficiency and practical planform.
Marsh, S.P.
1988-03-08
An explosive plane-wave air lens which enables a spherical wave form to be converted to a planar wave without the need to specially machine or shape explosive materials is described. A disc-shaped impactor having a greater thickness at its center than around its periphery is used to convert the spherical wave into a plane wave. When the wave reaches the impactor, the center of the impactor moves first because the spherical wave reaches the center of the impactor first. The wave strikes the impactor later in time as one moves radially along the impactor. Because the impactor is thinner as one moves radially outward, the velocity of the impactor is greater at the periphery than at the center. An acceptor explosive is positioned so that the impactor strikes the acceptor simultaneously. Consequently, a plane detonation wave is propagated through the acceptor explosive. 4 figs.
Marsh, Stanley P.
1988-01-01
An explosive plane-wave air lens which enables a spherical wave form to be converted to a planar wave without the need to specially machine or shape explosive materials is described. A disc-shaped impactor having a greater thickness at its center than around its periphery is used to convert the spherical wave into a plane wave. When the wave reaches the impactor, the center of the impactor moves first because the spherical wave reaches the center of the impactor first. The wave strikes the impactor later in time as one moves radially along the impactor. Because the impactor is thinner as one moves radially outward, the velocity of the impactor is greater at the periphery than at the center. An acceptor explosive is positioned so that the impactor strikes the acceptor simultaneously. Consequently, a plane detonation wave is propagated through the acceptor explosive.
Marsh, S.P.
1987-03-12
An explosive plane-wave air lens which enables a spherical wave form to be converted to a planar wave without the need to specially machine or shape explosive materials is described. A disc-shaped impactor having a greater thickness at its center than around its periphery is used to convert the spherical wave into a plane wave. When the wave reaches the impactor, the center of the impactor moves first because the spherical wave reaches the center of the impactor first. The wave strikes the impactor later in time as one moves radially along the impactor. Because the impactor is thinner as one moves radially outward, the velocity of the impactor is greater at the periphery than at the center. An acceptor explosive is positioned so that the impactor strikes the acceptor simultaneously. Consequently, a plane detonation wave is propagated through the acceptor explosive. 3 figs., 3 tabs.
NASA Astrophysics Data System (ADS)
Forgács, Péter; Lukács, Árpád; Romańczukiewicz, Tomasz
2013-12-01
It is shown that in a large class of systems, plane waves act as tractor beams: i.e., an incident plane wave can exert a pulling force on the scatterer. The underlying physical mechanism for the pulling force is due to the sufficiently strong scattering of the incoming wave into another mode carrying more momentum, in which case excess momentum is created behind the scatterer. This tractor beam or negative radiation pressure (NRP) effect, is found to be generic in systems with multiple scattering channels. In a birefringent medium, electromagnetic plane waves incident on a thin plate exert NRP of the same order of magnitude as optical radiation pressure, while in artificial dielectrics (metamaterials), the magnitude of NRP can even be macroscopic. In two dimensions, we study various scattering situations on vortices, and NRP is shown to occur by the scattering of heavy baryons into light leptons off cosmic strings, and by neutron scattering off vortices in the XY model.
Planetary Image Geometry Library
NASA Technical Reports Server (NTRS)
Deen, Robert C.; Pariser, Oleg
2010-01-01
The Planetary Image Geometry (PIG) library is a multi-mission library used for projecting images (EDRs, or Experiment Data Records) and managing their geometry for in-situ missions. A collection of models describes cameras and their articulation, allowing application programs such as mosaickers, terrain generators, and pointing correction tools to be written in a multi-mission manner, without any knowledge of parameters specific to the supported missions. Camera model objects allow transformation of image coordinates to and from view vectors in XYZ space. Pointing models, specific to each mission, describe how to orient the camera models based on telemetry or other information. Surface models describe the surface in general terms. Coordinate system objects manage the various coordinate systems involved in most missions. File objects manage access to metadata (labels, including telemetry information) in the input EDRs and RDRs (Reduced Data Records). Label models manage metadata information in output files. Site objects keep track of different locations where the spacecraft might be at a given time. Radiometry models allow correction of radiometry for an image. Mission objects contain basic mission parameters. Pointing adjustment ("nav") files allow pointing to be corrected. The object-oriented structure (C++) makes it easy to subclass just the pieces of the library that are truly mission-specific. Typically, this involves just the pointing model and coordinate systems, and parts of the file model. Once the library was developed (initially for Mars Polar Lander, MPL), adding new missions ranged from two days to a few months, resulting in significant cost savings as compared to rewriting all the application programs for each mission. Currently supported missions include Mars Pathfinder (MPF), MPL, Mars Exploration Rover (MER), Phoenix, and Mars Science Lab (MSL). Applications based on this library create the majority of operational image RDRs for those missions. A
A technique for calculating optimal Hohmann transfers with simultaneous plane and node rotations
NASA Astrophysics Data System (ADS)
Rogers, Christopher F.
This analysis presents eight nonlinear coupled equations whose solution provides sufficient information to characterize an optimal Hohmann transfer with simultaneous plane and node rotations. It also presents auxiliary equations which help provide other information of interest. The derivations utilize spherical geometry but otherwise deal very directly with the transfer geometry and thereby remain conceptually simple. The assumptions include initial and final circular orbits and impulsive burns. Numerical results illustrate the technique.
Cell division plane orientation based on tensile stress in Arabidopsis thaliana.
Louveaux, Marion; Julien, Jean-Daniel; Mirabet, Vincent; Boudaoud, Arezki; Hamant, Olivier
2016-07-26
Cell geometry has long been proposed to play a key role in the orientation of symmetric cell division planes. In particular, the recently proposed Besson-Dumais rule generalizes Errera's rule and predicts that cells divide along one of the local minima of plane area. However, this rule has been tested only on tissues with rather local spherical shape and homogeneous growth. Here, we tested the application of the Besson-Dumais rule to the divisions occurring in the Arabidopsis shoot apex, which contains domains with anisotropic curvature and differential growth. We found that the Besson-Dumais rule works well in the central part of the apex, but fails to account for cell division planes in the saddle-shaped boundary region. Because curvature anisotropy and differential growth prescribe directional tensile stress in that region, we tested the putative contribution of anisotropic stress fields to cell division plane orientation at the shoot apex. To do so, we compared two division rules: geometrical (new plane along the shortest path) and mechanical (new plane along maximal tension). The mechanical division rule reproduced the enrichment of long planes observed in the boundary region. Experimental perturbation of mechanical stress pattern further supported a contribution of anisotropic tensile stress in division plane orientation. Importantly, simulations of tissues growing in an isotropic stress field, and dividing along maximal tension, provided division plane distributions comparable to those obtained with the geometrical rule. We thus propose that division plane orientation by tensile stress offers a general rule for symmetric cell division in plants.
Plane waves in noncommutative fluids
NASA Astrophysics Data System (ADS)
Abdalla, M. C. B.; Holender, L.; Santos, M. A.; Vancea, I. V.
2013-08-01
We study the dynamics of the noncommutative fluid in the Snyder space perturbatively at the first order in powers of the noncommutative parameter. The linearized noncommutative fluid dynamics is described by a system of coupled linear partial differential equations in which the variables are the fluid density and the fluid potentials. We show that these equations admit a set of solutions that are monochromatic plane waves for the fluid density and two of the potentials and a linear function for the third potential. The energy-momentum tensor of the plane waves is calculated.
Space-Plane Spreadsheet Program
NASA Technical Reports Server (NTRS)
Mackall, Dale
1993-01-01
Basic Hypersonic Data and Equations (HYPERDATA) spreadsheet computer program provides data gained from three analyses of performance of space plane. Equations used to perform analyses derived from Newton's second law of physics, derivation included. First analysis is parametric study of some basic factors affecting ability of space plane to reach orbit. Second includes calculation of thickness of spherical fuel tank. Third produces ratio between volume of fuel and total mass for each of various aircraft. HYPERDATA intended for use on Macintosh(R) series computers running Microsoft Excel 3.0.
Investigating Fractal Geometry Using LOGO.
ERIC Educational Resources Information Center
Thomas, David A.
1989-01-01
Discusses dimensionality in Euclidean geometry. Presents methods to produce fractals using LOGO. Uses the idea of self-similarity. Included are program listings and suggested extension activities. (MVL)
The relationship between strain geometry and geometrically necessary dislocations
NASA Astrophysics Data System (ADS)
Hansen, Lars; Wallis, David
2016-04-01
single crystals and aggregates of olivine for which the strain geometry is known. Tested geometries include constrictional strain, flattening strain, and plane strain. We use measured lattice curvatures to calculate the densities and spatial distributions of geometrically necessary dislocations. Dislocation densities are calculated for each of the major dislocation types in olivine. These densities are then used to estimate the plastic strain geometry under the assumption that the population of geometrically necessary dislocations accurately represents the relative activity of different dislocations during deformation. Our initial results demonstrate compelling relationships between the imposed strain geometry and the calculated plastic strain geometry. In addition, the calculated plastic strain geometry is linked to the distribution of crystallographic orientations, giving insight into the nature of plastic anisotropy in textured olivine aggregates. We present this technique as a new microstructural tool for assessing the kinematic history of deformed rocks.
TES Limb-Geometry Observations of Aerosols
NASA Technical Reports Server (NTRS)
Smith, Michael D.
2003-01-01
The Thermal Emission Spectrometer (TES) on-board Mars Global Surveyor (MGS) has a pointing mirror that allows observations in the plane of the orbit anywhere from directly nadir to far above either the forward or aft limbs for details about the TES instrument). Nadir-geometry observations are defined as those where the field-of-view contains the surface of Mars (even if the actual observation is at a high emission angle far from true nadir). Limb-geometry observations are defined as those where the line-of-sight of the observations does not intersect the surface. At a number of points along the MGS orbit (typically every 10 deg. or 20 deg. of latitude) a limb sequence is taken, which includes a stack of overlapping TES spectra from just below the limb to more than 120 km above the limb. A typical limb sequence has approx. 20 individual spectra, and the projected size of a TES pixel at the limb is 13 km.
NASA Astrophysics Data System (ADS)
Liu, Siqi; Pen, Ue-Li; Macquart, J.-P.; Brisken, Walter; Deller, Adam
2016-05-01
We test the inclined sheet pulsar scintillation model (Pen & Levin) against archival very long baseline interferometry (VLBI) data on PSR 0834+06 and show that its scintillation properties can be precisely reproduced by a model in which refraction occurs on two distinct lens planes. These data strongly favour a model in which grazing-incidence refraction instead of diffraction off turbulent structures is the primary source of pulsar scattering. This model can reproduce the parameters of the observed diffractive scintillation with an accuracy at the percent level. Comparison with new VLBI proper motion results in a direct measure of the ionized interstellar medium (ISM) screen transverse velocity. The results are consistent with ISM velocities local to the PSR 0834+06 sight-line (through the Galaxy). The simple 1-D structure of the lenses opens up the possibility of using interstellar lenses as precision probes for pulsar lens mapping, precision transverse motions in the ISM, and new opportunities for removing scattering to improve pulsar timing. We describe the parameters and observables of this double screen system. While relative screen distances can in principle be accurately determined, a global conformal distance degeneracy exists that allows a rescaling of the absolute distance scale. For PSR B0834+06, we present VLBI astrometry results that provide (for the first time) a direct measurement of the distance of the pulsar. For most of the recycled millisecond pulsars that are the targets of precision timing observations, the targets where independent distance measurements are not available. The degeneracy presented in the lens modelling could be broken if the pulsar resides in a binary system.
Affine Contractions on the Plane
ERIC Educational Resources Information Center
Celik, D.; Ozdemir, Y.; Ureyen, M.
2007-01-01
Contractions play a considerable role in the theory of fractals. However, it is not easy to find contractions which are not similitudes. In this study, it is shown by counter examples that an affine transformation of the plane carrying a given triangle onto another triangle may not be a contraction even if it contracts edges, heights or medians.…
GPS: Geometry, Probability, and Statistics
ERIC Educational Resources Information Center
Field, Mike
2012-01-01
It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…
Linguistic geometry for autonomous navigation
Stilman, B.
1995-09-01
To discover the inner properties of human expert heuristics, which were successful in a certain class of complex control systems, we develop a formal theory, the Linguistic Geometry. This paper reports two examples of application of Linguistic Geometry to autonomous navigation of aerospace vehicles that demonstrate dramatic search reduction.
Lobachevsky's Geometry and Research of Geometry of the Universe
NASA Astrophysics Data System (ADS)
Brylevskaya, L. I.
2008-10-01
For the first time N. I. Lobachevsky gave a talk on the new geometry in 1826; three years after he had published a work "On the fundamentals of geometry", containing all fundamental theorems and methods of non-Euclidean geometry. A small part of the article was devoted to the study of geometry of the Universe. The interpretation of geometrical concepts in pure empirical way was typical for mathematicians at the beginning of the XIX century; in this connection it was important for scientists to find application of his geometry. Having the purpose to determine experimentally the properties of real physical Space, Lobachevsky decided to calculate the sum of angles in a huge triangle with two vertexes in opposite points of the terrestrial orbit and the third -- on the remote star. Investigating the possibilities of solution of the set task, Lobachevsky faced the difficulties of theoretical, technical and methodological character. More detailed research of different aspects of the problem led Lobachevsky to the comprehension of impossibility to obtain the values required for the goal achievement, and he called his geometry an imaginary geometry.
Gravitational scattering of zero-rest-mass plane waves
NASA Technical Reports Server (NTRS)
De Logi, W. K.; Kovacs, S. J., Jr.
1977-01-01
The Feyman-diagram technique is used to calculate the differential cross sections for the scattering of zero-rest-mass plane waves of spin 0, 1, and 2 by linearized Schwarzschild and Kerr geometries in the long-wavelength weak-field limit. It is found that the polarization of right (or left) circularly polarized electromagnetic waves is unaffected by the scattering process (i.e., helicity is conserved) and that the two helicity (polarization) states of the photon are scattered differently by the Kerr geometry. This coupling between the photon helicity and the angular momentum of the scatterer also leads to a partial polarization of unpolarized incident light. For gravitational waves, on the other hand, there is neither helicity conservation nor helicity-dependent scattering; the angular momentum of the scatterer has no polarizing effect on incident unpolarized gravitational waves.
An in-plane cantilever for wall shear stress measurement
NASA Astrophysics Data System (ADS)
Allen, N. J.; Sims-Williams, D. B.; Wood, D.
2012-07-01
A sensor capable of measuring small shear stresses in wind tunnel applications is presented. The sensor utilizes an in-plane cantilever concept for shear stress measurement, designed to minimize intrusiveness into the airflow and allow easy incorporation into wind tunnel test models. The sensor operates independently of input voltage, and can measure <1 Pa shear stresses with a sensitivity of 8.6 (mV V-1) Pa. Altering the geometry of the sensor has a direct effect on the sensitivity and so can be used to adapt the sensor for different applications.
Generation of a crowned pinion tooth surface by a plane
NASA Technical Reports Server (NTRS)
Litvin, F. L.; Zhang, J.; Handschuh, R. F.
1988-01-01
The topology of a crowned spur pinion tooth surface that reduces the level of transmission errors due to misalignment is described. The geometry of the modified pinion tooth surface and of the regular involute gear tooth surface is discussed. The tooth contact analysis between the meshing surfaces is also described. Generating a modified pinion tooth surface by a plane whose motion is controlled by a 5-degree-of-freedom system is investigated. The numerical results included indicate that the transmission error remains low as the gears are misaligned.
Characterization of the centroidal geometry of human ribs.
Kindig, Matthew W; Kent, Richard W
2013-11-01
While a number of studies have quantified overall ribcage morphology (breadth, depth, kyphosis/lordosis) and rib cross-sectional geometry in humans, few studies have characterized the centroidal geometry of individual ribs. In this study, a novel model is introduced to describe the centroidal path of a rib (i.e., the sequence of centroids connecting adjacent cross-sections) in terms of several physically-meaningful and intuitive geometric parameters. Surface reconstructions of rib levels 2-10 from 16 adult male cadavers (aged 31-75 years) were first extracted from CT scans, and the centroidal path was calculated in 3D for each rib using a custom numerical method. The projection of the centroidal path onto the plane of best fit (i.e., the "in-plane" centroidal path) was then modeled using two geometric primitives (a circle and a semiellipse) connected to give C1 continuity. Two additional parameters were used to describe the deviation of the centroidal path from this plane; further, the radius of curvature was calculated at various points along the rib length. This model was fit to each of the 144 extracted ribs, and average trends in rib size and shape with rib level were reported. In general, upper ribs (levels 2-5) had centroidal paths which were closer to circular, while lower ribs (levels 6-10) tended to be more elliptical; further the centroidal curvature at the posterior extremity was less pronounced for lower ribs. Lower ribs also tended to exhibit larger deviations from the best-fit plane. The rib dimensions and trends with subject stature were found to be consistent with findings previously reported in the literature. This model addresses a critical need in the biomechanics literature for the accurate characterization of rib geometry, and can be extended to a larger population as a simple and accurate way to represent the centroidal shape of human ribs.
Twisted sectors from plane partitions
NASA Astrophysics Data System (ADS)
Datta, Shouvik; Gaberdiel, Matthias R.; Li, Wei; Peng, Cheng
2016-09-01
Twisted sectors arise naturally in the bosonic higher spin CFTs at their free points, as well as in the associated symmetric orbifolds. We identify the coset representations of the twisted sector states using the description of W_{∞} representations in terms of plane partitions. We confirm these proposals by a microscopic null-vector analysis, and by matching the excitation spectrum of these representations with the orbifold prediction.
NASA Astrophysics Data System (ADS)
Bokhove, Henk; Smorenburg, C.; Visser, H.
1993-11-01
The Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) has been selected by ESA for the ENVISAT-Mission, scheduled for launch in 1998. The instrument will measure the concentration of a number of atmospheric trace gases in the earth atmosphere in a spectral region from 4.15 - 14.6 micrometers . Within this region measurements are performed with high spectral resolution. The MIPAS optical system consists of scan mirrors, a telescope, a Michelson interferometer, an afocal reducer and a focal plane assembly. TNO Institute of Applied Physics is involved in the design and development of the afocal reducer and the focal plane assembly. The beam reducing optics of the afocal reducer consist of 2 concave and one convex mirror. Both the housing and the mirrors are made of aluminum to ensure temperature invariance. The optics of the focal plane assembly consist of aluminum mirrors, dichroic beamsplitters and Ge lenses in front of the detectors. The optical/mechanical design is developed to the level that phase C2/D activities can start.
NASA Astrophysics Data System (ADS)
Conn Henry, Richard; Kilston, S.; Shostak, S.
2008-05-01
The strong advantages of SETI searches in the ecliptic plane have been pointed out by Kilston, Shostak, and Henry (2008). In our poster we show one possible history of civilizations in the galaxy, from birth, through galactic colonization, up to death - and even beyond. Should this scenario be correct, the pattern suggests that the best hope for success in SETI is exploration of the possibility that there are a few extremely ancient but non-colonizing civilizations; civilizations that, aeons ago, detected the existence of Earth (oxygen, and hence life) and of its Moon (stabilizing Earth's rotation) via observations of transits of the Sun (hence, ecliptic, which is stable over millions of years [Laskar et al. 2004]), and have been beaming voluminous information in our direction ever since, in their faint hope (now realized) that a technological "receiving” species would appear. To maintain such a targeted broadcast would be extremely cheap for an advanced civilization. A search of a swath centered on our ecliptic plane should easily find such civilizations, if they exist. We hope to carry out such a search, using the Allen Telescope Array. http://henry.pha.jhu.edu/poster.SETI.pdf References: Kilston, Steven; Shostak, Seth; & Henry, Richard Conn; "Who's Looking at You, Kid?: SETI Advantages near the Ecliptic Plane," AbSciCon 2008, April 14-17, Santa Clara, CA.; Laskar, J., et al., A&A 428, 261, 2004 This work was supported by Maryland Space Grant Consortium.
Quantum Consequences of Parameterizing Geometry
NASA Astrophysics Data System (ADS)
Wanas, M. I.
2002-12-01
The marriage between geometrization and quantization is not successful, so far. It is well known that quantization of gravity , using known quantization schemes, is not satisfactory. It may be of interest to look for another approach to this problem. Recently, it is shown that geometries with torsion admit quantum paths. Such geometries should be parameterizied in order to preserve the quantum properties appeared in the paths. The present work explores the consequences of parameterizing such geometry. It is shown that quantum properties, appeared in the path equations, are transferred to other geometric entities.
NASA Astrophysics Data System (ADS)
Belogurov, S.; Berchun, Yu; Chernogorov, A.; Malzacher, P.; Ovcharenko, E.; Semennikov, A.
2011-12-01
Due to conceptual difference between geometry descriptions in Computer-Aided Design (CAD) systems and particle transport Monte Carlo (MC) codes direct conversion of detector geometry in either direction is not feasible. An original set of tools has been developed for building a GEANT4/ROOT compatible geometry in the CATIA CAD system and exchanging it with mentioned MC packages using GDML file format. A Special structure of a CATIA product tree, a wide range of primitives, different types of multiple volume instantiation, and supporting macros have been implemented.
NASA Astrophysics Data System (ADS)
Frezza, F.; Schettini, G.; Tedeschi, N.
2011-08-01
Electromagnetic scattering by buried objects may involve a plane-wave expansion of the related fields, which depends on the objects' geometry. Furthermore, involved media in realistic cases are lossy, which requires the analytic continuation of formulae known for the lossless cases, due to the complex nature of the wave vectors. This problem has been covered in a previous paper, but the expression found still does not converge in some areas of space. In this paper, a new, convergent, expression of the spectrum of cylindrical functions in lossy media is analytically computed and its convergence limits are discussed.
Instability of supersymmetric microstate geometries
NASA Astrophysics Data System (ADS)
Eperon, Felicity C.; Reall, Harvey S.; Santos, Jorge E.
2016-10-01
We investigate the classical stability of supersymmetric, asymptotically flat, microstate geometries with five non-compact dimensions. Such geometries admit an "evanescent ergosurface": a timelike hypersurface of infinite redshift. On such a surface, there are null geodesics with zero energy relative to infinity. These geodesics are stably trapped in the potential well near the ergosurface. We present a heuristic argument indicating that this feature is likely to lead to a nonlinear instability of these solutions. We argue that the precursor of such an instability can be seen in the behaviour of linear perturbations: nonlinear stability would require that all linear perturbations decay sufficiently rapidly but the stable trapping implies that some linear perturbation decay very slowly. We study this in detail for the most symmetric microstate geometries. By constructing quasinormal modes of these geometries we show that generic linear perturbations decay slower than any inverse power of time.
Natural Language as a Tool for Analyzing the Proving Process: The Case of Plane Geometry Proof
ERIC Educational Resources Information Center
Robotti, Elisabetta
2012-01-01
In the field of human cognition, language plays a special role that is connected directly to thinking and mental development (e.g., Vygotsky, "1938"). Thanks to "verbal thought", language allows humans to go beyond the limits of immediately perceived information, to form concepts and solve complex problems (Luria, "1975"). So, it appears language…
A 1D exact treatment of shock waves within spectral methods in plane geometry
NASA Astrophysics Data System (ADS)
Bonazzola, Silvano; Marck, Jean-Alain
1991-12-01
A high-accuracy numerical technique is presented which employs two moving grids, respectively before and after the shock formation, to solve 1D Euler equations that are coupled with the transport equations for the entropy and the chemical abundances in cases with and without shock formation. Chebychev polynomial series are used to expand quantities on both sides of the matching point, and Rankine-Hugoniot conditions are used to ascertain the shock velocity after shock formation. Illustrative results are presented.
High-frequency techniques for RCS prediction of plate geometries
NASA Technical Reports Server (NTRS)
Balanis, Constantine A.; Polka, Lesley A.
1991-01-01
Radar cross section (RCS) prediction of several rectangular plate geometries is discussed using high-frequency techniques such as the Uniform Theory of Diffraction (UTD) for perfectly conducting and impedance wedges and the Method of Equivalent Currents (MEC). Previous reports have presented detailed solutions to the principal-plane scattering by a perfectly conducting and a coated rectangular plate and nonprincipal-plane scattering by a perfectly conducting plate. These solutions are briefly reviewed and a modified model is presented for the coated plate. Theoretical and experimental data are presented for the perfectly conducting geometries. Agreement between theory and experiment is very good near and at normal incidence. In regions near and at grazing incidence, the disagreement between the data vary according to diffraction distances and angles involved. It is these areas of disagreement which are of extreme interest as an explanation for the disagreement will yield invaluable insight into scattering mechanisms which are not yet identified as major contributors near and at grazing incidence. Areas of disagreement between theory and experiment are identified and examined in an attempt to better understand and predict near-grazing incidence, grazing incidence, and nonprincipal-plane diffractions.
Tails of plane wave spacetimes: Wave-wave scattering in general relativity
NASA Astrophysics Data System (ADS)
Harte, Abraham I.
2013-10-01
One of the most important characteristics of light in flat spacetime is that it satisfies Huygens’ principle: Initial data for the vacuum Maxwell equations evolve sharply along null (and not timelike) geodesics. In flat spacetime, there are no tails which linger behind expanding wavefronts. Tails generically do exist, however, if the background spacetime is curved. The only nonflat vacuum geometries where electromagnetic fields satisfy Huygens’ principle are known to be those associated with gravitational plane waves. This paper investigates whether perturbations to the plane wave geometry itself also propagate without tails. First-order perturbations to all locally constructed curvature scalars are indeed found to satisfy Huygens’ principles. Despite this, gravitational tails do exist. Locally, they can only perturb one plane wave spacetime into another plane wave spacetime. A weak localized beam of gravitational radiation passing through an arbitrarily strong plane wave therefore leaves behind only a slight perturbation to the waveform of the background plane wave. The planar symmetry of that wave cannot be disturbed by any linear tail. These results are obtained by first deriving the retarded Green function for Lorenz-gauge metric perturbations and then analyzing its consequences for generic initial-value problems.
SNAP Satellite Focal Plane Development
Bebek, C.; Akerlof, C.; Aldering, G.; Amanullah, R.; Astier, P.; Baltay, C.; Barrelet, E.; Basa, S.; Bercovitz, J.; Bergstrom, L.; Berstein, G.P.; Bester, M.; Bohlin, R.; Bonissent, A.; Bower, C.; Campbell, M.; Carithers, W.; Commins, E.; Day, C.; Deustua, S.; DiGennaro, R.; Ealet, A.; Ellis, R.; Emmett, W.; Eriksson, M.; Fouchez,D.; Fruchter, A.; Genat, J-F.; Goldhaber, G.; Goobar, A.; Groom, D.; Heetderks, H.; Holland, S.; Huterer, D.; Johnson, W.; Kadel, R.; Karcher,A.; Kim, A.; Kolbe, W.; Lafever, R.; Lamoureaux, J.; Lampton, M.; Lefevre, O.; Levi, M.; Levin, D.; Linder, E.; Loken, S.; Malina, R.; Mazure, A.; McKay, T.; McKee, S.; Miquel, R.; Morgan, N.; Mortsell, E.; Mostek, N.; Mufson, S.; Musser, J.; Roe, N.; Nugent, P.; Oluseyi, H.; Pain, R.; Palaio, N.; Pankow, D.; Perlmutter, S.; Prieto, E.; Rabinowitz,D.; Refregier, A.; Rhodes, J.; Schubnell, M.; Sholl, M.; Smadja, G.; Smith, R.; Smoot, G.; Snyder, J.; Spadafora, A.; Szymkowiak, A.; Tarle,G.; Taylor, K.; Tilquin, A.; Tomasch, A.; Vincent, D.; von der Lippe, H.; Walder, J-P.; Wang, G.
2003-07-07
The proposed SuperNova/Acceleration Probe (SNAP) mission will have a two-meter class telescope delivering diffraction-limited images to an instrumented 0.7 square degree field in the visible and near-infrared wavelength regime. The requirements for the instrument suite and the present configuration of the focal plane concept are presented. A two year R&D phase, largely supported by the Department of Energy, is just beginning. We describe the development activities that are taking place to advance our preparedness for mission proposal in the areas of detectors and electronics.
Traveling hairpin-shaped fluid vortices in plane Couette flow
NASA Astrophysics Data System (ADS)
Deguchi, K.; Nagata, M.
2010-11-01
Traveling-wave solutions are discovered in plane Couette flow. They are obtained when the so-called steady hairpin vortex state found recently by Gibson [J. Fluid Mech. 638, 243 (2009)]10.1017/S0022112009990863 and Itano and Generalis [Phys. Rev. Lett. 102, 114501 (2009)]10.1103/PhysRevLett.102.114501 is continued to sliding Couette flow geometry between two concentric cylinders by using the radius ratio as a homotopy parameter. It turns out that in the plane Couette flow geometry two traveling waves having the phase velocities with opposite signs are associated with their appearance from the steady hairpin vortex state, where the amplitude of the phase velocities increases gradually from zero as the Reynolds number is increased. The solutions obviously inherit the streaky structure of the hairpin vortex state, but shape preserving flow patterns propagate in the streamwise direction. Other striking features of the solution are asymmetric mean flow profiles and strong quasistreamwise vortices which occupy the vicinity of only the top or bottom moving boundary, depending on the sign of the phase velocity. Furthermore, we find that the pitchfork bifurcation associated with the appearance of the solution becomes imperfect when the flow is perturbed by a Poiseuille flow component.
Focal Plane Instrumentation of VERITAS
NASA Astrophysics Data System (ADS)
Nagai, T.; McKay, R.; Sleege, G.; Petry, D.
VERITAS is a new atmospheric Cherenkov imaging telescope array to detect very high energy gamma rays above 100 GeV. The array is located in southern Arizona, USA, at an altitude of 1270m above see level. The array currently consists of four 12 m telescopes, structurally resembling the Davis-Cotton design of the Whipple 10 m telescope. The VERITAS focal plane instruments are equipped with high-resolution (499 pixels) fast photo-multiplier-tube (PMT) cameras covering a 3.5 degree field of view with 0.148 degree pixel separation. Light concentrators reduce the dead-space between PMTs to 25% and shield the PMTs from ambient light. The PMTs are connected to high-speed pre-amplifiers improving the signal to noise ratio and allow single photoelectron measurements in situ at operating voltage. Current monitor circuits in the focus box provide real-time monitoring of the anode currents for each pixel and ambient conditions of the focus box. A charge injection system installed in the focus box allows daytime testing of the trigger and data acquisition system by injecting pulses of variable amplitude and length into pre-amplifier stage. A detailed description of the VERITAS focal plane instruments will be given in this presentation.
The Bolocam Galactic Plane Survey
NASA Technical Reports Server (NTRS)
Glenn, Jason; Aguirre, James; Bally, John; Battersby, Cara; Bradley, Eric Todd; Cyganowski, Claudia; Dowell, Darren; Drosback, Meredith; Dunham, Miranda K.; Evans, Neal J., II; Ginsburg, Adam; Harvey, Paul; Rosolowsky, Erik; Schlingman, Wayne; Shirley, Yancy L.; Stringfellow, Guy S.; Walawender, Josh; Williams, Jonathan
2009-01-01
The Bolocam Galactic Plane Survey (BGPS) is a 1.1 millimeter continuum survey of the northern Galactic Plane made with Bolocam and the Caltech Submillimeter Observatory. The coverage totals 170 square degrees, comprised of a contiguous range from -10.5 deg is less than or equal to 90.5 deg, 0.5 deg is less than or equal to b is less than or equal to 0.5 deg, with extended coverage in b in selected regions, and four targeted regions in the outer Galaxy, including: IC1396, toward the Perseus arm at l is approximately 111 deg, W3/4/5, and Gem OB1. Depths of the maps range from 30 to 60 mJy beam (sup 1). Approximately 8,400 sources were detected and the maps and source catalog have been made publicly available. Millimeter-wave thermal dust emission reveals dense regions within molecular clouds, thus the BGPS serves as a database for studies of the dense interstellar medium and star formation within the Milky Way.
Serious Play with Dynamic Plane Transformations
ERIC Educational Resources Information Center
King, James
2011-01-01
Transformations are a central organizing idea in geometry. They are included in most geometry curricula and are likely to appear with even greater emphasis in the future, given the central role they play in the "Common Core State Standards" for K-12 mathematics. One of the attractions of geometry is the ability to draw and construct the…
Earthquake cycles in complex geometries
NASA Astrophysics Data System (ADS)
Romanet, Pierre; Bhat, Harsha; Madariaga, Raul
2016-04-01
Our understanding of earthquake cycles, from a modelling perspective, comes mainly from theoretical, and numerical, work on a single straight fault. However, natural fault systems are geometrically complex. Modelling complex fault geometry (bends, kinks and multiple faults) is in itself a challenge as it is computationally intensive. To overcome this difficulty, we appeal to the Fast Multipole Method which was developed in the context of modelling N-body problems. This method is then used to model the quasi-dynamic response of multiple faults, with complex geometries, that are governed by rate and state friction laws. Our preliminary findings tell us that when stress interaction between faults, due to complex geometry, is accounted then even strongly rate-weakening faults (a-b)<0 show a complex spectrum of slow slip and dynamic ruptures.
Conventionalism and integrable Weyl geometry
NASA Astrophysics Data System (ADS)
Pucheu, M. L.
2015-03-01
Since the appearance of Einstein's general relativity, gravitation has been associated to the space-time curvature. This theory introduced a geometrodynamic language which became a convenient tool to predict matter behaviour. However, the properties of space-time itself cannot be measurable by experiments. Taking Poincaré idea that the geometry of space-time is merely a convention, we show that the general theory of relativity can be completely reformulated in a more general setting, a generalization of Riemannian geometry, namely, the Weyl integrable geometry. The choice of this new mathematical language implies, among other things, that the path of particles and light rays should now correspond to Weylian geodesies. Such modification in the dynamic of bodies brings a new perception of physical phenomena that we will explore.
Frustrated Order on Extrinsic Geometries
Mbanga, Badel L.; Grason, Gregory M.; Santangelo, Christian D.
2012-01-03
We study, numerically and theoretically, defects in an anisotropic liquid that couple to the extrinsic geometry of a surface. Though the intrinsic geometry tends to confine topological defects to regions of large Gaussian curvature, extrinsic couplings tend to orient the order along the local direction of maximum or minimum bending. This additional frustration is generically unavoidable, and leads to complex ground-state thermodynamics. Using the catenoid as a prototype, we show, in contradistinction to the well-known effects of intrinsic geometry, that extrinsic curvature expels disclinations from the region of maximum curvature above a critical coupling threshold. On catenoids lacking an “inside-outside” symmetry, defects are expelled altogether above a critical neck size.
Quantum geometry and gravitational entropy
Simon, Joan; Balasubramanian, Vijay; Czech, Bart Iomiej; Larjo, Klaus; Marolf, Donald; Simon, Joan
2007-05-29
Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of asymptotically AdS_5 x S5 universes. In this sector we devise a"coarse-grained metric operator" whose eigenstates are well described by a single spacetime topology and geometry. We show that such half-BPS universes have a non-vanishing entropy if and only if the metric is singular, and that the entropy arises from coarse-graining the geometry. Finally, we use our entropy formula to find the most entropic spacetimes with fixed asymptotic moments beyond the global charges.
Numerical simulations of aerodynamic contribution of flows about a space-plane-type configuration
NASA Technical Reports Server (NTRS)
Matsushima, Kisa; Takanashi, Susume; Fujii, Kozo; Obayashi, Shigeru
1987-01-01
The slightly supersonic viscous flow about the space-plane under development at the National Aerospace Laboratory (NAL) in Japan was simulated numerically using the LU-ADI algorithm. The wind-tunnel testing for the same plane also was conducted with the computations in parallel. The main purpose of the simulation is to capture the phenomena which have a great deal of influence to the aerodynamic force and efficiency but is difficult to capture by experiments. It includes more accurate representation of vortical flows with high angles of attack of an aircraft. The space-plane shape geometry simulated is the simplified model of the real space-plane, which is a combination of a flat and slender body and a double-delta type wing. The comparison between experimental results and numerical ones will be done in the near future. It could be said that numerical results show the qualitatively reliable phenomena.
Detection of trans–cis flips and peptide-plane flips in protein structures
Touw, Wouter G.; Joosten, Robbie P.; Vriend, Gert
2015-07-28
A method is presented to detect peptide bonds that need either a trans–cis flip or a peptide-plane flip. A coordinate-based method is presented to detect peptide bonds that need correction either by a peptide-plane flip or by a trans–cis inversion of the peptide bond. When applied to the whole Protein Data Bank, the method predicts 4617 trans–cis flips and many thousands of hitherto unknown peptide-plane flips. A few examples are highlighted for which a correction of the peptide-plane geometry leads to a correction of the understanding of the structure–function relation. All data, including 1088 manually validated cases, are freely available and the method is available from a web server, a web-service interface and through WHAT-CHECK.
ERIC Educational Resources Information Center
Lee, Chun-Yi; Chen, Ming-Jang
2014-01-01
Previous studies on the effects of virtual and physical manipulatives have failed to consider the impact of prior knowledge on the efficacy of manipulatives. This study focuses on the learning of plane geometry in junior high schools, including the sum of interior angles in polygons, the sum of exterior angles in polygons, and the properties of…
The Need (?) for Descriptive Geometry in a World of 3D Modeling.
