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Sample records for spherical geometry izmerenie

  1. Information geometry of the spherical model.

    PubMed

    Janke, W; Johnston, D A; Kenna, R

    2003-04-01

    Motivated by the observation that geometrizing statistical mechanics offers an interesting alternative to more standard approaches, we calculate the scaling behavior of the curvature R of the information geometry metric for the spherical model. We find that R approximately epsilon(-2), where epsilon=beta(c)-beta is the distance from criticality. The discrepancy from the naively expected scaling R approximately epsilon(-3) is explained and compared with that for the Ising model on planar random graphs, which shares the same critical exponents. PMID:12786435

  2. Characterizing student mathematics teachers' levels of understanding in spherical geometry

    NASA Astrophysics Data System (ADS)

    Guven, Bulent; Baki, Adnan

    2010-12-01

    This article presents an exploratory study aimed at the identification of students' levels of understanding in spherical geometry as van Hiele did for Euclidean geometry. To do this, we developed and implemented a spherical geometry course for student mathematics teachers. Six structured, task-based interviews were held with eight student mathematics teachers at particular times through the course to determine the spherical geometry learning levels. After identifying the properties of spherical geometry levels, we developed Understandings in Spherical Geometry Test to test whether or not the levels form hierarchy, and 58 student mathematics teachers took the test. The outcomes seemed to support our theoretical perspective that there are some understanding levels in spherical geometry that progress through a hierarchical order as van Hiele levels in Euclidean geometry.

  3. Characterizing Student Mathematics Teachers' Levels of Understanding in Spherical Geometry

    ERIC Educational Resources Information Center

    Guven, Bulent; Baki, Adnan

    2010-01-01

    This article presents an exploratory study aimed at the identification of students' levels of understanding in spherical geometry as van Hiele did for Euclidean geometry. To do this, we developed and implemented a spherical geometry course for student mathematics teachers. Six structured, "task-based interviews" were held with eight student…

  4. 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…

  5. Space Radiation Detector with Spherical Geometry

    NASA Technical Reports Server (NTRS)

    Wrbanek, John D. (Inventor); Fralick, Gustave C. (Inventor); Wrbanek, Susan Y. (Inventor)

    2012-01-01

    A particle detector is provided, the particle detector including a spherical Cherenkov detector, and at least one pair of detector stacks. In an embodiment of the invention, the Cherenkov detector includes a sphere of ultraviolet transparent material, coated by an ultraviolet reflecting material that has at least one open port. The Cherenkov detector further includes at least one photodetector configured to detect ultraviolet light emitted from a particle within the sphere. In an embodiment of the invention, each detector stack includes one or more detectors configured to detect a particle traversing the sphere.

  6. Space Radiation Detector with Spherical Geometry

    NASA Technical Reports Server (NTRS)

    Wrbanek, John D. (Inventor); Fralick, Gustave C. (Inventor); Wrbanek, Susan Y. (Inventor)

    2011-01-01

    A particle detector is provided, the particle detector including a spherical Cherenkov detector, and at least one pair of detector stacks. In an embodiment of the invention, the Cherenkov detector includes a sphere of ultraviolet transparent material, coated by an ultraviolet reflecting material that has at least one open port. The Cherenkov detector further includes at least one photodetector configured to detect ultraviolet light emitted from a particle within the sphere. In an embodiment of the invention, each detector stack includes one or more detectors configured to detect a particle traversing the sphere.

  7. Explosive fragmentation of liquids in spherical geometry

    NASA Astrophysics Data System (ADS)

    Milne, A.; Longbottom, A.; Frost, D. L.; Loiseau, J.; Goroshin, S.; Petel, O.

    2016-07-01

    Rapid acceleration of a spherical shell of liquid following central detonation of a high explosive causes the liquid to form fine jets that are similar in appearance to the particle jets that are formed during explosive dispersal of a packed layer of solid particles. Of particular interest is determining the dependence of the scale of the jet-like structures on the physical parameters of the system, including the fluid properties (e.g., density, viscosity, and surface tension) and the ratio of the mass of the liquid to that of the explosive. The present paper presents computational results from a multi-material hydrocode describing the dynamics of the explosive dispersal process. The computations are used to track the overall features of the early stages of dispersal of the liquid layer, including the wave dynamics, and motion of the spall and accretion layers. The results are compared with new experimental results of spherical charges surrounded by a variety of different fluids, including water, glycerol, ethanol, and vegetable oil, which together encompass a significant range of fluid properties. The results show that the number of jet structures is not sensitive to the fluid properties, but primarily dependent on the mass ratio. Above a certain mass ratio of liquid fill-to-explosive burster (F / B), the number of jets is approximately constant and consistent with an empirical model based on the maximum thickness of the accretion layer. For small values of F / B, the number of liquid jets is reduced, in contrast with explosive powder dispersal, where small F / B yields a larger number of particle jets. A hypothetical explanation of these features based on the nucleation of cavitation is explored numerically.

  8. Hexatic order and surface ripples in spherical geometries.

    PubMed

    Lenz, P; Nelson, D R

    2001-09-17

    In flat geometries, two-dimensional hexatic order has only a minor effect on capillary waves on a liquid substrate and on undulation modes in lipid bilayers. However, extended bond-orientational order alters the long-wavelength spectrum of these ripples in spherical geometries. We calculate this frequency shift and suggest that it might be detectable in lipid bilayer vesicles, at the surface of liquid metals, and in multielectron bubbles in liquid helium at low temperatures. Hexatic order also leads to a shift in the threshold for the fission instability induced in the later two systems by an excess of electric charge. PMID:11580526

  9. Viscous Rayleigh-Taylor instability in spherical geometry

    DOE PAGESBeta

    Mikaelian, Karnig O.

    2016-02-08

    We consider viscous fluids in spherical geometry, a lighter fluid supporting a heavier one. Chandrasekhar [Q. J. Mech. Appl. Math. 8, 1 (1955)] analyzed this unstable configuration providing the equations needed to find, numerically, the exact growth rates for the ensuing Rayleigh-Taylor instability. He also derived an analytic but approximate solution. We point out a weakness in his approximate dispersion relation (DR) and offer one that is to some extent improved.

  10. Viscous Rayleigh-Taylor instability in spherical geometry

    NASA Astrophysics Data System (ADS)

    Mikaelian, Karnig O.

    2016-02-01

    We consider viscous fluids in spherical geometry, a lighter fluid supporting a heavier one. Chandrasekhar [Q. J. Mech. Appl. Math. 8, 1 (1955), 10.1093/qjmam/8.1.1] analyzed this unstable configuration providing the equations needed to find, numerically, the exact growth rates for the ensuing Rayleigh-Taylor instability. He also derived an analytic but approximate solution. We point out a weakness in his approximate dispersion relation (DR) and offer a somewhat improved one. A third DR, based on transforming a planar DR into a spherical one, suffers no unphysical predictions and compares reasonably well with the exact work of Chandrasekhar and a more recent numerical analysis of the problem [Terrones and Carrara, Phys. Fluids 27, 054105 (2015), 10.1063/1.4921648].

  11. The AGCE related studies of baroclinic flows in spherical geometry

    NASA Technical Reports Server (NTRS)

    Hyun, J. M.

    1983-01-01

    Steady state, axisymmetric motions of a Boussineaq fluid continued in rotating spherical anmulus are considered. The motions are driven by latitudinally varying temperature gradient at the shells. Linearized formulations for a narrow gap are derived and the flow field is divided into the Ekman layers and the geostrophic interior. The Ekman layer flows are consistent with the known results for cylindrical geometries. Within the framework of rather restrictive assumptions, the interior flows are solved by a series of associated Legendre polynomials. The solutions show qualitative features valid at midlatitudes.

  12. Acoustic perturbations on steady spherical accretion in Schwarzschild geometry

    SciTech Connect

    Naskar, Tapan; Chakravarty, Nabajit; Bhattacharjee, Jayanta K.; Ray, Arnab K.

    2007-12-15

    The stationary background flow in the spherically symmetric infall of a compressible fluid, coupled to the space-time defined by the static Schwarzschild metric, has been subjected to linearized acoustic perturbations. The perturbative procedure is based on the continuity condition and it shows that the coupling of the flow with the geometry of space-time brings about greater stability for the flow, to the extent that the amplitude of the perturbation, treated as a standing wave, decays in time, as opposed to the amplitude remaining constant in the Newtonian limit. In qualitative terms this situation simulates the effect of a dissipative mechanism in the classical Bondi accretion flow, defined in the Newtonian construct of space and time. As a result of this approach it becomes impossible to define an acoustic metric for a conserved spherically symmetric flow, described within the framework of Schwarzschild geometry. In keeping with this view, the perturbation, considered separately as a high-frequency traveling wave, also has its amplitude reduced.

  13. Room geometry inference based on spherical microphone array eigenbeam processing.

    PubMed

    Mabande, Edwin; Kowalczyk, Konrad; Sun, Haohai; Kellermann, Walter

    2013-10-01

    The knowledge of parameters characterizing an acoustic environment, such as the geometric information about a room, can be used to enhance the performance of several audio applications. In this paper, a novel method for three-dimensional room geometry inference based on robust and high-resolution beamforming techniques for spherical microphone arrays is presented. Unlike other approaches that are based on the measurement and processing of multiple room impulse responses, here, microphone array signal processing techniques for uncontrolled broadband acoustic signals are applied. First, the directions of arrival (DOAs) and time differences of arrival (TDOAs) of the direct signal and room reflections are estimated using high-resolution robust broadband beamforming techniques and cross-correlation analysis. In this context, the main challenges include the low reflected-signal to background-noise power ratio, the low energy of reflected signals relative to the direct signal, and their strong correlation with the direct signal and among each other. Second, the DOA and TDOA information is combined to infer the room geometry using geometric relations. The high accuracy of the proposed room geometry inference technique is confirmed by experimental evaluations based on both simulated and measured data for moderately reverberant rooms. PMID:24116416

  14. Born Sensitivity Kernels in Spherical Geometry for Meridional Flows

    NASA Astrophysics Data System (ADS)

    Jackiewicz, Jason; Boening, Vincent; Roth, Markus; Kholikov, Shukur

    2016-05-01

    Measuring meridional flows deep in the solar convection zone is challenging because of their small amplitudes compared to other background signals. Typically such inferences are made using a ray theory that is best suited for slowly-varying flows. The implementation of finite-frequency Born theory has been shown to be more accurate for modeling flows of complex spatial structure in the near-surface region. Only until recently were such functions available in spherical geometry, which is necessary for applications to meridional flows. Here we compare these sensitivity kernels with corresponding ray kernels in a forward and inverse problem using numerical simulations. We show that they are suitable for inverting travel-time measurements and are more sensitive to small-scale variations of deep circulations.

  15. Technology in Spherical Geometry Investigations: Reflections on Spontaneous Use and Motivation

    ERIC Educational Resources Information Center

    Sinclair, Margaret

    2010-01-01

    Students in a graduate geometry class used items such as paper, ribbon, plastic spheres, cardboard tubes, and markers to carry out investigations in spherical geometry. The hands-on activities helped students develop a new appreciation of geometry as a study of shape and space; however, the difficulty of subduing wayward elastics and drawing lines…

  16. The solid angle (geometry factor) for a spherical surface source and an arbitrary detector aperture

    DOE PAGESBeta

    Favorite, Jeffrey A.

    2016-01-13

    It is proven that the solid angle (or geometry factor, also called the geometrical efficiency) for a spherically symmetric outward-directed surface source with an arbitrary radius and polar angle distribution and an arbitrary detector aperture is equal to the solid angle for an isotropic point source located at the center of the spherical surface source and the same detector aperture.

  17. Active plasma resonance spectroscopy: eigenfunction solutions in spherical geometry

    NASA Astrophysics Data System (ADS)

    Oberrath, J.; Brinkmann, R. P.

    2014-12-01

    The term active plasma resonance spectroscopy denotes a class of related techniques which utilize, for diagnostic purposes, the natural ability of plasmas to resonate on or near the electron plasma frequency ωpe: a radio frequent signal (in the GHz range) is coupled into the plasma via an antenna or probe, the spectral response is recorded, and a mathematical model is used to determine plasma parameters like the electron density. The mathematical model of an arbitrarily shaped probe-plasma system can be written in an abstract but very compact equation. It contains an appropriate operator, which describes the dynamical behavior and can be split into a conservative and a dissipative part. Based on the cold plasma model, this manuscript provides a solution strategy to determine the electrical admittance of a specific probe-plasma system derived from the abstract dynamical equation. Focusing on probes with a spherical-shaped probe tip the general admittance can be derived analytically. Therefore, the matrix representation of the resolvent of the dynamical operator is determined. This matrix representation is derived by means of the eigenfunctions and eigenvalues of the conservative operator. It can be shown that these eigenvalues represent the resonance frequencies of the probe-plasma system which are simply connected to the electron density. As an example, the result is applied to established probe designs: the spherical impedance probe and the multipole resonance probe.

  18. Stationary premixed flames in spherical and cylindrical geometries

    NASA Technical Reports Server (NTRS)

    Ronney, P. D.; Whaling, K. N.; Abbud-Madrid, A.; Gatto, J. L.; Pisowiscz, V. L.

    1994-01-01

    Stationary source-free spherical flames ('flame balls') in premixed combustible gases were studied by employing low-gravity (micro-g) environments in a drop tower and an aircraft flying parabolic trajectories to diminish the impact of buoyancy-induced convective flow. Flame balls were found in all mixture families tested when: (1) the Lewis number Le of the deficient reactant was sufficiently low; and (2) the compositions were sufficiently close to the flammability limits. Probably as a consequence of the reduction in buoyant convection, the flammability limits at micro-g were significantly more dilute than those at Earth gravity; for example, 3.35% H2 vs 4.0% H2 in lean H2-air mixtures. By comparison with analytical and computational models, it is inferred that the phenomenon is probably related to diffusive-thermal effects in low-Le mixtures in conjunction with flame-front curvature and radiative heat losses from the combustion products. The chemical reaction mechanism appears to play no qualitative role. In the aircraft experiments, the gravity levels (approximately equal 10(exp -2)g(sub 0)) were found to cause noticeable motion of flame balls due to buoyancy, which in turn influenced the behavior of flame balls. At these g levels, a new type of transient, nearly cylindrical flame structure, termed 'flame strings,' was observed.

  19. Simulations of plasma dynamo in cylindrical and spherical geometries

    NASA Astrophysics Data System (ADS)

    Khalzov, Ivan; Forest, Cary; Schnack, Dalton; Ebrahimi, Fatima

    2010-11-01

    We have performed the numerical investigation of plasma flow and possibility of dynamo effect in Madison Plasma Couette Experiment (MPCX) and Madison Plasma Dynamo Experiment (MPDX), which are being installed at the University of Wisconsin- Madison. Using the extended MHD code, NIMROD, we have studied several types of plasma flows appropriate for dynamo excitation. Calculations are done for isothermal compressible plasma model including two-fluid effects (Hall term), which is beyond the standard incompressible MHD picture. It is found that for magnetic Reynolds numbers exceeding the critical one the counter-rotating Von Karman flow (in cylinder) and Dudley- James flow (in sphere) result in self-generation of magnetic field. Depending on geometry and plasma parameters this field can either saturate at certain amplitude corresponding to a new stable equilibrium (laminar dynamo) or lead to turbulent dynamo. It is shown that plasma compressibility results in increase of the critical magnetic Reynolds number while two- fluid effects change the level of saturated dynamo field. The work is supported by NSF.

  20. 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.

  1. Ablation Front Rayleigh-Taylor Growth Experiments in Spherically Convergent Geometry

    SciTech Connect

    Glendinning, S.G.; Cherfils, C.; Colvin, J.; Divol, L.; Galmiche, D.; Haan, S.; Marinak, M.M.; Remington, B.A.; Richard, A.L.; Wallace, R.

    1999-11-03

    Experiments were performed on the Nova laser, using indirectly driven capsules mounted in cylindrical gold hohlraums, to measure the Rayleigh-Taylor growth at the ablation front by time-resolved radiography. Modulations were preformed on the surface of Ge-doped plastic capsules. With initial modulations of 4 {micro}m, growth factors of about 6 in optical depth were seen, in agreement with simulations using the radiation hydrocode FCI2. With initial modulations of 1 {micro}m, growth factors of about 100-150 in optical depth were seen. The Rayleigh-Taylor (RT) instability at the ablation front in an inertial confinement fusion capsule has been the subject of considerable investigation. Much of this research has been concentrated on planar experiments, in which RT growth is inferred from radiography. The evolution is somewhat different in a converging geometry; the spatial wavelength decreases (affecting the onset of nonlinear saturation), and the shell thickens and compresses rather than decompressing as in a planar geometry. In a cylindrically convergent geometry, the latter effect is proportional to the radius, while in spherically convergent geometry, the latter effect is proportional to the radius squared. Experiments were performed on the Nova and Omega lasers in cylindrical geometry (using both direct and indirect drive) and have been performed in spherical geometry using direct drive.

  2. TOA Lightning Location Retrieval on Spherical and Oblate Spheroidal Earth Geometries

    NASA Technical Reports Server (NTRS)

    Koshak, W. J.; Solakiewicz, R. J.; Arnold, James E. (Technical Monitor)

    2000-01-01

    A simple linear algebraic solution is introduced for retrieving the location and time-of-occurrence of lightning ground strikes on a spherical Earth from a network of four or more time-of-arrival (TOA) sensors. Since the solution accounts for Earth curvature, it represents an extension to earlier planar model results described by Koshak et al. A test of the retrieval method is provided using computer-simulated data sets. The method is easy to comprehend and completely avoids reference to the mathematics of spherical hyperbolas such as discussed by Lewis. A quasi-analytic extension to the spherical Earth solution is provided for an oblate spheroidal Earth geometry, and the importance/relevance of oblate effects are discussed. Future application of these methods in support of the North American National Lightning Detection Network (NALDN) described by Cummins et al. is desirable, but additional theoretical investigations are required to incorporate magnetic bearing information into the present solution process.

  3. Sum frequency generation image reconstruction: aliphatic membrane under spherical cap geometry.

    PubMed

    Volkov, Victor

    2014-10-01

    The article explores an opportunity to approach structural properties of phospholipid membranes using Sum Frequency Generation microscopy. To establish the principles of sum frequency generation image reconstruction in such systems, at first approach, we may adopt an idealistic spherical cap uniform assembly of hydrocarbon molecules. Quantum mechanical studies for decanoic acid (used here as a representative molecular system) provide necessary information on transition dipole moments and Raman tensors of the normal modes specific to methyl terminal - a typical moiety in aliphatic (and phospholipid) membranes. Relative degree of localization and frequencies of the normal modes of methyl terminals make nonlinearities of this moiety to be promising in structural analysis using Sum Frequency Generation imaging. Accordingly, the article describes derivations of relevant macroscopic nonlinearities and suggests a mapping procedure to translate amplitudes of the nonlinearities onto microscopy image plane according to geometry of spherical assembly, local molecular orientation, and optical geometry. Reconstructed images indicate a possibility to extract local curvature of bilayer envelopes of spherical character. This may have practical implications for structural extractions in membrane systems of practical relevance. PMID:25296798

  4. Sum frequency generation image reconstruction: Aliphatic membrane under spherical cap geometry

    SciTech Connect

    Volkov, Victor

    2014-10-07

    The article explores an opportunity to approach structural properties of phospholipid membranes using Sum Frequency Generation microscopy. To establish the principles of sum frequency generation image reconstruction in such systems, at first approach, we may adopt an idealistic spherical cap uniform assembly of hydrocarbon molecules. Quantum mechanical studies for decanoic acid (used here as a representative molecular system) provide necessary information on transition dipole moments and Raman tensors of the normal modes specific to methyl terminal – a typical moiety in aliphatic (and phospholipid) membranes. Relative degree of localization and frequencies of the normal modes of methyl terminals make nonlinearities of this moiety to be promising in structural analysis using Sum Frequency Generation imaging. Accordingly, the article describes derivations of relevant macroscopic nonlinearities and suggests a mapping procedure to translate amplitudes of the nonlinearities onto microscopy image plane according to geometry of spherical assembly, local molecular orientation, and optical geometry. Reconstructed images indicate a possibility to extract local curvature of bilayer envelopes of spherical character. This may have practical implications for structural extractions in membrane systems of practical relevance.

  5. Directional decomposition of the acoustic wave equation for fluids and metafluids in spherical geometries, with application to transformational acoustics

    NASA Astrophysics Data System (ADS)

    Olsson, Peter

    2016-03-01

    A new directional decomposition of the acoustic 3D wave equation is derived for spherically symmetric geometries, where the wave fields do not need to possess such a symmetry. This provides an alternative basis for various applications of techniques like invariant embedding and time domain Green functions in spherically symmetric geometries. Contrary to previous results on spherical wave splittings, the new decomposition is given in a very explicit form. The wave equation considered incorporates effects from radially varying compressibility and density, but also from anisotropic density, a property of certain so called metafluids. By applying the new spherical wave splitting, we show that all spherically symmetric acoustic metafluid cloaks are diffeomorphic images of a homogeneous and isotropic spherical ball of perfect fluid.

  6. CYCLIC MAGNETIC ACTIVITY DUE TO TURBULENT CONVECTION IN SPHERICAL WEDGE GEOMETRY

    SciTech Connect

    Kaepylae, Petri J.; Mantere, Maarit J.; Brandenburg, Axel

    2012-08-10

    We report on simulations of turbulent, rotating, stratified, magnetohydrodynamic convection in spherical wedge geometry. An initially small-scale, random, weak-amplitude magnetic field is amplified by several orders of magnitude in the course of the simulation to form oscillatory large-scale fields in the saturated state of the dynamo. The differential rotation is solar-like (fast equator), but neither coherent meridional poleward circulation nor near-surface shear layer develop in these runs. In addition to a poleward branch of magnetic activity beyond 50 Degree-Sign latitude, we find for the first time a pronounced equatorward branch at around 20 Degree-Sign latitude, reminiscent of the solar cycle.

  7. A standard test set for numerical approximations to the shallow water equations in spherical geometry

    SciTech Connect

    Williamson, D.L.; Hack, J.J.; Jakob, R.; Swarztrauber, P.N. ); Drake, J.B. )

    1991-08-01

    A suite of seven test cases is proposed for the evaluation of numerical methods intended for the solution of the shallow water equations in spherical geometry. The shallow water equations exhibit the major difficulties associated with the horizontal dynamical aspects of atmospheric modeling on the spherical earth. These cases are designed for use in the evaluation of numerical methods proposed for climate modeling and to identify the potential trade-offs which must always be made in numerical modeling. Before a proposed scheme is applied to a full baroclinic atmospheric model it must perform well on these problems in comparison with other currently accepted numerical methods. The cases are presented in order of complexity. They consist of advection across the poles, steady state geostrophically balanced flow of both global and local scales, forced nonlinear advection of an isolated low, zonal flow impinging on an isolated mountain, Rossby-Haurwitz waves and observed atmospheric states. One of the cases is also identified as a computer performance/algorithm efficiency benchmark for assessing the performance of algorithms adapted to massively parallel computers. 31 refs.

  8. Sensitivity Kernels for Flows in Time–Distance Helioseismology: Extension to Spherical Geometry

    NASA Astrophysics Data System (ADS)

    Böning, Vincent G. A.; Roth, Markus; Zima, Wolfgang; Birch, Aaron C.; Gizon, Laurent

    2016-06-01

    We extend an existing Born approximation method for calculating the linear sensitivity of helioseismic travel times to flows from Cartesian to spherical geometry. This development is necessary for using the Born approximation for inferring large-scale flows in the deep solar interior. As first sanity check, we compare two f-mode kernels from our spherical method and from an existing Cartesian method. The horizontal and total integrals agree to within 0.3%. As a second consistency test, we consider a uniformly rotating Sun and a travel distance of 42°. The analytical travel-time difference agrees with the forward-modeled travel-time difference to within 2%. In addition, we evaluate the impact of different choices of filter functions on the kernels for a meridional travel distance of 42°. For all filters, the sensitivity is found to be distributed over a large fraction of the convection zone. We show that the kernels depend on the filter function employed in the data analysis process. If modes of higher harmonic degree (90 ≲ l ≲ 170) are permitted, a noisy pattern of a spatial scale corresponding to l ≈ 260 appears near the surface. When mainly low-degree modes are used (l ≲ 70), the sensitivity is concentrated in the deepest regions and it visually resembles a ray-path-like structure. Among the different low-degree filters used, we find the kernel for phase-speed-filtered measurements to be best localized in depth.

  9. A quantification of the non-spherical geometry and accretion of collapsing cores

    NASA Astrophysics Data System (ADS)

    Smith, Rowan J.; Glover, Simon C. O.; Bonnell, Ian A.; Clark, Paul C.; Klessen, Ralf S.

    2011-02-01

    We present the first detailed classification of the structures of Class 0 cores in a high-resolution simulation of a giant molecular cloud. The simulated cloud contains 104 M⊙ and produces over 350 cores which allows for meaningful statistics. Cores are classified into three types according to how much they depart from spherical symmetry. We find that three-quarters of the cores are better described as irregular filaments than as spheres. Recent Herschel results have shown that cores are formed within a network of filaments, which we find has had a significant impact on the resulting core geometries. We show that the column densities and ram pressure seen by the protostar are not uniform and generally peak along the axes of the filament. The angular momentum vector of the material in the cores varies both in magnitude and direction, which will cause the rotation vector of the central source to fluctuate during the collapse of the core. In the case of the more massive stars, accretion from the environment outside the original core volume is even more important than that from the core itself. This additional gas is primarily accreted on to the cores along the dense filaments in which the cores are embedded, and the sections of the surfaces of the cores which do not coincide with a filament have very little additional material passing through them. The assumption of spherical symmetry cannot be applied to the majority of collapsing cores, and is never a good description of how stars accrete gas from outside the original core radius. This has ramifications for our understanding of collapsing cores, in particular their line profiles, the effect of radiation upon them and their ability to fragment.

  10. Efficient projection and backprojection scheme for spherically symmetric basis functions in divergent beam geometry

    SciTech Connect

    Ziegler, Andy; Koehler, Thomas; Nielsen, Tim; Proksa, Roland

    2006-12-15

    In cone-beam transmission tomography the measurements are performed with a divergent beam of x-rays. The reconstruction with iterative methods is an approach that offers the possibility to reconstruct the corresponding images directly from these measurements. Another approach based on spherically symmetric basis functions (blobs) has been reported with results demonstrating a better image quality for iterative reconstruction algorithms. When combining the two approaches (i.e., using blobs in iterative cone-beam reconstruction of divergent rays) the problem of blob sampling without introducing aliasing must be addressed. One solution to this problem is to select a blob size large enough to ensure a sufficient sampling, but this prevents a high resolution reconstruction, which is not desired. Another solution is a heuristic low-pass filtering, which removes this aliasing, but neglects the different contributions of blobs to the absorption depending on the spatial position in the volume and, therefore, cannot achieve the best image quality. This article presents a model of sampling the blobs which is motivated by the beam geometry. It can be used for high resolution reconstruction and can be implemented efficiently.

  11. Critical experiments on single-unit spherical plutonium geometries reflected and moderated by oil

    SciTech Connect

    Rothe, R.E.

    1997-05-01

    Experimental critical configurations are reported for several dozen spherical and hemispherical single-unit assemblies of plutonium metal. Most were solid but many were hollow-centered, thick, shell-like geometries. All were constructed of nested plutonium (mostly {sup 2139}Pu) metal hemispherical shells. Three kinds of critical configurations are reported. Two required interpolation and/or extrapolation of data to obtain the critical mass because reflector conditions were essentially infinite. The first finds the plutonium essentially fully reflected by a hydrogen-rich oil; the second is essentially unreflected. The third kind reports the critical oil reflector height above a large plutonium metal assembly of accurately known mass (no interpolation required) when that mass was too great to permit full oil reflection. Some configurations had thicknesses of mild steel just outside the plutonium metal, separating it from the oil. These experiments were performed at the Rocky Flats Critical Mass Laboratory in the late 1960s. They have not been published in a form suitable for benchmark-quality comparisons against state-of-the-art computational techniques until this paper. The age of the data and other factors lead to some difficulty in reconstructing aspects of the program and may, in turn, decrease confidence in certain details. Whenever this is true, the point is acknowledged. The plutonium metal was alpha-phase {sup 239}Pu containing 5.9 wt-% {sup 240}Pu. All assemblies were formed by nesting 1.667-mm-thick (nominal) bare plutonium metal hemispherical shells, also called hemishells, until the desired configuration was achieved. Very small tolerance gaps machined into radial dimensions reduced the effective density a small amount in all cases. Steel components were also nested hemispherical shells; but these were nominally 3.333-mm thick. Oil was used as the reflector because of its chemical compatibility with plutonium metal.

  12. Rapid Optimal SPH Particle Distributions in Spherical Geometries for Creating Astrophysical Initial Conditions

    NASA Astrophysics Data System (ADS)

    Raskin, Cody; Owen, J. Michael

    2016-04-01

    Creating spherical initial conditions in smoothed particle hydrodynamics simulations that are spherically conformal is a difficult task. Here, we describe two algorithmic methods for evenly distributing points on surfaces that when paired can be used to build three-dimensional spherical objects with optimal equipartition of volume between particles, commensurate with an arbitrary radial density function. We demonstrate the efficacy of our method against stretched lattice arrangements on the metrics of hydrodynamic stability, spherical conformity, and the harmonic power distribution of gravitational settling oscillations. We further demonstrate how our method is highly optimized for simulating multi-material spheres, such as planets with core-mantle boundaries.

  13. Low-complexity digital filter geometry for spherical coded imaging systems

    NASA Astrophysics Data System (ADS)

    Feng, Guotong; Shoaib, Mohammed; Robinson, M. D.

    2009-08-01

    Recent research in the area of electro-optical system design identified the benefits of spherical aberration for extending the depth-of-field of electro-optical imaging systems. In such imaging systems, spherical aberration is deliberately introduced by the optical system lowering system modulation transfer function (MTF) and then subsequently corrected using digital processing. Previous research, however, requires complex digital postprocessing algorithms severely limiting its applicability to only expensive systems. In this paper, we examine the ability of low-cost spatially invariant finite impulse response (FIR) digital filters to restore system MTF degraded by spherical aberration. We introduce an analytical model for choosing the minimum, and hence cheapest, FIR filter size capable of providing the critical level sharpening to render artifact-free images. We identify a robust quality criterion based on the post-processed MTF for developing this model. We demonstrate the reliability of the estimated model by showing simulated spherical coded imaging results. We also evaluate the hardware complexity of the FIR filters implemented for various spherical aberrations on a low-end Field-Programmable Gate Array (FPGA) platform.

  14. CSDUST3 - A radiation transport code for a dusty medium with 1-D planar, spherical or cylindrical geometry

    NASA Technical Reports Server (NTRS)

    Egan, Michael P.; Leung, Chun Ming; Spagna, George F., Jr.

    1988-01-01

    The program solves the radiation transport problem in a dusty medium with one-dimensional planar, spherical or cylindrical geometry. It determines self-consistently the effects of multiple scattering, absorption, and re-emission of photons on the temperature of dust grains and the characteristics of the internal radiation field. The program can treat radiation field anisotropy, linear anisotropic scattering, and multi-grain components. The program output consists of the dust-temperature distribution, flux spectrum, surface brightness at each frequency and the observed intensities (involving a convolution with a telescope beam pattern).

  15. Landau level quantization for massless Dirac fermions in the spherical geometry: Graphene fractional quantum Hall effect on the Haldane sphere

    NASA Astrophysics Data System (ADS)

    Arciniaga, Michael; Peterson, Michael R.

    2016-07-01

    We derive the single-particle eigenenergies and eigenfunctions for massless Dirac fermions confined to the surface of a sphere in the presence of a magnetic monopole, i.e., we solve the Landau level problem for electrons in graphene on the Haldane sphere. With the single-particle eigenfunctions and eigenenergies we calculate the Haldane pseudopotentials for the Coulomb interaction in the second Landau level and calculate the effective pseudopotentials characterizing an effective Landau level mixing Hamiltonian entirely in the spherical geometry to be used in theoretical studies of the fractional quantum Hall effect in graphene. Our treatment is analogous to the formalism in the planar geometry and reduces to the planar results in the thermodynamic limit.

  16. MODELING MAGNETIC FIELD STRUCTURE OF A SOLAR ACTIVE REGION CORONA USING NONLINEAR FORCE-FREE FIELDS IN SPHERICAL GEOMETRY

    SciTech Connect

    Guo, Y.; Ding, M. D.; Liu, Y.; Sun, X. D.; DeRosa, M. L.; Wiegelmann, T.

    2012-11-20

    We test a nonlinear force-free field (NLFFF) optimization code in spherical geometry using an analytical solution from Low and Lou. Several tests are run, ranging from idealized cases where exact vector field data are provided on all boundaries, to cases where noisy vector data are provided on only the lower boundary (approximating the solar problem). Analytical tests also show that the NLFFF code in the spherical geometry performs better than that in the Cartesian one when the field of view of the bottom boundary is large, say, 20 Degree-Sign Multiplication-Sign 20 Degree-Sign . Additionally, we apply the NLFFF model to an active region observed by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory (SDO) both before and after an M8.7 flare. For each observation time, we initialize the models using potential field source surface (PFSS) extrapolations based on either a synoptic chart or a flux-dispersal model, and compare the resulting NLFFF models. The results show that NLFFF extrapolations using the flux-dispersal model as the boundary condition have slightly lower, therefore better, force-free, and divergence-free metrics, and contain larger free magnetic energy. By comparing the extrapolated magnetic field lines with the extreme ultraviolet (EUV) observations by the Atmospheric Imaging Assembly on board SDO, we find that the NLFFF performs better than the PFSS not only for the core field of the flare productive region, but also for large EUV loops higher than 50 Mm.

  17. The synchrotron-self-Compton process in spherical geometries. II - Application to active galactic nuclei

    NASA Technical Reports Server (NTRS)

    Band, D. L.; Grindlay, J. E.

    1986-01-01

    Observational implications and constraints on spherical nonthermal synchrotron self-Compton models with applications to AGNs are discussed. The Compton optical depth of the source and the synchrotron optical depth are considered, and plausible electron distributions are discussed. The alpha(0x), alpha(rx), and alpha(0r) system of comparing the fluxes in different energy bands is related to the nonthermal models, and sample spectra are presented that show the spectral features the models can produce. The models are applied to radio-quiet AGNs. It is shown that the infrared and X-ray continua of the AGNs can be produced by nonthermal processes.

  18. Numerical study of laminar plasma dynamo in cylindrical and spherical geometries

    NASA Astrophysics Data System (ADS)

    Khalzov, Ivan; Bayliss, Adam; Ebrahimi, Fatima; Forest, Cary; Schnack, Dalton

    2009-05-01

    We have performed the numerical investigation of possibility of laminar dynamo in two new experiments, Plasma Couette and Plasma Dynamo, which have been designed at the University of Wisconsin-Madison. The plasma is confined by a strong multipole magnetic field localized at the boundary of cylindrical (Plasma Couette) or spherical (Plasma Dynamo) chamber. Electrodes positioned between the magnet rings can be biased with arbitrary potentials so that Lorenz force ExB drives any given toroidal velocity profile at the surface. Using the extended MHD code, NIMROD, we have modeled several types of plasma flows appropriate for dynamo excitation. It is found that for high magnetic Reynolds numbers the counter-rotating von Karman flow (in cylinder) and Dudley-James flow (in sphere) can lead to self-generation of non-axisymmetric magnetic field. This field saturates at certain amplitude corresponding to a new stable equilibrium. The structure of this equilibrium is considered.

  19. Gravity, Topography, Magnetics: Geoscience Data Analysis in Spherical and Planar Geometry

    NASA Astrophysics Data System (ADS)

    Simons, F. J.; Harig, C.; Lewis, K. W.; Plattner, A.

    2015-12-01

    Data in the Earth and planetary sciences (as well as in astronomy and cosmology, medical imaging, auditory signal processing, and computer vision) often inherently have a sphere (or an ellipsoid) as their domain. However, frequently our goal is to study phenomena in a specific region of the globe. We might either have data that only cover parts of the sphere (e.g. ocean altimetry, Shuttle radar topography), or we may seek to extract a local signal from a global data set (e.g. the continental fraction of the lithospheric magnetic field, or the portion of the time-varying geopotential that is due to ice mass changes). Spectral content is always finite: all sampled data are band-limited. When the region under study is not the whole sphere, but not small enough to justify two-dimensional projection either, the question arises how to best represent the data to perform our analysis, whatever our field of interest. We present SLEPIAN, a software suite with a multitude of numerical and computational tools, and several plotting routines, to accomplish ``spatiospectral'' spherical analysis in the geosciences and beyond.

  20. Topological constraints on spiral wave dynamics in spherical geometries with inhomogeneous excitability.

    PubMed

    Davidsen, Jörn; Glass, Leon; Kapral, Raymond

    2004-11-01

    We analyze the way topological constraints and inhomogeneity in the excitability influence the dynamics of spiral waves on spheres and punctured spheres of excitable media. We generalize the definition of an index such that it characterizes not only each spiral but also each hole in punctured, oriented, compact, two-dimensional differentiable manifolds and show that the sum of the indices is conserved and zero. We also show that heterogeneity and geometry are responsible for the formation of various spiral-wave attractors, in particular pairs of spirals in which one spiral acts as a source and a second as a sink--the latter similar to an antispiral. The results provide a basis for the analysis of the propagation of waves in heterogeneous excitable media in physical and biological systems. PMID:15600724

  1. Assessment of tissue optical parameters in a spherical geometry using three different optical spectroscopy methods: comparison based on a theoretical approach

    NASA Astrophysics Data System (ADS)

    Vaudelle, F.; Askoura, M.; L'Huillier, J. P.

    2015-07-01

    The non-invasive research of information inside biological tissues can be made by means of setups using continuous, time-dependent or frequency modulated light sources, which emit in the visible or near-infrared range. Moreover, the biological structures such as brain, breast or fruits, can be regarded as closer to a spherical shape than a slab. This paper focus on the retrieval of tissue optical parameters in a spherical geometry using fittings with analytical solutions adapted for semi-infinite geometry. The data were generated using three different optical spectroscopy methods: frequency-resolved, spatially-resolved, and time-resolved modes. Simulations based on a Monte Carlo code were performed on homogeneous spheres, with 18 spaced detectors located on their boundary. First, data are examined in the frequency domain. Second, they are treated with optimization algorithms to assess the optical coefficients. The computations show that the spatially-resolved measurements are often more robust than those related to the frequency-resolved mode. In the temporal domain, errors on the estimates are also exhibited with the fitting by the Fourier transform of a solution based on the semi-infinite geometry. Furthermore, when the analytical solution is modified by taking into account the spherical shape, the retrieval of the coefficients is improved.

  2. A comparison of angular difference schemes for one-dimensional spherical geometry S{sub N} equations

    SciTech Connect

    Lathrop, K.D.

    2000-03-01

    To investigate errors caused by angular differencing in approximating the streaming terms of the transport equation, five different approximations are evaluated for three test problems in one-dimensional spherical geometry. The following schemes are compared: diamond, special truncation error minimizing weighted diamond, linear continuous (the original S{sub N} scheme), linear discontinuous, and new quadratic continuous. To isolate errors caused by angular differencing, the approximations are derived from the transport equation without spatial differencing, and the resulting coupled ordinary differential equations (ODEs) are solved with an ODE solver. Results from the approximations are compared with analytic solutions derived for two-region purely absorbing spheres. Most of the approximations are derived by taking moments of the conservation form of the transport equation. The quadratic continuous approximation is derived taking the zeroth moment of both the transport equation and the first angular derivative of the transport equation. The advantages of this approach are described, In all of the approximations, the desirability is shown of using an initializing computation of the {mu} = {minus}1 angular flux to correctly compute the central flux and of having a difference approximation that ensures this central flux is the same for all directions. The behavior of the standard discrete ordinates equations in the diffusion limit is reviewed, and the linear and quadratic continuous approximations are shown to have the correct diffusion limit if an equal interval discrete quadrature is used. In all three test problems, the weighted diamond difference approximation has smaller maximum and average relative flux errors than the diamond or the linear continuous difference approximations. The quadratic continuous approximation and the linear discontinuous approximation are both more accurate than the other approximations, and the quadratic continuous approximation has a

  3. Euclidean, Spherical, and Hyperbolic Shadows

    ERIC Educational Resources Information Center

    Hoban, Ryan

    2013-01-01

    Many classical problems in elementary calculus use Euclidean geometry. This article takes such a problem and solves it in hyperbolic and in spherical geometry instead. The solution requires only the ability to compute distances and intersections of points in these geometries. The dramatically different results we obtain illustrate the effect…

  4. Method for characterization of a spherically bent crystal for K.alpha. X-ray imaging of laser plasmas using a focusing monochromator geometry

    SciTech Connect

    Kugland, Nathan; Doeppner, Tilo; Glenzer, Siegfried; Constantin, Carmen; Niemann, Chris; Neumayer, Paul

    2015-04-07

    A method is provided for characterizing spectrometric properties (e.g., peak reflectivity, reflection curve width, and Bragg angle offset) of the K.alpha. emission line reflected narrowly off angle of the direct reflection of a bent crystal and in particular of a spherically bent quartz 200 crystal by analyzing the off-angle x-ray emission from a stronger emission line reflected at angles far from normal incidence. The bent quartz crystal can therefore accurately image argon K.alpha. x-rays at near-normal incidence (Bragg angle of approximately 81 degrees). The method is useful for in-situ calibration of instruments employing the crystal as a grating by first operating the crystal as a high throughput focusing monochromator on the Rowland circle at angles far from normal incidence (Bragg angle approximately 68 degrees) to make a reflection curve with the He-like x-rays such as the He-.alpha. emission line observed from a laser-excited plasma.

  5. Spherical electrostatic electron spectrometer

    NASA Astrophysics Data System (ADS)

    Yang, T.-S.; Kolk, B.; Kachnowski, T.; Trooster, J.; Benczer-Koller, N.

    1982-06-01

    A high transmission, low energy spherical electrostatic electron spectrometer particularly suited to the geometry required for Mössbauer-conversion electron spectroscopy was built. A transmission of 13% at an energy resolution of 2% was obtained with an 0.5 cm diameter source of 13.6 keV electrons. Applications to the study of hyperfine interactions of surfaces and interfaces are discussed.

  6. Self-similar flows in spherical geometry

    NASA Astrophysics Data System (ADS)

    Gerin-Roze, Jean

    2007-06-01

    If we are looking at the implosion of a sphere starting with a strong shock, the study of self-similar flows is a classical problem. We will assume that: - The sphere contains a perfect gas with a polytropic coefficient γ=5/3. - The shock follows the equation: rc=A(-t)^α with t0

  7. Hollow spherical shell manufacture

    DOEpatents

    O'Holleran, T.P.

    1991-11-26

    A process is disclosed for making a hollow spherical shell of silicate glass composition in which an aqueous suspension of silicate glass particles and an immiscible liquid blowing agent is placed within the hollow spherical cavity of a porous mold. The mold is spun to reduce effective gravity to zero and to center the blowing agent, while being heated so as to vaporize the immiscible liquid and urge the water carrier of the aqueous suspension to migrate into the body of the mold, leaving a green shell compact deposited around the mold cavity. The green shell compact is then removed from the cavity, and is sintered for a time and a temperature sufficient to form a silicate glass shell of substantially homogeneous composition and uniform geometry. 3 figures.

  8. Hollow spherical shell manufacture

    DOEpatents

    O'Holleran, Thomas P.

    1991-01-01

    A process for making a hollow spherical shell of silicate glass composition in which an aqueous suspension of silicate glass particles and an immiscible liquid blowing agent is placed within the hollow spherical cavity of a porous mold. The mold is spun to reduce effective gravity to zero and to center the blowing agent, while being heated so as to vaporize the immiscible liquid and urge the water carrier of the aqueous suspension to migrate into the body of the mold, leaving a green shell compact deposited around the mold cavity. The green shell compact is then removed from the cavity, and is sintered for a time and a temperature sufficient to form a silicate glass shell of substantially homogeneous composition and uniform geometry.

  9. Spherical colloidal photonic crystals.

    PubMed

    Zhao, Yuanjin; Shang, Luoran; Cheng, Yao; Gu, Zhongze

    2014-12-16

    generated by evaporation-induced nanoparticle crystallization or polymerization of ordered nanoparticle crystallization arrays. In particular, because microfluidics was used for the generation of the droplet templates, the development of spherical colloidal PhCs has progressed significantly. These new strategies not only ensure monodispersity, but also increase the structural and functional diversity of the PhC beads, paving the way for the development of advanced optoelectronic devices. In this Account, we present the research progress on spherical colloidal PhCs, including their design, preparation, and potential applications. We outline various types of spherical colloidal PhCs, such as close-packed, non-close-packed, inverse opal, biphasic or multiphasic Janus structured, and core-shell structured geometries. Based on their unique optical properties, applications of the spherical colloidal PhCs for displays, sensors, barcodes, and cell culture microcarriers are presented. Future developments of the spherical colloidal PhC materials are also envisioned. PMID:25393430

  10. Spherical Camera

    NASA Technical Reports Server (NTRS)

    1997-01-01

    Developed largely through a Small Business Innovation Research contract through Langley Research Center, Interactive Picture Corporation's IPIX technology provides spherical photography, a panoramic 360-degrees. NASA found the technology appropriate for use in guiding space robots, in the space shuttle and space station programs, as well as research in cryogenic wind tunnels and for remote docking of spacecraft. Images of any location are captured in their entirety in a 360-degree immersive digital representation. The viewer can navigate to any desired direction within the image. Several car manufacturers already use IPIX to give viewers a look at their latest line-up of automobiles. Another application is for non-invasive surgeries. By using OmniScope, surgeons can look more closely at various parts of an organ with medical viewing instruments now in use. Potential applications of IPIX technology include viewing of homes for sale, hotel accommodations, museum sites, news events, and sports stadiums.

  11. Complete parametrization of the plasma-sheath transition and I-V curves for a cylindrical or spherical Langmuir probe according to the features of the probe, simultaneously including geometry, ionization and collisions

    NASA Astrophysics Data System (ADS)

    Morales Crespo, R.

    2015-08-01

    This paper solves and analyses the complete characterization of the plasma-sheath transition and the characteristic I-V curves of an active and collisional plasma close to a cylindrical or spherical wall considering a wide range of the parameter which describe the model to be useful for experimental measures. Despite the difficulty of including the three possible pre-sheath mechanisms, this characterization is obtained from a self-consistent model using three easily measurable parameters, namely the electric potential of the wall, the positive ion current collected by the wall, and the radius of the wall. These parameters are easy to measure and facilitate the diagnosis of plasmas from an experimental point of view.

  12. Radiative transfer in spherical atmospheres

    NASA Technical Reports Server (NTRS)

    Kalkofen, W.; Wehrse, R.

    1984-01-01

    A method for defining spherical model atmospheres in radiative/convective and hydrostatic equilibrium is presented. A finite difference form is found for the transfer equation and a matrix operator is developed as the discrete space analog (in curvilinear coordinates) of a formal integral in plane geometry. Pressure is treated as a function of temperature. Flux conservation is maintained within the energy equation, although the correct luminosity transport must be assigned for any given level of the atmosphere. A perturbed integral operator is used in a complete linearization of the transfer and constraint equations. Finally, techniques for generating stable solutions in economical computer time are discussed.

  13. Hexatic undulations in curved geometries.

    PubMed

    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

  14. Spatial symmetry breaking in rapidly rotating convective spherical shells

    NASA Technical Reports Server (NTRS)

    Zhang, Keke; Schubert, Gerald

    1995-01-01

    Many problems in geophysical and astrophysical convection systems are characterized by fast rotation and spherical shell geometry. The combined effects of Coriolis forces and spherical shell geometry produce a unique spatial symmetry for the convection pattern in a rapidly rotating spherical shell. In this paper, we first discuss the general spatial symmetries for rotating spherical shell convection. A special model, a spherical shell heated from below, is then used to illustrate how and when the spatial symmetries are broken. Symmetry breaking occurs via a sequence of spatial transitions from the primary conducting state to the complex multiple-layered columnar structure. It is argued that, because of the dominant effects of rotation, the sequence of spatial transitions identified from this particular model is likely to be generally valid. Applications of the spatial symmetry breaking to planetary convection problems are also discussed.

  15. Spherical quartz crystals investigated with synchrotron radiation

    NASA Astrophysics Data System (ADS)

    Pereira, N. R.; Macrander, A. T.; Hill, K. W.; Baronova, E. O.; George, K. M.; Kotick, J.

    2015-10-01

    The quality of x-ray spectra and images obtained from plasmas with spherically bent crystals depends in part on the crystal's x-ray diffraction across the entire crystal surface. We employ the energy selectivity and high intensity of synchrotron radiation to examine typical spherical crystals from alpha-quartz for their diffraction quality, in a perpendicular geometry that is particularly convenient to examine sagittal focusing. The crystal's local diffraction is not ideal: the most noticeable problems come from isolated regions that so far have failed to correlate with visible imperfections. Excluding diffraction from such problem spots has little effect on the focus beyond a decrease in background.

  16. Spherical quartz crystals investigated with synchrotron radiation.

    PubMed

    Pereira, N R; Macrander, A T; Hill, K W; Baronova, E O; George, K M; Kotick, J

    2015-10-01

    The quality of x-ray spectra and images obtained from plasmas with spherically bent crystals depends in part on the crystal's x-ray diffraction across the entire crystal surface. We employ the energy selectivity and high intensity of synchrotron radiation to examine typical spherical crystals from alpha-quartz for their diffraction quality, in a perpendicular geometry that is particularly convenient to examine sagittal focusing. The crystal's local diffraction is not ideal: the most noticeable problems come from isolated regions that so far have failed to correlate with visible imperfections. Excluding diffraction from such problem spots has little effect on the focus beyond a decrease in background. PMID:26520963

  17. Spherical quartz crystals investigated with synchrotron radiation

    SciTech Connect

    Pereira, N. R.; Macrander, A. T.; Hill, K. W.; Baronova, E. O.; George, K. M.; Kotick, J.

    2015-10-15

    The quality of x-ray spectra and images obtained from plasmas with spherically bent crystals depends in part on the crystal’s x-ray diffraction across the entire crystal surface. We employ the energy selectivity and high intensity of synchrotron radiation to examine typical spherical crystals from alpha-quartz for their diffraction quality, in a perpendicular geometry that is particularly convenient to examine sagittal focusing. The crystal’s local diffraction is not ideal: the most noticeable problems come from isolated regions that so far have failed to correlate with visible imperfections. Excluding diffraction from such problem spots has little effect on the focus beyond a decrease in background.

