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…
Dynamic fragmentation of powders in spherical geometry
NASA Astrophysics Data System (ADS)
Milne, A. M.; Floyd, E.; Longbottom, A. W.; Taylor, P.
2014-09-01
Experimental evidence from a wide range of sources shows that the expanding cloud of explosively disseminated material comprises of "particles" or fragments which have different dimensions from those associated with the original material. Photographic evidence shows jets or fingers behind these expanding fragments. Powders and liquids have often been used to surround explosives to act as blast mitigants; this is the main driver for our research. Other examples of areas where these features are observed include fuel air explosives and enhanced blast explosives as well as quasi-static pressure mitigation systems. In this paper, we consider the processes occurring when an explosive interacts with a surrounding layer of powder in spherical geometry. Results from explosive experiments designed to investigate the effects of powder grain size and powder fill-to-burster charge mass ratio (/) are presented and compared with results from numerical modelling to explore what determines the primary fragment size distribution resulting from explosive dissemination of a layer of material and when this process begins. The evidence clearly shows that the process starts during the first wave transit period of the powder material and, despite the surrounding material initially being a loose powder, shows the characteristics of a brittle fracture mechanism. Later time video evidence shows the same number of jets or fingers as are identified by X-rays of the early, primary fragmentation process. The number of fragments is only a very weak function of the initial grain size of the powder.
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…
Spherical perfect lens: Solutions of Maxwell's equations for spherical geometry
NASA Astrophysics Data System (ADS)
Anantha Ramakrishna, S.; Pendry, J. B.
2004-03-01
It has been recently proved that a slab of negative refractive index material acts as a perfect lens in that it makes accessible the subwavelength image information contained in the evanescent modes of a source. Here we elaborate on perfect lens solutions to spherical shells of negative refractive material where magnification of the near-field images becomes possible. The negative refractive materials then need to be spatially dispersive with ɛ(r)˜1/r and μ(r)˜1/r. We concentrate on lenslike solutions for the extreme near-field limit. Then the conditions for the TM and TE polarized modes become independent of μ and ɛ, respectively.
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.
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.
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.
Viscous Rayleigh-Taylor instability in spherical geometry
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.
Cellular dosimetry of diagnostic radionuclides for spherical and ellipsoidal geometry
NASA Astrophysics Data System (ADS)
Nettleton, Jo S.; Lawson, Richard S.
1996-09-01
Radionuclides which emit Auger electrons are widely used in diagnostic nuclear medicine. Studies have shown possible uptake of these in developing germ cells within the testes. In addition, mature sperm within the reproductive tract may be subject to uptake of radionuclides from the circulating blood pool. Though much work has been carried out concerning cellular dosimetry applied to spherical sources, such an approach may lead to significant errors when considering spermatids and spermatozoa, which are almost ellipsoidal in shape (with the long axis twice the short). A numerical method for determining geometrical reduction factors has been developed and used in conjunction with experimentally determined range - energy relationships for electrons, to determine dose gradients and S factors for homogeneous distributions of four commonly used diagnostic radionuclides (, , and ) throughout source regions of both spherical and ellipsoidal geometry at typical cellular dimensions. The results indicate that assumption of spherical geometry is acceptable when determining S factors for late-type germ cells, but introduces error into calculations of dose distribution towards the edge of the cell.
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].
Room geometry inference based on spherical microphone array eigenbeam processing.
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
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…
The solid angle (geometry factor) for a spherical surface source and an arbitrary detector aperture
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.
Weyl problem and Casimir effects in spherical shell geometry
NASA Astrophysics Data System (ADS)
Kolomeisky, Eugene B.; Zaidi, Hussain; Langsjoen, Luke; Straley, Joseph P.
2013-04-01
We compute the generic mode sum that quantifies the effect on the spectrum of a harmonic field when a spherical shell is inserted into vacuum. This encompasses a variety of problems including the Weyl spectral problem and the Casimir effect of quantum electrodynamics. This allows us to resolve several long-standing controversies regarding the question of universality of the Casimir self-energy; the resolution comes naturally through the connection to the Weyl problem. Specifically we demonstrate that in the case of a scalar field obeying Dirichlet or Neumann boundary conditions on the shell surface the Casimir self-energy is cutoff dependent while in the case of the electromagnetic field perturbed by a conductive shell the Casimir self-energy is universal. We additionally show that an analog nonrelativistic Casimir effect due to zero-point magnons takes place when a nonmagnetic spherical shell is inserted inside a bulk ferromagnet.
Variation of Space Radiation Exposure inside Spherical and Hemispherical Geometries
NASA Astrophysics Data System (ADS)
Lin, Zi-Wei; Baalla, Younes; Townsend, Lawrence
2008-10-01
We calculate the space radiation exposure to blood-forming organs everywhere inside a hemispherical dome that represents a lunar habitat. We derive the analytical path length distribution from any point inside a hemispherical or a spherical shell. Because the average path length increases with the distance from the center, the center of the hemispherical dome on the lunar surface has the largest radiation exposure while locations on the inner surface of the dome have the lowest exposure. This conclusion differs from an earlier study on a hemispherical dome but agrees with another earlier study on a spherical-shell shield. We also find that the reduction in the radiation exposure from the center to the inner edge of the dome can be as large as a factor of 3 or more for the radiation from solar particle events while being smaller for the radiation from galactic cosmic rays.
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.
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.
Fu, Riqiang; Gill, Richard L; Kim, Edward Y; Briley, Nicole E; Tyndall, Erin R; Xu, Jie; Li, Conggang; Ramamurthi, Kumaran S; Flanagan, John M; Tian, Fang
2015-11-11
Many essential cellular processes including endocytosis and vesicle trafficking require alteration of membrane geometry. These changes are usually mediated by proteins that can sense and/or induce membrane curvature. Using spherical nanoparticle supported lipid bilayers (SSLBs), we characterize how SpoVM, a bacterial development factor, interacts with differently curved membranes by magic angle spinning solid-state NMR. Our results demonstrate that SSLBs are an effective system for structural and topological studies of membrane geometry-sensitive molecules.
Multigroup Time-Independent Neutron Transport Code System for Plane or Spherical Geometry.
1986-12-01
Version 00 PALLAS-PL/SP solves multigroup time-independent one-dimensional neutron transport problems in plane or spherical geometry. The problems solved are subject to a variety of boundary conditions or a distributed source. General anisotropic scattering problems are treated for solving deep-penetration problems in which angle-dependent neutron spectra are calculated in detail.
Ablation Front Rayleigh-Taylor Growth Experiments in Spherically Convergent Geometry
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.
CYCLIC MAGNETIC ACTIVITY DUE TO TURBULENT CONVECTION IN SPHERICAL WEDGE GEOMETRY
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.
Bardhan, Jaydeep P.; Knepley, Matthew G.; Brune, Peter
2015-01-01
In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact that their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for calculations in separable geometries, we first re-derive Kirkwood’s classic results for a protein surrounded concentrically by a pure-water ion-exclusion (Stern) layer and then a dilute electrolyte, which is modeled with the linearized Poisson–Boltzmann equation. The eigenfunction-expansion approach provides a computationally efficient way to test some implications of nonlocal models, including estimating the reasonable range of the nonlocal length-scale parameter λ. Our results suggest that nonlocal solvent response may help to reduce the need for very high dielectric constants in calculating pH-dependent protein behavior, though more sophisticated nonlocal models are needed to resolve this question in full. An open-source MATLAB implementation of our approach is freely available online. PMID:26273581
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.
Critical experiments on single-unit spherical plutonium geometries reflected and moderated by oil
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Reuter, K.; Jenko, F.; Forest, C. B.; Bayliss, R. A.
2008-08-01
A parallel implementation of a nonlinear pseudo-spectral MHD code for the simulation of turbulent dynamos in spherical geometry is reported. It employs a dual domain decomposition technique in both real and spectral space. It is shown that this method shows nearly ideal scaling going up to 128 CPUs on Beowulf-type clusters with fast interconnect. Furthermore, the potential of exploiting single precision arithmetic on standard x86 processors is examined. It is pointed out that the MHD code thereby achieves a maximum speedup of 1.7, whereas the validity of the computations is still granted. The combination of both measures will allow for the direct numerical simulation of highly turbulent cases ( 1500
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.
Schulze, Ralf; Bruellmann, Dan Dominik; Roeder, Felix; D'Hoedt, Bernd
2004-10-01
A method is introduced, inferring the three-dimensional (3-D) location from the 2-D radiographic shadow of an opaque spherical reference body of known radius by considering its elliptical distortion, the 2-D shadow location and a known source-to-receptor distance. Three noncollinear spheres fixed to a rigid object constitute all possible degrees of freedom, i.e., the entire 3-D imaging geometry. The method may be used (a) to determine the 3-D imaging geometry from a single 2-D view and (b) to correct for foreshortening of object distances coplanar with the plane defined by the sphere triplet. Apart from the mathematical background the article describes a small feasibility experiment, performed with four different sphere diameters and a commercial dental ccd-receptor system (pixel length: 0.0195 mm). The mouse-cursor based image evaluation revealed an average underestimation of the critical depth- (x-) coordinate decreasing with increasing radius (-30.3% for r=0.5 mm to 2.8% for r=2.5 mm). Intraobserver reliability (the standard deviation between three single cursor-based assessments) ranged between 0% and 8% of the actual true depth. The main source of the input error is associated with the assessment of the amount of elliptical distortion, where subpixel accuracy is demanded. Consequently, software-based automated image evaluation is required using available methods for pattern recognition and point-spread correction. Provided sufficient accuracy, the method provides an important tool for foreshortening correction, depth assessment, motion analysis, and 3-D reconstruction from two or more 2-D views.
A comparison of angular difference schemes for one-dimensional spherical geometry S{sub N} equations
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
Shendeleva, Margarita L; Molloy, John A
2006-09-20
We report on the development of Monte Carlo software that can model media with spatially varying scattering coefficient, absorption, and refractive index. The varying refractive index is implemented by calculating curved photon paths in the medium. The results of the numerical simulations are compared with analytical solutions obtained using the diffusion approximation. The model under investigation is a scattering medium that contains a spherically symmetrical inclusion (inhomogeneity) created by variation in optical properties and having no sharp boundaries. The following steady-state cases are considered: (a) a nonabsorbing medium with a spherically symmetrical varying refractive index, (b) an inclusion with varying absorption and scattering coefficients and constant refractive index, and (c) an inclusion with varying absorption, scattering, and refractive index. In the latter case it is shown that the interplay between the absorption coefficient and the refractive index may create the effect of a hidden inclusion.
Bendert, J C; Blodgett, M E; Kelton, K F
2013-03-01
Expressions for absorption and the secondary scattering intensity ratio are presented for a small beam impinging off-center of a spherical amorphous sample. Large gradients in the absorption correction are observed from small offsets from the central axis. Additionally, the secondary scattering intensity ratio causes an intensity asymmetry in the detector image. The secondary scattering intensity ratio is presented in integral form and must be computed numerically. An analytic, small-angle, asymptotic series solution for the integral form of the absorption correction is also presented. PMID:23403964
NASA Astrophysics Data System (ADS)
Fokas, A. S.; Hauk, O.; Michel, V.
2012-03-01
The basic inverse problems for the functional imaging techniques of electroencephalography (EEG) and magnetoencephalography (MEG) consist in estimating the neuronal current in the brain from the measurement of the electric potential on the scalp and of the magnetic field outside the head. Here we present a rigorous derivation of the relevant formulae for a three-shell spherical model in the case of independent as well as simultaneous MEG and EEG measurements. Furthermore, we introduce an explicit and stable technique for the numerical implementation of these formulae via splines. Numerical examples are presented using the locations and the normal unit vectors of the real 102 magnetometers and 70 electrodes of the Elekta Neuromag (R) system. These results may have useful implications for the interpretation of the reconstructions obtained via the existing approaches.
NASA Astrophysics Data System (ADS)
Kong, Dali; Zhang, Keke; Schubert, Gerald
2016-10-01
Unlike the even gravitational coefficients of Jupiter that are caused by both the rotational distortion and the equatorially symmetric zonal winds, the odd jovian gravitational coefficients are directly linked to the depth of the equatorially antisymmetric zonal winds. Accurate estimation of the wind-induced odd coefficients and comparison with measurements of those coefficients would be key to understanding the structure of the zonal winds in the deep interior of Jupiter. We consider two problems in connection with the jovian odd gravitational coefficients. In the first problem, we show, by solving the governing equations for the northern hemisphere of Jupiter subject to an appropriate condition at the equatorial plane, that the effect of non-spherical geometry makes an insignificant contribution to the lowermost-order odd gravitational coefficients. In the second problem, we investigate the effect of the equatorial smoothing used to avoid the discontinuity in the winds across the equatorial plane when the thermal wind equation is adopted to compute the odd gravitational coefficients. We reveal that, because of the dominant effect of the equatorial smoothing, the odd gravitational coefficients so obtained for deep zonal winds do not reflect physically realistic dynamics taking place in the deep interior of Jupiter.
NASA Astrophysics Data System (ADS)
Sizova, N. L.; Novikova, N. E.; Manomenova, V. L.; Rudneva, E. B.; Voloshin, A. E.
2016-05-01
The microhardness on the (010) and (001) planes in K2Co(SO4)2 · 6H2O crystal has been measured by the Vickers indentation method. Its values are, respectively, 11500 and 1300 MPa. No microhardness anisotropy of the first kind is revealed on either plane. The fracture geometry under indentation by a spherical indenter and Vickers and Knoop indenters is studied. The crystal has lower brittleness than the isomorphic Cs2Ni(SO4)2 · 6H2O crystal.
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…
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.
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
Hollow spherical shell manufacture
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.
Hollow spherical shell manufacture
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.