ERIC Educational Resources Information Center
Croft, Frank M. Jr.
1998-01-01
Evaluates the use of modern CAD methods to solve geometric problems. Solves descriptive geometry problems using the layout and position of the successive auxiliary views from the projection of three-dimensional figures onto a two-dimensional plane of paper. (CCM)
Broken chiral symmetry on a null plane
Beane, Silas R.
2013-10-15
On a null-plane (light-front), all effects of spontaneous chiral symmetry breaking are contained in the three Hamiltonians (dynamical Poincaré generators), while the vacuum state is a chiral invariant. This property is used to give a general proof of Goldstone’s theorem on a null-plane. Focusing on null-plane QCD with N degenerate flavors of light quarks, the chiral-symmetry breaking Hamiltonians are obtained, and the role of vacuum condensates is clarified. In particular, the null-plane Gell-Mann–Oakes–Renner formula is derived, and a general prescription is given for mapping all chiral-symmetry breaking QCD condensates to chiral-symmetry conserving null-plane QCD condensates. The utility of the null-plane description lies in the operator algebra that mixes the null-plane Hamiltonians and the chiral symmetry charges. It is demonstrated that in a certain non-trivial limit, the null-plane operator algebra reduces to the symmetry group SU(2N) of the constituent quark model. -- Highlights: •A proof (the first) of Goldstone’s theorem on a null-plane is given. •The puzzle of chiral-symmetry breaking condensates on a null-plane is solved. •The emergence of spin-flavor symmetries in null-plane QCD is demonstrated.
RSRM Propellant Grain Geometry Modification
NASA Technical Reports Server (NTRS)
Schorr, Andrew A.; Endicott, Joni B.; McCool, Alex (Technical Monitor)
2000-01-01
This document is composed of viewgraphs about the RSRM propellant grain geometry modification project, which hopes to improve personnel and system safety by modifying propellant grain geometry to improve structural factors of safety. Using techniques such as Finite Element Analysis to determine blend radii required to reduce localized stresses, and ballistic predictions to ensure that the ballistics, ignition transient and Block Model have not been adversely affected, the project hopes to build and test FSM-10 with a new design, and determine flight effectivity pending successful test evaluation.
Geometry, topology, and string theory
Varadarajan, Uday
2003-07-10
A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.
Geometry of generalized depolarizing channels
Burrell, Christian K.
2009-10-15
A generalized depolarizing channel acts on an N-dimensional quantum system to compress the 'Bloch ball' in N{sup 2}-1 directions; it has a corresponding compression vector. We investigate the geometry of these compression vectors and prove a conjecture of Dixit and Sudarshan [Phys. Rev. A 78, 032308 (2008)], namely, that when N=2{sup d} (i.e., the system consists of d qubits), and we work in the Pauli basis then the set of all compression vectors forms a simplex. We extend this result by investigating the geometry in other bases; in particular we find precisely when the set of all compression vectors forms a simplex.
A molecular dynamics study of freezing in a confined geometry
NASA Technical Reports Server (NTRS)
Ma, Wen-Jong; Banavar, Jayanth R.; Koplik, Joel
1992-01-01
The dynamics of freezing of a Lennard-Jones liquid in narrow channels bounded by molecular walls is studied by computer simulation. The time development of ordering is quantified and a novel freezing mechanism is observed. The liquid forms layers and subsequent in-plane ordering within a layer is accompanied by a sharpening of the layer in the transverse direction. The effects of channel size, the methods of quench, the liquid-wall interaction and the roughness of walls on the freezing mechanism are elucidated. Comparison with recent experiments on freezing in confined geometries is presented.
Stability analysis of expansion-free charged planar geometry
NASA Astrophysics Data System (ADS)
Sharif, M.; Bhatti, M. Zaeem Ul Haq
2015-02-01
This paper analyzes the stability of a collapsing matter distribution enclosed by plane symmetry in the presence of electromagnetic field. The field equations, matching conditions as well as conservation laws are formulated for non-static planar geometry. We apply perturbation to obtain the dynamical equation for Newtonian and post-Newtonian eras with expansion-free scenario. The role of electric charge with anisotropic matter configuration is studied in the stability regions. We conclude that this system becomes more stable as compared to the uncharged case.
Optimal focal-plane restoration
NASA Technical Reports Server (NTRS)
Reichenbach, Stephen E.; Park, Stephen K.
1989-01-01
Image restoration can be implemented efficiently by calculating the convolution of the digital image and a small kernel during image acquisition. Processing the image in the focal-plane in this way requires less computation than traditional Fourier-transform-based techniques such as the Wiener filter and constrained least-squares filter. Here, the values of the convolution kernel that yield the restoration with minimum expected mean-square error are determined using a frequency analysis of the end-to-end imaging system. This development accounts for constraints on the size and shape of the spatial kernel and all the components of the imaging system. Simulation results indicate the technique is effective and efficient.
Functional Aesthetic Occlusal Plane (FAOP)
Câmara, Carlos Alexandre; Martins, Renato Parsekian
2016-01-01
ABSTRACT Introduction: A reasonable exposure of incisors and gingival tissues is generally considered more attractive than excess or lack of exposure. A reasonable gingival exposure is considered to be around 0 to 2 mm when smiling and 2-4 mm exposure of the maxillary incisor edge when the lips are at rest. Objective: The aim of this paper is to present the Functional Aesthetic Occlusal Plane (FAOP), which aims to help in the diagnosis of the relationships established among molars, incisors and the upper lip. Conclusion: FAOP can complement an existing and established orthodontic treatment plan, facilitating the visualization of functional and aesthetic demands by giving a greater focus on the position of incisors in the relationship established among the incisors, molars and the upper lip stomion. PMID:27653271
Polyscale, polymodal fault geometries: evolution and predictive capability
NASA Astrophysics Data System (ADS)
Blenkinsop, T. G.; Carvell, J.; Clarke, G.; Tonelli, M.
2012-12-01
The Late Permian Rangal coal measures on the edge of the Nebo synclinorium in the Bowen basin, NE Queensland, Australia, are cut by normal faults. Mining operations allow 13 faults to be mapped in some detail to depths of 200m. These faults cut Tertiary intrusions and a reverse fault as well as the coal seams, and show no obvious signs of reactivation. The steeply dipping faults are clustered into groups of two to four, separated by hundreds of meters. The faults trend ENE and NE; both trends of faults dip in both directions, defining a quadrimodal geometry. The odd axis construction for these faults suggests that vertical shortening was accompanied by horizontal extension along both principal directions of 153° and 063°. The mapped extents of the faults are limited by erosion and the depth to which the faults have been drilled, but displacement profiles along the lengths of the faults show maxima within the fault planes. The displacement profiles suggest that the currently mapped faults have similar lengths to the total preserved lengths of the faults, and that they will continue into the unmined ground to a limited, but predictable extent. The fault planes have a complex geometry, with segments of individual faults showing a similar variability in orientation to the ensemble of fault planes: the fault planes themselves are polymodal. Displacement profiles show a good correlation with segment orientation. An odd axis construction based on fault segments, rather than individual faults, gives principal extension directions within 4° of the above results. The variable orientation of fault segments, the correlation of the displacement profiles with fault orientation, and the similarity between the segment and ensemble fault kinematics suggest that the faults have evolved by propagation and linking of smaller polymodal faults in the same bulk strain field.ross section of polymodal fault at Hail Creek coal mine
NASA Astrophysics Data System (ADS)
Ueda, Takashi; Shimura, Masayasu; Choi, Gyung-Min; Tanahashi, Mamoru; Miyauchi, Toshio
2008-11-01
To investigate three-dimensional flame structures of turbulent premixed flame, dual-plane planar laser induced fluorescence (PLIF) of CH radical has been developed. The newly-developed dual-plane CH PLIF is combined with single-plane OH PLIF and stereoscopic particle image velocimetry (SPIV) to clarify the relation between flame geometry and turbulence characteristics. The laser sheets for OH PLIF and SPIV measurement are located at the center of two planes for CH PLIF. The separation between these two CH PLIF planes is selected to 500μm. The measurement was conducted in relatively high Reynolds number methane-air turbulent jet premixed flame. The experimental results show that various three-dimensional flame structures such as the handgrip structure, which has been shown by DNS, are included in high Reynolds number turbulent premixed flame. It was shown that the simultaneous measurement containing newly-developed dual- plane CH PLIF is useful for investigating the three-dimensional flame structure.
Teaching Activity-Based Taxicab Geometry
ERIC Educational Resources Information Center
Ada, Tuba
2013-01-01
This study aimed on the process of teaching taxicab geometry, a non-Euclidean geometry that is easy to understand and similar to Euclidean geometry with its axiomatic structure. In this regard, several teaching activities were designed such as measuring taxicab distance, defining a taxicab circle, finding a geometric locus in taxicab geometry, and…
Xiao, Yong; Holod, Ihor; Wang, Zhixuan; Lin, Zhihong; Zhang, Taige
2015-02-15
Developments in gyrokinetic particle simulation enable the gyrokinetic toroidal code (GTC) to simulate turbulent transport in tokamaks with realistic equilibrium profiles and plasma geometry, which is a critical step in the code–experiment validation process. These new developments include numerical equilibrium representation using B-splines, a new Poisson solver based on finite difference using field-aligned mesh and magnetic flux coordinates, a new zonal flow solver for general geometry, and improvements on the conventional four-point gyroaverage with nonuniform background marker loading. The gyrokinetic Poisson equation is solved in the perpendicular plane instead of the poloidal plane. Exploiting these new features, GTC is able to simulate a typical DIII-D discharge with experimental magnetic geometry and profiles. The simulated turbulent heat diffusivity and its radial profile show good agreement with other gyrokinetic codes. The newly developed nonuniform loading method provides a modified radial transport profile to that of the conventional uniform loading method.
LOGO Based Instruction in Geometry.
ERIC Educational Resources Information Center
Yusuf, Mian Muhammad
The objective of this pretest-posttest Quasi-Experimental Design study was to determine the effects of LOGO Based Instruction (LBI) compared to instruction by teacher lecture and pencil-and-paper activities on: (1) students' understanding of the concepts of point, ray, line, and line segment; (2) students' attitudes toward learning geometry,…
Exploring Bundling Theory with Geometry
ERIC Educational Resources Information Center
Eckalbar, John C.
2006-01-01
The author shows how instructors might successfully introduce students in principles and intermediate microeconomic theory classes to the topic of bundling (i.e., the selling of two or more goods as a package, rather than separately). It is surprising how much students can learn using only the tools of high school geometry. To be specific, one can…
General Relativity: Geometry Meets Physics
ERIC Educational Resources Information Center
Thomsen, Dietrick E.
1975-01-01
Observing the relationship of general relativity and the geometry of space-time, the author questions whether the rest of physics has geometrical explanations. As a partial answer he discusses current research on subatomic particles employing geometric transformations, and cites the existence of geometrical definitions of physical quantities such…
Teaching Geometry According to Euclid.
ERIC Educational Resources Information Center
Hartshorne, Robin
2000-01-01
This essay contains some reflections and questions arising from encounters with the text of Euclid's Elements. The reflections arise out of the teaching of a course in Euclidean and non-Euclidean geometry to undergraduates. It is concluded that teachers of such courses should read Euclid and ask questions, then teach a course on Euclid and later…
Analogical Reasoning in Geometry Education
ERIC Educational Resources Information Center
Magdas, Ioana
2015-01-01
The analogical reasoning isn't used only in mathematics but also in everyday life. In this article we approach the analogical reasoning in Geometry Education. The novelty of this article is a classification of geometrical analogies by reasoning type and their exemplification. Our classification includes: analogies for understanding and setting a…
Foucault pendulum through basic geometry
NASA Astrophysics Data System (ADS)
von Bergmann, Jens; von Bergmann, HsingChi
2007-10-01
We provide a thorough explanation of the Foucault pendulum that utilizes its underlying geometry on a level suitable for science students not necessarily familiar with calculus. We also explain how the geometrically understood Foucault pendulum can serve as a prototype for more advanced phenomena in physics known as Berry's phase or geometric phases.
Spectral geometry of symplectic spinors
NASA Astrophysics Data System (ADS)
Vassilevich, Dmitri
2015-10-01
Symplectic spinors form an infinite-rank vector bundle. Dirac operators on this bundle were constructed recently by Habermann, K. ["The Dirac operator on symplectic spinors," Ann. Global Anal. Geom. 13, 155-168 (1995)]. Here we study the spectral geometry aspects of these operators. In particular, we define the associated distance function and compute the heat trace asymptotics.
Exploring Fractal Geometry with Children.
ERIC Educational Resources Information Center
Vacc, Nancy Nesbitt
1999-01-01
Heightens the awareness of elementary school teachers, teacher educators, and teacher-education researchers of possible applications of fractal geometry with children and, subsequently, initiates discussion about the appropriateness of including this new mathematics in the elementary curriculum. Presents activities for exploring children's…
Differential geometry meets the cell.
Marshall, Wallace F
2013-07-18
A new study by Terasaki et al. highlights the role of physical forces in biological form by showing that connections between stacked endoplasmic reticulum cisternae have a shape well known in classical differential geometry, the helicoid, and that this shape is a predictable consequence of membrane physics.
Instructional Identities of Geometry Students
ERIC Educational Resources Information Center
Aaron, Wendy Rose; Herbst, Patricio
2012-01-01
We inspect the hypothesis that geometry students may be oriented toward how they expect that the teacher will evaluate them as students or otherwise oriented to how they expect that their work will give them opportunities to do mathematics. The results reported here are based on a mixed-methods analysis of twenty-two interviews with high school…
Physiological optics and physical geometry.
Hyder, D J
2001-09-01
Hermann von Helmholtz's distinction between "pure intuitive" and "physical" geometry must be counted as the most influential of his many contributions to the philosophy of science. In a series of papers from the 1860s and 70s, Helmholtz argued against Kant's claim that our knowledge of Euclidean geometry was an a priori condition for empirical knowledge. He claimed that geometrical propositions could be meaningful only if they were taken to concern the behaviors of physical bodies used in measurement, from which it followed that it was posterior to our acquaintance with this behavior. This paper argues that Helmholtz's understanding of geometry was fundamentally shaped by his work in sense-physiology, above all on the continuum of colors. For in the course of that research, Helmholtz was forced to realize that the color-space had no inherent metrical structure. The latter was a product of axiomatic definitions of color-addition and the empirical results of such additions. Helmholtz's development of these views is explained with detailed reference to the competing work of the mathematician Hermann Grassmann and that of the young James Clerk Maxwell. It is this separation between 1) essential properties of a continuum, 2) supplementary axioms concerning distance-measurement, and 3) the behaviors of the physical apparatus used to realize the axioms, which is definitive of Helmholtz's arguments concerning geometry.
Noncommutative geometry inspired entropic inflation
NASA Astrophysics Data System (ADS)
Nozari, Kourosh; Akhshabi, Siamak
2011-06-01
Recently Verlinde proposed that gravity can be described as an emergent phenomena arising from changes in the information associated with the positions of material bodies. By using noncommutative geometry as a way to describe the microscopic microstructure of quantum spacetime, we derive modified Friedmann equation in this setup and study the entropic force modifications to the inflationary dynamics of early universe.
Math Sense: Algebra and Geometry.
ERIC Educational Resources Information Center
Howett, Jerry
This book is designed to help students gain the range of math skills they need to succeed in life, work, and on standardized tests; overcome math anxiety; discover math as interesting and purposeful; and develop good number sense. Topics covered in this book include algebra and geometry. Lessons are organized around four strands: (1) skill lessons…
Signature geometry and quantum engineering
NASA Astrophysics Data System (ADS)
Samociuk, Stefan
2013-09-01
As the operating frequency of electromagnetic based devices increase, physical design geometry is playing an ever more important role. Evidence is considered in support of a relationship between the dimensionality of primitive geometric forms, such as transistors, and corresponding electromagnetic coupling efficiency. The industry of electronics is defined as the construction of devices by the patterning of primitive forms to physical materials. Examples are given to show the evolution of these primitives, down to nano scales, are requiring exacting geometry and three dimensional content. Consideration of microwave monolithic integrated circuits,(MMIC), photonics and metamaterials,(MM), support this trend and also add new requirements of strict geometric periodicity and multiplicity. Signature geometries,(SG), are characterized by distinctive attributes and examples are given. The transcendent form transcode algorithm, (TTA) is introduced as a multi dimensional SG and its use in designing photonic integrated circuits and metamaterials is discussed . A creative commons licensed research database, TRANSFORM, containing TTA geometries in OASIS file formats is described. An experimental methodology for using the database is given. Multidimensional SG and extraction of three dimensional cross sections as primitive forms is discussed as a foundation for quantum engineering and the exploitation of phenomena other than the electromagnetic.
Cell division plane orientation based on tensile stress in Arabidopsis thaliana
Louveaux, Marion; Julien, Jean-Daniel; Mirabet, Vincent; Boudaoud, Arezki; Hamant, Olivier
2016-01-01
Cell geometry has long been proposed to play a key role in the orientation of symmetric cell division planes. In particular, the recently proposed Besson–Dumais rule generalizes Errera’s rule and predicts that cells divide along one of the local minima of plane area. However, this rule has been tested only on tissues with rather local spherical shape and homogeneous growth. Here, we tested the application of the Besson–Dumais rule to the divisions occurring in the Arabidopsis shoot apex, which contains domains with anisotropic curvature and differential growth. We found that the Besson–Dumais rule works well in the central part of the apex, but fails to account for cell division planes in the saddle-shaped boundary region. Because curvature anisotropy and differential growth prescribe directional tensile stress in that region, we tested the putative contribution of anisotropic stress fields to cell division plane orientation at the shoot apex. To do so, we compared two division rules: geometrical (new plane along the shortest path) and mechanical (new plane along maximal tension). The mechanical division rule reproduced the enrichment of long planes observed in the boundary region. Experimental perturbation of mechanical stress pattern further supported a contribution of anisotropic tensile stress in division plane orientation. Importantly, simulations of tissues growing in an isotropic stress field, and dividing along maximal tension, provided division plane distributions comparable to those obtained with the geometrical rule. We thus propose that division plane orientation by tensile stress offers a general rule for symmetric cell division in plants. PMID:27436908
Meniscus Shape and Wetting Competition of a Drop between a Cone and a Plane.
Liang, Yu-En; Weng, Yu-Hsuan; Tsao, Heng-Kwong; Sheng, Yu-Jane
2016-08-23
The formation of a liquid bridge between a cone and a plane is related to dip-pen nanolithography. The meniscus shape and rupture process of a liquid meniscus between a cone and a plane are investigated by Surface Evolver, many-body dissipative particle dynamics, and macroscopic experiments. Dependent on the cone geometry, cone-plane separation, and wetting properties of cone and plane, three types of menisci can be observed before rupture and two types of wetting competition outcomes are seen after breakup. It is interesting to find that after rupture, the bulk of the liquid bridge volume is not necessarily retained by the cone which is more wettable. In fact, a sharp hydrophilic cone often loses wetting competition to a hydrophobic plane. To explain our findings, the "apparent" contact angle of the cone is introduced and the behavior of drop-on-cone/plane system is analogous to that of a liquid bridge between two parallel planes based on this concept. PMID:27483140
NASA Astrophysics Data System (ADS)
Pechereau, Francois; Jansky, Jaroslav; Bourdon, Anne
2012-10-01
In recent years, experimental studies on flue gas treatment have demonstrated the efficiency of plasma assisted catalysis for the treatment of a wide range of pollutants at a low energetic cost. In plasma reactors, usual catalyst supports are pellets, monoliths or porous media, and then atmospheric pressure discharges have to interact with many obstacles and to propagate in microcavities and pores. As a first step to better understand atmospheric pressure discharge dynamics in these complex geometries, in this work, we have carried out numerical simulations using a 2D-axisymmetric fluid model for a point-to-plane discharge with a dielectric plane obstacle placed in the path of the discharge. First, we have simulated the discharge ignition at the point electrode, its propagation in the gap and its impact and expansion on the dielectric plane. Depending on the applied voltage, the dielectric plane geometry and permittivity, we have identified conditions for the reignition of a second discharge behind the plane obstacle. These conditions will be discussed and compared with recent experimental results on the same configuration.
A Collaborative Knowledge Plane for Autonomic Networks
NASA Astrophysics Data System (ADS)
Mbaye, Maïssa; Krief, Francine
Autonomic networking aims to give network components self-managing capabilities. Several autonomic architectures have been proposed. Each of these architectures includes sort of a knowledge plane which is very important to mimic an autonomic behavior. Knowledge plane has a central role for self-functions by providing suitable knowledge to equipment and needs to learn new strategies for more accuracy.However, defining knowledge plane's architecture is still a challenge for researchers. Specially, defining the way cognitive supports interact each other in knowledge plane and implementing them. Decision making process depends on these interactions between reasoning and learning parts of knowledge plane. In this paper we propose a knowledge plane's architecture based on machine learning (inductive logic programming) paradigm and situated view to deal with distributed environment. This architecture is focused on two self-functions that include all other self-functions: self-adaptation and self-organization. Study cases are given and implemented.
Plane Wave in the System of N Particles with Zero Angular Momentum
NASA Astrophysics Data System (ADS)
Meremianin, A. V.
2016-09-01
The wave function of the system of N ≥ 3 free particles having zero total angular momentum is considered. This function is defined as the zeroth order multipole coefficient in the expansion of the product of N plane waves over the set of finite rotation matrices (i.e. Wigner D-functions). Several integral representations for that wave-function are obtained. It is demonstrated that the structure of the wave function for arbitrary number of particles remains that of the four-particle case. Special attention is paid to the "in-plane" geometry when particle's momenta vectors (or their conjugated Jacobi vectors) are coplanar.
Dynamics of Crowd Behaviors: From Complex Plane to Quantum Random Fields
NASA Astrophysics Data System (ADS)
Ivancevic, Vladimir G.; Reid, Darryn J.
2015-11-01
The following sections are included: * Complex Plane Dynamics of Crowds and Groups * Introduction * Complex-Valued Dynamics of Crowd and Group Behaviors * Kähler Geometry of Crowd and Group Dynamics * Computer Simulations of Crowds and Croups Dynamics * Braids of Agents' Behaviors in the Complex Plane * Hilbert-Space Control of Crowds and Groups Dynamics * Quantum Random Fields: A Unique Framework for Simulation, Optimization, Control and Learning * Introduction * Adaptive Quantum Oscillator * Optimization and Learning on Banach and Hilbert Spaces * Appendix * Complex-Valued Image Processing * Linear Integral Equations * Riemann-Liouville Fractional Calculus * Rigorous Geometric Quantization * Supervised Machine-Learning Methods * First-Order Logic and Quantum Random Fields
Duel-Plane Optical Disdrometer
NASA Astrophysics Data System (ADS)
Winsky, B. E.; Eichinger, W. E.
2011-12-01
Acquiring better drop-size distributions of rainfall will improve our understanding of the spatial and temporal variability of rainfall. In order to fully capture the spatial and temporal variability of rainfall, a robust, calibration free, low-cost instrument that provides an accurate drop-size distribution is required. Therefore, The University of Iowa Lidar Group has developed and built a new duel-plane optical disdrometer that meets these criteria. Two sheets of laser light, vertically spaced by 1 cm are produced by two 670nm laser beams passing through a collecting lens and culminating lens, respectively. The two sheets of laser light then pass through a convex lens located 20 cm from the lasers that focuses the light on a photo detector. A computer reads in and stores the voltages at 10 kHz. The velocity, diameter, shape and drop-size distribution of raindrops are extracted from the voltage measurements. Rainfall data collected in Iowa City, IA tested our disdrometer's robustness and accuracy of providing drop-size distributions. Our distrometer is advantageous because it is simple, low-cost, and requires no calibration.
Radioactivity in the galactic plane
NASA Technical Reports Server (NTRS)
Walraven, G. D.; Haymes, R. C.
1976-01-01
The paper reports the detection of a large concentration of interstellar radioactivity during balloon-altitude measurements of gamma-ray energy spectra in the band between 0.02 and 12.27 MeV from galactic and extragalactic sources. Enhanced counting rates were observed in three directions towards the plane of the Galaxy; a power-law energy spectrum is computed for one of these directions (designated B 10). A large statistical deviation from the power law in a 1.0-FWHM interval centered near 1.16 MeV is discussed, and the existence of a nuclear gamma-ray line at 1.15 MeV in B 10 is postulated. It is suggested that Ca-44, which emits gamma radiation at 1.156 MeV following the decay of radioactive Sc-44, is a likely candidate for this line, noting that Sc-44 arises from Ti-44 according to explosive models of supernova nucleosynthesis. The 1.16-MeV line flux inferred from the present data is shown to equal the predicted flux for a supernova at a distance of approximately 3 kpc and an age not exceeding about 100 years.
Galactic plane gamma-radiation
NASA Technical Reports Server (NTRS)
Hartman, R. C.; Kniffen, D. A.; Thompson, D. J.; Fichtel, C. E.; Ogelman, H. B.; Tumer, T.; Ozel, M. E.
1979-01-01
Analysis of the SAS 2 data together with the COS B results shows that the distribution of galactic gamma-radiation has several similarities to that of other large-scale tracers of galactic structure. The radiation is primarily confined to a thin disc which exhibits offsets from b = 0 degrees similar to warping at radio frequencies. The principal distinction of the gamma-radiation is a stronger contrast in intensity between the region from 310 to 45 degrees in longitude and the regions away from the center that can be attributed to a variation in cosmic-ray density as a function of position in Galaxy. The diffuse galactic gamma-ray energy spectrum shows no significant variation in direction, and the spectrum seen along the plane is the same as that for the galactic component of the gamma-radiation at high altitudes. The uniformity of the galactic gamma-ray spectrum, the smooth decrease in intensity as a function of altitude, and the absence of any galactic gamma-ray sources at high altitudes indicate a diffuse origin for bulk of the galactic gamma-radiation rather than a collection of localized sources.
Harmonic plane wave propagation in gyroelectric media
NASA Astrophysics Data System (ADS)
Hillion, Pierre
2006-05-01
We analyse the behaviour of harmonic plane waves in unbounded gyroelectric media once the refractive index in the direction of propagation is known from the Fresnel equation. We get, for the electric and magnetic fields, analytical expressions simple enough to use in a plane wave spectrum representation of more structured electromagnetic fields in these media. We also discuss the reflection and refraction of harmonic plane waves at the boundary between an isotropic medium and a gyroelectric material.
High-order exact solutions for pseudo-plane ideal flows
NASA Astrophysics Data System (ADS)
Sun, Che
2016-08-01
A steady pseudo-plane ideal flow (PIF) model is derived from the 3D Euler equations under Boussinesq approximation. The model is solved analytically to yield high-degree polynomial exact solutions. Unlike quadratic flows, the cubic and quartic solutions display reduced geometry in the form of straightline jet, circular vortex, and multipolar strain field. The high-order circular-vortex solutions are vertically aligned and even the non-aligned multipolar strain-field solutions display vertical concentricity. Such geometry reduction is explained by an analytical theorem stating that only straightline jet and circular vortex have functional solutions to the PIF model.
Connecting the behavior of granular layers on inclined planes to the nonlocal fluidity model
NASA Astrophysics Data System (ADS)
Kamrin, Ken; Henann, David
2014-03-01
Recently, a grain-size-sensitive rheology for granular flow has been proposed based on the nonlocal fluidity concept. While primarily intended to describe the effect that grain size has on developed flow fields, this talk will show how the same framework also explains the Hstop phenomenon commonly observed in thin granular layers on inclined planes, in which thinner layers appear to be stronger than thicker ones. Moreover, the experimental phase diagram for flow vs no-flow of a layer of glass beads in this geometry is well-predicted using the same modeling parameters that describe the steady flow of those beads in split-bottom cells and other geometries.
3D geometry analysis of the medial meniscus--a statistical shape modeling approach.
Vrancken, A C T; Crijns, S P M; Ploegmakers, M J M; O'Kane, C; van Tienen, T G; Janssen, D; Buma, P; Verdonschot, N
2014-10-01
The geometry-dependent functioning of the meniscus indicates that detailed knowledge on 3D meniscus geometry and its inter-subject variation is essential to design well functioning anatomically shaped meniscus replacements. Therefore, the aim of this study was to quantify 3D meniscus geometry and to determine whether variation in medial meniscus geometry is size- or shape-driven. Also we performed a cluster analysis to identify distinct morphological groups of medial menisci and assessed whether meniscal geometry is gender-dependent. A statistical shape model was created, containing the meniscus geometries of 35 subjects (20 females, 15 males) that were obtained from MR images. A principal component analysis was performed to determine the most important modes of geometry variation and the characteristic changes per principal component were evaluated. Each meniscus from the original dataset was then reconstructed as a linear combination of principal components. This allowed the comparison of male and female menisci, and a cluster analysis to determine distinct morphological meniscus groups. Of the variation in medial meniscus geometry, 53.8% was found to be due to primarily size-related differences and 29.6% due to shape differences. Shape changes were most prominent in the cross-sectional plane, rather than in the transverse plane. Significant differences between male and female menisci were only found for principal component 1, which predominantly reflected size differences. The cluster analysis resulted in four clusters, yet these clusters represented two statistically different meniscal shapes, as differences between cluster 1, 2 and 4 were only present for principal component 1. This study illustrates that differences in meniscal geometry cannot be explained by scaling only, but that different meniscal shapes can be distinguished. Functional analysis, e.g. through finite element modeling, is required to assess whether these distinct shapes actually influence
Nanostructured carbon films with oriented graphitic planes
Teo, E. H. T.; Kalish, R.; Kulik, J.; Kauffmann, Y.; Lifshitz, Y.
2011-03-21
Nanostructured carbon films with oriented graphitic planes can be deposited by applying energetic carbon bombardment. The present work shows the possibility of structuring graphitic planes perpendicular to the substrate in following two distinct ways: (i) applying sufficiently large carbon energies for deposition at room temperature (E>10 keV), (ii) utilizing much lower energies for deposition at elevated substrate temperatures (T>200 deg. C). High resolution transmission electron microscopy is used to probe the graphitic planes. The alignment achieved at elevated temperatures does not depend on the deposition angle. The data provides insight into the mechanisms leading to the growth of oriented graphitic planes under different conditions.
Plane wave spectrum of electromagnetic beams
NASA Astrophysics Data System (ADS)
Doicu, A.; Wriedt, T.
1997-02-01
A plane wave spectrum method of Gaussian beams can be derived by using Davis' approximations for the vector potential. An equivalent vector potential is introduced by considering the inverse Fourier transform of the spectrum function of the original vector potential in a given plane. The electromagnetic field, which corresponds to the equivalent vector potential, satisfies Maxwell's equations and can be written as a sum of plane waves. The beam shape coefficients, or the expansion coefficients in terms of regular spherical vector wave functions, are expressed as simple integrals. This version of the plane wave spectrum method offers the possibility to compute higher-order corrections for Gaussian beams.
Gully geometry: what are we measuring?
NASA Astrophysics Data System (ADS)
Casalí, Javier; Giménez, Rafael; Ángel Campo, Miguel
2014-05-01
Gully erosion has attracted the attention of many scientists during the last decades, and gullies are an important source of sediment within catchments. For succeeding in gully erosion research, gullies must be properly characterized. Characterization includes the determination of gully morphology and volume, being the definition of gully width (W) and depth (D) -and consequently related variables such as the well-known W/D ratio- key issues toward to this goal. However, and surprisingly, universally accepted criteria (rules or guidance) to define gully morphology are lacking. This because the protocol every researcher follows to measure the eroded channel geometry is generally taken for granted and most of the time even no explanation is given about it. For example, when analyzing a gully cross section we usually just identify gully depth with gully maximum depth. But, is this the right protocol? What does this length really represent? What is its meaning? All this uncertainties can lead to non-comparable results and then important inconsistencies. So, to define universal rules of procedure would allow gully scientists "speak the same language" and then deliver truly comparable gully geometry and volume. On the other hand, there are other misunderstandings. For example, very frequently we characterize or depict a whole gully only through some of its cross sections. Again, is this correct? The problem is even more complex when considering that gully geometry may (largely) change along the channel. The main aim of this presentation is to highlight some (unnoticed) common flaws when measuring and describing gully geometry, hoping ultimately to open a debate on that subject. For this last purpose, a conceptual approach to define gully cross section width and other derived variables is firstly proposed. It is based on the subtraction of a highly detailed digital elevation model of a landscape surface containing the studied gully (DEM1) from a detailed spatial
Stringy differential geometry, beyond Riemann
NASA Astrophysics Data System (ADS)
Jeon, Imtak; Lee, Kanghoon; Park, Jeong-Hyuck
2011-08-01
While the fundamental object in Riemannian geometry is a metric, closed string theories call for us to put a two-form gauge field and a scalar dilaton on an equal footing with the metric. Here we propose a novel differential geometry that treats the three objects in a unified manner, manifests not only diffeomorphism and one-form gauge symmetry but also O(D,D) T-duality, and enables us to rewrite the known low energy effective action of them as a single term. Further, we develop a corresponding vielbein formalism and gauge the internal symmetry that is given by a direct product of two local Lorentz groups, SO(1,D-1)×SŌ(1,D-1). We comment that the notion of cosmological constant naturally changes.
Geometry-invariant resonant cavities
Liberal, I.; Mahmoud, A. M.; Engheta, N.
2016-01-01
Resonant cavities are one of the basic building blocks in various disciplines of science and technology, with numerous applications ranging from abstract theoretical modelling to everyday life devices. The eigenfrequencies of conventional cavities are a function of their geometry, and, thus, the size and shape of a resonant cavity is selected to operate at a specific frequency. Here we demonstrate theoretically the existence of geometry-invariant resonant cavities, that is, resonators whose eigenfrequencies are invariant with respect to geometrical deformations of their external boundaries. This effect is obtained by exploiting the unusual properties of zero-index metamaterials, such as epsilon-near-zero media, which enable decoupling of the temporal and spatial field variations in the lossless limit. This new class of resonators may inspire alternative design concepts, and it might lead to the first generation of deformable resonant devices. PMID:27010103
Geometry of area without length
NASA Astrophysics Data System (ADS)
Ho, Pei-Ming; Inami, Takeo
2016-01-01
To define a free string by the Nambu-Goto action, all we need is the notion of area, and mathematically the area can be defined directly in the absence of a metric. Motivated by the possibility that string theory admits backgrounds where the notion of length is not well defined but a definition of area is given, we study space-time geometries based on the generalization of a metric to an area metric. In analogy with Riemannian geometry, we define the analogues of connections, curvatures, and Einstein tensor. We propose a formulation generalizing Einstein's theory that will be useful if at a certain stage or a certain scale the metric is ill defined and the space-time is better characterized by the notion of area. Static spherical solutions are found for the generalized Einstein equation in vacuum, including the Schwarzschild solution as a special case.
Geometry Dependence of Stellarator Turbulence
H.E. Mynick, P. Xanthopoulos and A.H. Boozer
2009-08-10
Using the nonlinear gyrokinetic code package GENE/GIST, we study the turbulent transport in a broad family of stellarator designs, to understand the geometry-dependence of the microturbulence. By using a set of flux tubes on a given flux surface, we construct a picture of the 2D structure of the microturbulence over that surface, and relate this to relevant geometric quantities, such as the curvature, local shear, and effective potential in the Schrodinger-like equation governing linear drift modes.
Tian, Xiaojuan; Itkis, Mikhail E.; Haddon, Robert C.
2015-01-01
The in-plane alignment of graphite nanoplatelets (GNPs) in thin thermal interface material (TIM) layers suppresses the though-plane heat transport thus limiting the performance of GNPs in the geometry normally required for thermal management applications. Here we report a disruption of the GNP in-plane alignment by addition of spherical microparticles. The degree of GNP alignment was monitored by measurement of the anisotropy of electrical conductivity which is extremely sensitive to the orientation of high aspect ratio filler particles. Scanning Electron Microscopy images of TIM layer cross-sections confirmed the suppression of the in-plane alignment. The hybrid filler formulations reported herein resulted in a synergistic enhancement of the through-plane thermal conductivity of GNP/Al2O3 and GNP/Al filled TIM layers confirming that the control of GNP alignment is an important parameter in the development of highly efficient GNP and graphene-based TIMs. PMID:26279183
Realizing in-plane surface diffraction by x-ray multiple-beam diffraction with large incidence angle
Huang, Xian-Rong Gog, Thomas; Assoufid, Lahsen; Peng, Ru-Wen; Siddons, D. P.
2014-11-03
Based on rigorous dynamical-theory calculations, we demonstrate the principle of an x-ray multiple-beam diffraction (MBD) scheme that overcomes the long-lasting difficulties of high-resolution in-plane diffraction from crystal surfaces. This scheme only utilizes symmetric reflection geometry with large incident angles but activates the out-of-plane and in-plane diffraction processes simultaneously and separately in the continuous MBD planes. The in-plane diffraction is realized by detoured MBD, where the intermediate diffracted waves propagate parallel to the surface, which corresponds to an absolute Bragg surface diffraction configuration that is extremely sensitive to surface structures. A series of MBD diffraction and imaging techniques may be developed from this principle to study surface/interface (misfit) strains, lateral nanostructures, and phase transitions of a wide range of (pseudo)cubic crystal structures, including ultrathin epitaxial films and multilayers, quantum dots, strain-engineered semiconductor or (multi)ferroic materials, etc.
Experimental realization of a metamaterial detector focal plane array.