  18. Spherical neutron generator

    DOEpatents

    Leung, Ka-Ngo

    2006-11-21

    A spherical neutron generator is formed with a small spherical target and a spherical shell RF-driven plasma ion source surrounding the target. A deuterium (or deuterium and tritium) ion plasma is produced by RF excitation in the plasma ion source using an RF antenna. The plasma generation region is a spherical shell between an outer chamber and an inner extraction electrode. A spherical neutron generating target is at the center of the chamber and is biased negatively with respect to the extraction electrode which contains many holes. Ions passing through the holes in the extraction electrode are focused onto the target which produces neutrons by D-D or D-T reactions.

  19. Molecular Geometry.

    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…

  20. Stability of spherical converging shock wave

    SciTech Connect

    Murakami, M.; Sanz, J.; Iwamoto, Y.

    2015-07-15

    Based on Guderley's self-similar solution, stability of spherical converging shock wave is studied. A rigorous linear perturbation theory is developed, in which the growth rate of perturbation is given as a function of the spherical harmonic number ℓ and the specific heats ratio γ. Numerical calculation reveals the existence of a γ-dependent cut-off mode number ℓ{sub c}, such that all the eigenmode perturbations for ℓ > ℓ{sub c} are smeared out as the shock wave converges at the center. The analysis is applied to partially spherical geometries to give significant implication for different ignition schemes of inertial confinement fusion. Two-dimensional hydrodynamic simulations are performed to verify the theory.

  1. Stability of spherical converging shock wave

    NASA Astrophysics Data System (ADS)

    Murakami, M.; Sanz, J.; Iwamoto, Y.

    2015-07-01

    Based on Guderley's self-similar solution, stability of spherical converging shock wave is studied. A rigorous linear perturbation theory is developed, in which the growth rate of perturbation is given as a function of the spherical harmonic number ℓ and the specific heats ratio γ. Numerical calculation reveals the existence of a γ-dependent cut-off mode number ℓc, such that all the eigenmode perturbations for ℓ > ℓc are smeared out as the shock wave converges at the center. The analysis is applied to partially spherical geometries to give significant implication for different ignition schemes of inertial confinement fusion. Two-dimensional hydrodynamic simulations are performed to verify the theory.

  2. Simulation on the aggregation process of spherical particle confined in a spherical shell

    NASA Astrophysics Data System (ADS)

    Wang, J.; Xu, J. J.; Zhang, L.

    2016-04-01

    The aggregation process of spherical particles confined in a spherical shell was studied by using a diffusion-limited cluster-cluster aggregation (DLCA) model. The influence of geometrical confinement and wetting-like properties of the spherical shell walls on the particle concentration profile, aggregate structure and aggregation kinetics had been explored. The results show that there will be either depletion or absorption particles near the shell walls depending on the wall properties. It is observed that there are four different types of density distribution which can be realized by modifying the property of the inner or outer spherical shell wall. In addition, the aggregate structure will become more compact in the confined spherical shell comparing to bulk system with the same particle volume fraction. The analysis on the aggregation kinetics indicates that geometrical confinement will promote the aggregation process by reducing the invalid movement of the small aggregates and by constraining the movement of those large aggregates. Due to the concave geometrical characteristic of the outer wall of the spherical shell, its effects on the aggregating kinetics and the structure of the formed aggregates are more evident than those of the inner wall. This study will provide some instructive information of controlling the density distribution of low-density porous polymer hollow spherical shells and helps to predict gel structures developed in confined geometries.

  3. Programmable shape transformation of elastic spherical domes.

    PubMed

    Abdullah, Arif M; Braun, Paul V; Hsia, K Jimmy

    2016-07-20

    We investigate mismatch strain driven programmable shape transformation of spherical domes and report the effects of different geometric and structural characteristics on dome behavior in response to applied mismatch strain. We envision a bilayer dome design where the differential swelling of the inner layer with respect to the passive outer layer in response to changes in dome surroundings (such as the introduction of an organic solvent) introduces mismatch strain within the bilayer system and causes dome shape transformation. Finite element analysis reveals that, in addition to snap-through, spherical domes undergo bifurcation buckling and eventually gradual bending to morph into cylinders with increasing mismatch strain. Besides demonstrating how the snap-through energy barrier depends on the spherical dome shape, our analysis identifies three distinct groups of dome geometries based on their mismatch strain-transformed configuration relationships. Our experiments with polymer-based elastic bilayer domes that exhibit differential swelling in organic solvents qualitatively confirm the finite element predictions. We establish that, in addition to externally applied stimuli (mismatch strain), bilayer spherical dome morphing can be tuned and hence programmed through its geometry and structural characteristics. Incorporation of an elastic instability mechanism such as snap-through within the framework of stimuli-responsive functional devices can improve their response time which is otherwise controlled by diffusion. Hence, our proposed design guidelines can be used to realize deployable, multi-functional, reconfigurable, and therefore, adaptive structures responsive to a diverse set of stimuli across multiple length scales. PMID:27435451

  4. Wide scanning spherical antenna

    NASA Technical Reports Server (NTRS)

    Shen, Bing (Inventor); Stutzman, Warren L. (Inventor)

    1995-01-01

    A novel method for calculating the surface shapes for subreflectors in a suboptic assembly of a tri-reflector spherical antenna system is introduced, modeled from a generalization of Galindo-Israel's method of solving partial differential equations to correct for spherical aberration and provide uniform feed to aperture mapping. In a first embodiment, the suboptic assembly moves as a single unit to achieve scan while the main reflector remains stationary. A feed horn is tilted during scan to maintain the illuminated area on the main spherical reflector fixed throughout the scan thereby eliminating the need to oversize the main spherical reflector. In an alternate embodiment, both the main spherical reflector and the suboptic assembly are fixed. A flat mirror is used to create a virtual image of the suboptic assembly. Scan is achieved by rotating the mirror about the spherical center of the main reflector. The feed horn is tilted during scan to maintain the illuminated area on the main spherical reflector fixed throughout the scan.

  5. Dark Geometry

    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.

  6. Large displacement spherical joint

    DOEpatents

    Bieg, Lothar F.; Benavides, Gilbert L.

    2002-01-01

    A new class of spherical joints has a very large accessible full cone angle, a property which is beneficial for a wide range of applications. Despite the large cone angles, these joints move freely without singularities.

  7. Recent Progress on Spherical Torus Research

    SciTech Connect

    Ono, Masayuki; Kaita, Robert

    2014-01-01

    The spherical torus or spherical tokamak (ST) is a member of the tokamak family with its aspect ratio (A = R0/a) reduced to A ~ 1.5, well below the normal tokamak operating range of A ≥ 2.5. As the aspect ratio is reduced, the ideal tokamak beta β (radio of plasma to magnetic pressure) stability limit increases rapidly, approximately as β ~ 1/A. The plasma current it can sustain for a given edge safety factor q-95 also increases rapidly. Because of the above, as well as the natural elongation κ, which makes its plasma shape appear spherical, the ST configuration can yield exceptionally high tokamak performance in a compact geometry. Due to its compactness and high performance, the ST configuration has various near term applications, including a compact fusion neutron source with low tritium consumption, in addition to its longer term goal of attractive fusion energy power source. Since the start of the two megaampere class ST facilities in 2000, National Spherical Torus Experiment (NSTX) in the US and Mega Ampere Spherical Tokamak (MAST) in UK, active ST research has been conducted worldwide. More than sixteen ST research facilities operating during this period have achieved remarkable advances in all of fusion science areas, involving fundamental fusion energy science as well as innovation. These results suggest exciting future prospects for ST research both near term and longer term. The present paper reviews the scientific progress made by the worldwide ST research community during this new mega-ampere-ST era.

  8. Scalar and vector spherical harmonic spectral equations of rotating magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

    Ivers, D. J.; Phillips, C. G.

    2008-12-01

    Vector spherical harmonic analyses have been used effectively to solve laminar and mean-field magnetohydrodynamic dynamo problems with product interactions, such as magnetic induction, anisotropic alpha-effect and anisotropic magnetic diffusion, that are difficult to analyse spectrally in spherical geometries. Spectral forms of the non-linear rotating, Boussinesq and anelastic, momentum, magnetic induction and heat equations are derived for spherical geometries from vector spherical harmonic expansions of the velocity, magnetic induction, vorticity, electrical current and gravitational acceleration and from scalar spherical harmonic expansions of the pressure and temperature. By combining the vector spherical harmonic spectral forms of the momentum equation and the magnetic induction equation with poloidal-toroidal representations of the velocity and the magnetic field, non-linear spherical harmonic spectral equations are also derived for the poloidal-toroidal potentials of the velocity or the momentum density in the anelastic approximation and the magnetic field. Both compact and spectral interaction expansion forms are given. Vector spherical harmonic spectral forms of the linearized rotating magnetic induction, momentum and heat equations for a general basic state can be obtained by linearizing the corresponding non-linear spectral equations. Similarly, the spherical harmonic spectral equations for the poloidal-toroidal potentials of the velocity and the magnetic field may be linearized. However, for computational applications, new alternative hybrid linearized spectral equations are derived. The algorithmically simpler hybrid equations depend on vector spherical harmonic expansions of the velocity, magnetic field, vorticity, electrical current and gravitational acceleration of the basic state and scalar spherical harmonic expansions of the poloidal-toroidal potentials of the perturbation velocity, magnetic field and temperature. The spectral equations derived

  9. Applications of Differential Geometry to Cartography

    ERIC Educational Resources Information Center

    Benitez, Julio; Thome, Nestor

    2004-01-01

    This work introduces an application of differential geometry to cartography. The mathematical aspects of some geographical projections of Earth surface are revealed together with some of its more important properties. An important problem since the discovery of the 'spherical' form of the Earth is how to compose a reliable map of the surface of…

  10. Spherical geodesic mesh generation

    SciTech Connect

    Fung, Jimmy; Kenamond, Mark Andrew; Burton, Donald E.; Shashkov, Mikhail Jurievich

    2015-02-27

    In ALE simulations with moving meshes, mesh topology has a direct influence on feature representation and code robustness. In three-dimensional simulations, modeling spherical volumes and features is particularly challenging for a hydrodynamics code. Calculations on traditional spherical meshes (such as spin meshes) often lead to errors and symmetry breaking. Although the underlying differencing scheme may be modified to rectify this, the differencing scheme may not be accessible. This work documents the use of spherical geodesic meshes to mitigate solution-mesh coupling. These meshes are generated notionally by connecting geodesic surface meshes to produce triangular-prismatic volume meshes. This mesh topology is fundamentally different from traditional mesh topologies and displays superior qualities such as topological symmetry. This work describes the geodesic mesh topology as well as motivating demonstrations with the FLAG hydrocode.

  11. Hollow spherical supramolecular dendrimers.

    PubMed

    Percec, Virgil; Peterca, Mihai; Dulcey, Andrés E; Imam, Mohammad R; Hudson, Steven D; Nummelin, Sami; Adelman, Peter; Heiney, Paul A

    2008-10-01

    The synthesis of a library containing 12 conical dendrons that self-assemble into hollow spherical supramolecular dendrimers is reported. The design principles for this library were accessed by development of a method that allows the identification of hollow spheres, followed by structural and retrostructural analysis of their Pm3n cubic lattice. The first hollow spherical supramolecular dendrimer was made by replacing the tapered dendron, from the previously reported tapered dendritic dipeptide that self-assembled into helical pores, with its constitutional isomeric conical dendron. This strategy generated a conical dendritic dipeptide that self-assembled into a hollow spherical supramolecular dendrimer that self-organizes in a Pm3n cubic lattice. Other examples of hollow spheres were assembled from conical dendrons without a dipeptide at their apex. These are conical dendrons originated from tapered dendrons containing additional benzyl ether groups at their apex. The inner part of the hollow sphere assembled from the dipeptide resembles the path of a spherical helix or loxodrome and, therefore, is chiral. The spheres assembled from other conical dendrons are nonhelical, even when they contain stereocenters on the alkyl groups from their periphery. Functionalization of the apex of the conical dendrons with diethylene glycol allowed the encapsulation of LiOTf and RbOTf in the center of the hollow sphere. These experiments showed that hollow spheres function as supramolecular dendritic capsules and therefore are expected to display functions complementary to those of other related molecular and supramolecular structures. PMID:18771261

  12. Spherical ion source

    NASA Technical Reports Server (NTRS)

    Hall, L. G.

    1969-01-01

    Radial focusing of electrons in ion source produces greater ion densities, resulting in higher resolution and focus capability for a given source volume. Electron beam is focused near exit aperture by spherical fields. High density ions allow focusing ion beam to high density at echo, allowing high current through small aperture.

  13. Retroreflector spherical satellite

    NASA Astrophysics Data System (ADS)

    Akentyev, A. S.; Vasiliev, V. P.; Sadovnikov, M. A.; Sokolov, A. L.; Shargorodskiy, V. D.

    2015-10-01

    Specific features of spherical retroreflector arrays for high-precision laser ranging are considered, and errors in distance measurements are analyzed. A version of a glass retroreflector satellite with a submillimeter "target error" is proposed. Its corner cube reflectors are located in depressions to reduce the working angular aperture, and their faces have a dielectric interference coating.

  14. Spherical mirror mount

    NASA Technical Reports Server (NTRS)

    Meyer, Jay L. (Inventor); Messick, Glenn C. (Inventor); Nardell, Carl A. (Inventor); Hendlin, Martin J. (Inventor)

    2011-01-01

    A spherical mounting assembly for mounting an optical element allows for rotational motion of an optical surface of the optical element only. In that regard, an optical surface of the optical element does not translate in any of the three perpendicular translational axes. More importantly, the assembly provides adjustment that may be independently controlled for each of the three mutually perpendicular rotational axes.

  15. 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.

  16. Close packing of rods on spherical surfaces

    NASA Astrophysics Data System (ADS)

    Smallenburg, Frank; Löwen, Hartmut

    2016-04-01

    We study the optimal packing of short, hard spherocylinders confined to lie tangential to a spherical surface, using simulated annealing and molecular dynamics simulations. For clusters of up to twelve particles, we map out the changes in the geometry of the closest-packed configuration as a function of the aspect ratio L/D, where L is the cylinder length and D the diameter of the rods. We find a rich variety of cluster structures. For larger clusters, we find that the best-packed configurations up to around 100 particles are highly dependent on the exact number of particles and aspect ratio. For even larger clusters, we find largely disordered clusters for very short rods (L/D = 0.25), while slightly longer rods (L/D = 0.5 or 1) prefer a global baseball-like geometry of smectic-like domains, similar to the behavior of large-scale nematic shells. Intriguingly, we observe that when compared to their optimal flat-plane packing, short rods adapt to the spherical geometry more efficiently than both spheres and longer rods. Our results provide predictions for experimentally realizable systems of colloidal rods trapped at the interface of emulsion droplets.

  17. Close packing of rods on spherical surfaces.

    PubMed

    Smallenburg, Frank; Löwen, Hartmut

    2016-04-28

    We study the optimal packing of short, hard spherocylinders confined to lie tangential to a spherical surface, using simulated annealing and molecular dynamics simulations. For clusters of up to twelve particles, we map out the changes in the geometry of the closest-packed configuration as a function of the aspect ratio L/D, where L is the cylinder length and D the diameter of the rods. We find a rich variety of cluster structures. For larger clusters, we find that the best-packed configurations up to around 100 particles are highly dependent on the exact number of particles and aspect ratio. For even larger clusters, we find largely disordered clusters for very short rods (L/D = 0.25), while slightly longer rods (L/D = 0.5 or 1) prefer a global baseball-like geometry of smectic-like domains, similar to the behavior of large-scale nematic shells. Intriguingly, we observe that when compared to their optimal flat-plane packing, short rods adapt to the spherical geometry more efficiently than both spheres and longer rods. Our results provide predictions for experimentally realizable systems of colloidal rods trapped at the interface of emulsion droplets. PMID:27131565

  18. Crack problems in cylindrical and spherical shells

    NASA Technical Reports Server (NTRS)

    Erdogan, F.

    1976-01-01

    Standard plate or shell theories were used as a starting point to study the fracture problems in thin-walled cylindrical and spherical shells, assuming that the plane of the crack is perpendicular to the surface of the sheet. Since recent studies have shown that local shell curvatures may have a rather considerable effect on the stress intensity factor, the crack problem was considered in conjunction with a shell rather than a plate theory. The material was assumed to be isotropic and homogeneous, so that approximate solutions may be obtained by approximating the local shell crack geometry with an ideal shell which has a solution, namely a spherical shell with a meridional crack, a cylindrical shell with a circumferential crack, or a cylindrical shell with an axial crack. A method of solution for the specially orthotropic shells containing a crack was described; symmetric and skew-symmetric problems are considered in cylindrical shells with an axial crack.

  19. Frequency domain photothermal radiometry with spherical solids

    SciTech Connect

    Wang, Chinhua; Liu, Yue; Mandelis, Andreas; Shen, Jun

    2007-04-15

    Motivated by increasing practical and industrial applications of photothermal techniques in the measurement of materials of various shapes with curvature, we extend the applications of photothermal diagnostics to solid spheres, in which both theoretical and experimental photothermal radiometry studies on spherical geometries and thermal diffusivity of the sample are discussed. Based on the Green function method, a full thermal-wave field distribution of a spherical solid is obtained. The characteristics of the thermal-wave field with respect to thermophysical properties of the material, the diameter of the solid, the size of the incident laser beam, and the measurement angle are discussed. Experimental results with steel spheres of different diameters exhibit good agreement between the theory and the experiments.

  20. Colloidal cholesteric liquid crystal in spherical confinement.

    PubMed

    Li, Yunfeng; Jun-Yan Suen, Jeffrey; Prince, Elisabeth; Larin, Egor M; Klinkova, Anna; Thérien-Aubin, Héloïse; Zhu, Shoujun; Yang, Bai; Helmy, Amr S; Lavrentovich, Oleg D; Kumacheva, Eugenia

    2016-01-01

    The organization of nanoparticles in constrained geometries is an area of fundamental and practical importance. Spherical confinement of nanocolloids leads to new modes of packing, self-assembly, phase separation and relaxation of colloidal liquids; however, it remains an unexplored area of research for colloidal liquid crystals. Here we report the organization of cholesteric liquid crystal formed by nanorods in spherical droplets. For cholesteric suspensions of cellulose nanocrystals, with progressive confinement, we observe phase separation into a micrometer-size isotropic droplet core and a cholesteric shell formed by concentric nanocrystal layers. Further confinement results in a transition to a bipolar planar cholesteric morphology. The distribution of polymer, metal, carbon or metal oxide nanoparticles in the droplets is governed by the nanoparticle size and yields cholesteric droplets exhibiting fluorescence, plasmonic properties and magnetic actuation. This work advances our understanding of how the interplay of order, confinement and topological defects affects the morphology of soft matter. PMID:27561545

  1. Colloidal cholesteric liquid crystal in spherical confinement

    PubMed Central

    Li, Yunfeng; Jun-Yan Suen, Jeffrey; Prince, Elisabeth; Larin, Egor M.; Klinkova, Anna; Thérien-Aubin, Héloïse; Zhu, Shoujun; Yang, Bai; Helmy, Amr S.; Lavrentovich, Oleg D.; Kumacheva, Eugenia

    2016-01-01

    The organization of nanoparticles in constrained geometries is an area of fundamental and practical importance. Spherical confinement of nanocolloids leads to new modes of packing, self-assembly, phase separation and relaxation of colloidal liquids; however, it remains an unexplored area of research for colloidal liquid crystals. Here we report the organization of cholesteric liquid crystal formed by nanorods in spherical droplets. For cholesteric suspensions of cellulose nanocrystals, with progressive confinement, we observe phase separation into a micrometer-size isotropic droplet core and a cholesteric shell formed by concentric nanocrystal layers. Further confinement results in a transition to a bipolar planar cholesteric morphology. The distribution of polymer, metal, carbon or metal oxide nanoparticles in the droplets is governed by the nanoparticle size and yields cholesteric droplets exhibiting fluorescence, plasmonic properties and magnetic actuation. This work advances our understanding of how the interplay of order, confinement and topological defects affects the morphology of soft matter. PMID:27561545

  2. Geometry of area without length

    NASA Astrophysics Data System (ADS)

    Ho, Pei-Ming; Inami, Takeo

    2016-01-01

    To define a free string by the Nambu-Goto action, all we need is the notion of area, and mathematically the area can be defined directly in the absence of a metric. Motivated by the possibility that string theory admits backgrounds where the notion of length is not well defined but a definition of area is given, we study space-time geometries based on the generalization of a metric to an area metric. In analogy with Riemannian geometry, we define the analogues of connections, curvatures, and Einstein tensor. We propose a formulation generalizing Einstein's theory that will be useful if at a certain stage or a certain scale the metric is ill defined and the space-time is better characterized by the notion of area. Static spherical solutions are found for the generalized Einstein equation in vacuum, including the Schwarzschild solution as a special case.

  3. Spherical and cylindrical imploding and exploding shock waves in plasma system dominated by pair production

    SciTech Connect

    ul Haq, Muhammad Noaman; Saeed, R.; Shah, Asif

    2010-08-15

    The propagation of ion acoustic shock waves in cylindrical and spherical geometries has been investigated. The plasma system consists of cold ions, Boltzmannian electrons and positrons. Spherical, cylindrical Korteweg-de Vries-Burger equations have been derived by reductive perturbation technique and their shock behavior is studied by employing finite difference method. Our main emphasis is on the behavior of shock as it moves toward and away from center of spherical and cylindrical geometries. It is noticed, that the shock wave strength and steepness accrues with time as it moves toward the center and shock enervates as it moves away from center. The strength of shock in spherical geometry is found to dominate over shock strength in cylindrical geometry. Positron concentration, kinematic viscosity are also found to have significant effect on the shock structure and propagation. The results may have relevance in the inertial confinement fusion plasmas.

  4. Spherical torus fusion reactor

    DOEpatents

    Peng, Yueng-Kay M.

    1989-04-04

    A fusion reactor is provided having a near spherical-shaped plasma with a modest central opening through which straight segments of toroidal field coils extend that carry electrical current for generating a toroidal magnet plasma confinement fields. By retaining only the indispensable components inboard of the plasma torus, principally the cooled toroidal field conductors and in some cases a vacuum containment vessel wall, the fusion reactor features an exceptionally small aspect ratio (typically about 1.5), a naturally elongated plasma cross section without extensive field shaping, requires low strength magnetic containment fields, small size and high beta. These features combine to produce a spherical torus plasma in a unique physics regime which permits compact fusion at low field and modest cost.

  5. Spherical torus fusion reactor

    DOEpatents

    Peng, Yueng-Kay M.

    1989-01-01

    A fusion reactor is provided having a near spherical-shaped plasma with a modest central opening through which straight segments of toroidal field coils extend that carry electrical current for generating a toroidal magnet plasma confinement fields. By retaining only the indispensable components inboard of the plasma torus, principally the cooled toroidal field conductors and in some cases a vacuum containment vessel wall, the fusion reactor features an exceptionally small aspect ratio (typically about 1.5), a naturally elongated plasma cross section without extensive field shaping, requires low strength magnetic containment fields, small size and high beta. These features combine to produce a spherical torus plasma in a unique physics regime which permits compact fusion at low field and modest cost.

  6. Spherical nitroguanidine process

    DOEpatents

    Sanchez, John A.; Roemer, Edward L.; Stretz, Lawrence A.

    1990-01-01

    A process of preparing spherical high bulk density nitroguanidine by dissing low bulk density nitroguanidine in N-methyl pyrrolidone at elevated temperatures and then cooling the solution to lower temperatures as a liquid characterized as a nonsolvent for the nitroguanidine is provided. The process is enhanced by inclusion in the solution of from about 1 ppm up to about 250 ppm of a metal salt such as nickel nitrate, zinc nitrate or chromium nitrate, preferably from about 20 to about 50 ppm.

  7. Spherical nitroguandine process

    SciTech Connect

    Sanchez, J.A.; Roemer, E.L.; Stretz, L.A.

    1990-10-30

    A process of preparing spherical high bulk density nitroguanidine by dissolving low bulk density nitroguanidine in N-methyl pyrrolidone at elevated temperatures and then cooling the solution to lower temperatures as a liquid characterized as a nonsolvent for the nitroguanidine is presented. The process is enhanced by inclusion in the solution of from about 1 ppm up to about 250 ppm of a metal salt such as nickel nitrate, zinc nitrate or chromium nitrate, preferably from about 20 to about 50 ppm.

  8. Recent progress on spherical torus research

    SciTech Connect

    Ono, Masayuki; Kaita, Robert

    2015-04-15

    The spherical torus or spherical tokamak (ST) is a member of the tokamak family with its aspect ratio (A = R{sub 0}/a) reduced to A ∼ 1.5, well below the normal tokamak operating range of A ≥ 2.5. As the aspect ratio is reduced, the ideal tokamak beta β (radio of plasma to magnetic pressure) stability limit increases rapidly, approximately as β ∼ 1/A. The plasma current it can sustain for a given edge safety factor q-95 also increases rapidly. Because of the above, as well as the natural elongation κ, which makes its plasma shape appear spherical, the ST configuration can yield exceptionally high tokamak performance in a compact geometry. Due to its compactness and high performance, the ST configuration has various near term applications, including a compact fusion neutron source with low tritium consumption, in addition to its longer term goal of an attractive fusion energy power source. Since the start of the two mega-ampere class ST facilities in 2000, the National Spherical Torus Experiment in the United States and Mega Ampere Spherical Tokamak in UK, active ST research has been conducted worldwide. More than 16 ST research facilities operating during this period have achieved remarkable advances in all fusion science areas, involving fundamental fusion energy science as well as innovation. These results suggest exciting future prospects for ST research both near term and longer term. The present paper reviews the scientific progress made by the worldwide ST research community during this new mega-ampere-ST era.

  9. Recent progress on spherical torus research

    NASA Astrophysics Data System (ADS)

    Ono, Masayuki; Kaita, Robert

    2015-04-01

    The spherical torus or spherical tokamak (ST) is a member of the tokamak family with its aspect ratio (A = R0/a) reduced to A ˜ 1.5, well below the normal tokamak operating range of A ≥ 2.5. As the aspect ratio is reduced, the ideal tokamak beta β (radio of plasma to magnetic pressure) stability limit increases rapidly, approximately as β ˜ 1/A. The plasma current it can sustain for a given edge safety factor q-95 also increases rapidly. Because of the above, as well as the natural elongation κ, which makes its plasma shape appear spherical, the ST configuration can yield exceptionally high tokamak performance in a compact geometry. Due to its compactness and high performance, the ST configuration has various near term applications, including a compact fusion neutron source with low tritium consumption, in addition to its longer term goal of an attractive fusion energy power source. Since the start of the two mega-ampere class ST facilities in 2000, the National Spherical Torus Experiment in the United States and Mega Ampere Spherical Tokamak in UK, active ST research has been conducted worldwide. More than 16 ST research facilities operating during this period have achieved remarkable advances in all fusion science areas, involving fundamental fusion energy science as well as innovation. These results suggest exciting future prospects for ST research both near term and longer term. The present paper reviews the scientific progress made by the worldwide ST research community during this new mega-ampere-ST era.

  10. Soft spherical nanostructures with a dodecagonal quasicrystal-like order.

    PubMed

    Rochal, S B; Konevtsova, O V; Shevchenko, I A; Lorman, V L

    2016-01-28

    We develop a theory which predicts curvature-related structural peculiarities of soft spherical nanostructures with a dodecagonal local arrangement of subunits. Spherical templates coated with a thin film of a soft quasicrystal (QC)-forming material constitute the most promising direction to realize these nanostructures. Disordered and perfect spherical nanostructures are simulated using two approaches. The first of them models a random QC-like spherical nanostructure with extended curvature-induced topological defects similar to scars in colloidal spherical crystals. The second approach is inspired by the physics of viral capsids. It deals with the most regular spherical nanostructures with a local QC-like order derived from three well-known planar dodecagonal tilings. We explain how the additional QC-like degrees of freedom assist the nanostructure stabilization and determine the point defect number and location without extended scar formation. Unusual for nanoassemblies snub cube geometry is shown to be the most energetically favorable global organization of these spherical QC nanostructures. PMID:26592422

  11. Asymptotics for spherical needlets

    NASA Astrophysics Data System (ADS)

    Baldi, P.; Kerkyacharian, G.; Marinucci, D.; Picard, D.

    We investigate invariant random fields on the sphere using a new type of spherical wavelets, called needlets. These are compactly supported in frequency and enjoy excellent localization properties in real space, with quasi-exponentially decaying tails. We show that, for random fields on the sphere, the needlet coefficients are asymptotically uncorrelated for any fixed angular distance. This property is used to derive CLT and functional CLT convergence results for polynomial functionals of the needlet coefficients: here the asymptotic theory is considered in the high-frequency sense. Our proposals emerge from strong empirical motivations, especially in connection with the analysis of cosmological data sets.

  12. Automated semi-spherical irradiance meter

    NASA Astrophysics Data System (ADS)

    Tecpoyotl-Torres, M.; Vera-Dimas, J. G.; Escobedo-Alatorre, J.; Cabello-Ruiz, R.; Varona, J.

    2011-09-01

    In this semi-spherical meter, a single detector is used to realize all measurements, which is located on the extreme of a rectangular ring (assumed as joined two mobile branches in order to compensate the weights), describing half-meridians from 0° up to 170°. The illumination source under test is located at the center of the mobile support, which can rotate 360° horizontally. The two combined movements allow us to obtain a semi-spherical geometry. The number of measurement points is determined by the two step-motors located under the mobile support of the luminary and on one of the two fixed arms, which support the mobile rectangular ring, respectively. The mechanical arrangement has the enough rigidity to support the precision required for the acquisition stage, based on a dsPIC. The main advantages of this arrange are: Its low costs (using recyclable materials only such as "electronic waste"), a reliable detection based on a single photo-detector, with an integrated amplification stage, and the mechanical design. The received power by the detector is useful to obtain the irradiance profile of the lighting sources under test. The semi-spherical geometry of the meter makes it useful for the analysis of directive and non directive sources, in accordance with the angle described by the mobile ring. In this work, special attention is given to LED lamps due to its impact in several sceneries of the daily life. A comparison between the irradiance patterns of two LED lamps is also given.

  13. Geometry and groups for cosmic topology

    SciTech Connect

    Kramer, Peter

    2011-03-21

    The Cosmic Microwave Background is measured by satellite observation with great precision. It offers insight into its origin in early states of the universe. Unexpected low multipole amplitudes of the incoming CMB radiation may be due to a multiply connected topology of cosmic 3-space. We present and analyze the geometry and homotopy for the family of Platonic spherical 3-manifolds, provide their harmonic analysis, and formulate topological selection rules.

  14. Spherical harmonic expansion of the Levitus Sea surface topography

    NASA Technical Reports Server (NTRS)

    Engelis, Theodossios

    1987-01-01

    Prior information for the stationary sea surface topography (SST) may be needed in altimetric solutions that intend to simultaneously improve the gravity field and determine the SST. For this purpose the oceanographically derived SST estimates are represented by a spherical harmonic expansion. The spherical harmonic coefficients are computed from a least squares adjustment of the data covering the majority of the oceanic regions of the world. Several tests are made to determine the optimum maximum degree of solution and the best configuration of the geometry of the data in order to obtain a solution that fits the data and also provides a good spectral representation of the SST.

  15. A Spherical Earth Solution for TOA Lightning Location Retrieval

    NASA Technical Reports Server (NTRS)

    Koshak, W. J.; Solakiewicz, R. J.

    1999-01-01

    The problem of retrieving ligntning, ground-strike location on a spherical Earth surface using a network of 4 or more time-of-arrival (TOA) sensors is considered, It is shown that this problem has an analytic solution and therefore does not require the use of nonlinear estimation theory (e.g., minimization). The mathematical robustness of the analytic solution is tested using computer-generated lightning sources and simulated TOA measurement errors. A summary of a quasi-analytic extension of the spherical Earth solution to an oblate spheroid Earth geometry is also provided.

  16. Strongly localized image states of spherical graphitic particles.

    PubMed

    Gumbs, Godfrey; Balassis, Antonios; Iurov, Andrii; Fekete, Paula

    2014-01-01

    We investigate the localization of charged particles by the image potential of spherical shells, such as fullerene buckyballs. These spherical image states exist within surface potentials formed by the competition between the attractive image potential and the repulsive centripetal force arising from the angular motion. The image potential has a power law rather than a logarithmic behavior. This leads to fundamental differences in the nature of the effective potential for the two geometries. Our calculations have shown that the captured charge is more strongly localized closest to the surface for fullerenes than for cylindrical nanotube. PMID:24587747

  17. Strongly Localized Image States of Spherical Graphitic Particles

    PubMed Central

    Gumbs, Godfrey

    2014-01-01

    We investigate the localization of charged particles by the image potential of spherical shells, such as fullerene buckyballs. These spherical image states exist within surface potentials formed by the competition between the attractive image potential and the repulsive centripetal force arising from the angular motion. The image potential has a power law rather than a logarithmic behavior. This leads to fundamental differences in the nature of the effective potential for the two geometries. Our calculations have shown that the captured charge is more strongly localized closest to the surface for fullerenes than for cylindrical nanotube. PMID:24587747

  18. Geometry in Medias Res

    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…

  19. Dynamic Geometry on WWW.

    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…

  20. Spherical grating spectrometers

    NASA Astrophysics Data System (ADS)

    O'Donoghue, Darragh; Clemens, J. Christopher

    2014-07-01

    We describe designs for spectrometers employing convex dispersers. The Offner spectrometer was the first such instrument; it has almost exclusively been employed on satellite platforms, and has had little impact on ground-based instruments. We have learned how to fabricate curved Volume Phase Holographic (VPH) gratings and, in contrast to the planar gratings of traditional spectrometers, describe how such devices can be used in optical/infrared spectrometers designed specifically for curved diffraction gratings. Volume Phase Holographic gratings are highly efficient compared to conventional surface relief gratings; they have become the disperser of choice in optical / NIR spectrometers. The advantage of spectrometers with curved VPH dispersers is the very small number of optical elements used (the simplest comprising a grating and a spherical mirror), as well as illumination of mirrors off axis, resulting in greater efficiency and reduction in size. We describe a "Half Offner" spectrometer, an even simpler version of the Offner spectrometer. We present an entirely novel design, the Spherical Transmission Grating Spectrometer (STGS), and discuss exemplary applications, including a design for a double-beam spectrometer without any requirement for a dichroic. This paradigm change in spectrometer design offers an alternative to all-refractive astronomical spectrometer designs, using expensive, fragile lens elements fabricated from CaF2 or even more exotic materials. The unobscured mirror layout avoids a major drawback of the previous generation of catadioptric spectrometer designs. We describe laboratory measurements of the efficiency and image quality of a curved VPH grating in a STGS design, demonstrating, simultaneously, efficiency comparable to planar VPH gratings along with good image quality. The stage is now set for construction of a prototype instrument with impressive performance.

  1. Spherically Symmetric Gravitational Fields

    NASA Astrophysics Data System (ADS)

    Vargas Moniz, P.

    The purpose of this paper is to investigate the quantum vacua directly implied by the wave function of a gravitational configuration characterized by the presence of an apparent horizon, namely the Vaidya space-time solution. Spherical symmetry is a main feature of this configuration, with a scalar field constituting a source [a Klein-Gordon geon or Berger-Chitre-Moncrief-Nutku (BCMN) type model]. The subsequent analysis requires solving a Wheeler-DeWitt equation near the apparent horizon (following the guidelinesintroduced by A. Tomimatsu,18; M. Pollock, 19 and developed by A. Hosoya and I. Oda20,21) with the scalar field herein expanded in terms of S2 spherical harmonics: midisuperspace quantization. The main results present in this paper are as follows. It is found that the mass function characteristic of the Vaidya metric is positive definite within this quantum approach. Furthermore, the inhomogeneous matter sector determines a descrip-tion in terms of open quantum (sub)systems, namely in the form of an harmonic oscillator whose frequency depends on the mass function. For this open (sub)system, a twofold approach is employed. On the one hand, an exact invariant observable is obtained from the effective Hamiltonian for the inhomogeneous matter modes. It is shown that this invariant admits a set of discrete eigenvalues which depend on the mass function. The corresponding set of eigenstates is constructed from a particular vacuum state. On the other hand, exact solutions are found for the Schrädinger equation associated with the inhomogeneous matter modes. This paper is concluded with a discussion, where two other issues are raised: (i) the possible application to realistic black hole dynamics of the results obtained for a simplified (BCMN) model and (ii) whether such vacuum states could be related with others defined instead within scalar field theories constructed in classical backgrounds.

  2. Heuristic Approach to the Schwarzschild Geometry

    NASA Astrophysics Data System (ADS)

    Visser, Matt

    In this article I present a simple Newtonian heuristic for motivating a weak-field approximation for the spacetime geometry of a point particle. The heuristic is based on Newtonian gravity, the notion of local inertial frames (the Einstein equivalence principle), plus the use of Galilean coordinate transformations to connect the freely falling local inertial frames back to the "fixed stars." Because of the heuristic and quasi-Newtonian manner in which the specific choice of spacetime geometry is motivated, we are at best justified in expecting it to be a weak-field approximation to the true spacetime geometry. However, in the case of a spherically symmetric point mass the result is coincidentally an exact solution of the full vacuum Einstein field equations — it is the Schwarzschild geometry in Painlevé-Gullstrand coordinates. This result is much stronger than the well-known result of Michell and Laplace whereby a Newtonian argument correctly estimates the value of the Schwarzschild radius — using the heuristic presented in this article one obtains the entire Schwarzschild geometry. The heuristic also gives sensible results — a Riemann flat geometry — when applied to a constant gravitational field. Furthermore, a subtle extension of the heuristic correctly reproduces the Reissner-Nordström geometry and even the de Sitter geometry. Unfortunately the heuristic construction is not truly generic. For instance, it is incapable of generating the Kerr geometry or anti-de Sitter space. Despite this limitation, the heuristic does have useful pedagogical value in that it provides a simple and direct plausibility argument (not a derivation) for the Schwarzschild geometry — suitable for classroom use in situations where the full power and technical machinery of general relativity might be inappropriate. The extended heuristic provides more challenging problems — suitable for use at the graduate level.

  3. 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…

  4. Double slotted socket spherical joint

    DOEpatents

    Bieg, Lothar F.; Benavides, Gilbert L.

    2001-05-22

    A new class of spherical joints is disclosed. These spherical joints are capable of extremely large angular displacements (full cone angles in excess of 270.degree.), while exhibiting no singularities or dead spots in their range of motion. These joints can improve or simplify a wide range of mechanical devices.

  5. Gravity inversion in spherical coordinates using tesseroids

    NASA Astrophysics Data System (ADS)

    Uieda, Leonardo; Barbosa, Valeria C. F.

    2014-05-01

    Satellite observations of the gravity field have provided geophysicists with exceptionally dense and uniform coverage of data over vast areas. This enables regional or global scale high resolution geophysical investigations. Techniques like forward modeling and inversion of gravity anomalies are routinely used to investigate large geologic structures, such as large igneous provinces, suture zones, intracratonic basins, and the Moho. Accurately modeling such large structures requires taking the sphericity of the Earth into account. A reasonable approximation is to assume a spherical Earth and use spherical coordinates. In recent years, efforts have been made to advance forward modeling in spherical coordinates using tesseroids, particularly with respect to speed and accuracy. Conversely, traditional space domain inverse modeling methods have not yet been adapted to use spherical coordinates and tesseroids. In the literature there are a range of inversion methods that have been developed for Cartesian coordinates and right rectangular prisms. These include methods for estimating the relief of an interface, like the Moho or the basement of a sedimentary basin. Another category includes methods to estimate the density distribution in a medium. The latter apply many algorithms to solve the inverse problem, ranging from analytic solutions to random search methods as well as systematic search methods. We present an adaptation for tesseroids of the systematic search method of "planting anomalous densities". This method can be used to estimate the geometry of geologic structures. As prior information, it requires knowledge of the approximate densities and positions of the structures. The main advantage of this method is its computational efficiency, requiring little computer memory and processing time. We demonstrate the shortcomings and capabilities of this approach using applications to synthetic and field data. Performing the inversion of gravity and gravity gradient

  6. Buckling of spherical capsules.

    PubMed

    Knoche, Sebastian; Kierfeld, Jan

    2011-10-01

    We investigate buckling of soft elastic capsules under negative pressure or for reduced capsule volume. Based on nonlinear shell theory and the assumption of a hyperelastic capsule membrane, shape equations for axisymmetric and initially spherical capsules are derived and solved numerically. A rich bifurcation behavior is found, which is presented in terms of bifurcation diagrams. The energetically preferred stable configuration is deduced from a least-energy principle both for prescribed volume and prescribed pressure. We find that buckled shapes are energetically favorable already at smaller negative pressures and larger critical volumes than predicted by the classical buckling instability. By preventing self-intersection for strongly reduced volume, we obtain a complete picture of the buckling process and can follow the shape from the initial undeformed state through the buckling instability into the fully collapsed state. Interestingly, the sequences of bifurcations and stable capsule shapes differ for prescribed volume and prescribed pressure. In the buckled state, we find a relation between curvatures at the indentation rim and the bending modulus, which can be used to determine elastic moduli from experimental shape analysis. PMID:22181297

  7. Immunomodulatory spherical nucleic acids

    PubMed Central

    Radovic-Moreno, Aleksandar F.; Chernyak, Natalia; Mader, Christopher C.; Nallagatla, Subbarao; Kang, Richard S.; Hao, Liangliang; Walker, David A.; Halo, Tiffany L.; Merkel, Timothy J.; Rische, Clayton H.; Anantatmula, Sagar; Burkhart, Merideth; Mirkin, Chad A.; Gryaznov, Sergei M.

    2015-01-01

    Immunomodulatory nucleic acids have extraordinary promise for treating disease, yet clinical progress has been limited by a lack of tools to safely increase activity in patients. Immunomodulatory nucleic acids act by agonizing or antagonizing endosomal toll-like receptors (TLR3, TLR7/8, and TLR9), proteins involved in innate immune signaling. Immunomodulatory spherical nucleic acids (SNAs) that stimulate (immunostimulatory, IS-SNA) or regulate (immunoregulatory, IR-SNA) immunity by engaging TLRs have been designed, synthesized, and characterized. Compared with free oligonucleotides, IS-SNAs exhibit up to 80-fold increases in potency, 700-fold higher antibody titers, 400-fold higher cellular responses to a model antigen, and improved treatment of mice with lymphomas. IR-SNAs exhibit up to eightfold increases in potency and 30% greater reduction in fibrosis score in mice with nonalcoholic steatohepatitis (NASH). Given the clinical potential of SNAs due to their potency, defined chemical nature, and good tolerability, SNAs are attractive new modalities for developing immunotherapies. PMID:25775582

  8. Consider a spherical cow

    SciTech Connect

    Harte, J.

    1985-01-01

    Consider a Spherical Cow describes relatively simple mathematical methods for developing quantitative answers to often complex environmental problems. Early chapters provide systematic insights into problem solving and identifying mathematical tools and models that lead to back of the envelope answers. Subsequent chapters treat increasingly complex problems. Solutions are sought at different levels, e.g., informed guesses, quantitative solutions based on detailed analytical models, and ultimately, critical evaluation of the consequences of removing simplifying assumptions from the models. The vehicle employed is a collection of 44 challenging problems, with clearly worked out solutions, plus ample exercises. The book, though directed at environmentalists, should appeal to chemists. Many of the problems are rooted in chemistry, including acid rain, the CO/sub 2/ greenhouse effect, chemical contamination, and the disturbing of cyclical chemical balances. Readers feeling a civic responsibility to think and speak more clearly on environmental issues will find the essential modeling and quantitative approaches valuable assets beyond the help provided by the usual courses in science and mathematics. In fact, the techniques of problem solving have broad applicability beyond the specific environmental examples covered in this text.

  9. A relativistic spherical vortex

    PubMed Central

    Pekeris, C. L.

    1976-01-01

    This investigation is concerned with stationary relativistic flows of an inviscid and incompressible fluid. In choosing a density-pressure relation to represent relativistic “incompressibility,” it is found that a fluid in which the velocity of sound equals the velocity of light is to be preferred for reasons of mathematical simplicity. In the case of axially symmetric flows, the velocity field can be derived from a stream function obeying a partial differential equation which is nonlinear. A transformation of variables is found which makes the relativistic differential equation linear. An exact solution is obtained for the case of a vortex confined to a stationary sphere. One can make all three of the components of velocity vanish on the surface of the sphere, as in the nonrelativistic Hicks spherical vortex. In the case of an isolated vortex on whose surface the pressure is made to vanish, it is found that the pressure at the center of the sphere becomes negative, as in the nonrelativistic case. A solution is also obtained for a relativistic vortex advancing in a fluid. The sphere is distorted into an oblate spheroid. The maximum possible velocity of advance of the vortex is (2/3) c. PMID:16578745

  10. Constraints on a spherically symmetric 5-d braneworld

    NASA Astrophysics Data System (ADS)

    Capistrano, A. J. S.

    2013-12-01

    We study the effect of the extrinsic curvature within the context of braneworld with constant curvature and the restrictions on a spherically symmetric geometry embedded in a 5-d bulk. As a counterexample, we recover the Schwarzschild-de Sitter black hole but with umbilical points. In a second case we find the correct geometrical structure of a black hole but the Newtonian gravity cannot be restored implying that a higher dynamical embedding must be considered.

  11. Plasma viscosity in spherical ICF implosion simulations

    NASA Astrophysics Data System (ADS)

    Vold, E.; Joglekar, A.; Ortega, M.; Moll, R.; Fenn, D.; Molvig, K.

    2016-05-01

    Inertial confinement fusion (ICF) hydrodynamic codes often ignore the effects of viscosity though recent research indicates plasma viscosity and mixing by classical transport processes may have a substantial impact on implosion dynamics. A Lagrangian hydrodynamic code in one-dimensional spherical geometry with plasma viscosity and mass transport, and including a three temperature model for ions, electrons, and radiation treated in a gray radiation diffusion approximation, is used to study differences between ICF implosions with and without plasma viscosity and to examine the role of artificial viscosity in a Lagrangian implosion simulation. It was found that plasma viscosity has substantial impacts on ICF shock dynamics characterized by shock burn timing, maximum burn temperatures, fuel compression, and time history of neutron production rates. Plasma viscosity reduces the need for artificial viscosity to maintain numerical stability in the Lagrangian formulation and this study suggests that artificial viscosity may provide an unphysical stability in implosion simulations.

  12. 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.

  13. General 2 charge geometries

    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.

  14. Geometry and Erdkinder.

    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…

  15. Cylindrical and Spherical Positron-Acoustic Shock Waves in Nonthermal Electron-Positron-Ion Plasmas

    NASA Astrophysics Data System (ADS)

    Rahman, M. M.; Alam, M. S.; Mamun, A. A.

    2015-06-01

    The nonlinear propagation of cylindrical and spherical positron-acoustic shock waves (PASWs) in an unmagnetized four-component plasma (containing nonthermal distributed hot positrons and electrons, cold mobile viscous positron fluid, and immobile positive ions) is investigated theoretically. The modified Burgers equation is derived by employing the reductive perturbation method. Analytically, the effects of cylindrical and spherical geometries, nonthermality of electrons and hot positrons, relative number density and temperature ratios, and cold mobile positron kinematic viscosity on the basic features (viz. polarity, amplitude, width, phase speed, etc.) of PASWs are briefly addressed. It is examined that the PASWs in nonplanar (cylindrical and spherical) geometry significantly differ from those in planar geometry. The relevance of our results may be useful in understanding the basic characteristics of PASWs in astrophysical and laboratory plasmas.

  16. Newtonian wormholes with spherical symmetry and tidal forces on test particles

    NASA Astrophysics Data System (ADS)

    Luz, Paulo; Lemos, José P. S.

    2015-06-01

    A spherically symmetric wormhole in Newtonian gravitation in curved space, enhanced with a connection between the mass density and the Ricci scalar, is presented. The wormhole, consisting of two connected asymptotically flat regions, inhabits a spherically symmetric curved space. The gravitational potential, gravitational field and the pressure that supports the fluid that permeates the Newtonian wormhole are computed. Particle dynamics and tidal effects in this geometry are studied. The possibility of having Newtonian black holes in this theory is sketched.

  17. Spherical crystal imaging spectrometer (SCIS) for cosmic x-ray spectroscopy.

    PubMed

    Schnopper, H W; Taylor, P O

    1980-10-01

    The application of a spherically bent crystal x-ray spectrometer to cosmic x-ray problems is discussed. This is the only geometry whose diffraction properties are preserved under all rotations of the spacecraft. The combination of Bragg reflection and spherical aberration provides for stigmatic imaging of extended sources and minimum spatial and/or spectral resolution loss arising from source extent and spacecraft pointing errors. The sensitivity of the instrument is discussed in the context of a Spacelab mission. PMID:20234612

  18. Macromolecule loading into spherical, elliptical, star-like and cubic calcium carbonate carriers.

    PubMed

    Parakhonskiy, Bogdan V; Yashchenok, Alexey M; Donatan, Senem; Volodkin, Dmitry V; Tessarolo, Francesco; Antolini, Renzo; Möhwald, Helmuth; Skirtach, Andre G

    2014-09-15

    We fabricated calcium carbonate particles with spherical, elliptical, star-like and cubical morphologies by varying relative salt concentrations and adding ethylene glycol as a solvent to slow down the rate of particle formation. The loading capacity of particles of different isotropic (spherical and cubical) and anisotropic (elliptical and star-like) geometries is investigated, and the surface area of such carriers is analysed. Potential applications of such drug delivery carriers are highlighted. PMID:25044943

  19. Milking the spherical cow - on aspherical dynamics in spherical coordinates

    NASA Astrophysics Data System (ADS)

    Pontzen, Andrew; Read, Justin I.; Teyssier, Romain; Governato, Fabio; Gualandris, Alessia; Roth, Nina; Devriendt, Julien

    2015-08-01

    Galaxies and the dark matter haloes that host them are not spherically symmetric, yet spherical symmetry is a helpful simplifying approximation for idealized calculations and analysis of observational data. The assumption leads to an exact conservation of angular momentum for every particle, making the dynamics unrealistic. But how much does that inaccuracy matter in practice for analyses of stellar distribution functions, collisionless relaxation, or dark matter core-creation? We provide a general answer to this question for a wide class of aspherical systems; specifically, we consider distribution functions that are `maximally stable', i.e. that do not evolve at first order when external potentials (which arise from baryons, large-scale tidal fields or infalling substructure) are applied. We show that a spherically symmetric analysis of such systems gives rise to the false conclusion that the density of particles in phase space is ergodic (a function of energy alone). Using this idea we are able to demonstrate that: (a) observational analyses that falsely assume spherical symmetry are made more accurate by imposing a strong prior preference for near-isotropic velocity dispersions in the centre of spheroids; (b) numerical simulations that use an idealized spherically symmetric setup can yield misleading results and should be avoided where possible; and (c) triaxial dark matter haloes (formed in collisionless cosmological simulations) nearly attain our maximally stable limit, but their evolution freezes out before reaching it.