Spherical colloidal photonic crystals.
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
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.
Radiative transfer in spherical atmospheres
NASA Astrophysics Data System (ADS)
Kalkofen, W.; Wehrse, R.
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.
Relativistic spherical plasma waves
NASA Astrophysics Data System (ADS)
Bulanov, S. S.; Maksimchuk, A.; Schroeder, C. B.; Zhidkov, A. G.; Esarey, E.; Leemans, W. P.
2012-02-01
Tightly focused laser pulses that diverge or converge in underdense plasma can generate wake waves, having local structures that are spherical waves. Here we study theoretically and numerically relativistic spherical wake waves and their properties, including wave breaking.
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.
Spherical quartz crystals investigated with synchrotron radiation
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.
Ellipsoidal geometry in asteroid thermal models - The standard radiometric model
NASA Technical Reports Server (NTRS)
Brown, R. H.
1985-01-01
The major consequences of ellipsoidal geometry in an othewise standard radiometric model for asteroids are explored. It is shown that for small deviations from spherical shape a spherical model of the same projected area gives a reasonable aproximation to the thermal flux from an ellipsoidal body. It is suggested that large departures from spherical shape require that some correction be made for geometry. Systematic differences in the radii of asteroids derived radiometrically at 10 and 20 microns may result partly from nonspherical geometry. It is also suggested that extrapolations of the rotational variation of thermal flux from a nonspherical body based solely on the change in cross-sectional area are in error.
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.
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…
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.
Stability of spherical converging shock wave
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.
Programmable shape transformation of elastic spherical domes.
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.
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.
Recent Progress on Spherical Torus Research
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.
Large displacement spherical joint
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.
Laboratory experiments on liquid metal spherical-Couette flows
NASA Astrophysics Data System (ADS)
Andres Triana, Santiago; Lathrop, Daniel
2005-11-01
We present experimental observations on liquid sodium flow in a spherical-Couette geometry. By applying an external magnetic field we are able to clearly identify at least two induced magnetic field modes with different poloidal patterns as well as different azimuthal wave numbers. The origin of many of these induced field oscillations appears to be related to inertial wave oscillations propagating in the spherical annulus. Possible implications for dynamo action and to the magneto-rotational instability will also be discussed.
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…
Spherical geodesic mesh generation
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.
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.
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.
Close packing of rods on spherical surfaces.
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.
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.
Close packing of rods on spherical surfaces.
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
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.
Colloidal cholesteric liquid crystal in spherical confinement.
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
Colloidal cholesteric liquid crystal in spherical confinement
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
Spherical Target Temperature by Extended CFAST Calculation
Ma, C W
2009-05-05
The purpose of this calculation is to evaluate the temperature at the surface of a spherical target made of polyethylene during a room fire. The current calculation is separated into 2 steps: (1) CFAST code calculation--Calculate the air temperature; radiation flux to the target from the fire, surrounding air, and walls; convection flux; and target temperature. (2) Extended model calculation--Calculate the temperature of the target sphere taking into account the density, heat capacity, heat conductivity, and the spherical geometry of the target by solving the coupled finite difference equations. The second step calculation utilizes the air temperature and radiation flux determined by the CFAST code calculation in the first step.
Colloidal cholesteric liquid crystal in spherical confinement
NASA Astrophysics Data System (ADS)
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
2016-08-01
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.
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.
Multipulse Thomson scattering system for the National Spherical Torus Experiment
Johnson, D.; Bretz, N.; LeBlanc, B.; Palladino, R.; Long, D.; Parsells, R.
1999-01-01
A design using a backscattering geometry is presented, which emphasizes high sensitivity and high spatial resolution at the outer edge of the National Spherical Torus Experiment, while providing full profile capability with a moderate number of channels. The design is based on Nd:YAG lasers and avalanche photodiode detectors to allow for high repetition rate measurements. {copyright} {ital 1999 American Institute of Physics.}
Lee, M.C.; Kendall, J.M.,JR.; Bahrami, P.A.; Wang, T.G.
1986-01-01
Fluid-dynamic and capillary forces can be used to form nearly perfect, very small spherical shells when a liquid that can solidify is passed through an annular die to form an annular jet. Gravity and certain properties of even the most ideal materials, however, can cause slight asymmetries. The primary objective of the present work is the control of this shell formation process in earth laboratories rather than space microgravity, through the development of facilities and methods that minimize the deleterious effects of gravity, aerodynamic drag, and uncontrolled cooling. The spherical shells thus produced can be used in insulation, recyclable filter materials, fire retardants, explosives, heat transport slurries, shock-absorbing armor, and solid rocket motors.
Spherical torus fusion reactor
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.
Spherical torus fusion reactor
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.
Spherical torus experiment (STX)
McManamy, T.J.; Lazarus, E.A.
1985-01-01
The principal engineering features of the proposed Spherical Torus Experiment (STX) are described. Design is dominated by the small bore available for the ohmic heating (OH) solenoid and structural considerations for a situation in which B/sub p/ is approximately equal to B/sub t/. Unique features of a spherical torus plasma include large elongations without shaping fields; an exceptionally high ratio of plasma current to toroidal field, giving the potential for stability at very high beta; strong paramagnetism; and a variety of configurations, ranging from tokamak (q/sub a/) to revised-field pinch (RFP) (q/sub a/ < 1). Access to this regime requires aspect ratios less than 2. A feasibility study has been done for a beam-heated device with A = 1.67, R0 = 0.45, and K = 2. 3 refs., 9 figs.
Recent progress on spherical torus research
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.
Spherical nitroguanidine process
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.
NASA Astrophysics Data System (ADS)
Georgiev, G. H.; Dinkova, C. L.
2013-10-01
Long spirals in the Euclidean plane have been introduced by A. Kurnosenko five years ago. Using a natural map of the shape sphere into the extended Gaussian plane we study spherical curves that are pre-images of plane long spirals. Loxodromes and spherical spiral antennas are typical examples of such spherical long spirals. The set of all planar spirals leaves invariant under an arbitrary similarity transformation. This set is divided in two disjoint classes by A. Kirnosenko. The first class is consist of the so-called short spirals which are widely used in geometric modeling. The second class of planar long spirals contains well-known logarithmic spiral and Archimedean spirals which have many applications in mathematics, astrophysics and industry. The notion of simplicial shape space is due to D. Kendall. The most popular simplicial shape space of order (2,3) is the set of equivalence classes of similar triangles in the plane. The sphere of radius 1/2 centered at the origin can be considered as a model of this quotient space, so-called the shape sphere. F. Bookstein and J. Lester showed that the one-point extension of the Euclidean plane, so-called the extended Gaussian plane, is another model of the same simplicial shape space. The present paper gives a description of long spirals on the shape sphere by the use a natural conformal mapping between two models. First, we examine long spirals in the extended Gaussian plane. After that, we describe some differential geometric properties of the shape sphere. Finally, we discuss parameterizations of long spirals on the shape sphere.
Geometry and groups for cosmic topology
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.
Geometry of Discrete-Time Spin Systems
NASA Astrophysics Data System (ADS)
McLachlan, Robert I.; Modin, Klas; Verdier, Olivier
2016-10-01
Classical Hamiltonian spin systems are continuous dynamical systems on the symplectic phase space (S^2)^n. In this paper, we investigate the underlying geometry of a time discretization scheme for classical Hamiltonian spin systems called the spherical midpoint method. As it turns out, this method displays a range of interesting geometrical features that yield insights and sets out general strategies for geometric time discretizations of Hamiltonian systems on non-canonical symplectic manifolds. In particular, our study provides two new, completely geometric proofs that the discrete-time spin systems obtained by the spherical midpoint method preserve symplecticity. The study follows two paths. First, we introduce an extended version of the Hopf fibration to show that the spherical midpoint method can be seen as originating from the classical midpoint method on T^*{R}^{2n} for a collective Hamiltonian. Symplecticity is then a direct, geometric consequence. Second, we propose a new discretization scheme on Riemannian manifolds called the Riemannian midpoint method. We determine its properties with respect to isometries and Riemannian submersions, and, as a special case, we show that the spherical midpoint method is of this type for a non-Euclidean metric. In combination with Kähler geometry, this provides another geometric proof of symplecticity.
Strongly Localized Image States of Spherical Graphitic Particles
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
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.
Strongly localized image states of spherical graphitic particles.
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
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…
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.
Double slotted socket spherical joint
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.
Spherical Torus Center Stack Design
C. Neumeyer; P. Heitzenroeder; C. Kessel; M. Ono; M. Peng; J. Schmidt; R. Woolley; I. Zatz
2002-01-18
The low aspect ratio spherical torus (ST) configuration requires that the center stack design be optimized within a limited available space, using materials within their established allowables. This paper presents center stack design methods developed by the National Spherical Torus Experiment (NSTX) Project Team during the initial design of NSTX, and more recently for studies of a possible next-step ST (NSST) device.
Features of spherical torus plasmas
Peng, Y.K.M.; Strickler, D.J.
1985-12-01
The spherical torus is a very small aspect ratio (A < 2) confinement concept obtained by retaining only the indispensable components inboard to the plasma torus. MHD equilibrium calculations show that spherical torus plasmas with safety factor q > 2 are characterized by high toroidal beta (..beta../sub t/ > 0.2), low poloidal beta (..beta../sub p/ < 0.3), naturally large elongation (kappa greater than or equal to 2), large plasma current with I/sub p//(aB/sub t0/) up to about 7 MA/mT, strong paramagnetism (B/sub t//B/sub t0/ > 1.5), and strong plasma helicity (F comparable to THETA). A large near-omnigeneous region is seen at the large-major-radius, bad-curvature region of the plasma in comparison with the conventional tokamaks. These features combine to engender the spherical torus plasma in a unique physics regime which permits compact fusion at low field and modest cost. Because of its strong paramagnetism and helicity, the spherical torus plasma shares some of the desirable features of spheromak and reversed-field pinch (RFP) plasmas, but with tokamak-like confinement and safety factor q. The general class of spherical tori, which includes the spherical tokamak (q > 1), the spherical pinch (1 > q > O), and the spherical RFP (q < O), have magnetic field configurations unique in comparison with conventional tokamaks and RFPs. 22 refs., 12 figs.
Unsteady Spherical Diffusion Flames in Microgravity
NASA Technical Reports Server (NTRS)
Atreya, Arvind; Berhan, S.; Chernovsky, M.; Sacksteder, Kurt R.
2001-01-01
The absence of buoyancy-induced flows in microgravity (mu-g) and the resulting increase in the reactant residence time significantly alters the fundamentals of many combustion processes. Substantial differences between normal gravity (ng) and (mu-g) flames have been reported in experiments on candle flames, flame spread over solids, droplet combustion, and others. These differences are more basic than just in the visible flame shape. Longer residence times and higher concentration of combustion products in the flame zone create a thermochemical environment that changes the flame chemistry and the heat and mass transfer processes. Processes such as flame radiation, that are often ignored in ng, become very important and sometimes even controlling. Furthermore, microgravity conditions considerably enhance flame radiation by: (i) the build-up of combustion products in the high-temperature reaction zone which increases the gas radiation, and (ii) longer residence times make conditions appropriate for substantial amounts of soot to form which is also responsible for radiative heat loss. Thus, it is anticipated that radiative heat loss may eventually extinguish the "weak" (low burning rate per unit flame area) mu-g diffusion flame. Yet, space shuttle experiments on candle flames show that in an infinite ambient atmosphere, the hemispherical candle flame in mu-g will burn indefinitely. This may be because of the coupling between the fuel production rate and the flame via the heat-feedback mechanism for candle flames, flames over solids and fuel droplet flames. Thus, to focus only on the gas-phase phenomena leading to radiative extinction, aerodynamically stabilized gaseous diffusion flames are examined. This enables independent control of the fuel flow rate to help identify conditions under which radiative extinction occurs. Also, spherical geometry is chosen for the mu-g experiments and modeling because: (i) It reduces the complexity by making the problem one
Immunomodulatory spherical nucleic acids.
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
2015-03-31
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.
Buckling of spherical capsules.
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
Immunomodulatory spherical nucleic acids
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
3DHZETRN: Shielded ICRU spherical phantom
NASA Astrophysics Data System (ADS)
Wilson, John W.; Slaba, Tony C.; Badavi, Francis F.; Reddell, Brandon D.; Bahadori, Amir A.
2015-01-01
A computationally efficient 3DHZETRN code capable of simulating High (H) Charge (Z) and Energy (HZE) and light ions (including neutrons) under space-like boundary conditions with enhanced neutron and light ion propagation was recently developed for a simple homogeneous shield object. Monte Carlo benchmarks were used to verify the methodology in slab and spherical geometry, and the 3D corrections were shown to provide significant improvement over the straight-ahead approximation in some cases. In the present report, the new algorithms with well-defined convergence criteria are extended to inhomogeneous media within a shielded tissue slab and a shielded tissue sphere and tested against Monte Carlo simulation to verify the solution methods. The 3D corrections are again found to more accurately describe the neutron and light ion fluence spectra as compared to the straight-ahead approximation. These computationally efficient methods provide a basis for software capable of space shield analysis and optimization.
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.
Combinatorial Geometry Printer Plotting.
1987-01-05
Picture generates plots of two-dimensional slices through the three-dimensional geometry described by the combinatorial geometry (CG) package used in such codes as MORSE and QAD-CG. These plots are printed on a standard line printer.
Spherical Model for Turbulence
NASA Astrophysics Data System (ADS)
Mou, Chung-Yu.
