Structure analysis for plane geometry figures
NASA Astrophysics Data System (ADS)
Feng, Tianxiao; Lu, Xiaoqing; Liu, Lu; Li, Keqiang; Tang, Zhi
2013-12-01
As there are increasing numbers of digital documents for education purpose, we realize that there is not a retrieval application for mathematic plane geometry images. In this paper, we propose a method for retrieving plane geometry figures (PGFs), which often appear in geometry books and digital documents. First, detecting algorithms are applied to detect common basic geometry shapes from a PGF image. Based on all basic shapes, we analyze the structural relationships between two basic shapes and combine some of them to a compound shape to build the PGF descriptor. Afterwards, we apply matching function to retrieve candidate PGF images with ranking. The great contribution of the paper is that we propose a structure analysis method to better describe the spatial relationships in such image composed of many overlapped shapes. Experimental results demonstrate that our analysis method and shape descriptor can obtain good retrieval results with relatively high effectiveness and efficiency.
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…
TEACHERS' GUIDE. NINTH GRADE PLANE AND SOLID GEOMETRY FOR THE ACADEMICALLY TALENTED.
ERIC Educational Resources Information Center
HORN, R.A.
MATERIALS ARE INTENDED FOR A UNIFIED AND ACCELERATED PLANE AND SOLID GEOMETRY COURSE AND FOR EASY MODIFICATION AND ADAPTATION BY EXPERIENCED OR INEXPERIENCED TEACHER. TEXTBOOKS TO WHICH THE GUIDE HAS BEEN KEYED ARE LISTED. UNITS ARE GIVEN FOR BOTH SEMESTERS WITH TIME ALLOTMENTS RECOMMENDED. EACH UNIT IS SUBDIVIDED INTO TOPICS AND OBJECTIVES,…
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)…
Multigroup Time-Independent Neutron Transport Code System for Plane or Spherical Geometry.
Energy Science and Technology Software Center (ESTSC)
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.
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.
Analysis of current-voltage characteristics in the wires-to-planes geometry during corona discharge
NASA Astrophysics Data System (ADS)
Ait Said, Hakim; Nouri, Hamou; Zebboudj, Youcef
2014-09-01
The behaviour of DC corona discharge in air that is free of particulate matter with the wires-to-plane geometry was analysed in this work. The formulae I = KV (V - V0) and I = A (V - V0)m commonly used for the current-voltage characteristics were used to determine the various corona parameters for the two polarities of the corona discharge. Using curve fitting, it has been shown that the geometric factors K and A and the exponent m are strongly affected by the number n of the discharging wires. However, the corona inception voltage determined from the measurements is weakly influenced when n is small, and it remained constant for n > 5 discharging wires. As for the breakdown voltage of the discharge, it is practically independent of the number n. Furthermore, it was verified that the two formulae above can be used for both negative and positive corona in multiple wires-to-plane geometries.
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
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
2016-04-01
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-fit 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% 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 Scenario 1
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.
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…
NASA Astrophysics Data System (ADS)
Huang, C.; Chan, Y.; Hu, J.; Lee, J.
2006-12-01
In the past decade, improvements in geodesy allow geologists to measure the surface displacement of the hanging wall of a fault more precisely. The improved geodetic observations provide opportunities to better characterize the deformational behaviors of the hanging wall block due to earthquake fault slip. In the case of the 1999 Chi-Chi earthquake, the hanging wall block of the earthquake fault showed complex deformation pattern at the kilometer scale. Because previous studies mainly characterize on the fault at the regional scale, it is of interest and also challenge to characterize the fault at a smaller scale with a higher resolution. In this study we reconstructed the geometry of a kilometer-scale patch of the fault plane using the displacement data collected from the densely distributed city planning benchmarks. The study area is approximately 4 km by 8 km in size, and contains as many as 924 benchmarks. Among the benchmarks, 62 have both horizontal and vertical displacement data, and the rest of the benchmarks have the horizontal displacement data. Based on the assumption of rigid block motion, we established the earthquake fault geometry using the 62 slip vectors. We then use fault parallel flow method to test the derived fault geometry model with satisfied results. The derived fault geometry model is rather consistent with the borehole data from the nearby 450 m well.
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.
Numerical investigation of the formation of Trichel pulses in a needle-plane geometry
NASA Astrophysics Data System (ADS)
Dordizadeh, Peyman; Adamiak, Kazimierz; Castle, G. S. Peter
2015-10-01
This paper presents a numerical investigation of the formation of the Trichel pulses in negative dc corona discharge for a needle-plane configuration in atmospheric air. A 2D axisymmetric model of the problem considering three charged species and consisting of a hyperboloid needle with a tip radius of 35 μm and needle-plane spacing of 6 mm over the voltage range of -3.5 kV to -12 kV has been studied. A commercial finite element package COMSOL was used for simultaneously solving three convection-diffusion equations along with Poisson’s equation. In order to obtain a better understanding of the processes which lead to the pulse formation, a close look is taken at one of the pulses. The distributions of the major charged species and the timeline of peak-values of charged species densities and electric field are presented. Through tracing the evolution of the locations of the peak densities of the charged species some new insights have been provided. The configuration of the model was chosen so that the simulation results could be compared with the experimental data published by Lama and Gallo. The numerical results were in acceptable agreement with the experimental values. Some explanations are given for the discrepancies between experimental and simulation results. It is also shown, that as the frequency of the pulses increases with voltage, the transition from Trichel pulse discharge to glow discharge initiates and full glow discharge is reached at -12 kV.
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
Role of EHD motion in the electrical conduction of liquids in a blade-plane geometry
Haidara, M.; Atten, P.
1985-05-01
A blade-plane electrode assembly is used to study electrical conduction in divergent fields and, more generally, to investigate high field conduction of dielectric liquids. The stationary current-voltage characteristics show two regimes of conduction: a quasi-ohmic regime and a V /SUP a/ one, V being the applied voltage and 3 < ..cap alpha.. < 6. The latter regime corresponds to dominance of charge injection by the blade, as revealed by the field distribution obtained by the Kerr technique. A liquid motion is induced by the Coulomb force which convects charge carriers and results in a decrease of the first transit time following the application of a voltage step. The transient injection currents exhibit a dependence upon the elapsed time during which no voltage is applied, and the possible origin of this phenomenon is discussed. Measurement of the liquid velocity by laser Doppler anemometry also exhibits two different laws of variation with applied voltage consistent with the two current regimes. In the steady-state conditions of the injection-dominant regime, the square of the measured velocity component w/sup 2/ varies as the electrical power input IV (I being the current). This is tentatively interpreted by the viscous dominated character of the induced motion.
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.
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
Liao, Che-Hao; Chang, Wen-Ming; Chen, Horng-Shyang; Chen, Chih-Yen; Yao, Yu-Feng; Chen, Hao-Tsung; Su, Chia-Ying; Ting, Shao-Ying; Kiang, Yean-Woei; Yang, C C
2012-07-01
With the nano-imprint lithography and the pulsed growth mode of metalorganic chemical vapor deposition, a regularly-patterned, c-axis nitride nanorod (NR) array of quite uniform geometry with simultaneous depositions of top-face, c-plane disc-like and sidewall, m-plane core-shell InGaN/GaN quantum well (QW) structures is formed. The differences of geometry and composition between these two groups of QW are studied with scanning electron microscopy, cathodoluminescence, and transmission electron microscopy (TEM). In particular, the strain state analysis results in TEM observations provide us with the information about the QW width and composition. It is found that the QW widths are narrower and the indium contents are higher in the sidewall m-plane QWs, when compared with the top-face c-plane QWs. Also, in the sidewall m-plane QWs, the QW width (indium content) decreases (increases) with the height on the sidewall. The observed results can be interpreted with the migration behaviors of the constituent atoms along the NR sidewall from the bottom. PMID:22772276
NASA Astrophysics Data System (ADS)
Casanovas, A. M.; Casanovas, J.; Lagarde, F.; Belarbi, A.
1992-10-01
SF6 samples (PSF6=100 or 200 kPa) were submitted to point-to-plane dc negative polarity corona discharges in the presence of water [concentration=2000 ppmv (parts per million by volume)] or without the addition of water. The stable gaseous byproducts formed, (SO2F2, SOF2, and S2F10) were assayed by gas-phase chromatography. The variation of their yields against the charge transported (up to 10 C) was studied for two metals (aluminum and stainless steel) constituting the plane electrode, at various values of the SF6 pressure, the water content, the gap spacing (2.5 and 8 mm), and the discharge current [12≤Ī (μA)≤25]. The results indicate an important effect of the metal constituting the plane electrode and of the moisture conditions, particularly on the production of SOF2 and S2F10.
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)
Hayes, Gavin P.; Wald, David J.; Keranen, Katie
2009-09-01
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 well-constrained 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 three-dimensional surface for the Sunda subduction zone and introduce the development of a new global three-dimensional subduction interface model: Slab1.0.
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)
Eifert, Alexander; Petit, Julien; Baier, Tobias; Bonaccurso, Elmar; Hardt, Steffen
2015-03-01
We use direct current (DC) corona discharge to create wettability gradients on polymer surfaces. The inhomogeneous current density distribution due to a point-to-plane arrangement induces local changes of the wettability of polymer surfaces, resulting in macroscopic wettability gradients. We found that condensation of water vapor on the surface allows a more precise characterization of the wettability gradient than macroscopic contact angle measurements. Condensation experiments allow characterizing different zones with different wettability. The wettability pattern depends on the stiffness of the substrate. We conjecture that Coulomb interactions influence the spatial distribution of wettability. Indirect measurements of the electrostatic surface potential after exposure support this assumption.
Differentialless geometry of plane curves
NASA Astrophysics Data System (ADS)
Latecki, Longin J.; Rosenfeld, Azriel
1997-10-01
We introduce a class of planar arcs and curves, called tame arcs, which is general enough to describe the boundaries of planar real objects. A tame arc can have smooth parts as well as sharp corners; thus a polygonal arc is tame. On the other hand, this class of arcs is restrictive enough to rule out pathological arcs which have infinitely many inflections or which turn infinitely often: a tame arc can have only finitely many inflections, and its total absolute turn must be finite. In order to relate boundary properties of discrete objects obtained by segmenting digital images to the corresponding properties of their continuous originals, the theory of tame arcs is based on concepts that can be directly transferred from the continuous to the discrete domain. A tame arc is composed of a finite number of supported arcs. We define supported digital arcs and motivate their definition by the fact that hey can be obtained by digitizing continuous supported arcs. Every digital arc is tame, since it contains a finite number of points, and therefore it can be decomposed into a finite number of supported digital arcs.