  20. Cylindrical and spherical electron acoustic solitary waves with nonextensive hot electrons

    SciTech Connect

    Pakzad, Hamid Reza

    2011-08-15

    Nonlinear propagation of cylindrical and spherical electron-acoustic solitons in an unmagnetized plasma consisting cold electron fluid, hot electrons obeying a nonextensive distribution and stationary ions, are investigated. For this purpose, the standard reductive perturbation method is employed to derive the cylindrical/spherical Korteweg-de-Vries equation, which governs the dynamics of electron-acoustic solitons. The effects of nonplanar geometry and nonextensive hot electrons on the behavior of cylindrical and spherical electron acoustic solitons are also studied by numerical simulations.

  1. Numerical solution of the radiation transport equation in disk geometry

    NASA Technical Reports Server (NTRS)

    Spagna, George F., Jr.; Leung, Chun Ming

    1987-01-01

    An efficient numerical method for solving the problem of radiation transport in a dusty medium with two dimensional (2-D) disk geometry is described. It is a generalization of the one-dimensional quasi-diffusion method in which the transport equation is cast in diffusion form and then solved as a boundary value problem. The method should be applicable to a variety of astronomical sources, the dynamics of which are angular-momentum dominated and hence not accurately treated by spherical geometry, e.g., protoplanetary nebulae, circumstellar disks, interstellar molecular clouds, accretion disks, and disk galaxies. The computational procedure and practical considerations for implementing the method are described in detail. To illustrate the effects of 2-D radiation transport, some model results (dust temperature distributions and IR flux spectra) for externally heated, interstellar dust clouds with spherically symmetric and disk geometry are compared.

  2. GGADT: Generalized Geometry Anomalous Diffraction Theory

    NASA Astrophysics Data System (ADS)

    Hoffman, John; Tarczon, Michael; Draine, Bruce T.

    2015-10-01

    GGADT uses anomalous diffraction theory (ADT) to compute the differential scattering cross section (or the total cross sections as a function of energy) for a specified grain of arbitrary geometry (natively supports spheres, ellipsoids, and clusters of spherical monomers). It is written in Fortran 95. ADT is valid when the grain is large compared to the wavelength of incident light. GGADT can calculate either the integrated cross sections (absorption, scattering, extinction) as a function of energy, or it can calculate the differential scattering cross section as a function of scattering angle.

  3. The surface geometry of exotic nuclei

    SciTech Connect

    Carlson, B. V.; Baldini-Neto, E.; Hirata, D.; Peru-Desenfants, S.; Berger, J.-F.; Chamon, L. C.

    2007-02-12

    We analyze the surface geometry of the spherical even-even Ca, Ni, Sn and Pb nuclei using two approaches: The relativistic Dirac-Hartree-Bogoliubov one with several parameter sets and the non-relativistic Hartree-Fock-Bogoliubov one with the Gogny force. The proton and neutron density distributions are fitted to two-parameter Fermi density distributions to obtain the half-density radii and diffuseness parameters. Those parameters allow us to determine the nature of the neutron skins predicted by the models. The calculations are compared with existing experimental data.

  4. Geometry-induced protein pattern formation

    PubMed Central

    Thalmeier, Dominik; Halatek, Jacob; Frey, Erwin

    2016-01-01

    Protein patterns are known to adapt to cell shape and serve as spatial templates that choreograph downstream processes like cell polarity or cell division. However, how can pattern-forming proteins sense and respond to the geometry of a cell, and what mechanistic principles underlie pattern formation? Current models invoke mechanisms based on dynamic instabilities arising from nonlinear interactions between proteins but neglect the influence of the spatial geometry itself. Here, we show that patterns can emerge as a direct result of adaptation to cell geometry, in the absence of dynamical instability. We present a generic reaction module that allows protein densities robustly to adapt to the symmetry of the spatial geometry. The key component is an NTPase protein that cycles between nucleotide-dependent membrane-bound and cytosolic states. For elongated cells, we find that the protein dynamics generically leads to a bipolar pattern, which vanishes as the geometry becomes spherically symmetrical. We show that such a reaction module facilitates universal adaptation to cell geometry by sensing the local ratio of membrane area to cytosolic volume. This sensing mechanism is controlled by the membrane affinities of the different states. We apply the theory to explain AtMinD bipolar patterns in Δ EcMinDE Escherichia coli. Due to its generic nature, the mechanism could also serve as a hitherto-unrecognized spatial template in many other bacterial systems. Moreover, the robustness of the mechanism enables self-organized optimization of protein patterns by evolutionary processes. Finally, the proposed module can be used to establish geometry-sensitive protein gradients in synthetic biological systems. PMID:26739566

  5. Compressible inviscid instability of rapidly expanding spherical material interfaces

    NASA Astrophysics Data System (ADS)

    Mankbadi, Mina R.; Balachandar, S.

    2012-03-01

    A high-order weighted essentially non-oscillatory scheme is employed to investigate the stability of a rapidly expanding material interface produced by a spherical shock tube. The flow structure is characterized by a forward moving primary shock, a backward moving secondary shock, and a spherical contact interface in-between. We consider herein the linear inviscid regime and focus on the development of the three-dimensional perturbations around the contact interface by solving a one-dimensional system of partial differential equations. Numerical simulations are performed to illustrate the effects of the contact interface's density discontinuity on the growth of the disturbances for various spherical wave numbers. In a spherical shock tube the instability is influenced by various mechanisms which include classical Rayleigh-Taylor (RT) effects, Bell-Plesset or geometry/curvature effects, the effects of impulsively accelerating the interface, and compressibility effects. Henceforth, the present instability will be referred to as non-classical RT instability to distinguish it from classical RT instability. For an extended intermediate time period, it can be shown that the small disturbances grow exponentially as in the classical RT instability. During this stage, the exponential growth rate increases with the spherical wave number, until it saturates for very large wave numbers due to the finite thickness limitation of the numerical representation of the contact interface. The results compare favorably with previous theoretical models; but indicate that in addition to compressibility, the space-time evolution of the contact interface's thickness plays a significant role. A parametric study is performed that varies the pressure and density ratios of the initial spherical container. The characteristics of the contact interface and the applicability of various instability theories is investigated for these regimes. Furthermore, varying the pressure and density ratios aids

  6. Localization and vector spherical harmonics

    NASA Astrophysics Data System (ADS)

    von Brecht, James H.

    2016-01-01

    This paper establishes the following localization property for vector spherical harmonics: a wide class of non-local, vector-valued operators reduce to local, multiplication-type operations when applied to a vector spherical harmonic. As localization occurs in a very precise, quantifiable and explicitly computable fashion, the localization property provides a set of useful formulae for analyzing vector-valued fractional diffusion and non-local differential equations defined on S d - 1. As such analyses require a detailed understanding of operators for which localization occurs, we provide several applications of the result in the context of non-local differential equations.

  7. Basketballs as spherical acoustic cavities

    NASA Astrophysics Data System (ADS)

    Russell, Daniel A.

    2010-06-01

    The sound field resulting from striking a basketball is found to be rich in frequency content, with over 50 partials in the frequency range of 0-12 kHz. The frequencies are found to closely match theoretical expectations for standing wave patterns inside a spherical cavity. Because of the degenerate nature of the mode shapes, explicit identification of the modes is not possible without internal investigation with a microphone probe. A basketball proves to be an interesting application of a boundary value problem involving spherical coordinates.

  8. The Beauty of Geometry

    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'…

  9. Geometry of multihadron production

    SciTech Connect

    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.

  10. Want to Play Geometry?

    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…

  11. 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…

  12. Geometry + Technology = Proof

    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…

  13. Collective neutrino oscillations in nonspherical geometry

    SciTech Connect

    Dasgupta, Basudeb; Dighe, Amol; Mirizzi, Alessandro; Raffelt, Georg

    2008-08-01

    The rich phenomenology of collective neutrino oscillations has been studied only in one-dimensional or spherically symmetric systems. Motivated by the nonspherical example of coalescing neutron stars, presumably the central engines of short gamma-ray bursts, we use the Liouville equation to formulate the problem for general source geometries. Assuming the neutrino ensemble displays self-maintained coherence, the problem once more becomes effectively one-dimensional along the streamlines of the overall neutrino flux. This approach for the first time provides a formal definition of the 'single-angle approximation' frequently used for supernova neutrinos and allows for a natural generalization to nonspherical geometries. We study the explicit example of a disk-shaped source as a proxy for coalescing neutron stars.

  14. Spherical microwave confinement and ball lightning

    NASA Astrophysics Data System (ADS)

    Robinson, William Richard

    This dissertation presents the results of research done on unconventional energy technologies from 1995 to 2009. The present civilization depends on an infrastructure that was constructed and is maintained almost entirely using concentrated fuels and ores, both of which will run out. Diffuse renewable energy sources rely on this same infrastructure, and hence face the same limitations. I first examined sonoluminescence directed toward fusion, but demonstrated theoretically that this is impossible. I next studied Low Energy Nuclear Reactions and developed methods for improving results, although these have not been implemented. In 2000, I began Spherical Microwave Confinement (SMC), which confines and heats plasma with microwaves in a spherical chamber. The reactor was designed and built to provide the data needed to investigate the possibility of achieving fusion conditions with microwave confinement. A second objective was to attempt to create ball lightning (BL). The reactor featured 20 magnetrons, which were driven by a capacitor bank and operated in a 0.2 s pulse mode at 2.45 GHz. These provided 20 kW to an icosahedral array of 20 antennas. Video of plasmas led to a redesign of the antennas to provide better coupling of the microwaves to the plasma. A second improvement was a grid at the base of the antennas, which provided corona electrons and an electric field to aid quick formation of plasmas. Although fusion conditions were never achieved and ball lightning not observed, experience gained from operating this basic, affordable system has been incorporated in a more sophisticated reactor design intended for future research. This would use magnets that were originally planned. The cusp geometry of the magnetic fields is suitable for electron cyclotron resonance in the same type of closed surface that in existing reactors has generated high-temperature plasmas. Should ball lightning be created, it could be a practical power source with nearly ideal

  15. Photoelectric sheath formation around small spherical objects in space

    NASA Astrophysics Data System (ADS)

    Misra, Shikha; Mishra, S. K.; Sodha, M. S.

    2015-04-01

    The formation of a photoelectron sheath around positively charged small (˜cm) spherical objects roaming in near earth space due to the solar radiation (with continuous spectrum) and the solar wind plasma has been investigated. The sheath structure has been derived, taking into account anisotropic photoelectron flux with the Poisson equation, spherical geometry of the object, and half Fermi Dirac distribution of photoelectron velocities. Two cases, viz., when the object is illuminated by (i) isotropic or (ii) unidirectional (parallel beam) radiation, have been analyzed. The analysis predicts a spherically symmetric sheath in case of isotropic illumination, while a symmetry in sheath about a θ = π / 4 is seen in case of parallel beam illumination; θ is the angle of incidence which is the angle made by the normal to a surface element with the direction of incidence of solar radiation. The radial and angular profiles of the electric potential and electron density in the photoelectron sheath have been evaluated and illustrated graphically; the dependence of the sheath structure on the solar wind plasma parameters, material properties of the spherical object, and its size have been discussed.

  16. Photoelectric sheath formation around small spherical objects in space

    SciTech Connect

    Misra, Shikha Sodha, M. S.; Mishra, S. K.

    2015-04-15

    The formation of a photoelectron sheath around positively charged small (∼cm) spherical objects roaming in near earth space due to the solar radiation (with continuous spectrum) and the solar wind plasma has been investigated. The sheath structure has been derived, taking into account anisotropic photoelectron flux with the Poisson equation, spherical geometry of the object, and half Fermi Dirac distribution of photoelectron velocities. Two cases, viz., when the object is illuminated by (i) isotropic or (ii) unidirectional (parallel beam) radiation, have been analyzed. The analysis predicts a spherically symmetric sheath in case of isotropic illumination, while a symmetry in sheath about a θ=π/4 is seen in case of parallel beam illumination; θ is the angle of incidence which is the angle made by the normal to a surface element with the direction of incidence of solar radiation. The radial and angular profiles of the electric potential and electron density in the photoelectron sheath have been evaluated and illustrated graphically; the dependence of the sheath structure on the solar wind plasma parameters, material properties of the spherical object, and its size have been discussed.

  17. Spherically symmetric high-velocity plasma expansions into background gases

    NASA Technical Reports Server (NTRS)

    Tan, T.-H.; Borovsky, J. E.

    1986-01-01

    Spherically symmetric plasmas with high expansion velocities have been produced by irradiating targets with eight beams from the Helios CO2 laser in the presence of gases at various pressures. Attention was given to the properties of the target-emitted ions in order to obtain information about the ion-acceleration mechanisms in plasma expansions. Photoionization of the ambient gases by the soft X-ray emission from the laser-irradiated targets produced background plasmas, permitting plasma counterstreaming experiments to be performed in spherical geometry. Successful laser-target coupling in the presence of back-ground gases is obtained; modification of the ion acceleration in accordance with isothermal-expansion models is observed; and an absence of collective coupling between collisionless counterstreaming plasmas is found.

  18. The propagation of particles and fields in wormhole geometries

    NASA Astrophysics Data System (ADS)

    Sarbach, Olivier; Zannias, Thomas

    2012-08-01

    We discuss several properties of static, spherically symmetric wormholes with particular emphasis on the behavior of causal geodesics and the propagation of linear fields. We show there always exist null geodesics which are trapped in a region close to the throat. Depending upon the detailed structure of the wormhole geometry, these trapped geodesics can be stable, unlike the case of the Schwarzschild black hole. We also show that test scalar fields propagating on such wormholes are stable. However, when a mixture of ghost and Klein-Gordon scalar fields is used as a source of the Einstein equations we prove that the resulting static, spherically symmetric wormhole configurations are linearly unstable.

  19. A Potential Field Model for Spherical Sub-domains

    NASA Astrophysics Data System (ADS)

    Fisher, George H.; Bercik, David; Welsch, Brian; Kazachenko, Maria D.; CGEM Team

    2016-05-01

    Potential field models are used widely in Solar Physics to estimate coronal magnetic field geometry and connectivity, to provide lower limits on magnetic energies, and to provide initial configurations for time-dependent models of magnetic fields in the solar atmosphere. Potential field models in a spherical geometry can be global, covering the entire Sun, or confined to localized sub-volumes of the sphere. Here, we focus on the latter case.We describe an efficient potential field model for localized spherical sub-volumes (wedges consisting of upper and lower limits of radius, co-latitude, and longitude), employing a finite-difference approach for the solution. The solution is derived in terms of a "poloidal" potential, which can then be used to find either the scalar potential or the vector potential for the magnetic field (if desired), as well as all three magnetic field components. The magnetic field components are computed on the faces of spherical voxels, and the finite difference grid is consistent with the well-known "Yee" grid. The inner spherical boundary is defined by radial magnetic field measurements, and at the outer radius a source-surface boundary condition is imposed.Potential field solutions on active region scales, at full HMI resolution, and with the source surface located a solar radius above the photosphere, can be obtained on a laptop computer in just a few minutes. The three-dimensional finite difference equations are solved using NCAR's FISHPACK elliptic equation solver.The potential field model was developed by the Coronal Global Evolutionary Model (CGEM) project, funded by the NASA and NSF Strategic Capabilities program. The potential field model described here was motivated by CGEM's need for such a model. The model will be released as open-source code when the model details are published.

  20. Gingerbread-House Geometry.

    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)

  1. What Is Geometry?

    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)

  2. 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.

  3. 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)

  4. Common Geometry Module

    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

  5. CMS Geometry Through 2020

    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.

  6. Gauge Measures Large Spherical Bearing Surfaces

    NASA Technical Reports Server (NTRS)

    Davis, George L.

    1992-01-01

    Radius of spherical portion of surface computed from reading of depth gauge. Measuring tool calibrated by applying it to reference spherical surface of known radius. Used onsite, so unnecessary to ship bearings to laboratory for examination by computerized test equipment.

  7. Electromagnetic decay modes in a spherical sample of two-level atoms

    NASA Astrophysics Data System (ADS)

    Friedberg, Richard; Manassah, Jamal T.

    2008-11-01

    We find the eigenmodes of the Lienard-Wiechert kernel for a spherical geometry. We show that these consist of two series corresponding to the classical electrodynamics multipole electric and magnetic series. The electric series possesses “anomalous modes”, absent in both the magnetic series and the “scalar photon” theory.

  8. Modal testing variability of spherical marine floats.

    SciTech Connect

    Robertson, A. N.; Hemez, F. M.; Salazar, I. F.; Duffey, T. A.

    2004-01-01

    This study investigates the variability in modal data obtained from testing a set of hollow, almost spherical marine floats. Four sources of variability are investigated: unit-to -unit variability, operator-to-operator variability, test repetition, and accelerometer placement. Because moving the accelerometers implies a test setup reconfiguration, it is expected that variability due to accelerometer placement should encompass variability due to test repetition. Similarly, the unit-to-unit variability should encompass both accelerometer placement variability and test-to -test variability. Impulse and frequency response functions are estimated from the measured excitation and response of the marine floats. A series of techniques are then used to assess the variation of the modal properties between each test, including: a measure of the spread of the frequency response functions in each test group; the variation of the temporal moments, spectral moments, and principal components; and the variability of resonant frequencies and modal damping ratios extracted from the data. The effects of mass and geometry on variability are also investigated. A strong correlation between the frequency and mass is found for the fundamental mode only. The main conclusion is that the majority of analysis techniques find the unit-to-unit variability to be the largest by a significant margin. The second largest is the variability caused by accelerometer placement. Next are the operator-to-operator variability and test-to -test variability.

  9. Spherically Symmetric Solutions of Light Galileon

    NASA Astrophysics Data System (ADS)

    Momeni, D.; Houndjo, M. J. S.; Güdekli, E.; Rodrigues, M. E.; Alvarenga, F. G.; Myrzakulov, R.

    2016-02-01

    We have been studied the model of light Galileon with translational shift symmetry ϕ → ϕ + c. The matter Lagrangian is presented in the form {L}_{φ }= -η (partial φ )2+β G^{μ ν }partial _{μ }φ partial _{ν }φ . We have been addressed two issues: the first is that, we have been proven that, this type of Galileons belong to the modified matter-curvature models of gravity in type of f(R,R^{μ ν }T_{μ ν }m). Secondly, we have been investigated exact solution for spherically symmetric geometries in this model. We have been found an exact solution with singularity at r = 0 in null coordinates. We have been proven that the solution has also a non-divergence current vector norm. This solution can be considered as an special solution which has been investigated in literature before, in which the Galileon's field is non-static (time dependence). Our scalar-shift symmetrized Galileon has the simple form of ϕ = t, which it is remembered by us dilaton field.

  10. Fresnel diffraction by spherical obstacles

    NASA Technical Reports Server (NTRS)

    Hovenac, Edward A.

    1989-01-01

    Lommel functions were used to solve the Fresnel-Kirchhoff diffraction integral for the case of a spherical obstacle. Comparisons were made between Fresnel diffraction theory and Mie scattering theory. Fresnel theory is then compared to experimental data. Experiment and theory typically deviated from one another by less than 10 percent. A unique experimental setup using mercury spheres suspended in a viscous fluid significantly reduced optical noise. The major source of error was due to the Gaussian-shaped laser beam.

  11. Viscosity in spherically symmetric accretion

    NASA Astrophysics Data System (ADS)

    Ray, Arnab K.

    2003-10-01

    The influence of viscosity on the flow behaviour in spherically symmetric accretion has been studied here. The governing equation chosen has been the Navier-Stokes equation. It has been found that at least for the transonic solution, viscosity acts as a mechanism that detracts from the effectiveness of gravity. This has been conjectured to set up a limiting scale of length for gravity to bring about accretion, and the physical interpretation of such a length scale has been compared with the conventional understanding of the so-called `accretion radius' for spherically symmetric accretion. For a perturbative presence of viscosity, it has also been pointed out that the critical points for inflows and outflows are not identical, which is a consequence of the fact that under the Navier-Stokes prescription, there is a breakdown of the invariance of the stationary inflow and outflow solutions - an invariance that holds good under inviscid conditions. For inflows, the critical point gets shifted deeper within the gravitational potential well. Finally, a linear stability analysis of the stationary inflow solutions, under the influence of a perturbation that is in the nature of a standing wave, has indicated that the presence of viscosity induces greater stability in the system than has been seen for the case of inviscid spherically symmetric inflows.

  12. Solutocapillary convection in spherical shells

    NASA Astrophysics Data System (ADS)

    Subramanian, Pravin; Zebib, Abdelfattah; McQuillan, Barry

    2005-01-01

    A linear stability study of solutocapillary driven Marangoni instabilities in small spherical shells is presented. The shells contain a binary fluid with an evaporating solvent. The viscosity is a strong function of the solvent concentration, the inner surface of the shell is assumed impermeable and stress free, while nonlinear boundary conditions are modeled and prescribed at the receding outer boundary. A time-dependent diffusive state is possible and may lose stability through the Marangoni mechanism due to surface tension dependence on solvent concentration (buoyant forces are negligible in this microscale problem). A frozen-time or quasisteady state linear stability analysis is performed to compute the critical Reynolds number and degree of surface harmonics, as well as the maximum growth rate of perturbations at specified parameters. The development of maximum growth rates in time was also computed by solving the initial value problem with random initial conditions. Results from both approaches are in good agreement except at short times where there is dependence on initial conditions. The physical problem models the manufacturing of spherical shells used as targets in inertial confinement fusion experiments where perfect sphericity is demanded for efficient fusion ignition. It is proposed that the Marangoni instability might be the source of observed surface roughness. Comparisons with the available experiments are made with reasonable qualitative and quantitative agreement.

  13. Spectral sharpening by spherical sampling.

    PubMed

    Finlayson, Graham D; Vazquez-Corral, Javier; Süsstrunk, Sabine; Vanrell, Maria

    2012-07-01

    There are many works in color that assume illumination change can be modeled by multiplying sensor responses by individual scaling factors. The early research in this area is sometimes grouped under the heading "von Kries adaptation": the scaling factors are applied to the cone responses. In more recent studies, both in psychophysics and in computational analysis, it has been proposed that scaling factors should be applied to linear combinations of the cones that have narrower support: they should be applied to the so-called "sharp sensors." In this paper, we generalize the computational approach to spectral sharpening in three important ways. First, we introduce spherical sampling as a tool that allows us to enumerate in a principled way all linear combinations of the cones. This allows us to, second, find the optimal sharp sensors that minimize a variety of error measures including CIE Delta E (previous work on spectral sharpening minimized RMS) and color ratio stability. Lastly, we extend the spherical sampling paradigm to the multispectral case. Here the objective is to model the interaction of light and surface in terms of color signal spectra. Spherical sampling is shown to improve on the state of the art. PMID:22751384

  14. Theoretical Study of a Spherical Plasma Focus

    NASA Astrophysics Data System (ADS)

    Ay, Yasar

    A theoretical model is developed for two concentric electrodes spherical plasma focus device in order to investigate the plasma sheath dynamics, radiative emission, and the ion properties. The work focuses on the model development of the plasma sheath dynamics and its validation, followed by studying of the radiation effects and the beam-ion properties in such unique geometry as a pulsed source for neutrons, soft and hard x-rays, and electron and ion beams. Chapter 1 is an introduction on fusion systems including plasma focus. Chapter 2 is an extensive literature survey on plasma focus modeling and experiments including the various radiations and their mechanism. Chapter 3 details modeling and validation of the plasma sheath dynamics model with comparison between hydrogen, deuterium, tritium and deuterium-tritium mixture for the production of pulsed neutrons. Chapter 4 is a study of the radiative phase, in which neutron yield is investigated, as well as the predicted beam-ion properties. Chapter 5 summarizes and discusses the results. Chapter 6 provides concluding remarks and proposed future works. The phases of the developed model are the rundown phase I, rundown phase II, the reflected phase and a radiative phase. The rundown phase I starts immediately after the completion of the gas breakdown and ends when the current sheath reaches the equator point of the spherical shape. Then immediately followed by rundown phase II to start and it ends when the shock front hits the axis, which is the beginning of the reflected shock phase. Reflected shock front moves towards the incoming current sheath and meets it which is both the end of the reflected shock phase and the beginning of the radiative phase. After the reflected shock front and the current sheath meet, the current sheath continues to move radially inward by compressing the produced plasma column until it reaches the axis. Since the discharge current contains important information about the plasma dynamic

  15. Hydrodynamic interactions of cilia on a spherical body

    NASA Astrophysics Data System (ADS)

    Nasouri, Babak; Elfring, Gwynn J.

    2015-11-01

    The emergence of metachronal waves in ciliated microorganisms can arise solely from the hydrodynamic interactions between the cilia. For a chain of cilia attached to a flat ciliate, it was observed that fluid forces can lead the system to form a metachronal wave. However, several microorganisms such as paramecium and volvox possess a curved shaped ciliate body. To understand the effect of this geometry on the formation of metachronal waves, we evaluate the hydrodynamic interactions of cilia near a large spherical body. Using a minimal model, we show that for a chain of cilia around the sphere, the embedded periodicity in the geometry leads the system to synchronize. We also report an emergent wave-like behavior when an asymmetry is introduced to the system.

  16. Spherically-arranged piecewise planar hologram for capturing a diffracted object wave field in 360 degree

    NASA Astrophysics Data System (ADS)

    Oh, Seungtaik; Seo, Hoyong; Hwang, Chi-Young; Lee, Beom-Ryeol; Son, Wookho

    2013-05-01

    We present a new method to record and reconstruct a diffracted object wave field in all directions. For this, we are going to use spherically-arranged holograms instead of a single spherical hologram. Our spherically-arranged holograms are constructed to store all components of plane waves propagating in all directions. One can use the well-known efficient FFT-based diffraction formulae such as Fresnel transform and angular spectrum method in generation and reconstruction of our spherically-arranged holograms. It is possible to synthesize a new hologram with an arbitrary position and orientation without the geometry of the object. Numerical experiments are presented to show the effectiveness of our method.

  17. Polymeric carriers: role of geometry in drug delivery

    PubMed Central

    Simone, Eric A; Dziubla, Thomas D; Muzykantov, Vladimir R

    2009-01-01

    The unique properties of synthetic nanostructures promise a diverse set of applications as carriers for drug delivery, which are advantageous in terms of biocompatibility, pharmacokinetics, targeting and controlled drug release. Historically, more traditional drug delivery systems have focused on spherical carriers. However, there is a growing interest in pursuing non-spherical carriers, such as elongated or filamentous morphologies, now available due to novel formulation strategies. Unique physiochemical properties of these supramolecular structures offer distinct advantages as drug delivery systems. In particular, results of recent studies in cell cultures and lab animals indicate that rational design of carriers of a given geometry (size and shape) offers an unprecedented control of their longevity in circulation and targeting to selected cellular and subcellular locations. This article reviews drug delivery aspects of non-spherical drug delivery systems, including material selection and formulation, drug loading and release, biocompatibility, circulation behavior, targeting and subcellular addressing. PMID:19040392

  18. Exact Relativistic Newtonian Representation of Gravitational static Spacetime Geometries

    NASA Astrophysics Data System (ADS)

    Ghosh, Shubhrangshu; Sarkar, Tamal; Bhadra, Arunava

    2016-09-01

    We construct a self-consistent relativistic Newtonian analogue corresponding to gravitational static spherical symmetric spacetime geometries, starting directly from a generalized scalar relativistic gravitational action in a Newtonian framework, which gives geodesic equations of motion identical to those of the parent metric. Consequently, the derived velocity-dependent relativistic scalar potential, which is a relativistic generalization of the Newtonian gravitational potential, exactly reproduces the relativistic gravitational features corresponding to any static spherical symmetric spacetime geometry in its entirety, including all the experimentally tested gravitational effects in the weak field up to the present. This relativistic analogous potential is expected to be quite useful in studying a wide range of astrophysical phenomena, especially in strong field gravity.

  19. Geometry and Cloaking Devices

    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.

  20. A Spherical Aerial Terrestrial Robot

    NASA Astrophysics Data System (ADS)

    Dudley, Christopher J.

    This thesis focuses on the design of a novel, ultra-lightweight spherical aerial terrestrial robot (ATR). The ATR has the ability to fly through the air or roll on the ground, for applications that include search and rescue, mapping, surveillance, environmental sensing, and entertainment. The design centers around a micro-quadcopter encased in a lightweight spherical exoskeleton that can rotate about the quadcopter. The spherical exoskeleton offers agile ground locomotion while maintaining characteristics of a basic aerial robot in flying mode. A model of the system dynamics for both modes of locomotion is presented and utilized in simulations to generate potential trajectories for aerial and terrestrial locomotion. Details of the quadcopter and exoskeleton design and fabrication are discussed, including the robot's turning characteristic over ground and the spring-steel exoskeleton with carbon fiber axle. The capabilities of the ATR are experimentally tested and are in good agreement with model-simulated performance. An energy analysis is presented to validate the overall efficiency of the robot in both modes of locomotion. Experimentally-supported estimates show that the ATR can roll along the ground for over 12 minutes and cover the distance of 1.7 km, or it can fly for 4.82 minutes and travel 469 m, on a single 350 mAh battery. Compared to a traditional flying-only robot, the ATR traveling over the same distance in rolling mode is 2.63-times more efficient, and in flying mode the system is only 39 percent less efficient. Experimental results also demonstrate the ATR's transition from rolling to flying mode.

  1. Superradiance in spherical layered nanostructures

    NASA Astrophysics Data System (ADS)

    Goupalov, S. V.

    2016-06-01

    We propose a design of a spherically symmetric nanostructure consisting of alternate concentric semiconductor and dielectric layers. The exciton states in different semiconductor layers of such a structure interact via the common electromagnetic field of light. We show that, if the exciton states in N semiconductor layers are in resonance with one another, then a superradiant state emerges under optical excitation of such a structure. We discuss the conditions under which superradiance can be observed and show that they strongly depend on the valence-band structure of the semiconductor layers.

  2. Electronic switching spherical array antenna

    NASA Technical Reports Server (NTRS)

    Stockton, R.

    1978-01-01

    This work was conducted to demonstrate the performance levels attainable with an ESSA (Electronic Switching Spherical Array) antenna by designing and testing an engineering model. The antenna was designed to satisfy general spacecraft environmental requirements and built to provide electronically commandable beam pointing capability throughout a hemisphere. Constant gain and beam shape throughout large volumetric coverage regions are the principle characteristics. The model is intended to be a prototype of a standard communications and data handling antenna for user scientific spacecraft with the Tracking and Data Relay Satellite System (TDRSS). Some additional testing was conducted to determine the feasibility of an integrated TDRSS and GPS (Global Positioning System) antenna system.

  3. APPARATUS FOR GRINDING SPHERICAL BODIES

    DOEpatents

    Burch, R.F. Jr.

    1963-09-24

    A relatively inexpensive device is described for grinding rough ceramic bodies into accurate spherical shapes using a conventional drill press and a belt sander. A horizontal disk with an abrasive-surfaced recess in its lower face is mounted eccentrically on a vertical shaft which is forced downward against a stop by a spring. Bodies to be ground are placed in the recess and are subjected to the abrasive action of the belt sander as the disk is rotated by the drill press. (AEC)

  4. Physics of Spherical Torus Plasmas

    SciTech Connect

    Peng, Yueng Kay Martin

    2000-01-01

    Broad and important progress in plasma tests, theory, new experiments, and future visions of the spherical torus (ST, or very low aspect ratio tokamaks) have recently emerged. These have substantially improved our understanding of the potential properties of the ST plasmas, since the preliminary calculation of the ST magnetohydrodynamic equilibria more than a decade ago. Exciting data have been obtained from concept exploration level ST experiments of modest capabilities (with major radii up to 35 cm), making important scientific contributions to toroidal confinement in general. The results have helped approval and construction of new and/or more powerful ST experiments, and stimulated an increasing number of theoretical calculations of interest to magnetic fusion energy. Utilizing the broad knowledge base from the successful tokamak and advanced tokamak research, a wide range of new ST physics features has been suggested. These properties of the ST plasma will be tested at the 1 MA level with major radius up to similar to 80 cm in the new proof of principle devices National Spherical Torus Experiment (NSTX, U.S.) [M. Peng , European Conf. Abst. 22C, 451 (1998); S. M. Kaye , Fusion Technol. 36, 16 (1999); M. Ono , "Exploration of Spherical Torus Physics in the NSTX Device," 17th IAEA Fusion Energy Conf., paper IAEA-CN-69/ICP/01 (R), Yokohama, Japan (1998)], Mega Ampere Spherical Tokamak (MAST, U.K.) [A. C. Darke , Fusion Technol. 1, 799 (1995); Q. W. Morris , Proc. Int. Workshop on ST (Ioffe Inst., St. Petersburg, 1997), Vol. 1, p. 290], and Globus-M (R.F.) [V. K. Gusev , European Conf. Abst. 22C, 576 (1998)], which have just started full experimental operation. New concept exploration experiments, such as Pegasus (University of Wisconsin) [R. Fonck and the PEGASUS Team, Bull. Am. Phys. Soc. 44, 267 (1999)], Helicity Injected Tokamak-II (HIT-II, University of Washington) [T. R. Jarboe , Phys. Plasmas 5, 1807 (1998)], and Current Drive Experiment-Upgrade (CDX

  5. Three-dimensional spherical analyses of cosmological spectroscopic surveys

    NASA Astrophysics Data System (ADS)

    Nicola, Andrina; Refregier, Alexandre; Amara, Adam; Paranjape, Aseem

    2014-09-01

    Spectroscopic redshift surveys offer great prospects for constraining the dark sector in cosmology. Future surveys will however be both deep and wide and will thus require an analysis in three-dimensional spherical geometry. We review and compare several methods which have been proposed in the literature for this purpose, focusing in particular on implementations of the spherical harmonic tomography (SHT) power spectrum Clij and the spherical Fourier Bessel (SFB) power spectrum Cl(k ,k'). Using a Fisher analysis, we compare the forecasted constraints on cosmological parameters using these statistics. These constraints typically rely on approximations such as the Limber approximation and make specific choices in the numerical implementation of each statistic. Using a series of toy models, we explore the applicability of these approximations and study the sensitivity of the SHT and SFB statistics to the details of their implementation. In particular, we show that overlapping redshift bins may improve cosmological constraints using the SHT statistic when the number of bins is small, and that the SFB constraints are quite robust to changes in the assumed distance-redshift relation. We also find that the SHT can be tailored to be more sensitive to modes at redshifts close to the survey boundary, while the SFB appears better suited to capture information beyond the smooth shape of the power spectrum. In this context, we discuss the pros and cons of the different techniques and their impact on the design and analysis of future wide field spectroscopic surveys.

  6. Performance of Spherically Focused Air-Coupled Ultrasonic Transducers

    NASA Astrophysics Data System (ADS)

    Chimenti, D. E.; Song, Junho

    2007-03-01

    This paper reports the development, testing, and performance evaluation of spherically focused capacitive air-coupled ultrasonic transducers 1 and 5 cm in diameter. A flexible micro-machined copper/polyimide backplate permits a conformal fit to a spherically shaped fixture, forming the rear capacitor plate. A spherically deformed 6-μm aluminized Mylar foil forms the front capacitor plate, completing the transducer. The device's frequency spectrum is centered near 800 kHz with -6dB points at about 400 and 1200 kHz. The device's focal-plane behavior is successfully modeled theoretically as a focused piston radiator. The imaging and defect detection capabilities of the new transducer are demonstrated in a series of critical tests: a 250-μm wire is easily imaged in a confocal geometry with a second device. Composite, honeycomb, and wood samples are imaged in through-transmission C-scans, showing internal defects. A printed circuit board is imaged, showing features as small as 200-μm.

  7. Nonlinear thermoelastic stress analysis of spherically curved solar panels

    SciTech Connect

    Vallabhan, C.V.G.; Vungutur, K.; Selvam, R.P.

    1984-10-01

    Spherically curved glass panels are used to concentrate solar energy onto a line focus in fixed mirror distributed focus type solar collectors. These solar panels consists of thin flat glass plates bent to form a spherical surface, glued onto a paper honeycomb backing, and covered with steel plate at the back and with plastic strips on the sides. Stresses are produced in the glass plates as they are formed into spherical surfaces. In addition, when the solar receiver is not in focus relative to the bowl and the sun, a mirror hot spot condition is developed, resulting in large thermally induced stresses within glass plates. The curved glass panel is modeled as a plate on elastic foundation in order to represent the behavior of the plate in relation to other panel components. Since lateral deflections of these plates are large compared to their thickness, nonlinear von Karman plate equations are used in the analysis. A computer model has been prepared to assist in the nonlinear analysis of stresses using finite difference method. The model has flexibility to analyze a variety of rectangular plate geometries subjected to thermal and other applied loads.

  8. Zonal Flow Velocimetry in Spherical Couette Flow using Acoustic Modes

    NASA Astrophysics Data System (ADS)

    Adams, Matthew M.; Mautino, Anthony R.; Stone, Douglas R.; Triana, Santiago A.; Lekic, Vedran; Lathrop, Daniel P.

    2015-11-01

    We present studies of spherical Couette flows using the technique of acoustic mode Doppler velocimetry. This technique uses rotational splittings of acoustic modes to infer the azimuthal velocity profile of a rotating flow, and is of special interest in experiments where direct flow visualization is impractical. The primary experimental system consists of a 60 cm diameter outer spherical shell concentric with a 20 cm diameter sphere, with air or nitrogen gas serving as the working fluid. The geometry of the system approximates that of the Earth's core, making these studies geophysically relevant. A turbulent shear flow is established in the system by rotating the inner sphere and outer shell at different rates. Acoustic modes of the fluid volume are excited using a speaker and measured via microphones, allowingdetermination of rotational splittings. Preliminary results comparing observed splittings with those predicted by theory are presented. While the majority of these studies were performed in the 60 cm diameter device using nitrogen gas, some work has also been done looking at acoustic modes in the 3 m diameter liquid sodium spherical Couette experiment. Prospects for measuring zonal velocity profiles in a wide variety of experiments are discussed.

  9. The Helen of Geometry

    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.

  10. The Geometry of Viruses.

    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)

  11. Gravity is Geometry.

    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)

  12. Sliding vane geometry turbines

    DOEpatents

    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.

  13. Making Solid Geometry Solid.

    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)

  14. Fractal geometry of music.

    PubMed Central

    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

  15. Geometry and physics

    PubMed Central

    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

  16. GEOMETRY, TENTATIVE GUIDES.

    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…

  17. 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.

  18. Listening to Geometry

    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…

  19. Geometry of PDE's. IV

    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.

  20. Collective Motion of Spherical Bacteria

    PubMed Central

    Rabani, Amit; Ariel, Gil; Be'er, Avraham

    2013-01-01

    A large variety of motile bacterial species exhibit collective motions while inhabiting liquids or colonizing surfaces. These collective motions are often characterized by coherent dynamic clusters, where hundreds of cells move in correlated whirls and jets. Previously, all species that were known to form such motion had a rod-shaped structure, which enhances the order through steric and hydrodynamic interactions. Here we show that the spherical motile bacteria Serratia marcescens exhibit robust collective dynamics and correlated coherent motion while grown in suspensions. As cells migrate to the upper surface of a drop, they form a monolayer, and move collectively in whirls and jets. At all concentrations, the distribution of the bacterial speed was approximately Rayleigh with an average that depends on concentration in a non-monotonic way. Other dynamical parameters such as vorticity and correlation functions are also analyzed and compared to rod-shaped bacteria from the same strain. Our results demonstrate that self-propelled spherical objects do form complex ordered collective motion. This opens a door for a new perspective on the role of cell aspect ratio and alignment of cells with regards to collective motion in nature. PMID:24376741

  1. A feasibility study for the spherical torus experiment

    SciTech Connect

    Lazarus, E; Peng, Yueng Kay Martin

    1985-10-01

    Oak Ridge National Laboratory (ORNL) proposes to build the Spherical Torus Experiment (STX), a very low aspect ratio toroidal confinement device. This proposal concentrates on tokamak operation of the experiment; however, it can in principle be operated as a pinch or reversed-field pinch as well. As a tokamak, the spherical torus confines a plasma that is characterized by high toroidal beta, low poloidal beta, large natural elongation, high plasma current for a given edge q, and strong paramagnetism. These features combine to offer the possibility of a compact, low-field fusion device. The figure below shows that when compared to a conventional tokamak the spherical torus represents a major change in geometry. The primary goals of the experiment will be to demonstrate a capability for high beta (20%) in the first stability regime, to extend our knowledge of tokamak confinement scaling, and to test oscillating-field current drive. The experiment will operate in the high-beta, collisionless regime, which is achieved in STX at low temperatures because of the geometry. At a minimum, operation of STX will help to resolve fundamental questions regarding the scaling of beta and confinement in tokamaks. Complete success in this program would have a significant impact on toroidal fusion research in that it would demonstrate solutions to the problems of beta and steady-state operation in the tokamak. The proposed device has a major radius of 0.45 m, a toroidai field of 0.5 T, a plasma current of 900 kA, and heating by neutral beam injection. We estimate 30 months for design, construction, and assembly. The budget estimate, including contingency and escalation, is $6.8 million.

  2. 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.

  3. Axi-symmetric patterns of active polar filaments on spherical and composite surfaces

    NASA Astrophysics Data System (ADS)

    Srivastava, Pragya; Rao, Madan

    2014-03-01

    Experiments performed on Fission Yeast cells of cylindrical and spherical shapes, rod-shaped bacteria and reconstituted cylindrical liposomes suggest the influence of cell geometry on patterning of cortical actin. A theoretical model based on active hydrodynamic description of cortical actin that includes curvature-orientation coupling predicts spontaneous formation of acto-myosin rings, cables and nodes on cylindrical and spherical geometries [P. Srivastava et al, PRL 110, 168104(2013)]. Stability and dynamics of these patterns is also affected by the cellular shape and has been observed in experiments performed on Fission Yeast cells of spherical shape. Motivated by this, we study the stability and dynamics of axi-symmetric patterns of active polar filaments on the surfaces of spherical, saddle shaped and conical geometry and classify the stable steady state patterns on these surfaces. Based on the analysis of the fluorescence images of Myosin-II during ring slippage we propose a simple mechanical model for ring-sliding based on force balance and make quantitative comparison with the experiments performed on Fission Yeast cells. NSF Grant DMR-1004789 and Syracuse Soft Matter Program.

  4. Plasma instability in fast spherical discharge induced by a preionization

    SciTech Connect

    Antsiferov, P. S.; Dorokhin, L. A.

    2015-04-07

    As it was shown earlier, fast discharge (dI/dt ∼ 10{sup 12 }A/s and I{sub max} ≈ 40 kA) in a spherical cavity (Al{sub 2}O{sub 3}, inner diameter 11 mm, 4 mm apertures for the current supply) filled with working gas (Ar and Xe, pressure 80 Pa), results in the formation of a plasma with the form close to spherical. The physical mechanism can be the cumulation of a convergent shock wave, which was originated near the inner surface of the discharge cavity. It was also shown for the cylindrical fast discharge that the preionization influences the dynamics of the cylindrical convergent shock wave, its evolutions becomes faster. The present work is devoted to the study of the influence of the preionization on the plasma formation in the fast discharge with spherical geometry (Ar, 80 Pa). The inductive storage with plasma erosion opening switch was used as a current driver. The spatial structure of the discharge plasma was studied by means of a pin-hole camera with the microchannel plate (MCP) detector with time gate of 5 ns. The extreme ultra violet spectra were studied by means of the grazing incidence spectrometer with the same MCP detector with time gate of 20 ns. Beside the expected effects (reduction of the spherical plasma formation time and some increase of the electron temperature), the preionization of the discharge by the current 500 A results also in the development of the plasma instabilities and destruction of the compact plasma ball in several tens of nanoseconds. Possible mechanism of the instability is discussed.

  5. Plasma instability in fast spherical discharge induced by a preionization

    NASA Astrophysics Data System (ADS)

    Antsiferov, P. S.; Dorokhin, L. A.

    2015-04-01

    As it was shown earlier, fast discharge (dI/dt ˜ 1012 A/s and Imax ≈ 40 kA) in a spherical cavity (Al2O3, inner diameter 11 mm, 4 mm apertures for the current supply) filled with working gas (Ar and Xe, pressure 80 Pa), results in the formation of a plasma with the form close to spherical. The physical mechanism can be the cumulation of a convergent shock wave, which was originated near the inner surface of the discharge cavity. It was also shown for the cylindrical fast discharge that the preionization influences the dynamics of the cylindrical convergent shock wave, its evolutions becomes faster. The present work is devoted to the study of the influence of the preionization on the plasma formation in the fast discharge with spherical geometry (Ar, 80 Pa). The inductive storage with plasma erosion opening switch was used as a current driver. The spatial structure of the discharge plasma was studied by means of a pin-hole camera with the microchannel plate (MCP) detector with time gate of 5 ns. The extreme ultra violet spectra were studied by means of the grazing incidence spectrometer with the same MCP detector with time gate of 20 ns. Beside the expected effects (reduction of the spherical plasma formation time and some increase of the electron temperature), the preionization of the discharge by the current 500 A results also in the development of the plasma instabilities and destruction of the compact plasma ball in several tens of nanoseconds. Possible mechanism of the instability is discussed.

  6. Geometry and mechanics of thin growing bilayers.

    PubMed

    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

  7. 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.

  8. Physics and geometry

    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.

  9. Puzzle geometry and rigidity

    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.

  10. 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.

  11. Cylindrical geometry hall thruster

    DOEpatents

    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.

  12. Measuring Spherical Harmonic Coefficients on a Sphere

    SciTech Connect

    Pollaine, S; Haan, S W

    2003-05-16

    The eigenfunctions of Rayleigh-Taylor modes on a spherical capsule are the spherical harmonics Y{sub l,m} These can be measured by measuring the surface perturbations along great circles and fitting them to the first few modes by a procedure described in this article. For higher mode numbers, it is more convenient to average the Fourier power spectra along the great circles, and then transform them to spherical harmonic modes by an algorithm derived here.

  13. Archimedes' floating bodies on a spherical Earth

    NASA Astrophysics Data System (ADS)

    Rorres, Chris

    2016-01-01

    Archimedes was the first to systematically find the centers of gravity of various solid bodies and to apply this concept in determining stable configurations of floating bodies. In this paper, we discuss an error in a proof developed by Archimedes that involves determining whether a uniform, spherical cap will float stably with its base horizontal in a liquid on a spherical Earth. We present a simpler, corrected proof and discuss aspects of his proof regarding a spherical cap that is not uniform.

  14. MUSCLE: MUltiscale Spherical-ColLapse Evolution

    NASA Astrophysics Data System (ADS)

    Neyrinck, Mark C.

    2016-05-01

    MUSCLE (MUltiscale Spherical ColLapse Evolution) produces low-redshift approximate N-body realizations accurate to few-Megaparsec scales. It applies a spherical-collapse prescription on multiple Gaussian-smoothed scales. It achieves higher accuracy than perturbative schemes (Zel'dovich and second-order Lagrangian perturbation theory - 2LPT), and by including the void-in-cloud process (voids in large-scale collapsing regions), solves problems with a single-scale spherical-collapse scheme.

  15. 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.

  16. Atomic and molecular effects on spherically convergent ion flow. I. Single atomic species

    SciTech Connect

    Emmert, G. A.; Santarius, J. F.

    2010-01-15

    A formalism for analyzing the effect of ion-neutral gas interactions on the flow of ions between nearly transparent electrodes in spherical geometry has been developed for atomic ions in a weakly ionized plasma, so that the important atomic effects are charge exchange and ion impact ionization. The formalism is applied to spherical, gridded, inertial-electrostatic confinement (IEC) devices. The formalism yields detailed information about the energy spectra of the ions and fast neutral atoms, and the resulting fusion rate for {sup 3}He ions in a background {sup 3}He gas. The results are illustrated with an example calculation for the Wisconsin IEC device operating on {sup 3}He.

  17. On the finite-size scalling equation for the spherical model

    SciTech Connect

    Brankov, J.G.; Tonchev, N.S. )

    1988-07-01

    The mean spherical model with an arbitrary interaction potential, the Fourier transform of which has a long-wavelength exponent {sigma}, 0 < {sigma} {<=} 2, is considered under periodic boundary conditions and fully finite geometry in d dimensions, when {sigma} < d < 2{sigma}. A new form of the finite-size scaling equation for the spherical field in the critical region is derived, which relates the temperature shift to Madelung-type lattice constants. The method of derivation makes use of the Poisson summation formula and a Laplace transformation of the momentum-space correlation function.

  18. Integral geometry and holography

    DOE PAGESBeta

    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

  19. 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.

  20. Emergent Complex Network Geometry

    PubMed Central

    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

  1. Integral geometry and holography

    SciTech Connect

    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 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 AdS3 whose kinematic space is two-dimensional de Sitter space.

  2. Libsharp - spherical harmonic transforms revisited

    NASA Astrophysics Data System (ADS)

    Reinecke, M.; Seljebotn, D. S.

    2013-06-01

    We present libsharp, a code library for spherical harmonic transforms (SHTs), which evolved from the libpsht library and addresses several of its shortcomings, such as adding MPI support for distributed memory systems and SHTs of fields with arbitrary spin, but also supporting new developments in CPU instruction sets like the Advanced Vector Extensions (AVX) or fused multiply-accumulate (FMA) instructions. The library is implemented in portable C99 and provides an interface that can be easily accessed from other programming languages such as C++, Fortran, Python, etc. Generally, libsharp's performance is at least on par with that of its predecessor; however, significant improvements were made to the algorithms for scalar SHTs, which are roughly twice as fast when using the same CPU capabilities. The library is available at http://sourceforge.net/projects/libsharp/ under the terms of the GNU General Public License.

  3. Nonadiabatic charged spherical gravitational collapse

    SciTech Connect

    Di Prisco, A.; Herrera, L.; Le Denmat, G.; MacCallum, M. A. H.; Santos, N. O.

    2007-09-15

    We present a complete set of the equations and matching conditions required for the description of physically meaningful charged, dissipative, spherically symmetric gravitational collapse with shear. Dissipation is described with both free-streaming and diffusion approximations. The effects of viscosity are also taken into account. The roles of different terms in the dynamical equation are analyzed in detail. The dynamical equation is coupled to a causal transport equation in the context of Israel-Stewart theory. The decrease of the inertial mass density of the fluid, by a factor which depends on its internal thermodynamic state, is reobtained, with the viscosity terms included. In accordance with the equivalence principle, the same decrease factor is obtained for the gravitational force term. The effect of the electric charge on the relation between the Weyl tensor and the inhomogeneity of the energy density is discussed.

  4. Wormhole dynamics in spherical symmetry

    SciTech Connect

    Hayward, Sean A.

    2009-06-15

    A dynamical theory of traversable wormholes is detailed in spherical symmetry. Generically a wormhole consists of a tunnel of trapped surfaces between two mouths, defined as temporal outer trapping horizons with opposite senses, in mutual causal contact. In static cases, the mouths coincide as the throat of a Morris-Thorne wormhole, with surface gravity providing an invariant measure of the radial curvature or ''flaring-out''. The null energy condition must be violated at a wormhole mouth. Zeroth, first, and second laws are derived for the mouths, as for black holes. Dynamic processes involving wormholes are reviewed, including enlargement or reduction, and interconversion with black holes. A new area of wormhole thermodynamics is suggested.