A new set of models for homogeneous, isotropic turbulence is considered in which the Navier-Stokes equations for incompressible fluid flow are generalized to a set of N coupled equations in N velocity fields. It is argued that in order to be useful these models must embody a new group of symmetries, and a general formalism is laid out for their construction. The work is motivated by similar techniques that have had extraordinary success in improving the theoretical understanding of equilibrium phase transitions in condensed matter systems. The key result is that these models simplify when N is large. The so-called spherical limit, N to infty, can be solved exactly, yielding a closed pair of nonlinear integral equations for the response and correlation functions. These equations, known as Kraichnan's Direct Interaction Approximation (DIA) equations, are, for the first time, solved fully in the scale-invariant turbulent regime, and the implications of these solutions for real turbulence (N = 1) are discussed. In particular, it is argued that previously applied renormalization group techniques, based on an expansion in the exponent, y, that characterizes the driving spectrum, are incorrect, and that the Kolmogorov exponent zeta has a nontrivial dependence on N, with zeta(N toinfty) = {3over2}. This value is remarkably close to the experimental result, zeta~{5over3}, which must therefore result from higher order corrections in powers of {1over N}. Prospects for calculating these corrections are briefly discussed: though daunting, such a calculations would, for the first time, provide a controlled perturbation expansion for the Kolmogorov, and other, exponents. Our techniques may also be applied to other nonequilibrium dynamical problems, such as the KPZ equation for interface growth, and perhaps to turbulence in nonlinear wave systems.
Spherical model for turbulence
NASA Astrophysics Data System (ADS)
Mou, Chung-Yu
A new set of models for homogeneous, isotropic turbulence is considered in which the Navier-Stokes equations for incompressible fluid flow are generalized to a set of N coupled equations in N velocity fields. It is argued that in order to be useful these models must embody a new group of symmetries, and a general formalism is laid out for their construction. The work is motivated by similar techniques that have had extraordinary success in improving the theoretical understanding of equilibrium phase transitions in condensed matter systems. The key result is that these models simplify when N is large. The so-called spherical limit, N approaches infinity, can be solved exactly, yielding a closed pair of nonlinear integral equations for the response and correlation functions. These equations, known as Kraichnan's Direct Interaction Approximation (DIA) equations, are, for the first time, solved fully in the scale-invariant turbulent regime, and the implications of these solutions for real turbulence (N = 1) are discussed. In particular, it is argued that previously applied renormalization group techniques, based on an expansion in the exponent, y, that characterizes the driving spectrum, are incorrect, and that the Kolmogorov exponent zeta has a nontrivial dependence on N, with zeta(N approaches infinity) = 3/2. This value is remarkably close to the experimental result, zeta approximately equals 5/3, which must therefore result from higher order corrections in powers of 1/N. Prospects for calculating these corrections are briefly discussed: though daunting, such a calculation would, for the first time, provide a controlled perturbation expansion for the Kolmogorov, and other exponents. Our techniques may also be applied to other nonequilibrium dynamical problems, such as the KPZ equation for interface growth, and perhaps to turbulence in nonlinear wave systems.
Spherical Strong-Shock Inferences on OMEGA
NASA Astrophysics Data System (ADS)
Nora, R.; Lafon, M.; Betti, R.; Theobald, W.; Seka, W.; Delettrez, J. A.
2014-10-01
A milestone for shock ignition is to experimentally verify the generation of several hundred Mbar shocks at shock-ignition-relevant laser intensities. This paper presents the first experimental evidence of strong shocks generated in a spherical geometry. Using the temporal delay between the launch of the strong shock at the outer surface of the spherical target and the time when the shock converges at the center, the shock properties can be inferred using radiation-hydrodynamic simulations. Peak ablation pressures exceeding 200 Mbar are inferred at laser intensities of ~ 3 ×1015 W/cm2. The shock strength is significantly enhanced by the coupling of copius amounts of hot electrons, up to 2 kJ with Thot ~ 50 to 100 keV. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0001944 and the Office of Fusion Energy Sciences Number DE-FG02-04ER54786.
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…
Spherical stellarator with plasma current
NASA Astrophysics Data System (ADS)
Moroz, Paul E.
1996-08-01
Recently proposed novel concept of a spherical stellarator (P. E. Moroz, ``Spherical stellarator configuration,'' to appear in Phys. Rev. Lett) is enhanced by adding the plasma current to the otherwise pure stellarator system. The coil configuration of this ultra low aspect ratio system differs from that of a spherical tokamak by inclination of external parts of the toroidal field coils. It is shown that the configuration considered possesses many attractive properties, including: wide flexibility of operating regimes, compact design and coil simplicity, good access to the plasma, closed vacuum flux surfaces with large enclosed volume, significant external rotational transform, strong magnetic well, and a high plasma β [β(0) in excess of 30%] equilibrium. It is shown that the bootstrap effect in a spherical stellarator, in principle, can supply the full plasma current required for the high-β equilibrium.
Toroidal equilibria in spherical coordinates
Tsui, K. H.
2008-11-15
The standard Grad-Shafranov equation for axisymmetric toroidal plasma equilibrium is customary expressed in cylindrical coordinates with toroidal contours, and through which benchmark equilibria are solved. An alternative approach to cast the Grad-Shafranov equation in spherical coordinates is presented. This equation, in spherical coordinates, is examined for toroidal solutions to describe low {beta} Solovev and high {beta} plasma equilibria in terms of elementary functions.
Macromolecule loading into spherical, elliptical, star-like and cubic calcium carbonate carriers.
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.
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.
Absorption and Ablation for Non-Planar Geometries
NASA Astrophysics Data System (ADS)
Oh, Benjamin; Sinko, John
2011-04-01
The Bouguer-Lambert-Beer absorption law is a critical component of analytical laser ablation models. This law has been found to be useful for planar applications but it can also have significance in non-planar geometries. To be accurate, these applications must take into consideration the precise physical setup. Certain geometries offer special properties that may be beneficial to laser propulsion methods, specifically those of uniform ablation using focusing nozzles. This paper investigates the special circumstances using modified forms of the absorption law that apply to the considered parabolic, conical and spherical non-planar geometries.
Cylindrical and spherical electron acoustic solitary waves with nonextensive hot electrons
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.
NASA Astrophysics Data System (ADS)
Egel, Amos; Lemmer, Uli
2014-11-01
Scattering particles find application in organic light emitting diodes (OLEDs) for an enhanced outcoupling of the generated light. This paper presents a computational scheme to exactly model the electromagnetic fields and the power outcoupling efficiency of a typical OLED geometry, comprising a thin film system with spherical scattering particles inside. The model is based on the expansion of the fields in plane and spherical vector wave functions, as well as the scattering matrix formalism for the layer system reflections. In a numerical application example, the effect of 1000 spherical high index scattering particles on the internal outcoupling from a realistic OLED structure is discussed.
Spherical harmonics in texture analysis
NASA Astrophysics Data System (ADS)
Schaeben, Helmut; van den Boogaart, K. Gerald
2003-07-01
The objective of this contribution is to emphasize the fundamental role of spherical harmonics in constructive approximation on the sphere in general and in texture analysis in particular. The specific purpose is to present some methods of texture analysis and pole-to-orientation probability density inversion in a unifying approach, i.e. to show that the classic harmonic method, the pole density component fit method initially introduced as a distinct alternative, and the spherical wavelet method for high-resolution texture analysis share a common mathematical basis provided by spherical harmonics. Since pole probability density functions and orientation probability density functions are probability density functions defined on the sphere Ω3⊂ R3 or hypersphere Ω4⊂ R4, respectively, they belong at least to the space of measurable and integrable functions L1( Ωd), d=3, 4, respectively. Therefore, first a basic and simplified method to derive real symmetrized spherical harmonics with the mathematical property of providing a representation of rotations or orientations, respectively, is presented. Then, standard orientation or pole probability density functions, respectively, are introduced by summation processes of harmonic series expansions of L1( Ωd) functions, thus avoiding resorting to intuition and heuristics. Eventually, it is shown how a rearrangement of the harmonics leads quite canonically to spherical wavelets, which provide a method for high-resolution texture analysis. This unified point of view clarifies how these methods, e.g. standard functions, apply to texture analysis of EBSD orientation measurements.
Geometry-induced protein pattern formation.
Thalmeier, Dominik; Halatek, Jacob; Frey, Erwin
2016-01-19
Protein patterns are known to adapt to cell shape and serve as spatial templates that choreograph downstream processes like cell polarity or cell division. However, how can pattern-forming proteins sense and respond to the geometry of a cell, and what mechanistic principles underlie pattern formation? Current models invoke mechanisms based on dynamic instabilities arising from nonlinear interactions between proteins but neglect the influence of the spatial geometry itself. Here, we show that patterns can emerge as a direct result of adaptation to cell geometry, in the absence of dynamical instability. We present a generic reaction module that allows protein densities robustly to adapt to the symmetry of the spatial geometry. The key component is an NTPase protein that cycles between nucleotide-dependent membrane-bound and cytosolic states. For elongated cells, we find that the protein dynamics generically leads to a bipolar pattern, which vanishes as the geometry becomes spherically symmetrical. We show that such a reaction module facilitates universal adaptation to cell geometry by sensing the local ratio of membrane area to cytosolic volume. This sensing mechanism is controlled by the membrane affinities of the different states. We apply the theory to explain AtMinD bipolar patterns in [Formula: see text] EcMinDE Escherichia coli. Due to its generic nature, the mechanism could also serve as a hitherto-unrecognized spatial template in many other bacterial systems. Moreover, the robustness of the mechanism enables self-organized optimization of protein patterns by evolutionary processes. Finally, the proposed module can be used to establish geometry-sensitive protein gradients in synthetic biological systems.
Robustness of oscillatory α2 dynamos in spherical wedges
NASA Astrophysics Data System (ADS)
Cole, E.; Brandenburg, A.; Käpylä, P. J.; Käpylä, M. J.
2016-10-01
Context. Large-scale dynamo simulations are sometimes confined to spherical wedge geometries by imposing artificial boundary conditions at high latitudes. This may lead to spatio-temporal behaviours that are not representative of those in full spherical shells. Aims: We study the connection between spherical wedge and full spherical shell geometries using simple mean-field dynamos. Methods: We solve the equations for one-dimensional time-dependent α2 and α2Ω mean-field dynamos with only latitudinal extent to examine the effects of varying the polar angle θ0 between the latitudinal boundaries and the poles in spherical coordinates. Results: In the case of constant α and ηt profiles, we find oscillatory solutions only with the commonly used perfect conductor boundary condition in a wedge geometry, while for full spheres all boundary conditions produce stationary solutions, indicating that perfect conductor conditions lead to unphysical solutions in such a wedge setup. To search for configurations in which this problem can be alleviated we choose a profile of the turbulent magnetic diffusivity that decreases toward the poles, corresponding to high conductivity there. Oscillatory solutions are now achieved with models extending to the poles, but the magnetic field is strongly concentrated near the poles and the oscillation period is very long. By changing both the turbulent magnetic diffusivity and α profiles so that both effects are more concentrated toward the equator, we see oscillatory dynamos with equatorward drift, shorter cycles, and magnetic fields distributed over a wider range of latitudes. Those profiles thus remove the sensitive and unphysical dependence on θ0. When introducing radial shear, we again see oscillatory dynamos, and the direction of drift follows the Parker-Yoshimura rule. Conclusions: A reduced α effect near the poles with a turbulent diffusivity concentrated toward the equator yields oscillatory dynamos with equatorward migration and
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
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.
Collective neutrino oscillations in nonspherical geometry
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.
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…
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…
Frolov, Vadim A; Escalada, Artur; Akimov, Sergey A; Shnyrova, Anna V
2015-01-01
Cellular membranes define the functional geometry of intracellular space. Formation of new membrane compartments and maintenance of complex organelles require division and disconnection of cellular membranes, a process termed membrane fission. Peripheral membrane proteins generally control membrane remodeling during fission. Local membrane stresses, reflecting molecular geometry of membrane-interacting parts of these proteins, sum up to produce the key membrane geometries of fission: the saddle-shaped neck and hour-glass hemifission intermediate. Here, we review the fundamental principles behind the translation of molecular geometry into membrane shape and topology during fission. We emphasize the central role the membrane insertion of specialized protein domains plays in orchestrating fission in vitro and in cells. We further compare individual to synergistic action of the membrane insertion during fission mediated by individual protein species, proteins complexes or membrane domains. Finally, we describe how local geometry of fission intermediates defines the functional design of the protein complexes catalyzing fission of cellular membranes. PMID:25062896
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
The method of planes pressure tensor for a spherical subvolume
Heyes, D. M. Smith, E. R. Dini, D. Zaki, T. A.
2014-02-07
Various formulas for the local pressure tensor based on a spherical subvolume of radius, R, are considered. An extension of the Method of Planes (MOP) formula of Todd et al. [Phys. Rev. E 52, 1627 (1995)] for a spherical geometry is derived using the recently proposed Control Volume formulation [E. R. Smith, D. M. Heyes, D. Dini, and T. A. Zaki, Phys. Rev. E 85, 056705 (2012)]. The MOP formula for the purely radial component of the pressure tensor is shown to be mathematically identical to the Radial Irving-Kirkwood formula. Novel offdiagonal elements which are important for momentum conservation emerge naturally from this treatment. The local pressure tensor formulas for a plane are shown to be the large radius limits of those for spherical surfaces. The radial-dependence of the pressure tensor computed by Molecular Dynamics simulation is reported for virtual spheres in a model bulk liquid where the sphere is positioned randomly or whose center is also that of a molecule in the liquid. The probability distributions of angles relating to pairs of atoms which cross the surface of the sphere, and the center of the sphere, are presented as a function of R. The variance in the shear stress calculated from the spherical Volume Averaging method is shown to converge slowly to the limiting values with increasing radius, and to be a strong function of the number of molecules in the simulation cell.
Photoelectric sheath formation around small spherical objects in space
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.