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)
Fainstein, A.; Etchegoin, P.; Chamberlain, M. P.; Cardona, M.; Tötemeyer, K.; Eberl, K.
1995-05-01
We present a detailed experimental study of optical phonon Raman scattering in GaAs/AlAs multiple quantum wells for several in-plane geometries. By exploiting a waveguided structure, we performed 90°, forward, and backscattering experiments with dispersed light propagating along the layers. Using these geometries, phonons with various propagation directions and polarized both parallel and perpendicular to the growth axis can be probed. The 90° data complete and correct earlier results obtained for the same geometry by Zucker et al., bringing them into accord with later experimental and theoretical work. Moreover, in-plane forward scattering data are reportd as a complementary check to these experiments. We discuss selection rules and scattering mechanisms, and compare the results with phonon energies calculated within a continuum model based on linear combinations of LO, TO, and interface modes. We find a very good agreement between the experiment and the predictions of the established theory of phonon modes and Raman scattering in semiconductor heterostructures.
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.
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)
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.
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…
ERIC Educational Resources Information Center
Vaughan, Herbert E.; Szabo, Steven
This is the teacher's edition of a text for the first year of a two-year high school geometry course. The course bases plane and solid geometry and trigonometry on the fact that the translations of a Euclidean space constitute a vector space which has an inner product. Volume 1 deals largely with affine geometry, and the notion of dimension is…
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…
Digital scanner infrared focal plane technology
NASA Astrophysics Data System (ADS)
Ortiz, M. A.; Malone, N. R.; Harris, M.; Shin, J.; Byers, S.; Price, D.; Vampola, J.
2011-09-01
Advancements in finer geometry and technology advancements in circuit design now allow placement of digital architecture on cryogenic focal planes while using less power than heritage analog designs. These advances in technology reduce the size, weight, and power of modern focal planes. In addition, the interface to the focal plane is significantly simplified and is more immune to Electromagnetic Interference (EMI). The cost of the customer's instrument after integration with the digital scanning Focal Plane Array (FPA) has been significantly reduced by placing digital architecture such as Analog to digital convertors and Low Voltage Differential Signaling (LVDS) Inputs and Outputs (I/O) on the Read Out Integrated Circuit (ROIC).
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…
NASA Astrophysics Data System (ADS)
Cembranos, J. A. R.; Dobado, A.; Maroto, A. L.
Extra-dimensional theories contain additional degrees of freedom related to the geometry of the extra space which can be interpreted as new particles. Such theories allow to reformulate most of the fundamental problems of physics from a completely different point of view. In this essay, we concentrate on the brane fluctuations which are present in brane-worlds, and how such oscillations of the own space-time geometry along curved extra dimensions can help to resolve the Universe missing mass problem. The energy scales involved in these models are low compared to the Planck scale, and this means that some of the brane fluctuations distinctive signals could be detected in future colliders and in direct or indirect dark matter searches.
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.
A novel grid geometry of long detector modules for a time-of-flight system
NASA Astrophysics Data System (ADS)
Daskalakis, G.; Panagiotou, A. D.; Ioannidis, G. S.
1993-05-01
We present a novel geometry for a large area TOF system, consisting of long detector modules arranged in X- Y directions in two planes. Such a GRID geometry has many advantages, including better particle identification and fewer modules (channels) for the same number of identified particles, compared to a single plane geometry, i.e. a TILE arrangement. We also present the mathematical algorithm for the general case of an n-plane GRID geometry and discuss its applicability.
NASA Astrophysics Data System (ADS)
Correa, Diego H.; Silva, Guillermo A.
2008-07-01
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.
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.
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
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…
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.
Geometry 3, Mathematics (Experimental): 5228.32.
ERIC Educational Resources Information Center
Josepher, Nelda; Temple, Aline
This is the second of a two quin series which introduces the student to all the theorems usually included in high school geometry; emphasis is on understanding and use of these theorems without proof. The course develops definitions and properties of the plane and solid figures and formulates methods for finding their linear measure, lateral and…
Rotating convection in elliptical geometries
NASA Astrophysics Data System (ADS)
Evonuk, M.
2014-12-01
Tidal interactions between hot jupiter planets and their host stars are likely to result in non-spherical geometries. These elliptical instabilities may have interesting effects on interior fluid convective patterns, which in turn influence the nature of the magnetic dynamo within these planets. Simulations of thermal convection in the 2D rotating equatorial plane are conducted to determine to first order the effect of ellipticity on convection for varying density contrasts with differing convective vigor and rotation rate. This survey is conducted in two dimensions in order to simulate a broad range of ellipticities and to maximize the parameter space explored.
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.
ERIC Educational Resources Information Center
Kuntz, Gilles
The first section of this paper on World Wide Web applications related to dynamic geometry addresses dynamic geometry and teaching, including the relationship between dynamic geometry and direct manipulation, key features of dynamic geometry environments, the importance of direct engagement of the learner using construction software for…
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…
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
Learning Geometry through Dynamic Geometry Software
ERIC Educational Resources Information Center
Forsythe, Sue
2007-01-01
In this article, the author investigates effective teaching and learning of geometrical concepts using dynamic geometry software (DGS). Based from her students' reactions to her project, the author found that her students' understanding of the concepts was better than if they had learned geometry through paper-based tasks. However, mixing computer…
ERIC Educational Resources Information Center
Vaughan, Herbert E.; Szabo, Steven
This is the teacher's edition of a text for the second year of a two-year high school geometry course. The course bases plane and solid geometry and trigonometry on the fact that the translations of a Euclidean space constitute a vector space which has an inner product. Congruence is a geometric topic reserved for Volume 2. Volume 2 opens with an…
Characterization of Finite Ground Coplanar Waveguide with Narrow Ground Planes
NASA Technical Reports Server (NTRS)
Ponchak, George E.; Tentzeris, Emmanouil M.; Katehi, Linda P. B.
1997-01-01
Coplanar waveguide with finite width ground planes is characterized through measurements, conformal mapping, and the Finite Difference Time Domain (FDTD) technique for the purpose of determining the optimum ground plane width. The attenuation and effective permittivity of the lines are related to its geometry. It is found that the characteristics of the Finite Ground Coplanar line (FGC) are not dependent on the ground plane width if it is greater than twice the center conductor width, but less than lambda(sub d)/8. In addition, electromagnetic field plots are presented which show for the first time that electric fields in the plane of the substrate terminate on the outer edge of the ground plane, and that the magnitude of these fields is related to the ground plane width.
Combinatorial Geometry Printer Plotting.
Energy Science and Technology Software Center (ESTSC)
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.
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.
NASA Astrophysics Data System (ADS)
Taylor, Marika
2006-03-01
Two charge BPS horizon free supergravity geometries are important in proposals for understanding black hole microstates. In this paper we construct a new class of geometries in the NS1-P system, corresponding to solitonic strings carrying fermionic as well as bosonic condensates. Such geometries are required to account for the full microscopic entropy of the NS1-P system. We then briefly discuss the properties of the corresponding geometries in the dual D1-D5 system.
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…
Beamlet focal plane diagnostic
Caird, J.A.; Nielsen, N.D.; Patton, H.G.; Seppala, L.G.; Thompson, C.E.; Wegner, P.J.
1996-12-01
This paper describes the major optical and mechanical design features of the Beamlet Focal Plane Diagnostic system as well as measurements of the system performance, and typical data obtained to date. We also discuss the NIF requirements on the focal spot that we are interested in measuring, and some of our plans for future work using this system.
Sensitivity analysis of imaging geometries for prostate diffuse optical tomography
NASA Astrophysics Data System (ADS)
Zhou, Xiaodong; Zhu, Timothy C.
2008-02-01
Endoscopic and interstitial diffuse optical tomography have been studied in clinical investigations for imaging prostate tissues, yet, there is no comprehensive comparison of how these two imaging geometries affect the quality of the reconstruction images. In this study, the effect of imaging geometry is investigated by comparing the cross-section of the Jacobian sensitivity matrix and reconstructed images for three-dimensional mathematical phantoms. Next, the effect of source-detector configurations and number of measurements in both geometries is evaluated using singular value analysis. The amount of information contained for each source-detector configuration and different number of measurements are compared. Further, the effect of different measurements strategies for 3D endoscopic and interstitial tomography is examined. The pros and cons of using the in-plane measurements and off-plane measurements are discussed. Results showed that the reconstruction in the interstitial geometry outperforms the endoscopic geometry when deeper anomalies are present. Eight sources 8 detectors and 6 sources 12 detectors are sufficient for 2D reconstruction with endoscopic and interstitial geometry respectively. For a 3D problem, the quantitative accuracy in the interstitial geometry is significantly improved using off-plane measurements but only slightly in the endoscopic geometry.
NASA Technical Reports Server (NTRS)
Munk, Max M
1923-01-01
This report deals with the calculation of the equilibrium, statistical stability, and damping of the tail plane. The author has simplified the present theory of longitudinal stability for the particular purpose of obtaining one definite coefficient characteristics of the effect of the tail plane. This coefficient is obtained by substituting certain aerodynamic characteristics and some dimensions of the airplane in a comparatively simple mathematical expression. Care has been taken to confine all aerodynamical information necessary for the calculation of the coefficient to the well-known curves representing the qualities of the wing section. This is done by making use of the present results of modern aerodynamics. All formulas and relations necessary for the calculation are contained in the paper. They give in some cases only an approximation of the real values. An example of calculation is added in order to illustrate the application of the method. The coefficient indicates not only whether the effect of the tail plane is great enough, but also whether it is not too great. It appears that the designer has to avoid a certain critical length of the fuselage, which inevitably gives rise to periodical oscillations of the airplane. The discussion also shows the way and in what direction to carry out experimental work.