Shrekenhamer, David; Xu, Wangren; Venkatesh, Suresh; Schurig, David; Sonkusale, Sameer; Padilla, Willie J
2012-10-26
We present a metamaterial absorber detector array that enables room-temperature, narrow-band detection of gigahertz (GHz) radiation in the S band (2-4 GHz). The system is implemented in a commercial printed circuit board process and we characterize the detector sensitivity and angular dependence. A modified metamaterial absorber geometry allows for each unit cell to act as an isolated detector pixel and to collectively form a focal plane array . Each pixel can have a dedicated microwave receiver chain and functions together as a hybrid device tuned to maximize the efficiency of detected power. The demonstrated subwavelength pixel shows detected sensitivity of -77 dBm, corresponding to a radiation power density of 27 nW/m(2), with pixel to pixel coupling interference below -14 dB at 2.5 GHz.
Granular flow down an inclined plane: Bagnold scaling and rheology.
Silbert, L E; Ertaş, D; Grest, G S; Halsey, T C; Levine, D; Plimpton, S J
2001-11-01
We have performed a systematic, large-scale simulation study of granular media in two and three dimensions, investigating the rheology of cohesionless granular particles in inclined plane geometries, i.e., chute flows. We find that over a wide range of parameter space of interaction coefficients and inclination angles, a steady-state flow regime exists in which the energy input from gravity balances that dissipated from friction and inelastic collisions. In this regime, the bulk packing fraction (away from the top free surface and the bottom plate boundary) remains constant as a function of depth z, of the pile. The velocity profile in the direction of flow vx(z) scales with height of the pile H, according to vx(z) proportional to H(alpha), with alpha=1.52+/-0.05. However, the behavior of the normal stresses indicates that existing simple theories of granular flow do not capture all of the features evidenced in the simulations.
Jet mixing into a heated cross flow in a cylindrical duct: Influence of geometry and flow variations
NASA Technical Reports Server (NTRS)
Hatch, M. S.; Sowa, W. A.; Samuelsen, G. S.; Holdeman, J. D.
1992-01-01
To examine the mixing characteristics of jets in an axi-symmetric can geometry, temperature measurements were obtained downstream of a row of cold jets injected into a heated cross stream. Parametric, non-reacting experiments were conducted to determine the influence of geometry and flow variations on mixing patterns in a cylindrical configuration. Results show that jet to mainstream momentum flux ratio and orifice geometry significantly impact the mixing characteristics of jets in a can geometry. For a fixed number of orifices, the coupling between momentum flux ratio and injector determines (1) the degree of jet penetration at the injection plane, and (2) the extent of circumferential mixing downstream of the injection plane. The results also show that, at a fixed momentum flux ratio, jet penetration decreases with (1) an increase in slanted slot aspect ratio, and (2) an increase in the angle of the slots with respect to the mainstream direction.
Network geometry with flavor: From complexity to quantum geometry
NASA Astrophysics Data System (ADS)
Bianconi, Ginestra; Rahmede, Christoph
2016-03-01
Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d -dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s =-1 ,0 ,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d . In d =1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d >1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t . Interestingly the NGF remains fully classical but
Network geometry with flavor: From complexity to quantum geometry.
Bianconi, Ginestra; Rahmede, Christoph
2016-03-01
Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d-dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s=-1,0,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d. In d=1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d>1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t. Interestingly the NGF remains fully classical but its
Network geometry with flavor: From complexity to quantum geometry.
Bianconi, Ginestra; Rahmede, Christoph
2016-03-01
Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d-dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s=-1,0,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d. In d=1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d>1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t. Interestingly the NGF remains fully classical but its
Solar Impulse's Solar-Powered Plane
Moniz, Ernest; Piccard, Bertrand; Reicher, Dan
2016-07-12
Solar Impulse lands in Washington, DC at Washington Dulles International Airport as part of its journey across the United States. Secretary Ernest Moniz speaks about how advancements like those at the Department of Energy are leading the way for innovations like the solar-powered plane. Footage of the solar-powered plane courtesy of Solar Impulse.
Aero-space plane figures of merit
NASA Technical Reports Server (NTRS)
Hunt, James L.; Martin, John G.
1992-01-01
The design environment of the aerospace plane is variable rich, intricately networked and sensitivity intensive. To achieve a viable design necessitates addressing three principal elements: knowledge of the 'figures of merit' and their relationships, the synthesis procedure, and the synergistic integration of advanced technologies across the discipline spectrum. This paper focuses on the 'figures of merit' that create the design of an aerospace plane.
Slipping and Rolling on an Inclined Plane
ERIC Educational Resources Information Center
Aghamohammadi, Cina; Aghamohammadi, Amir
2011-01-01
In the first part of the paper, using a direct calculation two-dimensional motion of a particle sliding on an inclined plane is investigated for general values of friction coefficient ([mu]). A parametric equation for the trajectory of the particle is also obtained. In the second part of the paper, the motion of a sphere on the inclined plane is…
Solar Impulse's Solar-Powered Plane
Moniz, Ernest; Piccard, Bertrand; Reicher, Dan
2013-07-08
Solar Impulse lands in Washington, DC at Washington Dulles International Airport as part of its journey across the United States. Secretary Ernest Moniz speaks about how advancements like those at the Department of Energy are leading the way for innovations like the solar-powered plane. Footage of the solar-powered plane courtesy of Solar Impulse.
Ground vortex formation for uniform and nonuniform jets impinging on a ground plane
NASA Astrophysics Data System (ADS)
Kuhlman, John M.; Cavage, William M.
1992-08-01
An experimental investigation of the impingement of a single circular jet on a ground plane in a cross flow is presented. This geometry is a simplified model of the interaction of propulsive jet exhaust from a V/STOL aircraft with the ground in forward flight. Variation of observed ground vortex size with cross flow-to-jet velocity ratio is consistent with previous observations.
Direct writing of in-plane-gated nanostructures by focused laser beam-induced doping
NASA Astrophysics Data System (ADS)
Baumgartner, P.; Wegscheider, W.; Bichler, M.; Groos, G.; Abstreiter, G.
1998-07-01
The fabrication technique of local doping with a focused laser beam is employed to fabricate electronic nanostructures. Zn-doped regions are used to fabricate in-plane electron channels in a high mobility GaAs/AlGaAs heterostructure. The operation of different devices, like quantum point contacts, single electron transistors or Aharonov-Bohm rings, is demonstrated. The coplanar gate geometry improves the performance of the devices in charge sensing applications.
Elasticity Solution of an Adhesively Bonded Cover Plate of Various Geometries
NASA Technical Reports Server (NTRS)
Aksel, G. N.; Erdogan, F.
1985-01-01
The plane strain of adhesively bonded structures consisting of two different isotropic adherends is considered. By expressing the x-y components of the displacements in terms of Fourier integrals and using the corresponding boundary and continuity conditions, the integral equations for the general problem are obtained and solved numerically by applying Gauss-Chebyshev integration scheme. The shear and the normal stresses in the adhesive are calculated for various geometries and material properties for a stiffened plate under uniaxial tension. Numerical results involving the stress intensity factors and the strain energy release rate are presented. The closed-form expressions for the Fredholm kernels are provided to obtain the solution for an arbitrary geometry and material properties. For the general geometry, the contribution of the normal stress is quite significant, while for symmetric geometries, the shear stress is dominant, the normal stress vanishes if the adherends are of the same material and the same thickness.
Extracting oblique planes from serial CT sections.
Rhodes, M L; Glenn, W V; Azaawi, Y M
1980-10-01
Although geometric principles describing planes oblique to an orthogonal image data set are well understood, no implementation has been offered for their practical specification, extraction, and display in a clinical environment. Fast image generation and ease of user specification-requisite credentials for successful clinical implementations-are handicapped by the large volume of data to process. Other difficulties further complicate an interactive solution. Once oblique planes are generated, their orientation is often difficult to perceive without visual cues that aid their registration with standard image formats. In addition, Moire patterns introduced by digital aliasing often currupt resultant views. In this paper, techniques are outlined for simplifying oblique plane specification, a methodology is presented for image construction, and an interactive approach is illustrated to register images for such general view planes. Finally, digital aliasing of oblique planes is discussed, and a solution is given for this application.
ERIC Educational Resources Information Center
Kutluca, Tamer
2013-01-01
The aim of this study is to investigate the effect of dynamic geometry software GeoGebra on Van Hiele geometry understanding level of students at 11th grade geometry course. The study was conducted with pre and posttest control group quasi-experimental method. The sample of the study was 42 eleventh grade students studying in the spring term of…
Study the Z-Plane Strip Capacitance
Parikh, H.; Swain, S.; /SLAC
2005-12-15
The BaBaR detector at the Stanford Linear Accelerator Center is currently undergoing an upgrade to improve its muon and neutral hadron detection system. The Resistive Plate Chambers (RPCs) that had been used till now have deteriorated in performance over the past few years and are being replaced by Limited Streamer Tube (LSTs). Each layer of the system consists of a set of up to 10 streamer tube modules which provide one coordinate ({phi} coordinate) and a single ''Z-plane'' which provides the Z coordinate of the hit. The large area Z-planes (up to 12m{sup 2}) are 1mm thick and contain 96 copper strips that detect the induced charge from avalanches created in the streamer tube wires. All the Z-planes needed for the upgrade have already been constructed, but only a third of the planes were installed last summer. After installing the 24 Z-planes last year, it was learned that 0.7% of the strips were dead when put inside the detector. This was mainly due to the delicate solder joint between the read-out cable and the strip, and since it is difficult to access or replace the Z-planes inside the detector, it is very important to perform various tests to make sure that the Z-planes will be efficient and effective in the long term. We measure the capacitance between the copper strips and the ground plane, and compare it to the theoretical value that we expect. Instead of measuring the capacitance channel by channel, which would be a very tedious job, we developed a more effective method of measuring the capacitance. Since all the Z-planes were built at SLAC, we also built a smaller 46 cm by 30 cm Z-plane with 12 strips just to see how they were constructed and to gain a better understanding about the solder joints.
The invariable plane of the solar system
NASA Astrophysics Data System (ADS)
Souami, D.; Souchay, J.
2012-04-01
The invariable plane of the solar system is defined as the plane perpendicular to the total angular momentum of the system and passing through its centre of mass. The idea of using the invariable plane as a reference plane in the study of the dynamics of solar system bodies goes back at least to Laplace [3]. The latest study on this plane dates back to Burkhardt [2]. The aim of this work is to determine at best the orientation of the invariable plane with respect to both the ICRS and the equinox-ecliptic of J2000.0, and to evaluate the accuracy of its determination. Such a determination is of fundamental interest in the topic of solar system studies, as suggested by the WGCCRE 2009 [1] for the determination of planet's and satellites' rotational elements. Using the long-term numerical ephemerides DE405, DE406 [6] and INPOP10a[4] over their entire available time span, we compute the total angular momentum of the solar system, as well as the individual contribution of each planet. We then deduce the orientation of the invariable plane for each ephemeris, and establish their relative differences. Preliminary results can be found in [5]. Here we update them with more accurate data, and a more complete analysis of the problem, taking into account the effect of the dwarf planet (1) Ceres as well as two of the biggest asteroids, (4) Vesta and (2) Pallas. Moreover, we give the orbital elements (inclination, longitude of the ascending node) with respect to the invariable plane. As given its accuracy of determination, and its fundamental dynamical meaning, the invariable plane provides a permanent natural reference plane that should be used when studying solar system dynamics, instead of the ecliptic. Thus, we recommend referring to it when working on long-term dynamics.
Low Ekman Number Dynamos in Cartesian Geometry
NASA Astrophysics Data System (ADS)
Stellmach, S.; Hansen, U.
2002-12-01
Fully self consistent 3d dynamo simulations in spherical geometry have become an important part of geomagnetic research during the last years. The parameter range accesible for these models is quite limited and far away from the values estimated for the Earth's core. Especially viscous effects are overestimated by many orders of magnitude in all models published today. In view of these difficulties, we use a plane layer dynamo model which is computationally less demanding to study dynamo processes in the regime of low viscosity. The calculations we present employ Ekman numbers in the range E=10-4-5 x 10-6 without using parameterizations such as hyperdiffusion. Full inertia with Pr=1 is included where Pr denotes the Prandtl number. We find subcritical dynamos which remain stable for two magnetic decay times and an example of an initially stable subcritical dynamo which starts to decay after more than one magnetic diffusion time. For both supercritical and subcritical cases, the force balances are analyzed in detail. We show that at low Ekman number the leading order force balance in our calculations is between Coriolis, buoyancy, pressure and Lorentz forces while both inertial and viscous forces are small in the bulk of the layer. The resulting flow is strongly influenced by the Taylor-Proudman effect and dominated by small scale structures. In the range of investigated Ekman numbers, the dominating length scales decrease with decreasing E. Although Taylor's constraint is not satisfied in the entire domain we find that the spatial mean value of the normalized Taylor integrals decreases with decreasing Ekman number.
Observation angle and plane characterisation for ISAR imaging of LEO space objects
NASA Astrophysics Data System (ADS)
Chen, Jin; Fu, Tuo; Chen, Defeng; Gao, Meiguo
2016-07-01
For inverse synthetic aperture radar (ISAR) imaging of low Earth orbit (LEO) space objects, examining the variations in the image plane of the object over the entire visible arc period allows more direct characterisation of the variations in the object imaging. In this study, the ideal turntable model was extended to determine the observation geometry of near-circular LEO objects. Two approximations were applied to the observation model to calculate the image plane's normal and observation angles for near-circular orbit objects. One approximation treats the orbit of the space object as a standard arc relative to the Earth during the radar observation period, and the other omits the effect of the rotation of the Earth on the observations. First, the closed-form solution of the image plane normal in various attitude-stabilisation approaches was determined based on geometric models. The characteristics of the image plane and the observation angle of the near-circular orbit object were then analysed based on the common constraints of the radar line-of-sight (LOS). Subsequently, the variations in the image plane and the geometric constraints of the ISAR imaging were quantified. Based on the image plane's normal, the rotational angular velocity of the radar LOS was estimated. The cross-range direction of the ISAR image was then calibrated. Three-dimensional imaging was then reconstructed based on dual station interferometry. Finally, simulations were performed to verify the result of the three-dimensional interferometric reconstruction and to calculate the reconstruction's precision errors.
[The Effect of Observation Geometry on Polarized Skylight Spectrum].
Zhang, Ren-bin; Wang, Ling-mei; Gao, Jun; Wang, Chi
2015-03-01
Study on polarized skylight spectral characters while observation geometry changing in different solar zenith angles (SZA), viewing zenith angles (VZA) or relative azimuth angles (RAA). Simulation calculation of cloudless daylight polarimetric spectrum is realized based on the solver, vector discrete ordinate method, of radiative transfer equation. In the Sun's principal and perpendicular plane, the spectral irradiance data, varying at wavelengths in the range between 0.4 and 3 μm, are calculated to extend the atmospheric polarization spectral information under the conditions: the MODTRAN solar reference spectrur is the only illuminant source; the main influencing factors of polarized radiative transfer include underlying surface albedo, aerosol layers and components, and the absorption of trace gases. Simulation analysis results: (1) While the relative azimuth angle is zero, the magnitude of spectrum U/I is lower than 10(-7) and V/I is negligible, the degree of polarization and the spectrum Q/I are shaped like the letter V or mirror-writing U. (2) In twilight, when the Sun is not in FOV of the detector, the polarization of the daytime sky has two maximum near 0.51 and 2.75 μm, and a minimum near 1.5 μm. For arbitrary observation geometry, the spectral signal of V/I may be ignored. According to observation geometry, choosing different spectral bands or polarized signal will be propitious to targets detection. PMID:26117882
Diminished Reality Based on Image Inpainting Considering Background Geometry.
Kawai, Norihiko; Sato, Tomokazu; Yokoya, Naokazu
2016-03-01
Diminished reality aims to remove real objects from video images and fill in the missing regions with plausible background textures in real time. Most conventional methods based on image inpainting achieve diminished reality by assuming that the background around a target object is almost planar. This paper proposes a new diminished reality method that considers background geometries with less constraints than the conventional ones. In this study, we approximate the background geometry by combining local planes, and improve the quality of image inpainting by correcting the perspective distortion of texture and limiting the search area for finding similar textures as exemplars. The temporal coherence of texture is preserved using the geometries and camera pose estimated by visual-simultaneous localization and mapping (SLAM). The mask region that includes a target object is robustly set in each frame by projecting a 3D region, rather than tracking the object in 2D image space. The effectiveness of the proposed method is successfully demonstrated using several experimental environments.
Diminished Reality Based on Image Inpainting Considering Background Geometry.
Kawai, Norihiko; Sato, Tomokazu; Yokoya, Naokazu
2016-03-01
Diminished reality aims to remove real objects from video images and fill in the missing regions with plausible background textures in real time. Most conventional methods based on image inpainting achieve diminished reality by assuming that the background around a target object is almost planar. This paper proposes a new diminished reality method that considers background geometries with less constraints than the conventional ones. In this study, we approximate the background geometry by combining local planes, and improve the quality of image inpainting by correcting the perspective distortion of texture and limiting the search area for finding similar textures as exemplars. The temporal coherence of texture is preserved using the geometries and camera pose estimated by visual-simultaneous localization and mapping (SLAM). The mask region that includes a target object is robustly set in each frame by projecting a 3D region, rather than tracking the object in 2D image space. The effectiveness of the proposed method is successfully demonstrated using several experimental environments. PMID:26829239
A Whirlwind Tour of Computational Geometry.
ERIC Educational Resources Information Center
Graham, Ron; Yao, Frances
1990-01-01
Described is computational geometry which used concepts and results from classical geometry, topology, combinatorics, as well as standard algorithmic techniques such as sorting and searching, graph manipulations, and linear programing. Also included are special techniques and paradigms. (KR)
Optimizing solar-cell grid geometry
NASA Technical Reports Server (NTRS)
Crossley, A. P.
1969-01-01
Trade-off analysis and mathematical expressions calculate optimum grid geometry in terms of various cell parameters. Determination of the grid geometry provides proper balance between grid resistance and cell output to optimize the energy conversion process.
The method of planes pressure tensor for a spherical subvolume
Heyes, D. M. Smith, E. R. Dini, D. Zaki, T. A.
2014-02-07
Various formulas for the local pressure tensor based on a spherical subvolume of radius, R, are considered. An extension of the Method of Planes (MOP) formula of Todd et al. [Phys. Rev. E 52, 1627 (1995)] for a spherical geometry is derived using the recently proposed Control Volume formulation [E. R. Smith, D. M. Heyes, D. Dini, and T. A. Zaki, Phys. Rev. E 85, 056705 (2012)]. The MOP formula for the purely radial component of the pressure tensor is shown to be mathematically identical to the Radial Irving-Kirkwood formula. Novel offdiagonal elements which are important for momentum conservation emerge naturally from this treatment. The local pressure tensor formulas for a plane are shown to be the large radius limits of those for spherical surfaces. The radial-dependence of the pressure tensor computed by Molecular Dynamics simulation is reported for virtual spheres in a model bulk liquid where the sphere is positioned randomly or whose center is also that of a molecule in the liquid. The probability distributions of angles relating to pairs of atoms which cross the surface of the sphere, and the center of the sphere, are presented as a function of R. The variance in the shear stress calculated from the spherical Volume Averaging method is shown to converge slowly to the limiting values with increasing radius, and to be a strong function of the number of molecules in the simulation cell.
The Geometry of Quasar Outflows
NASA Astrophysics Data System (ADS)
Ganguly, Rajib
2012-10-01
Quasar outflows are important for understanding the accretion and growth processes of the central black hole, but also potentially play a role in feedback to the galaxy, halting star formation and infall of gas. A big uncertainty lies in the geometry and density of these outflows, especially as a function of ionization and velocity. We aim to tackle this using the archival COS M grating spectra of 266 quasars. We separate the geometry of outflows into two parts: the solid angle subtended around the black hole, and the distance of the outflow from the central engine. Large numbers of quasars with high resolution spectra are required for each aspect of this statistical investigation. First, we will determine which/how many absorption-line systems are intrinsic through both partial covering methods and statistical assessments. Second, we will consider the incidence of intrinsic absorbers as a function of quasar property {e.g., radio-loudness, SED shape, black hole mass, bolometric luminosity}. This will reveal what determines the solid angle. This can only be done at moderate redshifts where quasars with a larger range of properties are observable, and hence requires HST/COS. Third, we will use the wide range of diagnostic lines to constrain the physical conditions of the absorbers. We will target the CIII*1175 complex and apply photoionization models to constrain the densities and ionization parameters. This will provide the largest set yet of intrinsic absorbers with systematic distance constraints. In tandem with the solid angles, this work will inform models regarding the geometry of quasar outflows.
The geometry of musical chords.
Tymoczko, Dmitri
2006-07-01
A musical chord can be represented as a point in a geometrical space called an orbifold. Line segments represent mappings from the notes of one chord to those of another. Composers in a wide range of styles have exploited the non-Euclidean geometry of these spaces, typically by using short line segments between structurally similar chords. Such line segments exist only when chords are nearly symmetrical under translation, reflection, or permutation. Paradigmatically consonant and dissonant chords possess different near-symmetries and suggest different musical uses.
Worldsheet geometries of ambitwistor string
NASA Astrophysics Data System (ADS)
Ohmori, Kantaro
2015-06-01
Mason and Skinner proposed the ambitwistor string theory which directly reproduces the formulas for the amplitudes of massless particles proposed by Cachazo, He and Yuan. In this paper we discuss geometries of the moduli space of worldsheets associated to the bosonic or the RNS ambitwistor string. Further, we investigate the factorization properties of the amplitudes when an internal momentum is near on-shell in the abstract CFT language. Along the way, we propose the existence of the ambitwistor strings with three or four fermionic worldsheet currents.
Ooguri, Hirosi; Yamazaki, Masahito
2009-04-24
We show how the smooth geometry of Calabi-Yau manifolds emerges from the thermodynamic limit of the statistical mechanical model of crystal melting defined in our previous paper. In particular, the thermodynamic partition function of molten crystals is shown to be equal to the classical limit of the partition function of the topological string theory by relating the Ronkin function of the characteristic polynomial of the crystal melting model to the holomorphic 3-form on the corresponding Calabi-Yau manifold. PMID:19518695
Exceptional geometry and Borcherds superalgebras
NASA Astrophysics Data System (ADS)
Palmkvist, Jakob
2015-11-01
We study generalized diffeomorphisms in exceptional geometry with U-duality group E n( n) from an algebraic point of view. By extending the Lie algebra {e}_n to an infinite-dimensional Borcherds superalgebra, involving also the extension to {e}_{n+1} , the generalized Lie derivatives can be expressed in a simple way, and the expressions take the same form for any n ≤ 7. The closure of the transformations then follows from the Jacobi identity and the grading of {e}_{n+1} with respect to {e}_n.
MTF comparisons between mesa and planar focal plane detector structures
NASA Astrophysics Data System (ADS)
Perley, Mitchell; Wehner, Justin; Buell, Dave; Micali, Jason; McCorkle, Joe; Rehfield, Mark; Williams, Dave; Dixon, Andrew; Malone, Neil
2013-09-01
Raytheon Vision Systems (RVS) has developed scanning, high-speed (<3klps), all digital, with on-chip Analog-to-Digital Conversion (ADC), mid-wave infrared (MWIR 3-5mm) focal plane arrays (FPA) with excellent modulation transfer function (MTF) performance. Using secondary ion mass spectrometry (SIMS) data and detailed models of the mesa geometry, RVS modeled the predicted detector MTF performance of detectors. These detectors have a mesa structure and geometry for improved MTF performance compared to planar HgCdTe and InSb detector structures and other similar detector structures such as nBn. The modeled data is compared to measured MTF data obtained from edge spread measurements and shows good agreement, Figure 1. The measured data was obtained using a custom advanced test set with 1µm precision alignment and automatic data acquisition for report generation in less than five minutes per FPA. The measured MTF values of 83 unique parts, Figure 2, had a standard deviation of 0.0094 and a mean absolute deviation of 0.0066 at half Nyquist frequency, showing excellent process repeatability and a design that supports high MTF with good repeatability.
Teaching Geometry: An Experiential and Artistic Approach.
ERIC Educational Resources Information Center
Ogletree, Earl J.
The view that geometry should be taught at every grade level is promoted. Primary and elementary school children are thought to rarely have any direct experience with geometry, except on an incidental basis. Children are supposed to be able to learn geometry rather easily, so long as the method and content are adapted to their development and…
Preservice Primary School Teachers' Elementary Geometry Knowledge
ERIC Educational Resources Information Center
Marchis, Iuliana
2012-01-01
Geometrical notions and properties occur in real-world problems, thus Geometry has an important place in school Mathematics curricula. Primary school curricula lays the foundation of Geometry knowledge, pupils learn Geometry notions and properties by exploring their environment. Thus it is very important that primary school teachers have a good…
Geometry in the Early Years: A Commentary
ERIC Educational Resources Information Center
Dindyal, Jaguthsing
2015-01-01
The primary goal of this paper is to provide a commentary on the teaching and learning of geometry in the early years of schooling with the set of papers in this issue as a guiding factor. It is structured around issues about geometry education of young learners, such as: what should we teach in geometry and why; representation of geometrical…
Engaging All Students with "Impossible Geometry"
ERIC Educational Resources Information Center
Wiest, Lynda R.; Ayebo, Abraham; Dornoo, Michael D.
2010-01-01
Geometry is an area in which Australian students performed particularly poorly on the 2007 Trends in International Mathematics and Science Study (TIMSS). One innovative area of recreational geometry that has rich potential to engage and challenge a wide variety of students is "impossible geometry." An impossible geometric object is a…
Geometry: Career Related Units. Teacher's Edition.
ERIC Educational Resources Information Center
Pierro, Mike; And Others
Using six geometry units as resource units, the document explores 22 math-related careers. The authors intend the document to provide senior high school students with career orientation and exploration experiences while they learn geometry skills. The units are to be considered as a part of a geometry course, not a course by themselves. The six…
Detection of trans–cis flips and peptide-plane flips in protein structures
Touw, Wouter G.; Joosten, Robbie P.; Vriend, Gert
2015-01-01
A coordinate-based method is presented to detect peptide bonds that need correction either by a peptide-plane flip or by a trans–cis inversion of the peptide bond. When applied to the whole Protein Data Bank, the method predicts 4617 trans–cis flips and many thousands of hitherto unknown peptide-plane flips. A few examples are highlighted for which a correction of the peptide-plane geometry leads to a correction of the understanding of the structure–function relation. All data, including 1088 manually validated cases, are freely available and the method is available from a web server, a web-service interface and through WHAT_CHECK. PMID:26249342
Determination of the occlusal plane using a custom-made occlusal plane analyzer: a clinical report.
Bedia, Sumit V; Dange, Shankar P; Khalikar, Arun N
2007-11-01
In fixed prosthodontic procedures, when it has been determined that restoration of all or most of the posterior teeth is necessary, the use of the Broderick occlusal plane analyzer provides an easy and practical method to determine an occlusal plane that will fulfill esthetic and functional occlusion requirements. However, several manufacturers of semiadjustable articulators offer no such occlusal plane analyzers for use with these instruments. This article demonstrates the use of a custom-made Broderick occlusal plane analyzer with a semiadjustable articulator to determine the correct curve of Spee for the occlusal plane.
Geometry of modified Newtonian dynamics
NASA Astrophysics Data System (ADS)
Skordis, Constantinos; Zlosnik, Tom
2012-02-01
Modified Newtonian dynamics is an empirical modification to Poisson’s equation which has had success in accounting for the “gravitational field” Φ in a variety of astrophysical systems. The field Φ may be interpreted in terms of the weak-field limit of a variety of spacetime geometries. Here we consider three of these geometries in a more comprehensive manner and look at the effect on timelike and null geodesics. In particular we consider the aquadratic Lagrangian (AQUAL) theory, tensor-vector-scalar (TeVeS) theory and generalized Einstein-aether theory. We uncover a number of novel features, some of which are specific to the theory considered while others are generic. In the case of AQUAL and TeVeS theories, the spacetime exhibits an excess (AQUAL) or deficit TeVeS solid angle akin to the case of a Barriola-Vilenkin global monopole. In the case of generalized Einstein-aether, a disformal symmetry of the action emerges in the limit of ∇→Φ→0. Finally, in all theories studied, massive particles can never reach spatial infinity while photons can do so only after experiencing infinite redshift.
Quanta of geometry: noncommutative aspects.
Chamseddine, Ali H; Connes, Alain; Mukhanov, Viatcheslav
2015-03-01
In the construction of spectral manifolds in noncommutative geometry, a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of real scalar fields naturally appears and implies, by equality with the index formula, the quantization of the volume. We first show that this condition implies that the manifold decomposes into disconnected spheres, which will represent quanta of geometry. We then refine the condition by involving the real structure and two types of geometric quanta, and show that connected spin manifolds with large quantized volume are then obtained as solutions. The two algebras M_{2}(H) and M_{4}(C) are obtained, which are the exact constituents of the standard model. Using the two maps from M_{4} to S^{4} the four-manifold is built out of a very large number of the two kinds of spheres of Planckian volume. We give several physical applications of this scheme such as quantization of the cosmological constant, mimetic dark matter, and area quantization of black holes. PMID:25793795
Turbine engine variable geometry device
NASA Technical Reports Server (NTRS)
Rogo, Casimir (Inventor); Lenz, Herman N. (Inventor)
1985-01-01
A variable geometry device for use with the turbine nozzle of a turbine engine of the type having a support housing and a combustion chamber contained within the support housing. A pair of spaced walls in the support housing define an annular and radially extending nozzle passageway. The outer end of the nozzle passageway is open to the combustion chamber while the inner end of the nozzle passageway is open to one or more turbine stages. A plurality of circumferentially spaced nozzle vanes are mounted to one of the spaced walls and protrude across the nozzle passageway. An annular opening is formed around the opposite spaced wall and an annular ring is axially slidably mounted within the opening. A motor is operatively connected to this ring and, upon actuation, axially displaces the ring within the nozzle passageway. In addition, the ring includes a plurality of circumferentially spaced slots which register with the nozzle vanes so that the vane geometry remains the same despite axial displacement of the ring.
Interactive rendering of dynamic geometry.
Ponchio, Federico; Hormann, Kai
2008-01-01
Fluid simulations typically produce complex three-dimensional (3D) isosurfaces whose geometry and topology change over time. The standard way of representing such "dynamic geometry" is by a set of isosurfaces that are extracted individually at certain time steps. An alternative strategy is to represent the whole sequence as a four-dimensional (4D) tetrahedral mesh. The iso-surface at a specific time step can then be computed by intersecting the tetrahedral mesh with a 3D hyperplane. This not only allows the animation of the surface continuously over time without having to worry about the topological changes, but also enables simplification algorithms to exploit temporal coherence. We show how to interactively render such 4D tetrahedral meshes by improving previous GPU-accelerated techniques and building an out-of-core multi-resolution structure based on quadric error simplification. As a second application, we apply our framework to time-varying surfaces that result from morphing one triangle mesh into another. PMID:18467764
Geometry and the quantum: basics
NASA Astrophysics Data System (ADS)
Chamseddine, Ali H.; Connes, Alain; Mukhanov, Viatcheslav
2014-12-01
Motivated by the construction of spectral manifolds in noncommutative geometry, we introduce a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. This commutation relation appears in two versions, one sided and two sided. It implies the quantization of the volume. In the one-sided case it implies that the manifold decomposes into a disconnected sum of spheres which will represent quanta of geometry. The two sided version in dimension 4 predicts the two algebras M 2(ℍ) and M 4(ℂ) which are the algebraic constituents of the Standard Model of particle physics. This taken together with the non-commutative algebra of functions allows one to reconstruct, using the spectral action, the Lagrangian of gravity coupled with the Standard Model. We show that any connected Riemannian Spin 4-manifold with quantized volume > 4 (in suitable units) appears as an irreducible representation of the two-sided commutation relations in dimension 4 and that these representations give a seductive model of the "particle picture" for a theory of quantum gravity in which both the Einstein geometric standpoint and the Standard Model emerge from Quantum Mechanics. Physical applications of this quantization scheme will follow in a separate publication.
Neuronal activity controls transsynaptic geometry
Glebov, Oleg O.; Cox, Susan; Humphreys, Lawrence; Burrone, Juan
2016-01-01
The neuronal synapse is comprised of several distinct zones, including presynaptic vesicle zone (SVZ), active zone (AZ) and postsynaptic density (PSD). While correct relative positioning of these zones is believed to be essential for synaptic function, the mechanisms controlling their mutual localization remain unexplored. Here, we employ high-throughput quantitative confocal imaging, super-resolution and electron microscopy to visualize organization of synaptic subdomains in hippocampal neurons. Silencing of neuronal activity leads to reversible reorganization of the synaptic geometry, resulting in a increased overlap between immunostained AZ and PSD markers; in contrast, the SVZ-AZ spatial coupling is decreased. Bayesian blinking and bleaching (3B) reconstruction reveals that the distance between the AZ-PSD distance is decreased by 30 nm, while electron microscopy shows that the width of the synaptic cleft is decreased by 1.1 nm. Our findings show that multiple aspects of synaptic geometry are dynamically controlled by neuronal activity and suggest mutual repositioning of synaptic components as a potential novel mechanism contributing to the homeostatic forms of synaptic plasticity. PMID:26951792
Alternative cosmology from cusp geometries
NASA Astrophysics Data System (ADS)
Rosa, Reinaldo; Herbin Stalder Díaz, Diego
We study an alternative geometrical approach on the problem of classical cosmological singularity. It is based on a generalized function f(x,y)=x(2+y^2=(1-z)z^n) which consists of a cusped projected coupled isosurface. Such a projected geometry is computed and analized into the context of Friedmann singularity-free cosmology where a pre-big bang scenario is considered. Assuming that the mechanism of cusp formation is described by non-linear oscillations of a pre- big bang extended very high energy density field (>3x10^{94} kg/m^3$), we show that the action under the gravitational field follows a tautochrone of revolution, understood here as the primary projected geometry that alternatively replaces the Friedmann singularity in the standard big bang theory. As shown here this new approach allows us to interpret the nature of both matter and dark energy from first geometric principles [1]. [1] Rosa et al. DOI: 10.1063/1.4756991
Fuzzy Logic for Incidence Geometry
2016-01-01
The paper presents a mathematical framework for approximate geometric reasoning with extended objects in the context of Geography, in which all entities and their relationships are described by human language. These entities could be labelled by commonly used names of landmarks, water areas, and so forth. Unlike single points that are given in Cartesian coordinates, these geographic entities are extended in space and often loosely defined, but people easily perform spatial reasoning with extended geographic objects “as if they were points.” Unfortunately, up to date, geographic information systems (GIS) miss the capability of geometric reasoning with extended objects. The aim of the paper is to present a mathematical apparatus for approximate geometric reasoning with extended objects that is usable in GIS. In the paper we discuss the fuzzy logic (Aliev and Tserkovny, 2011) as a reasoning system for geometry of extended objects, as well as a basis for fuzzification of the axioms of incidence geometry. The same fuzzy logic was used for fuzzification of Euclid's first postulate. Fuzzy equivalence relation “extended lines sameness” is introduced. For its approximation we also utilize a fuzzy conditional inference, which is based on proposed fuzzy “degree of indiscernibility” and “discernibility measure” of extended points. PMID:27689133
Weyl gravity and Cartan geometry
NASA Astrophysics Data System (ADS)
Attard, J.; François, J.; Lazzarini, S.
2016-04-01
We point out that the Cartan geometry known as the second-order conformal structure provides a natural differential geometric framework underlying gauge theories of conformal gravity. We are concerned with two theories: the first one is the associated Yang-Mills-like Lagrangian, while the second, inspired by [1], is a slightly more general one that relaxes the conformal Cartan geometry. The corresponding gauge symmetry is treated within the Becchi-Rouet-Stora-Tyutin language. We show that the Weyl gauge potential is a spurious degree of freedom, analogous to a Stueckelberg field, that can be eliminated through the dressing field method. We derive sets of field equations for both the studied Lagrangians. For the second one, they constrain the gauge field to be the "normal conformal Cartan connection.''Finally, we provide in a Lagrangian framework a justification of the identification, in dimension 4, of the Bach tensor with the Yang-Mills current of the normal conformal Cartan connection, as proved in [2].
Target Detection Using Fractal Geometry
NASA Technical Reports Server (NTRS)
Fuller, J. Joseph
1991-01-01
The concepts and theory of fractal geometry were applied to the problem of segmenting a 256 x 256 pixel image so that manmade objects could be extracted from natural backgrounds. The two most important measurements necessary to extract these manmade objects were fractal dimension and lacunarity. Provision was made to pass the manmade portion to a lookup table for subsequent identification. A computer program was written to construct cloud backgrounds of fractal dimensions which were allowed to vary between 2.2 and 2.8. Images of three model space targets were combined with these backgrounds to provide a data set for testing the validity of the approach. Once the data set was constructed, computer programs were written to extract estimates of the fractal dimension and lacunarity on 4 x 4 pixel subsets of the image. It was shown that for clouds of fractal dimension 2.7 or less, appropriate thresholding on fractal dimension and lacunarity yielded a 64 x 64 edge-detected image with all or most of the cloud background removed. These images were enhanced by an erosion and dilation to provide the final image passed to the lookup table. While the ultimate goal was to pass the final image to a neural network for identification, this work shows the applicability of fractal geometry to the problems of image segmentation, edge detection and separating a target of interest from a natural background.