Analytical solution of the simplified spherical harmonics equations in spherical turbid media
NASA Astrophysics Data System (ADS)
Edjlali, Ehsan; Bérubé-Lauzière, Yves
2016-10-01
We present for the first time an analytical solution for the simplified spherical harmonics equations (so-called SPN equations) in the case of a steady-state isotropic point source inside a spherical homogeneous absorbing and scattering medium. The SPN equations provide a reliable approximation to the radiative transfer equation for describing light transport inside turbid media. The SPN equations consist of a set of coupled partial differential equations and the eigen method is used to obtain a set of decoupled equations, each resembling the heat equation in the Laplace domain. The equations are solved for the realistic partial reflection boundary conditions accounting for the difference in refractive indices between the turbid medium and its environment (air) as occurs in practical cases of interest in biomedical optics. Specifically, we provide the complete solution methodology for the SP3, which is readily applicable to higher orders as well, and also give results for the SP5. This computationally easy to obtain solution is investigated for different optical properties of the turbid medium. For validation, the solution is also compared to the analytical solution of the diffusion equation and to gold standard Monte Carlo simulation results. The SP3 and SP5 analytical solutions prove to be in good agreement with the Monte Carlo results. This work provides an additional tool for validating numerical solutions of the SPN equations for curved geometries.
Trapped surfaces in spherical stars
Bizon, P.; Malec, E.; O'Murchadha, N.
1988-09-05
We give necessary and sufficient conditions for the existence of trapped surfaces in spherically symmetric spacetimes. These conditions show that the formation of trapped surfaces depends on both the degree of concentration and the average flow of the matter. The result can be considered as a partial validation of the cosmic-censorship hypothesis.
Extending standard mask lithography exposure technique to spherical surfaces
NASA Astrophysics Data System (ADS)
Stumpf, Daniela; Zeitner, Uwe D.
2014-06-01
Similar to planar lithography, the use of a mask to produce multiple copies of a binary master sample is also possible in the case of spherical surfaces. Evidently, the spherical mask needs to have the opposite radius of curvature of the desired substrate, and additional problems arising from the curved geometry have to be taken into consideration. Inhomogeneities of the illumination impinging on the resist-coated surface negatively influence the exposure result. Ways of overcoming these difficulties to obtain satisfactory results for the implementation of the exposure in a conventional mask aligner are shown. Despite a lowered contrast due to back reflections and a varying distance between mask and substrate, exposure results of sufficient quality are achieved with the help of an adapted aperture and the use of water as an immersion fluid.
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.
Noncommutative Geometry and Physics
Connes, Alain
2006-11-03
In this very short essay we shall describe a 'spectral' point of view on geometry which allows to start taking into account the lessons from both renormalization and of general relativity. We shall first do that for renormalization and explain in rough outline the content of our recent collaborations with Dirk Kreimer and Matilde Marcolli leading to the universal Galois symmetry of renormalizable quantum field theories provided by the renormalization group in its cosmic Galois group incarnation. As far as general relativity is concerned, since the functional integral cannot be treated in the traditional perturbative manner, it relies heavily as a 'sum over geometries' on the chosen paradigm of geometric space. This will give us the occasion to discuss, in the light of noncommutative geometry, the issue of 'observables' in gravity and our joint work with Ali Chamseddine on the spectral action, with a first attempt to write down a functional integral on the space of noncommutative geometries.
ERIC Educational Resources Information Center
Chern, Shiing-Shen
1990-01-01
Discussed are the major historical developments of geometry. Euclid, Descartes, Klein's Erlanger Program, Gaus and Riemann, globalization, topology, Elie Cartan, and an application to molecular biology are included as topics. (KR)
Proof in Transformation Geometry
ERIC Educational Resources Information Center
Bell, A. W.
1971-01-01
The first of three articles showing how inductively-obtained results in transformation geometry may be organized into a deductive system. This article discusses two approaches to enlargement (dilatation), one using coordinates and the other using synthetic methods. (MM)
ERIC Educational Resources Information Center
Emenaker, Charles E.
1999-01-01
Describes a sixth-grade interdisciplinary geometry unit based on Charles Dickens's "A Christmas Carol". Focuses on finding area, volume, and perimeter, and working with estimation, decimals, and fractions in the context of making gingerbread houses. (ASK)
Induced geometry from disformal transformation
NASA Astrophysics Data System (ADS)
Yuan, Fang-Fang; Huang, Peng
2015-05-01
In this note, we use the disformal transformation to induce a geometry from the manifold which is originally Riemannian. The new geometry obtained here can be considered as a generalization of Weyl integrable geometry. Based on these results, we further propose a geometry which is naturally a generalization of Weyl geometry.
Software Geometry in Simulations
NASA Astrophysics Data System (ADS)
Alion, Tyler; Viren, Brett; Junk, Tom
2015-04-01
The Long Baseline Neutrino Experiment (LBNE) involves many detectors. The experiment's near detector (ND) facility, may ultimately involve several detectors. The far detector (FD) will be significantly larger than any other Liquid Argon (LAr) detector yet constructed; many prototype detectors are being constructed and studied to motivate a plethora of proposed FD designs. Whether it be a constructed prototype or a proposed ND/FD design, every design must be simulated and analyzed. This presents a considerable challenge to LBNE software experts; each detector geometry must be described to the simulation software in an efficient way which allows for multiple authors to easily collaborate. Furthermore, different geometry versions must be tracked throughout their use. We present a framework called General Geometry Description (GGD), written and developed by LBNE software collaborators for managing software to generate geometries. Though GGD is flexible enough to be used by any experiment working with detectors, we present it's first use in generating Geometry Description Markup Language (GDML) files to interface with LArSoft, a framework of detector simulations, event reconstruction, and data analyses written for all LAr technology users at Fermilab. Brett is the other of the framework discussed here, the General Geometry Description (GGD).
2005-01-01
The Common Geometry Module (CGM) is a code library which provides geometry functionality used for mesh generation and other applications. This functionality includes that commonly found in solid modeling engines, like geometry creation, query and modification; CGM also includes capabilities not commonly found in solid modeling engines, like geometry decomposition tools and support for shared material interfaces. CGM is built upon the ACIS solid modeling engine, but also includes geometry capability developed beside and onmore » top of ACIS. CGM can be used as-is to provide geometry functionality for codes needing this capability. However, CGM can also be extended using derived classes in C++, allowing the geometric model to serve as the basis for other applications, for example mesh generation. CGM is supported on Sun Solaris, SGI, HP, IBM, DEC, Linux and Windows NT platforms. CGM also indudes support for loading ACIS models on parallel computers, using MPI-based communication. Future plans for CGM are to port it to different solid modeling engines, including Pro/Engineer or SolidWorks. CGM is being released into the public domain under an LGPL license; the ACIS-based engine is available to ACIS licensees on request.« less
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.
Modal testing variability of spherical marine floats.
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.
Modeling of non-spherical droplet dynamics
NASA Astrophysics Data System (ADS)
Deng, Zheng-Tao; Liaw, Goang-Shin; Chou, Lynn C.
1993-07-01
A two-dimensional time-dependent computer code based on the modified Arbitrary Lagrangian Eulerian (ALE) technique, has been developed to simulate non-spherical droplet dynamics and evaporation under convective flows at real rocket combustion chamber conditions. The equations of mass, momentum, energy and species are simultaneously solved for both liquid and gas phases with an accurate dynamic interface tracking. The jump boundary conditions across the deforming droplet surface are obtained by applying the integral forms of conservation of mass, momentum, and energy. At each time step, the interface geometry and flow properties at the droplet surface are implicitly solved by satisfying the interface boundary conditions. A Lagrangian technique was developed to track the arbitrarily moving interface between the liquid droplet and the external gas. An elliptic grid generator is adopted to dynamically reconstruct grids both inside and outside the droplet surface. This code has been used to study droplet oscillation, droplet deformation/breakup, nonspherical droplet evaporation in both low and high pressure convective flows. This presentation briefly describes the numerical algorithm for modeling of the nonspherical droplet dynamics and demonstrates the representative simulation results of nonspherical droplet evaporation at low and high pressure convective flows. Potential applications of this code to rocket combustor design and performance predictions are discussed.
Bidirectional slapper detonators in spherical explosion systems
NASA Astrophysics Data System (ADS)
Martinez, Ernest C.
1990-11-01
A bidirectional slapper detonator has been proven effective for producing a spherically expanding shock wave. Two bridge foils are used to propel flyers in opposite directions, thereby initiating two explosive pellets, each embedded in one hemisphere of a spherical system. This detonation system produces a nearly perfect spherically expanding detonation front.
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
Hydrodynamic interactions of cilia on a spherical body
NASA Astrophysics Data System (ADS)
Nasouri, Babak; Elfring, Gwynn J.
2016-03-01
Microorganisms develop coordinated beating patterns on surfaces lined with cilia known as metachronal waves. For a chain of cilia attached to a flat ciliate, it has been shown that hydrodynamic interactions alone can lead the system to synchronize. However, several microorganisms possess a curve-shaped ciliate body and so 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 natural periodicity in the geometry leads the system to synchronize. We also report an emergent wavelike behavior when an asymmetry is introduced to the system.
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.
Non-spherical particles for optical trap assisted nanopatterning
NASA Astrophysics Data System (ADS)
Tsai, Y.-C.; Fardel, R.; Panczyk, M. M.; Furst, E. M.; Arnold, C. B.
2013-09-01
Optical trap assisted nanopatterning is a laser direct-write technique that uses an optically trapped microsphere as a near-field objective. The type of feature that one can create with this technique depends on several factors, one of which is the shape of the microbead. In this paper, we examine how the geometry of the bead affects the focus of the light through a combination of experiments and simulations. We realize nanopatterning using non-spherical dielectric particles to shape the light-material interaction. We model the resulting nanoscale features with a finite difference time domain simulation and obtain very good agreement with the experiments. This work opens the way to systematic engineering of the microparticle geometry in order to tailor the near-field focus to specific nanopatterning applications.
Van der waals-like isotherms in a confined electrolyte by spherical and cylindrical nanopores.
Aguilar-Pineda, Gabriel E; Jiménez-Angeles, Felipe; Yu, Jiang; Lozada-Cassou, Marcelo
2007-03-01
Electrolytes confined by spherical, cylindrical, and slit-like charged nanopores are studied. Results for ionic distribution profiles, pressures of the confined fluid, and absorption isotherms are obtained through the hypernetted chain/mean spherical approximation (HNC/MSA) integral equations theory. In spherical and cylindrical geometries, an inward, non-monotonic behavior of the pressure is found as confinement increases, implying a negative compressibility. The pressure vs volume isotherms resemble liquid-vapor van der Waals-like phase transition diagrams. This effect is correlated with a charge separation inside a spherical pore previously reported (Phys. Rev. Lett., 79, 3656, 1997). Here, the mechanism of charge separation and negative compressibility are explored in detail. When compared with the slit-like pore pressure, important qualitative differences are found.
Polymeric carriers: role of geometry in drug delivery
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
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.
On the Explosion Geometry of Red Supergiant Stars
NASA Astrophysics Data System (ADS)
Leonard, Douglas Christopher; Dessart, Luc; Pignata, Giuliano; Hillier, D. John; Williams, George Grant; Smith, Paul S.; Khandrika, Harish; Bilinski, Christopher; Duong, Nhieu; Flatland, Kelsi; Gonzalez, Luis; Hoffman, Jennifer L.; Horst, Chuck; Huk, Leah; Milne, Peter; Rachubo, Alisa A.; Smith, Nathan
2015-08-01
From progenitor studies, type II-Plateau supernovae (SNe II-P) have been decisively and uniquely determined to arise from isolated red supergiant (RSG) stars with initial masses ranging from 8 to 16 solar masses (Smartt 2009), establishing the most homogeneous -- and well understood -- progenitor class of any type of core-collapse supernova. However, we must admit a fundamental truth: We do not know how these stars explode. A basic discriminant among proposed explosion models is explosion geometry, since some models predict severe distortions from spherical symmetry. A primary method to gain such geometric information is through spectropolarimetry of the expanding (but, unresolved) atmosphere, with higher degrees of linear polarization generally demanding larger departures from spherical symmetry. Initially, as a class, SNe II-P were found to be only weakly polarized at the early epochs observed, suggesting a nearly spherical explosion for RSG stars. However, late-time observations of SN 2004dj captured a dramatic spike in polarization at just the moment the "inner core" of the ejecta was first revealed in this SN II-P (i.e., at the "drop" off of the photometric plateau; Leonard et al. 2006). This raised the possibility that the explosion of RSGs might be driven by a strongly non-spherical mechanism, with the evidence for the asphericity cloaked at early times by the massive, opaque, quasi-spherical hydrogen envelope. In this presentation we shall describe the continuing work on the explosion geometry of RSGs being carried out 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 (Leonard et al. 2013), 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.
Ultrasonic analysis of Kevlar-epoxy filament wound spherical test specimens
Brosey, W.D.
1984-12-06
Increased use of composite materials in enclosed geometries such as cylindrical, spherical, or conical shapes has led to the desire to transfer and further develop the most promising nondestructive evaluation (NDE) techniques used on nonenclosed geometries to enclosed geometries. Known defects were placed within spherical Kevlar-epoxy filament wound test specimens to determine the extent to which they could be detected. These defects included Teflon shim-simulated delaminations, macrosphere-simulated voids, dry-band sets, variable tension, Kevlar 29 fiber, and an alternate high void content winding pattern. Ultrasonic C-scan analysis of Kevlar-epoxy filament wound spheres was performed to determine detectability of normal winding patterns and implanted flaw conditions in the composite using this technique. Ultrasonic waveform analysis was performed in both the time and frequency domains to determine the detectability and locatability of structural flaws within the composite.