Thermoacoustic engines in alternate geometry resonators
NASA Astrophysics Data System (ADS)
Lightfoot, Jay Alan
1997-10-01
The purpose of this research is to branch out from thermoacoustics in the plane wave geometry to study radial wave thermoacoustic engines. Two possible advantages of radial systems are proposed: a reduction in harmonic generation due to the natural anharmonicity of the resonator, and the possibility of improved engine performance using naturally sloped stacks. The radial wave prime mover is described. Experimental results for the temperature at which oscillations begin are compared with theoretical predictions. Accounting for a pore distribution in the stack and temperature discontinuities between the stack and heat exchangers, theory and experiment are shown to be in agreement. In addition, spectral measurements in the radial prime mover show that the anharmonicity of the resonator significantly reduces non-linear harmonic generation. To gain a better understanding of naturally sloped stacks in the radial engine, the physics of sloped stacks is extended to the plane geometry, where fewer constraints exist. A theoretical treatment of thermoacoustic engines with varying stack pore cross-section and/or varying resonator cross-section in the temperature gradient supporting stack region is presented along with numerical results for plane and radial wave prime movers and refrigerators. Results show significant improvements in refrigerator COP in plane wave systems.
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.)
Modelling the landing of a plane in a calculus lab
NASA Astrophysics Data System (ADS)
Morante, Antonio; Vallejo, José A.
2012-10-01
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.
Quantum Monte Carlo simulations in novel geometries
NASA Astrophysics Data System (ADS)
Iglovikov, Vladimir
Quantum Monte Carlo simulations are giving increasing insight into the physics of strongly interacting bosons, spins, and fermions. Initial work focused on the simplest geometries, like a 2D square lattice. Increasingly, modern research is turning to more rich structures such as honeycomb lattice of graphene, the Lieb lattice of the CuO2 planes of cuprate superconductors, the triangular lattice, and coupled layers. These new geometries possess unique features which affect the physics in profound ways, eg a vanishing density of states and relativistic dispersion ("Dirac point'') of a honeycomb lattice, frustration on a triangular lattice, and a flat bands on a Lieb lattice. This thesis concerns both exploring the performance of QMC algorithms on different geometries(primarily via the "sign problem'') and also applying those algorithms to several interesting open problems.
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.
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…
ERIC Educational Resources Information Center
Morris, Barbara H.
2004-01-01
This article describes a geometry project that used the beauty of stained-glass-window designs to teach middle school students about geometric figures and concepts. Three honors prealgebra teachers and a middle school mathematics gifted intervention specialist created a geometry project that covered the curriculum and also assessed students'…
Geometry of multihadron production
Bjorken, J.D.
1994-10-01
This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions.
ERIC Educational Resources Information Center
Kaufmann, Matthew L.; Bomer, Megan A.; Powell, Nancy Norem
2009-01-01
Students enter the geometry classroom with a strong concept of fairness and a sense of what it means to "play by the rules," yet many students have difficulty understanding the postulates, or rules, of geometry and their implications. Although they may never have articulated the properties of an axiomatic system, they have gained a practical…
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.
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.
Mosaic Focal Plane Development
NASA Astrophysics Data System (ADS)
Mason, David L.; Horner, Scott D.; Aamodt, Earl K.
2002-12-01
Advances in systems engineering, applied sciences, and manufacturing technologies have enabled the development of large ground based and spaced based astronomical instruments having a large Field of View (FOV) to capture a large portion of the universe in a single image. A larger FOV can be accomplished using light weighted optical elements, improved support structures, and the development of mosaic Focal Plane Assemblies (mFPA). A mFPA designed for astronomy can use multiple Charged Coupled Devices (CCD) mounted onto a single camera baseplate integrated at the instrument plane of focus. Examples of current, or proposed, missions utilizing mFPA technology include FAME, GEST, Kepler, GAIA, LSST, and SNAP. The development of a mFPA mandates tighter control on the design trades, component development, CCD characterization, component integration, and performance verification testing. This paper addresses the capability Lockheed Martin Space Systems Company's (LMSSC) Advanced Technology Center (ATC) has developed to perform CCD characterization, mFPA assembly and alignment, and mFPA system level testing.
Mosaic Focal Plane Development
NASA Astrophysics Data System (ADS)
Mason, D.; Horner, S.; Aamodt, E.
Advances in manufacturing and applied sciences have enabled the development of large ground and spaced based astronomical instruments having a Field of View (FOV) large enough to capture a large portion of the universe in a single image. A large FOV can be accomplished using light weighted optics, improved structures, and the development of mosaic Focal Plane Assemblies (mFPAs). A mFPA comprises multiple Charged Coupled Devices (CCD) mounted onto a single baseplate integrated at the focus plane of the instrument. Examples of current, or proposed, missions utilizing mFPA technology include FAME, GEST, Kepler, GAIA, LSST, and SNAP. The development of a mFPA mandates tight control on the design trades of component development, CCD definition and characterization, component integration, and performance verification testing. This paper addresses the results of the Lockheed Martin Space Systems Company (LMSSC), Advanced Technology Center (ATC) developed mFPA. The design trades and performance characterization are services provided by the LMSSC ATC but not detailed in this paper.
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…
Role of anisotropy in the expansion-free plane gravitational collapse
NASA Astrophysics Data System (ADS)
Sharif, M.; Azam, M.
2014-01-01
In this paper, we study the instability range of the collapsing fluid bounded by the plane geometry. For this purpose, the expansion-free dynamical equations in Newtonian and post-Newtonian regimes are obtained through perturbation scheme. We investigate the role of pressure anisotropy and energy density inhomogeneity in the instability ranges of expansion-free fluid. It is concluded that the instability regions for the plane geometry turns out to be large than the spherical case.
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.
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
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)
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)
Noncommutative Geometry and Physics
NASA Astrophysics Data System (ADS)
Connes, Alain
2006-11-01
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.
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)
Evaluation of imaging geometry for stationary chest tomosynthesis
NASA Astrophysics Data System (ADS)
Shan, Jing; Tucker, Andrew W.; Lee, Yueh Z.; Heath, Michael D.; Wang, Xiaohui; Foos, David; Lu, Jianping; Zhou, Otto
2014-03-01
We have recently demonstrated the feasibility of stationary digital chest tomosynthesis (s-DCT) using a dis- tributed carbon nanotube x-ray source array. The technology has the potential to increase the imaging resolution and speed by eliminating source motion. In addition, the flexibility in the spatial configuration of the individual sources allows new tomosynthesis imaging geometries beyond the linear scanning mode used in the conventional systems. In this paper, we report the preliminary results on the effects of the tomosynthesis imaging geometry on the image quality. The study was performed using a bench-top s-DCT system consisting of a CNT x-ray source array and a flat-panel detector. System MTF and ASF are used as quantitative measurement of the in-plane and in-depth resolution. In this study geometries with the x-ray sources arranged in linear, square, rectangular and circular configurations were investigated using comparable imaging doses. Anthropomorphic chest phantom images were acquired and reconstructed for image quality assessment. It is found that wider angular coverage results in better in-depth resolution, while the angular span has little impact on the in-plane resolution in the linear geometry. 2D source array imaging geometry leads to a more isotropic in-plane resolution, and better in-depth resolution compared to 1D linear imaging geometry with comparable angular coverage.
Energy Science and Technology Software Center (ESTSC)
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
NASA Astrophysics Data System (ADS)
Osborne, I.; Brownson, E.; Eulisse, G.; Jones, C. D.; Lange, D. J.; Sexton-Kennedy, E.
2014-06-01
CMS faces real challenges with upgrade of the CMS detector through 2020 and beyond. One of the challenges, from the software point of view, is managing upgrade simulations with the same software release as the 2013 scenario. We present the CMS geometry description software model, its integration with the CMS event setup and core software. The CMS geometry configuration and selection is implemented in Python. The tools collect the Python configuration fragments into a script used in CMS workflow. This flexible and automated geometry configuration allows choosing either transient or persistent version of the same scenario and specific version of the same scenario. We describe how the geometries are integrated and validated, and how we define and handle different geometry scenarios in simulation and reconstruction. We discuss how to transparently manage multiple incompatible geometries in the same software release. Several examples are shown based on current implementation assuring consistent choice of scenario conditions. The consequences and implications for multiple/different code algorithms are discussed.
NASA Astrophysics Data System (ADS)
Lee, Sangyeop; Lee, Hakjoon; Yoo, Taehee; Lee, Sanghoon; Liu, X.; Furdyna, J. K.
2013-05-01
Magnetic anisotropy of ferromagnetic semiconductor GaMnAs film with a low Mn concentration grown on a (001) GaAs substrate was investigated by Hall effect measurements. The presence of domains with in-plane and out-of-plane easy axes was identified in the film by analyzing hysteresis loops observed via the Hall resistance measured in various geometries. Quantitative analysis of the planar Hall resistance showed that the fraction of the sample with magnetic domains having a dominant out-of-plane easy axis was about 6 times larger than the fraction corresponding to domains with easy axis in the sample plane.
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.
NASA Astrophysics Data System (ADS)
Barkin, Yu. V.; Ferrandiz, J. M.
2009-04-01
theory of Mercury librations in longitude by using three characteristics of Mercury rotation determined in the paper [3]. Two from these parameters are values of angle of librations in longitude and angular velocity in moment of passage of perihelion of Mercury orbit on 17 April 2002: (^g)0 = 0007 ± 0001, (^?? )0 = (2.10± 0.06)? ars/d. Third parameter determined in [3] is a dynamical coefficient: K = (B -A)(4Cm ) = (5.08± 0.30) × 10-5. B > A are principal moment of inertia, corresponding to equatorial axes of inertia; Cm is a polar moment of inertia of the mantle of Mercury. 1 Analytical theory of plane Mercury librations. This theory describes forced and free librations of Mercury in longitude in the frame of plane problem about resonant librations of Mercury considered or as non-spherical rigid body, or as system of rigid non-spherical mantle and liquid ellipsoidal core. Saving the main terms for the perturbations of angle of librations ^g and angular velocity ^? in both mentioned cases we will have formulae [6]: ^g = K(E sin M + E sin2M + E sin 3M + E sin4M + E sin5M ) 1 2 3 4 5+K0 sin(E KM- - φ) (A)
NASA Astrophysics Data System (ADS)
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 φ 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 φ 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 φ to either the transverse or coronal planes of the patient.
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.
Lensless x-ray imaging in reflection geometry
Roy, S.; Parks, D.H.; Seu, K.A.; Turner, J.J.; Chao, W.; Anderson, E.H.; Cabrini, S.; Kevan, S.D.; Su, R.