  5. Non-Euclidean geometry of twisted filament bundle packing

    PubMed Central

    Bruss, Isaac R.; Grason, Gregory M.

    2012-01-01

    Densely packed and twisted assemblies of filaments are crucial structural motifs in macroscopic materials (cables, ropes, and textiles) as well as synthetic and biological nanomaterials (fibrous proteins). We study the unique and nontrivial packing geometry of this universal material design from two perspectives. First, we show that the problem of twisted bundle packing can be mapped exactly onto the problem of disc packing on a curved surface, the geometry of which has a positive, spherical curvature close to the center of rotation and approaches the intrinsically flat geometry of a cylinder far from the bundle center. From this mapping, we find the packing of any twisted bundle is geometrically frustrated, as it makes the sixfold geometry of filament close packing impossible at the core of the fiber. This geometrical equivalence leads to a spectrum of close-packed fiber geometries, whose low symmetry (five-, four-, three-, and twofold) reflect non-Euclidean packing constraints at the bundle core. Second, we explore the ground-state structure of twisted filament assemblies formed under the influence of adhesive interactions by a computational model. Here, we find that the underlying non-Euclidean geometry of twisted fiber packing disrupts the regular lattice packing of filaments above a critical radius, proportional to the helical pitch. Above this critical radius, the ground-state packing includes the presence of between one and six excess fivefold disclinations in the cross-sectional order. PMID:22711799

  6. Onthe static and spherically symmetric gravitational field

    NASA Astrophysics Data System (ADS)

    Gottlieb, Ioan; Maftei, Gheorghe; Mociutchi, Cleopatra

    Starting from a generalization of Einstein 's theory of gravitation, proposed by one of the authors (Cleopatra Mociutchi), the authors study a particular spherical symmetric case. Among other one obtain the compatibility conditions for the existence of the static and spherically symmetruic gravitational filed in the case of extended Einstein equation.

  7. Light-weight spherical submergence vessel

    NASA Technical Reports Server (NTRS)

    Baker, I.

    1974-01-01

    Design vessel with very low thickness-to-radius ratio to obtain low weight, and fabricate it with aid of precision tracer-lathe to limit and control imperfections in spherical shape. Vessel is thin-walled, spherical, monocoque shell constructed from hemispheres joined with sealed and bolted meridional flange.

  8. How Spherical Is a Cube (Gravitationally)?

    ERIC Educational Resources Information Center

    Sanny, Jeff; Smith, David

    2015-01-01

    An important concept that is presented in the discussion of Newton's law of universal gravitation is that the gravitational effect external to a spherically symmetric mass distribution is the same as if all of the mass of the distribution were concentrated at the center. By integrating over ring elements of a spherical shell, we show that the…

  9. Three-point spherical mirror mount

    DOEpatents

    Cutburth, Ronald W.

    1990-01-01

    A three-point spherical mirror mount for use with lasers is disclosed. The improved mirror mount is adapted to provide a pivot ring having an outer surface with at least three spaced apart mating points to engage an inner spherical surface of a support housing.

  10. Three-point spherical mirror mount

    DOEpatents

    Cutburth, R.W.

    1984-01-23

    A three-point spherical mirror mount for use with lasers is disclosed. The improved mirror mount is adapted to provide a pivot ring having an outer surface with at least three spaced apart mating points to engage an inner spherical surface of a support housing.

  11. Instability of spherically imploding shock waves

    SciTech Connect

    Chen, H.; Hilko, B.; Zhang, L.; Panarella, E.

    1995-12-31

    The importance of spherically imploding shock waves has increased recently due to their particular applications in inertial confinement fusion (ICF) and the Spherical Pinch (SP). In particular, the stability of spherically imploding shock waves plays a critical role in the ultimate success of ICF and SP. The instability of spherically imploding shock waves is now systematically investigated. The basic state is Guderley and Landau`s unsteady self-similar solution of the implosion of a spherical shock wave. The stability analysis is conducted by combining Chandresakhar`s approach to the stability of spherical flames together. The governing equations for disturbances are derived and they use the condition that perturbed gas flow is potential. The three dimensional perturbation velocity profile and a shock front perturbation are solved by using the kinematic and dynamic boundary conditions in the shock front. The time-dependent amplitudes of the perturbations are obtained by solving the system of ordinary differential equations. This enables them to study the time history of the spherically imploding shock wave subject to perturbations. The relative amplification and decay of the amplitudes of perturbations decides the stability/instability of the spherical imploding shock waves. Preliminary results are presented.

  12. Spherical combustion clouds in explosions

    NASA Astrophysics Data System (ADS)

    Kuhl, A. L.; Bell, J. B.; Beckner, V. E.; Balakrishnan, K.; Aspden, A. J.

    2013-05-01

    This study explores the properties of spherical combustion clouds in explosions. Two cases are investigated: (1) detonation of a TNT charge and combustion of its detonation products with air, and (2) shock dispersion of aluminum powder and its combustion with air. The evolution of the blast wave and ensuing combustion cloud dynamics are studied via numerical simulations with our adaptive mesh refinement combustion code. The code solves the multi-phase conservation laws for a dilute heterogeneous continuum as formulated by Nigmatulin. Single-phase combustion (e.g., TNT with air) is modeled in the fast-chemistry limit. Two-phase combustion (e.g., Al powder with air) uses an induction time model based on Arrhenius fits to Boiko's shock tube data, along with an ignition temperature criterion based on fits to Gurevich's data, and an ignition probability model that accounts for multi-particle effects on cloud ignition. Equations of state are based on polynomial fits to thermodynamic calculations with the Cheetah code, assuming frozen reactants and equilibrium products. Adaptive mesh refinement is used to resolve thin reaction zones and capture the energy-bearing scales of turbulence on the computational mesh (ILES approach). Taking advantage of the symmetry of the problem, azimuthal averaging was used to extract the mean and rms fluctuations from the numerical solution, including: thermodynamic profiles, kinematic profiles, and reaction-zone profiles across the combustion cloud. Fuel consumption was limited to ˜ 60-70 %, due to the limited amount of air a spherical combustion cloud can entrain before the turbulent velocity field decays away. Turbulent kinetic energy spectra of the solution were found to have both rotational and dilatational components, due to compressibility effects. The dilatational component was typically about 1 % of the rotational component; both seemed to preserve their spectra as they decayed. Kinetic energy of the blast wave decayed due to the

  13. Multigroup Complex Geometry Neutron Diffusion Code System.

    Energy Science and Technology Software Center (ESTSC)

    2002-12-18

    Version 01 SNAP-3D is based on SNAP2 and is a one- two- or three-dimensional multigroup diffusion code system. It is primarily intended for neutron diffusion calculations, but it can also carry out gamma-ray calculations if the diffusion approximation is accurate enough. It is suitable for fast and thermal reactor core calculations and for shield calculations. SNAP-3D can solve the multi-group neutron diffusion equations using finite difference methods in (x,y,z), (r,theta,z), (TRI,z), (HEX,z) or (spherical) coordinates.more » The one-dimensional slab and cylindrical geometries and the two-dimensional (x,y), (r,z), (r,theta), (HEX) and (TRI) are all treated as simple special cases of three-dimensional geometries. Numerous reflective and periodic symmetry options are available and may be used to reduce the number of mesh points necessary to represent the system. Extrapolation lengths can be specified at internal and external boundaries. The problem classes are: 1) eigenvalue search for critical k-effective, 2) eigenvalue search for critical buckling, 3) eigenvalue search for critical time-constant, 4) fixed source problems in which the sources are functions of regions, 5) fixed source problems in which the sources are provided, on disc, for every mesh point and group.« less

  14. Graded geometry and Poisson reduction

    SciTech Connect

    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.

  15. 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.…

  16. Geometry: Grades 10-12.

    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…

  17. 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.

  18. Statistical mechanics of thin spherical shells

    NASA Astrophysics Data System (ADS)

    Kosmrlj, Andrej; Nelson, David R.

    We explore how thermal fluctuations affect the mechanics of thin amorphous spherical shells via renormalization group calculations. It is well known that for flat solid membranes thermal fluctuations effectively increase the bending rigidity and reduce the bulk and shear moduli. This is still true for spherical shells. However, the additional coupling between the shell curvature, the local in-plane stretching modes and the local out-of-plane undulations leads to novel phenomena. In spherical shells thermal fluctuations effectively produce negative surface tension, which is equivalent to applying external pressure. We find that small spherical shells are stable, but for sufficiently large shells this thermally generated ``pressure'' becomes big enough to crush spherical shells. Such shells can be reinflated by increasing internal pressure, where the effective shell size grows non-linearly as a function of internal pressure with a power law exponent characteristic for thermally fluctuating flat membranes under uniform tension.

  19. Stability of imploding spherical shock waves

    NASA Astrophysics Data System (ADS)

    Chen, H. B.; Zhang, L.; Panarella, E.

    1995-12-01

    The stability of spherically imploding shock waves is systematically investigated in this letter. The basic state is Guderley and Landau's unsteady self-similar solution of the implosion of a spherical shock wave. The stability analysis is conducted by combining Chandrasekhar's approach to the stability of a viscous liquid drop with Zel'dovich's approach to the stability of spherical flames. The time-dependent amplitudes of the perturbations are obtained analytically by using perturbation method. The relative amplification and decay of the amplitudes of perturbations decides the stability/instability of the spherical imploding shock waves. It is found that the growth rate of perturbations is not in exponential form and near the collapse phase of the shocks, the spherically imploding shock waves are relatively stable.

  20. Stability of imploding spherical shock waves

    SciTech Connect

    Chen, H.B.; Zhang, L.; Panarella, E.

    1995-12-01

    The stability of spherically imploding shock waves is systematically investigated in this letter. The basic state is Guderley and Landau`s unsteady self-similar solution of the implosion of a spherical shock wave. The stability analysis is conducted by combining Chandrasekhar`s approach to the stability of a viscous liquid drop with Zel`dovich`s approach to the stability of spherical flames. The time-dependent amplitudes of the perturbations are obtained analytically by using perturbation method. The relative amplification and decay of the amplitudes of perturbations are obtained analytically by using perturbation method. The relative amplification and decay of the amplitudes of perturbations decides the stability/instability of the spherical imploding shock waves. It is found that the growth rate of perturbations is not in exponential form and near the collapse phase of the shocks, the spherically imploding shock waves are relatively stable. 14 refs., 1 fig.

  1. Geometry of Quantum States

    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

  2. Ribozyme-Spherical Nucleic Acids

    PubMed Central

    Hao, Liangliang; Kouri, Fotini M.; Briley, William E.; Stegh, Alexander H.; Mirkin, Chad A.

    2015-01-01

    Ribozymes are highly structured RNA sequences that can be tailored to recognize and cleave specific stretches of mRNA. Their current therapeutic efficacy remains low due to their large size and structural instability compared to shorter therapeutically relevant RNA such as small interfering RNA (siRNA) and microRNA (miRNA). Herein, a synthetic strategy that makes use of the spherical nucleic acid (SNA) architecture to stabilize ribozymes and transfect them into live cells is reported. The properties of this novel ribozyme SNA are characterized in the context of the targeted knockdown of O6-methylguanine-DNA methyltransferase (MGMT), a DNA repair protein involved in chemotherapeutic resistance of solid tumors, foremost glioblastoma multiforme (GBM). Data showing the direct cleavage of full-length MGMT mRNA, knockdown of MGMT protein, and increased sensitization of GBM cells to therapy-mediated apoptosis, independent of transfection agents, provide compelling evidence for the promising properties of this new chemical architecture. PMID:26271335

  3. Ribozyme-Spherical Nucleic Acids.

    PubMed

    Rouge, Jessica L; Sita, Timothy L; Hao, Liangliang; Kouri, Fotini M; Briley, William E; Stegh, Alexander H; Mirkin, Chad A

    2015-08-26

    Ribozymes are highly structured RNA sequences that can be tailored to recognize and cleave specific stretches of mRNA. Their current therapeutic efficacy remains low due to their large size and structural instability compared to shorter therapeutically relevant RNA such as small interfering RNA (siRNA) and microRNA (miRNA). Herein, a synthetic strategy that makes use of the spherical nucleic acid (SNA) architecture to stabilize ribozymes and transfect them into live cells is reported. The properties of this novel ribozyme-SNA are characterized in the context of the targeted knockdown of O(6)-methylguanine-DNA methyltransferase (MGMT), a DNA repair protein involved in chemotherapeutic resistance of solid tumors, foremost glioblastoma multiforme (GBM). Data showing the direct cleavage of full-length MGMT mRNA, knockdown of MGMT protein, and increased sensitization of GBM cells to therapy-mediated apoptosis, independent of transfection agents, provide compelling evidence for the promising properties of this new chemical architecture. PMID:26271335

  4. Osmotic buckling of spherical capsules.

    PubMed

    Knoche, Sebastian; Kierfeld, Jan

    2014-11-01

    We study the buckling of elastic spherical shells under osmotic pressure with the osmolyte concentration of the exterior solution as a control parameter. We compare our results for the bifurcation behavior with results for buckling under mechanical pressure control, that is, with an empty capsule interior. We find striking differences for the buckling states between osmotic and mechanical buckling. Mechanical pressure control always leads to fully collapsed states with opposite sides in contact, whereas uncollapsed states with a single finite dimple are generic for osmotic pressure control. For sufficiently large interior osmolyte concentrations, osmotic pressure control is qualitatively similar to buckling under volume control with the volume prescribed by the osmolyte concentrations inside and outside the shell. We present a quantitative theory which also captures the influence of shell elasticity on the relationship between osmotic pressure and volume. These findings are relevant for the control of buckled shapes in applications. We show how the osmolyte concentration can be used to control the volume of buckled shells. An accurate analytical formula is derived for the relationship between the osmotic pressure, the elastic moduli and the volume of buckled capsules. This also allows use of elastic capsules as osmotic pressure sensors or deduction of elastic properties and the internal osmolyte concentration from shape changes in response to osmotic pressure changes. We apply our findings to published experimental data on polyelectrolyte capsules. PMID:25209240

  5. Intrinsic cylindrical and spherical waves

    NASA Astrophysics Data System (ADS)

    Ludlow, I. K.

    2008-02-01

    Intrinsic waveforms associated with cylindrical and spherical Bessel functions are obtained by eliminating the factors responsible for the inverse radius and inverse square radius laws of wave power per unit area of wavefront. The resulting expressions are Riccati-Bessel functions for both cases and these can be written in terms of amplitude and phase functions of order v and wave variable z. When z is real, it is shown that a spatial phase angle of the intrinsic wave can be defined and this, together with its amplitude function, is systematically investigated for a range of fixed orders and varying z. The derivatives of Riccati-Bessel functions are also examined. All the component functions exhibit different behaviour in the near field depending on the order being less than, equal to or greater than 1/2. Plots of the phase angle can be used to display the locations of the zeros of the general Riccati-Bessel functions and lead to new relations concerning the ordering of the real zeros of Bessel functions and the occurrence of multiple zeros when the argument of the Bessel function is fixed.

  6. Plasma Effects in Spherical Implosions

    NASA Astrophysics Data System (ADS)

    Bellei, Claudio; Amendt, Peter; Wilks, Scott

    2011-10-01

    A remarkable self-similar solution to the problem of a spherically converging shock was published by Guderley in 1942. Being applicable to an ideal gas, this solution neglects viscosity, thermal conduction and radiation losses and presents singularities when the shock reaches the origin. Radiation hydrodynamic codes include the effects of non-ideality (with artificial viscosity in place of real viscosity), ensuring that the solution is well-behaved at all times. However during an ICF implosion, separation of the electron and ion species occurs at the shock front. For the high Mach number (M > 10) incoming (coalesced) shock that is typical of ICF scenarios, the width of the plasma shock front is comparable to the ion-ion mean-free-path λii ~ 1 μ m and much larger than the shock front width in an unionized gas at the same density (~10-2 μ m). Ahead of the plasma shock front, electrons pre-heat the inner gas over distances λei ~(mi /me) 1 / 2λii ~ 70 μ m. This decreases the strength of the incoming shock and lowers the temperature behind the rebound shock, a phenomenon analogous to the non-ideal gas effects found in hydro-codes. Prepared by LLNL under Contract DE-AC52-07NA27344.

  7. Study on Octahedral Spherical Hohlraum

    NASA Astrophysics Data System (ADS)

    Lan, Ke; Liu, Jie; Huo, Wenyi; Li, Zhichao; Yang, Dong; Li, Sanwei; Ren, Guoli; Chen, Yaohua; Jiang, Shaoen; He, Xian-Tu; Zhang, Weiyan

    2015-11-01

    In this talk, we report our recent study on octahedral spherical hohlraum which has six laser entrance holes (LEHs). First, our study shows that the octahedral hohlraums have robust high symmetry during the capsule implosion at hohlraum-to- capsule radius ratio larger than 3.7 and have potential superiority on low backscatter without supplementary technology. Second, we study the laser arrangement and constraints of the octahedral hohlraums and give their laser arrangement design for ignition facility. Third, we propose a novel octahedral hohlraum with LEH shields and cylindrical LEHs, in order to increase the laser coupling efficiency and improve the capsule symmetry and to mitigate the influence of the wall blowoff on laser transport. Fourth, we study the sensitivity of capsule symmetry inside the octahedral hohlraums to laser power balance, pointing accuracy, deviations from the optimal position and target fabrication accuracy, and compare the results with that of tradiational cylinders and rugby hohlraums. Finally, we present our recent experimental studies on the octahedral hohlraums on SGIII prototype laser facility.

  8. Sliding mode control of a spherical haptic device featuring electrorheological fluid

    NASA Astrophysics Data System (ADS)

    Han, Young-Min; Nguyen, Hung Quoc; Choi, Seung-Bok

    2006-03-01

    This paper presents force-feedback control performance of a new type of haptic device featuring spherical geometry and smart materials that can be used for minimally invasive surgery (MIS). A spherical electrorheological (ER) joint is designed and optimized based on the mathematical torque modeling. Force response of the manufactured ER joint is then experimentally evaluated. Subsequently, the 2-DOF force-feedback device is manufactured by integrating the spherical ER joint with AC motor. In order to achieve desired force trajectories of the haptic device, a sliding mode controller (SMC), which is robust to uncertainty, is formulated and experimentally realized. Tracking control performances for various force trajectories are presented in time domain, and their tracking errors are evaluated.

  9. Spherical ion acoustic waves in pair ion plasmas with nonthermal electrons

    NASA Astrophysics Data System (ADS)

    Selim, M. M.

    2016-04-01

    Propagation of nonplanar ion acoustic waves in a plasma composed of negative and positive ions and nonthermally distributed electrons is investigated using reductive perturbation theory. The spherical Kadomtsev-Petviashvili (SKP) equation which describes the dynamics of the nonlinear spherical ion acoustic waves is derived. It is found that compressive and rarefactive ion-acoustic solitary wave characteristics significantly depend on the density and mass ratios of the positive to negative ions, the nonthermal electron parameter, and the geometry factor. The possible regions for the existence of spherical ion acoustic waves are defined precisely for typical parameters of (H+, O2 -) and (H+, H-) plasmas in the D and F-regions of the Earth's ionosphere, as well as for laboratory plasma (Ar+, F-).

  10. Raga: Monte Carlo simulations of gravitational dynamics of non-spherical stellar systems

    NASA Astrophysics Data System (ADS)

    Vasiliev, Eugene

    2014-11-01

    Raga (Relaxation in Any Geometry) is a Monte Carlo simulation method for gravitational dynamics of non-spherical stellar systems. It is based on the SMILE software (ascl:1308.001) for orbit analysis. It can simulate stellar systems with a much smaller number of particles N than the number of stars in the actual system, represent an arbitrary non-spherical potential with a basis-set or spline spherical-harmonic expansion with the coefficients of expansion computed from particle trajectories, and compute particle trajectories independently and in parallel using a high-accuracy adaptive-timestep integrator. Raga can also model two-body relaxation by local (position-dependent) velocity diffusion coefficients (as in Spitzer's Monte Carlo formulation) and adjust the magnitude of relaxation to the actual number of stars in the target system, and model the effect of a central massive black hole.

  11. Mass inflation and curvature divergence near the central singularity in spherical collapse

    NASA Astrophysics Data System (ADS)

    Guo, Jun-Qi; Joshi, Pankaj S.; Galvez Ghersi, José T.

    2015-11-01

    We study spherical scalar collapse toward a black hole formation and examine the asymptotic dynamics near the central singularity of the formed black hole. It is found that, in the vicinity of the singularity, due to the strong backreaction of a scalar field on the geometry, the mass function inflates and the Kretschmann scalar grows faster than in the Schwarzschild geometry. In collapse, the Misner-Sharp mass is a locally conserved quantity, not providing information on the black hole mass that is measured at asymptotically flat regions.

  12. Logarithmic finite-size corrections in the three-dimensional mean spherical model

    SciTech Connect

    Brankov, J.G.; Danchev, D.M. )

    1993-05-01

    The finite-size scaling prediction about logarithmic corrections in the free energy arising from corners in the geometry of the system is tested on the three-dimensional mean spherical model. The general case of boundary conditions which are periodic in d[prime] [ge] 0 dimensions and free or fixed in the remaining 3 - d[prime] dimensions is considered. Logarithmic and double-logarithmic size corrections stemming from corners, edges, and surfaces are obtained. 15 refs.

  13. Kinetic energy cascades in quasi-geostrophic convection in a spherical shell

    NASA Astrophysics Data System (ADS)

    Reshetnyak, Maxim; Hejda, Pavel

    2012-07-01

    We consider triadic nonlinear interaction in the Navier-Stokes equation for quasi-geostrophic convection in a spherical shell. This approach helps us understand the origin of kinetic energy transport in the system and the particular scheme of mode interaction, as well as the locality of energy transfer. The peculiarity of convection in the sphere, concerned with the excitation of Rossby waves, is considered. The obtained results are compared with the results of our previous study on Cartesian geometry.

  14. Equivalence of the Path Integral for Fermions in Cartesian and Spherical Coordinates

    NASA Astrophysics Data System (ADS)

    Briggs, Andrew; Camblong, Horacio E.; Ordóñez, Carlos R.

    2013-06-01

    The path integral calculation for the free energy of a spin-1/2 Dirac-fermion gas is performed in spherical polar coordinates for a flat space-time geometry. Its equivalence with the Cartesian-coordinate representation is explicitly established. This evaluation involves a relevant limiting case of the fermionic path integral in a Schwarzschild background, whose near-horizon limit has been shown to be related to black hole thermodynamics.

  15. Worldwide complete spherical Bouguer and isostatic anomaly maps

    NASA Astrophysics Data System (ADS)

    Bonvalot, S.; Balmino, G.; Briais, A.; Peyrefitte, A.; Vales, N.; Biancale, R.; Gabalda, G.; Reinquin, F.

    2011-12-01

    We present here a set of digital maps of the Earth's gravity anomalies (surface "free air", Bouguer and isostatic), computed at Bureau Gravimetric International (BGI) as a contribution to the Global Geodetic Observing Systems (GGOS) and to the global geophysical maps published by the Commission for the Geological Map of the World (CGMW). The free air and Bouguer anomaly concept is extensively used in geophysical interpretation to investigate the density distributions in the Earth's interior. Complete Bouguer anomalies (including terrain effects) are usually computed at regional scales by integrating the gravity attraction of topography elements over and beyond a given area (under planar or spherical approximations). Here, we developed and applied a worldwide spherical approach aimed to provide a set of homogeneous and high resolution gravity anomaly maps and grids computed at the Earth's surface, taking into account a realistic Earth model and reconciling geophysical and geodetic definitions of gravity anomalies. This first version (1.0) has been computed by spherical harmonics analysis / synthesis of the Earth's topography-bathymetry up to degree 10800. The detailed theory of the spherical harmonics approach is given in Balmino et al., (Journal of Geodesy, submitted). The Bouguer and terrain corrections have thus been computed in spherical geometry at 1'x1' resolution using the ETOPO1 topography/bathymetry, ice surface and bedrock models from the NOAA (National Oceanic and Atmospheric Administration) and taking into account precise characteristics (boundaries and densities) of major lakes, inner seas, polar caps and of land areas below sea level. Isostatic corrections have been computed according to the Airy Heiskanen model in spherical geometry for a constant depth of compensation of 30km. The gravity information given here is provided by the Earth Geopotential Model (EGM2008), developed at degree 2160 by the National Geospatial Intelligence Agency (NGA) (Pavlis

  16. 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.

  17. Critique of information geometry

    SciTech Connect

    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.

  18. Geometry from Gauge Theory

    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.

  19. Geometry from Gauge Theory

    SciTech Connect

    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.

  20. 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.

  1. Two interacting particles in a spherical pore

    NASA Astrophysics Data System (ADS)

    Urrutia, Ignacio; Castelletti, Gabriela

    2011-02-01

    In this work we analytically evaluate, for the first time, the exact canonical partition function for two interacting spherical particles into a spherical pore. The interaction with the spherical substrate and between particles is described by an attractive square-well and a square-shoulder potential. In addition, we obtain exact expressions for both the one particle and an averaged two particle density distribution. We develop a thermodynamic approach to few-body systems by introducing a method based on thermodynamic measures [I. Urrutia, J. Chem. Phys. 134, 104503 (2010)] for nonhard interaction potentials. This analysis enables us to obtain expressions for the pressure, the surface tension, and the equivalent magnitudes for the total and Gaussian curvatures. As a by-product, we solve systems composed of two particles outside a fixed spherical obstacle. We study the low density limit for a many-body system confined to a spherical cavity and a many-body system surrounding a spherical obstacle. From this analysis we derive the exact first order dependence of the surface tension and Tolman length. Our findings show that the Tolman length goes to zero in the case of a purely hard wall spherical substrate, but contains a zero order term in density for square-well and square-shoulder wall-fluid potentials. This suggests that any nonhard wall-fluid potential should produce a non-null zero order term in the Tolman length.

  2. Dark matter and localised fermions from spherical orbifolds?

    NASA Astrophysics Data System (ADS)

    Cacciapaglia, Giacomo; Deandrea, Aldo; Deutschmann, Nicolas

    2016-04-01

    We study a class of six-dimensional models based on positive curvature surfaces (spherical 2-orbifolds) as extra-spaces. Using the Newman-Penrose formalism, we discuss the particle spectrum in this class of models. The fermion spectrum problem, which has been addressed with flux compactifications in the past, can be avoided using localised fermions. In this framework, we find that there are four types of geometry compatible with the existence of a stable dark matter candidate and we study the simplest case in detail. Using the complementarity between collider resonance searches and relic density constraints, we show that this class of models is under tension, unless the model lies in a funnel region characterised by a resonant Higgs s-channel in the dark matter annihilation.

  3. Static spherically symmetric wormholes in f( R, T) gravity

    NASA Astrophysics Data System (ADS)

    Zubair, M.; Waheed, Saira; Ahmad, Yasir

    2016-08-01

    In this work, we explore wormhole solutions in f( R, T) theory of gravity, where R is the scalar curvature and T is the trace of stress-energy tensor of matter. To investigate this, we consider a static spherically symmetric geometry with matter contents as anisotropic, isotropic, and barotropic fluids in three separate cases. By taking into account the Starobinsky f( R) model, we analyze the behavior of energy conditions for these different kinds of fluids. It is shown that the wormhole solutions can be constructed without exotic matter in few regions of space-time. We also give the graphical illustration of the results obtained and discuss the equilibrium picture for the anisotropic case only. It is concluded that the wormhole solutions with anisotropic matter are realistic and stable in this theory of gravity.

  4. Analysis and implementation of a space resolving spherical crystal spectrometer for x-ray Thomson scattering experiments

    SciTech Connect

    Harding, E. C.; Ao, T.; Bailey, J. E.; Loisel, G.; Sinars, D. B.; Geissel, M.; Rochau, G. A.; Smith, I. C.

    2015-04-15

    The application of a space-resolving spectrometer to X-ray Thomson Scattering (XRTS) experiments has the potential to advance the study of warm dense matter. This has motivated the design of a spherical crystal spectrometer, which is a doubly focusing geometry with an overall high sensitivity and the capability of providing high-resolution, space-resolved spectra. A detailed analysis of the image fluence and crystal throughput in this geometry is carried out and analytical estimates of these quantities are presented. This analysis informed the design of a new spectrometer intended for future XRTS experiments on the Z-machine. The new spectrometer collects 6 keV x-rays with a spherically bent Ge (422) crystal and focuses the collected x-rays onto the Rowland circle. The spectrometer was built and then tested with a foam target. The resulting high-quality spectra prove that a spherical spectrometer is a viable diagnostic for XRTS experiments.

  5. Analysis and implementation of a space resolving spherical crystal spectrometer for x-ray Thomson scattering experiments.

    PubMed

    Harding, E C; Ao, T; Bailey, J E; Loisel, G; Sinars, D B; Geissel, M; Rochau, G A; Smith, I C

    2015-04-01

    The application of a space-resolving spectrometer to X-ray Thomson Scattering (XRTS) experiments has the potential to advance the study of warm dense matter. This has motivated the design of a spherical crystal spectrometer, which is a doubly focusing geometry with an overall high sensitivity and the capability of providing high-resolution, space-resolved spectra. A detailed analysis of the image fluence and crystal throughput in this geometry is carried out and analytical estimates of these quantities are presented. This analysis informed the design of a new spectrometer intended for future XRTS experiments on the Z-machine. The new spectrometer collects 6 keV x-rays with a spherically bent Ge (422) crystal and focuses the collected x-rays onto the Rowland circle. The spectrometer was built and then tested with a foam target. The resulting high-quality spectra prove that a spherical spectrometer is a viable diagnostic for XRTS experiments. PMID:25933859

  6. Simulating higher-dimensional geometries in GADRAS using approximate one-dimensional solutions.

    SciTech Connect

    Thoreson, Gregory G.; Mitchell, Dean James; Harding, Lee T.

    2013-02-01

    The Gamma Detector Response and Analysis Software (GADRAS) software package is capable of simulating the radiation transport physics for one-dimensional models. Spherical shells are naturally one-dimensional, and have been the focus of development and benchmarking. However, some objects are not spherical in shape, such as cylinders and boxes. These are not one-dimensional. Simulating the radiation transport in two or three dimensions is unattractive because of the extra computation time required. To maintain computational efficiency, higher-dimensional geometries require approximations to simulate them in one-dimension. This report summarizes the theory behind these approximations, tests the theory against other simulations, and compares the results to experimental data. Based on the results, it is recommended that GADRAS users always attempt to approximate reality using spherical shells. However, if fissile material is present, it is imperative that the shape of the one-dimensional model matches the fissile material, including the use of slab and cylinder geometry.

  7. Wrinkling crystallography on spherical surfaces

    PubMed Central

    Brojan, Miha; Terwagne, Denis; Lagrange, Romain; Reis, Pedro M.

    2015-01-01

    We present the results of an experimental investigation on the crystallography of the dimpled patterns obtained through wrinkling of a curved elastic system. Our macroscopic samples comprise a thin hemispherical shell bound to an equally curved compliant substrate. Under compression, a crystalline pattern of dimples self-organizes on the surface of the shell. Stresses are relaxed by both out-of-surface buckling and the emergence of defects in the quasi-hexagonal pattern. Three-dimensional scanning is used to digitize the topography. Regarding the dimples as point-like packing units produces spherical Voronoi tessellations with cells that are polydisperse and distorted, away from their regular shapes. We analyze the structure of crystalline defects, as a function of system size. Disclinations are observed and, above a threshold value, dislocations proliferate rapidly with system size. Our samples exhibit striking similarities with other curved crystals of charged particles and colloids. Differences are also found and attributed to the far-from-equilibrium nature of our patterns due to the random and initially frozen material imperfections which act as nucleation points, the presence of a physical boundary which represents an additional source of stress, and the inability of dimples to rearrange during crystallization. Even if we do not have access to the exact form of the interdimple interaction, our experiments suggest a broader generality of previous results of curved crystallography and their robustness on the details of the interaction potential. Furthermore, our findings open the door to future studies on curved crystals far from equilibrium. PMID:25535355

  8. A Spherical Earth Solution for TOA Lightning Location Retrieval

    NASA Technical Reports Server (NTRS)

    Koshak, William J,

    1999-01-01

    With the advent of high-speed digital computers, the method of chi square minimization is a highly practical means for analyzing a wide variety of (otherwise intractable) nonlinear inversion problems in applied mathematical physics. Little thought or effort is required to apply the chi square method to obtain quick and reasonable estimates of a solution, and the method offers a means to assess retrieval errors. Because the method is simple and practical it is sometimes hastily applied to problems that can be solved by formal analytic or quasi-analytic means. Presently, Global Atmospherics Inc. (GAI) finds the minimum of a chi square function to analyze time-of-arrival (TOA) and magnetic bearing data derived from the National Lightning Detection Network (NLDN); ellipsoidal Earth geometry is assumed. An analytic solution to this problem has not yet been attained, but the consideration and solving of less general problem statements might eventually lead to a final solution. In the present study, the problem of retrieving lightning ground-strike location on a spherical Earth surface using a network of 4 or more time-of-arrival (TOA) sensors is considered. It is shown that this problem has an analytic solution and therefore does not require the use of nonlinear estimation theory (such as the chi square method mentioned above). The mathematical robustness of the analytic solution is tested using computer-generated lightning sources and simulated TOA measurement errors. A quasi-analytic extension of the spherical Earth solution for an oblate spheroidal Earth geometry is considered in a related study. The incorporation of magnetic bearing information into these analytic solutions would lead to a general and elegant analytic retrieval scheme that would most likely replace the chi square estimation theory currently employed by Global Atmospherics Inc. (GAI).

  9. A deformable spherical planet exploration robot

    NASA Astrophysics Data System (ADS)

    Liang, Yi-shan; Zhang, Xiu-li; Huang, Hao; Yang, Yan-feng; Jin, Wen-tao; Sang, Zhong-xun

    2013-03-01

    In this paper, a deformable spherical planet exploration robot has been introduced to achieve the task of environmental detection in outer space or extreme conditions. The robot imitates the morphology structure and motion mechanism of tumbleweeds. The robot is wind-driven. It consists of an axle, a spherical steel skeleton and twelve airbags. The axle is designed as two parts. The robot contracts by contracting the two-part axle. The spherical robot installs solar panels to provide energy for its control system.

  10. Bounce-free spherical hydrodynamic implosion

    SciTech Connect

    Kagan, Grigory; Tang Xianzhu; Hsu, Scott C.; Awe, Thomas J.

    2011-12-15

    In a bounce-free spherical hydrodynamic implosion, the post-stagnation hot core plasma does not expand against the imploding flow. Such an implosion scheme has the advantage of improving the dwell time of the burning fuel, resulting in a higher fusion burn-up fraction. The existence of bounce-free spherical implosions is demonstrated by explicitly constructing a family of self-similar solutions to the spherically symmetric ideal hydrodynamic equations. When applied to a specific example of plasma liner driven magneto-inertial fusion, the bounce-free solution is found to produce at least a factor of four improvement in dwell time and fusion energy gain.

  11. Spherically symmetric solutions in covariant Horava-Lifshitz gravity

    SciTech Connect

    Alexandre, Jean; Pasipoularides, Pavlos

    2011-04-15

    We study the most general case of spherically symmetric vacuum solutions in the framework of the covariant Horava-Lifshitz gravity, for an action that includes all possible higher order terms in curvature which are compatible with power-counting normalizability requirement. We find that solutions can be separated into two main classes: (i) solutions with nonzero radial shift function, and (ii) solutions with zero radial shift function. In the case (ii), spherically symmetric solutions are consistent with observations if we adopt the view of Horava and Melby-Tomson [P. Horava and C. M. Melby-Thompson, Phys. Rev. D 82, 064027 (2010).], according to which the auxiliary field A can be considered as a part of an effective general relativistic metric, which is valid only in the IR limit. On the other hand, in the case (i), consistency with observations implies that the field A should be independent of the spacetime geometry, as the Newtonian potential arises from the nonzero radial shift function. Also, our aim in this paper is to discuss and compare these two alternative but different assumptions for the auxiliary field A.

  12. Cosmic-ray Spectra at Spherical Termination Shocks

    NASA Technical Reports Server (NTRS)

    Florinski, V.; Jokiph, J. R.

    2003-01-01

    We discuss the nature of the steady-state spectra of particles accelerated at stationary spherical shocks, such as the solar wind termination shock. In addition to the two well-know spectral regions characterized by a power-law momentum dependence and a high-energy cutoff, a new region can be identified. This consists of an enhancement of the cosmic-ray intensity (or a " bump") just below the cutoff. Similar features have been seen previously in multidimensional models and cosmic-ray modified shocks, where they were explained by acceleration and drift in the latitudinal direction along the shock face and decreasing effective shock compression ratio, respectively. We show that a similar bump may be obtained in a purely spherically symmetric geometry with no drifts, and that this effect may also have contributed to the previous results. We attribute this effect to increased shock acceleration efficiency at certain energies. We also demonstrate that a one-dimensional planar shock with a reflecting wall upstream can give a similar effect. We conclude that care is necessary in interpreting observed bumps in any given situation.

  13. Kinetic Damping in the Spectrum of the Spherical Impedance Probe

    NASA Astrophysics Data System (ADS)

    Oberrath, Jens; Brinkmann, Ralf Peter

    2015-09-01

    Active plasma resonance spectroscopy is a widely used diagnostic method and several probes in different designs have been invented. One of them is the Spherical Impedance Probe. Its resonance behavior and the influence of kinetic effects on it can be described by a general kinetic model presented by the authors. It was theoretically shown that kinetic effects are responsible for a broadening of the resonance peak in the spectrum. However, the broadening of the resonance peak in a kinetically determined spectrum in the geometry of an existing probe is not evaluated, yet. We present such a spectrum of the Spherical Impedance Probe. Therefore, the general solution of the model is expanded in an orthonormal system of basis-functions. This expansion is truncated to determine an approximated spectrum. Its resonance peak shows clearly a broadening compared to a peak in a spectrum, which is determined by a fluiddynamical model. The authors acknowledge the support by the Research Service of Leuphana University Lueneburg, the Deutsche Forschungsgemeinschaft via the Ruhr University Research School and the Federal Ministry of Education and Research in frame of the PluTO+ projekt.

  14. Interaction model between a liquid film and a spherical probe

    NASA Astrophysics Data System (ADS)

    Ledesma Alonso, Rene; Legendre, Dominique; Tordjeman, Philippe

    2012-11-01

    To find a liquid surface profile, when performing AFM measurements, probe interaction effects should be identified. Herein, the behavior of a liquid film free surface (thickness E, surface tension γ and density difference Δρ), disposed over a flat surface and in the presence of a spherical probe (radius R) is forecast. A bump-like surface shape is observed, due to the probe/film interaction (characterized by the Hamaker constant Hpl). In addition, the attraction between the film and the substrate (depicted by Hsl) opposes the axial and radial deformation ranges. Several parameters portray the equilibrium shape: Bond Bo = (ΔρgR2) / γ and modified Hamaker Ha = 4Hpl / (3 πγR2) numbers, Hamaker ratio A =Hls /Hpl , separation distance D / R and film thickness E / R . We focus on the effect of geometry, nevertheless special attention is given to the role of physical parameters. Employing an augmented Young-Laplace equation, the equilibrium profile is described by a strongly non-linear ODE. A critical distance, below which the irreversible wetting process of the spherical probe occurs, is predicted. Our results provide simple relationships between parameters, which determine the optimal scanning conditions over liquid films.

  15. Virial pressure in systems of spherical active Brownian particles.

    PubMed

    Winkler, Roland G; Wysocki, Adam; Gompper, Gerhard

    2015-09-01

    The pressure of suspensions of self-propelled objects is studied theoretically and by simulation of spherical active Brownian particles (ABPs). We show that for certain geometries, the mechanical pressure as force/area of confined systems can be equally expressed by bulk properties, which implies the existence of a nonequilibrium equation of state. Exploiting the virial theorem, we derive expressions for the pressure of ABPs confined by solid walls or exposed to periodic boundary conditions. In both cases, the pressure comprises three contributions: the ideal-gas pressure due to white-noise random forces, an activity-induced pressure ("swim pressure"), which can be expressed in terms of a product of the bare and a mean effective particle velocity, and the contribution by interparticle forces. We find that the pressure of spherical ABPs in confined systems explicitly depends on the presence of the confining walls and the particle-wall interactions, which has no correspondence in systems with periodic boundary conditions. Our simulations of three-dimensional ABPs in systems with periodic boundary conditions reveal a pressure-concentration dependence that becomes increasingly nonmonotonic with increasing activity. Above a critical activity and ABP concentration, a phase transition occurs, which is reflected in a rapid and steep change of the pressure. We present and discuss the pressure for various activities and analyse the contributions of the individual pressure components. PMID:26221908

  16. Self-similar compression flows in spherical geometry: numerical calculations and implementations

    NASA Astrophysics Data System (ADS)

    Gerin-Roze, Jean

    2009-06-01

    During the previous APS-SCCM meeting(2007) we exhibited a set of theoretical solutions for the implosion of a sphere initiated by a strong shock. We assumed that: 1. The sphere contains a perfect gas with a polytropic coefficient γ=5/3. 2. The shock follows the equation: rs/r0=(-t/tfoc)^α where α is a positive constant and where --tfoc

  17. Diffusion tensor image registration using tensor geometry and orientation features.

    PubMed

    Yang, Jinzhong; Shen, Dinggang; Davatzikos, Christos; Verma, Ragini

    2008-01-01

    This paper presents a method for deformable registration of diffusion tensor (DT) images that integrates geometry and orientation features into a hierarchical matching framework. The geometric feature is derived from the structural geometry of diffusion and characterizes the shape of the tensor in terms of prolateness, oblateness, and sphericity of the tensor. Local spatial distributions of the prolate, oblate, and spherical geometry are used to create an attribute vector of geometric feature for matching. The orientation feature improves the matching of the WM fiber tracts by taking into account the statistical information of underlying fiber orientations. These features are incorporated into a hierarchical deformable registration framework to develop a diffusion tensor image registration algorithm. Extensive experiments on simulated and real brain DT data establish the superiority of this algorithm for deformable matching of diffusion tensors, thereby aiding in atlas creation. The robustness of the method makes it potentially useful for group-based analysis of DT images acquired in large studies to identify disease-induced and developmental changes. PMID:18982691

  18. Solar proton exposure of an ICRU sphere within a complex structure Part I: Combinatorial geometry.

    PubMed

    Wilson, John W; Slaba, Tony C; Badavi, Francis F; Reddell, Brandon D; Bahadori, Amir A

    2016-06-01

    The 3DHZETRN code, with improved neutron and light ion (Z≤2) transport procedures, was recently developed and compared to Monte Carlo (MC) simulations using simplified spherical geometries. It was shown that 3DHZETRN agrees with the MC codes to the extent they agree with each other. In the present report, the 3DHZETRN code is extended to enable analysis in general combinatorial geometry. A more complex shielding structure with internal parts surrounding a tissue sphere is considered and compared against MC simulations. It is shown that even in the more complex geometry, 3DHZETRN agrees well with the MC codes and maintains a high degree of computational efficiency. PMID:27345203

  19. Solar proton exposure of an ICRU sphere within a complex structure Part I: Combinatorial geometry

    NASA Astrophysics Data System (ADS)

    Wilson, John W.; Slaba, Tony C.; Badavi, Francis F.; Reddell, Brandon D.; Bahadori, Amir A.

    2016-06-01

    The 3DHZETRN code, with improved neutron and light ion (Z ≤ 2) transport procedures, was recently developed and compared to Monte Carlo (MC) simulations using simplified spherical geometries. It was shown that 3DHZETRN agrees with the MC codes to the extent they agree with each other. In the present report, the 3DHZETRN code is extended to enable analysis in general combinatorial geometry. A more complex shielding structure with internal parts surrounding a tissue sphere is considered and compared against MC simulations. It is shown that even in the more complex geometry, 3DHZETRN agrees well with the MC codes and maintains a high degree of computational efficiency.

  20. Solar Proton Transport within an ICRU Sphere Surrounded by a Complex Shield: Combinatorial Geometry

    NASA Technical Reports Server (NTRS)

    Wilson, John W.; Slaba, Tony C.; Badavi, Francis F.; Reddell, Brandon D.; Bahadori, Amir A.

    2015-01-01

    The 3DHZETRN code, with improved neutron and light ion (Z (is) less than 2) transport procedures, was recently developed and compared to Monte Carlo (MC) simulations using simplified spherical geometries. It was shown that 3DHZETRN agrees with the MC codes to the extent they agree with each other. In the present report, the 3DHZETRN code is extended to enable analysis in general combinatorial geometry. A more complex shielding structure with internal parts surrounding a tissue sphere is considered and compared against MC simulations. It is shown that even in the more complex geometry, 3DHZETRN agrees well with the MC codes and maintains a high degree of computational efficiency.

  1. Influence of the Geometry on Mantle Convection Models

    NASA Astrophysics Data System (ADS)

    Noack, L.; Tosi, N.

    2012-04-01

    Modelling of geodynamic processes like mantle or core convection has strongly improved over the last two decades thanks to the steady development of numerical codes that tend to incorporate a more and more realistic physics. High-performance parallel computations allow the simulation of complex problems, such as the self-consistent generation of tectonic plates or the formation of planetary magnetic fields. However, the need to perform broad explorations of the parameter space and the large computational demands imposed by the non-linear, multi-scale nature of convection require several simplifications, in the domain geometry as well as in the physical complexity of the problem. A straightforward approach to limit the computational complexity of the simulations is to decrease the total number of degrees of freedom of the problem by reducing either the number of dimensions or the size of the model domain. On the one hand, for a given resolution, a 3D spherical shell clearly needs a much larger number of grid points than a 2D cylindrical shell or a 2D Cartesian box. At the resolutions typically employed to solve mantle convection problems, this difference amounts to at least a factor of a few hundreds. On the other hand, for certain problems, only a relatively small part of the mantle may be of interest, as in the case of the modelling of subduction [1], mid-ocean ridges or transform faults [2]. We adapted the code GAIA [3] to solve the Stokes problem in several different geometries (Cartesian box, cylindrical, spherical and regional-spherical) and dimensions (2D and 3D) and started a benchmark along the lines of [4] to assess the loss of accuracy when using reduced domains instead of a 3D spherical shell [5]. In general, upwellings in Cartesian geometry are rather flat, whereas the spherical geometry changes their shape to more mushroom-like structures. Furthermore, the number of plumes, which is representative of the characteristic wavelength of convection, varies

  2. 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

  3. FY 2006 Miniature Spherical Retroreflectors Final Report

    SciTech Connect

    Anheier, Norman C.; Bernacki, Bruce E.; Krishnaswami, Kannan

    2006-12-28

    Research done by the Infrared Photonics team at Pacific Northwest National Laboratory (PNNL) is focused on developing miniature spherical retroreflectors using the unique optical and material properties of chalcogenide glass to reduce both performance limiting spherical aberrations. The optimized optical performance will provide efficient signal retroreflection that enables a broad range of remote detection scenarios for mid-wave infrared (MWIR) and long-wave infrared (LWIR) sensing applications. Miniature spherical retroreflectors can be developed to aid in the detection of signatures of nuclear proliferation or other chemical vapor or radiation signatures. Miniature spherical retroreflectors are not only well suited to traditional LIDAR methods for chemical plume detection and identification, but could enable remote detection of difficult semi-volatile chemical materials or low level radiation sources.

  4. Transformation of complex spherical harmonics under rotations

    NASA Astrophysics Data System (ADS)

    Romanowski, Zbigniew; Krukowski, Stanislaw

    2007-12-01

    The algorithm rotating the complex spherical harmonics is presented. The convenient and ready to use formulae for ell = 0, 1, 2, 3 are listed. Any rotation in {\\bb R}^3 space is determined by the rotation axis and the rotation angle. The complex spherical harmonics defined in the fixed coordinate system is expanded as a linear combination of the spherical harmonics defined in the rotated coordinate system having 2ell + 1 terms, which are given explicitly. The derived formulae could be applied in quantum molecular calculations. The algorithm is based on the Cartesian representation of the spherical harmonics. The possible application of the algorithm to the evaluation of molecular integrals between slater type orbitals (STO) is described.

  5. Sphericity determination using resonant ultrasound spectroscopy

    DOEpatents

    Dixon, R.D.; Migliori, A.; Visscher, W.M.

    1994-10-18

    A method is provided for grading production quantities of spherical objects, such as roller balls for bearings. A resonant ultrasound spectrum (RUS) is generated for each spherical object and a set of degenerate sphere-resonance frequencies is identified. From the degenerate sphere-resonance frequencies and known relationships between degenerate sphere-resonance frequencies and Poisson's ratio, a Poisson's ratio can be determined, along with a 'best' spherical diameter, to form spherical parameters for the sphere. From the RUS, fine-structure resonant frequency spectra are identified for each degenerate sphere-resonance frequency previously selected. From each fine-structure spectrum and associated sphere parameter values an asphericity value is determined. The asphericity value can then be compared with predetermined values to provide a measure for accepting or rejecting the sphere. 14 figs.

  6. Sphericity determination using resonant ultrasound spectroscopy

    DOEpatents

    Dixon, Raymond D.; Migliori, Albert; Visscher, William M.

    1994-01-01

    A method is provided for grading production quantities of spherical objects, such as roller balls for bearings. A resonant ultrasound spectrum (RUS) is generated for each spherical object and a set of degenerate sphere-resonance frequencies is identified. From the degenerate sphere-resonance frequencies and known relationships between degenerate sphere-resonance frequencies and Poisson's ratio, a Poisson's ratio can be determined, along with a "best" spherical diameter, to form spherical parameters for the sphere. From the RUS, fine-structure resonant frequency spectra are identified for each degenerate sphere-resonance frequency previously selected. From each fine-structure spectrum and associated sphere parameter values an asphericity value is determined. The asphericity value can then be compared with predetermined values to provide a measure for accepting or rejecting the sphere.

  7. FY 2005 Miniature Spherical Retroreflectors Final Report

    SciTech Connect

    Anheier, Norman C.; Bernacki, Bruce E.; Johnson, Bradley R.; Riley, Brian J.; Sliger, William A.

    2005-12-01

    Research done by the Infrared Photonics team at Pacific Northwest National Laboratory (PNNL) is focused on developing miniature spherical retroreflectors using the unique optical and material properties of chalcogenide glass to reduce both performance limiting spherical and chromatic aberrations. The optimized optical performance will provide efficient signal retroreflection that enables a broad range of remote detection scenarios for mid-wave infrared (MWIR) and long-wave infrared (LWIR) sensing applications. Miniature spherical retroreflectors can be developed to aid in the detection of signatures of nuclear proliferation or other chemical vapor or radiation signatures. Miniature spherical retroreflectors are not only well suited to traditional bistatic LIDAR methods for chemical plume detection and identification, but could enable remote detection of difficult semi-volatile chemical materials or low level radiation sources.