Aldoss, Osamah; Patel, Sonali; Harris, Kyle; Divekar, Abhay
2015-06-01
The objective of the study is to compare radiation dose between the frontal and lateral planes in a biplane cardiac catheterization laboratory. Tube angulation progressively increases patient and operator radiation dose in single-plane cardiac catheterization laboratories. This retrospective study captured biplane radiation dose in a pediatric cardiac catheterization laboratory between April 2010 and January 2014. Raw and time-indexed fluoroscopic, cineangiographic and total (fluoroscopic + cineangiographic) air kerma (AK, mGy) and kerma area product (PKA, µGym(2)/Kg) for each plane were compared. Data for 716 patients were analyzed: 408 (56.98 %) were male, the median age was 4.86 years, and the median weight was 17.35 kg. Although median beam-on time (minutes) was 4.2 times greater in the frontal plane, there was no difference in raw median total PKA between the two planes. However, when indexed to beam-on time, the lateral plane had a higher median-indexed fluoroscopic (0.75 vs. 1.70), cineangiographic (16.03 vs. 24.92), and total (1.43 vs. 5.15) PKA (p < 0.0001). The median time-indexed total PKA in the lateral plane is 3.6 times the frontal plane. This is the first report showing that the lateral plane delivers a higher dose than the frontal plane per unit time. Operators should consciously reduce the lateral plane beam-on time and incorporate this practice in radiation reduction protocols.
Streptococcus anginosus infections: crossing tissue planes.
Sunwoo, Bernie Y; Miller, Wallace T
2014-10-01
Streptococcus anginosus has long been recognized to cause invasive pyogenic infections. This holds true for thoracic infections where S. anginosus has a propensity for abscess and empyema formation. Early diagnosis is important given the significant morbidity and mortality associated with thoracic S. anginosus infections. Yet, distinguishing thoracic S. anginosus clinically is difficult. We present three cases of thoracic S. anginosus that demonstrated radiographic extension across tissue planes, including the interlobar fissure, diaphragm, and chest wall. Few infectious etiologies are known to cross tissue planes. Accordingly, we propose S. anginosus be considered among the differential diagnosis of potential infectious etiologies causing radiographic extension across tissue planes.
High-frequency techniques for RCS prediction of plate geometries
NASA Technical Reports Server (NTRS)
Balanis, Constantine A.; Polka, Lesley A.
1992-01-01
The principal-plane scattering from perfectly conducting and coated strips and rectangular plates is examined. Previous reports have detailed Geometrical Theory of Diffraction/Uniform Theory of Diffraction (GTD/UTD) solutions for these geometries. The GTD/UTD solution for the perfectly conducting plate yields monostatic radar cross section (RCS) results that are nearly identical to measurements and results obtained using the Moment Method (MM) and the Extended Physical Theory of Diffraction (EPTD). This was demonstrated in previous reports. The previous analysis is extended to bistatic cases. GTD/UTD results for the principal-plane scattering from a perfectly conducting, infinite strip are compared to MM and EPTD data. A comprehensive overview of the advantages and disadvantages of the GTD/UTD and of the EPTD and a detailed analysis of the results from both methods are provided. Several previous reports also presented preliminary discussions and results for a GTD/UTD model of the RCS of a coated, rectangular plate. Several approximations for accounting for the finite coating thickness, plane-wave incidence, and far-field observation were discussed. Here, these approximations are replaced by a revised wedge diffraction coefficient that implicitly accounts for a coating on a perfect conductor, plane-wave incidence, and far-field observation. This coefficient is computationally more efficient than the previous diffraction coefficient because the number of Maliuzhinets functions that must be calculated using numerical integration is reduced by a factor of 2. The derivation and the revised coefficient are presented in detail for the hard polarization case. Computations and experimental data are also included. The soft polarization case is currently under investigation.
The geometry and kinematics of flow perturbation folds
NASA Astrophysics Data System (ADS)
Alsop, G. I.; Holdsworth, R. E.
2002-05-01
Minor folds formed synchronous with ductile deformation in high strain zones can preserve a record of the scale and kinematics of heterogeneous flow. Using structures associated with WNW-directed Caledonian thrusting in N Scotland, we show that localised perturbations in flow resulted in the generation of predominantly cylindrical minor folds with hinges lying at low angles to the transport direction. These define a series of larger-scale fold culminations (reflecting 'surging flow') or depressions (reflecting 'slackening flow') that are bisected by transport-parallel culmination and depression surfaces. The fold patterns suggest a dominance of layer-normal differential shearing due to gradients in shear strain normal to transport. Culmination surfaces are marked by along-strike reversals in the polarity of structural facing and vergence of minor folds which, contrary to classic fold patterns, define reverse asymmetric relationships. Culmination surfaces separate folding in to clockwise (Z folds) and anticlockwise (S folds) domains relative to the transport lineation. The dip of fold axial planes systematically increases as their strike becomes sub-parallel to transport resulting in a 3D statistical fanning arrangement centred about the transport direction. Thus, mean S- and Z-fold axial planes intersect precisely parallel to the transport lineation and potentially provide a means of determining transport directions in cases where lineations are poorly preserved. Culminations display convergent fold patterns with fold hinges becoming sub-parallel to transport towards the culmination surface and underlying detachment, whilst axial planes define overall concave up listric geometries which are bisected by the culmination surface. Thus, around culminations and depressions there are ordered, scale-independent relationships between transport direction, shear sense, fold facing, vergence and hinge/axial plane orientations. The techniques described here can be applied and
Research on method of geometry and spectral calibration of pushbroom dispersive hyperspectral imager
NASA Astrophysics Data System (ADS)
He, Zhiping; Shu, Rong; Wang, Jianyu
2012-11-01
Development and application of airborne and aerospace hyperspectral imager press for high precision geometry and spectral calibration of pixels of image cube. The research of geometry and spectral calibration of pushbroom hyperspectral imager, its target is giving the coordinate of angle field of view and center wavelength of each detect unit in focal plane detector of hyperspectral imager, and achieves the high precision, full field of view, full channel geometry and spectral calibration. It is importance for imaging quantitative and deep application of hyperspectal imager. The paper takes the geometry and spectral calibration of pushbroom dispersive hyperspectral imager as case study, and research on the constitution and analysis of imaging mathematical model. Aimed especially at grating-dispersive hyperspectral imaging, the specialty of the imaging mode and dispersive method has been concretely analyzed. Based on the analysis, the theory and feasible method of geometry and spectral calibration of dispersive hyperspectral imager is set up. The key technique has been solved is As follows: 1). the imaging mathematical model and feasible method of geometry and spectral calibration for full pixels of image cube has been set up, the feasibility of the calibration method has been analyzed. 2). the engineering model and method of the geometry and spectral calibration of pushbroom dispersive hyperspectral imager has been set up and the calibration equipment has been constructed, and the calibration precision has been analyzed.
Differential Geometry Based Multiscale Models
Wei, Guo-Wei
2010-01-01
Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atom-istic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier–Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson–Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson–Nernst–Planck equations that
Differential geometry based multiscale models.
Wei, Guo-Wei
2010-08-01
Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atomistic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier-Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson-Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson-Nernst-Planck equations that are
Differential geometry based multiscale models.
Wei, Guo-Wei
2010-08-01
Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atomistic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier-Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson-Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson-Nernst-Planck equations that are
Plane Strain Testing with Passive Restraint
NASA Astrophysics Data System (ADS)
Makhnenko, Roman; Labuz, Joseph
2014-11-01
A plane strain condition for testing rock is developed through passive restraint in the form of a thick-walled cylinder. The so-called biaxial frame generates the intermediate principal stress that imposes a triaxial state of stress on a prismatic specimen. Major and minor principal stresses and corresponding strains are accurately measured, providing data to calculate the elastic (Young's modulus and Poisson's ratio), inelastic (dilatancy angle), and strength (friction angle and cohesion) parameters of the rock. Results of experiments conducted on Indiana limestone in plane strain compression are compared with the results of axisymmetric compression and extension. With proper system calibration, Young's modulus and Poisson's ratio are consistent among the tests. The plane strain apparatus enforces in-plane deformation with the three principal stresses at failure being different, and it allows one to determine the Paul-Mohr-Coulomb failure surface, which includes an intermediate stress effect.
Three-dimensional Allan fault plane analysis
Hoffman, K.S.; Taylor, D.R.; Schnell, R.T.
1994-12-31
Allan fault-plane analysis is a useful tool for determining hydrocarbon migration paths and the location of possible traps. While initially developed for Gulf coast deltaic and interdeltaic environments, fault-plane analysis has been successfully applied in many other geologic settings. Where the geology involves several intersecting faults and greater complexity, many two-dimensional displays are required in the investigation and it becomes increasingly difficult to accurately visualize both fault relationships and migration routes. Three-dimensional geospatial fault and structure modeling using computer techniques, however, facilitates both visualization and understanding and extends fault-plane analysis into much more complex situations. When a model is viewed in three dimensions, the strata on both sides of a fault can be seen simultaneously while the true structural character of one or more fault surfaces is preserved. Three-dimensional analysis improves the speed and accuracy of the fault plane methodology.
Attitude analysis in Flatland: The plane truth
NASA Technical Reports Server (NTRS)
Shuster, Malcolm D.
1993-01-01
Many results in attitude analysis are still meaningful when the attitude is restricted to rotations about a single axis. Such a picture corresponds to attitude analysis in the Euclidean plane. The present report formalizes the representation of attitude in the plane and applies it to some well-known problems. In particular, we study the connection of the 'additive' and 'multiplicative' formulations of the differential corrector for the quaternion in its two-dimensional setting.
Interactive graphics for geometry modeling
NASA Technical Reports Server (NTRS)
Wozny, M. J.
1984-01-01
An interactive vector capability to create geometry and a raster color shaded rendering capability to sample and verify interim geometric design steps through color snapshots is described. The development is outlined of the underlying methodology which facilitates computer aided engineering and design. At present, raster systems cannot match the interactivity and line-drawing capability of refresh vector systems. Consequently, an intermediate step in mechanical design is used to create objects interactively on the vector display and then scan convert the wireframe model to render it as a color shaded object on a raster display. Several algorithms are presented for rendering such objects. Superquadric solid primitive extend the class of primitives normally used in solid modelers.
Quantum gauge theories from geometry
NASA Astrophysics Data System (ADS)
Galehouse, Daniel C.
2006-03-01
Geometrical theories have been developed to describe quantum interacting particles with full mathematical covariance. They possess a sophisticated gauge structure that derives from the fundamental properties of the geometry. These theories are all implicitly quantized and come in three known types: Weyl, non-compactified Kaluza-Klein, and, as presented here, Dirac. The spin one-half particle is a conformal wave in an eight dimensional Riemannian space. The coordinates transform locally as spinors and project into space time to give the known gravitational and electromagnetic forces. The gauge structure of the weak interactions appears as well, as in this space the electron transforms into a neutrino under hyper-rotations. The possibility of including the strong interactions and the corresponding gauge system is discussed.
Noncommutative Geometry and Basic Physics
NASA Astrophysics Data System (ADS)
Kastler, Daniel
Alain Connes' noncommutative geometry, started in 1982 [0], widely developed in 1994 as expounded in his book at this date [0] (it has grown meanwhile) is a systematic quantization of mathematics parallel to the quantization of physics effected in the twenties.This theory widens the scope of mathematics in a manner congenial to physics, reorganizes the existing ("classical") mathematics of which it produces an hitherto unsuspected unification, and provides basic physics (the synthesis of elementary particles and gravitation) with a programme of renewal which has thus far achieved a clarification of the classical (tree-level) aspects of a new synthesis of the (Euclidean) standard model with gravitation [32],[33]: this is the subject of the present lectures - with the inherent tentative prediction of the Higgs mass.
Deep plane facelifting for facial rejuvenation.
Gordon, Neil; Adam, Stewart
2014-08-01
The purpose of this article is to provide the facial plastic surgeon with anatomical and embryologic evidence to support the use of the deep plane technique for optimal treatment of facial aging. A detailed description of the procedure is provided to allow safe and consistent performance. Insights into anatomical landmarks, technical nuances, and alternative approaches for facial variations are presented. The following points will be further elucidated in the article. The platysma muscle/submuscular aponeurotic system/galea are the continuous superficial cervical fascia encompassing the majority of facial fat, and this superficial soft tissue envelope is poorly anchored to the face. The deep cervical fascia binds the structural aspects of the face and covers the facial nerve and buccal fat pad. Facial aging is mainly due to gravity's long-term effects on the superficial soft tissue envelope, with more subtle effects on the deeper structural compartments. The deep plane is the embryologic cleavage plane between these fascial layers, and is the logical place for facial dissection. The deep plane allows access to the buccal fat pad for treatment of jowling. Soft tissue mobilization is maximized in deep plane dissections and requires careful hairline planning. Flap advancement creates tension only at the fascia level allowing natural, tension-free skin closure, and long-lasting outcomes. The deep plane advancement flap is well vascularized and resistant to complications.
Geometry of discrete quantum computing
NASA Astrophysics Data System (ADS)
Hanson, Andrew J.; Ortiz, Gerardo; Sabry, Amr; Tai, Yu-Tsung
2013-05-01
Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2n infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any real-world resources, and, if we have the idea of physical law as some kind of computational algorithm of the universe, we would be compelled to alter our descriptions of physics to be consistent with computable numbers. Our purpose here is to examine the geometric implications of using finite fields Fp and finite complexified fields \\mathbf {F}_{p^2} (based on primes p congruent to 3 (mod4)) as the basis for computations in a theory of discrete quantum computing, which would therefore become a computable theory. Because the states of a discrete n-qubit system are in principle enumerable, we are able to determine the proportions of entangled and unentangled states. In particular, we extend the Hopf fibration that defines the irreducible state space of conventional continuous n-qubit theories (which is the complex projective space \\mathbf {CP}^{2^{n}-1}) to an analogous discrete geometry in which the Hopf circle for any n is found to be a discrete set of p + 1 points. The tally of unit-length n-qubit states is given, and reduced via the generalized Hopf fibration to \\mathbf {DCP}^{2^{n}-1}, the discrete analogue of the complex projective space, which has p^{2^{n}-1} (p-1)\\,\\prod _{k=1}^{n-1} ( p^{2^{k}}+1) irreducible states. Using a measure of entanglement, the purity, we explore the entanglement features of discrete quantum states and find that the n-qubit states based on the complexified field \\mathbf {F}_{p^2} have pn(p - 1)n unentangled states (the product of the tally for a single qubit) with purity 1, and they have pn + 1(p - 1)(p + 1)n - 1 maximally entangled states with purity zero.
Changing the Structure Boundary Geometry
Karasev, Viktor; Dzlieva, Elena; Ivanov, Artyom
2008-09-07
Analysis of previously obtained results shows that hexagonal crystal lattice is the dominant type of ordering, in particular, in striated glow discharges. We explore the possibility for changing the dust distribution in horizontal cross sections of relatively highly ordered structures in a glow-discharge. Presuming that boundary geometry can affect dust distribution, we used cylindrical coolers held at 0 deg. C and placed against a striation containing a structure, to change the geometry of its outer boundary. By varying the number of coolers, their positions, and their separations from the tube wall, azimuthally asymmetric thermophoretic forces can be used to form polygonal boundaries and vary the angles between their segments (in a horizontal cross section). The corner in the structure's boundary of 60 deg. stimulates formation of hexagonal cells. The structure between the supported parallel boundaries is also characterized by stable hexagonal ordering. We found that a single linear boundary segment does not give rise to any sizable domain, but generates a lattice extending from the boundary (without edge defects). A square lattice can be formed by setting the angle equal to 90 deg. . However, angles of 45 deg. and 135 deg. turned out easier to form. Square lattice was created by forming a near-135 deg. corner with four coolers. It was noted that no grain ordering is observed in the region adjacent to corners of angles smaller than 30 deg. , which do not promote ordering into cells of any shape. Thus, manipulation of a structure boundary can be used to change dust distribution, create structures free of the ubiquitous edge defects that destroy orientation order, and probably change the crystal lattice type.
Digital breast tomosynthesis geometry calibration
NASA Astrophysics Data System (ADS)
Wang, Xinying; Mainprize, James G.; Kempston, Michael P.; Mawdsley, Gordon E.; Yaffe, Martin J.
2007-03-01
Digital Breast Tomosynthesis (DBT) is a 3D x-ray technique for imaging the breast. The x-ray tube, mounted on a gantry, moves in an arc over a limited angular range around the breast while 7-15 images are acquired over a period of a few seconds. A reconstruction algorithm is used to create a 3D volume dataset from the projection images. This procedure reduces the effects of tissue superposition, often responsible for degrading the quality of projection mammograms. This may help improve sensitivity of cancer detection, while reducing the number of false positive results. For DBT, images are acquired at a set of gantry rotation angles. The image reconstruction process requires several geometrical factors associated with image acquisition to be known accurately, however, vibration, encoder inaccuracy, the effects of gravity on the gantry arm and manufacturing tolerances can produce deviations from the desired acquisition geometry. Unlike cone-beam CT, in which a complete dataset is acquired (500+ projections over 180°), tomosynthesis reconstruction is challenging in that the angular range is narrow (typically from 20°-45°) and there are fewer projection images (~7-15). With such a limited dataset, reconstruction is very sensitive to geometric alignment. Uncertainties in factors such as detector tilt, gantry angle, focal spot location, source-detector distance and source-pivot distance can produce several artifacts in the reconstructed volume. To accurately and efficiently calculate the location and angles of orientation of critical components of the system in DBT geometry, a suitable phantom is required. We have designed a calibration phantom for tomosynthesis and developed software for accurate measurement of the geometric parameters of a DBT system. These have been tested both by simulation and experiment. We will present estimates of the precision available with this technique for a prototype DBT system.
ERIC Educational Resources Information Center
Allen, Frank B.; And Others
This is part one of a two-part SMSG mathematics text for high school students. Topics include plane geometry, real numbers, triangles and angles, congruence, construction, parallel lines, perpendicular lines, and parallelograms. The text is written in Spanish. (RH)
Convection in Slab and Spheroidal Geometries
NASA Technical Reports Server (NTRS)
Porter, David H.; Woodward, Paul R.; Jacobs, Michael L.
2000-01-01
Three-dimensional numerical simulations of compressible turbulent thermally driven convection, in both slab and spheroidal geometries, are reviewed and analyzed in terms of velocity spectra and mixing-length theory. The same ideal gas model is used in both geometries, and resulting flows are compared. The piecewise-parabolic method (PPM), with either thermal conductivity or photospheric boundary conditions, is used to solve the fluid equations of motion. Fluid motions in both geometries exhibit a Kolmogorov-like k(sup -5/3) range in their velocity spectra. The longest wavelength modes are energetically dominant in both geometries, typically leading to one convection cell dominating the flow. In spheroidal geometry, a dipolar flow dominates the largest scale convective motions. Downflows are intensely turbulent and up drafts are relatively laminar in both geometries. In slab geometry, correlations between temperature and velocity fluctuations, which lead to the enthalpy flux, are fairly independent of depth. In spheroidal geometry this same correlation increases linearly with radius over the inner 70 percent by radius, in which the local pressure scale heights are a sizable fraction of the radius. The effects from the impenetrable boundary conditions in the slab geometry models are confused with the effects from non-local convection. In spheroidal geometry nonlocal effects, due to coherent plumes, are seen as far as several pressure scale heights from the lower boundary and are clearly distinguishable from boundary effects.
Acoustic waves of different geometry in polydisperse bubble liquids: Theory and experiment
NASA Astrophysics Data System (ADS)
Nigmatulin, R. I.; Gubaidullin, D. A.; Fedorov, Yu. V.
2013-06-01
A mathematical model that determines the propagation of acoustic waves of different geometry in two-fraction mixtures of liquids with polydispersed gas bubbles of various compositions is presented. A unique dispersion relationship, which takes into account the propagation of the plane, spherical, and cylindrical perturbations in these mixtures, is derived. It is shown that the theoretical curves of the phase velocity and the damping factor agree well with the experimental data involving the resonant frequency range.
Modeling the transmission of beta rays through thin foils in planar geometry.
Stanga, D; De Felice, P; Keightley, J; Capogni, M; Ionescu, E
2016-01-01
This paper is concerned with the modeling of the transmission of beta rays through thin foils in planar geometry based on the plane source concept, using Monte Carlo simulation of electron transport and least squares fitting. Applications of modeling results for calculating the efficiency of large-area beta sources, transmission coefficient of beta rays through thin foils and the beta detection efficiency of large-area detectors used in surface contamination measurements are also presented. PMID:26524407
Double plane wave reverse time migration with plane wave Green's function
NASA Astrophysics Data System (ADS)
Zhao, Z.; Sen, M. K.; Stoffa, P. L.
2015-12-01
Reverse time migration (RTM) is effective in obtaining complex subsurface structures from seismic data. By solving the two-way wave equation, RTM can use entire wavefield for imaging. Although powerful computer are becoming available, the conventional pre-stack shot gather RTM is still computationally expensive. Solving forward and backward wavefield propagation for each source location and shot gather is extremely time consuming, especially for large seismic datasets. We present an efficient, accurate and flexible plane wave RTM in the frequency domain where we utilize a compressed plane wave dataset, known as the double plane wave (DPW) dataset. Provided with densely sampled seismic dataset, shot gathers can be decomposed into source and receiver plane wave components with minimal artifacts. The DPW RTM is derived under the Born approximation and utilizes frequency domain plane wave Green's function for imaging. Time dips in the shot profiles can help to estimate the range of plane wave components present in shot gathers. Therefore, a limited number of plane wave Green's functions are needed for imaging. Plane wave Green's functions can be used for imaging both source and receiver plane waves. Source and receiver reciprocity can be used for imaging plane wave components at no cost and save half of the computation time. As a result, the computational burden for migration is substantially reduced. Plane wave components can be migrated independently to recover specific targets with given dips, and ray parameter common image gathers (CIGs) can be generated after migration directly. The ray parameter CIGs can be used to justify the correctness of velocity models. Subsurface anisotropy effects can also be included in our imaging condition, provided with plane wave Green's functions in the anisotropic media.
The plane of symmetry of interplanetary dust in the inner solar system
NASA Technical Reports Server (NTRS)
Leinert, C.; Richter, I.; Pitz, E.; Hanner, M.
1980-01-01
Observations of the zodiacal light from the space probes Helios 1 and 2 between 1.0 and 0.3 AU show - superimposed on the general radial dependence - a systematic variation of brightness and brightness distribution with position in the orbit which is caused by the inclination of the symmetry plane of interplanetary dust with respect to the ecliptic. By suitable choice of the observing geometry, the inclination and the ascending node of the symmetry plane can be determined directly from the data without recourse to model calculations. The resulting values of i equals 3.0 plus or minus 0.3 deg, Omega equals 87 plus or minus 4 deg are not compatible with a concentration of interplanetary dust to the invariable plane of the solar system. The data support the simple view that the distribution of interplanetary dust in the inner solar system is characterized throughout by one plane of symmetry and suggest that this plane extends to at least 1 AU.
Biomechanical differences between incline and plane hopping.
Kannas, Theodoros M; Kellis, Eleftherios; Amiridis, Ioannis G
2011-12-01
Kannas, TM, Kellis, E, and Amiridis, IG. Biomechanical differences between incline and plane hopping. J Strength Cond Res 25(12): 3334-3341, 2011-The need for the generation of higher joint power output during performance of dynamic activities led us to investigate the force-length relationship of the plantar flexors during consecutive stretch-shortening cycles of hopping. The hypothesis of this study was that hopping (consecutive jumps with the knee as straight as possible) on an inclined (15°) surface might lead to a better jumping performance compared with hopping on a plane surface (0°). Twelve active men performed 3 sets of 10 consecutive hops on both an incline and plane surface. Ground reaction forces; ankle and knee joint kinematics; electromyographic (EMG) activity from the medial gastrocnemius (MG), soleus (Sol) and tibialis anterior (TA); and architectural data from the MG were recorded. The results showed that participants jumped significantly higher (p < 0.05) when hopping on an inclined surface (30.32 ± 8.18 cm) compared with hopping on a plane surface (27.52 ± 4.97 cm). No differences in temporal characteristics between the 2 types of jumps were observed. Incline hopping induced significantly greater ankle dorsiflexion and knee extension at takeoff compared with plane hopping (p < 0.05). The fascicle length of the MG was greater at initial contact with the ground during incline hopping (p < 0.05). Moreover, the EMG activities of Sol and TA during the propulsion phase were significantly higher during incline compared with that during plane hopping (p < 0.05). It does not seem unreasonable to suggest that, if the aim of hopping plyometrics is to improve plantar flexor explosivity, incline hopping might be a more effective exercise than hopping on a plane surface.
Contact Geometry of Hyperbolic Equations of Generic Type
NASA Astrophysics Data System (ADS)
The, Dennis
2008-08-01
We study the contact geometry of scalar second order hyperbolic equations in the plane of generic type. Following a derivation of parametrized contact-invariants to distinguish Monge-Ampère (class 6-6), Goursat (class 6-7) and generic (class 7-7) hyperbolic equations, we use Cartan's equivalence method to study the generic case. An intriguing feature of this class of equations is that every generic hyperbolic equation admits at most a nine-dimensional contact symmetry algebra. The nine-dimensional bound is sharp: normal forms for the contact-equivalence classes of these maximally symmetric generic hyperbolic equations are derived and explicit symmetry algebras are presented. Moreover, these maximally symmetric equations are Darboux integrable. An enumeration of several submaximally symmetric (eight and seven-dimensional) generic hyperbolic structures is also given.
Angiocardiographic methods for determination of left ventricular geometry and volume
NASA Technical Reports Server (NTRS)
Sandler, H.; Dodge, H. T.
1974-01-01
Methods are described for calculating left ventricular (LV) dimensions and chamber volumes from radiographic films. The use of biplane films for the calculation of LV volume and volume change is based on the assumption of an ellipsoidal geometry. Calculation of LV volumes from biplane films usually overestimated known volumes in postmortem hearts regardless of the methods used for volume calculation. The reasons for this are probably best explained by the fact that a smooth-surface ellipse is used to represent the irregular cavity of the LV chamber. LV volume calculated from data in a single plane compared favorably and closely with volumes calculated from biplane films. A table of normal values of ventricular volume established by angiographic studies is presented.
Extracting geometry information from point cloud of urban building
NASA Astrophysics Data System (ADS)
Yang, Changqiang; Ye, Zetian
2009-10-01
The main purpose of the algorithm in this paper is to extract geometry information (mainly includes the plane function, the outlines and the corners of the building surfaces) from the point cloud. The main process includes: filter and sort the point cloud, get fitting lines in each column and merge the fitting lines, get fitting faces from the fitting lines and merge the fitting faces, extract the outlines and corners of the merged faces. The advantage of the algorithm includes: A face's adjacent faces can be got, the disturbing points can be automatically removed and the computation amount is relatively small. The algorithm is particularly suit for the point cloud got by vehicle-borne laser scan.
INTERIOR OF SECOND FLOOR BRIDGE BETWEEN PLANING MILL AND CAR ...
INTERIOR OF SECOND FLOOR BRIDGE BETWEEN PLANING MILL AND CAR MACHINE SHOP, LOOKING SOUTH TOWARD PLANING MILL. - Southern Pacific, Sacramento Shops, Planing Mill, 111 I Street, Sacramento, Sacramento County, CA
Riemannian geometry of fluctuation theory: An introduction
NASA Astrophysics Data System (ADS)
Velazquez, Luisberis
2016-05-01
Fluctuation geometry was recently proposed as a counterpart approach of Riemannian geometry of inference theory (information geometry), which describes the geometric features of the statistical manifold M of random events that are described by a family of continuous distributions dpξ(x|θ). This theory states a connection among geometry notions and statistical properties: separation distance as a measure of relative probabilities, curvature as a measure about the existence of irreducible statistical correlations, among others. In statistical mechanics, fluctuation geometry arises as the mathematical apparatus of a Riemannian extension of Einstein fluctuation theory, which is also closely related to Ruppeiner geometry of thermodynamics. Moreover, the curvature tensor allows to express some asymptotic formulae that account for the system fluctuating behavior beyond the gaussian approximation, while curvature scalar appears as a second-order correction of Legendre transformation between thermodynamic potentials.
Effect of torso geometry on the magnetocardiogram.
Tripp, J H
1977-01-01
Calculations of the effect of torso geometry on the extracorporeal magnetic field produced by a simple cardiac source have been carried out. Contrary to the results at present in the literature, it is found that the field solution is stable under perturbations of geometry in the sense that small relative changes in geometry produce comparably small changes in the magnetic field. Thus, simplified torso models may have a wider range of validity and usefulness than was previously thought. PMID:890026
Combinatorial Intricacies of Labeled Fano Planes
NASA Astrophysics Data System (ADS)
Saniga, Metod
2016-08-01
Given a seven-element set $X = \\{1,2,3,4,5,6,7\\}$, there are 30 ways to define a Fano plane on it. Let us call a line of such Fano plane, that is to say an unordered triple from $X$, ordinary or defective according as the sum of two smaller integers from the triple is or is not equal to the remaining one, respectively. A point of the labeled Fano plane is said to be of order $s$, $0 \\leq s \\leq 3$, if there are $s$ {\\it defective} lines passing through it. With such structural refinement in mind, the 30 Fano planes are shown to fall into eight distinct types. Out of the total of 35 lines, nine ordinary lines are of five different kinds, whereas the remaining 26 defective lines yield as many as ten distinct types. It is shown, in particular, that no labeled Fano plane can have all points of zeroth order, or feature just one point of order two. A connection with prominent configurations in Steiner triple systems is also pointed out.
A Viewpoint on the Quantity "Plane Angle"
NASA Astrophysics Data System (ADS)
Eder, W. E.
1982-01-01
Properties of the quantity "plane angle" are explored under the hypothesis that it is a dimensional quantity. The exploration proceeds especially with respect to the physical concept, its mathematical treatment, vector concepts, measurement theory, units of related quantities, engineering pragmatism, and SI. An attempt is made to bring these different relations into a rational, logical and consistent framework, and thus to justify the hypothesis. Various types of vectorial quantities are recognized, and their properties described with an outline of the necessary algebraic manipulations. The concept of plane angle is amplified, and its interdependence with the circular arc is explored. The resulting units of plane angle form a class of similar scales of measurement. Consequences of the confirmed hypothesis are developed for mathematical expressions involving trigonometric functions, rotational volumes and areas, mathematical limits, differentiation and series expansion. Consequences for mechanical rotational quantities are developed, with proposals for revisions to a number of expressions for derived units within SI. A revised definition for the quantity "plane angle" is stated to take account of the developed insights. There is a clear need to reconsider the status of plane angle and some other quantities within the international framework of SI.
Focal Plane Metrology for the LSST Camera
A Rasmussen, Andrew P.; Hale, Layton; Kim, Peter; Lee, Eric; Perl, Martin; Schindler, Rafe; Takacs, Peter; Thurston, Timothy; /SLAC
2007-01-10
Meeting the science goals for the Large Synoptic Survey Telescope (LSST) translates into a demanding set of imaging performance requirements for the optical system over a wide (3.5{sup o}) field of view. In turn, meeting those imaging requirements necessitates maintaining precise control of the focal plane surface (10 {micro}m P-V) over the entire field of view (640 mm diameter) at the operating temperature (T {approx} -100 C) and over the operational elevation angle range. We briefly describe the hierarchical design approach for the LSST Camera focal plane and the baseline design for assembling the flat focal plane at room temperature. Preliminary results of gravity load and thermal distortion calculations are provided, and early metrological verification of candidate materials under cold thermal conditions are presented. A detailed, generalized method for stitching together sparse metrology data originating from differential, non-contact metrological data acquisition spanning multiple (non-continuous) sensor surfaces making up the focal plane, is described and demonstrated. Finally, we describe some in situ alignment verification alternatives, some of which may be integrated into the camera's focal plane.
GLAMER - II. Multiple-plane gravitational lensing
NASA Astrophysics Data System (ADS)
Petkova, Margarita; Metcalf, R. Benton; Giocoli, Carlo
2014-12-01
We present an extension to multiple planes of the gravitational lensing code GLAMER. The method entails projecting the mass in the observed light-cone on to a discrete number of lens planes and inverse ray-shooting from the image to the source plane. The mass on each plane can be represented as haloes, simulation particles, a projected mass map extracted form a numerical simulation or any combination of these. The image finding is done in a source-oriented fashion, where only regions of interest are iteratively refined on an initially coarse image plane grid. The calculations are performed in parallel on shared memory machines. The code is able to handle different types of analytic haloes (NFW, NSIE, power law, etc.), haloes extracted from numerical simulations and clusters constructed from semi-analytic models (MOKA). Likewise, there are several different options for modelling the source(s) which can be distributed throughout the light-cone. The distribution of matter in the light-cone can be either taken from a pre-existing N-body numerical simulations, from halo catalogues, or are generated from an analytic mass function. We present several tests of the code and demonstrate some of its applications such as generating mock images of galaxy and galaxy cluster lenses.
Disformal transformation in Newton-Cartan geometry
NASA Astrophysics Data System (ADS)
Huang, Peng; Yuan, Fang-Fang
2016-08-01
Newton-Cartan geometry has played a central role in recent discussions of the non-relativistic holography and condensed matter systems. Although the conformal transformation in non-relativistic holography can easily be rephrased in terms of Newton-Cartan geometry, we show that it requires a nontrivial procedure to arrive at the consistent form of anisotropic disformal transformation in this geometry. Furthermore, as an application of the newly obtained transformation, we use it to induce a geometric structure which may be seen as a particular non-relativistic version of the Weyl integrable geometry.
NASA Technical Reports Server (NTRS)
Rahmat-Samii, Y.; Galindo-Israel, V.; Mittra, R.
1980-01-01
The planar configuration with a probe scanning a polar geometry is discussed with reference to its usefulness in the determination of a far field from near-field measurements. The accuracy of the method is verified numerically, using the concept of probe compensation as a vector deconvolution. Advantages of the Jacobi-Bessel series over the fast Fourier transforms for the plane-polar geometry are demonstrated. Finally, the far-field pattern of the Viking high gain antenna is constructed from the plane-polar near-field measured data and compared with the previously measured far-field pattern.
Cusp geometry in MHD simulations
NASA Astrophysics Data System (ADS)
Siscoe, George; Crooker, Nancy; Siebert, Keith; Maynard, Nelson; Weimer, Daniel; White, Willard
2005-01-01
The MHD simulations described here show that the latitude of the high-altitude cusp decreases as the IMF swings from North to South, that there is a pronounced dawn dusk asymmetry at high-altitude associated with a dawn dusk component of the IMF, and that at the same time there is also a pronounced dawn dusk asymmetry at low-altitude. The simulations generate a feature that represents what has been called the cleft. It appears as a tail (when the IMF has a By component) attached to the cusp, extending either toward the dawn flank or the dusk flank depending on the dawn dusk orientation of the IMF. This one-sided cleft connects the cusp to the magnetospheric sash. We compare cusp geometry predicted by MHD simulations against published observations based on Hawkeye and DMSP data. Regarding the high-altitude predictions, the comparisons are not definitive, mainly because the observations are incomplete or mutually inconsistent. Regarding the low-altitude prediction of a strong dawn dusk asymmetry, the observations are unambiguous and are in good qualitative agreement with the prediction.
NASA Astrophysics Data System (ADS)
Anderson, Lara B.; Heckman, Jonathan J.; Katz, Sheldon
2014-05-01
T-branes are a non-abelian generalization of intersecting branes in which the matrix of normal deformations is nilpotent along some subspace. In this paper we study the geometric remnant of this open string data for six-dimensional F-theory vacua. We show that in the dual M-theory / IIA compactification on a smooth Calabi-Yau threefold X smth, the geometric remnant of T-brane data translates to periods of the three-form potential valued in the intermediate Jacobian of X smth. Starting from a smoothing of a singular Calabi-Yau, we show how to track this data in singular limits using the theory of limiting mixed Hodge structures, which in turn directly points to an emergent Hitchin-like system coupled to defects. We argue that the physical data of an F-theory compactification on a singular threefold involves specifying both a geometry as well as the remnant of three-form potential moduli and flux which is localized on the discriminant. We give examples of T-branes in compact F-theory models with heterotic duals, and comment on the extension of our results to four-dimensional vacua.
Eye movements and information geometry.
Lenz, Reiner
2016-08-01
The human visual system uses eye movements to gather visual information. They act as visual scanning processes and can roughly be divided into two different types: small movements around fixation points and larger movements between fixation points. The processes are often modeled as random walks, and recent models based on heavy tail distributions, also known as Levý flights, have been used in these investigations. In contrast to these approaches we do not model the stochastic processes, but we will show that the step lengths of the movements between fixation points follow generalized Pareto distributions (GPDs). We will use general arguments from the theory of extreme value statistics to motivate the usage of the GPD and show empirically that the GPDs provide good fits for measured eye tracking data. In the framework of information geometry the GPDs with a common threshold form a two-dimensional Riemann manifold with the Fisher information matrix as a metric. We compute the Fisher information matrix for the GPDs and introduce a feature vector describing a GPD by its parameters and different geometrical properties of its Fisher information matrix. In our statistical analysis we use eye tracker measurements in a database with 15 observers viewing 1003 images under free-viewing conditions. We use Matlab functions with their standard parameter settings and show that a naive Bayes classifier using the eigenvalues of the Fisher information matrix provides a high classification rate identifying the 15 observers in the database. PMID:27505658
Combinatorics, geometry, and mathematical physics
Chen, W.Y.C.; Louck, J.D.