2011-02-03
Lensless X-ray imaging techniques such as coherent diffraction imaging and ptychography, and Fourier transform holography can provide time-resolved, diffraction-limited images. Nearly all examples of these techniques have focused on transmission geometry, restricting the samples and reciprocal spaces that can be investigated. We report a lensless X-ray technique developed for imaging in Bragg and small-angle scattering geometries, which may also find application in transmission geometries. We demonstrate this by imaging a nanofabricated pseudorandom binary structure in small-angle reflection geometry. The technique can be used with extended objects, places no restriction on sample size, and requires no additional sample masking. The realization of X-ray lensless imaging in reflection geometry opens up the possibility of single-shot imaging of surfaces in thin films, buried interfaces in magnetic multilayers, organic photovoltaic and field-effect transistor devices, or Bragg planes in a single crystal.
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,…
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…
Microorganism billiards in closed plane curves
NASA Astrophysics Data System (ADS)
Krieger, Madison
Recent experiments and numerical simulations have demonstrated that many species of microorganisms reflect aspecularly from a solid surface -- due to steric and hydrodynamic interactions with the wall, their outgoing angle is fixed and independent of the angle of incidence. Motivated by these results, we discuss theory and computation of the ``aspecular billiard'', a modification of the classical billiard in which the outgoing angle is constant. We restrict our attention to closed plane curves, focusing on three canonical examples: the ellipse, the Bunimovich stadium, and the Sinai billiard. These systems can have a rich array of orbits, and the Lyapunov exponent is shown to be dependent on the billiard geometry and the outgoing angle. We apply these results to the design of tunable passive sorting mechanisms.
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.
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)
Hsü, K J; Hsü, A J
1990-01-01
Music critics have compared Bach's music to the precision of mathematics. What "mathematics" and what "precision" are the questions for a curious scientist. The purpose of this short note is to suggest that the mathematics is, at least in part, Mandelbrot's fractal geometry and the precision is the deviation from a log-log linear plot. PMID:11607061
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)
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.
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…
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.
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
Geometry of spinor regularization
NASA Technical Reports Server (NTRS)
Hestenes, D.; Lounesto, P.
1983-01-01
The Kustaanheimo theory of spinor regularization is given a new formulation in terms of geometric algebra. The Kustaanheimo-Stiefel matrix and its subsidiary condition are put in a spinor form directly related to the geometry of the orbit in physical space. A physically significant alternative to the KS subsidiary condition is discussed. Derivations are carried out without using coordinates.
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)
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.
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.
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.
Solution of the three-dimensional problem of plane wave diffraction by a two-period plane grating
NASA Astrophysics Data System (ADS)
Manenkov, S. A.
2016-03-01
Using the discrete source method, we develop an algorithm for solving the three-dimensional problem of wave scattering by a plane grating consisting of acoustically soft or acoustically stiff bodies. An efficient algorithm is proposed for determining the periodic Green's function of the grating. Numerical results are obtained for different geometries of the grating elements. The fulfillment of the energy conservation law is verified along with the fulfillment of the boundary condition at the surface of the central grating element.
Skyrmions in thin films with easy-plane magnetocrystalline anisotropy
NASA Astrophysics Data System (ADS)
Vousden, Mark; Albert, Maximilian; Beg, Marijan; Bisotti, Marc-Antonio; Carey, Rebecca; Chernyshenko, Dmitri; Cortés-Ortuño, David; Wang, Weiwei; Hovorka, Ondrej; Marrows, Christopher H.; Fangohr, Hans
2016-03-01
We demonstrate that chiral skyrmionic magnetization configurations can be found as the minimum energy state in B20 thin film materials with easy-plane magnetocrystalline anisotropy with an applied magnetic field perpendicular to the film plane. Our observations contradict results from prior analytical work, but are compatible with recent experimental investigations. The size of the observed skyrmions increase with the easy-plane magnetocrystalline anisotropy. We use a full micromagnetic model including demagnetization and a three-dimensional geometry to find local energy minimum (metastable) magnetization configurations using numerical damped time integration. We explore the phase space of the system and start simulations from a variety of initial magnetization configurations to present a systematic overview of anisotropy and magnetic field parameters for which skyrmions are metastable and global energy minimum (stable) states.
NASA Astrophysics Data System (ADS)
Souriau, Jean-Marie
1983-01-01
Differential geometry, the contemporary heir of the infinitesimal calculus of the 17th century, appears today as the most appropriate language for the description of physical reality. This holds at every level: The concept of “connexion,” for instance, is used in the construction of models of the universe as well as in the description of the interior of the proton. Nothing is apparently more contrary to the wisdom of physicists; all the same, “it works.” The pages that follow show the conceptual role played by this geometry in some examples—without entering into technical details. In order to achieve this, we shall often have to abandon the complete mathematical rigor and even full definitions; however, we shall be able to give a precise description of the connection of ideas thanks to some elements of group theory.
NASA Astrophysics Data System (ADS)
Smania, Daniel
2007-07-01
We describe a new and robust method to prove rigidity results in complex dynamics. The new ingredient is the geometry of the critical puzzle pieces: under control of geometry and ``complex bounds'', two generalized polynomial-like maps which admit a topological conjugacy, quasiconformal outside the filled-in Julia set, are indeed quasiconformally conjugate. The proof uses a new abstract removability-type result for quasiconformal maps, following ideas of Heinonen and Koskela and of Kallunki and Koskela, optimized for applications in complex dynamics. We prove, as the first application of this new method, that, for even criticalities distinct from two, the period two cycle of the Fibonacci renormalization operator is hyperbolic with 1 -dimensional unstable manifold.
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.
Failures of information geometry
NASA Astrophysics Data System (ADS)
Skilling, John
2015-01-01
Information H is a unique relationship between probabilities, based on the property of independence which is central to scientific methodology. Information Geometry makes the tempting but fallacious assumption that a local metric (conventionally based on information) can be used to endow the space of probability distributions with a preferred global Riemannian metric. No such global metric can conform to H, which is "from-to" asymmetric whereas geometrical length is by definition symmetric. Accordingly, any Riemannian metric will contradict the required structure of the very distributions which are supposedly being triangulated. It follows that probabilities do not form a metric space. We give counter-examples in which alternative formulations of information, and the use of information geometry, lead to unacceptable results.
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.
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.
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.
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.
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.
Emergent Complex Network Geometry
Wu, Zhihao; Menichetti, Giulia; Rahmede, Christoph; Bianconi, Ginestra
2015-01-01
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. PMID:25985280
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
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
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.
Geometry Career Unit: Junior High.
ERIC Educational Resources Information Center
Jensen, Daniel
The guide, the product of an exemplary career education program for junior high school students, was developed to show how geometry can be applied to real-life career-oriented areas and to bring a practical approach to the teaching of geometry. It is designed to show how some of the theorems or postulates in geometry are used in different careers.…
ERIC Educational Resources Information Center
Instructional Objectives Exchange, Los Angeles, CA.
Behavioral objectives, each accompanied by six sample test items, for secondary school geometry are presented. Objectives were determined by surveying the most widely used secondary school geometry textbooks, and cover 14 major categories of geometry, with sections on set theory and introductory trigonometry. Answers are provided. Categories…
Graded geometry and Poisson reduction
Cattaneo, A. S.; Zambon, M.
2009-02-02
The main result extends the Marsden-Ratiu reduction theorem in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry necessary for the proof. Further, we provide an alternative algebraic proof for the main result.
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.
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
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.
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, 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.
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.
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.
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.
SNS Device Made With Edge-Defined Geometry
NASA Technical Reports Server (NTRS)
Hunt, Brian D.; Foote, Marc C.
1992-01-01
YBa(2)Cu(3)O(7-delta)/Au/Nb superconductor/normal-conductor/superconductor (SNS) microbridge devices fabricated using now-standard lithographic techniques and edge geometry to define normally conducting links having submicron-by-several-microns cross-sectional dimensions. Edge geometry allows current to flow only in these planes and takes advantage of longer coherence length at critical YBa(2)Cu(3)O(7-delta)/Au/Nb interface. Sensitivity to damage on edge of YBa(2)Cu(3)O(7-delta)/Au/Nb reduced.
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.
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.
Critique of information geometry
NASA Astrophysics Data System (ADS)
Skilling, John
2014-12-01
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.
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.…
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
Optimization of starshades: focal plane versus pupil plane
NASA Astrophysics Data System (ADS)
Flamary, R.; Aime, C.
2014-09-01
We search for the best possible transmission for an external occulter coronagraph that is dedicated to the direct observation of terrestrial exoplanets. We show that better observation conditions are obtained when the flux in the focal plane is minimized in the zone in which the exoplanet is observed, instead of for the total flux received by the telescope. We describe the transmission of the occulter as a sum of basis functions. For each element of the basis, we numerically computed the Fresnel diffraction at the aperture of the telescope and the complex amplitude at its focus. The basis functions are circular disks that are linearly apodized over a few centimeters (truncated cones). We complemented the numerical calculation of the Fresnel diffraction for these functions by a comparison with pure circular disks (cylinder) for which an analytical expression, based on a decomposition in Lommel series, is available. The technique of deriving the optimal transmission for a given spectral bandwidth is a classical regularized quadratic minimization of intensities, but linear optimizations can be used as well. Minimizing the integrated intensity on the aperture of the telescope or for selected regions of the focal plane leads to slightly different transmissions for the occulter. For the focal plane optimization, the resulting residual intensity is concentrated behind the geometrical image of the occulter, in a blind region for the observation of an exoplanet, and the level of background residual starlight becomes very low outside this image. Finally, we provide a tolerance analysis for the alignment of the occulter to the telescope, which also favors the focal plane optimization. This means that telescope offsets of a few decimeters do not strongly reduce the efficiency of the occulter.
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.
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
Geometry and Mechanics of Thin Growing Bilayers
NASA Astrophysics Data System (ADS)
Pezzulla, Matteo; Smith, Gabriel; Nardinocchi, Paola; Holmes, Douglas
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 fourth's 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. NSF Grant CMMI-1300860.
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
Interactive visualizations of blowups of the plane.