NASA Astrophysics Data System (ADS)
Ochiai, T.; Nacher, J. C.
2011-09-01
Recently, the application of geometry and conformal mappings to artificial materials (metamaterials) has attracted the attention in various research communities. These materials, characterized by a unique man-made structure, have unusual optical properties, which materials found in nature do not exhibit. By applying the geometry and conformal mappings theory to metamaterial science, it may be possible to realize so-called "Harry Potter cloaking device". Although such a device is still in the science fiction realm, several works have shown that by using such metamaterials it may be possible to control the direction of the electromagnetic field at will. We could then make an object hidden inside of a cloaking device. Here, we will explain how to design invisibility device using differential geometry and conformal mappings.
2011-01-01
Cells are highly complex and orderly machines, with defined shapes and a startling variety of internal organizations. Complex geometry is a feature of both free-living unicellular organisms and cells inside multicellular animals. Where does the geometry of a cell come from? Many of the same questions that arise in developmental biology can also be asked of cells, but in most cases we do not know the answers. How much of cellular organization is dictated by global cell polarity cues as opposed to local interactions between cellular components? Does cellular structure persist across cell generations? What is the relationship between cell geometry and tissue organization? What ensures that intracellular structures are scaled to the overall size of the cell? Cell biology is only now beginning to come to grips with these questions. PMID:21880160
SAR imagery in non-Cartesian geometries
NASA Astrophysics Data System (ADS)
Dendal, Didier
1995-11-01
The subject of the reported work is the improvement of geometrical models for a SAR scanning in pushbroom, spotlight, scansar or bistatic imaging modes. This research has been motivated by the planetary cornerstone mission of ESA's long term program for European Space Science ('rendezvous' with a comet, and fly-bys of asteroids). In this specific context, the synthetic aperture radar is destined for an important role, but the rules and standard backgrounds of the Cartesian geometry are no longer justified. Several new techniques are proposed to handle with an optimal precision the data relative to celestial bodies with a complex geometry (coherent and non-coherent imagery). On the basis of a mathematical rigor (singleness of solutions, convergence of processes, biunivocity of transformations and generalizations), a lot of scenarios are discussed with key relations established (plane and spherical models, bodies with a symmetry of revolution and general bodies, specific sensor(s) trajectories as fly-bys or flight into orbit with the possibility of an approaching probe). The four methods developed are the tomographic analogy of radar principles (only known, previously, in the usual case of a straight line flight at constant altitude over a plane surface) and Hilbertian techniques for a direct adaptation to the scanned surface geometry, an automated autofocusing which enhances the contrast resulting from a Cartesian reconstruction and the coordinates transformation where the real space is converted into a fictitious space where Cartesian algorithms are fully rigorous. Beyond the fact that an interpolation step is often unavoidable, the major conclusion of the research is that all the prospected techniques are complementary and that the choice between the methods has to be made according to geometry, objectives and time requirements (reconstruction on board or not). In particular, coordinates transformation techniques are worthy of commendation in the case of plane
Computational synthetic geometry
Sturmfels, B. )
1988-01-01
This book deals with methods for realizing abstract geometric objects in concrete vector spaces. It considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It appears that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems, a variety of symbolic algorithms are discussed, and the methods are applied to obtain mathematical results on convex polytopes, projective configurations and the combinatories of Grassmann varieties.
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.
Physics of Spherical Torus Plasmas
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
APPARATUS FOR GRINDING SPHERICAL BODIES
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)
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.
Advanced geometries and regimes
Bulanov, S. S.; Bulanov, S. V.; Turchetti, G.; Limpouch, J.; Klimo, O.; Psikal, J.; Margarone, D.; Korn, G.
2013-07-26
We review and discuss different schemes of laser ion acceleration as well as advanced target geometries in connection with the development of the laser-driven proton source for hadron therapy of oncological diseases, which is a part of the ELIMED project.
Spacetime and Euclidean geometry
NASA Astrophysics Data System (ADS)
Brill, Dieter; Jacobson, Ted
2006-04-01
Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem.
ERIC Educational Resources Information Center
Cooper, Brett D.; Barger, Rita
2009-01-01
The many connections between music and mathematics are well known. The length of a plucked string determines its tone, the time signature of a piece of music is a ratio, and note durations are measured in fractions. One connection commonly overlooked is that between music and geometry--specifically, geometric transformations, including…
ERIC Educational Resources Information Center
Hartz, Viggo
1981-01-01
Allowing students to use a polystyrene cutter to fashion their own three-dimensional models is suggested as a means of allowing individuals to experience problems and develop ideas related to solid geometry. A list of ideas that can lead to mathematical discovery is provided. (MP)
Teaching Geometry with Tangrams.
ERIC Educational Resources Information Center
Russell, Dorothy S.; Bologna, Elaine M.
1982-01-01
Geometry is viewed as the most neglected area of the elementary school mathematics curriculum. Tangram activities provide numerous worthwhile mathematical experiences for children. A method of constructing tangrams through paper folding is followed by suggested spatial visualization, measurement, and additional activities. (MP)
Sliding vane geometry turbines
Sun, Harold Huimin; Zhang, Jizhong; Hu, Liangjun; Hanna, Dave R
2014-12-30
Various systems and methods are described for a variable geometry turbine. In one example, a turbine nozzle comprises a central axis and a nozzle vane. The nozzle vane includes a stationary vane and a sliding vane. The sliding vane is positioned to slide in a direction substantially tangent to an inner circumference of the turbine nozzle and in contact with the stationary vane.
ERIC Educational Resources Information Center
MacKeown, P. K.
1984-01-01
Clarifies two concepts of gravity--those of a fictitious force and those of how space and time may have geometry. Reviews the position of Newton's theory of gravity in the context of special relativity and considers why gravity (as distinct from electromagnetics) lends itself to Einstein's revolutionary interpretation. (JN)
ERIC Educational Resources Information Center
Martin, John
2010-01-01
The cycloid has been called the Helen of Geometry, not only because of its beautiful properties but also because of the quarrels it provoked between famous mathematicians of the 17th century. This article surveys the history of the cycloid and its importance in the development of the calculus.
Atiyah, Michael; Dijkgraaf, Robbert; Hitchin, Nigel
2010-01-01
We review the remarkably fruitful interactions between mathematics and quantum physics in the past decades, pointing out some general trends and highlighting several examples, such as the counting of curves in algebraic geometry, invariants of knots and four-dimensional topology. PMID:20123740
ERIC Educational Resources Information Center
Case, Christine L.
1991-01-01
Presented is an activity in which students make models of viruses, which allows them to visualize the shape of these microorganisms. Included are some background on viruses, the biology and geometry of viruses, directions for building viruses, a comparison of cells and viruses, and questions for students. (KR)
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…
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.
A feasibility study for the spherical torus experiment
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.
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.
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.
Gómez-Correa, J E; Coello, V; Garza-Rivera, A; Puente, N P; Chávez-Cerda, S
2016-03-10
Ray tracing in spherical Luneburg lenses has always been represented in 2D. All propagation planes in a 3D spherical Luneburg lens generate the same ray tracing, due to its radial symmetry. A geometry without radial symmetry generates a different ray tracing. For this reason, a new ray tracing method in 3D through spherical and elliptical Luneburg lenses using 2D methods is proposed. The physics of the propagation is shown here, which allows us to make a ray tracing associated with a vortex beam. A 3D ray tracing in a composite modified Luneburg lens that represents the human eye lens is also presented.
Gómez-Correa, J E; Coello, V; Garza-Rivera, A; Puente, N P; Chávez-Cerda, S
2016-03-10
Ray tracing in spherical Luneburg lenses has always been represented in 2D. All propagation planes in a 3D spherical Luneburg lens generate the same ray tracing, due to its radial symmetry. A geometry without radial symmetry generates a different ray tracing. For this reason, a new ray tracing method in 3D through spherical and elliptical Luneburg lenses using 2D methods is proposed. The physics of the propagation is shown here, which allows us to make a ray tracing associated with a vortex beam. A 3D ray tracing in a composite modified Luneburg lens that represents the human eye lens is also presented. PMID:26974795
Plasma instability in fast spherical discharge induced by a preionization
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.
How should spin-weighted spherical functions be defined?
NASA Astrophysics Data System (ADS)
Boyle, Michael
2016-09-01
Spin-weighted spherical functions provide a useful tool for analyzing tensor-valued functions on the sphere. A tensor field can be decomposed into complex-valued functions by taking contractions with tangent vectors on the sphere and the normal to the sphere. These component functions are usually presented as functions on the sphere itself, but this requires an implicit choice of distinguished tangent vectors with which to contract. Thus, we may more accurately say that spin-weighted spherical functions are functions of both a point on the sphere and a choice of frame in the tangent space at that point. The distinction becomes extremely important when transforming the coordinates in which these functions are expressed, because the implicit choice of frame will also transform. Here, it is proposed that spin-weighted spherical functions should be treated as functions on the spin or rotation groups, which simultaneously tracks the point on the sphere and the choice of tangent frame by rotating elements of an orthonormal basis. In practice, the functions simply take a quaternion argument and produce a complex value. This approach more cleanly reflects the geometry involved, and allows for a more elegant description of the behavior of spin-weighted functions. In this form, the spin-weighted spherical harmonics have simple expressions as elements of the Wigner 𝔇 representations, and transformations under rotation are simple. Two variants of the angular-momentum operator are defined directly in terms of the spin group; one is the standard angular-momentum operator L, while the other is shown to be related to the spin-raising operator ð.
VACUUM calculation in azimuthally symmetric geometry
Chance, M.S.
1996-11-01
A robustly accurate and effective method is presented to solve Laplace`s equation in general azimuthally symmetric geometry for the magnetic scalar potential in the region surrounding a plasma discharge which may or may not contain external conducting shells. These shells can be topologically toroidal or spherical, and may have toroidal gaps in them. The solution is incorporated into the various MHD stability codes either through the volume integrated perturbed magnetic energy in the vacuum region or through the continuity requirements for the normal component of the perturbed magnetic field and the total perturbed pressure across the unperturbed plasma-vacuum boundary. The method is based upon using Green`s second identity and the method of collocation. As useful byproducts, the eddy currents and the simulation of Mirnov loop measurements are calculated.
Geometry and mechanics of thin growing bilayers.
Pezzulla, Matteo; Smith, Gabriel P; Nardinocchi, Paola; Holmes, Douglas P
2016-05-11
We investigate how thin sheets of arbitrary shapes morph under the isotropic in-plane expansion of their top surface, which may represent several stimuli such as nonuniform heating, local swelling and differential growth. Inspired by geometry, an analytical model is presented that rationalizes how the shape of the disk influences morphing, from the initial spherical bending to the final isometric limit. We introduce a new measure of slenderness that describes a sheet in terms of both thickness and plate shape. We find that the mean curvature of the isometric state is three fourths the natural curvature, which we verify by numerics and experiments. We finally investigate the emergence of a preferred direction of bending in the isometric state, guided by numerical analyses. The scalability of our model suggests that it is suitable to describe the morphing of sheets spanning several orders of magnitude.
Geometry and mechanics of thin growing bilayers.
Pezzulla, Matteo; Smith, Gabriel P; Nardinocchi, Paola; Holmes, Douglas P
2016-05-11
We investigate how thin sheets of arbitrary shapes morph under the isotropic in-plane expansion of their top surface, which may represent several stimuli such as nonuniform heating, local swelling and differential growth. Inspired by geometry, an analytical model is presented that rationalizes how the shape of the disk influences morphing, from the initial spherical bending to the final isometric limit. We introduce a new measure of slenderness that describes a sheet in terms of both thickness and plate shape. We find that the mean curvature of the isometric state is three fourths the natural curvature, which we verify by numerics and experiments. We finally investigate the emergence of a preferred direction of bending in the isometric state, guided by numerical analyses. The scalability of our model suggests that it is suitable to describe the morphing of sheets spanning several orders of magnitude. PMID:27098344
Nebeck, H.E.
1986-08-01
The MAZE mesh generator represents an arbitrary two dimensional region of space as an ordered collection of quadrilateral elements. Each element is defined by its four corner points (nodes) and an integer material number. Models are created by subdividing the region(s) of interest into one or more PARTS and specifying the element distribution in each part. Then, parts can be merged together to form the meshed representation of the entire region. Applying boundary conditions and describing material properties completes the model construction process. This activity takes place in three distinct phases: phase I-define geometry, subdivide regions into elements; phase II-refine geometry, establish interface and boundary conditions; phase III-describe material properties. This work presents explanations and examples of the phase I commands, along with an overview of the MAZE mesh generation process.
Cylindrical geometry hall thruster
Raitses, Yevgeny; Fisch, Nathaniel J.
2002-01-01
An apparatus and method for thrusting plasma, utilizing a Hall thruster with a cylindrical geometry, wherein ions are accelerated in substantially the axial direction. The apparatus is suitable for operation at low power. It employs small size thruster components, including a ceramic channel, with the center pole piece of the conventional annular design thruster eliminated or greatly reduced. Efficient operation is accomplished through magnetic fields with a substantial radial component. The propellant gas is ionized at an optimal location in the thruster. A further improvement is accomplished by segmented electrodes, which produce localized voltage drops within the thruster at optimally prescribed locations. The apparatus differs from a conventional Hall thruster, which has an annular geometry, not well suited to scaling to small size, because the small size for an annular design has a great deal of surface area relative to the volume.
Measuring Spherical Harmonic Coefficients on a Sphere
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.
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.
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.
Inflation from quantum geometry.
Bojowald, Martin
2002-12-23
Quantum geometry predicts that a universe evolves through an inflationary phase at small volume before exiting gracefully into a standard Friedmann phase. This does not require the introduction of additional matter fields with ad hoc potentials; rather, it occurs because of a quantum gravity modification of the kinetic part of ordinary matter Hamiltonians. An application of the same mechanism can explain why the present day cosmological acceleration is so tiny.