  8. On the bidirectional vortex and other similarity solutions in spherical coordinates

    NASA Astrophysics Data System (ADS)

    Majdalani, Joseph; Rienstra, Sjoerd W.

    2007-03-01

    The bidirectional vortex refers to the bipolar, coaxial swirling motion that can be triggered, for example, in cyclone separators and some liquid rocket engines with tangential aft-end injectors. In this study, we present an exact solution to describe the corresponding bulk motion in spherical coordinates. To do so, we examine both linear and nonlinear solutions of the momentum and vorticity transport equations in spherical coordinates. The assumption will be that of steady, incompressible, inviscid, rotational, and axisymmetric flow. We further relate the vorticity to some power of the stream function. At the outset, three possible types of similarity solutions are shown to fulfill the momentum equation. While the first type is incapable of satisfying the conditions for the bidirectional vortex, it can be used to accommodate other physical settings such as Hill’s vortex. This case is illustrated in the context of inviscid flow over a sphere. The second leads to a closed-form analytical expression that satisfies the boundary conditions for the bidirectional vortex in a straight cylinder. The third type is more general and provides multiple solutions. The spherical bidirectional vortex is derived using separation of variables and the method of variation of parameters. The three-pronged analysis presented here increases our repertoire of general mean flow solutions that rarely appear in spherical geometry. It is hoped that these special forms will permit extending the current approach to other complex fluid motions that are easier to capture using spherical coordinates.

  9. Geometry of the human erythrocyte. I. Effect of albumin on cell geometry.

    PubMed Central

    Jay, A W

    1975-01-01

    The effects of albumin on the geometry of human erythrocytes have been studied. Individual red cells, hanging on edge from coverslips were photographed. Enlarged cell profiles were digitized using a Gradicon digitizer (Instronics Ltd., Stittsville, Ontario). Geometric parameters including diameter, area, volume, minimum cylindrical diameter, sphericity index, swelling index, maximum and minimum cell thickness, were calculated for each cell using a CDC 6400 computer. Maximum effect of human serum albumin was reached at about 1 g/liter. Studies of cell populations showed decreases in mean cell diameter of up to 6%, area 6%, and volume 15%, varying from sample to sample. The thickness of the rim was increased while that at the dimple was decreased. Studies of single cells showed that area and volume changes do not occur equally in all cells. Cells with lower sphericity indices showed larger effects. In the presence of albumin, up to 50% of the cells assumed cup-shapes (stomatocytes). These cells had smaller volumes but the same area as biconcave cells. Mechanical agitation could reversibly induce biconcave cells to assume cup shapes without area or volume changes. Experiments with de-fatted human albumins showed that the presence of bound fatty acids in varying concentrations does not alter the observed effects. Bovine serum albumin has similar effects on human erythrocytes as human serum albumin. Images FIGURE 2 FIGURE 6 FIGURE 9 PMID:1122337

  10. PREPARATION OF SPHERICAL URANIUM DIOXIDE PARTICLES

    DOEpatents

    Levey, R.P. Jr.; Smith, A.E.

    1963-04-30

    This patent relates to the preparation of high-density, spherical UO/sub 2/ particles 80 to 150 microns in diameter. Sinterable UO/sub 2/ powder is wetted with 3 to 5 weight per cent water and tumbled for at least 48 hours. The resulting spherical particles are then sintered. The sintered particles are useful in dispersion-type fuel elements for nuclear reactors. (AEC)

  11. Surface thermodynamics of planar, cylindrical, and spherical vapour-liquid interfaces of water.

    PubMed

    Lau, Gabriel V; Ford, Ian J; Hunt, Patricia A; Müller, Erich A; Jackson, George

    2015-03-21

    The test-area (TA) perturbation approach has been gaining popularity as a methodology for the direct computation of the interfacial tension in molecular simulation. Though originally implemented for planar interfaces, the TA approach has also been used to analyze the interfacial properties of curved liquid interfaces. Here, we provide an interpretation of the TA method taking the view that it corresponds to the change in free energy under a transformation of the spatial metric for an affine distortion. By expressing the change in configurational energy of a molecular configuration as a Taylor expansion in the distortion parameter, compact relations are derived for the interfacial tension and its energetic and entropic components for three different geometries: planar, cylindrical, and spherical fluid interfaces. While the tensions of the planar and cylindrical geometries are characterized by first-order changes in the energy, that of the spherical interface depends on second-order contributions. We show that a greater statistical uncertainty is to be expected when calculating the thermodynamic properties of a spherical interface than for the planar and cylindrical cases, and the evaluation of the separate entropic and energetic contributions poses a greater computational challenge than the tension itself. The methodology is employed to determine the vapour-liquid interfacial tension of TIP4P/2005 water at 293 K by molecular dynamics simulation for planar, cylindrical, and spherical geometries. A weak peak in the curvature dependence of the tension is observed in the case of cylindrical threads of condensed liquid at a radius of about 8 Å, below which the tension is found to decrease again. In the case of spherical drops, a marked decrease in the tension from the planar limit is found for radii below ∼ 15 Å; there is no indication of a maximum in the tension with increasing curvature. The vapour-liquid interfacial tension tends towards the planar limit for large

  12. Surface thermodynamics of planar, cylindrical, and spherical vapour-liquid interfaces of water

    SciTech Connect

    Lau, Gabriel V.; Müller, Erich A.; Jackson, George; Ford, Ian J.; Hunt, Patricia A.

    2015-03-21

    The test-area (TA) perturbation approach has been gaining popularity as a methodology for the direct computation of the interfacial tension in molecular simulation. Though originally implemented for planar interfaces, the TA approach has also been used to analyze the interfacial properties of curved liquid interfaces. Here, we provide an interpretation of the TA method taking the view that it corresponds to the change in free energy under a transformation of the spatial metric for an affine distortion. By expressing the change in configurational energy of a molecular configuration as a Taylor expansion in the distortion parameter, compact relations are derived for the interfacial tension and its energetic and entropic components for three different geometries: planar, cylindrical, and spherical fluid interfaces. While the tensions of the planar and cylindrical geometries are characterized by first-order changes in the energy, that of the spherical interface depends on second-order contributions. We show that a greater statistical uncertainty is to be expected when calculating the thermodynamic properties of a spherical interface than for the planar and cylindrical cases, and the evaluation of the separate entropic and energetic contributions poses a greater computational challenge than the tension itself. The methodology is employed to determine the vapour-liquid interfacial tension of TIP4P/2005 water at 293 K by molecular dynamics simulation for planar, cylindrical, and spherical geometries. A weak peak in the curvature dependence of the tension is observed in the case of cylindrical threads of condensed liquid at a radius of about 8 Å, below which the tension is found to decrease again. In the case of spherical drops, a marked decrease in the tension from the planar limit is found for radii below ∼ 15 Å; there is no indication of a maximum in the tension with increasing curvature. The vapour-liquid interfacial tension tends towards the planar limit for large

  13. 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.

  14. Spherically averaging ellipsoidal galaxy clusters in X-ray and Sunyaev-Zel'dovich studies - I. Analytical relations

    NASA Astrophysics Data System (ADS)

    Buote, David A.; Humphrey, Philip J.

    2012-02-01

    This is the first of two papers investigating the deprojection and spherical averaging of ellipsoidal galaxy clusters. We specifically consider applications to hydrostatic X-ray and Sunyaev-Zel'dovich (SZ) studies, though many of the results also apply to isotropic dispersion-supported stellar dynamical systems. Here we present analytical formulae for galaxy clusters described by a gravitational potential that is a triaxial ellipsoid of constant shape and orientation. For this model type we show that the mass bias due to spherically averaging X-ray observations is independent of the temperature profile, and for the special case of a scale-free logarithmic potential, there is exactly zero mass bias for any shape, orientation and temperature profile. The ratio of spherically averaged intracluster medium (ICM) pressures obtained from SZ and X-ray measurements depends only on the ICM intrinsic shape, projection orientation and H0, which provides another illustration of how cluster geometry can be recovered through a combination of X-ray and SZ measurements. We also demonstrate that YSZ and YX have different biases owing to spherical averaging, which leads to an offset in the spherically averaged ? relation. A potentially useful application of the analytical formulae presented is to assess the error range of an observable (e.g. mass, YSZ) accounting for deviations from assumed spherical symmetry, without having to perform the ellipsoidal deprojection explicitly. Finally, for dedicated ellipsoidal studies, we also generalize the spherical onion peeling method to the triaxial case for a given shape and orientation.

  15. Preparation and Optical Properties of Spherical Inverse Opals by Liquid Phase Deposition Using Spherical Colloidal Crystals

    NASA Astrophysics Data System (ADS)

    Aoi, Y.; Tominaga, T.

    2013-03-01

    Titanium dioxide (TiO2) inverse opals in spherical shape were prepared by liquid phase deposition (LPD) using spherical colloidal crystals as templates. Spherical colloidal crystals were produced by ink-jet drying technique. Aqueous emulsion droplets that contain polystyrene latex particles were ejected into air and dried. Closely packed colloidal crystals with spherical shape were obtained. The obtained spherical colloidal crystals were used as templates for the LPD. The templates were dispersed in the deposition solution of the LPD, i.e. a mixed solution of ammonium hexafluorotitanate and boric acid and reacted for 4 h at 30 °C. After the LPD process, the interstitial spaces of the spherical colloidal crystals were completely filled with titanium oxide. Subsequent heat treatment resulted in removal of templates and spherical titanium dioxide inverse opals. The spherical shape of the template was retained. SEM observations indicated that the periodic ordered voids were surrounded by titanium dioxide. The optical reflectance spectra indicated that the optical properties of the spherical titanium dioxide inverse opals were due to Bragg diffractions from the ordered structure. Filling in the voids of the inverse opals with different solvents caused remarkable changes in the reflectance peak.

  16. 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…

  17. 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…

  18. Linearized stability analysis of gravastars in noncommutative geometry

    NASA Astrophysics Data System (ADS)

    Lobo, Francisco S. N.; Garattini, Remo

    2013-12-01

    In this work, we find exact gravastar solutions in the context of noncommutative geometry, and explore their physical properties and characteristics. The energy density of these geometries is a smeared and particle-like gravitational source, where the mass is diffused throughout a region of linear dimension due to the intrinsic uncertainty encoded in the coordinate commutator. These solutions are then matched to an exterior Schwarzschild spacetime. We further explore the dynamical stability of the transition layer of these gravastars, for the specific case of β = M 2/ α < 1.9, where M is the black hole mass, to linearized spherically symmetric radial perturbations about static equilibrium solutions. It is found that large stability regions exist and, in particular, located sufficiently close to where the event horizon is expected to form.

  19. Generalized quantum gravity condensates for homogeneous geometries and cosmology

    NASA Astrophysics Data System (ADS)

    Oriti, Daniele; Pranzetti, Daniele; Ryan, James P.; Sindoni, Lorenzo

    2015-12-01

    We construct a generalized class of quantum gravity condensate states that allows the description of continuum homogeneous quantum geometries within the full theory. They are based on similar ideas already applied to extract effective cosmological dynamics from the group field theory formalism, and thus also from loop quantum gravity. However, they represent an improvement over the simplest condensates used in the literature, in that they are defined by an infinite superposition of graph-based states encoding in a precise way the topology of the spatial manifold. The construction is based on the definition of refinement operators on spin network states, written in a second quantized language. The construction also lends itself easily to application to the case of spherically symmetric quantum geometries.

  20. 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.

  1. 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.

  2. Numerical simulation of natural convection in a spherical container due to cooling at the center (idealization of the Lal/Kroes experiment)

    NASA Technical Reports Server (NTRS)

    Robertson, S. J.

    1981-01-01

    Natural convection in a spherical container with cooling at the center was numerically simulated using a numerical fluid dynamics computer program. The numerical analysis was simplified by assuming axisymmetric flow in the spherical container, with the symmetry axis being a sphere diagonal parallel to the gravity vector. This axisymmetric spherical geometry was intended as an idealization of the proposed Lal/Kroes crystal growing experiment to be performed on Spacelab. Results were obtained for a range of Rayleigh numbers from 25 to 10,000. The computed velocities were found to be approximately proportional to the Rayleigh number over the range of Rayleigh numbers investigated.

  3. Propagation of light in Schwarzschild geometry

    NASA Astrophysics Data System (ADS)

    Khorasani, Sina

    2010-02-01

    In this paper, the equivalent medium of Schwarzschild metric is discussed. The corresponding ray-tracing equations are integrated for the equivalent medium of the Schwarzschild geometry, which describes the curved space around a spherically symmetric, irrotational, and uncharged blackhole. We make comparison to the well-known expression by Einstein. While Einstein's estimate is reasonably good for large closest distances of approach to the star, it disregards the optical anisotropy of space. Instead, Virbhadra's estimate which takes the effects of anisotropy of Schwarzschild metric is shown to be more consistent with numerical simulations. Hence, a true physical anisotropy in the velocity of light under gravitational field does exist. We argue that the existence of such an optical anisotropy could be revealed exactly in the same way that the optical interferometry is expected to detect gravitational waves. Therefore, if no optical anisotropy under gravitational fields could be observed, then the possibility of interferometric detection of gravitational waves is automatically ruled out, and vice versa.

  4. Role of target geometry in phagocytosis

    PubMed Central

    Champion, Julie A.; Mitragotri, Samir

    2006-01-01

    Phagocytosis is a principal component of the body’s innate immunity in which macrophages internalize targets in an actin-dependent manner. Targets vary widely in shape and size and include particles such as pathogens and senescent cells. Despite considerable progress in understanding this complicated process, the role of target geometry in phagocytosis has remained elusive. Previous studies on phagocytosis have been performed using spherical targets, thereby overlooking the role of particle shape. Using polystyrene particles of various sizes and shapes, we studied phagocytosis by alveolar macrophages. We report a surprising finding that particle shape, not size, plays a dominant role in phagocytosis. All shapes were capable of initiating phagocytosis in at least one orientation. However, the local particle shape, measured by tangent angles, at the point of initial contact dictates whether macrophages initiate phagocytosis or simply spread on particles. The local shape determines the complexity of the actin structure that must be created to initiate phagocytosis and allow the membrane to move over the particle. Failure to create the required actin structure results in simple spreading and not internalization. Particle size primarily impacts the completion of phagocytosis in cases where particle volume exceeds the cell volume. PMID:16549762

  5. Effective geometry of a white dwarf

    SciTech Connect

    Bini, D.; Cherubini, C.; Filippi, S.

    2011-03-15

    The ''effective geometry'' formalism is used to study the perturbations of a white dwarf described as a self-gravitating fermion gas with a completely degenerate relativistic equation of state of barotropic type. The quantum nature of the system causes an absence of homological properties, manifested instead by polytropic stars, and requires a parametric study of the solutions both at the numerical and analytical level. We have explicitly derived a compact analytical parametric approximate solution of Pade type, which gives density curves and stellar radii in good accordance with already existing numerical results. After validation of this new type of approximate solutions, we use them to construct the effective acoustic metric governing general perturbations following Chebsch's formalism. Even in this quantum case, the stellar surface exhibits a curvature singularity due to the vanishing of density, as already evidenced in past studies on nonquantum self-gravitating polytropic stars. The equations of the theory are finally numerically integrated in the simpler case of irrotational spherical pulsating perturbations, including the effect of backreaction, in order to have a dynamical picture of the process occurring in the acoustic metric.

  6. Towards AN Easier Orientation for Spherical Photogrammetry

    NASA Astrophysics Data System (ADS)

    Fangi, G.

    2015-02-01

    For architectural metric documentation, Spherical Photogrammetry (SP) has demonstrated its validity and efficiency in many projects already. The speed of surveying is high, the accuracy and completeness of the plotting are satisfactory. However, there are still many problems to be solved. The weakest point is the orientation procedure, which is rather difficult to perform, in the sense that only very experienced people can run it, and few people only make use of it. The old orientation steps are 1) model formation (limited to binocular panoramas couples); 2) link of all the models in a block adjustment with independent model triangulation; 3) block bundle adjustment with 4 parameters/pano (3 coord.+1 orientation bearing); 4) block bundle adjustment with 6 parameters/pano, say the previous 4 + 2 correction angles around the horizontal axes. The panoramas must be spherical and quasi-horizontal. In order to make easier the orientation, enabling more people to use SP, an improved approach has been set up. It consists in the combination of any possible model formed either by three and two panoramas. The trinocular vision, say the combination of three different panoramas to form a unique model, has the advantage to be much more robust in comparison to binocular vision in the sense that the trinocular model is likely to be more error-free than any of the three composing binocular models. It contains less model deformation, the model coordinates are validated by the mutual comparison of the three intersecting binocular models. In addition, the number of possible trinocular models is normally much larger than the one of binocular models. The steps for a semi-automatic orientation of a block of panoramas proceed as follows: - Form any possible trinocular models by combination of the panoramas; - in case that no trinocular model has been formed, form any possible binocular model; - run a block adjustment with the algorithm of independent model, to link together the models in

  7. Spherical resonant-mass gravitational wave detectors

    NASA Astrophysics Data System (ADS)

    Zhou, Carl Z.; Michelson, Peter F.

    1995-03-01

    A spherical gravitational wave antenna is a very promising detector for gravitational wave astronomy because it has a large cross section, isotropic sky coverage, and can provide the capability of determining the wave direction. In this paper we discuss several aspects of spherical detectors, including the eigenfunctions and eigenfrequencies of the normal modes of an elastic sphere, the energy cross section, and the response functions that are used to obtain the noise-free solution to the inverse problem. Using the maximum likelihood estimation method the inverse problem in the presence of noise is solved. We also determine the false-alarm probability and the detection probability for a network of spherical detectors and estimate the detectable event rates for supernova collapses and binary coalescences.

  8. A quadrilateralized spherical cube Earth data base

    NASA Technical Reports Server (NTRS)

    Chan, F. K.

    1980-01-01

    A quadrilateralized spherical cube was constructed to form the basis for the rapid storage and retrieval of high resolution data obtained of the Earth's surface. The structure of this data base was derived from a spherical cube, which was obtained by radially projecting a cube onto its circumscribing sphere. An appropriate set of curvilinear coordinates were chosen such that the resolution cells on the spherical cube were of equal area and were also of essentially the same shape. The main properties of the Earth data base were that the indexing scheme was binary and telescopic in nature, the resolution cells were strung together in a two dimensional manner, the cell addresses were easily computed, and the conversion from geographic to data base coordinates was comparatively simple. It was concluded that this data base structure was perhaps the most viable one for handling remotely sensed data obtained by satellites.

  9. Background reduction of a spherical gaseous detector

    SciTech Connect

    Fard, Ali Dastgheibi; Loaiza, Pia; Piquemal, Fabrice; Giomataris, Ioannis; Gray, David; Gros, Michel; Magnier, Patrick; Navick, Xavier-François

    2015-08-17

    The Spherical gaseous detector (or Spherical Proportional Counter, SPC) is a novel type of detector. It consists of a large spherical volume filled with gas, using a single detection readout channel. The detector allows 100 % detection efficiency. SEDINE is a low background version of SPC installed at the Laboratoire Souterrain de Modane (LSM) underground laboratory (4800 m.w.e) looking for rare events at very low energy threshold, below 100 eV. This work presents the details on the chemical cleaning to reduce internal {sup 210}Pb surface contamination on the copper vessel and the external radon reduction achieved via circulation of pure air inside anti-radon tent. It will be also show the radon measurement of pure gases (Ar, N, Ne, etc) which are used in the underground laboratory for the low background experiments.

  10. Elastic properties of spherically anisotropic piezoelectric composites

    NASA Astrophysics Data System (ADS)

    Wei, En-Bo; Gu, Guo-Qing; Poon, Ying-Ming

    2010-09-01

    Effective elastic properties of spherically anisotropic piezoelectric composites, whose spherically anisotropic piezoelectric inclusions are embedded in an infinite non-piezoelectric matrix, are theoretically investigated. Analytical solutions for the elastic displacements and the electric potentials under a uniform external strain are derived exactly. Taking into account of the coupling effects of elasticity, permittivity and piezoelectricity, the formula is derived for estimating the effective elastic properties based on the average field theory in the dilute limit. An elastic response mechanism is revealed, in which the effective elastic properties increase as inclusion piezoelectric properties increase and inclusion dielectric properties decrease. Moreover, a piezoelectric response mechanism, of which the effective piezoelectric response vanishes due to the symmetry of spherically anisotropic composite, is also disclosed.

  11. Spherical aberration in electrically thin flat lenses.

    PubMed

    Ruphuy, Miguel; Ramahi, Omar M

    2016-08-01

    We analyze the spherical aberration of a new generation of lenses made of flat electrically thin inhomogeneous media. For such lenses, spherical aberration is analyzed quantitatively and qualitatively, and comparison is made to the classical gradient index rod. Both flat thin and thick lenses are made of gradient index materials, but the physical mechanisms and design equations are different. Using full-wave three-dimensional numerical simulation, we evaluate the spherical aberrations using the Maréchal criterion and show that the thin lens gives significantly better performance than the thick lens (rod). Additionally, based on ray tracing formulation, third-order analysis for longitudinal aberration and optical path difference are presented, showing strong overall performance of thin lenses in comparison to classical rod lenses. PMID:27505651

  12. Thermal Fluid Multiphysics Optimization of Spherical Tokamak

    SciTech Connect

    Lumsdaine, Arnold; Tipton, Joseph B; Peng, Yueng Kay Martin

    2012-01-01

    An experimental Fusion Nuclear Science Facility (FNSF) is required that will create the environment that simultaneously achieves high energy neutrons and high ion fluence necessary in order to bridge the gaps from ITER to the realization of a fusion nuclear power plant. One concept for achieving this is a high duty cycle spherical torus. This study will focus on thermal modeling of the spherical torus centerpost using computational fluid dynamics to effectively model the thermal transfer of the cooling fluid to the centerpost. The design of the fluid channels is optimized in order to minimize the temperature in the centerpost. Results indicate the feasibility of water cooling for a long-pulse spherical torus FNSF.

  13. Spherical shock waves in general relativity

    SciTech Connect

    Nutku, Y. )

    1991-11-15

    We present the metric appropriate to a spherical shock wave in the framework of general relativity. This is a Petrov type-{ital N} vacuum solution of the Einstein field equations where the metric is continuous across the shock and the Riemann tensor suffers a step-function discontinuity. Spherical gravitational waves are described by type-{ital N} Robinson-Trautman metrics. However, for shock waves the Robinson-Trautman solutions are unacceptable because the metric becomes discontinuous in the Robinson-Trautman coordinate system. Other coordinate systems that have so far been introduced for describing Robinson-Trautman solutions also suffer from the same defect. We shall present the {ital C}{sup 0}-form of the metric appropriate to spherical shock waves using Penrose's approach of identification with warp. Further extensions of Penrose's method yield accelerating, as well as coupled electromagnetic-gravitational shock-wave solutions.

  14. Design and implementation of spherical ultrasonic motor.

    PubMed

    Mashimo, Tomoaki; Toyama, Shigeki; Ishida, Hiroshi

    2009-11-01

    We present a mechanical design and implementation of spherical ultrasonic motor (SUSM) that is an actuator with multiple rotational degrees of freedom (multi-DOF). The motor is constructed of 3 annular stators and a spherical rotor and is much smaller and simpler than conventional multi-DOF mechanisms such as gimbals using servomotors. We designed a novel SUSM using experimental data from a single annular stator and a finite element method. The SUSM using a spherical rotor of diameter 20 mm without any reduction gear has demonstrated advantages of high responsiveness, good accuracy, and high torque at low speed. The dynamic implementation of SUSM was consistent with the driving model of SUSM based on a friction drive. PMID:19942537

  15. Static spherically symmetric wormholes with isotropic pressure

    NASA Astrophysics Data System (ADS)

    Cataldo, Mauricio; Liempi, Luis; Rodríguez, Pablo

    2016-06-01

    In this paper we study static spherically symmetric wormhole solutions sustained by matter sources with isotropic pressure. We show that such spherical wormholes do not exist in the framework of zero-tidal-force wormholes. On the other hand, it is shown that for the often used power-law shape function there are no spherically symmetric traversable wormholes sustained by sources with a linear equation of state p = ωρ for the isotropic pressure, independently of the form of the redshift function ϕ (r). We consider a solution obtained by Tolman at 1939 for describing static spheres of isotropic fluids, and show that it also may describe wormhole spacetimes with a power-law redshift function, which leads to a polynomial shape function, generalizing a power-law shape function, and inducing a solid angle deficit.

  16. Background reduction of a spherical gaseous detector

    NASA Astrophysics Data System (ADS)

    Fard, Ali Dastgheibi; Loaiza, Pia; Piquemal, Fabrice; Giomataris, Ioannis; Gray, David; Gros, Michel; Magnier, Patrick; Navick, Xavier-François; Savvidis, Ilias

    2015-08-01

    The Spherical gaseous detector (or Spherical Proportional Counter, SPC) is a novel type of detector. It consists of a large spherical volume filled with gas, using a single detection readout channel. The detector allows 100 % detection efficiency. SEDINE is a low background version of SPC installed at the Laboratoire Souterrain de Modane (LSM) underground laboratory (4800 m.w.e) looking for rare events at very low energy threshold, below 100 eV. This work presents the details on the chemical cleaning to reduce internal 210Pb surface contamination on the copper vessel and the external radon reduction achieved via circulation of pure air inside anti-radon tent. It will be also show the radon measurement of pure gases (Ar, N, Ne, etc) which are used in the underground laboratory for the low background experiments.

  17. Two electronic states in spherical quantum nanolayer

    NASA Astrophysics Data System (ADS)

    Aghekyan, N. G.; Kazaryan, E. M.; Kostanyan, A. A.; Sarkisyan, H. A.

    2010-10-01

    In this paper two electronic states in spherical quantum nanolayer are discussed. The Coulomb interaction between the electrons is discussed as perturbation. For confinement potential of the nanolayer the three-dimensional radial analog of Smorodinsky-Winternitz potential is considered. The problem is discussed within the frameworks of Russell-Saunders coupling scheme, thus, the spin-orbit interaction is considered weak. Therefore the eigenfunctions of the system is represented as a multiplication of its coordinate wave function and spin wave function. For this system the analogue of helium atom theory is represented. The eigenfunctions and energy states are obtained for one and two electron cases in the spherical quantum nanolayer. For the spherical nanolayer the dependence of perturbation energy, unperturbed system energy and the total energy for the ground state upon the inner radius is represented when the outer radius is fixed.

  18. Quasinormal modes for subtracted rotating and magnetized geometries

    NASA Astrophysics Data System (ADS)

    Cvetič, M.; Gibbons, G. W.; Saleem, Z. H.

    2014-12-01

    We obtain explicit separable solutions of the wave equation of massless minimally coupled scalar fields in the subtracted geometry of four-dimensional rotating and Melvin (magnetised) four-charge black holes of the STU model, a consistent truncation of maximally supersymmetric supergravity with four types of electromagnetic fields. These backgrounds possess a hidden SL (2 ,R )×SL (2 ,R )×SO (3 ) symmetry and faithfully model the near-horizon geometry of these black holes, but locate them in a confining asymptotically conical box. For each subtracted geometry we obtain two branches of quasinormal modes, given in terms of hypergeometric functions and spherical harmonics. One branch is over-damped and the other under-damped and they exhibit rotational splitting. No black hole bomb is possible because the Killing field which corotates with the horizon is everywhere timelike outside the black hole. A five-dimensional lift of these geometries is given locally by the product of a Bañados-Teitelboim-Zanelli black hole with a two-sphere. This allows an explicit analysis of the minimally coupled massive five-dimensional scalar field. Again, there are two branches, both damped; however, now their oscillatory parts are shifted by the quantized wave number k along the fifth circle direction.

  19. On The Explosion Geometry of Red Supergiant Stars

    NASA Astrophysics Data System (ADS)

    Leonard, Douglas C.; Supernova Spectropolarimetry Project (SNSPOL)

    2016-06-01

    From progenitor studies, type II-Plateau supernovae (SNe II-P) have been decisively and uniquely determined to arise from isolated red supergiant (RSG) stars, establishing the most homogeneous --- and well understood --- progenitor class of any type of core-collapse supernova. The physical process by which these stars explode, however, remains a mystery. A fundamental clue to the nature of the explosion mechanism is explosion geometry: In short, are supernovae round? Because young supernova atmospheres are electron-scattering dominated, their net linear polarization provides a direct probe of early-time supernova geometry, with higher degrees of polarization generally indicating greater departures from spherical symmetry. This presentation will describe the ongoing work being carried out on RSG explosion geometry by the SuperNova SpectroPOLarimetry project (SNSPOL), with a particular focus on SN 2013ej -- an SN II-P that exhibited remarkably high polarization just days after the explosion, and for which twelve epochs of spectropolarimetry trace an intriguing tale about its geometry deep into the nebular phase.We acknowledge support from NSF grants AST-1009571 and AST-1210311, under which part of this research was carried out.

  20. 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.

  1. 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)

  2. Toroidal membrane vesicles in spherical confinement.

    PubMed

    Bouzar, Lila; Menas, Ferhat; Müller, Martin Michael

    2015-09-01

    We investigate the morphology of a toroidal fluid membrane vesicle confined inside a spherical container. The equilibrium shapes are assembled in a geometrical phase diagram as a function of scaled area and reduced volume of the membrane. For small area the vesicle can adopt its free form. When increasing the area, the membrane cannot avoid contact and touches the confining sphere along a circular contact line, which extends to a zone of contact for higher area. The elastic energies of the equilibrium shapes are compared to those of their confined counterparts of spherical topology to predict under which conditions a topology change is favored energetically. PMID:26465512

  3. Electrode shapes for spherical Pierce flow

    SciTech Connect

    Mueller, D.W.

    1981-01-01

    The problem of obtaining the electrode shapes to produce a conically converging proton beam that has constant current density over each spherical surface of convergence is treated in spherical coordinates. A cone is taken from the Langmuir and Blodgett solution for the region within, and at the edge of, the conically converging beam. A solution for the LaPlace equation, required for the region outside the beam, is in terms of a power series in r and the Legendre polynomials of cos phi.

  4. Design of artificial spherical superposition compound eye

    NASA Astrophysics Data System (ADS)

    Cao, Zhaolou; Zhai, Chunjie; Wang, Keyi

    2015-12-01

    In this research, design of artificial spherical superposition compound eye is presented. The imaging system consists of three layers of lens arrays. In each channel, two lenses are designed to control the angular magnification and a field lens is added to improve the image quality and extend the field of view. Aspherical surfaces are introduced to improve the image quality. Ray tracing results demonstrate that the light from the same object point is focused at the same imaging point through different channels. Therefore the system has much higher energy efficiency than conventional spherical apposition compound eye.

  5. Evolution of non-spherical perturbations.

    NASA Astrophysics Data System (ADS)

    Boschan, P.

    1995-06-01

    In this paper I investigate the evolution of primordial non-spherical positive and negative fluctuations. They can be calculated by second order of perturbation theory. I solved analytically the second order equation for arbitrary density parameter {OMEGA}_M0_ and cosmological constant {LAMBDA} using the approximation introduced by Martell & Freundling (???). The second order solution is compared with the exact one in the spherical case. I find that the initial deformation grows rapidly for positive perturbations, while the negative perturbations (voids) are stable against deformations.

  6. Spherical harmonic analysis of steady photospheric flows

    NASA Technical Reports Server (NTRS)

    Hathaway, David H.

    1987-01-01

    A technique is presented in which full disk Doppler velocity measurements are analyzed using spherical harmonic functions to determine the characteristics of the spectrum of spherical harmonic modes and the nature of steady photospheric flows. Synthetic data are constructed in order to test the technique. In spite of the mode mixing due to the lack of information about the motions on the backside of the sun, solar rotation and differential rotation can be accurately measured and monitored for secular changes, and meridional circulations with small amplitudes can be measured. Furthermore, limb shift measurements can be accurately obtained, and supergranules can be fully resolved and separated from giant cells by their spatial characteristics.

  7. Research on the feature set construction method for spherical stereo vision

    NASA Astrophysics Data System (ADS)

    Zhu, Junchao; Wan, Li; Röning, Juha; Feng, Weijia

    2015-01-01

    Spherical stereo vision is a kind of stereo vision system built by fish-eye lenses, which discussing the stereo algorithms conform to the spherical model. Epipolar geometry is the theory which describes the relationship of the two imaging plane in cameras for the stereo vision system based on perspective projection model. However, the epipolar in uncorrected fish-eye image will not be a line but an arc which intersects at the poles. It is polar curve. In this paper, the theory of nonlinear epipolar geometry will be explored and the method of nonlinear epipolar rectification will be proposed to eliminate the vertical parallax between two fish-eye images. Maximally Stable Extremal Region (MSER) utilizes grayscale as independent variables, and uses the local extremum of the area variation as the testing results. It is demonstrated in literatures that MSER is only depending on the gray variations of images, and not relating with local structural characteristics and resolution of image. Here, MSER will be combined with the nonlinear epipolar rectification method proposed in this paper. The intersection of the rectified epipolar and the corresponding MSER region is determined as the feature set of spherical stereo vision. Experiments show that this study achieved the expected results.

  8. Three-dimensional spherical spatial boundary conditions differentially regulate osteogenic differentiation of mesenchymal stromal cells

    PubMed Central

    Lo, Yin-Ping; Liu, Yi-Shiuan; Rimando, Marilyn G.; Ho, Jennifer Hui-Chun; Lin, Keng-hui; Lee, Oscar K.

    2016-01-01

    The spatial boundary condition (SBC) arising from the surrounding microenvironment imposes specific geometry and spatial constraints that affect organogenesis and tissue homeostasis. Mesenchymal stromal cells (MSCs) sensitively respond to alterations of mechanical cues generated from the SBC. However, mechanical cues provided by a three-dimensional (3D) environment are deprived in a reductionist 2D culture system. This study investigates how SBC affects osteogenic differentiation of MSCs using 3D scaffolds with monodispersed pores and homogenous spherical geometries. MSCs cultured under SBCs with diameters of 100 and 150 μm possessed the greatest capability of osteogenic differentiation. This phenomenon was strongly correlated with MSC morphology, organization of actin cytoskeleton, and distribution of focal adhesion involving α2 and α5 integrins. Further silencing either α2 or α5 integrin significantly reduced the above mentioned mechanosensitivity, indicating that the α2 and α5 integrins as mechano-sensitive molecules mediate MSCs’ ability to provide enhanced osteogenic differentiation in response to different spherical SBCs. Taken together, the findings provide new insights regarding how MSCs respond to mechanical cues from the surrounding microenvironment in a spherical SBC, and such biophysical stimuli should be taken into consideration in tissue engineering and regenerative medicine in conjunction with biochemical cues. PMID:26884253

  9. Rayleigh-Taylor instability experiments in a cylindrically convergent geometry

    SciTech Connect

    Goodwin, B.; Weir, S.

    1995-08-25

    Due to the sensitivity of Rayleigh-Taylor instabilities to initial conditions and due to the difficulty of forming well controlled cylindrical or spherical fluid interfaces, Rayleigh-Taylor experiments are often performed with simple, planar interfaces. Rayleigh-Taylor instability phenomena of practical interest, however, (e.g., underwater explosions, supernova core collapses, and inertial confinement fusion capsule implosions) are typically associated with cylindrical or spherical interfaces in which convergent flow effects have an important influence on the dynamics of instability growth. Recently, Meshkov et.al. have developed a novel technique for studying Rayleigh-Taylor instability growth in a cylindrically convergent geometry. Their experiments utilized low-strength gelatin rings which are imploded by a detonating gas mixture of oxygen and acetylene. Since the gelatin itself has sufficient strength to resist significant deformation by gravity, no membranes are needed to define the ring shape. This experimental technique is attractive because it offers a high degree of control over the interfacial geometry and over the material`s strength and rigidity, which can be varied by adjusting the gelatin concentration. Finally, since both the gelatin and the explosive product gases are transparent, optical diagnostics can be used.

  10. 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)

  11. Emergent geometry from quantized spacetime

    SciTech Connect

    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.

  12. Casimir problem of spherical dielectrics: numerical evaluation for general permittivities.

    PubMed

    Brevik, I; Aarseth, J B; Høye, J S

    2002-08-01

    The Casimir mutual free energy F for a system of two dielectric concentric nonmagnetic spherical bodies is calculated, at arbitrary temperatures. The present paper is a continuation of an earlier investigation [Phys. Rev. E 63, 051101 (2001)], in which F was evaluated in full only for the case of ideal metals (refractive index n= infinity ). Here, analogous results are presented for dielectrics, for some chosen values of n. Our basic calculational method stems from quantum statistical mechanics. The Debye expansions for the Riccati-Bessel functions when carried out to a high order are found to be very useful in practice (thereby overflow/underflow problems are easily avoided), and also to give accurate results even for the lowest values of l down to l=1. Another virtue of the Debye expansions is that the limiting case of metals becomes quite amenable to an analytical treatment in spherical geometry. We first discuss the zero-frequency TE mode problem from a mathematical viewpoint and then, as a physical input, invoke the actual dispersion relations. The result of our analysis, based upon the adoption of the Drude dispersion relation at low frequencies, is that the zero-frequency TE mode does not contribute for a real metal. Accordingly, F turns out in this case to be only one-half of the conventional value at high temperatures. The applicability of the Drude model in this context has, however, been questioned recently, and we do not aim at a complete discussion of this issue here. Existing experiments are low-temperature experiments, and are so far not accurate enough to distinguish between the different predictions. We also calculate explicitly the contribution from the zero-frequency mode for a dielectric. For a dielectric, this zero-frequency problem is absent. PMID:12241249

  13. 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.

  14. Line-tension effects on heterogeneous nucleation on a spherical substrate and in a spherical cavity.

    PubMed

    Iwamatsu, Masao

    2015-04-01

    The line-tension effects on heterogeneous nucleation are considered when a spherical lens-shaped nucleus is nucleated on top of a spherical substrate and on the bottom of the wall of a spherical cavity. The effect of line tension on the nucleation barrier can be separated from the usual volume term. As the radius of the substrate increases, the nucleation barrier decreases and approaches that of a flat substrate. However, as the radius of the cavity increases, the nucleation barrier increases and approaches that of a flat substrate. A small spherical substrate is a less active nucleation site than a flat substrate, and a small spherical cavity is a more active nucleation site than a flat substrate. In contrast, the line-tension effect on the nucleation barrier is maximum when the radii of the nucleus and the substrate or cavity become comparable. Therefore, by tuning the size of the spherical substrate or spherical cavity, the effect of the line tension can be optimized. These results will be useful in broad range of applications from material processing to understanding of global climate, where the heterogeneous nucleation plays a vital role. PMID:25775383

  15. The Common Geometry Module (CGM).

    SciTech Connect

    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.

  16. Comparison of spherical and realistically shaped boundary element head models for transcranial magnetic stimulation navigation

    PubMed Central

    Nummenmaa, Aapo; Stenroos, Matti; Ilmoniemi, Risto J.; Okada, Yoshio C.; Hämäläinen, Matti S.; Raij, Tommi

    2013-01-01

    Objective MRI-guided real-time transcranial magnetic stimulation (TMS) navigators that apply electromagnetic modeling have improved the utility of TMS. However, their accuracy and speed depends on the assumed volume conductor geometry. Spherical models found in present navigators are computationally fast but may be inaccurate in some areas. Realistically-shaped boundary-element models (BEMs) could increase accuracy at a moderate computational cost, but it is unknown which model features have the largest influence on accuracy. Thus, we compared different types of spherical models and BEMs. Methods Globally and locally fitted spherical models and different BEMs with either one or three compartments and with different skull-to-brain conductivity ratios (1/1 – 1/80) were compared against a reference BEM. Results The one-compartment BEM at inner skull surface was almost as accurate as the reference BEM. Skull/brain conductivity ratio in the range 1/10 – 1/80 had only a minor influence. BEMs were superior to spherical models especially in frontal and temporal areas (up to 20 mm localization and 40% intensity improvement); in motor cortex all models provided similar results. Conclusions One-compartment BEMs offer a good balance between accuracy and computational cost. Significance Realistically-shaped BEMs may increase TMS navigation accuracy in several brain areas, such as in prefrontal regions often targeted in clinical applications. PMID:23890512

  17. Spherical Ethylene/Air Diffusion Flames Subject to Concentric DC Electric Field in Microgravity

    NASA Technical Reports Server (NTRS)

    Yuan, Z. -G.; Hegde, U.; Faeth, G. M.

    2001-01-01

    It is well known that microgravity conditions, by eliminating buoyant flow, enable many combustion phenomena to be observed that are not possible to observe at normal gravity. One example is the spherical diffusion flame surrounding a porous spherical burner. The present paper demonstrates that by superimposing a spherical electrical field on such a flame, the flame remains spherical so that we can study the interaction between the electric field and flame in a one-dimensional fashion. Flames are susceptible to electric fields that are much weaker than the breakdown field of the flame gases owing to the presence of ions generated in the high temperature flame reaction zone. These ions and the electric current of the moving ions, in turn, significantly change the distribution of the electric field. Thus, to understand the interplay between the electric field and the flame is challenging. Numerous experimental studies of the effect of electric fields on flames have been reported. Unfortunately, they were all involved in complex geometries of both the flow field and the electric field, which hinders detailed study of the phenomena. In a one-dimensional domain, however, the electric field, the flow field, the thermal field and the chemical species field are all co-linear. Thus the problem is greatly simplified and becomes more tractable.

  18. Eccentricity in Images of Circular and Spherical Targets and its Impact to 3D Object Reconstruction

    NASA Astrophysics Data System (ADS)

    Luhmann, T.

    2014-06-01

    This paper discusses a feature of projective geometry which causes eccentricity in the image measurement of circular and spherical targets. While it is commonly known that flat circular targets can have a significant displacement of the elliptical image centre with respect to the true imaged circle centre, it can also be shown that the a similar effect exists for spherical targets. Both types of targets are imaged with an elliptical contour. As a result, if measurement methods based on ellipses are used to detect the target (e.g. best-fit ellipses), the calculated ellipse centre does not correspond to the desired target centre in 3D space. This paper firstly discusses the use and measurement of circular and spherical targets. It then describes the geometrical projection model in order to demonstrate the eccentricity in image space. Based on numerical simulations, the eccentricity in the image is further quantified and investigated. Finally, the resulting effect in 3D space is estimated for stereo and multi-image intersections. It can be stated that the eccentricity is larger than usually assumed, and must be compensated for high-accuracy applications. Spherical targets do not show better results than circular targets. The paper is an updated version of Luhmann (2014) new experimental investigations on the effect of length measurement errors.

  19. Transfer matrix of a spherical scatterer

    SciTech Connect

    Podolsky, V.S.; Lisyansky, A.A.

    1996-11-01

    We derive the off-shell scattering matrix for a spherical scatterer. The result obtained generalizes the off-on-shell matrix commonly used in the theory of scalar waves propagation in random media. {copyright} {ital 1996 The American Physical Society.}

  20. Spherical hashing: binary code embedding with hyperspheres.

    PubMed

    Heo, Jae-Pil; Lee, Youngwoon; He, Junfeng; Chang, Shih-Fu; Yoon, Sung-Eui

    2015-11-01

    Many binary code embedding schemes have been actively studied recently, since they can provide efficient similarity search, and compact data representations suitable for handling large scale image databases. Existing binary code embedding techniques encode high-dimensional data by using hyperplane-based hashing functions. In this paper we propose a novel hypersphere-based hashing function, spherical hashing, to map more spatially coherent data points into a binary code compared to hyperplane-based hashing functions. We also propose a new binary code distance function, spherical Hamming distance, tailored for our hypersphere-based binary coding scheme, and design an efficient iterative optimization process to achieve both balanced partitioning for each hash function and independence between hashing functions. Furthermore, we generalize spherical hashing to support various similarity measures defined by kernel functions. Our extensive experiments show that our spherical hashing technique significantly outperforms state-of-the-art techniques based on hyperplanes across various benchmarks with sizes ranging from one to 75 million of GIST, BoW and VLAD descriptors. The performance gains are consistent and large, up to 100 percent improvements over the second best method among tested methods. These results confirm the unique merits of using hyperspheres to encode proximity regions in high-dimensional spaces. Finally, our method is intuitive and easy to implement. PMID:26440269

  1. Fast discharge in a spherical cavity

    SciTech Connect

    Antsiferov, P. S. Dorokhin, L. A.

    2014-04-15

    The work is devoted to the study of the plasma, created by a fast discharge in a spherical cavity. The discharge was driven by an inductive storage with plasma erosion opening switch (dI/dt ∼10{sup 12} A/s). The plasma was produced in a spherical cavity (alumina, 11 mm diameter). Xe, Ar, and He at the pressure 80 Pa were used as working gases. The time evolution of the spatial structure and of extreme ultraviolet (EUV) spectra of the discharge plasma was studied by means of micro channel plate detector. The discharges with Xe and Ar resulted in the stable appearance of the spherically shaped plasma with the diameter about 1–3 mm. The plasma emission in the EUV region lasts ∼500 ns. The EUV spectrum of Ar discharge at the moment of maximum of the electron temperature T{sub e} contains the lines of Ar X (ionization potential 478.7 eV), that indicates a value of T{sub e} in the range 50–100 eV. The mechanism of plasma appearance can be the cumulation of the convergent spherical shock wave, generated by fast heat deposition and magnetic pressure in working media near the inner surface of the discharge volume.

  2. Fluctuations of a spherical gravitational impulsive wave.

    NASA Astrophysics Data System (ADS)

    Hortaçsu, M.

    1993-02-01

    It is shown that quantum fluctuations, in particular vacuum polarization, vanish in the background of a spherical impulsive wave solution of the Einstein field equations, recently found by Nutku and Penrose. The calculation is done in first-order perturbation theory but arguments are given why it should persist to all orders.

  3. An Engineering Evaluation of Spherical Resorcinol Formaldehyde Resin

    SciTech Connect

    Birdwell Jr, Joseph F; Lee, Denise L; Taylor, Paul Allen; Collins, Robert T; Hunt, Rodney Dale

    2010-09-01

    A small column ion exchange (SCIX) system has been proposed for removal of cesium from caustic, supernatant, and dissolved salt solutions stored or generated from high-level tank wastes at the US Department of Energy (DOE) Hanford Site and Savannah River Sites. In both instances, deployment of SCIX systems, either in-tank or near-tank, is a means of expediting waste pretreatment and dispositioning with minimal or no new infrastructure requirements. Conceptually, the treatment approach can utilize a range of ion exchange media. Previously, both crystalline silicotitanate (CST), an inorganic, nonelutable sorbent, and resorcinol-formaldehyde (RF), an organic, elutable resin, have been considered for cesium removal from tank waste. More recently, Pacific Northwest National Laboratory (PNNL) evaluated use of SuperLig{reg_sign} 644, an elutable ion exchange medium, for the subject application. Results of testing indicate hydraulic limitations of the SuperLig{reg_sign} resin, specifically a high pressure drop through packed ion exchange columns. This limitation is likely the result of swelling and shrinkage of the irregularly shaped (granular) resin during repeated conversions between sodium and hydrogen forms as the resin is first loaded then eluted. It is anticipated that a similar flow limitation would exist in columns packed with conventional, granular RF resin. However, use of spherical RF resin is a likely means of mitigating processing limitations due to excessive pressure drop. Although size changes occur as the spherical resin is cycled through loading and elution operations, the geometry of the resin is expected to effectively mitigate the close packing that leads to high pressure drops across ion exchange columns. Multiple evaluations have been performed to determine the feasibility of using spherical RF resin and to obtain data necessary for design of an SCIX process. The work performed consisted of examination of radiation effects on resin performance

  4. Coherent plasmon coupling in spherical metallodielectric multilayer nanoresonators

    NASA Astrophysics Data System (ADS)

    Rohde, Charles Alan

    In this thesis we theoretically and experimentally investigate the subwavelength manipulation of light with nano-scale patterned metallodielectric resonators. By coupling light to surface plasmon excitations, we calculate the modified dispersion relation of the resulting surface plasmon polariton (SPP) modes in two types of subwavelength resonators: (i) closed, spherical micro-resonators with nano-scale metal-dielectic-metal shells; (ii) periodic, metal-dielectric-metal-layered silica surfaces. We show theoretically that with the proper geometric parameters, one can use sub-wavelength structure on spherical surfaces to manipulate the SPP dispersion relation in a highly tunable fashion. A tunable avoided-crossing of plasmonic dispersion bands is found to be the result of the coherent near-field coupling of silver nano-shell SPP modes. By developing our own stable computational algorithms, we calculated the far-field scattering of these metal-dielectric-metal layered micro-resonators. We demonstrate that the near-field interaction of the SPPs leads to a tunable, SPP induced transparency in the composite particle's scattering and extinction cross-sections. Utilizing finite element calculations, periodically-modulated metal-dielectric-metal layers are shown to alter the transmission properties of plasmon enhanced transmission through their support of interior surface plasmon (ISP) modes. Our simulations indicate that, subwavelength silver-silica-silver trilayers coating arrays of silica cylinders support ISP modes analogous to those found in spherical metal-dielectric-metal shells. We examine the coupling between ISP and radiating SPPs, and find the possibility of efficient free-space coupling to ISP modes in planar geometries. Further, the excitation of these ISP modes is found to predicate plasmon enhanced transmission, adding directionality and refined frequency selection. Experimentally, we show that self-assembled monolayers of silica spheres form a novel

  5. Spherically symmetric model atmospheres for late-type giant stars

    NASA Astrophysics Data System (ADS)

    Bennett, Philip Desmond

    The ATHENA computer code was developed to model the extended atmospheres of late-type giant and supergiant stars. The atmospheres are assumed to be static, spherically symmetric and in radiative and hydrostatic equilibrium. Molecular line blanketing (for now) is handled using the simplifying assumption of mean opacity. The complete linearization method of Auer and Mihalas, adapted to spherical geometry, is used to solve the model system. The radiative transfer is solved by using variable Eddington factors to close the system of moment transfer equations, and the entire system of transfer equations plus constraints is solved efficiently by arrangement into the Rybicki block matrix form. The variable Eddington factors are calculated from the full angle-dependent formal solution of the radiative transfer problem using the impact parameter method of Hummer, Kunas. We were guided by the work of Mihalas and Hummer in their development of extended models of O stars, but our method differs in the choice of the independent variable. The radius depth scale used by Mihals and Hummer was found to fail because of the strongly temperature-dependent opacities of late-type atmospheres. Instead, we were able to achieve an exact linearization of the radius. This permitted the use of the numerically well-behaved column mass or optical depth scales. The resulting formulation is analogous to the plane-parallel complete linearization method and reduces to this method in the compact atmosphere limit. Models of M giants were calculated for Teff = 3000K and 3500K with opacities of the CN, TiO, and H2O molecules included, and the results were in general agreement with other published spherical models. These models were calculated assuming radiative equilibrium. The importance of convective energy transport was estimated by calculating the convective flux that would result from the temperature structure of the models. The standard local mixing length theory was used for this purpose

  6. A new spherical model for computing the radiation field available for photolysis and heating at twilight

    NASA Technical Reports Server (NTRS)

    Dahlback, Arne; Stamnes, Knut

    1991-01-01

    Accurate computation of atmospheric photodissociation and heating rates is needed in photochemical models. These quantities are proportional to the mean intensity of the solar radiation penetrating to various levels in the atmosphere. For large solar zenith angles a solution of the radiative transfer equation valid for a spherical atmosphere is required in order to obtain accurate values of the mean intensity. Such a solution based on a perturbation technique combined with the discrete ordinate method is presented. Mean intensity calculations are carried out for various solar zenith angles. These results are compared with calculations from a plane parallel radiative transfer model in order to assess the importance of using correct geometry around sunrise and sunset. This comparison shows, in agreement with previous investigations, that for solar zenith angles less than 90 deg adequate solutions are obtained for plane parallel geometry as long as spherical geometry is used to compute the direct beam attenuation; but for solar zenith angles greater than 90 deg this pseudospherical plane parallel approximation overstimates the mean intensity.