Schenzel, Peter; Stussak, Christian
2013-06-01
Blowups are an important technique in algebraic geometry that permit the smoothing of singular algebraic varieties. It is a challenge to visualize this process even in the case of blowups of points X in the affine plane AA(IR)(2). First results were obtained by Brodmann with the aid of the so-called toroidal blowup, a compact embedding of the blowup into affine 3-space. In fact, Brodmann provides a rational parametrization of the toroidal blowup, but its visualization fails in the neighborhood of X because the parametrization tends to indefinite terms of the form 0/0. Our approach is based on implicitization of the parametric form. By methods from commutative algebra we are able to reduce the implicitization to the computation of a single, fairly simple resultant. This provides an algebraic equation of the implicit surface of the toroidal blowup including the so-called exceptional fiber associated with X. Surprisingly, the degree of the equation grows only linearly with the degree of the parametrization. By applying additional clipping techniques to the implicit surface we are able to visualize the toroidal blowup as well as its deformations by several parameters interactively in real time using GPU-based ray casting techniques. The methods of the paper provide insights in the structure of blowups of points, even if the points are interactively moved or tend to degenerations. PMID:22802122
High-frequency techniques for RCS prediction of plate geometries
NASA Technical Reports Server (NTRS)
Balanis, Constantine A.; Polka, Lesley A.
1991-01-01
Several different high-frequency methods for modeling the radar cross sections (RCSs) of plate geometries are examined. The Method of Equivalent Currents and a numerically derived corner diffraction coefficient are used to model the RCS of a rectangular, perfectly conducting plate in nonprincipal planes. The Uniform Theory of Diffraction is used to model the RCS of a rectangular, perfectly conducting plate in principal planes. For the soft polarization case, first-order and slope-diffraction terms are included. For the hard polarization case, up to four orders of diffraction are included. Finally, the Uniform Theory of Diffraction for impedance wedges and the Impedance Boundary Condition are used to model the RCS of a coated, rectangular plate in principal planes. In most of the cases considered, comparisons are made between theoretical and experimental results.
Eight plane IPND mechanical testing.
Zhao, A.; Guarino, V.; Wood, K.; Nephew, T.; Ayres, D.; Lee, A.; High Energy Physics; FNAL
2008-03-18
A mechanical test of an 8 plane IPND mechanical prototype, which was constructed using extrusions from the testing/tryout of the 16 cell prototype extrusion die in Argonne National Laboratory, was conducted. There were 4 vertical and 4 horizontal planes in this 8 plane IPND prototype. Each vertical plane had four 16 cell extrusions, while each horizontal plane had six 16 cell extrusions. Each plane was glued together using the formulation of Devcon adhesive, Devcon 60. The vertical extrusions used in the vertical planes shares the same dimensions as the horizontal extrusions in the horizontal planes with the average web thickness of 2.1 mm and the average wall thickness of 3.1 mm. This mechanical prototype was constructed with end-seals on the both ends of the vertical extrusions. The gaps were filled with epoxy between extrusions and end-seals. The overall dimension of IPND is 154.8 by 103.1 by 21.7 inches with the weight of approximately 1200 kg, as shown in a figure. Two similar mechanical tests of 3 layer and 11 layer prototypes have been done in order to evaluate the strength of the adhesive joint between extrusions in the NOvA detector. The test showed that the IPND prototype was able to sustain under the loading of weight of itself and scintillator. Two FEA models were built to verify the measurement data from the test. The prediction from FEA slice model seems correlated reasonably well to the test result, even under a 'rough' estimated condition for the wall thickness (from an untuned die) and an unknown property of 'garage type' extrusion. A full size of FEA 3-D model also agrees very well with the test data from strain gage readings. It is worthy to point out that the stress distribution of the structure is predominantly determined by the internal pressure, while the buckling stability relies more on the loading weight from the extrusions themselves and scintillate. Results of conducted internal pressure tests, including 3- cell, 11-cell and the IPND
Plane Wave and Coulomb Asymptotics
NASA Astrophysics Data System (ADS)
Mulligan, P. G.; Crothers, D. S. F.
2004-01-01
A simple plane wave solution of the Schrödinger Helmholtz equation is a quantum eigenfunction obeying both energy and linear momentum correspondence principles. Inclusion of the outgoing wave with scattering amplitude f obeys unitarity and the optical theorem. By closely considering the standard asymptotic development of the plane wave, we show that there is a problem with angular momentum when we consider forward scattering at the point of closest approach and at large impact parameter given semiclassically by (l + 1/2)/k where l is the azimuthal quantum number and may be large (J Leech et al, Phys. Rev. Lett. 88 257901 (2002)). The problem is resolved via non-uniform, non-standard analysis involving the Heaviside step function, unifying classical, semiclassical and quantum mechanics, and the treatment is extended to the case of pure Coulomb scattering.
Information geometry of Bayesian statistics
NASA Astrophysics Data System (ADS)
Matsuzoe, Hiroshi
2015-01-01
A survey of geometry of Bayesian statistics is given. From the viewpoint of differential geometry, a prior distribution in Bayesian statistics is regarded as a volume element on a statistical model. In this paper, properties of Bayesian estimators are studied by applying equiaffine structures of statistical manifolds. In addition, geometry of anomalous statistics is also studied. Deformed expectations and deformed independeces are important in anomalous statistics. After summarizing geometry of such deformed structues, a generalization of maximum likelihood method is given. A suitable weight on a parameter space is important in Bayesian statistics, whereas a suitable weight on a sample space is important in anomalous statistics.
Orbital Space Plane (OSP) Program
NASA Technical Reports Server (NTRS)
McKenzie, Patrick M.
2003-01-01
Lockheed Martin has been an active participant in NASA's Space Launch Initiative (SLI) programs over the past several years. SLI, part of NASA's Integrated Space Transportation Plan (ISTP), was restructured in November of 2002 to focus the overall theme of safer, more afford-able space transportation along two paths - the Orbital Space Plane Program and the Next Generation Launch Technology programs. The Orbital Space Plane Program has the goal of providing rescue capability from the International Space Station by 2008 and transfer capability for crew (and limited cargo) by 2012. The Next Generation Launch Technology program is combining research and development efforts from the 2nd Generation Reusable Launch Vehicle (2GRLV) program with cutting-edge, advanced space transportation programs (previously designated 3rd Generation) into one program aimed at enabling safe, reliable, cost-effective reusable launch systems by the middle of the next decade. Lockheed Martin is one of three prime contractors working to bring Orbital Space Plane system concepts to a system definition level of maturity by December of 2003. This paper and presentation will update the international community on the progress of the' OSP program, from an industry perspective, and provide insights into Lockheed Martin's role in enabling the vision of a safer, more affordable means of taking people to and from space.
Symmetry in finite phase plane
NASA Astrophysics Data System (ADS)
Zak, J.
2010-03-01
The known symmetries in one-dimensional systems are inversion and translations. These symmetries persist in finite phase plane, but a novel symmetry arises in view of the discrete nature of the coordinate xi and the momentum pi : xi and pi can undergo permutations. Thus, if xi assumes M discrete values, i = 0, 1,2,..., M - 1, a permutation will change the order of the set x0,x1,..., xM-1 into a new ordered set. Such a symmetry element does not exist for a continuous x-coordinate in an infinite phase plane. Thus, in a finite phase plane, translations can be replaced by permutations. This is also true for the inversion operator. The new permutation symmetry has been used for the construction of conjugate representations and for the splitting of the M-dimensional vector space into independent subspaces. This splitting is exhaustive in the sense that if M = iMi with Mi being prime numbers, the M-dimensional space splits into M1,M2,...Mn-dimensional independent subspaces. It is shown that following this splitting one can design new potentials with appropriate constants of motion. A related problem is the Weyl-Heisenberg group in the M-dimensional space which turns into a direct product of its subgroups in the Mi-dimensional subspaces. As an example we consider the case of M = 8.
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.
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.
Superfluid spin transport through easy-plane ferromagnetic insulators.
Takei, So; Tserkovnyak, Yaroslav
2014-06-01
Superfluid spin transport-dissipationless transport of spin-is theoretically studied in a ferromagnetic insulator with easy-plane anisotropy. We consider an open geometry where the spin current is injected into the ferromagnet from one side by a metallic reservoir with a nonequilibrium spin accumulation and ejected into another metallic reservoir located downstream. Spin transport is studied using a combination of magnetoelectric circuit theory, Landau-Lifshitz-Gilbert phenomenology, and microscopic linear-response theory. We discuss how spin superfluidity can be probed in a magnetically mediated negative electron-drag experiment. PMID:24949786
Integrable mappings of the plane preserving biquadratic invariant curves II
NASA Astrophysics Data System (ADS)
Iatrou, Apostolos; Roberts, John A. G.
2002-03-01
We review recently introduced curve-dependent McMillan maps which are mappings of the plane that preserve biquadratic foliations. We show that they are measure preserving and thus integrable. We discuss the geometry of these maps including their fixed points and their stability. We consider the normal forms of symmetric and asymmetric biquadratic curves and the normal forms for their associated McMillan maps. We further discuss the dynamics on biquadratic curves by considering the possibility of parametrizing them by Jacobian elliptic or rational functions.
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.
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.
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.
Cloud geometry effects on atmospheric solar absorption
Fu, Q.; Cribb, M.C.; Barker, H.W.; Krueger, S.K.; Grossman, A.
2000-04-15
A 3D broadband solar radiative transfer scheme is formulated by integrating a Monte Carlo photon transport algorithm with the Fu-Liou radiation model. It is applied to fields of tropical mesoscale convective clouds and subtropical marine boundary layer clouds that were generated by a 2D cloud-resolving model. The effects of cloud geometry on the radiative energy budget are examined by comparing the full-resolution Monte Carlo results with those from the independent column approximation (ICA) that applies the plane-parallel radiation model to each column. For the tropical convective cloud system, it is found that cloud geometry effects always enhance atmospheric solar absorption regardless of solar zenith angle. In a large horizontal domain (512 km), differences in domain-averaged atmospheric absorption between the Monte Carlo and the ICA are less than 4 W m{sup {minus}2} in the daytime. However, for a smaller domain (e.g., 75 km) containing a cluster of deep convective towers, domain-averaged absorption can be enhanced by more than 20 W m{sup {minus}2}. For a subtropical marine boundary layer cloud system during the stratus-to-cumulus transition, calculations show that the ICA works very well for domain-averaged fluxes of the stratocumulus cloud fields even for a very small domain (4.8 km). For the trade cumulus cloud field, the effects of cloud sides and horizontal transport of photons become more significant. Calculations have also been made for both cloud systems including black carbon aerosol and a water vapor continuum. It is found that cloud geometry produces no discernible effects on the absorption enhancement due to the black carbon aerosol and water vapor continuum. The current study indicates that the atmospheric absorption enhancement due to cloud-related 3D photon transport is small. This enhancement could not explain the excess absorption suggested by recent studies.