NASA Astrophysics Data System (ADS)
Bengtsson, Ingemar; Zyczkowski, Karol
2007-12-01
Preface; 1. Convexity, colours and statistics; 2. Geometry of probability distributions; 3. Much ado about spheres; 4. Complex projective spaces; 5. Outline of quantum mechanics; 6. Coherent states and group actions; 7. The stellar representation; 8. The space of density matrices; 9. Purification of mixed quantum states; 10. Quantum operations; 11. Duality: maps versus states; 12. Density matrices and entropies; 13. Distinguishability measures; 14. Monotone metrics and measures; 15. Quantum entanglement; Epilogue; Appendices; References; Index.
Freezing in confined geometries
NASA Technical Reports Server (NTRS)
Sokol, P. E.; Ma, W. J.; Herwig, K. W.; Snow, W. M.; Wang, Y.; Koplik, Joel; Banavar, Jayanth R.
1992-01-01
Results of detailed structural studies, using elastic neutron scattering, of the freezing of liquid O2 and D2 in porous vycor glass, are presented. The experimental studies have been complemented by computer simulations of the dynamics of freezing of a Lennard-Jones liquid in narrow channels bounded by molecular walls. Results point to a new simple physical interpretation of freezing in confined geometries.
Integral geometry and holography
Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel; Sully, James
2015-10-27
We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS_{3}/CFT_{2} correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulk curve. We explain how basic geometric concepts -- points, distances and angles -- are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS_{3} whose kinematic space is two-dimensional de Sitter space.
Integral geometry and holography
Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel; Sully, James
2015-10-27
We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS3/CFT2 correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulkmore » curve. We explain how basic geometric concepts -- points, distances and angles -- are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS3 whose kinematic space is two-dimensional de Sitter space.« less
Emergent Complex Network Geometry
NASA Astrophysics Data System (ADS)
Wu, Zhihao; Menichetti, Giulia; Rahmede, Christoph; Bianconi, Ginestra
2015-05-01
Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant for routing problems, inference and data mining. In real growing networks, topological, structural and geometrical properties emerge spontaneously from their dynamical rules. Nevertheless we still miss a model in which networks develop an emergent complex geometry. Here we show that a single two parameter network model, the growing geometrical network, can generate complex network geometries with non-trivial distribution of curvatures, combining exponential growth and small-world properties with finite spectral dimensionality. In one limit, the non-equilibrium dynamical rules of these networks can generate scale-free networks with clustering and communities, in another limit planar random geometries with non-trivial modularity. Finally we find that these properties of the geometrical growing networks are present in a large set of real networks describing biological, social and technological systems.
Wormhole dynamics in spherical symmetry
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.
Nonadiabatic charged spherical gravitational collapse
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.
Non-Euclidean geometry of twisted filament bundle packing
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
Geometry for the Secondary School
ERIC Educational Resources Information Center
Moalem, D.
1977-01-01
A sequential but non-axiomatic high school geometry course which includes Euclidean, transformation, and analytic geometry and vectors and matrices, and emphasizes the invariance property of transformations, is outlined. Sample problems, solutions, and comments are included. (MN)
Instability of spherically imploding shock waves
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.
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.
Three-point spherical mirror mount
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.
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…
Three-point spherical mirror mount
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.
Multigroup Complex Geometry Neutron Diffusion Code System.
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
Multigroup Complex Geometry Neutron Diffusion Code System.
MCCALLIEN, C. W.J.
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. 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.
Computer-Aided Geometry Modeling
NASA Technical Reports Server (NTRS)
Shoosmith, J. N. (Compiler); Fulton, R. E. (Compiler)
1984-01-01
Techniques in computer-aided geometry modeling and their application are addressed. Mathematical modeling, solid geometry models, management of geometric data, development of geometry standards, and interactive and graphic procedures are discussed. The applications include aeronautical and aerospace structures design, fluid flow modeling, and gas turbine design.
Teaching of Geometry in Bulgaria
ERIC Educational Resources Information Center
Bankov, Kiril
2013-01-01
Geometry plays an important role in the school mathematics curriculum all around the world. Teaching of geometry varies a lot (Hoyls, Foxman, & Kuchemann, 2001). Many countries revise the objectives, the content, and the approaches to the geometry in school. Studies of the processes show that there are not common trends of these changes…
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
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.
Stability of imploding spherical shock waves
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.
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
Fast calculation of spherical computer generated hologram using spherical wave spectrum method.
Jackin, Boaz Jessie; Yatagai, Toyohiko
2013-01-14
A fast calculation method for computer generation of spherical holograms in proposed. This method is based on wave propagation defined in spectral domain and in spherical coordinates. The spherical wave spectrum and transfer function were derived from boundary value solutions to the scalar wave equation. It is a spectral propagation formula analogous to angular spectrum formula in cartesian coordinates. A numerical method to evaluate the derived formula is suggested, which uses only N(logN)2 operations for calculations on N sampling points. Simulation results are presented to verify the correctness of the proposed method. A spherical hologram for a spherical object was generated and reconstructed successfully using the proposed method.
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.
A study of the collapse loading of spherical shells.
Pepin, J. E.; Thacker, B. H.; Riha, D. S.; McKeighan, P. C.
2004-01-01
Current arms control agreements have provided the impetus for national directives to cease production of new strategic weapons and to end nuclear testing. This has placed a tremendous burden on the national laboratories for assuring stockpile certification. The Stockpile Stewardship Program's fundamental objective within the Department of Energy (DOE) is to maintain a high confidence in the safety, reliability, and performance of the existing U.S. nuclear weapons stockpile. As such, enhanced evaluation capabilities are needed to quantify the effect of possible anomalies that may arise in a weapon (e.g., due to aging mechanisms), and assess its performance, safety and overall reliability. Validated numerical methods must be employed in determining the reliability of specific weapon components, including the overall weapon system. The validated numerical models must, however, be based on accurate information of each component's geometry and material properties in an aged condition. Once these variables are known, extrapolation of potential lifetime of the weapon can be determined with some level of confidence. The goal is to develop an engineering capability that provides a reliability-based structural evaluation technique for performing weapon reliability assessments. To enhance the analyst's confidence with these new methods, an integrated experiment and analysis project has been developed. The focus of this project is to generate accurate probabilistic structural response simulations using numerical models of commercially available, stainless steel spherical marine floats, under collapse loads, and compare with experimental results. The spherical marine float geometry was chosen because of its simple shape, yet highly complex nonlinear deformation behavior, leading to complex states-of-stress. There is also a variability associated with geometry and mechanical properties of commercially available (i.e., off-the-shelf) marine floats. The variability is not uncommon
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.
Spherical accretion and AGN feedback
NASA Astrophysics Data System (ADS)
Nulsen, Paul
2014-06-01
For a supermassive black hole accreting from a hot, quasi-spherical atmosphere, it is almost inevitable that the fluid approximation fails inside some point within the Bondi radius, but well outside the black hole event horizon. Within the region where the particle mean free paths exceed the radius, the flow must be modeled in terms of the Fokker-Planck equation. In the absence of magnetic fields, it is analogous to the "loss cone" problem for consumption of stars by a black hole. The accretion rate is suppressed well below the Bondi accretion rate and a significant power must be conveyed outward for the flow to proceed. This situation is complicated significantly by the presence of a magnetic field, but I will argue that the main outcomes are similar. I will also argue that the power emerging from such a flow, although generally far too little to suppress cooling on large scales, is an important ingredient of the AGN feedback cycle on scales comparable to the Bondi radius.
Generalized spherical and simplicial coordinates
NASA Astrophysics Data System (ADS)
Richter, Wolf-Dieter
2007-12-01
Elementary trigonometric quantities are defined in l2,p analogously to that in l2,2, the sine and cosine functions are generalized for each p>0 as functions sinp and cosp such that they satisfy the basic equation cosp([phi])p+sinp([phi])p=1. The p-generalized radius coordinate of a point [xi][set membership, variant]Rn is defined for each p>0 as . On combining these quantities, ln,p-spherical coordinates are defined. It is shown that these coordinates are nearly related to ln,p-simplicial coordinates. The Jacobians of these generalized coordinate transformations are derived. Applications and interpretations from analysis deal especially with the definition of a generalized surface content on ln,p-spheres which is nearly related to a modified co-area formula and an extension of Cavalieri's and Torricelli's indivisibeln method, and with differential equations. Applications from probability theory deal especially with a geometric interpretation of the uniform probability distribution on the ln,p-sphere and with the derivation of certain generalized statistical distributions.
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.
Ribozyme-Spherical Nucleic Acids
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
Osmotic buckling of spherical capsules.
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
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.
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.
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.
NASA Astrophysics Data System (ADS)
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.
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
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.
Simulating higher-dimensional geometries in GADRAS using approximate one-dimensional solutions.
Thoreson, Gregory G.; Mitchell, Dean J; 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.
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.
Critique of information geometry
Skilling, John
2014-12-05
As applied to probability, information geometry fails because probability distributions do not form a metric space. Probability theory rests on a compelling foundation of elementary symmetries, which also support information (aka minus entropy, Kullback-Leibler) H(p;q) as the unique measure of divergence from source probability distribution q to destination p. Because the only compatible connective H is from≠to asymmetric, H(p;q)≠H(q;p), there can be no compatible geometrical distance (which would necessarily be from=to symmetric). Hence there is no distance relationship compatible with the structure of probability theory. Metrics g and densities sqrt(det(g)) interpreted as prior probabilities follow from the definition of distance, and must fail likewise. Various metrics and corresponding priors have been proposed, Fisher's being the most popular, but all must behave unacceptably. This is illustrated with simple counter-examples.
Optically defined mechanical geometry
NASA Astrophysics Data System (ADS)
Barasheed, Abeer Z.; Müller, Tina; Sankey, Jack C.
2016-05-01
In the field of optomechanics, radiation forces have provided a particularly high level of control over the frequency and dissipation of mechanical elements. Here we propose a class of optomechanical systems in which light exerts a similarly profound influence over two other fundamental parameters: geometry and mass. By applying an optical trap to one lattice site of an extended phononic crystal, we show it is possible to create a tunable, localized mechanical mode. Owing to light's simultaneous and constructive coupling with the structure's continuum of modes, we estimate that a trap power at the level of a single intracavity photon should be capable of producing a significant effect within a realistic, chip-scale device.
Magnetism in curved geometries
NASA Astrophysics Data System (ADS)
Streubel, Robert; Fischer, Peter; Kronast, Florian; Kravchuk, Volodymyr P.; Sheka, Denis D.; Gaididei, Yuri; Schmidt, Oliver G.; Makarov, Denys
2016-09-01
Extending planar two-dimensional structures into the three-dimensional space has become a general trend in multiple disciplines, including electronics, photonics, plasmonics and magnetics. This approach provides means to modify conventional or to launch novel functionalities by tailoring the geometry of an object, e.g. its local curvature. In a generic electronic system, curvature results in the appearance of scalar and vector geometric potentials inducing anisotropic and chiral effects. In the specific case of magnetism, even in the simplest case of a curved anisotropic Heisenberg magnet, the curvilinear geometry manifests two exchange-driven interactions, namely effective anisotropy and antisymmetric exchange, i.e. Dzyaloshinskii–Moriya-like interaction. As a consequence, a family of novel curvature-driven effects emerges, which includes magnetochiral effects and topologically induced magnetization patterning, resulting in theoretically predicted unlimited domain wall velocities, chirality symmetry breaking and Cherenkov-like effects for magnons. The broad range of altered physical properties makes these curved architectures appealing in view of fundamental research on e.g. skyrmionic systems, magnonic crystals or exotic spin configurations. In addition to these rich physics, the application potential of three-dimensionally shaped objects is currently being explored as magnetic field sensorics for magnetofluidic applications, spin-wave filters, advanced magneto-encephalography devices for diagnosis of epilepsy or for energy-efficient racetrack memory devices. These recent developments ranging from theoretical predictions over fabrication of three-dimensionally curved magnetic thin films, hollow cylinders or wires, to their characterization using integral means as well as the development of advanced tomography approaches are in the focus of this review.
Magnetism in curved geometries
NASA Astrophysics Data System (ADS)
Streubel, Robert; Fischer, Peter; Kronast, Florian; Kravchuk, Volodymyr P.; Sheka, Denis D.; Gaididei, Yuri; Schmidt, Oliver G.; Makarov, Denys
2016-09-01
Extending planar two-dimensional structures into the three-dimensional space has become a general trend in multiple disciplines, including electronics, photonics, plasmonics and magnetics. This approach provides means to modify conventional or to launch novel functionalities by tailoring the geometry of an object, e.g. its local curvature. In a generic electronic system, curvature results in the appearance of scalar and vector geometric potentials inducing anisotropic and chiral effects. In the specific case of magnetism, even in the simplest case of a curved anisotropic Heisenberg magnet, the curvilinear geometry manifests two exchange-driven interactions, namely effective anisotropy and antisymmetric exchange, i.e. Dzyaloshinskii-Moriya-like interaction. As a consequence, a family of novel curvature-driven effects emerges, which includes magnetochiral effects and topologically induced magnetization patterning, resulting in theoretically predicted unlimited domain wall velocities, chirality symmetry breaking and Cherenkov-like effects for magnons. The broad range of altered physical properties makes these curved architectures appealing in view of fundamental research on e.g. skyrmionic systems, magnonic crystals or exotic spin configurations. In addition to these rich physics, the application potential of three-dimensionally shaped objects is currently being explored as magnetic field sensorics for magnetofluidic applications, spin-wave filters, advanced magneto-encephalography devices for diagnosis of epilepsy or for energy-efficient racetrack memory devices. These recent developments ranging from theoretical predictions over fabrication of three-dimensionally curved magnetic thin films, hollow cylinders or wires, to their characterization using integral means as well as the development of advanced tomography approaches are in the focus of this review.