1998-11-01
This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). Combinatorics and geometry have been among the most active areas of mathematics over the past few years because of newly discovered inter-relations between them and their potential for applications. In this project, the authors set out to identify problems in physics, chemistry, and biology where these methods could impact significantly. In particular, the experience suggested that the areas of unitary symmetry and discrete dynamical systems could be brought more strongly under the purview of combinatorial methods. Unitary symmetry deals with the detailed description of the quantum mechanics of many-particle systems, and discrete dynamical systems with chaotic systems. The depth and complexity of the mathematics in these physical areas of research suggested that not only could significant advances be made in these areas, but also that here would be a fertile feedback of concept and structure to enrich combinatorics itself by setting new directions. During the three years of this project, the goals have been realized beyond expectation, and in this report the authors set forth these advancements and justify their optimism.
An interactive approach to surface-fitting complex geometries for flowfield applications
NASA Technical Reports Server (NTRS)
Dejarnette, Fred R.; Hamilton, H. Harris, II; Cheatwood, F. Mcneil
1987-01-01
Numerical flowfield methods require a geometry subprogram which can calculate body coordinates, slopes, and radii of curvature for typical aircraft and spacecraft configurations. The objective of this paper is to develop a new surface-fitting technique which addresses two major problems with existing geometry packages: computer storage requirements and the time required of the user for the initial set-up of the geometry model. In the present method, coordinates of cross sections are fit in a least-squares sense using segments of general conic sections. After fitting each cross section, the next step is to blend the cross-sectional curve-fits in the longitudinal direction using general conics to fit specific meridional half-planes. For the initial setup of the geometry model, an interactive, completely menu-driven computer code has been developed to allow the user to make modifications to the initial fit for a given cross section or meridional cut. Graphic displays are provided to assist the user in the visualization of the effect of each modification. The completed model may be viewed from any angle using the code's three-dimensional graphics package. Geometry results for the modeling of the Space Shuttle and a proposed Aeroassist Flight Experiment (AFE) geometry are presented, in addition to calculated heat-transfer rates based on these models.
Electromagnetic diffraction by plane reflection diffraction gratings
NASA Technical Reports Server (NTRS)
Bocker, R. P.; Marathay, A. S.
1972-01-01
A plane wave theory was developed to study electromagnetic diffraction by plane reflection diffraction gratings of infinite extent. A computer program was written to calculate the energy distribution in the various orders of diffraction for the cases when the electric or magnetic field vectors are parallel to the grating grooves. Within the region of validity of this theory, results were in excellent agreement with those in the literature. Energy conservation checks were also made to determine the region of validity of the plane wave theory. The computer program was flexible enough to analyze any grating profile that could be described by a single value function f(x). Within the region of validity the program could be used with confidence. The computer program was used to investigate the polarization and blaze properties of the diffraction grating.
Solid-state curved focal plane arrays
NASA Technical Reports Server (NTRS)
Nikzad, Shouleh (Inventor); Hoenk, Michael (Inventor); Jones, Todd (Inventor)
2010-01-01
The present invention relates to curved focal plane arrays. More specifically, the present invention relates to a system and method for making solid-state curved focal plane arrays from standard and high-purity devices that may be matched to a given optical system. There are two ways to make a curved focal plane arrays starting with the fully fabricated device. One way, is to thin the device and conform it to a curvature. A second way, is to back-illuminate a thick device without making a thinned membrane. The thick device is a special class of devices; for example devices fabricated with high purity silicon. One surface of the device (the non VLSI fabricated surface, also referred to as the back surface) can be polished to form a curved surface.
Optimal plane change by low aerodynamic forces
NASA Technical Reports Server (NTRS)
Vinh, Nguyen X.; Ma, Der-Ming
1990-01-01
This paper presents the exact dimensionless equations of motion and the necessary conditions for the computation of the optimal trajectories of a hypervelocity vehicle flying through a nonrotating spherical planetary atmosphere. It is shown that there are two types of maneuvers with nearly identical plane change. In the hard maneuver, the vehicle is pulled down to low altitude for aerodyamic plane change before exit at the prescribed final speed. In the slow maneuver which is described in detail in this paper, the vehicle remains in orbital flight with a small incremental plane change during each passage through the perigee. This maneuver requires several revolutions, and the technique for computation is similar to that in the problem of contraction of orbit.
Turbulent boundary layers over nonstationary plane boundaries
NASA Technical Reports Server (NTRS)
Roper, A. T.
1976-01-01
Methods of predicting integral parameters and skin-friction coefficients of turbulent boundary layers developing over moving-ground-planes are evaluated using test information from three different wind tunnel facilities at the NASA Langley Research Center. These data include test information from the VSTOL tunnel which is presented for the first time. The three methods evaluated were: (1) relative integral parameter method, (2) relative power law method, and (3) modified law of the wall method. Methods (1) and (2) can be used to predict moving-ground-plane shape factors with an expected accuracy of + or - 10%. They may also be used to predict moving-ground-plane displacement and momentum thicknesses with lower expected accuracy. This decrease in accuracy can be traced to the failure of approximations upon which these methods are based to prove universal when compared with VSTOL tunnel test results.
A miniature robotic plane meteorological sounding system
NASA Astrophysics Data System (ADS)
Ma, Shuqing; Chen, Hongbin; Wang, Gai; Pan, Yi; Li, Qiang
2004-12-01
This article presents a miniature robotic plane meteorological sounding system (RPMSS), which consists of three major subsystems: a miniature robotic plane, an air-borne meteorological sounding and flight control system, and a ground-based system. Take-off and landing of the miniature aircraft are guided by radio control, and the flight of the robotic plane along a pre-designed trajectory is automatically piloted by an onboard navigation system. The observed meteorological data as well as all flight information are sent back in real time to the ground, then displayed and recorded by the ground-based computer. The ground-based subsystem can also transmit instructions to the air-borne control subsystem. Good system performance has been demonstrated by more than 300 hours of flight for atmospheric sounding.
Are rotating planes of satellite galaxies ubiquitous?
NASA Astrophysics Data System (ADS)
Phillips, John I.; Cooper, Michael C.; Bullock, James S.; Boylan-Kolchin, Michael
2015-11-01
We compare the dynamics of satellite galaxies in the Sloan Digital Sky Survey to simple models in order to test the hypothesis that a large fraction of satellites corotate in coherent planes. We confirm the previously reported excess of corotating satellite pairs located near diametric opposition with respect to their host, but show that this signal is unlikely to be due to rotating discs (or planes) of satellites. In particular, no overabundance of corotating satellites pairs is observed within ˜20°-50° of direct opposition, as would be expected for planar distributions inclined relative to the line of sight. Instead, the excess corotation for satellite pairs within ˜10° of opposition is consistent with random noise associated with undersampling of an underlying isotropic velocity distribution. Based upon the observed dynamics of the luminous satellite population, we conclude that at most 10 per cent of isolated hosts harbour corotating satellite planes (as traced by bright satellites).
Restricted numerical shadow and the geometry of quantum entanglement
NASA Astrophysics Data System (ADS)
Puchała, Zbigniew; Miszczak, Jarosław Adam; Gawron, Piotr; Dunkl, Charles F.; Holbrook, John A.; Życzkowski, Karol
2012-10-01
The restricted numerical range WR(A) of an operator A acting on a D-dimensional Hilbert space is defined as a set of all possible expectation values of this operator among pure states which belong to a certain subset R of the set of pure quantum states of dimension D. One considers for instance the set of real states, or in the case of composite spaces, the set of product states and the set of maximally entangled states. Combining the operator theory with a probabilistic approach we introduce the restricted numerical shadow of A—a normalized probability distribution on the complex plane supported in WR(A). Its value at point z \\in { C} is equal to the probability that the expectation value <ψ|A|ψ> is equal to z, where |ψ> represents a random quantum state in subset R distributed according to the natural measure on this set, induced by the unitarily invariant Fubini-Study measure. Studying restricted shadows of operators of a fixed size D = NANB we analyse the geometry of sets of separable and maximally entangled states of the NA × NB composite quantum system. Investigating trajectories formed by evolving quantum states projected into the plane of the shadow, we study the dynamics of quantum entanglement. A similar analysis extended for operators on D = 23-dimensional Hilbert space allows us to investigate the structure of the orbits of GHZ and W quantum states of a three-qubit system.
Spin-orbit torque magnetization switching controlled by geometry.
Safeer, C K; Jué, Emilie; Lopez, Alexandre; Buda-Prejbeanu, Liliana; Auffret, Stéphane; Pizzini, Stefania; Boulle, Olivier; Miron, Ioan Mihai; Gaudin, Gilles
2016-02-01
Magnetization reversal by an electric current is essential for future magnetic data storage technology, such as magnetic random access memories. Typically, an electric current is injected into a pillar-shaped magnetic element, and switching relies on the transfer of spin momentum from a ferromagnetic reference layer (an approach known as spin-transfer torque). Recently, an alternative technique has emerged that uses spin-orbit torque (SOT) and allows the magnetization to be reversed without a polarizing layer by transferring angular momentum directly from the crystal lattice. With spin-orbit torque, the current is no longer applied perpendicularly, but is in the plane of the magnetic thin film. Therefore, the current flow is no longer restricted to a single direction and can have any orientation within the film plane. Here, we use Kerr microscopy to examine spin-orbit torque-driven domain wall motion in Co/AlOx wires with different shapes and orientations on top of a current-carrying Pt layer. The displacement of the domain walls is found to be highly dependent on the angle between the direction of the current and domain wall motion, and asymmetric and nonlinear with respect to the current polarity. Using these insights, devices are fabricated in which magnetization switching is determined entirely by the geometry of the device. PMID:26551017
Spin-orbit torque magnetization switching controlled by geometry
NASA Astrophysics Data System (ADS)
Safeer, C. K.; Jué, Emilie; Lopez, Alexandre; Buda-Prejbeanu, Liliana; Auffret, Stéphane; Pizzini, Stefania; Boulle, Olivier; Miron, Ioan Mihai; Gaudin, Gilles
2016-02-01
Magnetization reversal by an electric current is essential for future magnetic data storage technology, such as magnetic random access memories. Typically, an electric current is injected into a pillar-shaped magnetic element, and switching relies on the transfer of spin momentum from a ferromagnetic reference layer (an approach known as spin-transfer torque). Recently, an alternative technique has emerged that uses spin-orbit torque (SOT) and allows the magnetization to be reversed without a polarizing layer by transferring angular momentum directly from the crystal lattice. With spin-orbit torque, the current is no longer applied perpendicularly, but is in the plane of the magnetic thin film. Therefore, the current flow is no longer restricted to a single direction and can have any orientation within the film plane. Here, we use Kerr microscopy to examine spin-orbit torque-driven domain wall motion in Co/AlOx wires with different shapes and orientations on top of a current-carrying Pt layer. The displacement of the domain walls is found to be highly dependent on the angle between the direction of the current and domain wall motion, and asymmetric and nonlinear with respect to the current polarity. Using these insights, devices are fabricated in which magnetization switching is determined entirely by the geometry of the device.
Axisymmetric curvature-driven instability in a model divertor geometry
Farmer, W. A.; Ryutov, D. D.
2013-09-15
A model problem is presented which qualitatively describes a pressure-driven instability which can occur near the null-point in the divertor region of a tokamak where the poloidal field becomes small. The model problem is described by a horizontal slot with a vertical magnetic field which plays the role of the poloidal field. Line-tying boundary conditions are applied at the planes defining the slot. A toroidal field lying parallel to the planes is assumed to be very strong, thereby constraining the possible structure of the perturbations. Axisymmetric perturbations which leave the toroidal field unperturbed are analyzed. Ideal magnetohydrodynamics is used, and the instability threshold is determined by the energy principle. Because of the boundary conditions, the Euler equation is, in general, non-separable except at marginal stability. This problem may be useful in understanding the source of heat transport into the private flux region in a snowflake divertor which possesses a large region of small poloidal field, and for code benchmarking as it yields simple analytic results in an interesting geometry.
Wake Geometry Measurements and Analytical Calculations on a Small-Scale Rotor Model
NASA Technical Reports Server (NTRS)
Ghee, Terence A.; Berry, John D.; Zori, Laith A. J.; Elliott, Joe W.
1996-01-01
An experimental investigation was conducted in the Langley 14- by 22-Foot Subsonic Tunnel to quantify the rotor wake behind a scale model helicopter rotor in forward level flight at one thrust level. The rotor system in this test consisted of a four-bladed fully articulated hub with blades of rectangular planform and an NACA 0012 airfoil section. A laser light sheet, seeded with propylene glycol smoke, was used to visualize the vortex geometry in the flow in planes parallel and perpendicular to the free-stream flow. Quantitative measurements of wake geometric proper- ties, such as vortex location, vertical skew angle, and vortex particle void radius, were obtained as well as convective velocities for blade tip vortices. Comparisons were made between experimental data and four computational method predictions of experimental tip vortex locations, vortex vertical skew angles, and wake geometries. The results of these comparisons highlight difficulties of accurate wake geometry predictions.
An interactive user-friendly approach to surface-fitting three-dimensional geometries
NASA Technical Reports Server (NTRS)
Cheatwood, F. Mcneil; Dejarnette, Fred R.
1988-01-01
A surface-fitting technique has been developed which addresses two problems with existing geometry packages: computer storage requirements and the time required of the user for the initial setup of the geometry model. Coordinates of cross sections are fit using segments of general conic sections. The next step is to blend the cross-sectional curve-fits in the longitudinal direction using general conics to fit specific meridional half-planes. Provisions are made to allow the fitting of fuselages and wings so that entire wing-body combinations may be modeled. This report includes the development of the technique along with a User's Guide for the various menus within the program. Results for the modeling of the Space Shuttle and a proposed Aeroassist Flight Experiment geometry are presented.
A magnetic method for determining the geometry of hydraulic fractures
Byerlee, J.D.; Johnston, M.J.S.
1976-01-01
We propose a method that may be used to determine the spatial orientation of the fracture plane developed during hydraulic fracture. In the method, magnetic particles are injected into the crack with the fracturing fluid so as to generate a sheet of magnetized material. Since the magnetization of a body with extreme dimension ratios, such as a crack, exceeds that of an equidimensional body and since this magnetization is sensitive both to orientation and geometry, this could be used to obtain information about the crack. By measuring the vertical and horizontal components of the magnetic field and field gradients at the earth's surface surrounding the injection well with superconducting magnetometers having 10-4 gamma sensitivity and also by measuring field direction within the well itself, it should be possible to calculate the orientation and perhaps infer the approximate geometry of the fracture surface. Experiments on electric field potential operated in conjunction with this experiment could further constrain estimates of shape and orientation. ?? 1976 Birkha??user Verlag.
Note: A novel integrated microforce measurement system for plane-plane contact research
NASA Astrophysics Data System (ADS)
Dong, W.; Rostoucher, D.; Gauthier, M.
2010-11-01
The evaluation of plane-plane contact force has become a big issue in micro-/nano research, for example in microassembly. However with the lack of effective experimental equipments, the research on plane-plane contact has been limited to theoretical formulations or virtual simulation. In this paper, a microforce sensor and precision parallel robot integrated system is proposed for the microforce measurement of plane-plane contact. In the proposed system, the two objects are fixed on the parallel robot end-platform and the microforce sensor probe tip, respectively, and the high precision robot system is employed to provide six degree-of-freedom motions between both objects. So it is convenient for the microforce measurement between the planar objects with different orientations. As a significant application, the proposed system is utilized for measurements of pull-off force between planar objects, in which the validation of the system is demonstrated in practice. The proposed microforce measurement system is generic, which can be extended to a variety of microforce measurements in plane-plane contact.
Hybrid Extrinsic Silicon Focal Plane Architecture
NASA Astrophysics Data System (ADS)
Pommerrenig, D. H.; Meinhardt, T.; Lowe, J.
1981-02-01
Large-area focal planes require mechanical assembly techniques which must be compatible with optical alignment, minimum deadspace, and cryogenic requirements in order to achieve optimum performance. Hybrid extrinsic silicon has been found particularly suitable for such an application. It will be shown that by choosing a large-area extrinsic silicon detector array which is hybrid-mated to a multiplicity of multiplexers a very cost-effective and high-density focal plane module can be assembled. Other advantages of this approach are inherent optical alignment and excellent performance.
Trajectory optimization for the national aerospace plane
NASA Technical Reports Server (NTRS)
Lu, Ping
1993-01-01
During the past six months the research objectives outlined in the last semi-annual report were accomplished. Specifically, these are: three-dimensional (3-D) fuel-optimal ascent trajectory of the aerospace plane and the effects of thrust vectoring control (TVC) on the fuel consumption and trajectory shaping were investigated; the maximum abort landing area (footprint) was studied; preliminary assessment of simultaneous design of the ascent trajectory and the vehicle configuration for the aerospace plane was also conducted. The work accomplished in the reporting period is summarized.
Computer Model Of Focal Plane Array
NASA Astrophysics Data System (ADS)
Thvedt, Tom A.; Willoughby, Charles T.; Salcido, Michael M.; Dereniak, Eustace L.
1987-11-01
This paper presents a computer program for simulation of an infrared focal plane array. Standard equations are used to support a menu driven program developed for an IBM personal computer. The terms and equations for each section are presented and samples of actual screen displays of a currently available device are also included. The program is intended to provide the user with a better capability to understand and to study the tradeoffs of fabrication parameters versus the focal plane array performance (i.e. CTE, both spatial and temporal dynamic range, MTF, and noise) used for an optical sensor system analysis. Only surface channel devices are considered in the simulation.
NASA Technical Reports Server (NTRS)
Platnick, S.
1999-01-01
Photon transport in a multiple scattering medium is critically dependent on scattering statistics, in particular the average number of scatterings. A superposition technique is derived to accurately determine the average number of scatterings encountered by reflected and transmitted photons within arbitrary layers in plane-parallel, vertically inhomogeneous clouds. As expected, the resulting scattering number profiles are highly dependent on cloud particle absorption and solar/viewing geometry. The technique uses efficient adding and doubling radiative transfer procedures, avoiding traditional time-intensive Monte Carlo methods. Derived superposition formulae are applied to a variety of geometries and cloud models, and selected results are compared with Monte Carlo calculations. Cloud remote sensing techniques that use solar reflectance or transmittance measurements generally assume a homogeneous plane-parallel cloud structure. The scales over which this assumption is relevant, in both the vertical and horizontal, can be obtained from the superposition calculations. Though the emphasis is on photon transport in clouds, the derived technique is applicable to any scattering plane-parallel radiative transfer problem, including arbitrary combinations of cloud, aerosol, and gas layers in the atmosphere.
NASA Astrophysics Data System (ADS)
Steinberg, Adam Michael; Driscoll, James F.; Ceccio, Steven L.
2009-09-01
A new orthogonal-plane cinema-stereoscopic particle image velocimetry (OPCS-PIV) diagnostic has been used to measure the dynamics of three-dimensional turbulence-flame interactions. The diagnostic employed two orthogonal PIV planes, with one aligned perpendicular and one aligned parallel to the streamwise flow direction. In the plane normal to the flow, temporally resolved slices of the nine-component velocity gradient tensor were determined using Taylor’s hypothesis. Volumetric reconstruction of the 3D turbulence was performed using these slices. The PIV plane parallel to the streamwise flow direction was then used to measure the evolution of the turbulence; the path and strength of 3D turbulent structures as they interacted with the flame were determined from their image in this second plane. Structures of both vorticity and strain-rate magnitude were extracted from the flow. The geometry of these structures agreed well with predictions from direct numerical simulations. The interaction of turbulent structures with the flame also was observed. In three dimensions, these interactions had complex geometries that could not be reflected in either planar measurements or simple flame-vortex configurations.
Detonation diffraction through different geometries
NASA Astrophysics Data System (ADS)
Sorin, Rémy; Zitoun, Ratiba; Khasainov, Boris; Desbordes, Daniel
2009-04-01
We performed the study of the diffraction of a self-sustained detonation from a cylindrical tube (of inner diameter d) through different geometric configurations in order to characterise the transmission processes and to quantify the transmission criteria to the reception chamber. For the diffraction from a tube to the open space the transmission criteria is expressed by d c = k c · λ (with λ the detonation cell size and k c depending on the mixture and on the operture configuration, classically 13 for alkane mixtures with oxygen). The studied geometries are: (a) a sharp increase of diameter ( D/ d > 1) with and without a central obstacle in the diffracting section, (b) a conical divergent with a central obstacle in the diffracting section and (c) an inversed intermediate one end closed tube insuring a double reflection before a final diffraction between the initiator tube and the reception chamber. The results for case A show that the reinitiation process depends on the ratio d/ λ. For ratios below k c the re-ignition takes place at the receptor tube wall and at a fixed distance from the step, i.e. closely after the diffracted shock reflection shows a Mach stem configuration. For ratios below a limit ratio k lim (which depends on D/ d) the re-ignition distance increases with the decrease of d/λ. For both case A and B the introduction of a central obstacle (of blockage ratio BR = 0.5) at the exit of the initiator tube decreases the critical transmission ratio k c by 50%. The results in configuration C show that the re-ignition process depends both on d/ λ and the geometric conditions. Optimal configuration is found that provides the transmission through the two successive reflections (from d = 26 mm to D ch = 200 mm) at as small d/ λ as 2.2 whatever the intermediate diameter D is. This configuration provides a significant improvement in the detonation transmission conditions.
Quantum groups: Geometry and applications
Chu, C.S.
1996-05-13
The main theme of this thesis is a study of the geometry of quantum groups and quantum spaces, with the hope that they will be useful for the construction of quantum field theory with quantum group symmetry. The main tool used is the Faddeev-Reshetikhin-Takhtajan description of quantum groups. A few content-rich examples of quantum complex spaces with quantum group symmetry are treated in details. In chapter 1, the author reviews some of the basic concepts and notions for Hopf algebras and other background materials. In chapter 2, he studies the vector fields of quantum groups. A compact realization of these vector fields as pseudodifferential operators acting on the linear quantum spaces is given. In chapter 3, he describes the quantum sphere as a complex quantum manifold by means of a quantum stereographic projection. A covariant calculus is introduced. An interesting property of this calculus is the existence of a one-form realization of the exterior differential operator. The concept of a braided comodule is introduced and a braided algebra of quantum spheres is constructed. In chapter 4, the author considers the more general higher dimensional quantum complex projective spaces and the quantum Grassman manifolds. Differential calculus, integration and braiding can be introduced as in the one dimensional case. Finally, in chapter 5, he studies the framework of quantum principal bundle and construct the q-deformed Dirac monopole as a quantum principal bundle with a quantum sphere as the base and a U(1) with non-commutative calculus as the fiber. The first Chern class can be introduced and integrated to give the monopole charge.
A geometric calibration method for inverse geometry computed tomography using P-matrices
NASA Astrophysics Data System (ADS)
Slagowski, Jordan M.; Dunkerley, David A. P.; Hatt, Charles R.; Speidel, Michael A.
2016-03-01
Accurate and artifact free reconstruction of tomographic images requires precise knowledge of the imaging system geometry. This work proposes a novel projection matrix (P-matrix) based calibration method to enable C-arm inverse geometry CT (IGCT). The method is evaluated for scanning-beam digital x-ray (SBDX), a C-arm mounted inverse geometry fluoroscopic technology. A helical configuration of fiducials is imaged at each gantry angle in a rotational acquisition. For each gantry angle, digital tomosynthesis is performed at multiple planes and a composite image analogous to a cone-beam projection is generated from the plane stack. The geometry of the C-arm, source array, and detector array is determined at each angle by constructing a parameterized 3D-to-2D projection matrix that minimizes the sum-of-squared deviations between measured and projected fiducial coordinates. Simulations were used to evaluate calibration performance with translations and rotations of the source and detector. In a geometry with 1 mm translation of the central ray relative to the axis-of-rotation and 1 degree yaw of the detector and source arrays, the maximum error in the recovered translational parameters was 0.4 mm and maximum error in the rotation parameter was 0.02 degrees. The relative rootmean- square error in a reconstruction of a numerical thorax phantom was 0.4% using the calibration method, versus 7.7% without calibration. Changes in source-detector-distance were the most challenging to estimate. Reconstruction of experimental SBDX data using the proposed method eliminated double contour artifacts present in a non-calibrated reconstruction. The proposed IGCT geometric calibration method reduces image artifacts when uncertainties exist in system geometry.
A transient, quadratic nodal method for triangular-Z geometry
DeLorey, T.F.
1993-06-01
Many systematically-derived nodal methods have been developed for Cartesian geometry due to the extensive interest in Light Water Reactors. These methods typically model the transverse-integrated flux as either an analytic or low order polynomial function of position within the node. Recently, quadratic nodal methods have been developed for R-Z and hexagonal geometry. A static and transient quadratic nodal method is developed for triangular-Z geometry. This development is particularly challenging because the quadratic expansion in each node must be performed between the node faces and the triangular points. As a consequence, in the 2-D plane, the flux and current at the points of the triangles must be treated. Quadratic nodal equations are solved using a non-linear iteration scheme, which utilizes the corrected, mesh-centered finite difference equations, and forces these equations to match the quadratic equations by computing discontinuity factors during the solution. Transient nodal equations are solved using the improved quasi-static method, which has been shown to be a very efficient solution method for transient problems. Several static problems are used to compare the quadratic nodal method to the Coarse Mesh Finite Difference (CMFD) method. The quadratic method is shown to give more accurate node-averaged fluxes. However, it appears that the method has difficulty predicting node leakages near reactor boundaries and severe material interfaces. The consequence is that the eigenvalue may be poorly predicted for certain reactor configurations. The transient methods are tested using a simple analytic test problem, a heterogeneous heavy water reactor benchmark problem, and three thermal hydraulic test problems. Results indicate that the transient methods have been implemented correctly.
Estimating fracture geometry in the naturally fractured Antrim Shale
Hopkins, C.W.; Frantz, J.H. Jr.; Hill, D.G.
1995-12-31
The Antrim Shale of the Michigan Basin has been an active gas play with over 3,500 wells drilled over the last 5 years. There is substantial evidence that the Antrim must be fracture stimulated to be economical and that two-stage treatments provide the best results. However, due to the shallow depths (500-2300 ft) and naturally fractured nature of the Antrim, fracture geometry is complex, and determination of optimal fracture treatments is not straight forward. Because historical field comparisons did not provide insight on the optimal fracture treatments, the Gas Research Institute (GRI) instituted a field-based project for the specific purpose of evaluating the geometry of hydraulic fractures in the Antrim. Open- and cased-hole tests were performed on two separate Antrim wells - a shallow producer (600 {+-} ft) and a deep producer (1550 {+-} ft). Open-hole testing and data collection consisted of in-situ stress and mechanical property testing with Halliburton`s THE{trademark} Tool (9 tests) and a detailed suite of geophysical logs including dipole sonic logs and natural fracture detection logs. Cased-hole testing consisted of pre- and post-fracture injection/falloff tests, minifracture treatments, multiple isotope tracer and tracer logs, and treating pressure and production data analysis. The shallow depths, low in-situ stresses, and extremely fractured nature of the Antrim probably results in the preferential opening of existing fractures instead of the creation of new fracture planes. As a result, the creation of multiple fractures and severe near wellbore tortuosity is likely. Therefore, the natural fractures are responsible for increased leakoff and will greatly impact created fracture geometry. The results also suggest that creating long propped hydraulic fractures in the Antrim is not likely due to the creation of multiple fractures.
Geometry and earthquake potential of the shoreline fault, central California
Hardebeck, Jeanne L.
2013-01-01
The Shoreline fault is a vertical strike‐slip fault running along the coastline near San Luis Obispo, California. Much is unknown about the Shoreline fault, including its slip rate and the details of its geometry. Here, I study the geometry of the Shoreline fault at seismogenic depth, as well as the adjacent section of the offshore Hosgri fault, using seismicity relocations and earthquake focal mechanisms. The Optimal Anisotropic Dynamic Clustering (OADC) algorithm (Ouillon et al., 2008) is used to objectively identify the simplest planar fault geometry that fits all of the earthquakes to within their location uncertainty. The OADC results show that the Shoreline fault is a single continuous structure that connects to the Hosgri fault. Discontinuities smaller than about 1 km may be undetected, but would be too small to be barriers to earthquake rupture. The Hosgri fault dips steeply to the east, while the Shoreline fault is essentially vertical, so the Hosgri fault dips towards and under the Shoreline fault as the two faults approach their intersection. The focal mechanisms generally agree with pure right‐lateral strike‐slip on the OADC planes, but suggest a non‐planar Hosgri fault or another structure underlying the northern Shoreline fault. The Shoreline fault most likely transfers strike‐slip motion between the Hosgri fault and other faults of the Pacific–North America plate boundary system to the east. A hypothetical earthquake rupturing the entire known length of the Shoreline fault would have a moment magnitude of 6.4–6.8. A hypothetical earthquake rupturing the Shoreline fault and the section of the Hosgri fault north of the Hosgri–Shoreline junction would have a moment magnitude of 7.2–7.5.
Computing Bisectors in a Dynamic Geometry Environment
ERIC Educational Resources Information Center
Botana, Francisco
2013-01-01
In this note, an approach combining dynamic geometry and automated deduction techniques is used to study the bisectors between points and curves. Usual teacher constructions for bisectors are discussed, showing that inherent limitations in dynamic geometry software impede their thorough study. We show that the interactive sketching of bisectors…
Geometry and Education in the Internet Age.
ERIC Educational Resources Information Center
Kortenkamp, Ulrich H.; Richter-Gebert, Jurgen
This paper discusses the requirements of Interactive Geometry Systems (IGSs) and how they can be fulfilled, explains how a geometry tool can benefit from the Internet, and presents Cinderella's Cafe. Cinderella's Cafe is a new IGS with a high mathematical background that uses the most general mathematical models whenever possible, is highly…
Improving African American Achievement in Geometry Honors
ERIC Educational Resources Information Center
Mims, Adrian B.
2010-01-01
This case study evaluated the significance of implementing an enrichment mathematics course during the summer to rising African American ninth graders entitled, "Geometry Honors Preview." In the past, 60 to 70 percent of African American students in this school district had withdrawn from Geometry Honors by the second academic quarter. This study…
Historical Digressions in Greek Geometry Lessons.
ERIC Educational Resources Information Center
Thomaidis, Yannis
1991-01-01
Presents an attempt to combine the history of mathematics of ancient Greece with the course on theoretical geometry taught in Greek secondary schools. Three sections present the history of ancient Greek geometry, geometrical constructions using straightedges and compasses, and an application of Ptolemy's theorem in solving ancient astronomy…
Different lattice geometries with a synthetic dimension
NASA Astrophysics Data System (ADS)
Suszalski, Dominik; Zakrzewski, Jakub
2016-09-01
The possibility of creating different geometries with the help of an extra synthetic dimension in optical lattices is studied. The additional linear potential together with Raman-assisted tunnelings are used to engineer well-controlled tunnelings between available states. The great flexibility of the system allows us to obtain different geometries of synthetic lattices with the possibility for adding synthetic gauge fields.
The slab geometry laser. I - Theory
NASA Technical Reports Server (NTRS)
Eggleston, J. M.; Kane, T. J.; Kuhn, K.; Byer, R. L.; Unternahrer, J.
1984-01-01
Slab geometry solid-state lasers offer significant performance improvements over conventional rod-geometry lasers. A detailed theoretical description of the thermal, stress, and beam-propagation characteristics of a slab laser is presented. The analysis includes consideration of the effects of the zig-zag optical path, which eliminates thermal and stress focusing and reduces residual birefringence.
Cell division intersects with cell geometry.
Moseley, James B; Nurse, Paul
2010-07-23
Single-celled organisms monitor cell geometry and use this information to control cell division. Such geometry-sensing mechanisms control both the decision to enter into cell division and the physical orientation of the chromosome segregation machinery, suggesting that signals controlling cell division may be linked to the mechanisms that ensure proper chromosome segregation.
Reasoning by Contradiction in Dynamic Geometry
ERIC Educational Resources Information Center
Baccaglini-Frank, Anna; Antonini, Samuele; Leung, Allen; Mariotti, Maria Alessandra
2013-01-01
This paper addresses contributions that dynamic geometry systems (DGSs) may give in reasoning by contradiction in geometry. We present analyses of three excerpts of students' work and use the notion of pseudo object, elaborated from previous research, to show some specificities of DGS in constructing proof by contradiction. In particular, we…
Teaching Geometry to Visually Impaired Students
ERIC Educational Resources Information Center
Pritchard, Christine K.; Lamb, John H.
2012-01-01
NCTM (2000) described geometry as "a means of describing, analyzing, and understanding the world and seeing beauty in its structures" (p. 309). Dossey et al. (2002) captured the essence of this aspect of visualization by stating that geometry fosters in students an ability to "visualize and mentally manipulate geometric objects." (p. 200).…
Making Euclidean Geometry Compulsory: Are We Prepared?
ERIC Educational Resources Information Center
Van Putten, Sonja; Howie, Sarah; Stols, Gerrit
2010-01-01
This study investigated the attitude towards, as well as the level of understanding of Euclidean geometry in pre-service mathematics education (PME) students. In order to do so, a case study was undertaken within which a one group pre-post-test procedure was conducted around a geometry module, and a representative group of students was interviewed…
Stop Teaching and Let Students Learn Geometry
ERIC Educational Resources Information Center
Bosse, Michael J.; Adu-Gyamfi, Kwaku
2011-01-01
For many high school students as well as preservice teachers, geometry can be difficult to learn without experiences that allow them to build their own understanding. The authors' approach to geometry instruction--with its integration of content, multiple representations, real-world examples, reading and writing, communication and collaboration as…
An approach for management of geometry data
NASA Technical Reports Server (NTRS)
Dube, R. P.; Herron, G. J.; Schweitzer, J. E.; Warkentine, E. R.
1980-01-01
The strategies for managing Integrated Programs for Aerospace Design (IPAD) computer-based geometry are described. The computer model of geometry is the basis for communication, manipulation, and analysis of shape information. IPAD's data base system makes this information available to all authorized departments in a company. A discussion of the data structures and algorithms required to support geometry in IPIP (IPAD's data base management system) is presented. Through the use of IPIP's data definition language, the structure of the geometry components is defined. The data manipulation language is the vehicle by which a user defines an instance of the geometry. The manipulation language also allows a user to edit, query, and manage the geometry. The selection of canonical forms is a very important part of the IPAD geometry. IPAD has a canonical form for each entity and provides transformations to alternate forms; in particular, IPAD will provide a transformation to the ANSI standard. The DBMS schemas required to support IPAD geometry are explained.
Teaching Geometry through Problem-Based Learning
ERIC Educational Resources Information Center
Schettino, Carmel
2011-01-01
About seven years ago, the mathematics teachers at the author's secondary school came to the conclusion that they were not satisfied with their rather traditional geometry textbook. The author had already begun using a problem-based approach to teaching geometry in her classes, a transition for her and her students that inspired her to write about…
A Multivariate Model of Achievement in Geometry
ERIC Educational Resources Information Center
Bailey, MarLynn; Taasoobshirazi, Gita; Carr, Martha
2014-01-01
Previous studies have shown that several key variables influence student achievement in geometry, but no research has been conducted to determine how these variables interact. A model of achievement in geometry was tested on a sample of 102 high school students. Structural equation modeling was used to test hypothesized relationships among…
Readings in Geometry from the Arithmetic Teacher.
ERIC Educational Resources Information Center
Brydegaard, Marguerite; Inskeep, James E., Jr.
This is a book of readings from the "Arithmetic Teacher" on selected topics in geometry. The articles chosen are samples of material published in the journal from its beginning in February 1954 through February 1970. The articles are of three major types. The first is classified "involvement." These articles describe geometry units in which the…
FINAL REPORT: GEOMETRY AND ELEMENTARY PARTICLE PHYSICS
Singer, Isadore M.
2008-03-04
The effect on mathematics of collaborations between high-energy theoretical physics and modern mathematics has been remarkable. Mirror symmetry has revolutionized enumerative geometry, and Seiberg-Witten invariants have greatly simplified the study of four manifolds. And because of their application to string theory, physicists now need to know cohomology theory, characteristic classes, index theory, K-theory, algebraic geometry, differential geometry, and non-commutative geometry. Much more is coming. We are experiencing a deeper contact between the two sciences, which will stimulate new mathematics essential to the physicists’ quest for the unification of quantum mechanics and relativity. Our grant, supported by the Department of Energy for twelve years, has been instrumental in promoting an effective interaction between geometry and string theory, by supporting the Mathematical Physics seminar, postdoc research, collaborations, graduate students and several research papers.