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…
Achievement in Writing Geometry Proofs.
ERIC Educational Resources Information Center
Senk, Sharon L.
In 1981 a nationwide assessment of achievement in writing geometry proofs was conducted by the Cognitive Development and Achievement in Secondary School Geometry project. Over 1,500 students in 11 schools in 5 states participated. This paper describes the sample, instruments, grading procedures, and selected results. Results include: (1) at the…
Limits of downstream hydraulic geometry
NASA Astrophysics Data System (ADS)
Wohl, Ellen
2004-10-01
Adjustments to flow width, depth, and velocity in response to changes in discharge are commonly characterized by using downstream hydraulic geometry relationships. The spatial limits of these relationships within a drainage basin have not been systematically quantified. Where the erosional resistance of the channel substrate is sufficiently large, hydraulic driving forces presumably will be unable to adjust channel form. Data sets from 10 mountain rivers in the United States, Panama, Nepal, and New Zealand are used in this study to explore the limits of downstream hydraulic geometry relationships. Where the ratio of stream power to sediment size (Ω/D84) exceeds 10,000 kg/s3, downstream hydraulic geometry is well developed; where the ratio falls below 10,000 kg/s3, downstream hydraulic geometry relationships are poorly developed. These limitations on downstream hydraulic geometry have important implications for channel engineering and simulations of landscape change.
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.
NASA Technical Reports Server (NTRS)
Piland, William M.
1987-01-01
An account is given of the technology development management objectives thus far planned for the DOD/NASA National Aero-Space Plane (NASP). The technology required by NASP will first be developed in ground-based facilities and then integrated during the design and construction of the X-30 experimental aircraft. Five airframe and three powerplant manufacturers are currently engaged in an 18-month effort encompassing design studies and tradeoff analyses. The first flight of the X-30 is scheduled for early 1993.
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.
NASA Astrophysics Data System (ADS)
Pinkie, Benjamin; Wichman, Adam R.; Bellotti, Enrico
2015-09-01
Finite-difference time-domain and finite element method simulations are used to evaluate two-dimensional spot-scan profiles of p-on- n double-layer planar heterostructure (DLPH) detector arrays with abrupt p-type diffusions. The modulation transfer function (MTF) is calculated from the spot-scan profiles. An asymmetric dark and photo current collection mechanism is identified and explained as a result of electric field bunching through the corners of polygonal diffusions in DLPH arrays. The MTF consequences of the asymmetric collection are studied for triangular, square, and hexagonal diffusions in square and hexagonal arrays. We show that the placement and shape of the diffusion relative to the pixel can modify the MTF by several percent. The magnitude of the effect is largest for diffusions with fewer degrees of rotational symmetry.
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…
Discrete ordinates cross-sections generation in parallel plane geometry -- 1: Concept
Yavuz, M.
1998-12-31
Cross-section formulations derived from the linear Boltzman transport equation have been the subjects of several studies. In these studies, theoretical foundations and concepts are provided, and the solution techniques are derived. The author presents new methods for generating cross-section sets for transport problems, with an arbitrary scattering anisotropy of order L (L {le} N {minus} 1), approximated by the S{sub N} (and P{sub N{minus}1}) methods. The formulations require knowledge of the eigensolutions, which may be determined by a recent eigenvalue equation found in Yavuz. The motivation for this study is to generate few-group cross sections for pin cells (and/or assemblies) using a Monte Carlo code, for example, MCNP, with a continuous-energy cross-section library. However, this work is a first step, and it describes a new concept to perform inverse transport calculations, provided that the surface Green`s functions over desired angular and energy intervals are known.
Chemical etching and organometallic chemical vapor deposition on varied geometries of GaAs
NASA Technical Reports Server (NTRS)
Bailey, Sheila G.; Landis, Geoffrey A.; Wilt, David M.
1989-01-01
Results of micron-spaced geometries produced by wet chemical etching and subsequent OMCVD growth on various GaAs surfaces are presented. The polar lattice increases the complexity of the process. The slow-etch planes defined by anisotropic etching are not always the same as the growth facets produced during MOCVD deposition, especially for deposition on higher-order planes produced by the hex groove etching.
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.
Image plane sweep volume illumination.
Sundén, Erik; Ynnerman, Anders; Ropinski, Timo
2011-12-01
In recent years, many volumetric illumination models have been proposed, which have the potential to simulate advanced lighting effects and thus support improved image comprehension. Although volume ray-casting is widely accepted as the volume rendering technique which achieves the highest image quality, so far no volumetric illumination algorithm has been designed to be directly incorporated into the ray-casting process. In this paper we propose image plane sweep volume illumination (IPSVI), which allows the integration of advanced illumination effects into a GPU-based volume ray-caster by exploiting the plane sweep paradigm. Thus, we are able to reduce the problem complexity and achieve interactive frame rates, while supporting scattering as well as shadowing. Since all illumination computations are performed directly within a single rendering pass, IPSVI does not require any preprocessing nor does it need to store intermediate results within an illumination volume. It therefore has a significantly lower memory footprint than other techniques. This makes IPSVI directly applicable to large data sets. Furthermore, the integration into a GPU-based ray-caster allows for high image quality as well as improved rendering performance by exploiting early ray termination. This paper discusses the theory behind IPSVI, describes its implementation, demonstrates its visual results and provides performance measurements. PMID:22034331
Rewritable photochromic focal plane masks
NASA Astrophysics Data System (ADS)
Molinari, Emilio; Bertarelli, Chiara; Bianco, Andrea; Bortoletto, Fabio; Conconi, Paolo; Crimi, Giuseppe; Gallazzi, Maria C.; Giro, Enrico; Lucotti, Andrea; Pernechele, Claudio; Zerbi, Filippo M.; Zerbi, Giuseppe
2003-02-01
The application of organic photochromic materials in astronomy is opening new possibilities which we are investigating in order to design innovative devices for future instrumentation. The photochromic property of transparent/opaque transition (although in a limited wavelength range) and the changes in intrinsic refractive index have led our studies to application in astronomic spectrographs, both as focal plane mask (for MOS application) and as dispersive elements (volume phase holographic gratings, VPHG), respectively. In both cases the possibility to write and erase devices with suitable irradiation has revealed a new perspective for non-disposable and fully customizable items for spectroscopy. Pursuing this goal we have synthesized a series of novel photochromic materials belonging to the diarylethenes. They fulfill the requirements of thermal stability and fatigue resistance necessary to build functional devices. Prototypes of high contrast focal plane mask working in the H-alpha spectral region have been manufactured and characterized both in laboratory and with the AFOSC camera at Asiago telescope (1.8 m). A custom writing robot (ARATRO) which, taking imaging frames and with the aid of interactive mask design software and ad hoc control electronics, is able to write MOS masks, has been constructed. The design of the MOS masks allow the fitting in the AFOSC slit wheel. The overall set-up is ready for the sky tests.
Distance geometry and geometric algebra
NASA Astrophysics Data System (ADS)
Dress, Andreas W. M.; Havel, Timothy F.
1993-10-01
As part of his program to unify linear algebra and geometry using the language of Clifford algebra, David Hestenes has constructed a (well-known) isomorphism between the conformal group and the orthogonal group of a space two dimensions higher, thus obtaining homogeneous coordinates for conformal geometry.(1) In this paper we show that this construction is the Clifford algebra analogue of a hyperbolic model of Euclidean geometry that has actually been known since Bolyai, Lobachevsky, and Gauss, and we explore its wider invariant theoretic implications. In particular, we show that the Euclidean distance function has a very simple representation in this model, as demonstrated by J. J. Seidel.(18)
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.
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.
The Dilemma of Descriptive Geometry
ERIC Educational Resources Information Center
Boleslavski, Moshe
1977-01-01
Proposes that engineering students undergo a preparatory summer school training program in fundamentals of engineering drawing, descriptive geometry, and mathematics prior to being admitted to regular engineering studies. (SL)
Emergent geometry from quantized spacetime
Yang, Hyun Seok; Sivakumar, M.
2010-08-15
We examine the picture of emergent geometry arising from a mass-deformed matrix model. Because of the mass deformation, a vacuum geometry turns out to be a constant curvature spacetime such as d-dimensional sphere and (anti-)de Sitter spaces. We show that the mass-deformed matrix model giving rise to the constant curvature spacetime can be derived from the d-dimensional Snyder algebra. The emergent geometry beautifully confirms all the rationale inferred from the algebraic point of view that the d-dimensional Snyder algebra is equivalent to the Lorentz algebra in (d+1)-dimensional flat spacetime. For example, a vacuum geometry of the mass-deformed matrix model is completely described by a G-invariant metric of coset manifolds G/H defined by the Snyder algebra. We also discuss a nonlinear deformation of the Snyder algebra.
Interaction of morphogens with geometry
NASA Astrophysics Data System (ADS)
Cummings, F. W.
2005-09-01
Morphogen patterns are viewed as being affected by epithelial sheet geometry in early development. As the total area of the (closed) sheet changes, the changing geometry acts back in turn to change the morphogen pattern. A number of constraints are given on the functional form of the Gauss and Mean curvatures, considered as functions of the morphogen concentrations and their derivatives. It is shown that the constraints are sufficient to motivate a convincing dependence of the two curvatures on the morphogen concentrations.
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.
The Common Geometry Module (CGM).
Tautges, Timothy James
2004-12-01
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 on 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 includes 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.
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.
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…
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.
Analysis of out-of-plane thermal microactuators
NASA Astrophysics Data System (ADS)
Atre, Amarendra
2006-02-01
Out-of-plane thermal microactuators find applications in optical switches to motivate micromirrors. Accurate analysis of such actuators is beneficial for improving existing designs and constructing more energy efficient actuators. However, the analysis is complicated by the nonlinear deformation of the thermal actuators along with temperature-dependent properties of polysilicon. This paper describes the development, modeling issues and results of a three-dimensional multiphysics nonlinear finite element model of surface micromachined out-of-plane thermal actuators. The model includes conductive and convective cooling effects and takes into account the effect of variable air gap on the response of the actuator. The model is implemented to investigate the characteristics of two diverse MUMPs fabricated out-of-plane thermal actuators. Reasonable agreement is observed between simulated and measured results for the model that considers the influence of air gap on actuator response. The usefulness of the model is demonstrated by implementing it to observe the effect of actuator geometry variation on steady-state deflection response.