Physics of Spherical Torus Plasmas
NASA Astrophysics Data System (ADS)
Peng, Y.-K. M.
1999-11-01
Broad and important progress in plasma tests, theory, new experiments, and future visions of the Spherical Torus (ST, or Very Low Aspect Ratio Tokamak) have emerged recently. These have substantially improved our understanding of the potential properties of the ST plasmas, since the preliminary calculation of the ST MHD equilibria more than a decade ago [Peng and Strickler, Nucl. Fusion 26 (1986) 576.]. Exciting data have been obtained from Concept Exploration-level ST experiments of modest capabilities (with major radii up to 35 cm). These include START (U.K.), HIT-I and II (University of Washington), CDX-U (PPPL), HIST and TS-3 (Japan), etc., and made important scientific contributions to toroidal confinement in general. These results have helped approval 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 (AT) research, a wide range of new ST physics features have been suggested. These properties of the ST plasma will be tested at the 1-MA level (with major radii up to 80 cm) in the new Proof-of-Principle devices NSTX (U.S.), MAST (U.K.), and Globus-M (R.F.), which are scheduled to resume experiments before this APS meeting. New Concept Exploration tests such as Pegasus (University of Wisconsin) and others in Japan present additional opportunities for progress. This tutorial paper will summarize our understanding and projections of the physics of the ST plasmas, the investigation of which will hopefully bring new excitement and enthusiasm for fusion energy sciences research in the U.S. and the world. the address below:
Wrinkling crystallography on spherical surfaces
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
Virial pressure in systems of spherical active Brownian particles.
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.
Virial pressure in systems of spherical active Brownian particles.
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
Dynamo-driven plasmoid ejections above a spherical surface
NASA Astrophysics Data System (ADS)
Warnecke, J.; Brandenburg, A.; Mitra, D.
2011-10-01
Aims: We extend earlier models of turbulent dynamos with an upper, nearly force-free exterior to spherical geometry, and study how flux emerges from lower layers to the upper ones without being driven by magnetic buoyancy. We also study how this affects the possibility of plasmoid ejection. Methods: A spherical wedge is used that includes northern and southern hemispheres up to mid-latitudes and a certain range in longitude of the Sun. In radius, we cover both the region that corresponds to the convection zone in the Sun and the immediate exterior up to twice the radius of the Sun. Turbulence is driven with a helical forcing function in the interior, where the sign changes at the equator between the two hemispheres. Results: An oscillatory large-scale dynamo with equatorward migration is found to operate in the turbulence zone. Plasmoid ejections occur in regular intervals, similar to what is seen in earlier Cartesian models. These plasmoid ejections are tentatively associated with coronal mass ejections (CMEs). The magnetic helicity is found to change sign outside the turbulence zone, which is in agreement with recent findings for the solar wind. Movie is available in electronic form at http://www.aanda.org
Spherical bearing. [to reduce vibration effects
NASA Technical Reports Server (NTRS)
Myers, W. N.; Hein, L. A. (Inventor)
1978-01-01
A spherical bearing including an inner ball with an opening for receiving a shaft and a spherical outer surface is described. Features of the bearing include: (1) a circular outer race including a plurality of circumferentially spaced sections extending around the inner ball for snugly receiving the inner ball; and (2) a groove extending circumferentially around the race producing a thin wall portion which permits the opposed side portions to flex relative to the ball for maximizing the physical contact between the inner surface of the race and the spherical outer surface of the ball.
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
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.
Solar proton exposure of an ICRU sphere within a complex structure Part I: Combinatorial geometry.
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
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.
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
Compound catadioptric telescopes with all spherical surfaces.
Sigler, R D
1978-05-15
Catadioptric, all spherical Cassegrainian and Gregorian telescopes with one and two full aperture corrector lenses are investigated. Appropriate closed form third-order aberration equations are presented, and a variety of aplanatic and anastigmatic solutions are indicated. PMID:20198015
FY 2005 Miniature Spherical Retroreflectors Final Report
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.
Sphericity determination using resonant ultrasound spectroscopy
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.
Sphericity determination using resonant ultrasound spectroscopy
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.
FY 2006 Miniature Spherical Retroreflectors Final Report
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.
Vacuum static non-spherical GR equations
NASA Astrophysics Data System (ADS)
Karbanovski, V. V.; Beloushko, K. E.; Markov, V. N.; Kairov, T. V.; Melehina, O. V.
2015-11-01
The vacuum static non-spherical equations are considered. The new solutions, which not contain in class of the Schwarzschild-like metrics and also its generalization are obtain. The perspectives for further investigations are discussed.
Feasibility study for the Spherical Torus Experiment
Lazarus, E.A.; Attenberger, S.E.; Baylor, L.R.; Borowski, S.K.; Brown, R.L.; Carreras, B.A.; Charlton, L.A.; Chipley, K.K.; Dalton, G.R.; Fowler, R.H.
1985-10-01
The design of the Spherical Torus Experiment (STX) is discussed. The physics of the plasma are given in a magnetohydrodynamic model. The structural aspects and instrumentation of the device are described. 19 refs., 103 figs. (WRF)
Compound catadioptric telescopes with all spherical surfaces.
Sigler, R D
1978-05-15
Catadioptric, all spherical Cassegrainian and Gregorian telescopes with one and two full aperture corrector lenses are investigated. Appropriate closed form third-order aberration equations are presented, and a variety of aplanatic and anastigmatic solutions are indicated.
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
Geometry of the human erythrocyte. I. Effect of albumin on cell geometry.
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
Surface thermodynamics of planar, cylindrical, and spherical vapour-liquid interfaces of water.
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
Surface thermodynamics of planar, cylindrical, and spherical vapour-liquid interfaces of water
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
PREPARATION OF SPHERICAL URANIUM DIOXIDE PARTICLES
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)
Exact spherical solutions in Einsteinian gravitostatics
NASA Astrophysics Data System (ADS)
Ionescu-Pallas, Nicolae
The author found a new solution of the Einstein's field equations with nonvanishing cosmological constant, corresponding to a Spherical source of Radius R. The solution imply 2 Poisson-type equations and the solution is expressed in terms of the total energy of the Spherical source. Outside the source the found solution acquires the known form. The author establishes a direct connection between Einstein's gravitostatics and Newtonian one.
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.
Investigating Fractal Geometry Using LOGO.
ERIC Educational Resources Information Center
Thomas, David A.
1989-01-01
Discusses dimensionality in Euclidean geometry. Presents methods to produce fractals using LOGO. Uses the idea of self-similarity. Included are program listings and suggested extension activities. (MVL)
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.
Spherical-shell boundaries for two-dimensional compressible convection in a star
NASA Astrophysics Data System (ADS)
Pratt, J.; Baraffe, I.; Goffrey, T.; Geroux, C.; Viallet, M.; Folini, D.; Constantino, T.; Popov, M.; Walder, R.
2016-10-01
Context. Studies of stellar convection typically use a spherical-shell geometry. The radial extent of the shell and the boundary conditions applied are based on the model of the star investigated. We study the impact of different two-dimensional spherical shells on compressible convection. Realistic profiles for density and temperature from an established one-dimensional stellar evolution code are used to produce a model of a large stellar convection zone representative of a young low-mass star, like our sun at 106 years of age. Aims: We analyze how the radial extent of the spherical shell changes the convective dynamics that result in the deep interior of the young sun model, far from the surface. In the near-surface layers, simple small-scale convection develops from the profiles of temperature and density. A central radiative zone below the convection zone provides a lower boundary on the convection zone. The inclusion of either of these physically distinct layers in the spherical shell can potentially affect the characteristics of deep convection. Methods: We perform hydrodynamic implicit large eddy simulations of compressible convection using the MUltidimensional Stellar Implicit Code (MUSIC). Because MUSIC has been designed to use realistic stellar models produced from one-dimensional stellar evolution calculations, MUSIC simulations are capable of seamlessly modeling a whole star. Simulations in two-dimensional spherical shells that have different radial extents are performed over tens or even hundreds of convective turnover times, permitting the collection of well-converged statistics. Results: To measure the impact of the spherical-shell geometry and our treatment of boundaries, we evaluate basic statistics of the convective turnover time, the convective velocity, and the overshooting layer. These quantities are selected for their relevance to one-dimensional stellar evolution calculations, so that our results are focused toward studies exploiting the so
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.
GPS: Geometry, Probability, and Statistics
ERIC Educational Resources Information Center
Field, Mike
2012-01-01
It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…
Linguistic geometry for autonomous navigation
Stilman, B.
1995-09-01
To discover the inner properties of human expert heuristics, which were successful in a certain class of complex control systems, we develop a formal theory, the Linguistic Geometry. This paper reports two examples of application of Linguistic Geometry to autonomous navigation of aerospace vehicles that demonstrate dramatic search reduction.
Competitive interaction between two different spherical sinks.
McDonald, Nyrée; Strieder, William
2004-10-22
Competitive interactions within diverse mixed populations of chemically active sites are prevalent throughout nature, science, and engineering. Their effects are readily seen in the distribution of dead and surviving aerobic cells within a thick biofilm and particle shape changes during the growth and coarsening of crystals. Even in the most dilute case, competition for a reactant requires at least two spheres/cells, and the solution of the two-spherical sink problem is of interest for several reasons. The solution accurately describes lower cell concentration behavior (10(8) cells/l), and like the Smoluchowski diffusion-reaction treatment for a single sphere, the analysis is extremely helpful in understanding the fundamental phenomena of the effect on the first spherical sink of the presence of a second different spherical sink. In addition these exact solutions are required for the systematic extension to higher density behavior by rigorous expansions in the spherical sink densities. The method of the twin spherical expansion is used with a formal matrix elimination scheme to generate an exact solution for two distinct spherical sinks of differing sizes and kinetics. The two sinks exist in a medium, which supplies a reactant to the sinks via Fickian diffusion. The two sinks compete for the same reactant with different first-order reactions occurring at the surface of each sink. Earlier work focused on two spherical sinks of the same size with identical surface reaction kinetics. This work has been advanced to allow for diversity in the theory of cellular or reactive sink competition. A number of interesting higher order interactive phenomena are observed in this paper when the different reactive sinks are in close proximity. (c) 2004 American Institute of Physics.
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.
Zonal spherical aberration correction utilizing axial electrodes
NASA Astrophysics Data System (ADS)
Chao, Liang C.
2005-01-01
Spherical aberration is important in focused ion beam applications where large aperture angles are needed to obtain high beam currents because it results in large tails on the current density distribution. Merwe has shown that for coaxial lenses, negative spherical aberration can be found for rays pass through zonal regions. Merwe"s calculation is valid only for periodic or quasi-periodic lenses and requires a constant axial potential distribution. We have calculated zonal focusing properties of lenses with axial electrodes using nine-point finite difference method and direct ray tracing. Our calculation results indicate that an axial electrode protruding partially into the lens can correct the spherical aberration. When a three-element electrostatic lens is operated at deceleration mode, the introduction of an axial electrode creates zonal regions where the spherical aberration is negative. At deceleration mode, the induced surface charges on the axial electrode have an opposite sign relative to the primary beam. This is in agreement with our previous findings on the study of the correction of spherical aberration utilizing space charges. Same phenomenon was found when an axial electrode is used in conjunction with a cathode lens.
Role of target geometry in phagocytosis
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
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.
Lopes, Daniel Simões; Neptune, Richard R; Gonçalves, Artur A; Ambrósio, Jorge A; Silva, Miguel T
2015-11-01
In this work, MacConaill's classification that the articular surface of the femoral head is better represented by ovoidal shapes rather than purely spherical shapes is computationally tested. To test MacConaill's classification, a surface fitting framework was developed to fit spheres, ellipsoids, superellipsoids, ovoids, and superovoids to computed tomography (CT) data of the femoral proximal epiphysis. The framework includes several image processing and computational geometry techniques, such as active contour segmentation and mesh smoothing, where implicit surface fitting is performed with genetic algorithms. By comparing the surface fitting error statistics, the results indicate that (super)ovoids fit femoral articular surfaces better than spherical or (super)ellipsoidal shapes.
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
The ESSA solution. [Electronic Switching Spherical Array
NASA Technical Reports Server (NTRS)
Hockensmith, R. P.; Stockton, R.
1977-01-01
ESSA (Electronic Switching Spherical Array) is a fixed truncated spherical antenna with its elements over the complete surface, conceived to satisfy many future antenna system requirements. Constant gain and beam shape throughout large volumetric coverage regions are the principle characteristics. In the present paper, the two existing types of ESSA are discussed. ESSA I is a simple nonphase correcting aperture approach characterized by light weight, low dc power consumption, gain between +7 and +14 dB, and 90% spherical coverage. ESSA II is a phase corrected aperture which would have very low sidelobe levels and improved gain over ESSA I (12 to 22 dB), but would be heavier and require more dc power.
Thermal Fluid Multiphysics Optimization of Spherical Tokamak
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.
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.
Design and implementation of spherical ultrasonic motor.
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.
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.
Background reduction of a spherical gaseous detector
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.