Drawing Dynamic Geometry Figures Online with Natural Language for Junior High School Geometry
ERIC Educational Resources Information Center
Wong, Wing-Kwong; Yin, Sheng-Kai; Yang, Chang-Zhe
2012-01-01
This paper presents a tool for drawing dynamic geometric figures by understanding the texts of geometry problems. With the tool, teachers and students can construct dynamic geometric figures on a web page by inputting a geometry problem in natural language. First we need to build the knowledge base for understanding geometry problems. With the…
Visuospatial Working Memory in Intuitive Geometry, and in Academic Achievement in Geometry
ERIC Educational Resources Information Center
Giofre, David; Mammarella, Irene C.; Ronconi, Lucia; Cornoldi, Cesare
2013-01-01
A study was conducted on the involvement of visuospatial working memory (VSWM) in intuitive geometry and in school performance in geometry at secondary school. A total of 166 pupils were administered: (1) six VSWM tasks, comprising simple storage and complex span tasks; and (2) the intuitive geometry task devised by Dehaene, Izard, Pica, and…
Flow in out-of-plane double S-bonds
NASA Technical Reports Server (NTRS)
Schmidt, M. C.; Whitelaw, J. H.; Yianneskis, M.
1986-01-01
Developing flows in two out-of-plane double S-bend configurations have been measured by laser-Doppler anemometry. The first duct had a rectangular cross-section 40mmx40mm at the inlet and consisted of a uniform area 22.5 deg. - 22.5 deg. S-duct upstream with a 22.5 deg.- 22.5 deg. S- diffuser downstream. The second duct had a circular cross-section and consisted of a 45 deg. - 45 deg. uniform area S-duct upstream with a 22.5 deg. -22.5 deg. S-diffuser downstream. In both configurations the ratio of the mean radius of curvature to the inlet hydraulic diameter was 7.0, the exit-to-inlet area ratio of the diffusers was 1.5 and the ducts were connected so that the centerline of the S-duct lay in a plane normal to that of the S-diffuser. Streamwise and cross-stream velocity components were measured in laminar flow for the rectangular duct and in turbulent flow for both configurations; measurements of the turbulence levels, cross-correlations and wall static pressures were also made in the turbulent flow cases. Secondary flows of the first kind are present in the first S-duct and they are complemented or counteracted by the secondary flows generated by the area expansion and by the curvature of the S-diffusers downstream. Cross-stream velocities with magnitudes up to 0.19 and 0.11 of the bulk velocity were measured in the laminar and turbulent flows respectively in the rectangular duct and six cross-flow vortices were evident at the exit of the duct in both flow cases. The turbulent flow in the circular duct was qualitatively similar to that in the rectangular configuration, but the cross-stream velocities measured at the exit plane were smaller in the circular geometry. The results are presented in sufficient detail and accuracy for the assessment of numerical calculation methods and are listed in tabular form for this purpose.
Deep-Plane Lipoabdominoplasty in East Asians
Jang, Jun-Young; Hong, Yoon Gi; Sim, Hyung Bo; Sun, Sang Hoon
2016-01-01
Background The objective of this study was to develop a new surgical technique by combining traditional abdominoplasty with liposuction. This combination of operations permits simpler and more accurate management of various abdominal deformities. In lipoabdominoplasty, the combination of techniques is of paramount concern. Herein, we introduce a new combination of liposuction and abdominoplasty using deep-plane flap sliding to maximize the benefits of both techniques. Methods Deep-plane lipoabdominoplasty was performed in 143 patients between January 2007 and May 2014. We applied extensive liposuction on the entire abdomen followed by a sliding flap through the deep plane after repairing the diastasis recti. The abdominal wound closure was completed with repair of Scarpa's fascia. Results The average amount of liposuction aspirate was 1,400 mL (700–3,100 mL), and the size of the average excised skin ellipse was 21.78×12.81 cm (from 15×10 to 25×15 cm). There were no major complications such as deep-vein thrombosis or pulmonary embolism. We encountered 22 cases of minor complications: one wound infection, one case of skin necrosis, two cases of undercorrection, nine hypertrophic scars, and nine seromas. These complications were solved by conservative management or simple revision. Conclusions The use of deep-plane lipoabdominoplasty can correct abdominal deformities more effectively and with fewer complications than traditional abdominoplasty. PMID:27462568
Trajectory optimization for the National Aerospace Plane
NASA Technical Reports Server (NTRS)
Lu, Ping
1993-01-01
The objective of this second phase research is to investigate the optimal ascent trajectory for the National Aerospace Plane (NASP) from runway take-off to orbital insertion and address the unique problems associated with the hypersonic flight trajectory optimization. The trajectory optimization problem for an aerospace plane is a highly challenging problem because of the complexity involved. Previous work has been successful in obtaining sub-optimal trajectories by using energy-state approximation and time-scale decomposition techniques. But it is known that the energy-state approximation is not valid in certain portions of the trajectory. This research aims at employing full dynamics of the aerospace plane and emphasizing direct trajectory optimization methods. The major accomplishments of this research include the first-time development of an inverse dynamics approach in trajectory optimization which enables us to generate optimal trajectories for the aerospace plane efficiently and reliably, and general analytical solutions to constrained hypersonic trajectories that has wide application in trajectory optimization as well as in guidance and flight dynamics. Optimal trajectories in abort landing and ascent augmented with rocket propulsion and thrust vectoring control were also investigated. Motivated by this study, a new global trajectory optimization tool using continuous simulated annealing and a nonlinear predictive feedback guidance law have been under investigation and some promising results have been obtained, which may well lead to more significant development and application in the near future.
Plane Smoothers for Multiblock Grids: Computational Aspects
NASA Technical Reports Server (NTRS)
Llorente, Ignacio M.; Diskin, Boris; Melson, N. Duane
1999-01-01
Standard multigrid methods are not well suited for problems with anisotropic discrete operators, which can occur, for example, on grids that are stretched in order to resolve a boundary layer. One of the most efficient approaches to yield robust methods is the combination of standard coarsening with alternating-direction plane relaxation in the three dimensions. However, this approach may be difficult to implement in codes with multiblock structured grids because there may be no natural definition of global lines or planes. This inherent obstacle limits the range of an implicit smoother to only the portion of the computational domain in the current block. This report studies in detail, both numerically and analytically, the behavior of blockwise plane smoothers in order to provide guidance to engineers who use block-structured grids. The results obtained so far show alternating-direction plane smoothers to be very robust, even on multiblock grids. In common computational fluid dynamics multiblock simulations, where the number of subdomains crossed by the line of a strong anisotropy is low (up to four), textbook multigrid convergence rates can be obtained with a small overlap of cells between neighboring blocks.
In plane oscillation of a bifilar pendulum
NASA Astrophysics Data System (ADS)
Hinrichsen, Peter F.
2016-11-01
The line tensions, the horizontal and vertical accelerations as well as the period of large angle oscillations parallel to the plane of a bifilar suspension are presented and have been experimentally investigated using strain gauges and a smart phone. This system has a number of advantages over the simple pendulum for studying large angle oscillations, and for measuring the acceleration due to gravity.
A Method for Measuring a Plane Angle.
ERIC Educational Resources Information Center
Roberts, George D.; Roberts, G. Gilbert
1978-01-01
Derivation of formulas and example problems for determining the size of a plane angle are given to help in drafting work. The authors state that a small hand calculator will provide greater accuracy in solving these problems than a protractor. (MF)
Selective plane illumination microscopy on a chip.
Paiè, Petra; Bragheri, Francesca; Bassi, Andrea; Osellame, Roberto
2016-04-26
Selective plane illumination microscopy can image biological samples at a high spatiotemporal resolution. Complex sample preparation and system alignment normally limit the throughput of the method. Using femtosecond laser micromachining, we created an integrated optofluidic device that allows obtaining continuous flow imaging, three-dimensional reconstruction and high-throughput analysis of large multicellular spheroids at a subcellular resolution.
Dual band QWIP focal plane array
NASA Technical Reports Server (NTRS)
Gunapala, Sarath D. (Inventor); Choi, Kwong Kit (Inventor); Bandara, Sumith V. (Inventor)
2005-01-01
A quantum well infrared photodetector (QWIP) that provides two-color image sensing. Two different quantum wells are configured to absorb two different wavelengths. The QWIPs are arrayed in a focal plane array (FPA). The two-color QWIPs are selected for readout by selective electrical contact with the two different QWIPs or by the use of two different wavelength sensitive gratings.
MTI Focal Plane Assembly Design and Performance
Ballard, M.; Rienstra, J.L.
1999-06-17
The focal plane assembly for the Multispectral Thermal Imager (MTI) consists of sensor chip assemblies, optical filters, and a vacuum enclosure. Sensor chip assemblies, composed of linear detector arrays and readout integrated circuits, provide spatial resolution in the cross-track direction for the pushbroom imager. Optical filters define 15 spectral bands in a range from 0.45 {micro}m to 10.7 {micro}m. All the detector arrays are mounted on a single focal plane and are designed to operate at 75 K. Three pairs of sensor chip assemblies (SCAs) are required to provide cross-track coverage in all 15 spectral bands. Each pair of SCAs includes detector arrays made from silicon, iridium antimonide, and mercury cadmium telluride. Read out integrated circuits multiplex the signals from the detectors to 18 separate video channels. Optical filter assemblies defining the spectral bands are mounted over the linear detector arrays. Each filter assembly consists of several filter strips bonded together side-by-side. The MTI focal plane assembly has been integrated with the rest of the payload and has undergone detailed testing and calibration. This paper includes representative test data for the various spectral bands and the overall performance of the focal plane assembly.
Simple Harmonic Motion in Harmonic Plane Waves.
ERIC Educational Resources Information Center
Benumof, Reuben
1980-01-01
Discusses the distribution of kinetic and potential energy in transverse and longitudinal waves and examines the transmission of power and momentum. This discussion is intended to aid in understanding the simple harmonic motion of a particle involved in the propagation of a harmonic mechanical plane wave. (HM)
Large Format Multicolor QWIP Focal Plane Arrays
NASA Technical Reports Server (NTRS)
Soibel, A.; Gunapala, S. D.; Bandara, S. V.; Liu, J. K.; Mumolo, J. M.; Ting, D. Z.; Hill, C. J.; Nguyen, J.
2009-01-01
Mid-wave infrared (MWIR) and long-wave infrared (LWIR) multicolor focal plane array (FPA) cameras are essential for many DoD and NASA applications including Earth and planetary remote sensing. In this paper we summarize our recent development of large format multicolor QWIP FPA that cover MWIR and LWIR bands.
Towards Dualband Megapixel QWIP Focal Plane Arrays
NASA Technical Reports Server (NTRS)
Gunapala, S. D.; Bandara, S. V.; Liu, J. K.; Mumolo, J. M.; Hill, C. J.; Rafol, S. B.; Salazar, D.; Woolaway, J.; LeVan, P. D.; Tidrow, M. Z.
2006-01-01
Mid-wavelength infrared (MWIR) and long-wavelength infrared (LWIR) 1024 x 1024 pixel quantum well infrared photodetector (QWIP) focal planes have been demonstrated with excellent imaging performance. The MWIR QWIP detector array has demonstrated a noise equivalent differential temperature (NEDT) of 17 mK at a 95 K operating temperature with f/2.5 optics at 300 K background and the LWIR detector array has demonstrated a NEDT of 13 mK at a 70 K operating temperature with the same optical and background conditions as the MWIR detector array after the subtraction of system noise. Both MWIR and LWIR focal planes have shown background limited performance (BLIP) at 90 K and 70 K operating temperatures respectively, with similar optical and background conditions. In addition, we have demonstrated MWIR and LWIR pixel co-registered simultaneously readable dualband QWIP focal plane arrays. In this paper, we will discuss the performance in terms of quantum efficiency, NEDT, uniformity, operability, and modulation transfer functions of the 1024 x 1024 pixel arrays and the progress of dualband QWIP focal plane array development work.
Microscale out-of-plane anemometer
NASA Technical Reports Server (NTRS)
Liu, Chang (Inventor); Chen, Jack (Inventor)
2005-01-01
A microscale out-of-plane thermal sensor. A resistive heater is suspended over a substrate by supports raised with respect to the substrate to provide a clearance underneath the resistive heater for fluid flow. A preferred fabrication process for the thermal sensor uses surface micromachining and a three-dimensional assembly to raise the supports and lift the resistive heater over the substrate.
Multifocal planes head-mounted displays.
Rolland, J P; Krueger, M W; Goon, A
2000-07-01
Stereoscopic head-mounted displays (HMD's) provide an effective capability to create dynamic virtual environments. For a user of such environments, virtual objects would be displayed ideally at the appropriate distances, and natural concordant accommodation and convergence would be provided. Under such image display conditions, the user perceives these objects as if they were objects in a real environment. Current HMD technology requires convergent eye movements. However, it is currently limited by fixed visual accommodation, which is inconsistent with real-world vision. A prototype multiplanar volumetric projection display based on a stack of laminated planes was built for medical visualization as discussed in a paper presented at a 1999 Advanced Research Projects Agency workshop (Sullivan, Advanced Research Projects Agency, Arlington, Va., 1999). We show how such technology can be engineered to create a set of virtual planes appropriately configured in visual space to suppress conflicts of convergence and accommodation in HMD's. Although some scanning mechanism could be employed to create a set of desirable planes from a two-dimensional conventional display, multiplanar technology accomplishes such function with no moving parts. Based on optical principles and human vision, we present a comprehensive investigation of the engineering specification of multiplanar technology for integration in HMD's. Using selected human visual acuity and stereoacuity criteria, we show that the display requires at most 27 equally spaced planes, which is within the capability of current research and development display devices, located within a maximal 26-mm-wide stack. We further show that the necessary in-plane resolution is of the order of 5 microm.
Determining the ice-binding planes of antifreeze proteins by fluorescence-based ice plane affinity.
Basu, Koli; Garnham, Christopher P; Nishimiya, Yoshiyuki; Tsuda, Sakae; Braslavsky, Ido; Davies, Peter
2014-01-15
Antifreeze proteins (AFPs) are expressed in a variety of cold-hardy organisms to prevent or slow internal ice growth. AFPs bind to specific planes of ice through their ice-binding surfaces. Fluorescence-based ice plane affinity (FIPA) analysis is a modified technique used to determine the ice planes to which the AFPs bind. FIPA is based on the original ice-etching method for determining AFP-bound ice-planes. It produces clearer images in a shortened experimental time. In FIPA analysis, AFPs are fluorescently labeled with a chimeric tag or a covalent dye then slowly incorporated into a macroscopic single ice crystal, which has been preformed into a hemisphere and oriented to determine the a- and c-axes. The AFP-bound ice hemisphere is imaged under UV light to visualize AFP-bound planes using filters to block out nonspecific light. Fluorescent labeling of the AFPs allows real-time monitoring of AFP adsorption into ice. The labels have been found not to influence the planes to which AFPs bind. FIPA analysis also introduces the option to bind more than one differently tagged AFP on the same single ice crystal to help differentiate their binding planes. These applications of FIPA are helping to advance our understanding of how AFPs bind to ice to halt its growth and why many AFP-producing organisms express multiple AFP isoforms.
Determining the Ice-binding Planes of Antifreeze Proteins by Fluorescence-based Ice Plane Affinity
Basu, Koli; Garnham, Christopher P.; Nishimiya, Yoshiyuki; Tsuda, Sakae; Braslavsky, Ido; Davies, Peter
2014-01-01
Antifreeze proteins (AFPs) are expressed in a variety of cold-hardy organisms to prevent or slow internal ice growth. AFPs bind to specific planes of ice through their ice-binding surfaces. Fluorescence-based ice plane affinity (FIPA) analysis is a modified technique used to determine the ice planes to which the AFPs bind. FIPA is based on the original ice-etching method for determining AFP-bound ice-planes. It produces clearer images in a shortened experimental time. In FIPA analysis, AFPs are fluorescently labeled with a chimeric tag or a covalent dye then slowly incorporated into a macroscopic single ice crystal, which has been preformed into a hemisphere and oriented to determine the a- and c-axes. The AFP-bound ice hemisphere is imaged under UV light to visualize AFP-bound planes using filters to block out nonspecific light. Fluorescent labeling of the AFPs allows real-time monitoring of AFP adsorption into ice. The labels have been found not to influence the planes to which AFPs bind. FIPA analysis also introduces the option to bind more than one differently tagged AFP on the same single ice crystal to help differentiate their binding planes. These applications of FIPA are helping to advance our understanding of how AFPs bind to ice to halt its growth and why many AFP-producing organisms express multiple AFP isoforms. PMID:24457629
NASA Astrophysics Data System (ADS)
Sakaamini, Ahmad; Amami, Sadek; Murray, Andrew James; Ning, Chuangang; Madison, Don
2016-10-01
Ionisation triple differential cross sections have been determined experimentally and theoretically for the neutral molecule N2 over a range of geometries from coplanar to the perpendicular plane. Data were obtained at incident electron energies ∼10 and ∼20 eV above the ionisation potential of the 3σ g, 1π u and 2σ g states, using both equal and non-equal outgoing electron energies. The data were taken with the incident electron beam in the scattering plane (ψ = 0°), at 45° to this plane and orthogonal to the plane (ψ = 90°). The set of nine measured differential cross sections at a given energy were then inter-normalised to each other. The data are compared to new calculations using various distorted wave methods, and differences between theory and experiment are discussed.
Varied line spacing plane holographic grating recorded by using uniform line spacing plane gratings.
Qing, Ling; Gang, Wu; Bin, Liu; Qiuping, Wang
2006-07-20
Uniform line spacing plane gratings are introduced into a recording system to generate aspherical wavefronts for recording varied line spacing plane holographic gratings. Analytical expressions of groove parameters are derived to the fourth order. A ray-tracing validation algorithm is provided based on Fermat's principle and a local search method. The recording parameters are optimized to record a varied line spacing plane holographic grating with the aid of derived analytical expressions. A design example demonstrates the exactness of the analytical expressions and the superiority of recording optics with auxiliary gratings. PMID:16826244
Magnetic field geometry of an unusual cometary cloud Gal 110-13
NASA Astrophysics Data System (ADS)
Neha, S.; Maheswar, G.; Soam, A.; Lee, C. W.; Tej, A.
2016-04-01
Aims: We carried out optical polarimetry of an isolated cloud, Gal 110-13, to map the plane-of-the-sky magnetic field geometry. The main aim of the study is to understand the most plausible mechanism responsible for the unusual cometary shape of the cloud in the context of its magnetic field geometry. Methods: When unpolarized starlight passes through the intervening interstellar dust grains that are aligned with their short axes parallel to the local magnetic field, it gets linearly polarized. The plane-of-the-sky magnetic field component can therefore be traced by doing polarization measurements of background stars projected on clouds. Because the light in the optical wavelength range is most efficiently polarized by the dust grains typically found in the outer layers of the molecular clouds, optical polarimetry enables us to trace the magnetic field geometry of the outer layers of the clouds. Results: We made R-band polarization measurements of 207 stars in the direction of Gal 110-13. The distance of Gal 110-13 was determined as ~450 ± 80 pc using our polarization and 2MASS near-infrared data. The foreground interstellar contribution was removed from the observed polarization values by observing a number of stars located in the vicinity of Gal 110-13 which has Hipparcos parallax measurements. The plane-of-the-sky magnetic field lines are found to be well ordered and aligned with the elongated structure of Gal 110-13. Using structure function analysis, we estimated the strength of the plane-of-the-sky component of the magnetic field as ~25 μG. Conclusions: Based on our results and comparing them with those from simulations, we conclude that compression by the ionization fronts from 10 Lac is the most plausible cause of the comet-like morphology of Gal 110-13 and of the initiation of subsequent star formation.
Angular-dependent Raman study of a- and s-plane InN
Filintoglou, K.; Katsikini, M. Arvanitidis, J.; Lotsari, A.; Dimitrakopulos, G. P.; Vouroutzis, N.; Ves, S.; Christofilos, D.; Kourouklis, G. A.; Ajagunna, A. O.; Georgakilas, A.; Zoumakis, N.
2015-02-21
Angular-dependent polarized Raman spectroscopy was utilized to study nonpolar a-plane (11{sup ¯}20) and semipolar s-plane (101{sup ¯}1) InN epilayers. The intensity dependence of the Raman peaks assigned to the vibrational modes A{sub 1}(TO), E{sub 1}(TO), and E{sub 2}{sup h} on the angle ψ that corresponds to rotation around the growth axis, is very well reproduced by using expressions taking into account the corresponding Raman tensors and the experimental geometry, providing thus a reliable technique towards assessing the sample quality. The s- and a-plane InN epilayers grown on nitridated r-plane sapphire (Al{sub 2}O{sub 3}) exhibit good crystalline quality as deduced from the excellent fitting of the experimental angle-dependent peak intensities to the theoretical expressions as well as from the small width of the Raman peaks. On the contrary, in the case of the s-plane epilayer grown on non-nitridated r-plane sapphire, fitting of the angular dependence is much worse and can be modeled only by considering the presence of two structural modifications, rotated so as their c-axes are almost perpendicular to each other. Although the presence of the second variant is verified by transmission electron and atomic force microscopies, angular dependent Raman spectroscopy offers a non-destructive and quick way for its quantification. Rapid thermal annealing of this sample did not affect the angular dependence of the peak intensities. The shift of the E{sub 1}(TO) and E{sub 2}{sup h} Raman peaks was used for the estimation of the strain state of the samples.
Single-Plane Magnetically Focused Elongated Small Field Proton Beams.
McAuley, Grant A; Slater, James M; Wroe, Andrew J
2015-08-01
We previously performed Monte Carlo simulations of magnetically focused proton beams shaped by a single quadrapole magnet and thereby created narrow elongated beams with superior dose delivery characteristics (compared to collimated beams) suitable for targets of similar geometry. The present study seeks to experimentally validate these simulations using a focusing magnet consisting of 24 segments of samarium cobalt permanent magnetic material adhered into a hollow cylinder. Proton beams with properties relevant to clinical radiosurgery applications were delivered through the magnet to a water tank containing a diode detector or radiochromic film. Dose profiles were analyzed and compared with analogous Monte Carlo simulations. The focused beams produced elongated beam spots with high elliptical symmetry, indicative of magnet quality. Experimental data showed good agreement with simulations, affirming the utility of Monte Carlo simulations as a tool to model the inherent complexity of a magnetic focusing system. Compared to target-matched unfocused simulations, focused beams showed larger peak to entrance ratios (26% to 38%) and focused simulations showed a two-fold increase in beam delivery efficiency. These advantages can be attributed to the magnetic acceleration of protons in the transverse plane that tends to counteract the particle outscatter that leads to degradation of peak to entrance performance in small field proton beams. Our results have important clinical implications and suggest rare earth focusing magnet assemblies are feasible and could reduce skin dose and beam number while delivering enhanced dose to narrow elongated targets (eg, in and around the spinal cord) in less time compared to collimated beams.
Valley polarization in graphene with out-of-plane deformations
NASA Astrophysics Data System (ADS)
Zhai, Dawei; Sandler, Nancy
At low energy, the energy dispersion of graphene shows a conical valley structure with the conduction and valence bands touching at the Dirac points. The existence of two inequivalent Dirac points in the Brillouin zone, thus two valleys, suggests they may be used as new degrees of freedom to carry information. Several schemes based on different mechanisms have been advanced to achieve valley separation in this material, however the proposed setups remain challenging for experimental observation. In this work we investigate graphene with out-of-plane deformations- one of the most naturally occurring and practically realizable settings, as a candidate system to produce valley polarization. Local strains produced by the deformations serve as scattering potentials for electronic states. A second-order Born approximation calculation based on the continuum model reveals the existence of valley polarization and its dependence on the geometrical parameters of the deformations. We characterize the efficiency of valley filtering for different geometries and energies and discuss their implementation in currently available experimental setups. Work supported by NSF-DMR 1508325.
Dissipative N-point-vortex Models in the Plane
NASA Astrophysics Data System (ADS)
Shashikanth, Banavara N.
2010-02-01
A method is presented for constructing point vortex models in the plane that dissipate the Hamiltonian function at any prescribed rate and yet conserve the level sets of the invariants of the Hamiltonian model arising from the SE (2) symmetries. The method is purely geometric in that it uses the level sets of the Hamiltonian and the invariants to construct the dissipative field and is based on elementary classical geometry in ℝ3. Extension to higher-dimensional spaces, such as the point vortex phase space, is done using exterior algebra. The method is in fact general enough to apply to any smooth finite-dimensional system with conserved quantities, and, for certain special cases, the dissipative vector field constructed can be associated with an appropriately defined double Nambu-Poisson bracket. The most interesting feature of this method is that it allows for an infinite sequence of such dissipative vector fields to be constructed by repeated application of a symmetric linear operator (matrix) at each point of the intersection of the level sets.
Analysis of surface modes in photonic crystals by a plane-wave transfer-matrix method.
Che, Ming; Li, Zhi-Yuan
2008-09-01
We have developed a plane-wave transfer-matrix method (PWTMM) with the aid of the interpolation technique to analyze the dispersion relation of surface modes in photonic crystal or photonic crystal surface waveguide. The proposed approach has been applied to several surface structures in two-dimensional photonic crystals. The calculated dispersion relation of the surface modes is in good agreement with the result obtained by the conventional plane-wave expansion method in combination with the supercell technique. The developed PWTMM needs to handle only a single unit-cell layer domain and is therefore numerically friendly. The proposed approach can become an efficient and accurate numerical tool to understand and design surface modes in different two-dimensional and three-dimensional photonic crystals with complex geometries.
Influence of meniscus shape in the cross sectional plane on the knee contact mechanics.
Łuczkiewicz, Piotr; Daszkiewicz, Karol; Witkowski, Wojciech; Chróścielewski, Jacek; Zarzycki, Witold
2015-06-01
We present a three dimensional finite element analysis of stress distribution and menisci deformation in the human knee joint. The study is based on the Open Knee model with the geometry of the lateral meniscus which shows some degenerative disorders. The nonlinear analysis of the knee joint under compressive axial load is performed. We present results for intact knee, knee with complete radial posterior meniscus root tear and knee with total meniscectomy of medial or lateral meniscus. We investigate how the meniscus shape in the cross sectional plane influences knee-joint mechanics by comparing the results for flat (degenerated) lateral and normal medial meniscus. Specifically, the deformation of the menisci in the coronal plane and the corresponding stress values in cartilages are studied. By analysing contact resultant force acting on the menisci in axial plane we have shown that restricted extrusion of the torn lateral meniscus can be attributed to small slope of its cross section in the coronal plane. Additionally, the change of the contact area and the resultant force acting on the menisci as the function of compressive load are investigated.
Cross-plane heat transfer through single-layer carbon structures.
Zhang, Huaichen; Nedea, Silvia V; Rindt, Camilo C M; Smeulders, David M J
2016-02-21
Graphene-based nano-structures have been recently proposed to function as additives to improve the conductivity of thermally sluggish phase change materials (PCMs). Based on the existing research studies, the improvement is dependent not only on the matrix material, but also on the geometry of the carbon structure. To gain more insight into the nano-scale thermal transport problem, we launched the current pilot research using water as the matrix material, to represent the hydroxyl-group-rich sugar alcohols as PCMs. We have found that the heat conduction across a graphene layer to water is much faster than the heat conduction to the graphene layer itself. Also, the high graphene-water thermal contact resistance fails to acknowledge the fast thermal kinetics of the low frequency phonons. In the investigation of the geometry effect, the cross-plane heat transfer coefficient is found to decrease with decreasing CNT diameter except CNT(9,9). PMID:26818392
In-plane thermal conductivity determination through thermoreflectance analysis and measurements
NASA Astrophysics Data System (ADS)
Aubain, Max S.; Bandaru, Prabhakar R.
2011-10-01
A scanning thermoreflectance (TR) technique through which the surface temperature profile of heated thin films may be ascertained and modeled to yield the in-plane thermal conductivity (κip) is discussed. The TR intensity is shown to be a sensitive function of the film thickness, its thermo-optic materials properties, and the substrate geometry. A reduction in the thermal conductivity of silicon thin films is then demonstrated deploying the technique. A comparison of the estimated conductivity values to those obtained using other methodologies supports the validity of our method and suggests that complete isolation of the thin film from the substrate may not be required for extracting κip.
Note: Arc discharge plasma source with plane segmented LaB6 cathode.
Akhmetov, T D; Davydenko, V I; Ivanov, A A; Kreter, A; Mishagin, V V; Savkin, V Ya; Shulzhenko, G I; Unterberg, B
2016-05-01
A plane cathode composed of close-packed hexagonal LaB6 (lanthanum hexaboride) segments is described. The 6 cm diameter circular cathode is heated by radiation from a graphite foil flat spiral. The cathode along with a hollow copper anode is used for the arc discharge plasma production in a newly developed linear plasma device. A separately powered coil located around the anode is used to change the magnetic field strength and geometry in the anode region. Different discharge regimes were realized using this coil. PMID:27250481
Polar flexoelectric in-plane and out-of-plane switching in bent core nematic mixtures
NASA Astrophysics Data System (ADS)
Elamain, Omaima; Hegde, Gurumurthy; Komitov, Lachezar
2016-07-01
Polar electro-optic response, arising from the coupling between an applied in-plane and out-of-plane dc electric field, respectively, and the flexoelectric polarization of bent core nematic liquid crystal mixtures with hybrid alignment is studied in conventional sandwich cells with homeotropic anchoring at one of the cell substrates and planar at the other. Such a hybrid alignment, however, results in a splay/bend elastic deformation of the nematic giving rise of a flexoelectric polarization. It was found that a pronounced polar electro-optic response, both in-plane and out of plane, took place in the bent core nematic mixtures at very low voltages due to the high flexoelectric polarization in these mixtures, compared with the one observed in calamitic liquid crystals.
Ultrawide phononic band gap for combined in-plane and out-of-plane waves.
Bilal, Osama R; Hussein, Mahmoud I
2011-12-01
We consider two-dimensional phononic crystals formed from silicon and voids, and present optimized unit-cell designs for (1) out-of-plane, (2) in-plane, and (3) combined out-of-plane and in-plane elastic wave propagation. To feasibly search through an excessively large design space (~10(40) possible realizations) we develop a specialized genetic algorithm and utilize it in conjunction with the reduced Bloch mode expansion method for fast band-structure calculations. Focusing on high-symmetry plain-strain square lattices, we report unit-cell designs exhibiting record values of normalized band-gap size for all three categories. For the case of combined polarizations, we reveal a design with a normalized band-gap size exceeding 60%.
In-plane vibrations of a rectangular plate: Plane wave expansion modelling and experiment
NASA Astrophysics Data System (ADS)
Arreola-Lucas, A.; Franco-Villafañe, J. A.; Báez, G.; Méndez-Sánchez, R. A.
2015-04-01
Theoretical and experimental results for in-plane vibrations of a uniform rectangular plate with free boundary conditions are obtained. The experimental setup uses electromagnetic-acoustic transducers and a vector network analyzer. The theoretical calculations were obtained using the plane wave expansion method applied to the in-plane thin plate vibration theory. The agreement between theory and experiment is excellent for the lower 95 modes covering a very wide frequency range from DC to 20 kHz. Some measured normal-mode wave amplitudes were compared with the theoretical predictions; very good agreement was observed. The excellent agreement of the classical theory of in-plane vibrations confirms its reliability up to very high frequencies
Edee, Kofi; Granet, Gérard; Plumey, Jean-Píerre
2007-04-01
We investigate the electromagnetic modeling of plane-wave diffraction by nonperiodic surfaces by using the curvilinear coordinate method (CCM). This method is often used with a Fourier basis expansion, which results in the periodization of both the geometry and the electromagnetic field. We write the CCM in a complex coordinate system in order to introduce the perfectly matched layer concept in a simple and efficient way. The results, presented for a perfectly conducting surface, show the efficiency of the model.
Intraoperative tracking of aortic valve plane
Nguyen, Duc Long Hung; Garreau, Mireille; Auffret, Vincent; Le Breton, Hervé; Verhoye, Jean-Philippe; Haigron, Pascal
2013-01-01
The main objective of this work is to track the aortic valve plane in intra-operative fluoroscopic images in order to optimize and secure Transcatheter Aortic Valve Implantation (TAVI) procedure. This paper is focused on the issue of aortic valve calcifications tracking in fluoroscopic images. We propose a new method based on the Tracking-Learning-Detection approach, applied to the aortic valve calcifications in order to determine the position of the aortic valve plane in intra-operative TAVI images. This main contribution concerns the improvement of object detection by updating the recursive tracker in which all features are tracked jointly. The approach has been evaluated on four patient databases, providing an absolute mean displacement error less than 10 pixels ≈ 2mm). Its suitability for the TAVI procedure has been analyzed. PMID:24110703
NASA Technical Reports Server (NTRS)
Mendez, Bruce
1988-01-01
The National Aerospace Plane is an extremely versatile and adaptable aircraft. It can be developed into an Orient Express that would dramatically improve trade with countries in Asia and elsewhere: a commuter transport to ferry men and materials to space, an advanced tactical fighter or bomber, and an unparalleled high altitude spy-plane to observe troubled spots all over the globe. Utilizing the technology developed by this pilot program, it will be possible to quickly and easily get to low Earth orbit, go halfway around the world in a fraction of the time it previously took, and lead the world in the development of advanced technology to improve our lives and the lives of many others.
A conceptual study of Japan's rocket plane
NASA Astrophysics Data System (ADS)
Shibato, Yoji; Fukushima, Yukio; Miwada, Makoto
1989-10-01
NASDA's H-II Orbiting Plane, designated 'HOPE', is an unmanned winged vehicle that is to be launched as the upper stage of the H-II rocket. HOPE is currently in its conceptual development stage, and is expected to become operational at the end of the 1990s. As payloads increase, HOPE will be lofted atop launch vehicles that add solid-rocket boosters or more powerful LH2/LOX liquid-fueled rocket lower stages to the H-II baseline; HOPE payloads 1.5-3 times greater than those typical of the H-II baseline will then become possible. A preliminary design projection is made for a next-generation, reusable 'rocket-plane'.
The Focal Plane Package for Solar B
NASA Astrophysics Data System (ADS)
Title, A.; Tsuneta, S.
The Focal Plane Package (FPP) of the JAXA Solar B Solar Optical Telescope (SOT) combines an advanced version of Stokes Polarimeter, a tunable birefringent filter, and a set of narrow spectral filters. The Stokes Polarimeter and the filter systems can operate simultaneously allowing the construction of precise vector magnetograms and images in a range of spectral lines. Both the Stokes Polarimeter and the filter systems have controllable fields of view and cadence. A local correlation tracker in the FFP operates a high speed tip-tilt mirror to stabilize the image in all focal planes. The time sequences of precise vector magnetic maps uncompromised by seeing will enable new understanding of how flux emerges through and disappears from the solar surface. The tunable filter can measure the flows in the atmosphere from the lower photosphere through the Chromosphere enabling new insights in the magneto-hydrodynamics of magnetic evolution.
Image-plane processing of visual information
NASA Technical Reports Server (NTRS)
Huck, F. O.; Fales, C. L.; Park, S. K.; Samms, R. W.
1984-01-01
Shannon's theory of information is used to optimize the optical design of sensor-array imaging systems which use neighborhood image-plane signal processing for enhancing edges and compressing dynamic range during image formation. The resultant edge-enhancement, or band-pass-filter, response is found to be very similar to that of human vision. Comparisons of traits in human vision with results from information theory suggest that: (1) Image-plane processing, like preprocessing in human vision, can improve visual information acquisition for pattern recognition when resolving power, sensitivity, and dynamic range are constrained. Improvements include reduced sensitivity to changes in lighter levels, reduced signal dynamic range, reduced data transmission and processing, and reduced aliasing and photosensor noise degradation. (2) Information content can be an appropriate figure of merit for optimizing the optical design of imaging systems when visual information is acquired for pattern recognition. The design trade-offs involve spatial response, sensitivity, and sampling interval.
Improvements of the Focal Plane of SASSYER
NASA Astrophysics Data System (ADS)
Crump, Danielle; Heinz, Andreas; Winkler, Ryan; Frank, Daniel; Qian, Jing; Fetea, Mirela
2007-10-01
The Small Angle Separator System at Yale for Evaporation Residues (SASSYER) at Yale University is a gas-filled recoil separator, specializing in the investigation of the production and the structure of nuclei heavier than ^208Pb. New instrumentation for the focal plane of SASSYER under development at WNSL at Yale will replace the previous equipment with a compact chamber for double-sided silicon detectors (DSSD). Here we are reporting on improvements of the focal plane of SASSYER, including DSSD electronics, a detector cooling system, and ion optics tests. MUX-16 boards from MESYTEC, 16 channel multiplexed amplifiers, were tested and quantified. An alcohol cooling system, related to the DSSD, was characterized. The ion optics tests extracted effective magnetic rigidities of the separator. Results of the tests will be presented. This work was supported by the NSF grant PHY 0555665, Jeffress Fund J-809, and USDOE grant DE-FG02-91ER-40609.
Split-field pupil plane determination apparatus
Salmon, Joseph T.
1996-01-01
A split-field pupil plane determination apparatus (10) having a wedge assembly (16) with a first glass wedge (18) and a second glass wedge (20) positioned to divide a laser beam (12) into a first laser beam half (22) and a second laser beam half (24) which diverge away from the wedge assembly (16). A wire mask (26) is positioned immediately after the wedge assembly (16) in the path of the laser beam halves (22, 24) such that a shadow thereof is cast as a first shadow half (30) and a second shadow half (32) at the input to a relay telescope (14). The relay telescope (14) causes the laser beam halves (22, 24) to converge such that the first shadow half (30) of the wire mask (26) is aligned with the second shadow half (32) at any subsequent pupil plane (34).