Possible Laminographic and Tomosynthesis Applications for Wolter Microscope Scan Geometries
Schneberk, D; Jackson, J; Martz, H
2004-10-05
The Wolter microscope includes a number of attractive features for x-ray imaging, and possible connections to laminographic and tomosynthesis 3D object recovery algorithms. This type of instrument employs x-ray optics to sift out single energy x-rays from a broader spectral energy source, and direct those x-rays to a ''focus plane'' similar to the operation of a optical microscope (see Figure 1 for schematic of a Wolter instrument). Unlike optical microscopes the 3D object can be thick in the direction of the x-rays and in this case more of the intensity of the image is affected by the out-of-focus planes, since the ray-paths span the entire depth of the object. It is clear that the ''in-focus'' plane of a Wolter contain more 3D information than a simple ''point-projection'' radiograph. However, it is not clear just how the impact of the out-of-focus planes obscures or distorts features of interest for the in-focus planes. Further, it is not clear just how object positioning can be combined with multiple acquisitions to enable recovery of other planes within the object function or the entire object function. Of particular interest here are Wolter microscopes configured for mesoscale objects (mm extent with um features). Laminographic and tomosynthesis scanning methods can be strategic for this type of inspection instrument. First, photon output for inspection purposes can be meager in this type of ''small field of view'' system. With laboratory x-ray sources a single image can require up to 10 minutes to accumulate adequate signal. Techniques that can obtain 3D object information from small numbers of views, rotational or translational, are consequently at a premium. Laminographic and tomosynthesis scanning methods require relatively small numbers of views (2-30). Secondly, the Wolter microscope scan geometry in a single view is a fit with the type of source-detector geometry achieved through source-object-detector re-positioning in laminographic and tomosynthesis
Determination of the diffuser reference plane for accurate illuminance responsivity calibrations
Hovila, Jari; Mustonen, Maria; Kaerhae, Petri; Ikonen, Erkki
2005-10-01
It is difficult to predict where the effective measurement plane is situated with dome-shaped diffusers often used in commercial photometers and radiometers. Insufficient knowledge of this plane could lead to large systematic errors in calibration of the illuminance responsivity of photometers. We propose a method that can be used to determine this reference plane accurately, based on the inverse-square law between the measured signal and the distance from the source. The method is demonstrated with three commercial photometers with dome-shaped diffusers of different geometries. By taking into account the measured shifts of the reference planes (5.0{+-}0.5 mm, 7.8{+-}0.3 mm, and 8.5{+-}0.7 mm), we reduced the systematic measurement errors up to 2% to statistical uncertainty components at the level of 0.2%.
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.
An Automated Approach for Slicing Plane Placement in Visual Data Analysis.
Obermaier, Harald; Joy, Kenneth I
2015-12-01
Effective display and visual analysis of complex 3D data is a challenging task. Occlusions, overlaps, and projective distortions-as frequently caused by typical 3D rendering techniques-can be major obstacles to unambiguous and robust data analysis. Slicing planes are a ubiquitous tool to resolve several of these issues. They act as simple clipping geometry to provide clear cut-away views of the data. We propose to enhance the visualization and analysis process by providing methods for automatic placement of such slicing planes based on local optimization of gradient vector flow. The final obtained slicing planes maximize the total amount of information displayed with respect to a pre-specified importance function. We demonstrate how such automated slicing plane placement is able to support and enrich 3D data visualization and analysis in multiple scenarios, such as volume or surface rendering, and evaluate its performance in several benchmark data sets. PMID:26529461
The UKIDSS Galactic Plane Survey
NASA Astrophysics Data System (ADS)
Lucas, P. W.; Hoare, M. G.; Longmore, A.; Schröder, A. C.; Davis, C. J.; Adamson, A.; Bandyopadhyay, R. M.; de Grijs, R.; Smith, M.; Gosling, A.; Mitchison, S.; Gáspár, A.; Coe, M.; Tamura, M.; Parker, Q.; Irwin, M.; Hambly, N.; Bryant, J.; Collins, R. S.; Cross, N.; Evans, D. W.; Gonzalez-Solares, E.; Hodgkin, S.; Lewis, J.; Read, M.; Riello, M.; Sutorius, E. T. W.; Lawrence, A.; Drew, J. E.; Dye, S.; Thompson, M. A.
2008-11-01
The UKIDSS Galactic Plane Survey (GPS) is one of the five near-infrared Public Legacy Surveys that are being undertaken by the UKIDSS consortium, using the Wide Field Camera on the United Kingdom Infrared Telescope. It is surveying 1868 deg2 of the northern and equatorial Galactic plane at Galactic latitudes -5° < b < 5° in the J, H and K filters and a ~200-deg2 area of the Taurus-Auriga-Perseus molecular cloud complex in these three filters and the 2.12 μm (1-0) H2 filter. It will provide data on ~2 × 109 sources. Here we describe the properties of the data set and provide a user's guide for its exploitation. We also present brief Demonstration Science results from DR2 and from the Science Verification programme. These results illustrate how GPS data will frequently be combined with data taken in other wavebands to produce scientific results. The Demonstration Science comprises six studies. (1) A GPS-Spitzer-GLIMPSE cross-match for the star formation region G28.983-0.603 to identify YSOs. This increases the number of YSOs identified by a factor of 10 compared to GLIMPSE alone. (2) A wide-field study of the M17 nebula, in which an extinction map of the field is presented and the effect of source confusion on luminosity functions in different subregions is noted. (3) H2 emission in the ρ Ophiuchi dark cloud. All the molecular jets are traced back to a single active clump containing only a few protostars, which suggests that the duration of strong jet activity and associated rapid accretion in low-mass protostars is brief. (4) X-ray sources in the nuclear bulge. The GPS data distinguishes local main-sequence counterparts with soft X-ray spectra from nuclear bulge giant counterparts with hard X-ray spectra. (5) External galaxies in the zone of avoidance. The galaxies are clearly distinguished from stars in fields at longitudes l > 90°. (6) IPHAS-GPS optical-infrared spectrophotometric typing. The (i' - J) versus (J - H) diagram is used to distinguish A-F type
NASA Technical Reports Server (NTRS)
Jackson, Wade C.; Portanova, Marc A.
1995-01-01
This paper summarizes three areas of research which were performed to characterize out-of-plane properties of composite materials. In the first investigation, a series of tests was run to characterize the through-the-thickness tensile strength for a variety of composites that included 2D braids, 2D and 3D weaves, and prepreg tapes. A new test method based on a curved beam was evaluated. Failures were significantly different between the 2D materials and the 3D weaves. The 2D materials delaminated between layers due to out-of-plane tensile stresses while the 3D weaves failed due to the formation of radial cracks between the surface plies caused by high circumferential stresses along the inner radius. The strength of the 2D textile composites did not increase relative to the tapes. Final failure in the 3D weaves was caused by a circumferential crack similar to the 2D materials and occurred at a lower bending moment than in other materials. The early failures in the 3D weaves were caused by radial crack formation rather than a low through-the-thickness strength. The second investigation focused on the development of a standard impact test method to measure impact damage resistance. The only impact tests that currently exist are compression after impact (CAI) tests which incorporate elements of both damage resistance and damage tolerance. A new impact test method is under development which uses a quasi-static indentation (QSI) test to directly measure damage resistance. Damage resistance is quantified in terms of the contact force to produce a unit of damage where a metric for damage may be area in C-scan, depth of residual dent , penetration, damage growth, etc. A final draft of an impact standard that uses a QSI test method will be presented to the ASTM Impact Task Group on impact. In the third investigation, the impact damage resistance behavior of a variety of textile materials was studied using the QSI test method. In this study, the force where large damage
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.
Reflections on the Hyperbolic Plane
NASA Astrophysics Data System (ADS)
Lecian, Orchidea Maria
2013-12-01
The most general solution to the Einstein equations in 4 = 3 + 1 dimensions in the asymptotic limit close to the cosmological singularity under the BKL (Belinskii-Khalatnikov-Lifshitz) hypothesis can be visualized by the behavior of a billiard ball in a triangular domain on the Upper Poincaré Half Plane (UPHP). The billiard system (named "big billiard") can be schematized by dividing the successions of trajectories according to Poincaré return map on the sides of the billiard table, according to the paradigms implemented by the BKL investigation and by the CB-LKSKS (Chernoff-Barrow-Lifshitz-Khalatnikov-Sinai-Khanin-Shchur) one. Different maps are obtained, according to different symmetry-quotienting mechanisms used to analyze the dynamics. In the inhomogeneous case, new structures have been uncovered, such that, in this framework, the billiard table (named "small billiard") consists of 1/6 of the previous one. The connections between the symmetry-quotienting mechanisms are further investigated on the UPHP. The relation between the complete billiard and the small billiard are also further explained according to the role of Weyl reflections. The quantum properties of the system are sketched as well, and the physical interpretation of the wave function is further developed. In particular, a physical interpretation for the symmetry-quotienting maps is proposed.
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.
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.
Collinearity-preserving functions between Desarguesian planes
Carter, David S.; Vogt, Andrew
1980-01-01
Using concepts from valuation theory, we obtain a characterization of all collinearity-preserving functions from one affine or projective Desarguesian plane into another. The case in which the planes are projective and the range contains a quadrangle has been treated previously in the literature. Our results permit one or both planes to be affine and include cases in which the range contains a triangle but no quadrangle. A key theorem is that, with the exception of certain embeddings defined on planes of order 2 and 3, every collinearity-preserving function from one affine Desarguesian plane into another can be extended to a collinearity-preserving function between enveloping projective planes. PMID:16592845
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.
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.
Hexatic undulations in curved geometries.
Lenz, Peter; Nelson, David R
2003-03-01
We discuss the influence of two-dimensional hexatic order on capillary waves and undulation modes in spherical and cylindrical geometries. In planar geometries, extended bond-orientational order has only a minor effect on the fluctuations of liquid surfaces or lipid bilayers. However, in curved geometries, the long-wavelength spectrum of these ripples is altered. We calculate this frequency shift and discuss applications to spherical vesicles, liquid metal droplets, bubbles and cylindrical jets coated with surface-active molecules, and to multielectron bubbles in liquid helium at low temperatures. Hexatic order also leads to a shift in the threshold for the fission instability of charged droplets and bubbles, and for the Plateau-Rayleigh instability of liquid jets. PMID:12689068
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. PMID:27436908
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
Sagittal plane biomechanics. American Diabetes Association.