  7. Aspheric versus Spherical Posterior Chamber Intraocular Lenses

    PubMed Central

    Jafarinasab, Mohammad-Reza; Feizi, Sepehr; Baghi, Ahmad-Reza; Ziaie, Hossein; Yaseri, Mehdi

    2010-01-01

    Purpose To compare spherical aberration and contrast sensitivity function following implantation of four different foldable posterior chamber intraocular lenses (IOLs), namely Sensar, Akreos AO, Tecnis, and AcrySof IQ. Methods In this randomized clinical trial, 68 eyes of 68 patients with senile cataracts underwent phacoemulsification and IOL implantation with Sensar (n=17), Akreos AO (n=17), Tecnis (n=17), or AcrySof IQ (n=17). Uncorrected visual acuity (UCVA) and best spectacle-corrected visual acuity (BSCVA), spherical aberration and contrast sensitivity function (CSF) were compared among the study groups, 3 months after surgery. Results There was no significant difference between the study groups in terms of age (P = 0.21). Mean postoperative BSCVA with Sensar, Akreos AO, Tecnis, and AcrySof IQ was 0.15±0.10, 0.12±0.9, 0.08±0.08, and 0.08±0.07 logMAR, respectively (P=0.08). Spherical aberration measured over a 4 mm pupil was significantly higher with Sensar and Akreos AO than the two other IOLs. The difference between Tecnis and AcrySof IQ was significantly in favor of the former IOL. Over a 6 mm pupil, spherical aberrations were comparable with Sensar and Akreos AO, furthermore spherical aberration was also comparable among eyes implanted with Akreos AO, AcrySof IQ, and Tecnis. Sensar yielded significantly inferior results as compared to Acrysof IQ and Tecnis. CSF with Sensar was inferior to the three aspheric IOLs at the majority of spatial frequencies. Tecnis yielded significantly better mesopic CSF at 1.5 and 3 cycles per degree spatial frequencies. Conclusion Tecnis and AcrySof IQ provided significantly better visual function as compared to Sensar and Akreos AO, especially with smaller pupil size. However, this difference diminished with increasing pupil size. PMID:22737364

  8. Microwave and optical ray geometry

    NASA Astrophysics Data System (ADS)

    Cornbleet, S.

    The laws of refraction and reflection are examined, and the zero-distance phase front is discussed, taking into account aspects of definition and general derivation, refraction in a circular interface, reflection in a circle, reflection in a general curve, geometrical constructions, and caustic approximations. Other subjects explored are related to the inversion theorem of Damien, the mechanical description of optical surfaces, ray-tracing in nonuniform media, rays in linear and cylindrical media, rays in spherical and axisymmetric media, geodesics, rays and trajectories, curves and their formulae, derived curves, applications of Abel's integral, and the radiation patterns of Luneburg lenses. Attention is given to a geometrical method of optical design, lens bending, the general two-surface reflector system, the ray-tracing equations, expansions of the ray equations, transformations of the spherical lenses, and rays in an angular variable medium.

  9. Influence of modification of gravity on the dynamics of radiating spherical fluids

    NASA Astrophysics Data System (ADS)

    Yousaf, Z.; Bamba, Kazuharu; Bhatti, M. Zaeem ul Haq

    2016-03-01

    We explore the evolutionary behaviors of compact objects in a modified gravitational theory with the help of structure scalars. Particularly, we consider the spherical geometry coupled with heat- and radiation-emitting shearing viscous matter configurations. We construct structure scalars by splitting the Riemann tensor orthogonally in f (R ,T ) gravity with and without constant R and T constraints, where R is the Ricci scalar and T is the trace of the energy-momentum tensor. We investigate the influence of the modification of gravity on the physical meaning of scalar functions for radiating spherical matter configurations. It is explicitly demonstrated that even in modified gravity, the evolutionary phases of relativistic stellar systems can be analyzed through the set of modified scalar functions.

  10. Distortion of a spherical gaseous interface accelerated by a plane shock wave.

    PubMed

    Layes, Guillaume; Jourdan, Georges; Houas, Lazhar

    2003-10-24

    The evolution of a spherical gaseous interface accelerated by a plane weak shock wave has been investigated in a square cross section shock tube via a multiple exposure shadowgraph diagnostic. Different gaseous bubbles, i.e., helium, nitrogen, and krypton, were introduced in air at atmospheric pressure in order to study the Richtmyer-Meshkov instability in the spherical geometry for negative, close to zero, and positive initial density jumps across the interface. We show that the bubble distortion is strongly different for the three cases and we present the experimental velocity and volume of the developed vortical structures. We prove that at late times the bubble velocities reach constant values which are in good agreement with previous calculations. Finally, we point out that, in our flow conditions, the gaseous bubble motion and shape are mainly influenced by vorticity and aerodynamic forces. PMID:14611354

  11. Experiments on Thermal Convection in Rotating Spherical Shells With Radial Gravity: The Geophysical Fluid Flow Cell

    NASA Technical Reports Server (NTRS)

    Hart, John E.

    1996-01-01

    Experiments designed to study the fluid dynamics of buoyancy driven circulations in rotating spherical shells were conducted on the United States Microgravity Laboratory 2 spacelab mission. These experiments address several aspects of prototypical global convection relevant to large scale motions on the Sun, Earth, and on the giant planets. The key feature is the consistent modeling of radially directed gravity in spherical geometry by using dielectric polarization forces. Imagery of the planforms of thermally driven flows for rapidly-rotating regimes shows an initial separation and eventual merger of equatorial and polar convection as the heating (i.e. the Rayleigh number) is increased. At low rotation rates, multiple-states of motion for the same external parameters were observed.

  12. Spherically symmetric self-dual Yang-Mills instantons on curved backgrounds in all even dimensions

    SciTech Connect

    Radu, Eugen; Tchrakian, D. H.; Yang Yisong

    2008-02-15

    We present several different classes of self-dual Yang-Mills instantons in all even d-dimensional backgrounds with Euclidean signature. In d=4p+2 the only solutions we found are on constant curvature dS (de Sitter) and AdS (anti-de Sitter) backgrounds and are evaluated in closed form. In d=4p an interesting class of instantons are given on black hole backgrounds. One class of solutions are (Euclidean) time-independent and spherically symmetric in d-1 dimensions, and the other class are spherically symmetric in all d dimensions. Some of the solutions in the former class are evaluated numerically, all the rest being given in closed form. Analytic proofs of existence covering all numerically evaluated solutions are given. All instantons studied have finite action and vanishing energy momentum tensor and do not disturb the geometry.

  13. Occurrence of spherical ceramic debris in indentation and sliding contact

    NASA Technical Reports Server (NTRS)

    Miyoshi, K.; Buckley, D. H.

    1982-01-01

    Indenting experiments were conducted with the silicon carbide (0001) surface in contact with a spherical diamond indenter in air. Sliding friction experiments were also conducted with silicon carbide in contact with iron and iron-based binary alloys at room temperature and 800 C. Fracture pits with a spherical particle and spherical wear debris were observed as a result of indenting and sliding. Spherical debris may be produced by a mechanism that involves a spherical-shaped fracture along the circular or spherical stress trajectories under the inelastic deformation zone.

  14. Cylindrical and Spherical Electron-Acoustic Shock Waves in Electron-Positron-Ion Plasmas with Nonextensive Electrons and Positrons

    NASA Astrophysics Data System (ADS)

    Rafat, A.; M. M., Rahman; M. S., Alam; A. A., Mamun

    2015-02-01

    Electron-acoustic shock waves (EASWs) in an unmagnetized four-component plasma (containing hot electrons and positrons following the q-nonextensive distribution, cold mobile viscous electron fluid, and immobile positive ions) are studied in nonplanar (cylindrical and spherical) geometry. With the help of the reductive perturbation method, the modified Burgers equation is derived. Analytically, the effects of nonplanar geometry, nonextensivity, relative number density and temperature ratios, and cold electron kinematic viscosity on the basic properties (viz. amplitude, width, speed, etc.) of EASWs are discussed. It is examined that the EASWs in nonplanar geometry significantly differ from those in planar geometry. The results of this investigation can be helpful in understanding the nonlinear features of EASWs in various astrophysical plasmas.

  15. Thermal convection in a 3D spherical shell with strongly temperature and pressure dependent viscosity

    NASA Astrophysics Data System (ADS)

    Stemmer, K.; Harder, H.; Hansen, U.

    2004-12-01

    The style of convection in planetary mantles is presumably dominated by the strong dependence of the viscosity of the mantle material on temperature and pressure. While several efforts have been undertaken in cartesian geometry to investigate convection in media with strong temperature dependent viscosity, spherical models are still in their infancy and still limited to modest parameters. Spectral approaches are usually employed for spherical convection models which do not allow to take into account lateral variations, like temperature dependent viscosity. We have developed a scheme, based on a finite volume discretization, to treat convection in a spherical shell with strong temperature dependent viscosity. Our approach has been particularly tailored to run efficiently on parallel computers. The spherical shell is topologically divided into six cubes. The equations are formulated in primitive variables, and are treated in the cartesian cubes. In order to ensure mass conservation a SIMPLER pressure correction procedure is applied and to handle strong viscosity variations up to Δ η =106 and high Rayleigh-numbers up to Ra=108 the pressure correction algorithm is combined with a pressure weighted interpolation method to satisfy the incompressibility condition and to avoid oscillations. We study thermal convection in a basal and mixed-mode heated shell with stress free and isothermal boundary conditions, as a function of the Rayleigh-number and viscosity contrast. Besides the temperature dependence we have further explored the effects of pressure on the viscosity. As a general result we observe the existence of three regimes (mobile, sluggish and stagnant lid), characterized by the type of surface motion. Laterally averaged depth-profiles of velocity, temperature and viscosity exhibit significant deviations from the isoviscous case. As compared to cartesian geometries, convection in a spherical shell possesses strong memory for the initial state. At strong

  16. Simulation of angle on geometry anisotropic semivariogram modeling in the case of oil in Jatibarang reservoir

    NASA Astrophysics Data System (ADS)

    Sari, Rr. Kurnia Novita; Neswan, Oki

    2015-12-01

    Anisotropic semivariogram modeling can be aplied in petroleum industry where the angle between a pair of wells has important function in defining the spatial correlation between wells. In geometry anisotropic, function of range is formulated in trigonometric functions of the angle between pairs of wells that have periodicity property. The fluctuations of range will affect on shifting geometry anisotropic models with different properties for each quadrant of angle. In three semivariogram models (exponential, spherical and gaussian), the increasing of angle give difference influence for range function and the shifting of semivariogram value.

  17. Impact of contact lens zone geometry and ocular optics on bifocal retinal image quality

    PubMed Central

    Bradley, Arthur; Nam, Jayoung; Xu, Renfeng; Harman, Leslie; Thibos, Larry

    2014-01-01

    Purpose To examine the separate and combined influences of zone geometry, pupil size, diffraction, apodisation and spherical aberration on the optical performance of concentric zonal bifocals. Methods Zonal bifocal pupil functions representing eye + ophthalmic correction were defined by interleaving wavefronts from separate optical zones of the bifocal. A two-zone design (a central circular inner zone surrounded by an annular outer-zone which is bounded by the pupil) and a five-zone design (a central small circular zone surrounded by four concentric annuli) were configured with programmable zone geometry, wavefront phase and pupil transmission characteristics. Using computational methods, we examined the effects of diffraction, Stiles Crawford apodisation, pupil size and spherical aberration on optical transfer functions for different target distances. Results Apodisation alters the relative weighting of each zone, and thus the balance of near and distance optical quality. When spherical aberration is included, the effective distance correction, add power and image quality depend on zone-geometry and Stiles Crawford Effect apodisation. When the outer zone width is narrow, diffraction limits the available image contrast when focused, but as pupil dilates and outer zone width increases, aberrations will limit the best achievable image quality. With two-zone designs, balancing near and distance image quality is not achieved with equal area inner and outer zones. With significant levels of spherical aberration, multi-zone designs effectively become multifocals. Conclusion Wave optics and pupil varying ocular optics significantly affect the imaging capabilities of different optical zones of concentric bifocals. With two-zone bifocal designs, diffraction, pupil apodisation spherical aberration, and zone size influence both the effective add power and the pupil size required to balance near and distance image quality. Five-zone bifocal designs achieve a high degree of

  18. 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.

  19. Quantum geometry and gravitational entropy

    SciTech Connect

    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.

  20. 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.

  1. 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…

  2. Geometry of generalized depolarizing channels

    SciTech Connect

    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.

  3. Geometry, topology, and string theory

    SciTech Connect

    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.

  4. Measurement of reflectivity of spherically bent crystals using Kα signal from hot electrons produced by laser-matter interaction

    SciTech Connect

    Antonelli, L.; Forestier-Colleoni, P.; Folpini, G.; Bouillaud, R.; Fedeli, L.; Fourment, C.; Giuffrida, L.; Hulin, S.; Santos, J. J.; Volpe, L.; Batani, D.; Faenov, A.; Pikuz, S.

    2015-07-15

    In an experiment at the laser facility ECLIPSE of the CELIA laboratory, University of Bordeaux, we measure the reflectivity of spherically bent crystals that are commonly used to investigate the propagation of fast electrons through the Kα radiation they generate in matter. The experimental reflectivity compares well with predictions from a ray-tracing code that takes into account the specific geometry, although the crystals seem to suffer from aging problems.

  5. Mode-selective quantization and multimodal effective models for spherically layered systems

    NASA Astrophysics Data System (ADS)

    Dzsotjan, D.; Rousseaux, B.; Jauslin, H. R.; des Francs, G. Colas; Couteau, C.; Guérin, S.

    2016-08-01

    We propose a geometry-specific, mode-selective quantization scheme in coupled field-emitter systems which makes it easy to include material and geometrical properties, and intrinsic losses, as well as the positions of an arbitrary number of quantum emitters. The method is presented through the example of a spherically symmetric, nonmagnetic, arbitrarily layered system. We follow it up by a framework to project the system on simpler, effective cavity QED models. Maintaining a well-defined connection to the original quantization, we derive the emerging effective quantities from the full, mode-selective model in a mathematically consistent way. We discuss the uses and limitations of these effective models.

  6. Spherical roller bearing analysis. SKF computer program SPHERBEAN. Volume 1: Analysis

    NASA Technical Reports Server (NTRS)

    Kleckner, R. J.; Pirvics, J.

    1980-01-01

    The models and associated mathematics used within the SPHERBEAN computer program for prediction of the thermomechanical performance characteristics of high speed lubricated double row spherical roller bearings are presented. The analysis allows six degrees of freedom for each roller and three for each half of an optionally split cage. Roller skew, free lubricant, inertial loads, appropriate elastic and friction forces, and flexible outer ring are considered. Roller quasidynamic equilibrium is calculated for a bearing with up to 30 rollers per row, and distinct roller and flange geometries are specifiable. The user is referred to the material contained here for formulation assumptions and algorithm detail.

  7. Formation of sheet plumes, current coils, and helical magnetic fields in a spherical magnetohydrodynamic dynamo

    NASA Astrophysics Data System (ADS)

    Miyagoshi, Takehiro; Kageyama, Akira; Sato, Tetsuya

    2011-07-01

    Aiming at understanding of magnetic field generation process in rapidly rotating stars and planets represented by the Earth, computer simulations of magnetohydrodynamic (MHD) dynamo were performed in a rotating spherical shell geometry. Thermal convection and dynamo process with Ekman number of the order of 10-7 were studied. New structures of convection motion, dynamo-generated electrical current, and magnetic field are found. The flow is organized as a set of thin, sheet-like plumes. The current is made of small-scale coil structure with magnetic flux tubes within each of the coil. These flux tubes are connected each other to form a large scale helical magnetic field structure.

  8. Clusters of polyhedra in spherical confinement

    NASA Astrophysics Data System (ADS)

    Teich, Erin; van Anders, Greg; Klotsa, Daphne; Dshemuchadse, Julia; Glotzer, Sharon

    Dense particle packing in a confining volume is a rich, largely unexplored problem, with applications in blood clotting, plasmonics, industrial packaging and transport, colloidal molecule design, and information storage. We report simulation results for dense clusters of the Platonic solids in spherical confinement, for up to N = 60 constituent particles. We discuss similarities between clusters in terms of symmetry, a connection to spherical codes, and generally the interplay between isotropic geometrical confinement and anisotropic particle shape. Our results showcase the structural diversity and experimental utility of families of solutions to the problem of packing in confinement. E.T. acknowledges support by the National Science Foundation Graduate Research Fellowship under Grant No. DGE 1256260.

  9. A Simple Weighing Method for Spherical Cells.

    PubMed

    Zhao, Qili; Shirinzadeh, Bijan; Cui, Maosheng; Sun, Mingzhu; Zhao, Xin

    2015-08-01

    This article presents a simple weighing method for spherical cells to avoid the high cost of correlated devices in traditional cell-weighing methods. In this method, the constant falling speeds of the spherical objects in liquid are derived to estimate their masses online. Using this method, the detected density of one type of microbead is highly in accordance with the known value. This method is proved to be capable of detecting tiny variations of the cell mass (at least within 1% of the cell mass). Finally, the proposed method is applied in nuclear transplantation operations, and, for the first time, the proper amount of the removed cytoplasm in porcine enucleation is estimated. The proposed method is able to weigh cells with a success rate of 92% at an average speed of 22 s/cell, and it can be performed on traditional microoperation systems, which makes it easily applicable in biological applications. PMID:25911396

  10. Lindblad dynamics of a quantum spherical spin

    NASA Astrophysics Data System (ADS)

    Wald, Sascha; Henkel, Malte

    2016-03-01

    The coherent quantum dynamics of a single bosonic spin variable, subject to a constraint derived from the quantum spherical model of a ferromagnet, and coupled to an external heat bath, is studied through the Lindblad equation for the reduced density matrix. Closed systems of equations of motion for several quantum observables are derived and solved exactly. The relationship to the single-mode Dicke model from quantum optics is discussed. The analysis of the interplay of the quantum fluctuation and the dissipation and their influence on the relaxation of the time-dependent magnetisation leads to the distinction of qualitatively different regimes of weak and strong quantum couplings. Considering the model’s behaviour in an external field as a simple mean-field approximation of the dynamics of a quantum spherical ferromagnet, the magnetic phase diagram appears to be re-entrant and presents a quantum analogue of well-established classical examples of fluctuation-induced order.

  11. Nonlinear cosmological spherical collapse of quintessence

    NASA Astrophysics Data System (ADS)

    Rekier, J.; Füzfa, A.; Cordero-Carrión, I.

    2016-02-01

    We present a study of the fully relativistic spherical collapse in the presence of quintessence using on numerical relativity, following the method proposed by the authors in a previous article [Phys. Rev. D 91, 024025 (2015)]. We ascertain the validity of the method by studying the evolution of a spherically symmetric quintessence inhomogeneity on a de Sitter background and we find that it has an impact on the local expansion around the center of coordinates. We then proceed to compare the results of our method to those of the more largely adopted top-hat model. We find that quintessence inhomogeneities do build up under the effect that matter inhomogeneities have on the local space-time, yet remain very small due to the presence of momentum transfer from the over-dense to the background regions. We expect that these might have an even more important role in modified theories of gravitation.

  12. Flow past a porous approximate spherical shell

    NASA Astrophysics Data System (ADS)

    Srinivasacharya, D.

    2007-07-01

    In this paper, the creeping flow of an incompressible viscous liquid past a porous approximate spherical shell is considered. The flow in the free fluid region outside the shell and in the cavity region of the shell is governed by the Navier Stokes equation. The flow within the porous annulus region of the shell is governed by Darcy’s Law. The boundary conditions used at the interface are continuity of the normal velocity, continuity of the pressure and Beavers and Joseph slip condition. An exact solution for the problem is obtained. An expression for the drag on the porous approximate spherical shell is obtained. The drag experienced by the shell is evaluated numerically for several values of the parameters governing the flow.

  13. Imaging with Spherically Bent Crystals or Reflectors

    SciTech Connect

    Bitter, M; Hill, K W; Scott, S; Ince-Cushman, A; Reinke, M; Podpaly, Y; Rice, J E; Beiersdorfer, P

    2010-06-01

    This paper consists of two parts: Part I describes the working principle of a recently developed x-ray imaging crystal spectrometer, where the astigmatism of spherically bent crystals is being used with advantage to record spatially resolved spectra of highly charged ions for Doppler measurements of the ion-temperature and toroidal plasmarotation- velocity profiles in tokamak plasmas. This type of spectrometer was thoroughly tested on NSTX and Alcator C-Mod, and its concept was recently adopted for the design of the ITER crystal spectrometers. Part II describes imaging schemes, where the astigmatism has been eliminated by the use of matched pairs of spherically bent crystals or reflectors. These imaging schemes are applicable over a wide range of the electromagnetic radiation, which includes microwaves, visible light, EUV radiation, and x-rays. Potential applications with EUV radiation and x-rays are the diagnosis of laserproduced plasmas, imaging of biological samples with synchrotron radiation, and lithography.

  14. Electron Bernstein waves in spherical torus plasmas

    SciTech Connect

    Saveliev, A. N.

    2006-11-30

    Propagation and absorption of the electron Bernstein waves (EBWs) in spherical tokamaks (STs) have been intensively discussed in recent years because the EBWs coupled with an externally launched electromagnetic beam seem to be the only opportunity for microwave plasma heating and current drive in the electron cyclotron (EC) frequency range in the STs. The whole problem of the electron Bernstein heating and current drive (EBWHCD) in spherical plasmas is naturally divided into three major parts: coupling of incident electromagnetic waves (EMWs) to the EBWs near the upper hybrid resonance (UHR) surface, propagation and absorption of the EBWs in the plasma interior and generation of noninductive current driven by the EBWs. The present paper is a brief survey of the most important theoretical and numerical results on the issue of EBWs.

  15. Testing the spherical evolution of cosmic voids

    NASA Astrophysics Data System (ADS)

    Demchenko, Vasiliy; Cai, Yan-Chuan; Heymans, Catherine; Peacock, John A.

    2016-08-01

    We study the spherical evolution model for voids in ΛCDM, where the evolution of voids is governed by dark energy at an earlier time than that for the whole universe or in overdensities. We show that the presence of dark energy suppresses the growth of peculiar velocities, causing void shell-crossing to occur at progressively later epochs as ΩΛ increases. We apply the spherical model to evolve the initial conditions of N-body simulated voids and compare the resulting final void profiles. We find that the model is successful in tracking the evolution of voids with radii greater than 30 h-1Mpc, implying that void profiles could be used to constrain dark energy. We find that the initial peculiar velocities of voids play a significant role in shaping their evolution. Excluding the peculiar velocity in the evolution model delays the time of shell crossing.

  16. Velocity and velocity bounds in static spherically symmetric metrics

    NASA Astrophysics Data System (ADS)

    Arraut, Ivan; Batic, Davide; Nowakowski, Marek

    2011-08-01

    We find simple expressions for velocity of massless particles with dependence on the distance, r, in Schwarzschild coordinates. For massive particles these expressions give an upper bound for the velocity. Our results apply to static spherically symmetric metrics. We use these results to calculate the velocity for different cases: Schwarzschild, Schwarzschild-de Sitter and Reissner-Nordström with and without the cosmological constant. We emphasize the differences between the behavior of the velocity in the different metrics and find that in cases with naked singularity there always exists a region where the massless particle moves with a velocity greater than the velocity of light in vacuum. In the case of Reissner-Nordström-de Sitter we completely characterize the velocity and the metric in an algebraic way. We contrast the case of classical naked singularities with naked singularities emerging from metric inspired by noncommutative geometry where the radial velocity never exceeds one. Furthermore, we solve the Einstein equations for a constant and polytropic density profile and calculate the radial velocity of a photon moving in spaces with interior metric. The polytropic case of radial velocity displays an unexpected variation bounded by a local minimum and maximum.

  17. 3-D Spherical Mantle Convection with Radial Basis Functions

    NASA Astrophysics Data System (ADS)

    Flyer, N.; Wright, G. B.; Yuen, D.

    2008-12-01

    In the past 25 years a wide variety of numerical methods, such as finite-difference, finite-volume , finite- elements, and pseudospectral methods have been employed to study the problem of 3-D mantle convection. All have specialized strengths but also serious weaknesses. The first three methods are generally considered low-order and can involve high algorithmic complexity (as in triangular elements). Spectrally accurate methods do not practically allow for local mesh refinement and often involve cumbersome algebra. Here, we introduce a new grid/mesh-free approach using radial basis functions (RBFs). It has the advantage of being spectrally accurate for arbitrary node layouts in multi-dimensions with extreme algorithmic simplicity, and naturally permits local node refinement. It has been shown for shallow-water equations and vortex flows that RBFs outperform other numerical methods in the sense that they obtain a much higher accuracy for the same spatial resolution while being able to take unusually large time steps. One virtue of the RBF scheme is the ability to use a simple Cartesian geometry while implementing the required boundary conditions for the temperature, velocity and stresses on a spherical surface of both the outer( planetary surface ) and inner shell ( core-mantle boundary ). The velocity and stress components are expressed in terms of the scalar potential approach (Zebib and Schubert, 1982) and the other remaining variable is the perturbed temperature field. We have studied the problem from the onset of convection to a modest nonlinear regime.

  18. Experimental study of the dynamics of a spherical flame

    NASA Technical Reports Server (NTRS)

    Oppenheim, A. K.; Kamel, M. M.; Varvatsoulis, C.

    1973-01-01

    Preliminary results of an experimental study conducted to investigate the dynamic behavior of flames in explosive gases are presented. The medium was an equimolar acetylene-oxygen mixture maintained initially at a pressure of 110 torr. and room temperature in an experimental vessel 9 cm in internal diameter. Ignition was performed by means of a neodymium laser beam focused on a 0.3 mm diameter steel wire. Experimental observations were performed by the use of a stroboscopic laser-schlieren system yielding a set of photographic records of wave phenomena at a frequency of 200,000 per second. The records reveal the existence of a number of shocks which by a thorough analysis of the blast wave generated by the ignition process, are shown to be due entirely to the flame generated flow field. The capability of a flame to form blast waves in an expanding spherical geometry is thus established, providing an experimental demonstration of the significance the dynamic effects of combustion can achieve.

  19. Direct Simulation of Extinction in a Slab of Spherical Particles

    NASA Technical Reports Server (NTRS)

    Mackowski, D.W.; Mishchenko, Michael I.

    2013-01-01

    The exact multiple sphere superposition method is used to calculate the coherent and incoherent contributions to the ensemble-averaged electric field amplitude and Poynting vector in systems of randomly positioned nonabsorbing spherical particles. The target systems consist of cylindrical volumes, with radius several times larger than length, containing spheres with positional configurations generated by a Monte Carlo sampling method. Spatially dependent values for coherent electric field amplitude, coherent energy flux, and diffuse energy flux, are calculated by averaging of exact local field and flux values over multiple configurations and over spatially independent directions for fixed target geometry, sphere properties, and sphere volume fraction. Our results reveal exponential attenuation of the coherent field and the coherent energy flux inside the particulate layer and thereby further corroborate the general methodology of the microphysical radiative transfer theory. An effective medium model based on plane wave transmission and reflection by a plane layer is used to model the dependence of the coherent electric field on particle packing density. The effective attenuation coefficient of the random medium, computed from the direct simulations, is found to agree closely with effective medium theories and with measurements. In addition, the simulation results reveal the presence of a counter-propagating component to the coherent field, which arises due to the internal reflection of the main coherent field component by the target boundary. The characteristics of the diffuse flux are compared to, and found to be consistent with, a model based on the diffusion approximation of the radiative transfer theory.

  20. Gravito-inertial modes in a differentially rotating spherical shell

    NASA Astrophysics Data System (ADS)

    Mirouh, Giovanni M.; Baruteau, Clément; Rieutord, Michel; Ballot, Jérôme

    2015-09-01

    While many intermediate- and high-mass main sequence stars are rapidly and differentially rotating, the effects of rotation on oscillation modes are poorly known. In this communication we present a first study of axisymmetric gravito-inertial modes in the radiative zone of a differentially rotating star. We consider a simplified model where the radiative zone of the star is a linearly stratified rotating fluid within a spherical shell, with differential rotation due to baroclinic effects. We solve the eigenvalue problem with high-resolution spectral computations and determine the propagation domain of the waves through the theory of characteristics. We explore the propagation properties of two kinds of modes: those that can propagate in the entire shell and those that are restricted to a sub-domain. Some of the modes that we find concentrate kinetic energy around short-period shear layers known as attractors. We describe various geometries for the propagation domains, conditioning the surface visibility of the corresponding modes.

  1. Interaction between two spherical particles in a nematic liquid crystal

    NASA Astrophysics Data System (ADS)

    Fukuda, Jun-Ichi; Stark, Holger; Yoneya, Makoto; Yokoyama, Hiroshi

    2004-04-01

    We numerically investigate the interaction between two spherical particles in a nematic liquid crystal mediated by elastic distortions in the orientational order. We pay attention to the cases where two particles with equal radii R0 impose rigid normal anchoring on their surfaces and carry a pointlike topological defect referred to as a hyperbolic hedgehog. To describe the geometry of our system, we use bispherical coordinates, which prove useful in the implementation of boundary conditions at the particle surfaces and at infinity. We adopt the Landau de Gennes continuum theory in terms of a second-rank tensor order parameter Qij for the description of the orientational order of a nematic liquid crystal. We also utilize an adaptive mesh refinement scheme that has proven to be an efficient way of dealing with topological defects whose core size is much smaller than the particle size. When the two “dipoles,” composed of a particle and a hyperbolic hedgehog, are in parallel directions, the two-particle interaction potential is attractive for large interparticle distances D and proportional to D-3 as expected from the form of the dipole-dipole interaction, until the well-defined potential minimum at D≃2.46 R0 is reached. For the antiparallel configuration with no hedgehogs between the two particles, the interaction potential is repulsive and behaves as D-2 for D≲10 R0 , which is stronger than the dipole-dipole repulsion ( ˜ D-3 ) expected theoretically as an asymptotic behavior for large D .

  2. Spherical indentation of free-standing acellular extracellular matrix membranes.

    PubMed

    Cloonan, Aidan J; O'Donnell, Michael R; Lee, William T; Walsh, Michael T; De Barra, Eamonn; McGloughlin, Tim M

    2012-01-01

    Numerous scaffold materials have been developed for tissue engineering and regenerative medicine applications to replace or repair damaged tissues and organs. Naturally occurring scaffold materials derived from acellular xenogeneic and autologous extracellular matrix (ECM) are currently in clinical use. These biological scaffold materials possess inherent variations in mechanical properties. Spherical indentation or ball burst testing has commonly been used to evaluate ECM and harvested tissue due to its ease of use and simulation of physiological biaxial loading, but has been limited by complex material deformation profiles. An analytical methodology has been developed and applied to experimental load-deflection data of a model hyperelastic material and lyophilized ECM scaffolds. An optimum rehydration protocol was developed based on water absorption, hydration relaxation and dynamic mechanical analysis. The analytical methodology was compared with finite element simulations of the tests and excellent correlation was seen between the computed biaxial stress resultants and geometry deformations. A minimum rehydration period of 5 min at 37°C was sufficient for the evaluated multilaminated ECM materials. The proposed approach may be implemented for convenient comparative analysis of ECM materials and source tissues, process optimization or during lot release testing. PMID:21864728

  3. Evolution of linear perturbations in spherically symmetric dust spacetimes

    NASA Astrophysics Data System (ADS)

    February, S.; Larena, J.; Clarkson, C.; Pollney, D.

    2014-09-01

    We present results from a numerical code implementing a new method to solve the master equations describing the evolution of linear perturbations in a spherically symmetric but inhomogeneous background. This method can be used to simulate several configurations of physical interest, such as relativistic corrections to structure formation, the lensing of gravitational waves (GWs) and the evolution of perturbations in a cosmological void model. This paper focuses on the latter problem, i.e. structure formation in a Hubble scale void in the linear regime. This is considerably more complicated than linear perturbations of a homogeneous and isotropic background because the inhomogeneous background leads to coupling between density perturbations and rotational modes of the spacetime geometry, as well as GWs. Previous analyses of this problem ignored this coupling in the hope that the approximation does not affect the overall dynamics of structure formation in such models. We show that for a giga-parsec void, the evolution of the density contrast is well approximated by the previously studied decoupled evolution only for very large-scale modes. However, the evolution of the gravitational potentials within the void is inaccurate at more than the 10% level, and is even worse on small scales.

  4. Compact spherical neutron polarimeter using high-Tc YBCO films

    NASA Astrophysics Data System (ADS)

    Wang, T.; Parnell, S. R.; Hamilton, W. A.; Li, F.; Washington, A. L.; Baxter, D. V.; Pynn, R.

    2016-03-01

    We describe a simple, compact device for spherical neutron polarimetry measurements at small neutron scattering angles. The device consists of a sample chamber with very low (<0.01 G) magnetic field flanked by regions within which the neutron polarization can be manipulated in a controlled manner. This allows any selected initial and final polarization direction of the neutrons to be obtained. We have constructed a prototype device using high-Tc superconducting films and mu-metal to isolate regions with different magnetic fields and tested device performance in transmission geometry. Finite-element methods were used to simulate the device's field profile and these have been verified by experiment using a small solenoid as a test sample. Measurements are reported using both monochromatic and polychromatic neutron sources. The results show that the device is capable of extracting sample information and distinguishing small angular variations of the sample magnetic field. As a more realistic test, we present results on the characterization of a 10 μm thick Permalloy film in zero magnetic field, as well as its response to an external magnetic field.

  5. Radio flares of compact binary mergers: the effect of non-trivial outflow geometry

    NASA Astrophysics Data System (ADS)

    Margalit, Ben; Piran, Tsvi

    2015-10-01

    The next generation gravitational waves (GW) detectors are most sensitive to GW emitted by compact (neutron star/black hole) binary mergers. If one of those is a neutron star the merger will also emit electromagnetic radiation via three possible channels: gamma-ray bursts and their (possibly orphan) afterglows, Li-Paczynski Macronovae and radio flares. This accompanying electromagnetic radiation is vitally important in confirming the GW detections. It could also reveal a wealth of information regarding the merger and will open a window towards multimessenger astronomy. Identifying and characterizing these counterparts is therefore of utmost importance. In this work, we explore late time radio flares emitted by the dynamically ejected outflows. We build upon previous work and consider the effect of the outflow's non-trivial geometry. Using an approximate method, we estimate the radio light-curves for several ejected matter distributions obtained in numerical simulations. Our method provides an upper limit to the effect of non-sphericity. Together with the spherical estimates, the resulting light curves bound the actual signal. We find that while non-spherical geometries can in principle lead to an enhanced emission, in most cases they result in an increase in the time-scale compared with a corresponding spherical configuration. This would weaken somewhat these signals and might decrease the detection prospects.

  6. Intrinsic geometry of a tidally deformed Kerr horizon

    NASA Astrophysics Data System (ADS)

    Poisson, Eric

    2013-04-01

    The intrinsic metric of a tidally deformed black-hole horizon can be presented in a coordinate system adapted to the horizon's null generators, with one coordinate acting as a running parameter along each generator, and two coordinates acting as constant generator labels. The metric is invariant under reparametrizations of the generators, and as such the horizon's intrinsic geometry is known to be gauge invariant. We consider a Kerr black hole deformed by a slowly-evolving external tidal field, and describe the intrinsic geometry of its event horizon in terms of the electric and magnetic tidal moments that characterize the tidal environment. When the black hole is slowly rotating, the horizon's geometry can be described in terms of a deviation from an otherwise spherical surface, and the deformation can be characterized by gauge invariant Love numbers. Some aspects of this tidal deformation have direct analogues in Newtonian physics. Some do not, and I will describe the similarities and differences between the tidal deformation of rotating black holes in general relativity and rotating fluid bodies in Newtonian physics.

  7. Electromagnetic signatures of thin accretion disks in wormhole geometries

    SciTech Connect

    Harko, Tiberiu; Kovacs, Zoltan; Lobo, Francisco S. N.

    2008-10-15

    In this paper, we study the physical properties and characteristics of matter forming thin accretion disks in static and spherically symmetric wormhole spacetimes. In particular, the time averaged energy flux, the disk temperature, and the emission spectra of the accretion disks are obtained for these exotic geometries and are compared with the Schwarzschild solution. It is shown that more energy is emitted from the disk in a wormhole geometry than in the case of the Schwarzschild potential and the conversion efficiency of the accreted mass into radiation is more than a factor of 2 higher for the wormholes than for static black holes. These effects in the disk radiation are confirmed in the radial profiles of temperature corresponding to theses flux distributions, and in the emission spectrum {omega}L({omega}) of the accretion disks. We conclude that specific signatures appear in the electromagnetic spectrum, thus leading to the possibility of distinguishing wormhole geometries by using astrophysical observations of the emission spectra from accretion disks.

  8. Spherical Cancer Models in Tumor Biology1

    PubMed Central

    Weiswald, Louis-Bastien; Bellet, Dominique; Dangles-Marie, Virginie

    2015-01-01

    Three-dimensional (3D) in vitro models have been used in cancer research as an intermediate model between in vitro cancer cell line cultures and in vivo tumor. Spherical cancer models represent major 3D in vitro models that have been described over the past 4 decades. These models have gained popularity in cancer stem cell research using tumorospheres. Thus, it is crucial to define and clarify the different spherical cancer models thus far described. Here, we focus on in vitro multicellular spheres used in cancer research. All these spherelike structures are characterized by their well-rounded shape, the presence of cancer cells, and their capacity to be maintained as free-floating cultures. We propose a rational classification of the four most commonly used spherical cancer models in cancer research based on culture methods for obtaining them and on subsequent differences in sphere biology: the multicellular tumor spheroid model, first described in the early 70s and obtained by culture of cancer cell lines under nonadherent conditions; tumorospheres, a model of cancer stem cell expansion established in a serum-free medium supplemented with growth factors; tissue-derived tumor spheres and organotypic multicellular spheroids, obtained by tumor tissue mechanical dissociation and cutting. In addition, we describe their applications to and interest in cancer research; in particular, we describe their contribution to chemoresistance, radioresistance, tumorigenicity, and invasion and migration studies. Although these models share a common 3D conformation, each displays its own intrinsic properties. Therefore, the most relevant spherical cancer model must be carefully selected, as a function of the study aim and cancer type. PMID:25622895

  9. Nonlinear axisymmetric flexural vibration of spherical shells

    NASA Technical Reports Server (NTRS)

    Kunieda, H.

    1972-01-01

    Axisymmetric responses are presented of a nonshallow thin-walled spherical shell on the basis of nonlinear bending theory. An ordinary differential equation with nonlinearity of quadratic as well as cubic terms associated with variable time is derived. The derivation is based on the assumption that the deflection mode is the sum of four Legendre polynomials, and the Galerkin procedure is applied. The equation is solved by asymptotic expansion, and a first approximate solution is adopted. Unstable regions of this solution are discussed.

  10. Wave equation on spherically symmetric Lorentzian metrics

    SciTech Connect

    Bokhari, Ashfaque H.; Al-Dweik, Ahmad Y.; Zaman, F. D.; Kara, A. H.; Karim, M.

    2011-06-15

    Wave equation on a general spherically symmetric spacetime metric is constructed. Noether symmetries of the equation in terms of explicit functions of {theta} and {phi} are derived subject to certain differential constraints. By restricting the metric to flat Friedman case the Noether symmetries of the wave equation are presented. Invertible transformations are constructed from a specific subalgebra of these Noether symmetries to convert the wave equation with variable coefficients to the one with constant coefficients.

  11. Sequential and Parallel Algorithms for Spherical Interpolation

    NASA Astrophysics Data System (ADS)

    De Rossi, Alessandra

    2007-09-01

    Given a large set of scattered points on a sphere and their associated real values, we analyze sequential and parallel algorithms for the construction of a function defined on the sphere satisfying the interpolation conditions. The algorithms we implemented are based on a local interpolation method using spherical radial basis functions and the Inverse Distance Weighted method. Several numerical results show accuracy and efficiency of the algorithms.

  12. Testing spherical evolution for modelling void abundances

    NASA Astrophysics Data System (ADS)

    Achitouv, Ixandra; Neyrinck, Mark; Paranjape, Aseem

    2015-08-01

    We compare analytical predictions of void volume functions to those measured from N-body simulations, detecting voids with the ZOBOV void finder. We push to very small, non-linear voids, below few Mpc radius, by considering the unsampled dark matter density field. We also study the case where voids are identified using haloes. We develop analytical formula for the void abundance of both the excursion set approach and the peaks formalism. These formulas are valid for random walks smoothed with a top-hat filter in real space, with a large class of realistic barrier models. We test the extent to which the spherical evolution approximation, which forms the basis of the analytical predictions, models the highly aspherical voids that occur in the cosmic web, and are found by a watershed-based algorithm such as ZOBOV. We show that the volume function returned by ZOBOV is quite sensitive to the choice of treatment of subvoids, a fact that has not been appreciated previously. For reasonable choices of subvoid exclusion, we find that the Lagrangian density δv of the ZOBOV voids - which is predicted to be a constant δv ≈ -2.7 in the spherical evolution model - is different from the predicted value, showing substantial scatter and scale dependence. This result applies to voids identified at z = 0 with effective radius between 1 and 10 h-1 Mpc. Our analytical approximations are flexible enough to give a good description of the resulting volume function; however, this happens for choices of parameter values that are different from those suggested by the spherical evolution assumption. We conclude that analytical models for voids must move away from the spherical approximation in order to be applied successfully to observations, and we discuss some possible ways forward.

  13. Spherically symmetric solutions in a FRW background

    NASA Astrophysics Data System (ADS)

    Moradpour, H.; Riazi, N.

    2015-02-01

    We impose perfect fluid concept along with slow expansion approximation to derive new solutions which, considering non-static spherically symmetric metrics, can be treated as Black Holes (BHs). We will refer to these solutions as Quasi BHs. Mathematical and physical features such as Killing vectors, singularities, and mass have been studied. Their horizons and thermodynamic properties have also been investigated. In addition, relationship with other related works (including McVittie's) are described.

  14. Selfsimilar Spherical Compression Waves in Gas Dynamics

    NASA Astrophysics Data System (ADS)

    Meyer-ter-Vehn, J.; Schalk, C.

    1982-08-01

    A synopsis of different selfsimilar spherical compression waves is given pointing out their fundamental importance for the gas dynamics of inertial confinement fusion. Strong blast waves, various forms of isentropic compression waves, imploding shock waves and the solution for non-isentropic collapsing hollow spheres are included. A classification is given in terms of six singular points which characterise the different solutions and the relations between them. The presentation closely follows Guderley's original work on imploding shock waves

  15. Selfsimilar spherical compression waves in gas dynamics

    NASA Astrophysics Data System (ADS)

    Meyer-Ter-Vehn, J.; Schalk, C.

    1982-05-01

    A synopsis of different selfsimilar spherical compression waves is given pointing out their fundamental importance for the gas dynamics of inertial confinement fusion. Strong blast waves, various forms of isentropic collapsing hollow spheres are included. A classification is given in terms of six singular points which characterize the different solutions and the relations between them. The presentation closely follows Guderley's original work on imploding shock waves.

  16. On Recurrence Formulae of Solid Spherical Monogenics

    SciTech Connect

    Bock, S.; Guerlebeck, K.

    2008-09-01

    We construct a new orthonormal basis of solid spherical monogenics in L{sub 2}. The important property of the basis polynomials is that the hypercomplex derivative as well as the primitive yield (up to a factor) again a basis function of the same system. Besides we refine a decomposition theorem for monogenic functions. With these properties the polynomial system provides a powerful tool to analyze orthogonal series expansions.

  17. Spherical cloaking with homogeneous isotropic multilayered structures.

    PubMed

    Qiu, Cheng-Wei; Hu, Li; Xu, Xiaofei; Feng, Yijun

    2009-04-01

    We propose a practical realization of electromagnetic spherical cloaking by layered structure of homogeneous isotropic materials. By mimicking the classic anisotropic cloak by many alternating thin layers of isotropic dielectrics, the permittivity and permeability in each isotropic layer can be properly determined by effective medium theory in order to achieve invisibility. The model greatly facilitates modeling by Mie theory and realization by multilayer coating of dielectrics. Eigenmode analysis is also presented to provide insights of the discretization in multilayers. PMID:19518392

  18. Spherical ion kinetic simulations of DT implosions

    SciTech Connect

    Vidal, F.; Matte, J.P.; Casanova, M.; Larroche, O.

    1995-10-01

    The implosion of the DT plasma in an ablatively driven glass microballoon was simulated with a spherical ion kinetic code. The ion velocity distribution functions were strongly non-Maxwellian, and mostly depleted of fast ions. A high viscosity contributed to fuel heating, while large ion heat fluxes towards the pusher strongly cooled the fuel. This latter kinetic effect may explain in part why hydrodynamic simulations usually predict higher neutron yields than are measured.

  19. Recent Progress on Spherical Torus Research and Implications for Fusion Energy Development Path

    NASA Astrophysics Data System (ADS)

    Ono, Masayuki

    2014-10-01

    The spherical torus or spherical tokamak (ST) is a member of the tokamak family with its aspect ratio (A =R0 / a) reduced to A near 1.5, well below the normal tokamak operating range of A equal to 2.5 or greater. As the aspect ratio is reduced, the ideal tokamak beta (radio of plasma to magnetic pressure) stability limit increases rapidly, approximately as 1/A. The plasma current it can sustain for a given edge safety factor q-95 also increases rapidly. Because of the above, as well as the natural plasma elongation which makes its plasma shape appear spherical, the ST configuration can yield exceptionally high tokamak performance in a compact geometry. Due to its compactness and high performance, the ST configuration has various near term applications, including a compact fusion neutron source with low tritium consumption, in addition to the longer term goal of an attractive fusion energy power source. Since the start of the two mega-ampere class ST facilities in 2000, the National Spherical Torus Experiment (NSTX) in the US and Mega Ampere Spherical Tokamak (MAST) in the UK, active ST research has been conducted worldwide. More than sixteen ST research facilities operating during this period have achieved remarkable advances in all areas of fusion research, including fundamental fusion energy science as well as technological innovation. These results suggest exciting future prospects for ST research in both the near and longer term. The talk will summarize the key physics results from worldwide ST experiments, and describe ST community plans to provide the database for FNSF design while improving predictive capabilities for ITER and beyond. This work supported by DoE Contract No. DE-AC02-09CH11466.

  20. Antenna system providing a spherical radiation pattern

    NASA Technical Reports Server (NTRS)

    Sickles, II, Louis (Inventor)

    1993-01-01

    An antenna system provides a substantially spherical radiation pattern about a structure located above ground level, by locating the individual radiation pattern of each of a plurality of individual antennae, each positioned to have a radiation pattern covering only a portion of the desired sphere, and then applying all antenna signals, during either transmission or reception time intervals, through space-diversity and/or time-diversity apparatus, to cause the patterns of all of the antennae to combine into the desired substantially-spherical pattern. The antennae may have substantially hemispherical patterns, with each antenna of a pair thereof being directed in a direction generally opposite to the other antenna of that pair. Time domain multiple access (TDMA) operation of a master system station, with transmission in different time slots for different portions of the coverage sphere, and selection of the strongest received signal from among all of the plurality N of signals simultaneously received by the plurality N of antennae, can provide the desired spherical radiation pattern in both the transmission and reception modes of operation.

  1. Afterburning in spherical premixed turbulent explosions

    SciTech Connect

    Bradley, D.; Lawes, M.; Scott, M.J. . Dept. of Mechanical Engineering); Mushi, E.M.J. )

    1994-12-01

    During the early stages of spherical turbulent flame propagation, more than half of the gas behind the visible flame front may be unburned. Previous models of the afterburning of the gas behind the apparent flame front have been extended in the present work, to include the effects of flame quenching, consequent upon localized flame stretch. The predictions of the model cover, the spatial and temporal variations of the fraction burned, the flame propagation rate, and the mass burning rate. They are all in dimensionless form and are well supported by associated experimental measurements in a fan-stirred bomb with controlled turbulence. The proportion of the gas that is unburned decreases with time and increases with the product of the Karlovitz stretch factor and the Lewis number. Simultaneous photographs were taken of the spherical schlieren image and of that due to Mie scattering from small seed particles in a thin laser sheet that sectioned the spherical flame. These clearly showed the amount of unburned gas within the sphere and, along with other evidence suggest laminar flamelet burning across a scale of distance which is close to the Taylor confirm the predictions of the fraction of gas unburned and of the rate at which it is burning.

  2. Batdorf parameter for the spherical shells tectonics

    NASA Astrophysics Data System (ADS)

    Kikuchi, Kazuhei; Nagahama, Hiroyuki

    2015-04-01

    The buckling phenomena of the subducting lithosphere due to the sphericity of the earth has been studied as spherical shell tectonics which happen the megaquake along the boundary of subducting lithosphere. The earthquake scale is decided by slab length or arc length. However, a relationship between slab length and the normalized hydrostatic pressure along the bottom circumferential edge of a hemispherical shell has not been clear yet. So, by using the data set of the geometrical parameters for subducting lithosphere andBuckingham's Pi-theorem, we found out a new linear relationship between Batdorf parameter Z = L2(l - v2)0.5/(Rh) for the measurement of the slab length L and the normalized hydrostatic pressure along the bottom circumferential edge of a hemispherical shell Q = qRL2/(π2D), where D = Eh3/[12(1 - v2)] with E = modulus of elasticity of lithosphere, R is Earth radius, q is the hydrostatic pressure along the bottom circumferential edge of a hemispherical shell, and h is the thickness of subducting lithosphere. In the engineering sciences, a similar relationship between Batdorf parameter for the panel length and normalized hydrostatic pressure was proposed for the buckling of partially liquid-filled circular cylindrical shells under hydrostatic pressure. Moreover, by previous researches, the slab length is approximately proportional to the arc length or the lithosphere thickness related to lithosphere age. Therefore, the Batdorf parameter for subducting lithosphere is an important parameter for the spherical shells tectonics.