Strings in plane wave backgrounds reexamined
Jofre, O.; Nunez, C. Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires )
1994-10-15
String theory in an exact plane wave background is explored. The four-tachyon scattering amplitude is constructed. The spectrum of states found from the poles in the factorization turns out to be equivalent to that of the theory in flat space-time. The massless vertex operator is obtained from the residue of the first order pole. It exhibits nontrivial modifications with respect to the flat space case.
The Kepler photometer focal plane array
NASA Astrophysics Data System (ADS)
Argabright, V. S.; VanCleve, J. E.; Bachtell, E. E.; Hegge, M. J.; McArthur, S. P.; Dumont, F. C.; Rudeen, A. C.; Pullen, J. L.; Teusch, D. A.; Tennant, D. S.; Atcheson, P. D.
2008-07-01
The Kepler instrument is designed to detect Earth size planets in the "habitable zone" orbiting 9
Fractal Geometry in the High School Classroom.
ERIC Educational Resources Information Center
Camp, Dane R.
1995-01-01
Discusses classroom activities that involve applications of fractal geometry. Includes an activity sheet that explores Pascal's triangle, Sierpinsky's gasket, and modular arithmetic in two and three dimensions. (Author/MKR)
The Soap-Bubble-Geometry Contest.
ERIC Educational Resources Information Center
Morgan, Frank; Melnick, Edward R.; Nicholson, Ramona
1997-01-01
Presents an activity on soap-bubble geometry using a guessing contest, explanations, and demonstrations that allow students to mesh observation and mathematical reasoning to discover that mathematics is much more than just number crunching. (ASK)
Emergence of wave equations from quantum geometry
Majid, Shahn
2012-09-24
We argue that classical geometry should be viewed as a special limit of noncommutative geometry in which aspects which are inter-constrained decouple and appear arbitrary in the classical limit. In particular, the wave equation is really a partial derivative in a unified extra-dimensional noncommutative geometry and arises out of the greater rigidity of the noncommutative world not visible in the classical limit. We provide an introduction to this 'wave operator' approach to noncommutative geometry as recently used[27] to quantize any static spacetime metric admitting a spatial conformal Killing vector field, and in particular to construct the quantum Schwarzschild black hole. We also give an introduction to our related result that every classical Riemannian manifold is a shadow of a slightly noncommutative one wherein the meaning of the classical Ricci tensor becomes very natural as the square of a generalised braiding.
The Oak Leaf: Connecting Geometry and Biology.
ERIC Educational Resources Information Center
Snyder, Judy
1999-01-01
Presents an activity that integrates biology and mathematics. Involves students in actual biological research and uses geometry, statistics, and computers to interpret data about the leaves of a tree. (ASK)
Minimal five dimensional supergravities and complex geometries
Herdeiro, Carlos A. R.
2010-07-28
We discuss the relation between solutions admitting Killing spinors of minimal super-gravities in five dimensions, both timelike and null, and complex geometries. For the timelike solutions the results may be summarised as follows. In the ungauged case (vanishing cosmological constant {Lambda} 0) the solutions are determined in terms of a hyper-Kaehler base space; in the gauged case ({Lambda}<0) the complex geometry is Kaehler; in the de Sitter case ({Lambda}>0) the complex geometry is hyper-Kaehler with torsion (HKT). For the null solutions we shall focus on the de Sitter case, for which the solutions are determined by a constrained Einstein-Weyl 3-geometry called Gauduchon-Tod space. The method for constructing explicit solutions is discussed in each case.
Focal plane scanner with reciprocating spatial window
NASA Technical Reports Server (NTRS)
Mao, Chengye (Inventor)
2000-01-01
A focal plane scanner having a front objective lens, a spatial window for selectively passing a portion of the image therethrough, and a CCD array for receiving the passed portion of the image. All embodiments have a common feature whereby the spatial window and CCD array are mounted for simultaneous relative reciprocating movement with respect to the front objective lens, and the spatial window is mounted within the focal plane of the front objective. In a first embodiment, the spatial window is a slit and the CCD array is one-dimensional, and successive rows of the image in the focal plane of the front objective lens are passed to the CCD array by an image relay lens interposed between the slit and the CCD array. In a second embodiment, the spatial window is a slit, the CCD array is two-dimensional, and a prism-grating-prism optical spectrometer is interposed between the slit and the CCD array so as to cause the scanned row to be split into a plurality of spectral separations onto the CCD array. In a third embodiment, the CCD array is two-dimensional and the spatial window is a rectangular linear variable filter (LVF) window, so as to cause the scanned rows impinging on the LVF to be bandpass filtered into spectral components onto the CCD array through an image relay lens interposed between the LVF and the CCD array.
The European Galactic Plane Surveys: EGAPS
NASA Astrophysics Data System (ADS)
Groot, P. J.; Drew, J.; Greimel, R.; Gaensicke, B.; Knigge, C.; Irwin, M.; Mampaso, A.; Augusteijn, T.; Morales-Rueda, L.; Barlow, M.; Iphas Collaboration; Uvex Collaboration; Vphas+ Collaboration
2006-08-01
Introduction: The European Galactic Plane Surveys (EGAPS) will for the first time ever map the complete galactic plane (10x360 degrees) down to 21st magnitude in u', g', r', i' and H-alpha and partly in He I 5875. It will complete a database of ~1 billion objects. The aim of EGAPS is to study populations of short-lived stellar and binary phases in our Galaxy and combine these population studies with stellar and binary evolutionary codes to vastly improve our understanding of crucial phases of stellar evolution. Target populations include Wolf-Rayet stars, planetary nebulae, white dwarfs (in binaries), cataclysmic variables and other mass-transferring binaries. Methods: EGAPS is using the INT+WFC on La Palma for the Northern Hemisphere and will use the VST+Omegacam in the Southern Hemisphere. Results: The Northern red survey (IPHAS, using r', i', and Halpha) has started in 2003 and is currently 70% complete. The northern blue survey (UVEX; u',g',r' and HeI) has started in June 2006. Results include the detection of a number of rare planetary nebulae, cataclysmic variables, red-dwarf white dwarf binaries in clusters, a possible AM CVn candidate, and a deep photometric and spectroscopic investigation of the Cyg X region. Discussion: EGAPS will revolutionize the field of galactic stellar astrophysics by completing the first ever digital, multicolour survey of the Galactic Plane.
Hamiltonian maps in the complex plane
Greene, J.M.; Percival, I.C.
1981-01-01
Following Arnol'd's proof of the KAM theorem, an analogy with the vertical pendulum, and some general arguments concerning maps in the complex plane, detailed calculations are presented and illustrated graphically for the standard map at the golden mean frequency. The functional dependence of the coordinate q on the canonical angle variable theta is analytically continued into the complex theta-plane, where natural boundaries are found at constant absolute values of Im theta. The boundaries represent the appearance of chaotic motion in the complex plane. Two independent numerical methods based on Fourier analysis in the angle variable were used, one based on a variation-annihilation method and the other on a double expansion. The results were further checked by direct solution of the complex equations of motion. The numerically simpler, but intrinsically complex, semipendulum and semistandard map are also studied. We conjecture that natural boundaries appear in the analogous analytic continuation of the invariant tori or KAM surfaces of general nonintegrable systems.
Locomotion of granulocytes on an inclined plane.
Doroszewski, J; Lewandowska, K; Wierzbicki, W
1986-01-01
The paper presents a quantitative study of the trajectories of rat granulocytes (PMNs) migrating on a glass surface inclined at various angles, i.e. under the action of gravitational force component parallel to the plane. The action of the force of the order of 5 X 10(-13) N (component parallel to the plane inclined at 80 degrees) accompanied by the decrease of a gravitational component perpendicular to the surface does not disrupt the adhesion contact of migrating PMNs with the serum coated glass surface. Under the action of the external force parallel to the surface, the PMNs exhibit a tendency to migrate in the direction of the force vector and the angles between elementary segments (steps) of cell trajectories are smaller in comparison with migration on a horizontal plane (0 degrees inclination). It has been found that the mean velocity of motion of PMNs locomoting on a steep slope (70 degrees and 80 degrees) is greater in comparison with the migration velocity on a horizontal surface. The increase of velocity concerns not only cells migrating in the downward direction, but also those which move upwards. Possible mechanisms of the influence of external force on direction and rate of migration of granulocytes are discussed, namely modification of adhesion force, stimulation of cell motile activity, individual variability of cell adhesive and migration properties, shortening of transient locomotory adhesions.
Linearized motion estimation for articulated planes.
Datta, Ankur; Sheikh, Yaser; Kanade, Takeo
2011-04-01
In this paper, we describe the explicit application of articulation constraints for estimating the motion of a system of articulated planes. We relate articulations to the relative homography between planes and show that these articulations translate into linearized equality constraints on a linear least-squares system, which can be solved efficiently using a Karush-Kuhn-Tucker system. The articulation constraints can be applied for both gradient-based and feature-based motion estimation algorithms and to illustrate this, we describe a gradient-based motion estimation algorithm for an affine camera and a feature-based motion estimation algorithm for a projective camera that explicitly enforces articulation constraints. We show that explicit application of articulation constraints leads to numerically stable estimates of motion. The simultaneous computation of motion estimates for all of the articulated planes in a scene allows us to handle scene areas where there is limited texture information and areas that leave the field of view. Our results demonstrate the wide applicability of the algorithm in a variety of challenging real-world cases such as human body tracking, motion estimation of rigid, piecewise planar scenes, and motion estimation of triangulated meshes.
Restoring Aperture Profile At Sample Plane
Jackson, J L; Hackel, R P; Lungershausen, A W
2003-08-03
Off-line conditioning of full-size optics for the National Ignition Facility required a beam delivery system to allow conditioning lasers to rapidly raster scan samples while achieving several technical goals. The main purpose of the optical system designed was to reconstruct at the sample plane the flat beam profile found at the laser aperture with significant reductions in beam wander to improve scan times. Another design goal was the ability to vary the beam size at the sample to scan at different fluences while utilizing all of the laser power and minimizing processing time. An optical solution was developed using commercial off-the-shelf lenses. The system incorporates a six meter relay telescope and two sets of focusing optics. The spacing of the focusing optics is changed to allow the fluence on the sample to vary from 2 to 14 Joules per square centimeter in discrete steps. More importantly, these optics use the special properties of image relaying to image the aperture plane onto the sample to form a pupil relay with a beam profile corresponding almost exactly to the flat profile found at the aperture. A flat beam profile speeds scanning by providing a uniform intensity across a larger area on the sample. The relayed pupil plane is more stable with regards to jitter and beam wander. Image relaying also reduces other perturbations from diffraction, scatter, and focus conditions. Image relaying, laser conditioning, and the optical system designed to accomplish the stated goals are discussed.
Infrared fiber optic focal plane dispersers
NASA Technical Reports Server (NTRS)
Goebel, J. H.
1981-01-01
Far infrared transmissive fiber optics as a component in the design of integrated far infrared focal plane array utilization is discussed. A tightly packed bundle of fibers is placed at the focal plane, where an array of infrared detectors would normally reside, and then fanned out in two or three dimensions to individual detectors. Subsequently, the detectors are multiplexed by cryogenic electronics for relay of the data. A second possible application is frequency up-conversion (v sub 1 + v sub 2 = v sub 3), which takes advantage of the nonlinear optical index of refraction of certain infrared transmissive materials in fiber form. Again, a fiber bundle is utilized as above, but now a laser of frequency v sub 1 is mixed with the incoming radiation of frequency v sub 1 within the nonlinear fiber material. The sum, v sub 2 is then detected by near infrared or visible detectors which are more sensitive than those available at v sub 2. Due to the geometrical size limitations of detectors such as photomultipliers, the focal plane dispersal technique is advantageous for imaging up-conversion.
Phase distribution in complex geometry conduits
Lahey, R.T. Jr.; Lopez de Bertodano, M.; Jones, O.C. Jr.
1992-12-31
Some of the most important and challenging problems in two-phase flow today have to do with the understanding and prediction of multidimensional phenomena, in particular, lateral phase distribution in both simple and complex geometry conduits. A prior review paper summarized the state-of-the-art in the understanding of phase distribution phenomena, and the ability to perform mechanistic multidimensional predictions. The purpose of this paper is to update that review, with particular emphasis on complex geometry conduit predictive capabilities.
Validation of efficiency transfer for Marinelli geometries.
Ferreux, Laurent; Pierre, Sylvie; Thanh, Tran Thien; Lépy, Marie-Christine
2013-11-01
In the framework of environmental measurements by gamma-ray spectrometry, some laboratories need to characterize samples in geometries for which a calibration is not directly available. A possibility is to use an efficiency transfer code, e.g., ETNA. However, validation for large volume sources, such as Marinelli geometries, is needed. With this aim in mind, ETNA is compared, initially to a Monte Carlo simulation (PENELOPE) and subsequently to experimental data obtained with a high-purity germanium detector (HPGe).
NASA Astrophysics Data System (ADS)
Le Courtois, Florent; Thomas, Jean-Hugh; Poisson, Franck; Pascal, Jean-Claude
2016-06-01
Thanks to its easy implementation and robust performance, beamforming is applied for source localisation in several fields. Its effectiveness depends greatly on the array sensor configuration. This paper introduces a criterion to improve the array beampattern and increase the accuracy of sound source localisation. The beamwidth and the maximum sidelobe level are used to quantify the spatial variation of the beampattern through a new criterion. This criterion is shown to be useful, especially for the localisation of moving sources. A genetic algorithm is proposed for the optimisation of microphone placement. Statistical analysis of the optimised arrays provides original results on the algorithm performance and on the optimal microphone placement. An optimised array is tested to localise the sound sources of a high speed train. The results show an accurate separation.
Mali, Kunal S; Zöphel, Lukas; Ivasenko, Oleksandr; Müllen, Klaus; De Feyter, Steven
2013-10-01
In this work, we provide evidence for multiple non-planar adsorption geometries of a novel pyrenocyanine derivative at the liquid-solid interface under ambient conditions. When adsorbed at the organic liquid-solid interface, lead pyrenocyanine forms well-ordered monolayers that exhibit peculiar non-periodic contrast variation. The different contrast of the adsorbed molecules is attributed to dissimilar adsorption geometries which arise from the non-planar conformation of the molecules. The non-planarity of the molecular backbone in turn arises due to a combination of the angularly extended pyrene subunits and the presence of the large lead ion, which is too big to fit inside the central cavity and thus is located out of the aromatic plane. The two possible locations of the lead atom, namely below and above the aromatic plane, could be identified as depression and protrusion in the central cavity, respectively. The manifestation of such multiple adsorption geometries on the structure of the resultant monolayer is discussed in detail. The packing density of these 2D arrays of molecules could be tuned by heating of the sample wherein the molecular packing changes from a low-density, pseudo six-fold symmetric to a high-density, two-fold symmetric arrangement. Finally, a well-ordered two-component system could be constructed by incorporating C60 molecules in the adlayer of lead pyrenocyanine at the liquid-solid interface.
The impact of galaxy geometry and mass evolution on the survival of star clusters
Madrid, Juan P.; Hurley, Jarrod R.; Martig, Marie
2014-04-01
Direct N-body simulations of globular clusters in a realistic Milky-Way-like potential are carried out using the code NBODY6 to determine the impact of the host galaxy disk mass and geometry on the survival of star clusters. A relation between disk mass and star-cluster dissolution timescale is derived. These N-body models show that doubling the mass of the disk from 5 × 10{sup 10} M {sub ☉} to 10 × 10{sup 10} M {sub ☉} halves the dissolution time of a satellite star cluster orbiting the host galaxy at 6 kpc from the galactic center. Different geometries in a disk of identical mass can determine either the survival or dissolution of a star cluster orbiting within the inner 6 kpc of the galactic center. Furthermore, disk geometry has measurable effects on the mass loss of star clusters up to 15 kpc from the galactic center. N-body simulations performed with a fine output time step show that at each disk crossing the outer layers of star clusters experiences an increase in velocity dispersion of ∼5% of the average velocity dispersion in the outer section of star clusters. This leads to an enhancement of mass loss—a clearly discernable effect of disk shocking. By running models with different inclinations, we determine that star clusters with an orbit that is perpendicular to the Galactic plane have larger mass loss rates than do clusters that evolve in the Galactic plane or in an inclined orbit.
The effect of averaging adjacent planes for artifact reduction in matrix inversion tomosynthesis
Godfrey, Devon J.; Page McAdams, H.; Dobbins, James T. III
2013-02-15
Purpose: Matrix inversion tomosynthesis (MITS) uses linear systems theory and knowledge of the imaging geometry to remove tomographic blur that is present in conventional backprojection tomosynthesis reconstructions, leaving in-plane detail rendered clearly. The use of partial-pixel interpolation during the backprojection process introduces imprecision in the MITS modeling of tomographic blur, and creates low-contrast artifacts in some MITS planes. This paper examines the use of MITS slabs, created by averaging several adjacent MITS planes, as a method for suppressing partial-pixel artifacts. Methods: Human chest tomosynthesis projection data, acquired as part of an IRB-approved pilot study, were used to generate MITS planes, three-plane MITS slabs (MITSa3), five-plane MITS slabs (MITSa5), and seven-plane MITS slabs (MITSa7). These were qualitatively examined for partial-pixel artifacts and the visibility of normal and abnormal anatomy. Additionally, small (5 mm) subtle pulmonary nodules were simulated and digitally superimposed upon human chest tomosynthesis projection images, and their visibility was qualitatively assessed in the different reconstruction techniques. Simulated images of a thin wire were used to generate modulation transfer function (MTF) and slice-sensitivity profile curves for the different MITS and MITS slab techniques, and these were examined for indications of partial-pixel artifacts and frequency response uniformity. Finally, mean-subtracted, exposure-normalized noise power spectra (ENNPS) estimates were computed and compared for MITS and MITS slab reconstructions, generated from 10 sets of tomosynthesis projection data of an acrylic slab. The simulated in-plane MTF response of each technique was also combined with the square root of the ENNPS estimate to yield stochastic signal-to-noise ratio (SNR) information about the different reconstruction techniques. Results: For scan angles of 20 Degree-Sign and 5 mm plane separation, seven MITS
Free and friction-induced in-plane vibration of annular disks
NASA Astrophysics Data System (ADS)
Tzou, Kevin Ihwa
1998-12-01
Vibration and noise from disk brakes negatively affect passenger comfort and perceptions of quality in both the automotive and aircraft industries. With regulatory pressure for stopping distance and the emphasis on smaller and lighter components, new brakes not only have to meet design and performance requirements, but must minimize vibration as well. Although materials and geometries vary from application to application, disk brakes generally consist of rotating annular disk(s) subjected to in-plane friction which dissipates the kinetic energy of the vehicle. During this process, friction-induced vibration of the disk(s) occurs, resulting in brake noise. Although sound radiation results from a disk's out-of-plane vibration, substantial in-plane motions must also be present due to the in-plane friction. This in-plane vibration can play a key role in the dynamics of the friction interface and hence, in brake noise and vibration. In this thesis, experimental and analytical methods are used to study the in-plane vibration of annular disks with a view toward understanding disk brake vibration. The issues that are addressed and the major findings include: (1) Characterization of in-plane modes in annular disks. For automotive rotors and thick annular disks, in-plane modes of vibration have frequencies that are both comparable to low-order bending modes and within the measured range for brake squeal. Despite the large in-plane friction force provided by disk brakes, no existing model includes in-plane disk motion with in-plane friction. A three-dimensional vibration model is used to determine frequencies and mode shapes for an annular disk subject to two boundary conditions: all surfaces traction-free, and all free except for a constrained inner edge. (2) Identification of frequency clusters. Using experimental and analytical methods, the frequencies for families of in-plane modes are found to converge to a common value with increasing disk thickness to the limit of the
Contextual phase estimation from two-plane intensity measurements.
Deepak, V Joshua; Ivan, J Solomon
2016-06-01
In this work we construct examples of paraxial light fields whose intensities defined at all points in space do not have a corresponding cross-spectrally pure field amplitude reproducing the same set of transported intensities at all transverse planes. Nevertheless, two spatially separated transverse plane intensities as drawn from these examples are shown to have a corresponding cross-spectrally pure field amplitude, which, through paraxial free propagation between these two planes, reproduces the drawn transverse plane intensities. And the phase associated with such a field amplitude at a given transverse plane is found to be contextual, and intrinsically dependent on the pairing plane. PMID:27409450
Holomorphic Parabolic Geometries and Calabi-Yau Manifolds
NASA Astrophysics Data System (ADS)
McKay, Benjamin
2011-09-01
We prove that the only complex parabolic geometries on Calabi-Yau manifolds are the homogeneous geometries on complex tori. We also classify the complex parabolic geometries on homogeneous compact Kähler manifolds.
Geometry of the 20 November 2003 magnetic cloud
NASA Astrophysics Data System (ADS)
Marubashi, Katsuhide; Cho, Kyung-Suk; Kim, Yeon-Han; Park, Yong-Deuk; Park, Sung-Hong
2012-01-01
This study is an attempt to find a coherent interpretation of the link between the 20 November 2003 magnetic cloud (MC) and its solar source. Most previous studies agree on the orientation of the MC, but the orientation is nearly perpendicular to the axis of the post-eruption arcade (PEA) or the orientation of the neutral line in the solar source region. We first determine the geometry of this MC by fitting methods with both torus and cylinder models. Three possible geometries are obtained, which can reproduce the observed magnetic field variations associated with the MC, one from the cylinder fit and two from the torus fit. The cylinder fit gives the MC orientation with a tilt of a large angle (˜60°) from the ecliptic plane and nearly perpendicular to the PEA axis, being similar to those from previous studies. In contrast, two torus fit results give the MC axis with tilt angles less than 20° from the ecliptic plane. The two torus results correspond to the spacecraft encounter with the eastern flank of the flux rope loop (model A) and the western flank of the loop (model B), respectively. In either case, the orientation of the loop around the apex is nearly parallel to the PEA as observed by the SOHO/extreme ultraviolet imaging telescope instrument in the most plausible solar source region of a halo coronal mass ejection (CME), which appeared in the field of view of Large Angle and Spectrometric Coronagraph (LASCO) C2 at 08:50 UT, 18 November 2003. The magnetic helicity of the PEA region is positive in agreement with the helicity of the MC. The 3-D reconstruction from the Solar Mass Ejection Imager data shows that the main part of the ejected plasma expands mainly to the west of the Sun-Earth line. Thus, we reach the most straightforward interpretation of the link between the MC and its solar source as follows. The MC was created in association with the launch of the CME that was first observed by the LASCO C2 at 08:50 UT, 18 November 2003, and propagated
Geometry-induced protein pattern formation.
Thalmeier, Dominik; Halatek, Jacob; Frey, Erwin
2016-01-19
Protein patterns are known to adapt to cell shape and serve as spatial templates that choreograph downstream processes like cell polarity or cell division. However, how can pattern-forming proteins sense and respond to the geometry of a cell, and what mechanistic principles underlie pattern formation? Current models invoke mechanisms based on dynamic instabilities arising from nonlinear interactions between proteins but neglect the influence of the spatial geometry itself. Here, we show that patterns can emerge as a direct result of adaptation to cell geometry, in the absence of dynamical instability. We present a generic reaction module that allows protein densities robustly to adapt to the symmetry of the spatial geometry. The key component is an NTPase protein that cycles between nucleotide-dependent membrane-bound and cytosolic states. For elongated cells, we find that the protein dynamics generically leads to a bipolar pattern, which vanishes as the geometry becomes spherically symmetrical. We show that such a reaction module facilitates universal adaptation to cell geometry by sensing the local ratio of membrane area to cytosolic volume. This sensing mechanism is controlled by the membrane affinities of the different states. We apply the theory to explain AtMinD bipolar patterns in [Formula: see text] EcMinDE Escherichia coli. Due to its generic nature, the mechanism could also serve as a hitherto-unrecognized spatial template in many other bacterial systems. Moreover, the robustness of the mechanism enables self-organized optimization of protein patterns by evolutionary processes. Finally, the proposed module can be used to establish geometry-sensitive protein gradients in synthetic biological systems.
Twisted geometries, twistors, and conformal transformations
NASA Astrophysics Data System (ADS)
Lângvik, Miklos; Speziale, Simone
2016-07-01
The twisted geometries of spin network states are described by simple twistors, isomorphic to null twistors with a timelike direction singled out. The isomorphism depends on the Immirzi parameter γ and reduces to the identity for γ =∞ . Using this twistorial representation, we study the action of the conformal group SU(2,2) on the classical phase space of loop quantum gravity, described by twisted geometry. The generators of translations and conformal boosts do not preserve the geometric structure, whereas the dilatation generator does. It corresponds to a one-parameter family of embeddings of T*SL(2,C) in twistor space, and its action preserves the intrinsic geometry while changing the extrinsic one—that is the boosts among polyhedra. We discuss the implication of this action from a dynamical point of view and compare it with a discretization of the dilatation generator of the continuum phase space, given by the Lie derivative of the group character. At leading order in the continuum limit, the latter reproduces the same transformation of the extrinsic geometry, while also rescaling the areas and volumes and preserving the angles associated with the intrinsic geometry. Away from the continuum limit, its action has an interesting nonlinear structure but is in general incompatible with the closure constraint needed for the geometric interpretation. As a side result, we compute the precise relation between the extrinsic geometry used in twisted geometries and the one defined in the gauge-invariant parametrization by Dittrich and Ryan and show that the secondary simplicity constraints they posited coincide with those dynamically derived in the toy model of [Classical Quantum Gravity 32, 195015 (2015)].
Studies in computational geometry motivated by mesh generation
Smith, W.D.
1989-01-01
This thesis sprawls over most of discrete and computational geometry. There are four loose bodies of theory developed. (1) A quantitative and algorithmic theory of crossing number and crossing-free line segment graphs in the plane. As five applications of this theory: the author disproves two long - standing conjectures on the crossing number of the complete and complete bipartite graphs, he presents the first exponential algorithm for planar minimum Steiner tree, and the first subexponential algorithms for planar traveling salesman tour and optimum triangulation, and he presents an algorithm for generating all non-isomorphic V-vertex planar graphs, in O(V{sup 3)}time per graph, using O(V) total workspace. (2) Mesh generation, and the triangulation of polytopes: He has the strongest bounds on the number of d-simplices required to triangulate the d-cube, and new triangulation methods in the plane. A quantitative and qualitative - and practical - theory of finite element mesh quality suggest a new, simple strategy for generating good meshes. (3) The theory of geometrical graphs on N point sites in d-space. This subsumes many new results in: geometrical probability, sphere packing, and extremal configurations. An array of new multidimensional search date structures are used to devise fast algorithms for construction many geometrical graphs. (4) Useful new results concerning the mensuration and structure of d-polytopes. In particular he extensively generalizes the famous formula of Heron and Alexandria (75 AD), for the area of a triangle, and he presents the first linear time congruence algorithm for 3 -dimensional polyhedra. He closes with the largest bibliography of the field, containing over 3000 references.
The geometry of sound rays in a wind
NASA Astrophysics Data System (ADS)
Gibbons, G. W.; Warnick, C. M.
2011-05-01
We survey the close relationship between sound and light rays and geometry. In the case where the medium is at rest, the geometry is the classical geometry of Riemann. In the case where the medium is moving, the more general geometry known as Finsler geometry is needed. We develop these geometries ab initio, with examples, and in particular show how sound rays in a stratified atmosphere with a wind can be mapped to a problem of circles and straight lines.
NASA Astrophysics Data System (ADS)
Warren, Linda M.; Baluyut, Elena C.; Osburg, Timothy; Lisac, Kristen; Kokkinen, Siiri
2015-12-01
In the northwestern Pacific, the Pacific plate subducts to the west at the Japan, Kuril, and Kamchatka trenches. Throughout most of the subduction zone, the subducting slab is planar and dipping at an angle of 30°-60°, with the exception of a fold in the southern Kuril segment. To investigate how the slab deforms in response to the applied forces and which mechanism generates the earthquakes, we analyze the rupture properties of 111 large (MW≥5.7) intermediate-depth and deep-focus earthquakes (60-656 km depth) from 1990 to 2014 in the Japan-Kuril-Kamchatka subduction zone. For each earthquake, we use rupture directivity to estimate rupture direction and rupture speed and to distinguish the fault plane from the auxiliary plane of the focal mechanism. Seventy six percent of the earthquakes with sufficient station coverage are well modeled by unilateral rupture propagation. The estimated rupture speeds range from zero to supershear. The estimated rupture directions allow identification of the fault plane as the more horizontal nodal plane for 30 earthquakes, while an additional 11 earthquakes rupture toward the intersection of the nodal planes, so the fault plane cannot be identified. Combining our newly identified fault planes with previously identified fault planes in the region, we observe that in planar slab segments, most earthquakes slip along a dominant fault orientation. For a steeply dipping slab, this orientation is subhorizontal. In more sharply bent slab segments, such as the Kuril fold, deformation is accommodated along more variable fault orientations, including subvertical faults. The correlation of slab geometry with fault orientation suggests that the local stress field controls fault orientations.
Seismicity and Geometry Properties of the Hellenic Subduction Zone
NASA Astrophysics Data System (ADS)
Papadimitriou, E. E.; Karakostas, V. G.; Vallianatos, F.; Makropoulos, C.; Drakatos, G.
2014-12-01
Recent seismicity and fault plane solutions of earthquakes that occurred along the Hellenic Arc-Trench system are engaged for approximating the geometry of the subducted oceanic plate. Seismicity and focal mechanisms confirm the gentle subduction (~15o-20o) of the oceanic crust reaching a depth of 20 km at a distance of 100 km from the trench. The slab is then bending at larger angles, and in particular at ~45o up to the depth of 80 km and at ~65o up to the depth of 180 km, when seismicity ceased. This geometry of the slab is shown in a bunch of cross sections normal to the convergence strike, up to ~25o (east Crete Island). To the east the sparse inslab seismicity reveals an almost vertical dipping of the lower part (from 80 km downdip) of the descending slab. The slab interface that accommodates hazardous earthquakes is clearly nonplanar with the main seismic moment release taking place on its up-dip side. The fore-arc, upper plate seismicity, is remarkably low in comparison with both subduction and back arc seismicity, and confined inside a seismogenic layer having a width not exceeding the 20km. Offshore seismicity is spatially variable forming distinctive streaks thus revealing that parts of the oceanic crust are probably slipped aseismically. This observation along with the fact that coupling in the Hellenic arc is only about a tenth of the plate motion, imply the presence of areas of lower and higher coupling across the subduction interface. Areas of high coupling imply areas of the slab interface subjected to high normal forces and correlate with earthquake asperities. Although asperity distributions vary substantially through time, identification of such characteristics in the seismogenesis can have a significant impact in the seismic hazard assessment. This research has been co-funded by the European Union (European Social Fund) and Greek national resources under the framework of the "THALES Program: SEISMO FEAR HELLARC" project.
The control of limb geometry in cat posture.
Lacquaniti, F; Le Taillanter, M; Lopiano, L; Maioli, C
1990-07-01
1. The aim of this study is to address the problem of the controlled variable in quadrupedal stance. In particular, we considered whether the projection of the centre of mass of the body on the support surface or the joint torques or the geometrical configuration of the limbs are primarily controlled. 2. Cats were trained to stand freely on a platform which could be tilted in the sagittal plane by up to +/- 20 deg. The normal and tangential components of the contact forces at each paw were measured by means of load cells. The position of limb joints was recorded by means of the ELITE system. 3. The projection of the centre of body mass on the platform, as well as the orientation and length of limb axes, varied to only a limited extent with tilt angle. In particular, the limb axes were closely lined up with the vertical, as were the vectors of the contact forces at the paws. As a result, the torques at the proximal joints (scapula and hip) were close to zero and the torques at the other joints varied little with table tilt. 4. In order to test the different hypotheses on postural control, an external load (10-20% of the animal weight) was applied to the cat forequarters. The projected centre of mass consistently shifted forwards, contrary to the hypothesis that this parameter is controlled in stance. Instead, the geometry of limb posture remained unmodified after load application, even though the torques at forelimb joints were much greater than in the control. 5. This postural behaviour showed no sign of adaptation over a period of 24 h of continuous load application. 6. It is concluded that limb geometry is primarily controlled in stance. The results are discussed in the context of current notions on hierarchical control and body scheme.
National aero-space plane: Flight mechanics
NASA Technical Reports Server (NTRS)
Mciver, Duncan E.; Morrell, Frederick R.
1990-01-01
The current status and plans of the U.S. National Aero-Space Plane (NASP) program are reviewed. The goal of the program is to develop technology for single stage, hypersonic vehicles which use airbreathing propulsion to fly directly to orbit. The program features an X-30 flight research vehicle to explore altitude-speed regimes not amenable to ground testing. The decision to build the X-30 is now scheduled for 1993, with the first flight in the late 1990's. The flight mechanics, controls, flight management, and flight test considerations for the X-30 are discussed.
Fraunhofer plane analysis of particle field holograms.
Ewan, B C
1980-04-15
Using the recently developed Fraunhofer plane particle size analyzer, comparisons have been made between direct and holographically recorded particle field measurements. The usefulness of the combination is discussed in terms of the considerable time factor gain in hologram analysis and the improvement in time resolution of the instrument to that of pulsed lasers. The time resolution is demonstrated by the observation of the time development of the particle size distribution associated with a fuel injector during and after the few milliseconds of nozzle opening.
Characterization of DECam focal plane detectors
Diehl, H.Thomas; Angstadt, Robert; Campa, Julia; Cease, Herman; Derylo, Greg; Emes, John H.; Estrada, Juan; Kibik, Donna; Flaugher, Brenna L.; Holland, Steve E.; Jonas, Michelle; /Fermilab /Madrid, CIEMAT /LBL, Berkeley /Argonne /Pennsylvania U.
2008-06-01
DECam is a 520 Mpix, 3 square-deg FOV imager being built for the Blanco 4m Telescope at CTIO. This facility instrument will be used for the 'Dark Energy Survey' of the southern galactic cap. DECam has chosen 250 ?m thick CCDs, developed at LBNL, with good QE in the near IR for the focal plane. In this work we present the characterization of these detectors done by the DES team, and compare it to the DECam technical requirements. The results demonstrate that the detectors satisfy the needs for instrument.
Black Plane Solutions and Localized Gravitational Energy
Roberts, Jennifer
2015-01-01
We explore the issue of gravitational energy localization for static plane-symmetric solutions of the Einstein-Maxwell equations in 3+1 dimensions with asymptotic anti-de Sitter behavior. We apply three different energy-momentum complexes, the Einstein, Landau-Lifshitz, and Møller prescriptions, to the metric representing this category of solutions and determine the energy distribution for each. We find that the three prescriptions offer identical energy distributions, suggesting their utility for this type of model. PMID:27347499
Optimal multiple-pass aeroassisted plane change
NASA Technical Reports Server (NTRS)
Vinh, Nguyen X.; Ma, Der-Ming
1990-01-01
This paper presents the exact dimensionless equation of motion and the necessary conditions for the computation of the optimal trajectories of a hypervelocity vehicle flying through a non-rotating spherical planetary atmosphere. Numerical solution is then presented for the case when the vehicle makes several passages through the atmosphere near the perigee of its orbit. While the orbit is slowly contracting, aerodynamic maneuver is performed to obtain the maximum plane change. Several plots were presented to show the optimal variations of the lift coefficient and the bank angle and the various elements of the orbit.
National Aero-Space Plane (NASP) program
NASA Technical Reports Server (NTRS)
Tank, Ming H.
1991-01-01
A program to develop the technology for reusable airbreathing hypersonic/transatmospheric vehicles is addressed. Information on the following topics is presented in viewgraph form: (1) the National Aerospace Plane (NASP) program schedule; (2) the NASP program organization; (3) competitive strategy; (4) propulsion options; (5) wind tunnel data available for NASP; (6) ground track of envelope expansion; and (7) altitude vs. Mach number. A NASP/Space Shuttle comparison, NASP configuration matrix, and the propulsion concept of a high speed scramjet are also briefly addressed.
Braiding patterns on an inclined plane.
Mertens, Keith; Putkaradze, Vakhtang; Vorobieff, Peter
2004-07-01
A jet of fluid flowing down a partially wetting, inclined plane usually meanders but--by maintaining a constant flow rate--meandering can be suppressed, leading to the emergence of a beautiful braided structure. Here we show that this flow pattern can be explained by the interplay between surface tension, which tends to narrow the jet, and fluid inertia, which drives the jet to widen. These observations dispel misconceptions about the relationship between braiding and meandering that have persisted for over 20 years.
Optimizing snake locomotion on an inclined plane.
Wang, Xiaolin; Osborne, Matthew T; Alben, Silas
2014-01-01
We develop a model to study the locomotion of snakes on inclined planes. We determine numerically which snake motions are optimal for two retrograde traveling-wave body shapes, triangular and sinusoidal waves, across a wide range of frictional parameters and incline angles. In the regime of large transverse friction coefficients, we find power-law scalings for the optimal wave amplitudes and corresponding costs of locomotion. We give an asymptotic analysis to show that the optimal snake motions are traveling waves with amplitudes given by the same scaling laws found in the numerics.
Focal-plane architectures and signal processing
NASA Astrophysics Data System (ADS)
Jayadev, T. S.
1991-11-01
This paper discusses the relationship of focal plane architectures and signal processing functions currently used in infrared sensors. It then discusses the development of an algorithm derived from the models developed by biologists to explain the functions of insect eyes and the hardware realization of this algorithm using commercially available silicon chips. The conclusion of this study is that there are important lessons to be learned from the architecture of biological sensors, which may lead to new techniques in electro-optic sensor design.