Dananberg, H J
2000-01-01
During walking, the center of body mass must pass from behind the weightbearing foot to in front of it. For this to take place, the foot must function as a sagittal plane pivot. Because the range required for this motion is approximately five times as great as both frontal and transverse plane motion, its evaluation should become an essential part of a podiatric biomechanical assessment. Lack of proper sagittal plane motion and its sequelae are described. PMID:10659532
Individualized Geometry: A Geometry Unit for the Intermediate Grades.
ERIC Educational Resources Information Center
Geissler, Dennis; Larson, Richard
This geometry unit for the intermediate grades is based on the Holt Mathematics Series (levels 3-6), using the concepts of Individually Guided Education (IGE). It is divided into seven levels, one for grade 3 and two each for grades 4-6. Each is designed for both individual and group learning. A vocabulary list is used as a key for activities; a…
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)
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.
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.
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.
Recent developments in surgical skin planing.
AYRES, S; WILSON, J W; LUIKART, R
1958-02-01
In surgical skin planing steel wire brushes have been largely replaced by the less hazardous diamond chip burs or "fraises" and serrated steel wheels. In addition to acne pits and wrinkling, multiple actinic (senile) keratoses are an important indication for planing. Planing provides a nonscarring method for the treatment of existing keratoses, as well as a prophylaxis against skin cancer by replacing the sun-damaged, precancerous epidermis with new epidermal cells derived from the cutaneous adnexa (pilosebaceous and sweat gland units). There are clinical landmarks indicating the depth of planing which can serve as a guide to the operator and can be correlated with microscopic findings. The results of experiments on the comparative effects of refrigerants on animal and human skin indicate that human facial skin can tolerate considerable freezing with ethyl chloride or dichlorotetrafluoroethane (Freon 114) but that mixtures containing large proportions of the much colder dichlorodifluoromethane (Freon 12) may be undesirable. Refreezing an area of the skin in order to perform a more adequate planing is not considered hazardous.THE REGENERATION OF THE SKIN FOLLOWING PLANING HAS THREE COMPONENTS: Epidermal, adnexal and dermal. The cells of the epidermis and the adnexa are equipotential. A knowledge of the anatomy of the acne pit enables the operator to decide which pits can be benefited by planing and which should be excised before planing. The successful treatment of acne pits of the face by planing in patients having keloids elsewhere on the body is reported. PMID:13500217
RCS Analysis of Plate Geometries, parts 1 and 2
NASA Technical Reports Server (NTRS)
Balanis, Constantine A.; Polka, Lesley A.; Polycarpou, Anastasis C.
1993-01-01
High-frequency techniques for Radar Cross Section (RCS) prediction of plate geometries and a physical optics/equivalent currents model for the RCS of trihedral corner reflectors are addressed. In part 1, a Uniform Theory of Diffraction (UTD) model for the principal-plane radar cross section (RCS) of a perfectly conducting, rectangular plate coated on one side with an electrically thin, lossy dielectric is presented. In part 2, the scattering in the interior regions of both square and triangular trihedral corner reflectors are examined.
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.
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
Differential geometry of groups in string theory
Schmidke, W.B. Jr.
1990-09-01
Techniques from differential geometry and group theory are applied to two topics from string theory. The first topic studied is quantum groups, with the example of GL (1{vert bar}1). The quantum group GL{sub q}(1{vert bar}1) is introduced, and an exponential description is derived. The algebra and coproduct are determined using the invariant differential calculus method introduced by Woronowicz and generalized by Wess and Zumino. An invariant calculus is also introduced on the quantum superplane, and a representation of the algebra of GL{sub q}(1{vert bar}1) in terms of the super-plane coordinates is constructed. The second topic follows the approach to string theory introduced by Bowick and Rajeev. Here the ghost contribution to the anomaly of the energy-momentum tensor is calculated as the Ricci curvature of the Kaehler quotient space Diff(S{sup 1})/S{sup 1}. We discuss general Kaehler quotient spaces and derive an expression for their Ricci curvatures. Application is made to the string and superstring diffeomorphism groups, considering all possible choices of subgroup. The formalism is extended to associated holomorphic vector bundles, where the Ricci curvature corresponds to the anomaly for different ghost sea levels. 26 refs.
Synchrotron-radiation plane-wave GID topography (abstract)
NASA Astrophysics Data System (ADS)
Novikov, D. V.; Gog, T.; Griebenow, M.; Materlik, G.
1995-02-01
X-ray-diffraction topography is a traditional tool for investigating the real structure of crystals and provides high sensitivity to lattice constant variations with good space resolution. However, recent advances in technology and the growing importance of surface regions of single-crystal and multilayer systems require new approaches to this method, which are made possible by the high brightness and wide tunability of synchrotron radiation. In this work the SR plane-wave grazing-incidence diffraction (GID) topography is discussed as an effective tool for depth-resolved investigations of near-surface defect structures in single crystals and epitaxial layers. The favorable properties of synchrotron radiation enable one to avoid the usual limitations on applicability of this diffraction geometry and investigate all classes of defects in real materials. The experiments were performed at the beamlines ROEMO1 and CEMO of HASYLAB, using double-crystal Ge/asymmetric Si monochromators. The image formation of near-surface dislocations and the effects of refraction on rough surfaces were investigated. Oblique diffraction planes were used to compare the topography in skew incoplanar and coplanar geometries. The latter is shown to be more effective, as it utilizes the wavelength tunability of SR and allows one to vary the diffraction conditions in a wide range from usual highly asymmetric to grazing incidence below the critical angle of total external reflection (and the penetration depth from hundreds to tens of nanometers) without off-plane rotations and provides pictures free of complicated geometrical distortions. The dislocation images at different diffraction conditions proved to be qualitatively the same for near-surface defects, while the structure distortions, produced by the defects in the underlying layers, become invisible at grazing incidence, due to both depth resolution of the method and inevitable loss of lattice-parameter resolution. This might be a
Semi-local inversion of the geodesic ray transform in the hyperbolic plane
NASA Astrophysics Data System (ADS)
Courdurier, Matias; Saez, Mariel
2013-06-01
The inversion of the ray transform on the hyperbolic plane has applications in geophysical exploration and in medical imaging techniques (such as electrical impedance tomography). The geodesic ray transform has been studied in more general geometries and including attenuation, but all of the available inversion formulas require knowledge of the ray transform for all the geodesics. In this paper we present a different inversion formula for the ray transform on the hyperbolic plane, which has the advantage of only requiring knowledge of the ray transform in a reduced family of geodesics. The required family of geodesics is directly related to the set where the original function is to be recovered.
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
Approximations useful for the prediction of electrostatic discharges for simple electrode geometries
NASA Technical Reports Server (NTRS)
Edmonds, L.
1986-01-01
The report provides approximations for estimating the capacitance and the ratio of electric field strength to potential for a certain class of electrode geometries. The geometry consists of an electrode near a grounded plane, with the electrode being a surface of revolution about the perpendicular to the plane. Some examples which show the accuracy of the capacitance estimate and the accuracy of the estimate of electric field over potential can be found in the appendix. When it is possible to estimate the potential of the electrode, knowing the ratio of electric field to potential will help to determine if an electrostatic discharge is likely to occur. Knowing the capacitance will help to determine the strength of the discharge (the energy released by it) if it does occur. A brief discussion of discharge mechanisms is given. The medium between the electrode and the grounded plane may be a neutral gas, a vacuum, or an unchanged homogeneous isotropic dielectric.
Approximations useful for the prediction of electrostatic discharges for simple electrode geometries
NASA Technical Reports Server (NTRS)
Edmonds, Larry D.
1988-01-01
The report provides approximations for estimating the capacitance and the ratio of electric field strength to potential for a certain class of electrode geometries. The geometry consists of an electrode near a grounded plane, with the electrode being a surface of revolution about the perpendicular to the plane. Some examples which show the accuracy of the capacitance estimate and the accuracy of the estimate of electric field over potential can be found in the appendix. When it is possible to estimate the potential of the electrode, knowing the ratio of electric field to potential will help to determine if an electrostatic discharge is likely to occur. Knowing the capacitance will help to determine the strength of the discharge (the energy released by it) if it does occur. A brief discussion of discharge mechanisms is given. The medium between the electrode and the grounded plane may be a neutral gas, a vacuum, or an unchanged homogeneous isotropic dielectric.
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…
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…
Logo Activities in Elementary Geometry.
ERIC Educational Resources Information Center
Libeskind, Shlomo; And Others
These activities were designed for use at the University of Montana, where they were tested for four quarters in a mathematics for elementary teachers course on informal geometry. They are for use with Apple II-Plus computers with 64K memory or Apple IIe computers and MIT Logo. (Modifications are necessary if the activities are to be used with…
Towards a Navajo Indian Geometry.
ERIC Educational Resources Information Center
Pinxten, Rik; And Others
This book examines the Navajo system of spatial knowledge and describes a culture-based curriculum for the development of an intuitive geometry based on the child's experience of the physical world. Aspects of the Navajo cosmology relevant to spatial knowledge are discussed: the structure of the world; the dynamic nature of the universe;…
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…
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.
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…
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…
Computer Environments for Learning Geometry.
ERIC Educational Resources Information Center
Clements, Douglas H.; Battista, Michael T.
1994-01-01
Reviews research describing computer functions of construction-oriented computer environments and evaluates their contributions to students' learning of geometry. Topics discussed include constructing geometric concepts; the use of LOGO in elementary school mathematics; software that focuses on geometric construction; and implications for the…
Dislocation dynamics in confined geometry
NASA Astrophysics Data System (ADS)
Gómez-García, D.; Devincre, B.; Kubin, L.
1999-05-01
A simulation of dislocation dynamics has been used to calculate the critical stress for a threading dislocation moving in a confined geometry. The optimum conditions for conducting simulations in systems of various sizes, down to the nanometer range, are defined. The results are critically compared with the available theoretical and numerical estimates for the problem of dislocation motion in capped layers.
Improving Student Reasoning in Geometry
ERIC Educational Resources Information Center
Wong, Bobson; Bukalov, Larisa
2013-01-01
In their years of teaching geometry, Wong and Bukalov realized that the greatest challenge has been getting students to improve their reasoning. Many students have difficulty writing formal proofs--a task that requires a good deal of reasoning. Wong and Bukalov reasoned that the solution was to divide the lessons into parallel tasks, allowing…