  3. Scaling Relationships for Spherical Polymer Brushes Revisited.

    PubMed

    Chen, Guang; Li, Hao; Das, Siddhartha

    2016-06-16

    In this short paper, we revisit the scaling relationships for spherical polymer brushes (SPBs), i.e., polymer brushes grafted to rigid, spherical particles. Considering that the brushes can be described to be encased in a series of hypothetical spherical blobs, we identify significant physical discrepancies in the model of Daoud and Cotton (Journal of Physics, 1982), which is considered to be the state of the art in scaling modeling of SPBs. We establish that the "brush" configuration of the polymer molecules forming the SPBs is possible only if the swelling ratio (which is the ratio of the end-to-end length of the blob-encased polymer segment to the corresponding coil-like polymer segment) is always less than unity-a notion that has been erroneously overlooked in the model of Daoud and Cotton. We also provide new scaling arguments that (a) establish this swelling (or more appropriately shrinking) ratio as a constant (less than unity) for the case of "good" solvent, (b) recover the scaling predictions for blob dimension and monomer number and monomer concentration distributions within the blob, and PMID:27232497

  4. Quantum corrected spherical collapse: A phenomenological framework

    SciTech Connect

    Ziprick, Jonathan; Kunstatter, Gabor

    2010-08-15

    A phenomenological framework is presented for incorporating quantum gravity motivated corrections into the dynamics of spherically symmetric collapse. The effective equations are derived from a variational principle that guarantees energy conservation and the existence of a Birkhoff theorem. The gravitational potential can be chosen as a function of the areal radius to yield specific nonsingular static spherically symmetric solutions that generically have two horizons. For a specific choice of potential, the effective stress energy tensor violates only the dominant energy condition. The violations are maximum near the inner horizon and die off rapidly. A numerical study of the quantum corrected collapse of a spherically symmetric scalar field in this case reveals that the modified gravitational potential prevents the formation of a central singularity and ultimately yields a static, mostly vacuum, spacetime with two horizons. The matter 'piles up' on the inner horizon giving rise to mass inflation at late times. The Cauchy horizon is transformed into a null, weak singularity, but in contrast to Einstein gravity, the absence of a central singularity renders this null singularity stable.

  5. Next Step Spherical Torus Design Studies

    SciTech Connect

    C. Neumeyer; P. Heitzenroeder; C. Kessel; M. Ono; M. Peng; J. Schmidt; R. Woolley; I. Zatz

    2002-11-08

    Studies are underway to identify and characterize a design point for a Next Step Spherical Torus (NSST) experiment. This would be a ''Proof of Performance'' device which would follow and build upon the successes of the National Spherical Torus Experiment (NSTX) a ''Proof of Principle'' device which has operated at PPPL since 1999. With the Decontamination and Decommissioning (D&D) of the Tokamak Fusion Test Reactor (TFTR) nearly completed, the TFTR test cell and facility will soon be available for a device such as NSST. By utilizing the TFTR test cell, NSST can be constructed for a relatively low cost on a short time scale. In addition, while furthering spherical torus (ST) research, this device could achieve modest fusion power gain for short-pulse lengths, a significant step toward future large burning plasma devices now under discussion in the fusion community. The selected design point is Q=2 at HH=1.4, P subscript ''fusion''=60 MW, 5 second pulse, with R subscript ''0''=1.5 m, A=1.6, I subscript ''p''=10vMA, B subscript ''t''=2.6 T, CS flux=16 weber. Most of the research would be conducted in D-D, with a limited D-T campaign during the last years of the program.

  6. Spherically symmetric thick branes cosmological evolution

    NASA Astrophysics Data System (ADS)

    Bernardini, A. E.; Cavalcanti, R. T.; da Rocha, Roldão

    2015-01-01

    Spherically symmetric time-dependent solutions for the 5D system of a scalar field canonically coupled to gravity are obtained and identified as an extension of recent results obtained by Ahmed et al. (JHEP 1404:061. arXiv:1312.3576 [hep-th], 2014). The corresponding cosmology of models with regularized branes generated by such a 5D scalar field scenario is also investigated. It has been shown that the anisotropic evolution of the warp factor and consequently the Hubble like parameter are both driven by the radial coordinate on the brane, which leads to an emergent thick brane-world scenario with spherically symmetric time dependent warp factor. Meanwhile, the separability of variables depending on fifth dimension, , which is exhibited by the equations of motion, allows one to recover the extra dimensional profiles obtained in Ahmed et al. (2014), namely the extra dimensional part of the scale (warp) factor and the scalar field dependence on . Therefore, our results are mainly concerned with the time dependence of a spherically symmetric warp factor. Besides evincing possibilities for obtaining asymmetric stable brane-world scenarios, the extra dimensional profiles here obtained can also be reduced to those ones investigated in Ahmed et al. (2014).

  7. 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,…

  8. 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…

  9. 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…

  10. 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.

  11. 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…

  12. Foucault pendulum through basic geometry

    NASA Astrophysics Data System (ADS)

    von Bergmann, Jens; von Bergmann, HsingChi

    2007-10-01

    We provide a thorough explanation of the Foucault pendulum that utilizes its underlying geometry on a level suitable for science students not necessarily familiar with calculus. We also explain how the geometrically understood Foucault pendulum can serve as a prototype for more advanced phenomena in physics known as Berry's phase or geometric phases.

  13. A Microcomputer Descriptive Geometry Tutorial.

    ERIC Educational Resources Information Center

    Zongyi, Zuo

    1990-01-01

    A software package which can aid descriptive geometry instruction is described. Included are the features of the software and the software configuration. This software has been honored as the best and most advanced software of its kind in the People's Republic of China. (KR)

  14. 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…

  15. 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…

  16. 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;…

  17. 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…

  18. 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.

  19. 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…

  20. Noncommutative geometry inspired entropic inflation

    NASA Astrophysics Data System (ADS)

    Nozari, Kourosh; Akhshabi, Siamak

    2011-06-01

    Recently Verlinde proposed that gravity can be described as an emergent phenomena arising from changes in the information associated with the positions of material bodies. By using noncommutative geometry as a way to describe the microscopic microstructure of quantum spacetime, we derive modified Friedmann equation in this setup and study the entropic force modifications to the inflationary dynamics of early universe.

  1. Van Hiele Guidelines for Geometry.

    ERIC Educational Resources Information Center

    Davey, Geoff; Holliday, Jack

    1992-01-01

    Describes five skills underpinning the understanding of geometry for primary and lower secondary mathematics students. Skill categories identified include (1) visual; (2) verbal; (3) drawing; (4) logical; and (5) application. Gives examples of skills appropriate for Van Hiele levels 1-3. (MDH)

  2. 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…

  3. The basics of information geometry

    NASA Astrophysics Data System (ADS)

    Caticha, Ariel

    2015-01-01

    To what extent can we distinguish one probability distribution from another? Are there quantitative measures of distinguishability? The goal of this tutorial is to approach such questions by introducing the notion of the "distance" between two probability distributions and exploring some basic ideas of such an "information geometry".

  4. The Idea of Order at Geometry Class.

    ERIC Educational Resources Information Center

    Rishel, Thomas

    The idea of order in geometry is explored using the experience of assignments given to undergraduates in a college geometry course "From Space to Geometry." Discussed are the definition of geometry, and earth measurement using architecture, art, and common experience. This discussion concludes with a consideration of the question of whether…

  5. Teaching Activity-Based Taxicab Geometry

    ERIC Educational Resources Information Center

    Ada, Tuba

    2013-01-01

    This study aimed on the process of teaching taxicab geometry, a non-Euclidean geometry that is easy to understand and similar to Euclidean geometry with its axiomatic structure. In this regard, several teaching activities were designed such as measuring taxicab distance, defining a taxicab circle, finding a geometric locus in taxicab geometry, and…

  6. Spherical Joint Piston and Connecting Rod Developed

    NASA Technical Reports Server (NTRS)

    1996-01-01

    Under an interagency agreement with the Department of Energy, the NASA Lewis Research Center manages a Heavy-Duty Diesel Engine Technology (HDET) research program. The overall program objectives are to reduce fuel consumption through increased engine efficiency, reduce engine exhaust emissions, and provide options for the use of alternative fuels. The program is administered with a balance of research contracts, university research grants, and focused in-house research. The Cummins Engine Company participates in the HDET program under a cost-sharing research contract. Cummins is researching and developing in-cylinder component technologies for heavy-duty diesel engines. An objective of the Cummins research is to develop technologies for a low-emissions, 55-percent thermal efficiency (LE-55) engine. The best current-production engines in this class achieve about 46-percent thermal efficiency. Federal emissions regulations are driving this technology. Regulations for heavy duty diesel engines were tightened in 1994, more demanding emissions regulations are scheduled for 1998, and another step is planned for 2002. The LE-55 engine emissions goal is set at half of the 1998 regulation level and is consistent with plans for 2002 emissions regulations. LE-55 engine design requirements to meet the efficiency target dictate a need to operate at higher peak cylinder pressures. A key technology being developed and evaluated under the Cummins Engine Company LE-55 engine concept is the spherical joint piston and connecting rod. Unlike conventional piston and connecting rod arrangements which are joined by a pin forming a hinged joint, the spherical joint piston and connecting rod use a ball-and-socket joint. The ball-and-socket arrangement enables the piston to have an axisymmetric design allowing rotation within the cylinder. The potential benefits of piston symmetry and rotation are reduced scuffing, improved piston ring sealing, improved lubrication, mechanical and thermal

  7. Geometry in Transition: A Model of Emergent Geometry

    SciTech Connect

    Delgadillo-Blando, Rodrigo; O'Connor, Denjoe; Ydri, Badis

    2008-05-23

    We study a three matrix model with global SO(3) symmetry containing at most quartic powers of the matrices. We find an exotic line of discontinuous transitions with a jump in the entropy, characteristic of a 1st order transition, yet with divergent critical fluctuations and a divergent specific heat with critical exponent {alpha}=1/2. The low temperature phase is a geometrical one with gauge fields fluctuating on a round sphere. As the temperature increased the sphere evaporates in a transition to a pure matrix phase with no background geometrical structure. Both the geometry and gauge fields are determined dynamically. It is not difficult to invent higher dimensional models with essentially similar phenomenology. The model presents an appealing picture of a geometrical phase emerging as the system cools and suggests a scenario for the emergence of geometry in the early Universe.

  8. Forward model of thermally-induced acoustic signal specific to intralumenal detection geometry

    NASA Astrophysics Data System (ADS)

    Mukherjee, Sovanlal; Bunting, Charles F.; Piao, Daqing

    2011-03-01

    This work investigates a forward model associated with intra-lumenal detection of acoustic signal originated from transient thermal-expansion of the tissue. The work is specific to intra-lumenal thermo-acoustic tomography (TAT) which detects the contrast of tissue dielectric properties with ultrasonic resolution, but it is also extendable to intralumenal photo-acoustic tomography (PAT) which detects the contrast of light absorption properties of tissue with ultrasound resolution. Exact closed-form frequency-domain or time-domain forward model of thermally-induced acoustic signal have been studied rigorously for planar geometry and two other geometries, including cylindrical and spherical geometries both of which is specific to external-imaging, i.e. breast or brain imaging using an externally-deployed applicator. This work extends the existing studies to the specific geometry of internal or intra-lumenal imaging, i.e., prostate imaging by an endo-rectally deployed applicator. In this intra-lumenal imaging geometry, both the source that excites the transient thermal-expansion of the tissue and the acoustic transducer that acquires the thermally-induced acoustic signal are assumed enclosed by the tissue and on the surface of a long cylindrical applicator. The Green's function of the frequency-domain thermo-acoustic equation in spherical coordinates is expanded to cylindrical coordinates associated with intra-lumenal geometry. Inverse Fourier transform is then applied to obtain a time-domain solution of the thermo-acoustic pressure wave for intra-lumenal geometry. Further employment of the boundary condition to the "convex" applicator-tissue interface would render an exact forward solution toward accurate reconstruction for intra-lumenal thermally-induced acoustic imaging.

  9. Geometry-Induced Rigidity in Nonspherical Pressurized Elastic Shells

    NASA Astrophysics Data System (ADS)

    Lazarus, A.; Florijn, H. C. B.; Reis, P. M.

    2012-10-01

    We present results from an experimental investigation of the indentation of nonspherical pressurized elastic shells with a positive Gauss curvature. A predictive framework is proposed that rationalizes the dependence of the local rigidity of an indented shell on the curvature in the neighborhood of the locus of indentation, the in-out pressure differential, and the material properties. In our approach, we combine classic theory for spherical shells with recent analytical developments for the pressurized case, and proceed, for the most part, by analogy, guided by our own experiments. By way of example, our results elucidate why an eggshell is significantly stiffer when compressed along its major axis, as compared to doing so along its minor axis. The prominence of geometry in this class of problems points to the relevance and applicability of our findings over a wide range of length scales.

  10. Investigation of properties of lithium niobate crystals in confined geometries

    NASA Astrophysics Data System (ADS)

    Veenhuizen, Keith; Stone, Greg; Knabe, Bastian; McAnany, Sean; Buse, Karsten; Jain, Himanshu; Dierolf, Volkmar

    The properties of ferroelectric materials in confined geometries, specifically lithium niobate nanocrystals and crystal lines in glass, were studied. Batches of LiNbO3 nanocrystals have been synthesized from various initial ratios of lithium to niobium using the sol-gel method. The batches were analyzed via Raman spectroscopy and SEM imaging to gain information about their size, morphology, stoichiometry, and defect content. The nanocrystals are very sensitive to the initial stoichiometric ratio in the synthesis step. Raman spectra reveal the resultant nanocrystal stoichiometry depends on the initial stoichiometry of the batch, the spectra also reveal an extra phase is present besides LiNbO3 in some batches, and high quality spherical nanocrystals can be synthesized at certain initial stoichiometric ratios. In addition, lines of LiNbO3 were crystallized in lithium-niobo-silica glass systems with varying amounts of silica to understand and control the nucleation and crystallization of the crystals in glass.

  11. Series in vector spherical harmonics: An efficient tool for solution of nonlinear problems in spherical plasmas

    NASA Astrophysics Data System (ADS)

    Xu, S.; Ostrikov, K. N.

    2000-07-01

    The series expansion of the plasma fields and currents in vector spherical harmonics has been demonstrated to be an efficient technique for solution of nonlinear problems in spherically bounded plasmas. Using this technique, it is possible to describe the nonlinear plasma response to the rotating high-frequency magnetic field applied to the magnetically confined plasma sphere. The effect of the external magnetic field on the current drive and field configuration is studied. The results obtained are important for continuous current drive experiments in compact toruses.

  12. Spherical Harmonic Transforms with S2HAT (Scalable Spherical Harmonic Transform) Library

    NASA Astrophysics Data System (ADS)

    Fabbian, G.; Szydlarski, M.; Stompor, R.; Grigori, L.; Falcou, J.

    2012-09-01

    We present the Scalable Spherical Harmonic Transform library (S2HAT) - a portable, massively parallel, scalable library for calculating scalar and spin-weighted spherical harmonic transforms on different computer architectures, including distributed-memory, hybrid multi-/many- core platforms, as well as clusters of many GPUs and CPUs. Here we comment on the two latter cases. The numerical complexity of the library transforms is O(npix1/2ℓmax2). The S2HAT library is publicly available.

  13. The Dirac-Hestenes Equation for Spherical Symmetric Potentials in the Spherical and Cartesian Gauges

    NASA Astrophysics Data System (ADS)

    da Rocha, Roldão; Rodrigues, Waldyr A.

    In this paper, using the apparatus of the Clifford bundle formalism, we show how straightforwardly solve in Minkowski space-time the Dirac-Hestenes equation — which is an appropriate representative in the Clifford bundle of differential forms of the usual Dirac equation — by separation of variables for the case of a potential having spherical symmetry in the Cartesian and spherical gauges. We show that, contrary to what is expected at a first sight, the solution of the Dirac-Hestenes equation in both gauges has exactly the same mathematical difficulty.

  14. Geometry-invariant resonant cavities

    NASA Astrophysics Data System (ADS)

    Liberal, I.; Mahmoud, A. M.; Engheta, N.

    2016-03-01

    Resonant cavities are one of the basic building blocks in various disciplines of science and technology, with numerous applications ranging from abstract theoretical modelling to everyday life devices. The eigenfrequencies of conventional cavities are a function of their geometry, and, thus, the size and shape of a resonant cavity is selected to operate at a specific frequency. Here we demonstrate theoretically the existence of geometry-invariant resonant cavities, that is, resonators whose eigenfrequencies are invariant with respect to geometrical deformations of their external boundaries. This effect is obtained by exploiting the unusual properties of zero-index metamaterials, such as epsilon-near-zero media, which enable decoupling of the temporal and spatial field variations in the lossless limit. This new class of resonators may inspire alternative design concepts, and it might lead to the first generation of deformable resonant devices.

  15. Geometry-invariant resonant cavities

    PubMed Central

    Liberal, I.; Mahmoud, A. M.; Engheta, N.

    2016-01-01

    Resonant cavities are one of the basic building blocks in various disciplines of science and technology, with numerous applications ranging from abstract theoretical modelling to everyday life devices. The eigenfrequencies of conventional cavities are a function of their geometry, and, thus, the size and shape of a resonant cavity is selected to operate at a specific frequency. Here we demonstrate theoretically the existence of geometry-invariant resonant cavities, that is, resonators whose eigenfrequencies are invariant with respect to geometrical deformations of their external boundaries. This effect is obtained by exploiting the unusual properties of zero-index metamaterials, such as epsilon-near-zero media, which enable decoupling of the temporal and spatial field variations in the lossless limit. This new class of resonators may inspire alternative design concepts, and it might lead to the first generation of deformable resonant devices. PMID:27010103

  16. Information geometry of Boltzmann machines.

    PubMed

    Amari, S; Kurata, K; Nagaoka, H

    1992-01-01

    A Boltzmann machine is a network of stochastic neurons. The set of all the Boltzmann machines with a fixed topology forms a geometric manifold of high dimension, where modifiable synaptic weights of connections play the role of a coordinate system to specify networks. A learning trajectory, for example, is a curve in this manifold. It is important to study the geometry of the neural manifold, rather than the behavior of a single network, in order to know the capabilities and limitations of neural networks of a fixed topology. Using the new theory of information geometry, a natural invariant Riemannian metric and a dual pair of affine connections on the Boltzmann neural network manifold are established. The meaning of geometrical structures is elucidated from the stochastic and the statistical point of view. This leads to a natural modification of the Boltzmann machine learning rule. PMID:18276427

  17. Spherical transceivers for ultrafast optical wireless communications

    NASA Astrophysics Data System (ADS)

    Jin, Xian; Hristovski, Blago A.; Collier, Christopher M.; Geoffroy-Gagnon, Simon; Born, Brandon; Holzman, Jonathan F.

    2016-02-01

    Optical wireless communications (OWC) offers the potential for high-speed and mobile operation in indoor networks. Such OWC systems often employ a fixed transmitter grid and mobile transceivers, with the mobile transceivers carrying out bi-directional communication via active downlinks (ideally with high-speed signal detection) and passive uplinks (ideally with broad angular retroreflection and high-speed modulation). It can be challenging to integrate all of these bidirectional communication capabilities within the mobile transceivers, however, as there is a simultaneous desire for compact packaging. With this in mind, the work presented here introduces a new form of transceiver for bi-directional OWC systems. The transceiver incorporates radial photoconductive switches (for high-speed signal detection) and a spherical retro-modulator (for broad angular retroreflection and high-speed all-optical modulation). All-optical retromodulation are investigated by way of theoretical models and experimental testing, for spherical retro-modulators comprised of three glasses, N-BK7, N-LASF9, and S-LAH79, having differing levels of refraction and nonlinearity. It is found that the spherical retro-modulator comprised of S-LAH79, with a refractive index of n ≍ 2 and a Kerr nonlinear index of n2 ≍ (1.8 ± 0.1) × 10-15 cm2/W, yields both broad angular retroreflection (over a solid angle of 2π steradians) and ultrafast modulation (over a duration of 120 fs). Such transceivers can become important elements for all-optical implementations in future bi-directional OWC systems.

  18. Deterministic phase retrieval employing spherical illumination

    NASA Astrophysics Data System (ADS)

    Martínez-Carranza, J.; Falaggis, K.; Kozacki, T.

    2015-05-01

    Deterministic Phase Retrieval techniques (DPRTs) employ a series of paraxial beam intensities in order to recover the phase of a complex field. These paraxial intensities are usually generated in systems that employ plane-wave illumination. This type of illumination allows a direct processing of the captured intensities with DPRTs for recovering the phase. Furthermore, it has been shown that intensities for DPRTs can be acquired from systems that use spherical illumination as well. However, this type of illumination presents a major setback for DPRTs: the captured intensities change their size for each position of the detector on the propagation axis. In order to apply the DPRTs, reescalation of the captured intensities has to be applied. This condition can increase the error sensitivity of the final phase result if it is not carried out properly. In this work, we introduce a novel system based on a Phase Light Modulator (PLM) for capturing the intensities when employing spherical illumination. The proposed optical system enables us to capture the diffraction pattern of under, in, and over-focus intensities. The employment of the PLM allows capturing the corresponding intensities without displacing the detector. Moreover, with the proposed optical system we can control accurately the magnification of the captured intensities. Thus, the stack of captured intensities can be used in DPRTs, overcoming the problems related with the resizing of the images. In order to prove our claims, the corresponding numerical experiments will be carried out. These simulations will show that the retrieved phases with spherical illumination are accurate and can be compared with those that employ plane wave illumination. We demonstrate that with the employment of the PLM, the proposed optical system has several advantages as: the optical system is compact, the beam size on the detector plane is controlled accurately, and the errors coming from mechanical motion can be suppressed easily.

  19. Extending dark optical trapping geometries.

    PubMed

    Arnold, Aidan S

    2012-07-01

    New counterpropagating geometries are presented for localizing ultracold atoms in the dark regions created by the interference of Laguerre-Gaussian laser beams. In particular dark helices, an "optical revolver," axial lattices of rings, and axial lattices of ring lattices of rings are considered and a realistic scheme for achieving phase stability is explored. The dark nature of these traps will enable their use as versatile tools for low-decoherence atom interferometry with zero differential light shifts. PMID:22743436

  20. Geometry Dependence of Stellarator Turbulence

    SciTech Connect

    H.E. Mynick, P. Xanthopoulos and A.H. Boozer

    2009-08-10

    Using the nonlinear gyrokinetic code package GENE/GIST, we study the turbulent transport in a broad family of stellarator designs, to understand the geometry-dependence of the microturbulence. By using a set of flux tubes on a given flux surface, we construct a picture of the 2D structure of the microturbulence over that surface, and relate this to relevant geometric quantities, such as the curvature, local shear, and effective potential in the Schrodinger-like equation governing linear drift modes.

  1. The physics of spherical torus plasmas

    NASA Astrophysics Data System (ADS)

    Peng, Y.-K. M.

    2000-05-01

    Broad and important progress in plasma tests, theory, new experiments, and future visions of the spherical torus (ST, or very low aspect ratio tokamaks) have recently emerged. These have substantially improved our understanding of the potential properties of the ST plasmas, since the preliminary calculation of the ST magnetohydrodynamic equilibria more than a decade ago. Exciting data have been obtained from concept exploration level ST experiments of modest capabilities (with major radii up to 35 cm), making important scientific contributions to toroidal confinement in general. The results have helped approval and construction of new and/or more powerful ST experiments, and stimulated an increasing number of theoretical calculations of interest to magnetic fusion energy. Utilizing the broad knowledge base from the successful tokamak and advanced tokamak research, a wide range of new ST physics features has been suggested. These properties of the ST plasma will be tested at the 1 MA level with major radius up to ˜80 cm in the new proof of principle devices National Spherical Torus Experiment (NSTX, U.S.) [M. Peng et al., European Conf. Abst. 22C, 451 (1998); S. M. Kaye et al., Fusion Technol. 36, 16 (1999); M. Ono et al., "Exploration of Spherical Torus Physics in the NSTX Device," 17th IAEA Fusion Energy Conf., paper IAEA-CN-69/ICP/01 (R), Yokohama, Japan (1998)], Mega Ampere Spherical Tokamak (MAST, U.K.) [A. C. Darke et al., Fusion Technol. 1, 799 (1995); Q. W. Morris et al., Proc. Int. Workshop on ST (Ioffe Inst., St. Petersburg, 1997), Vol. 1, p. 290], and Globus-M (R.F.) [V. K. Gusev et al., European Conf. Abst. 22C, 576 (1998)], which have just started full experimental operation. New concept exploration experiments, such as Pegasus (University of Wisconsin) [R. Fonck and the PEGASUS Team, Bull. Am. Phys. Soc. 44, 267 (1999)], Helicity Injected Tokamak-II (HIT-II, University of Washington) [T. R. Jarboe et al., Phys. Plasmas 5, 1807 (1998)], and Current

  2. Stress analysis of spherical-mirror panels

    SciTech Connect

    Parks, V J; Sanford, R J

    1982-04-01

    An experimental analysis is reported of the stresses that occur in elastically deformed, spherically curved glass mirrors for solar energy applications. Bending and membrance stresses generated in forming the glass and the effects of springback are analyzed. In addition, thermal stresses caused by focusing the sun's rays on a small region of the mirrors are analyzed. Methods used in the analysis included the use of grids, photoelasticity, and strain gages. Results of the analysis are compared with a theoretical analysis performed by Shelltech Associates in a parallel effort.

  3. Compressive sensing with a spherical microphone array.

    PubMed

    Fernandez-Grande, Efren; Xenaki, Angeliki

    2016-02-01

    A wave expansion method is proposed in this work, based on measurements with a spherical microphone array, and formulated in the framework provided by Compressive Sensing. The method promotes sparse solutions via ℓ1-norm minimization, so that the measured data are represented by few basis functions. This results in fine spatial resolution and accuracy. This publication covers the theoretical background of the method, including experimental results that illustrate some of the fundamental differences with the "conventional" least-squares approach. The proposed methodology is relevant for source localization, sound field reconstruction, and sound field analysis. PMID:26936583

  4. Effect of cavitation on spherical blast waves

    NASA Astrophysics Data System (ADS)

    Kumar, S.

    1984-09-01

    For spherical blast waves propagating through a self-gravitating gas with an energy input Eα = E0tβ, where Eα is the energy released up to time t, E0 is a functional constant, and β is a constant, kinetic, internal heat, and gravitational potential energies have been computed. Taking the parameter A2, which characterises the gravitational field, equal to 2, variations of the percentages of these energies for β = 0, 1/2, 4/3, and 3 with shock strength have been presented. For β = 3, the effect of cavitation on the percentages of kinetic energy and internal heat energies has been explored.

  5. Vacuum energy of a spherical plasma shell

    SciTech Connect

    Bordag, M.; Khusnutdinov, N.

    2008-04-15

    We consider the vacuum energy of the electromagnetic field interacting with a spherical plasma shell together with a model for the classical motion of the shell. We calculate the heat kernel coefficients, especially that for the TM mode, and carry out the renormalization by redefining the parameters of the classical model. It turns out that this is possible and results in a model which, in the limit of the plasma shell becoming an ideal conductor, reproduces the vacuum energy found by Boyer in 1968.

  6. libsharp: Library for spherical harmonic transforms

    NASA Astrophysics Data System (ADS)

    Reinecke, Martin

    2014-02-01

    Libsharp is a collection of algorithms for efficient conversion between maps on the sphere and their spherical harmonic coefficients. It supports a wide range of pixelisations (including HEALPix, GLESP, and ECP). This library is a successor of libpsht; it adds MPI support for distributed memory systems and SHTs of fields with arbitrary spin, and also supports new developments in CPU instruction sets like the Advanced Vector Extensions (AVX) or fused multiply-accumulate (FMA) instructions. libsharp is written in portable C99; it provides an interface accessible to other programming languages such as C++, Fortran, and Python.

  7. Numerical investigations of gaseous spherical diffusion flames

    NASA Astrophysics Data System (ADS)

    Lecoustre, Vivien R.

    Spherical diffusion flames have several unique characteristics that make them attractive from experimental and theoretical perspectives. They can be modeled with one spatial dimension, which frees computational resources for detailed chemistry, transport, and radiative loss models. This dissertation is a numerical study of two classes of spherical diffusion flames: hydrogen micro-diffusion flames, emphasizing kinetic extinction, and ethylene diffusion flames, emphasizing sooting limits. The flames were modeled using a one-dimensional, time-accurate diffusion flame code with detailed chemistry and transport. Radiative losses from products were modeled using a detailed absorption/emission statistical narrow band model and the discrete ordinates method. During this work the code has been enhanced by the implementation of a soot formation/oxidation model using the method of moments. Hydrogen micro-diffusion flames were studied experimentally and numerically. The experiments involved gas jets of hydrogen. At their quenching limits, these flames had heat release rates of 0.46 and 0.25 W in air and in oxygen, respectively. These are the weakest flames ever observed. The modeling results confirmed the quenching limits and revealed high rates of reactant leakage near the limits. The effects of the burner size and mass flow rate were predicted to have a significant impact on the flame chemistry and species distribution profiles, favoring kinetic extinction. Spherical ethylene diffusion flames at their sooting limits were also examined. Seventeen normal and inverse spherical flames were considered. Initially sooty, these flames were experimentally observed to reach their sooting limits 2 s after ignition. Structure of the flames at 2 s was considered, with an emphasis on the relationships among local temperature, carbon to oxygen atom ratio (C/O), and scalar dissipation rate. A critical C/O ratio was identified, along with two different sooting limit regimes. Diffusion flames

  8. Outdoor measurements of spherical acoustic shock decay.

    PubMed

    Young, Sarah M; Gee, Kent L; Neilsen, Tracianne B; Leete, Kevin M

    2015-09-01

    Prior anechoic measurements of a small acetylene-oxygen balloon explosion were used to study spherical weak-shock decay over short ranges [Muhlestein et al., J. Acoust. Soc. Am. 131, 2422-2430 (2012)]. Here, longer-range measurements conducted at the Bonneville Salt Flats with a larger balloon are described. Waveform and spectral characteristics and comparisons of the peak pressure decay with an analytical weak-shock model are presented. Weak shocks persist to at least 305 m, with an amplitude decay that is predicted reasonably well using the model. Deviations are discussed in the context of atmospheric effects and nonlinear ground reflections. PMID:26428831

  9. Spherical Combustion Layer in a TNT Explosion

    SciTech Connect

    Kuhl, A L; Ferguson, R E

    2001-12-09

    A theoretical model of combustion in spherical TNT explosions at large Reynolds, Peclet and Damk hler numbers is described. A key feature of the model is that combustion is treated as material transformations in the Le Chatelier plane, rather than ''heat release''. In the limit considered here, combustion is concentrated on thin exothermic sheets (boundaries between fuel and oxidizer). The products expand along the sheet, thereby inducing vorticity on either side of the sheet that continues to feed the process. The results illustrate the linking between turbulence (vorticity) and exothermicity (dilatation) in the limit of fast chemistry thereby demonstrating the controlling role that fluid dynamics plays in such problems.

  10. Multistability in rotating spherical shell convection.

    PubMed

    Feudel, F; Seehafer, N; Tuckerman, L S; Gellert, M

    2013-02-01

    The multiplicity of stable convection patterns in a rotating spherical fluid shell heated from the inner boundary and driven by a central gravity field is presented. These solution branches that arise as rotating waves (RWs) are traced for varying Rayleigh number while their symmetry, stability, and bifurcations are studied. At increased Rayleigh numbers all the RWs undergo transitions to modulated rotating waves (MRWs) which are classified by their spatiotemporal symmetry. The generation of a third frequency for some of the MRWs is accompanied by a further loss of symmetry. Eventually a variety of MRWs, three-frequency solutions, and chaotic saddles and attractors control the dynamics for higher Rayleigh numbers. PMID:23496624

  11. The Los Alamos National Laboratory source geometry experiment

    SciTech Connect

    Stump, B.W.; Pearson, D.C.; Edwards, C.L.; Baker, D.F.

    1995-09-01

    The Source Geometry Experiment was successfully conducted over the time period 17 April to 7 May 95. Recording in the mine was conducted 24 April to 4 May 95. Five single sources were instrumented that included four cylindrical charges at different burdens (distance from the free face) and a pseudo-spherical charge. Nine production shots conducted during the two week visit to the mine were also recorded. Included in these production shots were a number of explosions designed to primarily bulk (no cast) the overburden and a number which cast material into the mine pit. Instrumentation was divided into six primary types: (1) Near-source accelerometers were deployed at distances of approximately 20 to 300 m [14, three-component 25 g/volt accelerometers and 16, three-component 1 g/volt accelerometers]; (2) Linear array of velocity gauges to quantify wave propagation effects [4-11 three component strong motion velocity gauges]; (3)Far-field velocity gages deployed in an azimuthal array around the mine at ranges from 500 to 2500 m [8, three component velocity gauges]; (4) High speed film and multiple camera video designed to quantify the two and three dimensional affects around the explosions [2 high speed cameras and 3 Hi-8 video cameras]; (5) Velocity of detonation and detonation time measurements of selected explosions [2 VODR systems]; and (6) Pre and post shot laser survey. Any one shot had as many as 154 channels of data. Although the complete data set is still being assembled, quality checked and analyzed, it appears that nearly 2,000 channels of data were successfully recovered during the experiment. Preliminary analysis of the data illustrates the: (1) Significant spall accompanied both the cylindrical and spherical single sources; (2) Similarity of waveforms from the cylindrical and spherical single sources; (3) Strong variations in the body and surface wave generation from the nine production shot.

  12. 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.

  13. Spherical Rayleigh-Taylor growth of three-dimensional broadband perturbations on OMEGA

    SciTech Connect

    Smalyuk, V. A.; Hu, S. X.; Hager, J. D.; Delettrez, J. A.; Meyerhofer, D. D.; Sangster, T. C.; Shvarts, D.

    2009-11-15

    Spherical Rayleigh-Taylor (RT) growth experiments of three-dimensional (3D) broadband nonuniformities were conducted in the acceleration phase of spherical implosions on OMEGA [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)]. The targets consisted of 20- and 24-{mu}m-thick plastic spherical shells having diagnostic openings for backlighter x rays to image shell modulations. Experiments were conducted with square laser pulses at a low drive intensity of {approx}2x10{sup 14} W/cm{sup 2}, high drive intensity of {approx}1x10{sup 15} W/cm{sup 2}, and a shaped pulse consisting of a low-intensity foot and high-intensity drive part (peak intensity of {approx}1x10{sup 15} W/cm{sup 2}). In low-intensity experiments, large RT growth was measured, resulting in shells being broken up by 3D modulations at the end of the drive. In the high-intensity experiments, no RT growth of the 3D modulations was detected. In the shaped-pulse experiments, perturbations grew during the low-intensity part of the drive and were stabilized later during the high-intensity part of the drive. The measured RT growth stabilization with the high-intensity drive was similar to previous observations in planar geometry [V. A. Smalyuk et al., Phys. Rev. Lett. 101, 025002 (2008)].

  14. Spherical Rayleigh-Taylor Growth of Three-Dimensional Broadband Perturbations on OMEGA

    SciTech Connect

    Smalyuk, V.A.; Hu, S.X.; Hager, J.D.; Delettrez, J.A.; Meyerhofer, D.D.; Sangster, T.C.; Shvarts, D.

    2009-11-10

    Spherical Rayleigh–Taylor (RT) growth experiments of three-dimensional (3D) broadband nonuniformities were conducted in the acceleration phase of spherical implosions on OMEGA [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)]. The targets consisted of 20- and 24-um-thick plastic spherical shells having diagnostic openings for backlighter x rays to image shell modulations. Experiments were conducted with square laser pulses at a low drive intensity of ~2 x 10^14 W/cm^2, high drive intensity of ~1 x 10^15 W/cm^2, and a shaped pulse consisting of a low-intensity foot and high-intensity drive part (peak intensity of ~1 x 10^15 W/cm^2). In low-intensity experiments, large RT growth was measured, resulting in shells being broken up by 3D modulations at the end of the drive. In the high-intensity experiments, no RT growth of the 3D modulations was detected. In the shaped-pulse experiments, perturbations grew during the low-intensity part of the drive and were stabilized later during the high-intensity part of the drive. The measured RT growth stabilization with the high-intensity drive was similar to previous observations in planar geometry [V. A. Smalyuk et al., Phys. Rev. Lett. 101, 025002 (2008)].

  15. Expansion of arbitrary electromagnetic fields in terms of vector spherical wave functions.

    PubMed

    Moreira, Wendel Lopes; Neves, Antonio Alvaro Ranha; Garbos, Martin K; Euser, Tijmen G; Cesar, Carlos Lenz

    2016-02-01

    Since 1908, when Mie reported analytical expressions for the fields scattered by a spherical particle upon incidence of plane-waves, generalizing his analysis for the case of an arbitrary incident wave has been an open question because of the cancellation of the prefactor radial spherical Bessel function. This cancellation was obtained before by our own group for a highly focused beam centered in the objective. In this work, however, we show for the first time how these terms can be canceled out for any arbitrary incident field that satisfies Maxwells equations, and obtain analytical expressions for the beam shape coefficients. We show several examples on how to use our method to obtain analytical beam shape coefficients for: Bessel beams, general hollow waveguide modes and specific geometries such as cylindrical and rectangular. Our method uses the vector potential, which shows the interesting characteristic of being gauge invariant. These results are highly relevant for speeding up numerical calculation of light scattering applications such as the radiation forces acting on spherical particles placed in an arbitrary electromagnetic field, as in an optical tweezers system. PMID:26906812

  16. Two-dimensional axisymmetric formulation of high order spherical harmonics methods for radiative heat transfer

    NASA Astrophysics Data System (ADS)

    Ge, Wenjun; Modest, Michael F.; Marquez, Ricardo

    2015-05-01

    The spherical harmonics (PN) method is a radiative transfer equation solver, which approximates the radiative intensity as a truncated series of spherical harmonics. For general 3-D configurations, N(N + 1) / 2 intensity coefficients must be solved from a system of coupled second-order elliptic PDEs. In 2-D axisymmetric applications, the number of equations and intensity coefficients reduces to (N + 1) 2 / 4 if the geometric relations of the intensity coefficients are taken into account. This paper presents the mathematical details for the transformation and its implementation on the OpenFOAM finite volume based CFD software platform. The transformation and implementation are applicable to any arbitrary axisymmetric geometry, but the examples to test the new formulation are based on a wedge grid, which is the most common axisymmetric geometry in CFD simulations, because OpenFOAM and most other platforms do not have true axisymmetric solvers. Two example problems for the new axisymmetric PN formulation are presented, and the results are verified with that of the general 3-D PN solver, a Photon Monte Carlo solver and exact solutions.

  17. Left ventricular sphericity index predicts systolic dysfunction in rats with experimental aortic regurgitation.

    PubMed

    Roscani, Meliza Goi; Polegato, Bertha Fulan; Minamoto, Suzana Erico Tanni; Lousada, Ana Paula Mena; Minicucci, Marcos; Azevedo, Paula; Matsubara, Luiz Shiguero; Matsubara, Beatriz Bojikian

    2014-05-15

    Although an increased left ventricular (LV) diastolic diameter (DD) and a decreased ejection fraction have been used as markers for the surgical replacement of an insufficient aortic valve, these signals may be observed when irreversible myocardium damage has already occurred. The aim of this study was to determine whether change in LV geometry predicts systolic dysfunction in experimental aortic regurgitation. Male Wistar rats underwent surgical acute aorta regurgitation (aorta regurgitation group; n = 23) or a sham operation (sham group; n = 12). After the procedure, serial transthoracic echocardiograms were performed at 1, 4, 8, and 16 wk. At the end of protocol, the LV, lungs, and liver were dissected and weighed. During the follow-up, no animal developed overt heart failure. There was a correlation between the LV sphericity index and reduced fractional shortening (P < 0.001) over time. A multiple regression model showed that the LVDD-sphericity index association at 8 wk was a better predictor of decreased fractional shortening at week 16 (R(2) = 0.50; P < 0.001) than was the LVDD alone (R(2) = 0.39; P = 0.001). LV geometry associated with increased LVDD improved the prediction of systolic dysfunction in experimental aortic regurgitation. PMID:24699853

  18. Turbulent convection in rapidly rotating spherical shells: A model for equatorial and high latitude jets on Jupiter and Saturn

    NASA Astrophysics Data System (ADS)

    Heimpel, Moritz; Aurnou, Jonathan

    2007-04-01

    The origin of zonal jets on the jovian planets has long been a topic of scientific debate. In this paper we show that deep convection in a spherical shell can generate zonal flow comparable to that observed on Jupiter and Saturn, including a broad prograde equatorial jet and multiple alternating jets at higher latitudes. We present fully turbulent, 3D spherical numerical simulations of rapidly rotating convection with different spherical shell geometries. The resulting global flow fields tend to be segregated into three regions (north, equatorial, and south), bounded by the tangent cylinder that circumscribes the inner boundary equator. In all of our simulations a strong prograde equatorial jet forms outside the tangent cylinder, whereas multiple jets form in the northern and southern hemispheres, inside the tangent cylinder. The jet scaling of our numerical models and of Jupiter and Saturn is consistent with the theory of geostrophic turbulence, which we extend to include the effect of spherical shell geometry. Zonal flow in a spherical shell is distinguished from that in a full sphere or a shallow layer by the effect of the tangent cylinder, which marks a reversal in the sign of the planetary β-parameter and a jump in the Rhines length. This jump is manifest in the numerical simulations as a sharp equatorward increase in jet widths—a transition that is also observed on Jupiter and Saturn. The location of this transition gives an estimate of the depth of zonal flow, which seems to be consistent with current models of the jovian and saturnian interiors.

  19. Network geometry with flavor: From complexity to quantum geometry

    NASA Astrophysics Data System (ADS)

    Bianconi, Ginestra; Rahmede, Christoph

    2016-03-01

    Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d -dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s =-1 ,0 ,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d . In d =1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d >1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t . Interestingly the NGF remains fully classical but

  20. Network geometry with flavor: From complexity to quantum geometry.

    PubMed

    Bianconi, Ginestra; Rahmede, Christoph

    2016-03-01

    Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d-dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s=-1,0,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d. In d=1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d>1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t. Interestingly the NGF remains fully classical but its

  1. Flow above and within granular media composed of spherical and non-spherical particles - using a 3D numerical model

    NASA Astrophysics Data System (ADS)

    Bartzke, Gerhard; Kuhlmann, Jannis; Huhn, Katrin

    2016-04-01

    The entrainment of single grains and, hence, their erosion characteristics are dependent on fluid forcing, grain size and density, but also shape variations. To quantitatively describe and capture the hydrodynamic conditions around individual grains, researchers commonly use empirical approaches such as laboratory flume tanks. Nonetheless, it is difficult with such physical experiments to measure the flow velocities in the direct vicinity or within the pore spaces of sediments, at a sufficient resolution and in a non-invasive way. As a result, the hydrodynamic conditions in the water column, at the fluid-porous interface and within pore spaces of a granular medium of various grain shapes is not yet fully understood. For that reason, there is a strong need for numerical models, since these are capable of quantifying fluid speeds within a granular medium. A 3D-SPH (Smooth Particle Hydrodynamics) numerical wave tank model was set up to provide quantitative evidence on the flow velocities in the direct vicinity and in the interior of granular beds composed of two shapes as a complementary method to the difficult task of in situ measurement. On the basis of previous successful numerical wave tank models with SPH, the model geometry was chosen in dimensions of X=2.68 [m], Y=0.48 [m], and Z=0.8 [m]. Three suites of experiments were designed with a range of particle shape models: (1) ellipsoids with the long axis oriented in the across-stream direction, (2) ellipsoids with the long axis oriented in the along-stream direction, and (3) spheres. Particle diameters ranged from 0.04 [m] to 0.08 [m]. A wave was introduced by a vertical paddle that accelerated to 0.8 [m/s] perpendicular to the granular bed. Flow measurements showed that the flow velocity values into the beds were highest when the grains were oriented across the stream direction and lowest in case when the grains were oriented parallel to the stream, indicating that the model was capable to simulate simultaneously

  2. Conservative interpolation between general spherical meshes

    NASA Astrophysics Data System (ADS)

    Kritsikis, E.; Aechtner, M.; Meurdesoif, Y.; Dubos, T.

    2015-06-01

    An efficient, local, explicit, second-order, conservative interpolation algorithm between spherical meshes is presented. The cells composing the source and target meshes may be either spherical polygons or longitude-latitude quadrilaterals. Second-order accuracy is obtained by piecewise-linear finite volume reconstruction over the source mesh. Global conservation is achieved through the introduction of a supermesh, whose cells are all possible intersections of source and target cells. Areas and intersections are computed exactly to yield a geometrically exact method. The main efficiency bottleneck caused by the construction of the supermesh is overcome by adopting tree-based data structures and algorithms, from which the mesh connectivity can also be deduced efficiently. The theoretical second-order accuracy is verified using a smooth test function and pairs of meshes commonly used for atmospheric modelling. Experiments confirm that the most expensive operations, especially the supermesh construction, have O(NlogN) computational cost. The method presented is meant to be incorporated in pre- or post-processing atmospheric modelling pipelines, or directly into models for flexible input/output. It could also serve as a basis for conservative coupling between model components, e.g. atmosphere and ocean.

  3. Clusters of polyhedra in spherical confinement

    PubMed Central

    Teich, Erin G.; van Anders, Greg; Klotsa, Daphne; Dshemuchadse, Julia; Glotzer, Sharon C.

    2016-01-01

    Dense particle packing in a confining volume remains a rich, largely unexplored problem, despite applications in blood clotting, plasmonics, industrial packaging and transport, colloidal molecule design, and information storage. Here, we report densest found clusters of the Platonic solids in spherical confinement, for up to N=60 constituent polyhedral particles. We examine the interplay between anisotropic particle shape and isotropic 3D confinement. Densest clusters exhibit a wide variety of symmetry point groups and form in up to three layers at higher N. For many N values, icosahedra and dodecahedra form clusters that resemble sphere clusters. These common structures are layers of optimal spherical codes in most cases, a surprising fact given the significant faceting of the icosahedron and dodecahedron. We also investigate cluster density as a function of N for each particle shape. We find that, in contrast to what happens in bulk, polyhedra often pack less densely than spheres. We also find especially dense clusters at so-called magic numbers of constituent particles. Our results showcase the structural diversity and experimental utility of families of solutions to the packing in confinement problem. PMID:26811458

  4. Fabrication of Spherical Reflectors in Outer Space

    NASA Technical Reports Server (NTRS)

    Wang, Yu; Dooley, Jennifer; Dragovan, Mark; Serivens, Wally

    2005-01-01

    A process is proposed for fabrication of lightweight spherical reflectors in outer space for telescopes, radio antennas, and light collectors that would be operated there. The process would obviate the relatively massive substrates and frames needed to support such reflectors in normal Earth gravitation. According to the proposal, fabrication of a reflector would begin with blowing of a bubble to the specified reflector radius. Taking advantage of the outer-space vacuum as a suitable environment for evaporative deposition of metal, a metal-evaporation source would be turned on and moved around the bubble to deposit a reflective metal film over the specified reflector area to a thickness of several microns. Then the source would be moved and aimed to deposit more metal around the edge of the reflector area, increasing the thickness there to approximately equal to 100 micron to form a frame. Then the bubble would be deflated and peeled off the metal, leaving a thin-film spherical mirror having an integral frame. The mirror would then be mounted for use. The feasibility of this technology has been proved by fabricating a prototype at JPL. As shown in the figure, a 2-in. (.5-cm) diameter hemispherical prototype reflector was made from a polymer bubble coated with silver, forming a very smooth surface.

  5. Clusters of polyhedra in spherical confinement.

    PubMed

    Teich, Erin G; van Anders, Greg; Klotsa, Daphne; Dshemuchadse, Julia; Glotzer, Sharon C

    2016-02-01

    Dense particle packing in a confining volume remains a rich, largely unexplored problem, despite applications in blood clotting, plasmonics, industrial packaging and transport, colloidal molecule design, and information storage. Here, we report densest found clusters of the Platonic solids in spherical confinement, for up to [Formula: see text] constituent polyhedral particles. We examine the interplay between anisotropic particle shape and isotropic 3D confinement. Densest clusters exhibit a wide variety of symmetry point groups and form in up to three layers at higher N. For many N values, icosahedra and dodecahedra form clusters that resemble sphere clusters. These common structures are layers of optimal spherical codes in most cases, a surprising fact given the significant faceting of the icosahedron and dodecahedron. We also investigate cluster density as a function of N for each particle shape. We find that, in contrast to what happens in bulk, polyhedra often pack less densely than spheres. We also find especially dense clusters at so-called magic numbers of constituent particles. Our results showcase the structural diversity and experimental utility of families of solutions to the packing in confinement problem. PMID:26811458

  6. Saltation of Non-Spherical Sand Particles

    PubMed Central

    Wang, Zhengshi; Ren, Shan; Huang, Ning

    2014-01-01

    Saltation is an important geological process and the primary source of atmospheric mineral dust aerosols. Unfortunately, no studies to date have been able to precisely reproduce the saltation process because of the simplified theoretical models used. For example, sand particles in most of the existing wind sand movement models are considered to be spherical, the effects of the sand shape on the structure of the wind sand flow are rarely studied, and the effect of mid-air collision is usually neglected. In fact, sand grains are rarely round in natural environments. In this paper, we first analyzed the drag coefficients, drag forces, and starting friction wind speeds of sand grains with different shapes in the saltation process, then established a sand saltation model that considers the coupling effect between wind and the sand grains, the effect of the mid-air collision of sand grains, and the effect of the sand grain shape. Based on this model, the saltation process and sand transport rate of non-spherical sand particles were simulated. The results show that the sand shape has a significant impact on the saltation process; for the same wind speed, the sand transport rates varied for different shapes of sand grains by as much as several-fold. Therefore, sand shape is one of the important factors affecting wind-sand movement. PMID:25170614

  7. Understanding pop-ins in spherical nanoindentation

    SciTech Connect

    Pathak, Siddhartha; Riesterer, Jessica L.; Kalidindi, Surya R.; Michler, Johann

    2014-10-24

    In this study, pop-ins, or sudden displacement-bursts at constant load in a nanoindentation test, are typically attributed to the difficulty of setting up potent dislocation sources in the very small indentation zones in these experiments. Such displacement (and strain) bursts would intuitively indicate a sharp drop in stress during the pop-in event itself. However, spherical indentation stress-strain curves routinely exhibit a high and stable indentation stress value during the pop-in, and the indentation stresses decrease only after a further finite amount of additional indentation displacement has been applied. In order to understand this discrepancy, we utilize a combination of interrupted spherical indentation tests along with depth profiling of the residual indentation surfaces using in-situ atomic force microscopy (AFM) to study pop-ins. The AFM surface profile maps show that there is an asymmetric profile change over a limited region around the indentation contact area for a single pop-in; the asymmetry disappears upon further loading beyond the pop-in. A plausible sequence of physical processes (related to metal plasticity) occurring underneath the indenter during and immediately after the occurrence of the pop-in is proposed to explain these observations.