Beam geometry selection using sequential beam addition
Popple, Richard A. Brezovich, Ivan A.; Fiveash, John B.
2014-05-15
Purpose: The selection of optimal beam geometry has been of interest since the inception of conformal radiotherapy. The authors report on sequential beam addition, a simple beam geometry selection method, for intensity modulated radiation therapy. Methods: The sequential beam addition algorithm (SBA) requires definition of an objective function (score) and a set of candidate beam geometries (pool). In the first iteration, the optimal score is determined for each beam in the pool and the beam with the best score selected. In the next iteration, the optimal score is calculated for each beam remaining in the pool combined with the beam selected in the first iteration, and the best scoring beam is selected. The process is repeated until the desired number of beams is reached. The authors selected three treatment sites, breast, lung, and brain, and determined beam arrangements for up to 11 beams from a pool comprised of 25 equiangular transverse beams. For the brain, arrangements were additionally selected from a pool of 22 noncoplanar beams. Scores were determined for geometries comprised equiangular transverse beams (EQA), as well as two tangential beams for the breast case. Results: In all cases, SBA resulted in scores superior to EQA. The breast case had the strongest dependence on beam geometry, for which only the 7-beam EQA geometry had a score better than the two tangential beams, whereas all SBA geometries with more than two beams were superior. In the lung case, EQA and SBA scores monotonically improved with increasing number of beams; however, SBA required fewer beams to achieve scores equivalent to EQA. For the brain case, SBA with a coplanar pool was equivalent to EQA, while the noncoplanar pool resulted in slightly better scores; however, the dose-volume histograms demonstrated that the differences were not clinically significant. Conclusions: For situations in which beam geometry has a significant effect on the objective function, SBA can identify
1. VIEW WEST SOUTHWEST, UPPER STATION. INCLINE PLANE TRACK AND ...
1. VIEW WEST SOUTHWEST, UPPER STATION. INCLINE PLANE TRACK AND LOWER STATION. - Monongahela Incline Plane, Connecting North side of Grandview Avenue at Wyoming Street with West Carson Street near Smithfield Street, Pittsburgh, Allegheny County, PA
5. VIEW SOUTHWEST, LOWER STATION FRONT, INCLINE PLANE TRACK, UPPER ...
5. VIEW SOUTHWEST, LOWER STATION FRONT, INCLINE PLANE TRACK, UPPER STATION. - Monongahela Incline Plane, Connecting North side of Grandview Avenue at Wyoming Street with West Carson Street near Smithfield Street, Pittsburgh, Allegheny County, PA
129. HEAD OF PLANE 12 EAST AT HIGH ST. IN ...
129. HEAD OF PLANE 12 EAST AT HIGH ST. IN NEWARK. FLUME AND POWER HOUSE ARE IN RIGHT HAND SIDE OF PHOTOGRAPH. THIS IS THE LAST DOUBLE TRACKED PLANE ON THE MORRIS CANAL. - Morris Canal, Phillipsburg, Warren County, NJ
3. INCLINE PLANE CAR INTERIOR, UPPER COMPARTMENT. Monongahela Incline ...
3. INCLINE PLANE CAR INTERIOR, UPPER COMPARTMENT. - Monongahela Incline Plane, Connecting North side of Grandview Avenue at Wyoming Street with West Carson Street near Smithfield Street, Pittsburgh, Allegheny County, PA
4. VIEW SOUTHWEST, LOWER STATION FRONT, INCLINE PLANE TRACK, UPPER ...
4. VIEW SOUTHWEST, LOWER STATION FRONT, INCLINE PLANE TRACK, UPPER STATION. - Monongahela Incline Plane, Connecting North side of Grandview Avenue at Wyoming Street with West Carson Street near Smithfield Street, Pittsburgh, Allegheny County, PA
10. LOWER STATION, FIRST FLOOR, INCLINE PLANE TRCK LOOKING SOUTH ...
10. LOWER STATION, FIRST FLOOR, INCLINE PLANE TRCK LOOKING SOUTH SOUTHEAST, UPPER STATION. - Monongahela Incline Plane, Connecting North side of Grandview Avenue at Wyoming Street with West Carson Street near Smithfield Street, Pittsburgh, Allegheny County, PA
PLANING MILL, FIRST FLOOR INTERIOR, LOOKING SOUTH. THE LARGE DEVICE ...
PLANING MILL, FIRST FLOOR INTERIOR, LOOKING SOUTH. THE LARGE DEVICE IS A WHEEL BORING MACHINE USED DURING THE TIME THIS AREA WAS A WHEEL SHOP. - Southern Pacific, Sacramento Shops, Planing Mill, 111 I Street, Sacramento, Sacramento County, CA
55. LOOKING EAST FROM HEAD OF PLANE 2 EAST. POWER ...
55. LOOKING EAST FROM HEAD OF PLANE 2 EAST. POWER HOUSE AND FLUME VISIBLE TO RIGHT, TAILRACE RUNNING THROUGH CENTER OF PHOTOGRAPH. CRADLE TO INCLINED PLANE 3 EAST IS VISIBLE IN BACKGROUND TO LEFT. - Morris Canal, Phillipsburg, Warren County, NJ
5. VIEW WEST, PERSPECTIVE UP INCLINED PLANE FROM TOP OF ...
5. VIEW WEST, PERSPECTIVE UP INCLINED PLANE FROM TOP OF ABUTMENT, FILL CONFIGURATION - Laurel Hill Quarry, Incline Plane, Both sides of State Route 56, 2.4 miles East of State Route 711, Seward, Westmoreland County, PA
6. VIEW WEST, PERSPECTIVE UP INCLINED PLANE FROM MIDSLOPE VICINITY, ...
6. VIEW WEST, PERSPECTIVE UP INCLINED PLANE FROM MID-SLOPE VICINITY, CUT CONFIGURATION - Laurel Hill Quarry, Incline Plane, Both sides of State Route 56, 2.4 miles East of State Route 711, Seward, Westmoreland County, PA
2. VIEW SOUTH, PERSPECTIVE OF ABUTMENT AND INCLINED PLANE ON ...
2. VIEW SOUTH, PERSPECTIVE OF ABUTMENT AND INCLINED PLANE ON WEST SIDE OF PA ROUTE 56 - Laurel Hill Quarry, Incline Plane, Both sides of State Route 56, 2.4 miles East of State Route 711, Seward, Westmoreland County, PA
3. VIEW NORTHWEST, PERSPECTIVE OF ABUTMENT AND INCLINED PLANE ON ...
3. VIEW NORTHWEST, PERSPECTIVE OF ABUTMENT AND INCLINED PLANE ON WEST SIDE OF PA ROUTE 56 - Laurel Hill Quarry, Incline Plane, Both sides of State Route 56, 2.4 miles East of State Route 711, Seward, Westmoreland County, PA
Geometry of Fractional Quantum Hall Fluids
NASA Astrophysics Data System (ADS)
Cho, Gil Young
2015-03-01
Fractional quantum Hall (FQH) fluids of two-dimensional electron gases (2DEG) in large magnetic fields are fascinating topological states of matter. As such they are characterized by universal properties such as their fractional quantum Hall conductivity, fractionally charged anyonic excitations and a degeneracy of topological origin on surfaces with the topology of a torus. Quite surprisingly these topological fluids also couple to the geometry on which the 2DEG resides and have universal responses to adiabatic changes in the geometry. These responses are given by a Wen-Zee term (which describes the coupling of the currents to the spin connection of the geometry) and a gravitational Chern-Simons term which reflects the universal energy and momentum transport along the edges of the FQH state. We use a field theory of the FQH states to derive these universal responses. To account for the coupling to the background geometry, we show that the concept of flux attachment needs to be modified and use it to derive the geometric responses from Chern-Simons theories. We show that the resulting composite particles minimally couple to the spin connection of the geometry. Taking account of the framing anomaly of the quantum Chern-Simons theories, we derive a consistent theory of geometric responses from the Chern-Simons effective field theories and from parton constructions, and apply it to both abelian and non-abelian states. This work was supported in part by the NSF Grant DMR-1408713.
Topology Changing Transitions in Bubbling Geometries
Horava, Petr; Shepard, Peter G.
2005-02-15
Topological transitions in bubbling half-BPS Type IIB geometries with SO(4) x SO(4) symmetry can be decomposed into a sequence of n elementary transitions. The half-BPS solution that describes the elementary transition is seeded by a phase space distribution of fermions filling two diagonal quadrants. We study the geometry of this solution in some detail. We show that this solution can be interpreted as a time dependent geometry, interpolating between two asymptotic pp-waves in the far past and the far future. The singular solution at the transition can be resolved in two different ways, related by the particle-hole duality in the effective fermion description. Some universal features of the topology change are governed by two-dimensional Type 0B string theory, whose double scaling limit corresponds to the Penrose limit of AdS_5 x S^5 at topological transition. In addition, we present the full class of geometries describing the vicinity of the most general localized classical singularity that can occur in this class of half-BPS bubbling geometries.
Topology Changing Transitions in Bubbling Geometries
Horava, Petr; Shepard, Peter G.
2005-02-15
Topological transitions in bubbling half-BPS Type IIB geometries with SO(4) x SO(4) symmetry can be decomposed into a sequence of n elementary transitions. The half-BPS solution that describes the elementary transition is seeded by a phase space distribution of fermions filling two diagonal quadrants. We study the geometry of this solution in some detail. We show that this solution can be interpreted as a time dependent geometry, interpolating between two asymptotic pp-waves in the far past and the far future. The singular solution at the transition can be resolved in two different ways, related by the particle-hole duality in the effective fermion description. Some universal features of the topology change are governed by two-dimensional Type 0B string theory, whose double scaling limit corresponds to the Penrose limit of AdS_5 x S5 at topological transition. In addition, we present the full class of geometries describing the vicinity of the most general localized classical singularity that can occur in this class of half-BPS bubbling geometries.
Nikiforov, Alexander; Gamez, Jose A.; Thiel, Walter; Huix-Rotllant, Miquel; Filatov, Michael
2014-09-28
Quantum-chemical computational methods are benchmarked for their ability to describe conical intersections in a series of organic molecules and models of biological chromophores. Reference results for the geometries, relative energies, and branching planes of conical intersections are obtained using ab initio multireference configuration interaction with single and double excitations (MRCISD). They are compared with the results from more approximate methods, namely, the state-interaction state-averaged restricted ensemble-referenced Kohn-Sham method, spin-flip time-dependent density functional theory, and a semiempirical MRCISD approach using an orthogonalization-corrected model. It is demonstrated that these approximate methods reproduce the ab initio reference data very well, with root-mean-square deviations in the optimized geometries of the order of 0.1 Å or less and with reasonable agreement in the computed relative energies. A detailed analysis of the branching plane vectors shows that all currently applied methods yield similar nuclear displacements for escaping the strong non-adiabatic coupling region near the conical intersections. Our comparisons support the use of the tested quantum-chemical methods for modeling the photochemistry of large organic and biological systems.
Phase-field simulations of GaN growth by selective area epitaxy on complex mask geometries
Aagesen, Larry K.; Coltrin, Michael Elliott; Han, Jung; Thornton, Katsuyo
2015-05-15
Three-dimensional phase-field simulations of GaN growth by selective area epitaxy were performed. Furthermore, this model includes a crystallographic-orientation-dependent deposition rate and arbitrarily complex mask geometries. The orientation-dependent deposition rate can be determined from experimental measurements of the relative growth rates of low-index crystallographic facets. Growth on various complex mask geometries was simulated on both c-plane and a-plane template layers. Agreement was observed between simulations and experiment, including complex phenomena occurring at the intersections between facets. The sources of the discrepancies between simulated and experimental morphologies were also investigated. We found that the model provides a route to optimize masks andmore » processing conditions during materials synthesis for solar cells, light-emitting diodes, and other electronic and opto-electronic applications.« less
Phase-field simulations of GaN growth by selective area epitaxy from complex mask geometries
Aagesen, Larry K.; Thornton, Katsuyo; Coltrin, Michael E.; Han, Jung
2015-05-21
Three-dimensional phase-field simulations of GaN growth by selective area epitaxy were performed. The model includes a crystallographic-orientation-dependent deposition rate and arbitrarily complex mask geometries. The orientation-dependent deposition rate can be determined from experimental measurements of the relative growth rates of low-index crystallographic facets. Growth on various complex mask geometries was simulated on both c-plane and a-plane template layers. Agreement was observed between simulations and experiment, including complex phenomena occurring at the intersections between facets. The sources of the discrepancies between simulated and experimental morphologies were also investigated. The model provides a route to optimize masks and processing conditions during materials synthesis for solar cells, light-emitting diodes, and other electronic and opto-electronic applications.
Phase-field simulations of GaN growth by selective area epitaxy on complex mask geometries
Aagesen, Larry K.; Coltrin, Michael Elliott; Han, Jung; Thornton, Katsuyo
2015-05-15
Three-dimensional phase-field simulations of GaN growth by selective area epitaxy were performed. Furthermore, this model includes a crystallographic-orientation-dependent deposition rate and arbitrarily complex mask geometries. The orientation-dependent deposition rate can be determined from experimental measurements of the relative growth rates of low-index crystallographic facets. Growth on various complex mask geometries was simulated on both c-plane and a-plane template layers. Agreement was observed between simulations and experiment, including complex phenomena occurring at the intersections between facets. The sources of the discrepancies between simulated and experimental morphologies were also investigated. We found that the model provides a route to optimize masks and processing conditions during materials synthesis for solar cells, light-emitting diodes, and other electronic and opto-electronic applications.
The influence of non-planar geometry on the flow within a distal end-to-side anastomosis
NASA Astrophysics Data System (ADS)
Sherwin, S. J.; Doorly, D. J.; Peiro, J.; Caro, C. G.
1998-11-01
The pattern of the flow in arteries is strongly influenced by the three-dimensional shape of the geometry. Curvature and torsion of the wall geometry alters the axial velocity distribution, and introduces cross flow velocity components. In this investigation we have considered flow in a model geometry of a fully occluded 45^o distal end-to-side anastomosis. Previous investigations have typically focused on planar end-to-side anastomoses where the bypass and host vessels have a plane of symmetry. We have increased the complexity of the model by considering a non-planar geometry produced by deforming the bypass vessel out of the plane of symmetry. The flows have been numerically and experimentally investigated using a spectral/hp element algorithm and magnetic resonance imaging. The significant effect of the non-planar geometry is to introduce a bulk rotation of the two secondary flow cells present in flow within a planar geometry. A reduction in wall shear stress is observed at the bed of the anastomosis and a larger absolute flux of velocity is seen within the occluded region proximal to the anastomosis. Current investigations have considered the role of pulsatility in the form of a non-reversing sinusoidal oscillation. In this case a separation bubble, not present in the steady case, is seen at the toe of the anastomosis during the systolic part of the cycle. The role of geometry and pulsatility on particle motion has also been addressed with a view to determining the shear exposure on particle within these types of flows.
63. CANAL BOAT IN CRADLE AT TOP OF PLANE. TO ...
63. CANAL BOAT IN CRADLE AT TOP OF PLANE. TO PASS OVER THE SUMMIT (THE HUMP OF LAND AT THE TOP OF PLANE TO HOLD BACK THE WATER AT THAT LEVEL), THE BOATS HAVE SEEN HINGED AND TWO CRADLES ARE USED TO CARRY THE BOAT UP THE PLANE. - Morris Canal, Phillipsburg, Warren County, NJ
Plane Transformations in a Complex Setting II: Isometries
ERIC Educational Resources Information Center
Dana-Picard, Thierry
2007-01-01
This paper is the second part of a study of plane transformations using a complex setting. The first part was devoted to homotheties and translations, now attention is turned towards plane isometries. The group theoretic properties of plane isometries are easy to derive and images of classical geometrical objects by these transformations are…
1. LOOKING TOWARD PLANE 9 WEST. BASIN HAS BEEN DRAINED ...
1. LOOKING TOWARD PLANE 9 WEST. BASIN HAS BEEN DRAINED AND SLOPE OF PLANE 9 IS VISIBLE BETWEEN ROW OF TREES IN BACKGROUND. STONEWORK ON LEFT IS ABUTMENT TO BRIDGE THAT CROSSED OVER THE CANAL. - Morris Canal, Inclined Plane 9 West, Port Warren, Warren County, NJ
Son, Hyeon-ho; Oh, Kyunghwan
2015-05-01
A novel angular spectrum method was proposed to numerically analyze off-axis free-space light propagation on a translated plane to an arbitrary angle. Utilizing a shifted angular spectrum method based on an oblique incident plane wave assumption, a generalized light propagation formulation was obtained in a wide range of both tilt angles and sampling intervals, which overcame the limitations of prior attempts. A detailed comparison of the proposed angular spectrum method with prior methods is numerically presented for diffractive optics and computer-generated holograms. The validity of the proposed method was confirmed experimentally by reconstructing a digital holographic image using a spatial light modulator.
Energy spectrum of layered semiconductors in a magnetic field parallel to the layers: Voigt geometry
NASA Astrophysics Data System (ADS)
Yoo, K. H.; Ram-Mohan, L. R.
2010-11-01
The electronic band structure of zinc-blende layered semiconductor heterostructures is investigated theoretically in the presence of an in-plane magnetic field, a configuration we label as the Voigt geometry. We use a Lagrangian formulation for modeling the band structure in the individual layers within the kṡP model. This approach has been shown by us to provide the correct ordering of the derivatives appearing in the multiband description of Schrödinger’s equations for the envelope functions through the application of the principle of stationary action. Finite element modeling of the action integral provides a natural and efficient approach to the inclusion of in-plane magnetic fields in the energy-level analysis. Calculations for quantum wells and superlattices are presented, and the complex energy-level structure obtained for the layered structures.
GEMPAK: An arbitrary aircraft geometry generator
NASA Technical Reports Server (NTRS)
Stack, S. H.; Edwards, C. L. W.; Small, W. J.
1977-01-01
A computer program, GEMPAK, has been developed to aid in the generation of detailed configuration geometry. The program was written to allow the user as much flexibility as possible in his choices of configurations and the detail of description desired and at the same time keep input requirements and program turnaround and cost to a minimum. The program consists of routines that generate fuselage and planar-surface (winglike) geometry and a routine that will determine the true intersection of all components with the fuselage. This paper describes the methods by which the various geometries are generated and provides input description with sample input and output. Also included are descriptions of the primary program variables and functions performed by the various routines. The FORTRAN program GEMPAK has been used extensively in conjunction with interfaces to several aerodynamic and plotting computer programs and has proven to be an effective aid in the preliminary design phase of aircraft configurations.
First-order Dyson coordinates and geometry.
Hermes, Matthew R; Hirata, So
2013-08-15
The mathematical constructs of the Dyson coordinates and geometry are introduced. The former are a unitary transformation of the normal coordinates and the anharmonic vibrational counterpart of the Dyson orbitals in electronic structure theory. The first-order Dyson coordinates bring the sums of the harmonic force constants and their first-order diagrammatic perturbation corrections (the first-order Dyson self-energy) to a diagonal form. The first-order Dyson geometry has no counterpart in electronic structure theory. It is the point on the potential energy surface at which the sums of the energy gradients and their first-order diagrammatic perturbation corrections vanish. It agrees with the vibrationally averaged geometry of vibrational self-consistent field (VSCF) theory in the bulk limit. These constructs provide a unified view of the relationship of VSCF and its diagrammatically size-consistent modifications as well as the self-consistent phonon method widely used in solid-state physics.
Geometry optimization of branchings in vascular networks
NASA Astrophysics Data System (ADS)
Khamassi, Jamel; Bierwisch, Claas; Pelz, Peter
2016-06-01
Progress has been made in developing manufacturing technologies which enable the fabrication of artificial vascular networks for tissue cultivation. However, those networks are rudimentary designed with respect to their geometry. This restricts long-term biological functionality of vascular cells which depends on geometry-related fluid mechanical stimuli and the avoidance of vessel occlusion. In the present work, a bioinspired geometry optimization for branchings in artificial vascular networks has been conducted. The analysis could be simplified by exploiting self-similarity properties of the system. Design rules in the form of two geometrical parameters, i.e., the branching angle and the radius ratio of the daughter branches, are derived using the wall shear stress as command variable. The numerical values of these parameters are within the range of experimental observations. Those design rules are not only beneficial for tissue engineering applications. Moreover, they can be used as indicators for diagnoses of vascular diseases or for the layout of vascular grafts.
Numerical algebraic geometry and algebraic kinematics
NASA Astrophysics Data System (ADS)
Wampler, Charles W.; Sommese, Andrew J.
In this article, the basic constructs of algebraic kinematics (links, joints, and mechanism spaces) are introduced. This provides a common schema for many kinds of problems that are of interest in kinematic studies. Once the problems are cast in this algebraic framework, they can be attacked by tools from algebraic geometry. In particular, we review the techniques of numerical algebraic geometry, which are primarily based on homotopy methods. We include a review of the main developments of recent years and outline some of the frontiers where further research is occurring. While numerical algebraic geometry applies broadly to any system of polynomial equations, algebraic kinematics provides a body of interesting examples for testing algorithms and for inspiring new avenues of work.
Supersymmetric geometries of IIA supergravity III
NASA Astrophysics Data System (ADS)
Gran, Ulf; Papadopoulos, George; von Schultz, Christian
2016-06-01
We find that (massive) IIA backgrounds that admit a {G}_2ltimes {mathbb{R}}^8 invariant Killing spinor must exhibit a null Killing vector field which leaves the Killing spinor invariant and that the rotation of the Killing vector field satisfies a certain g2 instanton condition. This result together with those in [4] and [5] complete the classification of geometries of all (massive) IIA backgrounds that preserve one supersymmetry. We also explore the geometry of a class of backgrounds which admit a {G}_2ltimes {mathbb{R}}^8 invariant Killing spinor and where in addition an appropriate 1-form bilinear vanishes. In all cases, we express the fluxes of the theory in terms of the geometry.
Geometry of fractional quantum Hall fluids
NASA Astrophysics Data System (ADS)
Cho, Gil Young; You, Yizhi; Fradkin, Eduardo
2014-09-01
We use the field theory description of the fractional quantum Hall states to derive the universal response of these topological fluids to shear deformations and curvature of their background geometry, i.e., the Hall viscosity, and the Wen-Zee term. To account for the coupling to the background geometry, we show that the concept of flux attachment needs to be modified and use it to derive the geometric responses from Chern-Simons theories. We show that the resulting composite particles minimally couple to the spin connection of the geometry. We derive a consistent theory of geometric responses from the Chern-Simons effective field theories and from parton constructions, and apply it to both Abelian and non-Abelian states.
Students' misconceptions and errors in transformation geometry
NASA Astrophysics Data System (ADS)
Ada, Tuba; Kurtuluş, Aytaç
2010-10-01
This study analyses the students' performances in two-dimensional transformation geometry and explores the mistakes made by the students taking the analytic geometry course given by researchers. An examination was given to students of Education Faculties who have taken the analytic geometry course at Eskisehir Osmangazi University in Turkey. The subject of this study included 126 third-year students in the Department of Mathematics Education. Data were collected from a seven questions exam. This exam consisted of three procedural questions, two conceptual questions and two procedural-conceptual questions. In data analysis, a descriptor code key was used. When the students' overall performances were considered for all seven questions, the results showed that they did not understand how to apply rotation transformation. The mostly observed mistakes showed that the students seemed to know the algebraic meaning of translation and also rotation but they did not seem to understand the geometric meaning of them.
Pearson's Functions to Describe FSW Weld Geometry
Lacombe, D.; Coupard, D.; Tcherniaeff, S.; Girot, F.; Gutierrez-Orrantia, M. E.
2011-01-17
Friction stir welding (FSW) is a relatively new joining technique particularly for aluminium alloys that are difficult to fusion weld. In this study, the geometry of the weld has been investigated and modelled using Pearson's functions. It has been demonstrated that the Pearson's parameters (mean, standard deviation, skewness, kurtosis and geometric constant) can be used to characterize the weld geometry and the tensile strength of the weld assembly. Pearson's parameters and process parameters are strongly correlated allowing to define a control process procedure for FSW assemblies which make radiographic or ultrasonic controls unnecessary. Finally, an optimisation using a Generalized Gradient Method allows to determine the geometry of the weld which maximises the assembly tensile strength.
Interfacial geometry dictates cancer cell tumorigenicity
NASA Astrophysics Data System (ADS)
Lee, Junmin; Abdeen, Amr A.; Wycislo, Kathryn L.; Fan, Timothy M.; Kilian, Kristopher A.
2016-08-01
Within the heterogeneous architecture of tumour tissue there exists an elusive population of stem-like cells that are implicated in both recurrence and metastasis. Here, by using engineered extracellular matrices, we show that geometric features at the perimeter of tumour tissue will prime a population of cells with a stem-cell-like phenotype. These cells show characteristics of cancer stem cells in vitro, as well as enhanced tumorigenicity in murine models of primary tumour growth and pulmonary metastases. We also show that interfacial geometry modulates cell shape, adhesion through integrin α5β1, MAPK and STAT activity, and initiation of pluripotency signalling. Our results for several human cancer cell lines suggest that interfacial geometry triggers a general mechanism for the regulation of cancer-cell state. Similar to how a growing tumour can co-opt normal soluble signalling pathways, our findings demonstrate how cancer can also exploit geometry to orchestrate oncogenesis.
Laws of granular solids: geometry and topology.
DeGiuli, Eric; McElwaine, Jim
2011-10-01
In a granular solid, mechanical equilibrium requires a delicate balance of forces at the disordered grain scale. To understand how macroscopic rigidity can emerge in this amorphous solid, it is crucial that we understand how Newton's laws pass from the disordered grain scale to the laboratory scale. In this work, we introduce an exact discrete calculus, in which Newton's laws appear as differential relations at the scale of a single grain. Using this calculus, we introduce gauge variables that describe identically force- and torque-balanced configurations. In a first, intrinsic formulation, we use the topology of the contact network, but not its geometry. In a second, extrinsic formulation, we introduce geometry with the Delaunay triangulation. These formulations show, with exact methods, how topology and geometry in a disordered medium are related by constraints. In particular, we derive Airy's expression for a divergence-free, symmetric stress tensor in two and three dimensions.
Gauge Fields, Scalars, Warped Geometry, and Strings
Silverstein, Eva M
2000-12-07
We review results on several interesting phenomena in warped compactifications of M theory, as presented at Strings 2000. The behavior of gauge fields in dimensional reduction from d + 1 to d dimensions in various backgrounds is explained from the point of view of the holographic duals (and a point raised in the question session at the conference is addressed). We summarize the role of additional fields (in particular scalar fields) in 5d warped geometries in making it possible for Poincare-invariant domain wall solutions to exist to a nontrivial order in a controlled approximation scheme without fine-tuning of parameters in the 5d action (and comment on the status of the singularities arising in the general relativistic description of these solutions). Finally, we discuss briefly the emergence of excitations of wrapped branes in warped geometries whose effective thickness, as measured along the Poincare slices in the geometry, grows as the energy increases.
The orientation of Listing's Plane in microgravity.
Clarke, Andrew H; Haslwanter, Thomas
2007-11-01
The orientation of Listing's Plane (LP) was examined under one-g and zero-g conditions during parabolic flight. Ten healthy subjects participated in the experiment. In zero-g the orientation of LP was consistently altered. LP elevation was tilted backwards by approx. 10 degrees (p=0.003). The azimuth angles of the left and right eyes also diverged in zero-g, with a statistically significant change (p=0.04) in the vergence angle between 6.1 degrees and 11.8 degrees . A discernible dissociation in torsional eye position was also observed, which proved to be statistically significant (p=0.03). The thickness of LP was found to be of the order of 1 degrees , and was not significantly altered by the transitions between one-g and zero-g. Additional control experiments involving repeated measurements of LP under normal laboratory conditions demonstrated that the parameters of LP remain stable in the individual. The parabolic flight results demonstrate that in contrast to re-orientation in the one-g gravitational field, the elimination of gravity represents a qualitative change for the vestibular and oculomotor systems. It appears that given the lack of voluntary control of ocular torsion, the tonic otolith afferences are instrumental in the stabilisation of torsional eye position and consequently of Listing's Plane. The observed torsional divergence also provides support for the so-called otolith asymmetry hypothesis.
Trajectory optimization for the National aerospace plane
NASA Technical Reports Server (NTRS)
Lu, Ping
1993-01-01
While continuing the application of the inverse dynamics approach in obtaining the optimal numerical solutions, the research during the past six months has been focused on the formulation and derivation of closed-form solutions for constrained hypersonic flight trajectories. Since it was found in the research of the first year that a dominant portion of the optimal ascent trajectory of the aerospace plane is constrained by dynamic pressure and heating constraints, the application of the analytical solutions significantly enhances the efficiency in trajectory optimization, provides a better insight to understanding of the trajectory and conceivably has great potential in guidance of the vehicle. Work of this period has been reported in four technical papers. Two of the papers were presented in the AIAA Guidance, Navigation, and Control Conference (Hilton Head, SC, August, 1992) and Fourth International Aerospace Planes Conference (Orlando, FL, December, 1992). The other two papers have been accepted for publication by Journal of Guidance, Control, and Dynamics, and will appear in 1993. This report briefly summarizes the work done in the past six months and work currently underway.
Burnett description for plane Poiseuille flow.
Uribe, F J; Garcia, A L
1999-10-01
Two recent works have shown that at small Knudsen number (K) the pressure and temperature profiles in plane Poiseuille flow exhibit a different qualitative behavior from the profiles obtained by the Navier-Stokes equations. Tij and Santos [J. Stat. Phys. 76, 1399 (1994)] used the Bhatnagar-Gross-Kook model to show that the temperature profile is bimodal and the pressure profile is nonconstant. Malek-Mansour, Baras, and Garcia [Physica A 240, 255 (1997)] qualitatively confirmed these predictions in computer experiments using the direct simulation Monte Carlo method (DSMC). In this paper we compare the DSMC measurements of hydrodynamic variables and non-equilibrium fluxes with numerical solutions of the Burnett equations. Given that they are in better agreement with molecular-dynamics simulations [E. Salomons and M. Mareschal, Phys. Rev. Lett. 69, 269 (1992)] of strong shock waves than Navier-Stokes [F. J. Uribe, R. M. Velasco, and L. S. García-Colín, Phys. Rev. Lett. 81, 2044 (1998)], and that they are second order in Knudsen number suggests that the Burnett equations may provide a better description for large K. We find that for plane Poiseuille flow the Burnett equations do not predict the bimodal temperature profile but do recover many of the other anomalous features (e.g., nonconstant pressure and nonzero parallel heat flux).
Burnett description for plane Poiseuille flow
NASA Astrophysics Data System (ADS)
Uribe, F. J.; Garcia, Alejandro L.
1999-10-01
Two recent works have shown that at small Knudsen number (K) the pressure and temperature profiles in plane Poiseuille flow exhibit a different qualitative behavior from the profiles obtained by the Navier-Stokes equations. Tij and Santos [J. Stat. Phys. 76, 1399 (1994)] used the Bhatnagar-Gross-Kook model to show that the temperature profile is bimodal and the pressure profile is nonconstant. Malek-Mansour, Baras, and Garcia [Physica A 240, 255 (1997)] qualitatively confirmed these predictions in computer experiments using the direct simulation Monte Carlo method (DSMC). In this paper we compare the DSMC measurements of hydrodynamic variables and non-equilibrium fluxes with numerical solutions of the Burnett equations. Given that they are in better agreement with molecular-dynamics simulations [E. Salomons and M. Mareschal, Phys. Rev. Lett. 69, 269 (1992)] of strong shock waves than Navier-Stokes [F. J. Uribe, R. M. Velasco, and L. S. García-Colín, Phys. Rev. Lett. 81, 2044 (1998)], and that they are second order in Knudsen number suggests that the Burnett equations may provide a better description for large K. We find that for plane Poiseuille flow the Burnett equations do not predict the bimodal temperature profile but do recover many of the other anomalous features (e.g., nonconstant pressure and nonzero parallel heat flux).
Characterization of the KATRIN Focal Plane Detector
NASA Astrophysics Data System (ADS)
Bodine, Laura; Leber, Michelle; Myers, Allan; Tolich, Kazumi; Vandevender, Brent; Wall, Brandon
2008-10-01
The Karlsruhe Tritium Neutrino (KATRIN) Experiment is a next generation tritium beta decay experiment designed to measure directly the electron neutrino mass with a sensitivity of 0.2 eV. In the experiment, electrons from tritium decay of a gaseous source are magnetically guided through analyzing solenoidal retarding electrostatic spectrometers and detected via a focal plane detector. The focal plane detector is a 90mm diameter, 500 micron thick monolithic silicon pin-diode array with 148 pixels. The diode contacts have a titanium nitride overlayer and are connected to preamplifiers via an array of spring-loaded pogo pins. This novel connection scheme minimizes backgrounds from radioactive materials near the detector, facilitates characterization and replacement of the detector wafer, but requires a unique mounting design. The force of the pins strains the silicon, possibly altering the detector properties and performance. Results on the mechanical, thermal and electrical performance of a prototype detector under stress from pogo pin readouts will be presented.
Target plane imager for inertial confinement fusion
Swift, C.D.; Bliss, E.S.; Jones, W.A.; Seppala, L.G.
1985-01-30
The Nova laser, completed in December 1984 at Lawrence Livermore National Laboratory, is being used to conduct inertial confinement fusion experiments. It is capable of focusing more than 100 kJ of energy on small fusion targets. This paper discusses an optical system called the target plane imager that is used during the beam alignment phase of these experiments. The TPI includes a three meter long periscope with a wide field of view, F/3 objective. The telescope relays images of the target focal plane to viewing optics and a video sensor located outside the target chamber. Operation of the system is possible at three wavelengths: 1.05..mu.., 0.527..mu.., and 0.351..mu... These are the three wavelengths at which the ten Nova laser beams can irradiate targets. Both nearfield and farfield images of the ten beams can be viewed with the TPI. This instrument is used to properly align the laser to the target before each target irradiation.
Waveguide Metacouplers for In-Plane Polarimetry
NASA Astrophysics Data System (ADS)
Pors, Anders; Bozhevolnyi, Sergey I.
2016-06-01
The state of polarization (SOP) is an inherent property of the vectorial nature of light and a crucial parameter in a wide range of remote sensing applications. Nevertheless, the SOP is rather cumbersome to probe experimentally, as conventional detectors respond only to the intensity of the light, hence losing the phase information between orthogonal vector components. In this work, we propose a type of polarimeter that is compact and well suited for in-plane optical circuitry while allowing for immediate determination of the SOP through simultaneous retrieval of the associated Stokes parameters. The polarimeter is based on plasmonic phase-gradient birefringent metasurfaces that facilitate normal incident light to launch in-plane photonic-waveguide modes propagating in six predefined directions with the coupling efficiencies providing a direct measure of the incident SOP. The functionality and accuracy of the polarimeter, which essentially is an all-polarization-sensitive waveguide metacoupler, is confirmed through full-wave simulations at the operation wavelength of 1.55 μ m .
A jumping cylinder on an inclined plane
NASA Astrophysics Data System (ADS)
Gómez, R. W.; Hernández-Gómez, J. J.; Marquina, V.
2012-09-01
The problem of a cylinder of mass m and radius r, with its centre of mass out of the cylinder’s axis, rolling on an inclined plane that makes an angle α with respect to the horizontal, is analysed. The equation of motion is partially solved to obtain the site where the cylinder loses contact with the inclined plane (jumps). Several simplifications are made: the analysed system consists of an homogeneous disc with a one-dimensional straight line mass parallel to the disc axis at a distance y < r of the centre of the cylinder. To compare our results with experimental data, we use a styrofoam cylinder to which a long brass rod is embedded parallel to the disc axis at a distance y < r from it, so the centre of mass lies at a distance d from the centre of the cylinder. Then the disc rolls without slipping on a long wooden ramp inclined at 15°, 30° and 45° with respect to the horizontal. To determine the jumping site, the movements are recorded with a high-speed video camera (Casio EX ZR100) at 240 and 480 frames per second. The experimental results agree well with the theoretical predictions.
Drag reduction at a plane wall
NASA Technical Reports Server (NTRS)
Hill, D. C.
1993-01-01
The objective is to determine by analytical means how drag on a plane wall may be modified favorably using a minimal amount of flow information - preferably only information at the wall. What quantities should be measured? How should that information be assimilated in order to arrive at effective control? As a prototypical problem, incompressible, viscous flow, governed by the Navier-Stokes equations, past a plane wall at which the no-slip condition was modified was considered. The streamwise and spanwise velocity components are required to be zero, but the normal component is to be specified according to some control law. The challenge is to choose the wall-normal velocity component based on flow conditions at the wall so that the mean drag is as small as possible. There can be no net mass flux through the wall, and the total available control energy is constrained. A turbulent flow is highly unsteady and has detailed spatial structure. The mean drag on the wall is the integral over the wall of the local shear forces exerted by the fluid, which is then averaged in time; it is a 'macroscopic' property of the flow. It is not obvious how unsteady boundary control is to be applied in order to modify the mean flow most effectively, especially in view of the non- self-adjoint nature of the governing equations. An approximate analytical solution to the suboptimal scheme is pursued.