  8. Understanding pop-ins in spherical nanoindentation

    DOE PAGESBeta

    Pathak, Siddhartha; Riesterer, Jessica L.; Kalidindi, Surya R.; Michler, Johann

    2014-10-24

    In this study, pop-ins, or sudden displacement-bursts at constant load in a nanoindentation test, are typically attributed to the difficulty of setting up potent dislocation sources in the very small indentation zones in these experiments. Such displacement (and strain) bursts would intuitively indicate a sharp drop in stress during the pop-in event itself. However, spherical indentation stress-strain curves routinely exhibit a high and stable indentation stress value during the pop-in, and the indentation stresses decrease only after a further finite amount of additional indentation displacement has been applied. In order to understand this discrepancy, we utilize a combination of interruptedmore » spherical indentation tests along with depth profiling of the residual indentation surfaces using in-situ atomic force microscopy (AFM) to study pop-ins. The AFM surface profile maps show that there is an asymmetric profile change over a limited region around the indentation contact area for a single pop-in; the asymmetry disappears upon further loading beyond the pop-in. A plausible sequence of physical processes (related to metal plasticity) occurring underneath the indenter during and immediately after the occurrence of the pop-in is proposed to explain these observations.« less

  9. Experimental drag histories of shocked spherical particles

    NASA Astrophysics Data System (ADS)

    Prestridge, Katherine; Orlicz, Greg; Martinez, Adam

    2015-11-01

    The horizontal shock tube (HST) facility at Los Alamos is used to investigate the drag forces on micrometer-sized particles dispersed in air when they are accelerated by a shock. Eight-frame, high-speed particle tracking velocimetry/accelerometry (PTVA) diagnostics are implemented to measure the trajectory of individual particles with high spatial and temporal resolution, and a shadowgraphy system is used to measure the shock position on each image. We present experiments over a range of Reynolds numbers, Mach numbers, particle sizes, and particle densities that explore the drag forces on solid, spherical, non-deforming particles. Experimental drag coefficients are calculated from eight dynamic measurements of particle position versus time, for Mach 1.3 and Mach 1.2 experiments. Experimental results show drag coefficients significantly larger than those predicted by the standard drag model for solid, spherical particles. These results are consistent with measurements made by Rudinger (1970) and Sommerfeld (1985). We will present experimental results and analysis of unsteady drag as a function of particle Reynolds number, Mach number and Stokes number.

  10. Ultrarelativistic bound states in the spherical well

    NASA Astrophysics Data System (ADS)

    Żaba, Mariusz; Garbaczewski, Piotr

    2016-07-01

    We address an eigenvalue problem for the ultrarelativistic (Cauchy) operator (-Δ)1/2, whose action is restricted to functions that vanish beyond the interior of a unit sphere in three spatial dimensions. We provide high accuracy spectral data for lowest eigenvalues and eigenfunctions of this infinite spherical well problem. Our focus is on radial and orbital shapes of eigenfunctions. The spectrum consists of an ordered set of strictly positive eigenvalues which naturally splits into non-overlapping, orbitally labelled E(k,l) series. For each orbital label l = 0, 1, 2, …, the label k = 1, 2, … enumerates consecutive lth series eigenvalues. Each of them is 2l + 1-degenerate. The l = 0 eigenvalues series E(k,0) are identical with the set of even labeled eigenvalues for the d = 1 Cauchy well: E(k,0)(d = 3) = E2k(d = 1). Likewise, the eigenfunctions ψ(k,0)(d = 3) and ψ2k(d = 1) show affinity. We have identified the generic functional form of eigenfunctions of the spherical well which appear to be composed of a product of a solid harmonic and of a suitable purely radial function. The method to evaluate (approximately) the latter has been found to follow the universal pattern which effectively allows to skip all, sometimes involved, intermediate calculations (those were in usage, while computing the eigenvalues for l ≤ 3).

  11. Understanding pop-ins in spherical nanoindentation

    SciTech Connect

    Pathak, Siddhartha E-mail: siddharthapathak@gmail.com; Riesterer, Jessica L.; Michler, Johann; Kalidindi, Surya R.

    2014-10-20

    Pop-ins, or sudden displacement-bursts at constant load in a nanoindentation test, are typically attributed to the difficulty of setting up potent dislocation sources in the very small indentation zones in these experiments. Such displacement (and strain) bursts would intuitively indicate a sharp drop in stress during the pop-in event itself. However, spherical indentation stress-strain curves routinely exhibit a high and stable indentation stress value during the pop-in, and the indentation stresses decrease only after a further finite amount of additional indentation displacement has been applied. In order to understand this discrepancy, we utilize a combination of interrupted spherical indentation tests along with depth profiling of the residual indentation surfaces using in-situ atomic force microscopy (AFM) to study pop-ins. The AFM surface profile maps show that there is an asymmetric profile change over a limited region around the indentation contact area for a single pop-in; the asymmetry disappears upon further loading beyond the pop-in. A plausible sequence of physical processes (related to metal plasticity) occurring underneath the indenter during and immediately after the occurrence of the pop-in is proposed to explain these observations.

  12. Spherically symmetric conformal gravity and ``gravitational bubbles''

    NASA Astrophysics Data System (ADS)

    Berezin, V. A.; Dokuchaev, V. I.; Eroshenko, Yu. N.

    2016-01-01

    The general structure of the spherically symmetric solutions in the Weyl conformal gravity is described. The corresponding Bach equations are derived for the special type of metrics, which can be considered as the representative of the general class. The complete set of the pure vacuum solutions is found. It consists of two classes. The first one contains the solutions with constant two-dimensional curvature scalar of our specific metrics, and the representatives are the famous Robertson-Walker metrics. One of them we called the ``gravitational bubbles'', which is compact and with zero Weyl tensor. Thus, we obtained the pure vacuum curved space-times (without any material sources, including the cosmological constant) what is absolutely impossible in General Relativity. Such a phenomenon makes it easier to create the universe from ``nothing''. The second class consists of the solutions with varying curvature scalar. We found its representative as the one-parameter family. It appears that it can be conformally covered by the thee-parameter Mannheim-Kazanas solution. We also investigated the general structure of the energy-momentum tensor in the spherical conformal gravity and constructed the vectorial equation that reveals clearly some features of non-vacuum solutions. Two of them are explicitly written, namely, the metrics à la Vaidya, and the electrovacuum space-time metrics.

  13. Bidispersed Sphere Packing on Spherical Surfaces

    NASA Astrophysics Data System (ADS)

    Atherton, Timothy; Mascioli, Andrew; Burke, Christopher

    Packing problems on spherical surfaces have a long history, originating in the classic Thompson problem of finding the ground state configuration of charges on a sphere. Such packings contain a minimal number of defects needed to accommodate the curvature; this is predictable using the Gauss-Bonnet theorem from knowledge of the topology of the surface and the local symmetry of the ordering. Famously, the packing of spherical particles on a sphere contains a 'scar' transition, where additional defects over those required by topology appear above a certain critical number of particles and self-organize into chains or scars. In this work, we study the packing of bidispersed packings on a sphere, and hence determine the interaction of bidispersity and curvature. The resultant configurations are nearly crystalline for low values of bidispersity and retain scar-like structures; these rapidly become disordered for intermediate values and approach a so-called Appollonian limit at the point where smaller particles can be entirely accommodated within the voids left by the larger particles. We connect our results with studies of bidispersed packings in the bulk and on flat surfaces from the literature on glassy systems and jamming. Supported by a Cottrell Award from the Research Corporation for Science Advancement.

  14. Quasi-spherical direct drive fusion.

    SciTech Connect

    VanDevender, J. Pace; Abbott, Lucas M.; Langston, William L.; McDaniel, Dillon Heirman; Nash, Thomas J.; Roderick, Norman Frederick; Silva, M.

    2007-01-01

    The authors present designs of quasi-spherical direction drive z-pinch loads for machines such as ZR at 28 MA load current with a 150 ns implosion time (QSDDI). A double shell system for ZR has produced a 2D simulated yield of 12 MJ, but the drive for this system on ZR has essentially no margin. A double shell system for a 56 MA driver at 150 ns implosion has produced a simulated yield of 130 MJ with considerable margin in attaining the necessary temperature and density-radius product for ignition. They also represent designs for a magnetically insulated current amplifier, (MICA), that modify the attainable ZR load current to 36 MA with a 28 ns rise time. The faster pulse provided by a MICA makes it possible to drive quasi-spherical single shell implosions (QSDD2). They present results from 1D LASNEX and 2D MACH2 simulations of promising low-adiabat cryogenic QSDD2 capsules and 1D LASNEX results of high-adiabat cryogenic QSDD2 capsules.

  15. Modeling spherical explosions with aluminized energetic materials

    NASA Astrophysics Data System (ADS)

    Massoni, J.; Saurel, R.; Lefrançois, A.; Baudin, G.

    2006-11-01

    This paper deals with the numerical solution and validation of a reactive flow model dedicated to the study of spherical explosions with an aluminized energetic material. Situations related to air blast as well as underwater explosions are examined. Such situations involve multiscale phenomena associated with the detonation reaction zone, the aluminium reaction zone, the shock propagation distance and the bubble oscillation period. A detonation tracking method is developed in order to avoid the detonation structure computation. An ALE formulation is combined to the detonation tracking method in order to solve the material interface between detonation products and the environment as well as shock propagation. The model and the algorithm are then validated over a wide range of spherical explosions involving several types of explosives, both in air and liquid water environment. Large-scale experiments have been done in order to determine the blast wave effects with explosive compositions of variable aluminium content. In all situations the agreement between computed and experimental results is very good.

  16. Spherical polytropic balls cannot mimic black holes

    NASA Astrophysics Data System (ADS)

    Saida, Hiromi; Fujisawa, Atsuhito; Yoo, Chul-Moon; Nambu, Yasusada

    2016-04-01

    The so-called black hole shadow is a dark region which is expected to appear in a fine image of optical observation of black holes. It is essentially an absorption cross section of the black hole, and the boundary of shadow is determined by unstable circular orbits of photons (UCOP). If there exists a compact object possessing UCOP but no black hole horizon, it can provide us with the same shadow image as black holes, and detection of a shadow image cannot be direct evidence of black hole existence. This paper examines whether or not such compact objects can exist under some suitable conditions. We investigate thoroughly the static spherical polytropic ball of perfect fluid with single polytrope index, and then investigate a representative example of a piecewise polytropic ball. Our result is that the spherical polytropic ball which we have investigated cannot possess UCOP, if the speed of sound at the center is subluminal (slower than light). This means that, if the polytrope treated in this paper is a good model of stellar matter in compact objects, the detection of a shadow image can be regarded as good evidence of black hole existence. As a by-product, we have found the upper bound of the mass-to-radius ratio of a polytropic ball with single index, M_{ast }/R_{ast } < 0.281, under the condition of subluminal sound speed.

  17. Initial assessments of ignition spherical torus

    SciTech Connect

    Peng, Y.K.M.; Borowski, S.K.; Bussell, G.T.; Dalton, G.R.; Gorker, G.E.; Haines, J.R.; Hamilton, W.R.; Kalsi, S.S.; Lee, V.D.; Miller, J.B.

    1985-12-01

    Initial assessments of ignition spherical tori suggest that they can be highly cost effective and exceptionally small in unit size. Assuming advanced methods of current drive to ramp up the plasma current (e.g., via lower hybrid wave at modest plasma densities and temperatures), the inductive solenoid can largely be eliminated. Given the uncertainties in plasma energy confinement times and the effects of strong paramagnetism on plasma pressure, and allowing for the possible use of high-strength copper alloys (e.g., C-17510, Cu-Ni-Be alloy), ignition spherical tori with a 50-s burn are estimated to have major radii ranging from 1.0 to 1.6 m, aspect ratios from 1.4 to 1.7, vacuum toroidal fields from 2 to 3 T, plasma currents from 10 to 19 MA, and fusion power from 50 to 300 MW. Because of its modest field strength and simple poloidal field coil configuration, only conventional engineering approaches are needed in the design. A free-standing toroidal field coil/vacuum vessel structure is assessed to be feasible and relatively independent of the shield structure and the poloidal field coils. This exceptionally simple configuration depends significantly, however, on practical fabrication approaches of the center conductor post, about which there is presently little experience. 19 refs.

  18. Spherical compression of a magnetic field

    SciTech Connect

    Fowler, C.M.

    1996-09-01

    In an interesting paper, Rutkevich obtained the electromagnetic wave solution for the compression of a magnetic field contained by an imploding, perfectly conducting cylindrical shell or liner. The magnetic and electric susceptibilities were taken as constant. The solution was obtained by Laplace transforms. In his paper, he also considered the corresponding plane problem when driving together two perfectly conducting, parallel plates that confine a magnetic field. He compared the method of solution obtained by Laplace transforms with that obtained by the method of characteristics which was used to obtain the original solution. He concluded his paper by noting that the transform method is more versatile that the characteristic method. Somewhat later, Bodulinskii and Medvedev obtained a solution for the wave structure generated when an initial magnetic field is compressed by the implosion of a conducting spherical liner. Again, the solution was obtained by transform methods. In this paper, we outline the solution to the spherical problem using the method of characteristics. The utility of this method is described for some other situations.

  19. Rayleigh scattering of a spherical sound wave.

    PubMed

    Godin, Oleg A

    2013-02-01

    Acoustic Green's functions for a homogeneous medium with an embedded spherical obstacle arise in analyses of scattering by objects on or near an interface, radiation by finite sources, sound attenuation in and scattering from clouds of suspended particles, etc. An exact solution of the problem of diffraction of a monochromatic spherical sound wave on a sphere is given by an infinite series involving products of Bessel functions and Legendre polynomials. In this paper, a simple, closed-form solution is obtained for scattering by a sphere with a radius that is small compared to the wavelength. Soft, hard, impedance, and fluid obstacles are considered. The solution is valid for arbitrary positions of the source and receiver relative to the scatterer. Low-frequency scattering is shown to be rather sensitive to boundary conditions on the surface of the obstacle. Low-frequency asymptotics of the scattered acoustic field are extended to transient incident waves. The asymptotic expansions admit an intuitive interpretation in terms of image sources and reduce to classical results in appropriate limiting cases. PMID:23363090

  20. SPHERICAL INDENTATION OF SiC

    SciTech Connect

    Wereszczak, Andrew A; Johanns, Kurt E

    2007-01-01

    Instrumented Hertzian indentation testing was performed on several grades of SiCs and the results and preliminary interpretations are presented. The grades included hot-pressed and sintered compositions. One of the hot-pressed grades was additionally subjected to high temperature heat treatment to produce a coarsened grain microstructure to enable the examination of exaggerated grain size on indentation response. Diamond spherical indenters were used in the testing. Indentation load, indentation depth of penetration, and acoustic activity were continually measured during each indentation test. Indentation response and postmortem analysis of induced damage (e.g., ring/cone, radial and median cracking, quasi-plasticity) are compared and qualitatively as a function of grain size. For the case of SiC-N, the instrumented spherical indentation showed that yielding initiated at an average contact stress 12-13 GPa and that there was another event (i.e., a noticeable rate increase in compliance probably associated with extensive ring and radial crack formations) occurring around an estimated average contact stress of 19 GPa.

  1. Non-stationary spherical random media and their effect on long-period mantle waves

    NASA Astrophysics Data System (ADS)

    Meschede, Matthias; Romanowicz, Barbara

    2015-12-01

    We present a method to construct non-stationary and anisotropic second-order random model realizations that can be used for numerical wave propagation simulations in various geometries. Models are generated directly from a given covariance matrix using its eigenvector decomposition (principal component or Karhunen-Loève method). Because this decomposition is very expensive computationally in 3-D, we use model symmetries to reduce the size of the covariance matrix to its non-stationary components. Stationary components can then be described through their power spectrum, such that models with axisymmetric or spherically symmetric statistics can be generated from a 1-D covariance matrix. We focus in particular on models with spherically symmetric statistics that are important to study wave propagation in the Earth. We use this method to show the influence of hypothetical small-scale structure in the Earth's mantle on the elastic wavefield. To this end, we extend tomographic models beyond their spatial resolution limit with different distributions of small-scale scatterers that generate a coda and attenuate direct waves (scattering attenuation). We observe that scattering attenuation of fundamental mode Rayleigh waves is small (0.5-2 per cent of the total attenuation), if the elastic mantle structure does not become significantly stronger at smaller scales. At the examined heterogeneity strengths, scattering attenuation scales linearly with the model variance. The long-period fundamental mode Rayleigh wave coda is difficult to measure because it is weak and overlaps with other signals. However, it can be shown that its intensity also scales linearly with model power, and that it depends strongly on the spherical geometry of the Earth. It can therefore be used to distinguish between models with different small-scale power. We show qualitatively that the coda generated by the type of random models we consider can explain observed scattered energy at long periods (100 s).

  2. Two-fluid simulations of driven reconnection in the mega-ampere spherical tokamak

    SciTech Connect

    Stanier, A.; Browning, P.; Gordovskyy, M.; McClements, K. G.; Gryaznevich, M. P.

    2013-12-15

    In the merging-compression method of plasma start-up, two flux-ropes with parallel toroidal current are formed around in-vessel poloidal field coils, before merging to form a spherical tokamak plasma. This start-up method, used in the Mega-Ampere Spherical Tokamak (MAST), is studied as a high Lundquist number and low plasma-beta magnetic reconnection experiment. In this paper, 2D fluid simulations are presented of this merging process in order to understand the underlying physics, and better interpret the experimental data. These simulations examine the individual and combined effects of tight-aspect ratio geometry and two-fluid physics on the merging. The ideal self-driven flux-rope dynamics are coupled to the diffusion layer physics, resulting in a large range of phenomena. For resistive MHD simulations, the flux-ropes enter the sloshing regime for normalised resistivity η≲10{sup −5}. In Hall-MHD, three regimes are found for the qualitative behaviour of the current sheet, depending on the ratio of the current sheet width to the ion-sound radius. These are a stable collisional regime, an open X-point regime, and an intermediate regime that is highly unstable to tearing-type instabilities. In toroidal axisymmetric geometry, the final state after merging is a MAST-like spherical tokamak with nested flux-surfaces. It is also shown that the evolution of simulated 1D radial density profiles closely resembles the Thomson scattering electron density measurements in MAST. An intuitive explanation for the origin of the measured density structures is proposed, based upon the results of the toroidal Hall-MHD simulations.

  3. Effect of conductor geometry on source localization: Implications for epilepsy studies

    SciTech Connect

    Schlitt, H.; Heller, L.; Best, E.; Ranken, D.; Aaron, R.

    1994-07-01

    We shall discuss the effects of conductor geometry on source localization for applications in epilepsy studies. The most popular conductor model for clinical MEG studies is a homogeneous sphere. However, several studies have indicated that a sphere is a poor model for the head when the sources are deep, as is the case for epileptic foci in the mesial temporal lobe. We believe that replacing the spherical model with a more realistic one in the inverse fitting procedure will improve the accuracy of localizing epileptic sources. In order to include a realistic head model in the inverse problem, we must first solve the forward problem for the realistic conductor geometry. We create a conductor geometry model from MR images, and then solve the forward problem via a boundary integral equation for the electric potential due to a specified primary source. One the electric potential is known, the magnetic field can be calculated directly. The most time-intensive part of the problem is generating the conductor model; fortunately, this needs to be done only once for each patient. It takes little time to change the primary current and calculate a new magnetic field for use in the inverse fitting procedure. We present the results of a series of computer simulations in which we investigate the localization accuracy due to replacing the spherical model with the realistic head model in the inverse fitting procedure. The data to be fit consist of a computer generated magnetic field due to a known current dipole in a realistic head model, with added noise. We compare the localization errors when this field is fit using a spherical model to the fit using a realistic head model. Using a spherical model is comparable to what is usually done when localizing epileptic sources in humans, where the conductor model used in the inverse fitting procedure does not correspond to the actual head.

  4. Low resolution brain electromagnetic tomography in a realistic geometry head model: a simulation study

    NASA Astrophysics Data System (ADS)

    Ding, Lei; Lai, Yuan; He, Bin

    2005-01-01

    It is of importance to localize neural sources from scalp recorded EEG. Low resolution brain electromagnetic tomography (LORETA) has received considerable attention for localizing brain electrical sources. However, most such efforts have used spherical head models in representing the head volume conductor. Investigation of the performance of LORETA in a realistic geometry head model, as compared with the spherical model, will provide useful information guiding interpretation of data obtained by using the spherical head model. The performance of LORETA was evaluated by means of computer simulations. The boundary element method was used to solve the forward problem. A three-shell realistic geometry (RG) head model was constructed from MRI scans of a human subject. Dipole source configurations of a single dipole located at different regions of the brain with varying depth were used to assess the performance of LORETA in different regions of the brain. A three-sphere head model was also used to approximate the RG head model, and similar simulations performed, and results compared with the RG-LORETA with reference to the locations of the simulated sources. Multi-source localizations were discussed and examples given in the RG head model. Localization errors employing the spherical LORETA, with reference to the source locations within the realistic geometry head, were about 20-30 mm, for four brain regions evaluated: frontal, parietal, temporal and occipital regions. Localization errors employing the RG head model were about 10 mm over the same four brain regions. The present simulation results suggest that the use of the RG head model reduces the localization error of LORETA, and that the RG head model based LORETA is desirable if high localization accuracy is needed.

  5. Properties of cylindrical and spherical heavy ion-acoustic solitary and shock structures in a multispecies plasma with superthermal electrons

    NASA Astrophysics Data System (ADS)

    Shah, M. G.; Rahman, M. M.; Hossen, M. R.; Mamun, A. A.

    2016-02-01

    A theoretical investigation on heavy ion-acoustic (HIA) solitary and shock structures has been accomplished in an unmagnetized multispecies plasma consisting of inertialess kappa-distributed superthermal electrons, Boltzmann light ions, and adiabatic positively charged inertial heavy ions. Using the reductive perturbation technique, the nonplanar (cylindrical and spherical) Kortewg-de Vries (KdV) and Burgers equations have been derived. The solitary and shock wave solutions of the KdV and Burgers equations, respectively, have been numerically analyzed. The effects of superthermality of electrons, adiabaticity of heavy ions, and nonplanar geometry, which noticeably modify the basic features (viz. polarity, amplitude, phase speed, etc.) of small but finite amplitude HIA solitary and shock structures, have been carefully investigated. The HIA solitary and shock structures in nonplanar geometry have been found to distinctly differ from those in planar geometry. Novel features of our present attempt may contribute to the physics of nonlinear electrostatic perturbation in astrophysical and laboratory plasmas.

  6. The Effect of Geometry Instruction with Dynamic Geometry Software; GeoGebra on Van Hiele Geometry Understanding Levels of Students

    ERIC Educational Resources Information Center

    Kutluca, Tamer

    2013-01-01

    The aim of this study is to investigate the effect of dynamic geometry software GeoGebra on Van Hiele geometry understanding level of students at 11th grade geometry course. The study was conducted with pre and posttest control group quasi-experimental method. The sample of the study was 42 eleventh grade students studying in the spring term of…

  7. Effects of Idealized Joint Geometry on Finite Element Predictions of Cartilage Contact Stresses in the Hip

    PubMed Central

    Anderson, Andrew E.; Ellis, Benjamin J.; Maas, Steve A.; Weiss, Jeffrey A.

    2010-01-01

    Computational models may have the ability to quantify the relationship between hip morphology, cartilage mechanics and osteoarthritis. Most models have assumed the hip joint to be a perfect ball and socket joint and have neglected deformation at the interface between bone/cartilage. The objective of this study was to analyze finite element (FE) models of hip cartilage mechanics with varying degrees of simplified geometry and a model with a rigid bone material assumption to elucidate the effects on predictions of cartilage stress. A previously validated subject-specific FE model of a cadaveric hip joint was used as the basis for the models. Geometry for the bone/cartilage interface was either: 1) subject-specific (i.e. irregular), 2) spherical, or 3) a rotational conchoid. Cartilage was assigned either a varying (irregular) or constant thickness (smoothed). Loading conditions simulated walking, stair climbing and descending stairs. FE predictions of contact stress for the simplified models were compared with predictions from the subject-specific model. Both spheres and conchoids provided a good approximation of native hip joint geometry (average fitting error ~0.5 mm). However, models with spherical/conchoid bone geometry and smoothed articulating cartilage surfaces grossly underestimated peak and average contact pressures (50% and 25% lower, respectively) and overestimated contact area when compared to the subject-specific FE model. Models incorporating subject-specific bone geometry with smoothed articulating cartilage also underestimated pressures and predicted evenly distributed patterns of contact. The model with rigid bones predicted much higher pressures than the subject-specific model with deformable bones. The results demonstrate that simplifications to the geometry of the bone/cartilage interface, cartilage surface and bone material properties can have a dramatic effect on the predicted magnitude and distribution of cartilage contact pressures in the hip

  8. Optimizing solar-cell grid geometry

    NASA Technical Reports Server (NTRS)

    Crossley, A. P.

    1969-01-01

    Trade-off analysis and mathematical expressions calculate optimum grid geometry in terms of various cell parameters. Determination of the grid geometry provides proper balance between grid resistance and cell output to optimize the energy conversion process.

  9. A Whirlwind Tour of Computational Geometry.

    ERIC Educational Resources Information Center

    Graham, Ron; Yao, Frances

    1990-01-01

    Described is computational geometry which used concepts and results from classical geometry, topology, combinatorics, as well as standard algorithmic techniques such as sorting and searching, graph manipulations, and linear programing. Also included are special techniques and paradigms. (KR)

  10. The Geometry of Quasar Outflows

    NASA Astrophysics Data System (ADS)

    Ganguly, Rajib

    2012-10-01

    Quasar outflows are important for understanding the accretion and growth processes of the central black hole, but also potentially play a role in feedback to the galaxy, halting star formation and infall of gas. A big uncertainty lies in the geometry and density of these outflows, especially as a function of ionization and velocity. We aim to tackle this using the archival COS M grating spectra of 266 quasars. We separate the geometry of outflows into two parts: the solid angle subtended around the black hole, and the distance of the outflow from the central engine. Large numbers of quasars with high resolution spectra are required for each aspect of this statistical investigation. First, we will determine which/how many absorption-line systems are intrinsic through both partial covering methods and statistical assessments. Second, we will consider the incidence of intrinsic absorbers as a function of quasar property {e.g., radio-loudness, SED shape, black hole mass, bolometric luminosity}. This will reveal what determines the solid angle. This can only be done at moderate redshifts where quasars with a larger range of properties are observable, and hence requires HST/COS. Third, we will use the wide range of diagnostic lines to constrain the physical conditions of the absorbers. We will target the CIII*1175 complex and apply photoionization models to constrain the densities and ionization parameters. This will provide the largest set yet of intrinsic absorbers with systematic distance constraints. In tandem with the solid angles, this work will inform models regarding the geometry of quasar outflows.

  11. Worldsheet geometries of ambitwistor string

    NASA Astrophysics Data System (ADS)

    Ohmori, Kantaro

    2015-06-01

    Mason and Skinner proposed the ambitwistor string theory which directly reproduces the formulas for the amplitudes of massless particles proposed by Cachazo, He and Yuan. In this paper we discuss geometries of the moduli space of worldsheets associated to the bosonic or the RNS ambitwistor string. Further, we investigate the factorization properties of the amplitudes when an internal momentum is near on-shell in the abstract CFT language. Along the way, we propose the existence of the ambitwistor strings with three or four fermionic worldsheet currents.

  12. Emergent Calabi-Yau geometry.

    PubMed

    Ooguri, Hirosi; Yamazaki, Masahito

    2009-04-24

    We show how the smooth geometry of Calabi-Yau manifolds emerges from the thermodynamic limit of the statistical mechanical model of crystal melting defined in our previous paper. In particular, the thermodynamic partition function of molten crystals is shown to be equal to the classical limit of the partition function of the topological string theory by relating the Ronkin function of the characteristic polynomial of the crystal melting model to the holomorphic 3-form on the corresponding Calabi-Yau manifold. PMID:19518695

  13. Application of spherical gratings in synchrotron radiation spectroscopy

    SciTech Connect

    Hogrefe, H.; Howells, M.R.; Hoyer, E.

    1986-05-01

    The recent development in gracing incidence grating monochromator design is discussed and the performance limiting for such instruments are examined. Especially the aberrations of toroidal and spherical gratings are investigated using the optical path function concept. It is shown that large radius spherical gratings, which can be produced with better slope tolerances than aspherics, also yield smaller overall line curvature than toroids. Therefore, a new simple spherical grating monochromator design is proposed and its performance is analyzed.

  14. Parameters of lossless transmission lines with spherical T-waves

    NASA Astrophysics Data System (ADS)

    Kniaz, A. I.; Draganov, V. M.

    1983-04-01

    The analogy between plane-parallel and spherical-parallel fields is used to derive a unified formula for the parameters (capacitance and wave resistance) of a cylindrical system of conductors with a plane transverse wave and of a system of conical conductors with a spherical transverse wave. This makes it possible to transform previously developed formulas into formulas for determining the parameters of lossless transmission lines with spherical transverse waves. Some examples of the application of the proposed approach are considered.

  15. GENERAL: Non-Spherical Gravitational Collapse of Strange Quark Matter

    NASA Astrophysics Data System (ADS)

    S, Zade S.; D, Patil K.; N, Mulkalwar P.

    2008-05-01

    We study the non-spherical gravitational collapse of the strange quark null fluid. The interesting feature which emerges is that the non-spherical collapse of charged strange quark matter leads to a naked singularity whereas the gravitational collapse of neutral quark matter proceeds to form a black hole. We extend the earlier work of Harko and Cheng [Phys. Lett. A 266 (2000) 249] to the non-spherical case.

  16. Theory of diffusion-influenced reactions in complex geometries.

    PubMed

    Galanti, Marta; Fanelli, Duccio; Traytak, Sergey D; Piazza, Francesco

    2016-06-21

    Chemical transformations involving the diffusion of reactants and subsequent chemical fixation steps are generally termed "diffusion-influenced reactions" (DIR). Virtually all biochemical processes in living media can be counted among them, together with those occurring in an ever-growing number of emerging nano-technologies. The role of the environment's geometry (obstacles, compartmentalization) and distributed reactivity (competitive reactants, traps) is key in modulating the rate constants of DIRs, and is therefore a prime design parameter. Yet, it is a formidable challenge to build a comprehensive theory that is able to describe the environment's "reactive geometry". Here we show that such a theory can be built by unfolding this many-body problem through addition theorems for special functions. Our method is powerful and general and allows one to study a given DIR reaction occurring in arbitrary "reactive landscapes", made of multiple spherical boundaries of given size and reactivity. Importantly, ready-to-use analytical formulas can be derived easily in most cases. PMID:27241805

  17. The role of pore geometry in single nanoparticle detection

    SciTech Connect

    Davenport, Matthew; Healy, Ken; Pevarnik, Matthew; Teslich, Nick; Cabrini, Stefano; Morrison, Alan P.; Siwy, Zuzanna S.; Letant, Sonia E.

    2012-08-22

    In this study, we observe single nanoparticle translocation events via resistive pulse sensing using silicon nitride pores described by a range of lengths and diameters. Pores are prepared by focused ion beam milling in 50 nm-, 100 nm-, and 500 nm-thick silicon nitride membranes with diameters fabricated to accommodate spherical silica nanoparticles with sizes chosen to mimic that of virus particles. In this manner, we are able to characterize the role of pore geometry in three key components of the detection scheme, namely, event magnitude, event duration, and event frequency. We find that the electric field created by the applied voltage and the pore’s geometry is a critical factor. We develop approximations to describe this field, which are verified with computer simulations, and interactions between particles and this field. In so doing, we formulate what we believe to be the first approximation for the magnitude of ionic current blockage that explicitly addresses the invariance of access resistance of solid-state pores during particle translocation. These approximations also provide a suitable foundation for estimating the zeta potential of the particles and/or pore surface when studied in conjunction with event durations. We also verify that translocation achieved by electro-osmostic transport is an effective means of slowing translocation velocities of highly charged particles without compromising particle capture rate as compared to more traditional approaches based on electrophoretic transport.

  18. The role of pore geometry in single nanoparticle detection

    DOE PAGESBeta

    Davenport, Matthew; Healy, Ken; Pevarnik, Matthew; Teslich, Nick; Cabrini, Stefano; Morrison, Alan P.; Siwy, Zuzanna S.; Letant, Sonia E.

    2012-08-22

    In this study, we observe single nanoparticle translocation events via resistive pulse sensing using silicon nitride pores described by a range of lengths and diameters. Pores are prepared by focused ion beam milling in 50 nm-, 100 nm-, and 500 nm-thick silicon nitride membranes with diameters fabricated to accommodate spherical silica nanoparticles with sizes chosen to mimic that of virus particles. In this manner, we are able to characterize the role of pore geometry in three key components of the detection scheme, namely, event magnitude, event duration, and event frequency. We find that the electric field created by the appliedmore » voltage and the pore’s geometry is a critical factor. We develop approximations to describe this field, which are verified with computer simulations, and interactions between particles and this field. In so doing, we formulate what we believe to be the first approximation for the magnitude of ionic current blockage that explicitly addresses the invariance of access resistance of solid-state pores during particle translocation. These approximations also provide a suitable foundation for estimating the zeta potential of the particles and/or pore surface when studied in conjunction with event durations. We also verify that translocation achieved by electro-osmostic transport is an effective means of slowing translocation velocities of highly charged particles without compromising particle capture rate as compared to more traditional approaches based on electrophoretic transport.« less

  19. Engaging All Students with "Impossible Geometry"

    ERIC Educational Resources Information Center

    Wiest, Lynda R.; Ayebo, Abraham; Dornoo, Michael D.

    2010-01-01

    Geometry is an area in which Australian students performed particularly poorly on the 2007 Trends in International Mathematics and Science Study (TIMSS). One innovative area of recreational geometry that has rich potential to engage and challenge a wide variety of students is "impossible geometry." An impossible geometric object is a…

  20. Geometry: Career Related Units. Teacher's Edition.

    ERIC Educational Resources Information Center

    Pierro, Mike; And Others

    Using six geometry units as resource units, the document explores 22 math-related careers. The authors intend the document to provide senior high school students with career orientation and exploration experiences while they learn geometry skills. The units are to be considered as a part of a geometry course, not a course by themselves. The six…

  1. Preservice Primary School Teachers' Elementary Geometry Knowledge

    ERIC Educational Resources Information Center

    Marchis, Iuliana

    2012-01-01

    Geometrical notions and properties occur in real-world problems, thus Geometry has an important place in school Mathematics curricula. Primary school curricula lays the foundation of Geometry knowledge, pupils learn Geometry notions and properties by exploring their environment. Thus it is very important that primary school teachers have a good…

  2. Teaching Geometry: An Experiential and Artistic Approach.

    ERIC Educational Resources Information Center

    Ogletree, Earl J.

    The view that geometry should be taught at every grade level is promoted. Primary and elementary school children are thought to rarely have any direct experience with geometry, except on an incidental basis. Children are supposed to be able to learn geometry rather easily, so long as the method and content are adapted to their development and…

  3. Fisher information geometry of the barycenter map

    NASA Astrophysics Data System (ADS)

    Itoh, Mitsuhiro; Satoh, Hiroyasu

    2015-01-01

    We report Fisher information geometry of the barycenter map associated with Busemann function Bθ of an Hadamard manifold X and present its application to Riemannian geometry of X from viewpoint of Fisher information geometry. This report is an improvement of [I-Sat'13] together with a fine investigation of the barycenter map.

  4. Geometry in the Early Years: A Commentary

    ERIC Educational Resources Information Center

    Dindyal, Jaguthsing

    2015-01-01

    The primary goal of this paper is to provide a commentary on the teaching and learning of geometry in the early years of schooling with the set of papers in this issue as a guiding factor. It is structured around issues about geometry education of young learners, such as: what should we teach in geometry and why; representation of geometrical…

  5. Circle of least confusion of a spherical reflector.

    PubMed

    Hosken, Robert W

    2007-06-01

    A simple, tractable equation is provided for determining the size and location of the circle of least confusion of a concave spherical reflector. This method is exact for the object at infinity and with wave effects neglected. Designers of large radius Arecibo-like telescopes, both radio and optical, with symmetrical, spherical primaries should find the method useful. The mathematical results are valid for apertures with an angle of incidence up to 45 degrees. Comparisons of the location of the disk of least confusion with longitudinal spherical aberration and the radius of the disk with transverse spherical aberration are presented. PMID:17514263

  6. Motion of a porous sphere in a spherical container

    NASA Astrophysics Data System (ADS)

    Srinivasacharya, D.

    2005-08-01

    The creeping motion of a porous sphere at the instant it passes the center of a spherical container has been investigated. The Brinkman's model for the flow inside the porous sphere and the Stokes equation for the flow in the spherical container were used to study the motion. The stream function (and thus the velocity) and pressure (both for the flow inside the porous sphere and inside the spherical container) are calculated. The drag force experienced by the porous spherical particle and wall correction factor is determined. To cite this article: D. Srinivasacharya, C. R. Mecanique 333 (2005).

  7. Neuronal activity controls transsynaptic geometry.

    PubMed

    Glebov, Oleg O; Cox, Susan; Humphreys, Lawrence; Burrone, Juan

    2016-01-01

    The neuronal synapse is comprised of several distinct zones, including presynaptic vesicle zone (SVZ), active zone (AZ) and postsynaptic density (PSD). While correct relative positioning of these zones is believed to be essential for synaptic function, the mechanisms controlling their mutual localization remain unexplored. Here, we employ high-throughput quantitative confocal imaging, super-resolution and electron microscopy to visualize organization of synaptic subdomains in hippocampal neurons. Silencing of neuronal activity leads to reversible reorganization of the synaptic geometry, resulting in a increased overlap between immunostained AZ and PSD markers; in contrast, the SVZ-AZ spatial coupling is decreased. Bayesian blinking and bleaching (3B) reconstruction reveals that the distance between the AZ-PSD distance is decreased by 30 nm, while electron microscopy shows that the width of the synaptic cleft is decreased by 1.1 nm. Our findings show that multiple aspects of synaptic geometry are dynamically controlled by neuronal activity and suggest mutual repositioning of synaptic components as a potential novel mechanism contributing to the homeostatic forms of synaptic plasticity. PMID:26951792

  8. Quanta of Geometry: Noncommutative Aspects

    NASA Astrophysics Data System (ADS)

    Chamseddine, Ali H.; Connes, Alain; Mukhanov, Viatcheslav

    2015-03-01

    In the construction of spectral manifolds in noncommutative geometry, a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of real scalar fields naturally appears and implies, by equality with the index formula, the quantization of the volume. We first show that this condition implies that the manifold decomposes into disconnected spheres, which will represent quanta of geometry. We then refine the condition by involving the real structure and two types of geometric quanta, and show that connected spin manifolds with large quantized volume are then obtained as solutions. The two algebras M2(H ) and M4(C ) are obtained, which are the exact constituents of the standard model. Using the two maps from M4 to S4 the four-manifold is built out of a very large number of the two kinds of spheres of Planckian volume. We give several physical applications of this scheme such as quantization of the cosmological constant, mimetic dark matter, and area quantization of black holes.

  9. Weyl gravity and Cartan geometry

    NASA Astrophysics Data System (ADS)

    Attard, J.; François, J.; Lazzarini, S.

    2016-04-01

    We point out that the Cartan geometry known as the second-order conformal structure provides a natural differential geometric framework underlying gauge theories of conformal gravity. We are concerned with two theories: the first one is the associated Yang-Mills-like Lagrangian, while the second, inspired by [1], is a slightly more general one that relaxes the conformal Cartan geometry. The corresponding gauge symmetry is treated within the Becchi-Rouet-Stora-Tyutin language. We show that the Weyl gauge potential is a spurious degree of freedom, analogous to a Stueckelberg field, that can be eliminated through the dressing field method. We derive sets of field equations for both the studied Lagrangians. For the second one, they constrain the gauge field to be the "normal conformal Cartan connection.''Finally, we provide in a Lagrangian framework a justification of the identification, in dimension 4, of the Bach tensor with the Yang-Mills current of the normal conformal Cartan connection, as proved in [2].

  10. Turbine engine variable geometry device

    NASA Technical Reports Server (NTRS)

    Rogo, Casimir (Inventor); Lenz, Herman N. (Inventor)

    1985-01-01

    A variable geometry device for use with the turbine nozzle of a turbine engine of the type having a support housing and a combustion chamber contained within the support housing. A pair of spaced walls in the support housing define an annular and radially extending nozzle passageway. The outer end of the nozzle passageway is open to the combustion chamber while the inner end of the nozzle passageway is open to one or more turbine stages. A plurality of circumferentially spaced nozzle vanes are mounted to one of the spaced walls and protrude across the nozzle passageway. An annular opening is formed around the opposite spaced wall and an annular ring is axially slidably mounted within the opening. A motor is operatively connected to this ring and, upon actuation, axially displaces the ring within the nozzle passageway. In addition, the ring includes a plurality of circumferentially spaced slots which register with the nozzle vanes so that the vane geometry remains the same despite axial displacement of the ring.

  11. Target Detection Using Fractal Geometry

    NASA Technical Reports Server (NTRS)

    Fuller, J. Joseph

    1991-01-01

    The concepts and theory of fractal geometry were applied to the problem of segmenting a 256 x 256 pixel image so that manmade objects could be extracted from natural backgrounds. The two most important measurements necessary to extract these manmade objects were fractal dimension and lacunarity. Provision was made to pass the manmade portion to a lookup table for subsequent identification. A computer program was written to construct cloud backgrounds of fractal dimensions which were allowed to vary between 2.2 and 2.8. Images of three model space targets were combined with these backgrounds to provide a data set for testing the validity of the approach. Once the data set was constructed, computer programs were written to extract estimates of the fractal dimension and lacunarity on 4 x 4 pixel subsets of the image. It was shown that for clouds of fractal dimension 2.7 or less, appropriate thresholding on fractal dimension and lacunarity yielded a 64 x 64 edge-detected image with all or most of the cloud background removed. These images were enhanced by an erosion and dilation to provide the final image passed to the lookup table. While the ultimate goal was to pass the final image to a neural network for identification, this work shows the applicability of fractal geometry to the problems of image segmentation, edge detection and separating a target of interest from a natural background.

  12. Neuronal activity controls transsynaptic geometry

    PubMed Central

    Glebov, Oleg O.; Cox, Susan; Humphreys, Lawrence; Burrone, Juan

    2016-01-01

    The neuronal synapse is comprised of several distinct zones, including presynaptic vesicle zone (SVZ), active zone (AZ) and postsynaptic density (PSD). While correct relative positioning of these zones is believed to be essential for synaptic function, the mechanisms controlling their mutual localization remain unexplored. Here, we employ high-throughput quantitative confocal imaging, super-resolution and electron microscopy to visualize organization of synaptic subdomains in hippocampal neurons. Silencing of neuronal activity leads to reversible reorganization of the synaptic geometry, resulting in a increased overlap between immunostained AZ and PSD markers; in contrast, the SVZ-AZ spatial coupling is decreased. Bayesian blinking and bleaching (3B) reconstruction reveals that the distance between the AZ-PSD distance is decreased by 30 nm, while electron microscopy shows that the width of the synaptic cleft is decreased by 1.1 nm. Our findings show that multiple aspects of synaptic geometry are dynamically controlled by neuronal activity and suggest mutual repositioning of synaptic components as a potential novel mechanism contributing to the homeostatic forms of synaptic plasticity. PMID:26951792

  13. Quanta of geometry: noncommutative aspects.

    PubMed

    Chamseddine, Ali H; Connes, Alain; Mukhanov, Viatcheslav

    2015-03-01

    In the construction of spectral manifolds in noncommutative geometry, a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of real scalar fields naturally appears and implies, by equality with the index formula, the quantization of the volume. We first show that this condition implies that the manifold decomposes into disconnected spheres, which will represent quanta of geometry. We then refine the condition by involving the real structure and two types of geometric quanta, and show that connected spin manifolds with large quantized volume are then obtained as solutions. The two algebras M_{2}(H) and M_{4}(C) are obtained, which are the exact constituents of the standard model. Using the two maps from M_{4} to S^{4} the four-manifold is built out of a very large number of the two kinds of spheres of Planckian volume. We give several physical applications of this scheme such as quantization of the cosmological constant, mimetic dark matter, and area quantization of black holes. PMID:25793795

  14. Geometry and the quantum: basics

    NASA Astrophysics Data System (ADS)

    Chamseddine, Ali H.; Connes, Alain; Mukhanov, Viatcheslav

    2014-12-01

    Motivated by the construction of spectral manifolds in noncommutative geometry, we introduce a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. This commutation relation appears in two versions, one sided and two sided. It implies the quantization of the volume. In the one-sided case it implies that the manifold decomposes into a disconnected sum of spheres which will represent quanta of geometry. The two sided version in dimension 4 predicts the two algebras M 2(ℍ) and M 4(ℂ) which are the algebraic constituents of the Standard Model of particle physics. This taken together with the non-commutative algebra of functions allows one to reconstruct, using the spectral action, the Lagrangian of gravity coupled with the Standard Model. We show that any connected Riemannian Spin 4-manifold with quantized volume > 4 (in suitable units) appears as an irreducible representation of the two-sided commutation relations in dimension 4 and that these representations give a seductive model of the "particle picture" for a theory of quantum gravity in which both the Einstein geometric standpoint and the Standard Model emerge from Quantum Mechanics. Physical applications of this quantization scheme will follow in a separate publication.

  15. Alternative cosmology from cusp geometries

    NASA Astrophysics Data System (ADS)

    Rosa, Reinaldo; Herbin Stalder Díaz, Diego

    We study an alternative geometrical approach on the problem of classical cosmological singularity. It is based on a generalized function f(x,y)=x(2+y^2=(1-z)z^n) which consists of a cusped projected coupled isosurface. Such a projected geometry is computed and analized into the context of Friedmann singularity-free cosmology where a pre-big bang scenario is considered. Assuming that the mechanism of cusp formation is described by non-linear oscillations of a pre- big bang extended very high energy density field (>3x10^{94} kg/m^3$), we show that the action under the gravitational field follows a tautochrone of revolution, understood here as the primary projected geometry that alternatively replaces the Friedmann singularity in the standard big bang theory. As shown here this new approach allows us to interpret the nature of both matter and dark energy from first geometric principles [1]. [1] Rosa et al. DOI: 10.1063/1.4756991

  16. Microtearing modes in spherical and conventional tokamaks

    NASA Astrophysics Data System (ADS)

    Moradi, S.; Pusztai, I.; Guttenfelder, W.; Fülöp, T.; Mollén, A.

    2013-06-01

    The onset and characteristics of microtearing modes (MTM) in the core of spherical (NSTX) and conventional tokamaks (ASDEX Upgrade and JET) are studied through local linear gyrokinetic simulations with GYRO (Candy and Belli 2011 General Atomics Report GA-A26818). For experimentally relevant core plasma parameters in the NSTX and ASDEX Upgrade tokamaks, in agreement with previous works, we find MTMs as the dominant linear instability. Also, for JET-like core parameters considered in our study an MTM is found as the most unstable mode. In all of these plasmas, finite collisionality is needed for MTMs to become unstable and the electron temperature gradient is found to be the fundamental drive. However, a significant difference is observed in the dependence of the linear growth rate of MTMs on electron temperature gradient. While it varies weakly and non-monotonically in JET and ASDEX Upgrade plasmas, in NSTX it increases with the electron temperature gradient.

  17. Spherically-Convergent, Advanced-Fuel Systems

    NASA Astrophysics Data System (ADS)

    Barnes, D. C.; Nebel, R. A.; Schauer, M. M.; Umstadter, K. R.

    1998-11-01

    Combining nonneutral electron confinement with spherical ion convergence leads to a cm sized reactor volume with high power density.(R. A. Nebel and D. C. Barnes, Fusion Technol.), to appear (1998); D. C. Barnes and R. A. Nebel, Phys. of Plasmas 5, 2498 (1998). This concept is being investigated experimentally,(D. C. Barnes, T. B. Mitchell, and M. M. Schauer, Phys. Plasmas) 4, 1745 (1997). and results will be reported. We argue that D-D operation of such a system offers all the advantages of aneutronic fusion cycles. In particular, no breeding or large tritium inventory is required, and material problems seem tractable based on previous LWR experience. In addition the extremely small unit size leads to a massively modular system which is easily maintained and repaired, suggesting a very high availability. It may also be possible to operate such a system with low or aneutronic fuels. Preliminary work in this direction will be presented.

  18. Stability of Spherical Vesicles in Electric Fields

    PubMed Central

    2010-01-01

    The stability of spherical vesicles in alternating (ac) electric fields is studied theoretically for asymmetric conductivity conditions across their membranes. The vesicle deformation is obtained from a balance between the curvature elastic energies and the work done by the Maxwell stresses. The present theory describes and clarifies the mechanisms for the four types of morphological transitions observed experimentally on vesicles exposed to ac fields in the frequency range from 500 to 2 × 107 Hz. The displacement currents across the membranes redirect the electric fields toward the membrane normal to accumulate electric charges by the Maxwell−Wagner mechanism. These accumulated electric charges provide the underlying molecular mechanism for the morphological transitions of vesicles as observed on the micrometer scale. PMID:20575588

  19. Electronic Switching Spherical Array (ESSA) antenna systems

    NASA Technical Reports Server (NTRS)

    Hockensmith, R. P.

    1984-01-01

    ESSA (Electronic Switching Spherical Array) is an antenna system conceived, developed and qualified for linking satellite data transmissions with NASA's tracking and data relay satellites (TDRSS) and tracking and data acquisition satellites (TDAS). ESSA functions in the S band frequency region, cover 2 pi or more steradians with directional gain and operates in multiple selectable modes. ESSA operates in concert with the NASA's TDRS standard transponder in the retrodirective mode or independently in directional beam, program track and special modes. Organizations and projects to the ESSA applications for NASA's space use are introduced. Coverage gain, weight power and implementation and other performance information for satisfying a wide range of data rate requirements are included.

  20. Indentation of pressurized viscoplastic polymer spherical shells

    NASA Astrophysics Data System (ADS)

    Tvergaard, V.; Needleman, A.

    2016-08-01

    The indentation response of polymer spherical shells is investigated. Finite deformation analyses are carried out with the polymer characterized as a viscoelastic/viscoplastic solid. Both pressurized and unpressurized shells are considered. Attention is restricted to axisymmetric deformations with a conical indenter. The response is analyzed for various values of the shell thickness to radius ratio and various values of the internal pressure. Two sets of material parameters are considered: one set having network stiffening at a moderate strain and the other having no network stiffening until very large strains are attained. The transition from an indentation type mode of deformation to a structural mode of deformation involving bending that occurs as the indentation depth increases is studied. The results show the effects of shell thickness, internal pressure and polymer constitutive characterization on this transition and on the deformation modes in each of these regimes.