A spherical Taylor-Couette dynamo
NASA Astrophysics Data System (ADS)
Marcotte, Florence; Gissinger, Christophe
2016-04-01
We present a new scenario for magnetic field amplification in the planetary interiors where an electrically conducting fluid is confined in a differentially rotating, spherical shell (spherical Couette flow) with thin aspect-ratio. When the angular momentum sufficiently decreases outwards, a primary hydrodynamic instability is widely known to develop in the equatorial region, characterized by pairs of counter-rotating, axisymmetric toroidal vortices (Taylor vortices) similar to those observed in cylindrical Couette flow. We characterize the subcritical dynamo bifurcation due to this spherical Taylor-Couette flow and study its evolution as the flow successively breaks into wavy and turbulent Taylor vortices for increasing Reynolds number. We show that the critical magnetic Reynolds number seems to reach a constant value as the Reynolds number is gradually increased. The role of global rotation on the dynamo threshold and the implications for planetary interiors are finally discussed.
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.
Spherical aberration in electrically thin flat lenses.
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
The spherically symmetric Standard Model with gravity
NASA Astrophysics Data System (ADS)
Balasin, H.; Böhmer, C. G.; Grumiller, D.
2005-08-01
Spherical reduction of generic four-dimensional theories is revisited. Three different notions of "spherical symmetry" are defined. The following sectors are investigated: Einstein-Cartan theory, spinors, (non-)abelian gauge fields and scalar fields. In each sector a different formalism seems to be most convenient: the Cartan formulation of gravity works best in the purely gravitational sector, the Einstein formulation is convenient for the Yang-Mills sector and for reducing scalar fields, and the Newman-Penrose formalism seems to be the most transparent one in the fermionic sector. Combining them the spherically reduced Standard Model of particle physics together with the usually omitted gravity part can be presented as a two-dimensional (dilaton gravity) theory.
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.
Quantum Consequences of Parameterizing Geometry
NASA Astrophysics Data System (ADS)
Wanas, M. I.
2002-12-01
The marriage between geometrization and quantization is not successful, so far. It is well known that quantization of gravity , using known quantization schemes, is not satisfactory. It may be of interest to look for another approach to this problem. Recently, it is shown that geometries with torsion admit quantum paths. Such geometries should be parameterizied in order to preserve the quantum properties appeared in the paths. The present work explores the consequences of parameterizing such geometry. It is shown that quantum properties, appeared in the path equations, are transferred to other geometric entities.
NASA Astrophysics Data System (ADS)
Belogurov, S.; Berchun, Yu; Chernogorov, A.; Malzacher, P.; Ovcharenko, E.; Semennikov, A.
2011-12-01
Due to conceptual difference between geometry descriptions in Computer-Aided Design (CAD) systems and particle transport Monte Carlo (MC) codes direct conversion of detector geometry in either direction is not feasible. An original set of tools has been developed for building a GEANT4/ROOT compatible geometry in the CATIA CAD system and exchanging it with mentioned MC packages using GDML file format. A Special structure of a CATIA product tree, a wide range of primitives, different types of multiple volume instantiation, and supporting macros have been implemented.
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
Molecular dynamics simulation study of friction force and torque on a rough spherical particle.
Kohale, Swapnil C; Khare, Rajesh
2010-06-21
Recent developments in techniques of micro- and nanofluidics have led to an increased interest in nanoscale hydrodynamics in confined geometries. In our previous study [S. C. Kohale and R. Khare, J. Chem. Phys. 129, 164706 (2008)], we analyzed the friction force experienced by a smooth spherical particle that is translating in a fluid confined between parallel plates. The magnitude of three effects--velocity slip at particle surface, the presence of confining surfaces, and the cooperative hydrodynamic interactions between periodic images of the moving particle--that determine the friction force was quantified in that work using molecular dynamics simulations. In this work, we have studied the motion of a rough spherical particle in a confined geometry. Specifically, the friction force experienced by a translating particle and the torque experienced by a rotating particle are studied using molecular dynamics simulations. Our results demonstrate that the surface roughness of the particle significantly reduces the slip at the particle surface, thus leading to higher values of the friction force and hence a better agreement with the continuum predictions. The particle size dependence of the friction force and the torque values is shown to be consistent with the expectations from the continuum theory. As was observed for the smooth sphere, the cooperative hydrodynamic interactions between the images of the sphere have a significant effect on the value of the friction force experienced by the translating sphere. On the other hand, the torque experienced by a spherical particle that is rotating at the channel center is insensitive to this effect.
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.
Rayleigh-Taylor instability experiments in a cylindrically convergent geometry
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.
Toroidal membrane vesicles in spherical confinement.
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.
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.
Toroidal membrane vesicles in spherical confinement
NASA Astrophysics Data System (ADS)
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.
Mass transport in annular spherical system
NASA Astrophysics Data System (ADS)
Bauer, Helmut F.
The mass transport between two concentric spheres with inlet and outlet at the poles was determined for ideal liquid flow (plug flow) and laminar flow for constant concentration at the spherical walls and constant concentration at the inlet. Velocity distribution and local concentration profiles were determined analytically for various widths of the annular spherical conduit and various diffusive flow parameters. It is found that with the increase of this parameter, the decay becomes quite rapid and that the same effect occurs for increasing diameter ratio of the spheres. This configuration may possibly be used as a basic element of an artificial kidney.
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.
Instability of supersymmetric microstate geometries
NASA Astrophysics Data System (ADS)
Eperon, Felicity C.; Reall, Harvey S.; Santos, Jorge E.
2016-10-01
We investigate the classical stability of supersymmetric, asymptotically flat, microstate geometries with five non-compact dimensions. Such geometries admit an "evanescent ergosurface": a timelike hypersurface of infinite redshift. On such a surface, there are null geodesics with zero energy relative to infinity. These geodesics are stably trapped in the potential well near the ergosurface. We present a heuristic argument indicating that this feature is likely to lead to a nonlinear instability of these solutions. We argue that the precursor of such an instability can be seen in the behaviour of linear perturbations: nonlinear stability would require that all linear perturbations decay sufficiently rapidly but the stable trapping implies that some linear perturbation decay very slowly. We study this in detail for the most symmetric microstate geometries. By constructing quasinormal modes of these geometries we show that generic linear perturbations decay slower than any inverse power of time.
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.
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
Thompson, Kevin P
2009-05-01
Building off an earlier work on multinodal third-order aberrations [J. Opt. Soc. Am. A22, 1389 (2005)], this is the first in a series of papers that derives and illustrates the characteristic multinodal geometry for each of the fifth-order aberrations. Part I (as this paper will be referred to) will present the spherical aberration family: specifically, W(060), W(240M) and W(242), and W(080) (fifth-order spherical, oblique spherical, and seventh-order spherical). Nodal aberration theory is proving to be very effective as both an optical design tool for fully unobscured off-axis telescopes and as an analysis method, particularly in the context of the response of any imaging optical systems to misalignment. It is important to recognize that this multinodal approach to aberration theory is not restricted to small perturbations. The remaining papers in this series will result in a complete presentation of the intrinsic characteristic multinodal properties of each of the fifth-order aberrations. As such, this series provides a definitive theory of the optical aberrations of (nonanamorphic) imaging systems with a circular aperture stop. PMID:19412225
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.
METHOD OF MAKING SPHERICAL ACTINIDE CARBIDE
White, G.D.; O'Rourke, D.C.
1962-12-25
This patent describes a method of making uniform, spherical, nonpyrophoric UC. UO/sub 2/ and carbon are mixed in stoichiometric proportions and passed through a plasma flame of inert gas at 10,000 to 13,000 deg C. (AEC)
Spherical Model of Interests in Croatia
ERIC Educational Resources Information Center
Sverko, Iva
2008-01-01
In order to analyze the validity of spherical model of interests in Croatia, three Croatian samples of primary school students (N = 437), secondary school students (N = 540) and university students (N = 630) were administered a translated version of the Personal Globe Inventory (PGI, [Tracey, T.J.G. (2002). Personal Globe Inventory: Measurement of…
Supersymmetric extension of the quantum spherical model
NASA Astrophysics Data System (ADS)
Gomes, Pedro R. S.; Bienzobaz, P. F.; Gomes, M.
2012-06-01
In this work, we present a supersymmetric extension of the quantum spherical model, both in components and also in the superspace formalisms. We find the solution for short- and long-range interactions through the imaginary time formalism path integral approach. The existence of critical points (classical and quantum) is analyzed and the corresponding critical dimensions are determined.
Spherical fields as nonparaxial accelerating waves.
Alonso, Miguel A; Bandres, Miguel A
2012-12-15
We introduce nonparaxial spatially accelerating waves whose two-dimensional transverse profiles propagate along semicircular trajectories while approximately preserving their shape. We derive these waves by considering imaginary displacements on spherical fields, leading to simple closed-form expressions. The structure of these waves also allows the closed-form description of pulses.
Spherical torus, compact fusion at low field
Peng, Y.K.M.
1985-02-01
A spherical torus is obtained by retaining only the indispensable components on the inboard side of a tokamak plasma, such as a cooled, normal conductor that carries current to produce a toroidal magnetic field. The resulting device features an exceptionally small aspect ratio (ranging from below 2 to about 1.3), a naturally elongated D-shaped plasma cross section, and ramp-up of the plasma current primarily by noninductive means. As a result of the favorable dependence of the tokamak plasma behavior to decreasing aspect ratio, a spherical torus is projected to have small size, high beta, and modest field. Assuming Mirnov confinement scaling, an ignition spherical torus at a field of 2 T features a major radius of 1.5 m, a minor radius of 1.0 m, a plasma current of 14 MA, comparable toroidal and poloidal field coil currents, an average beta of 24%, and a fusion power of 50 MW. At 2 T, a Q = 1 spherical torus will have a major radius of 0.8 m, a minor radius of 0.5 m, and a fusion power of a few megawatts.
Fast discharge in a spherical cavity
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.
An Engineering Evaluation of Spherical Resorcinol Formaldehyde Resin
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
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.
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.
Spherically symmetric self-dual Yang-Mills instantons on curved backgrounds in all even dimensions
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.
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.
Ghosh, Aurobrata; Tsigaridas, Elias; Mourrain, Bernard; Deriche, Rachid
2013-07-01
Antipodally symmetric spherical functions play a pivotal role in diffusion MRI in representing sub-voxel-resolution microstructural information of the underlying tissue. This information is described by the geometry of the spherical function. In this paper we propose a method to automatically compute all the extrema of a spherical function. We then classify the extrema as maxima, minima and saddle-points to identify the maxima. We take advantage of the fact that a spherical function can be described equivalently in the spherical harmonic (SH) basis, in the symmetric tensor (ST) basis constrained to the sphere, and in the homogeneous polynomial (HP) basis constrained to the sphere. We extract the extrema of the spherical function by computing the stationary points of its constrained HP representation. Instead of using traditional optimization approaches, which are inherently local and require exhaustive search or re-initializations to locate multiple extrema, we use a novel polynomial system solver which analytically brackets all the extrema and refines them numerically, thus missing none and achieving high precision. To illustrate our approach we consider the Orientation Distribution Function (ODF). In diffusion MRI the ODF is a spherical function which represents a state-of-the-art reconstruction algorithm whose maxima are aligned with the dominant fiber bundles. It is, therefore, vital to correctly compute these maxima to detect the fiber bundle directions. To demonstrate the potential of the proposed polynomial approach we compute the extrema of the ODF to extract all its maxima. This polynomial approach is, however, not dependent on the ODF and the framework presented in this paper can be applied to any spherical function described in either the SH basis, ST basis or the HP basis.
Interfacial geometry and D-variation effects in two-phase systems. [binary alloys
NASA Technical Reports Server (NTRS)
Tenney, D. R.; Unnam, J.
1979-01-01
Numerical solutions of the governing diffusion equation for two-phase concentration dependent diffusion coefficients are examined. Solutions were also calculated for planar, cylindrical, and spherical geometries to compare the effect of interface geometries with those caused by concentration-dependent diffusion coefficients, and two methods of averaging D were considered to determine the best averaging method for different types of D-variations. The effects of interface-location criteria on mass conservation and convergence of interface location, diffusion coefficient variation in the alpha and beta-phases of a two-phase binary alloy system, effect of D(alpha) variation in a cylindrical couple on beta-phase thickness, and geometry and D-variation effects on the degree of homogenization were determined. It is concluded that typical D(alpha)-variations can have a greater influence on the kinetics of interdiffusion than the geometry.
Energy levels of GaAs/AlxGa1-xAs/AlAs spherical quantum dot with an impurity
NASA Astrophysics Data System (ADS)
Boz, Figen Karaca; Nisanci, Beyza; Aktas, Saban; Okan, S. Erol
2016-11-01
We have calculated the energy levels and the radial probability distributions of an electron with an impurity in a spherical quantum dot which is layered as GaAs/AlxGa1-xAs/AlAs. The numerical method used is the fourth-order Runge-Kutta method in the framework of the effective mass approximation. The variation of the energy levels have been calculated as functions of the radius of the GaAs sphere and the thickness of AlxGa1-xAs spherical layer considering effective mass and dielectric constant mismatches. The results have presented the importance of the geometry on the electronic properties of the spherical GaAs/AlxGa1-xAs/AlAs quantum dot.
NASA Astrophysics Data System (ADS)
Kang, Songgao; Lu, Kaichang; Zhu, Yafei
1991-12-01
The relationship between aberration and the aberration coefficient is the basic formulation in the field of aberration theory. The Seidel's formulations can only be used in the case of low performance (small aperture and small field), so that a set of correct relations between spherical aberration (SA) and spherical aberration coefficient (SAC) must be derived for the application of large aperture and small viewing field.
Arnida; Janát-Amsbury, M.M.; Ray, A.; Peterson, C. M.; Ghandehari, H.
2010-01-01
Spherical and rod-shaped gold nanoparticles with surface poly (ethylene glycol) (PEG) chains were characterized for size, shape, charge, poly dispersity and surface plasmon resonance. The nanoparticles were injected intravenously to 6–8 weeks old female nu/nu mice bearing orthotopic ovarian tumors and their biodistribution in vital organs was compared. Gold nanorods were taken up to a lesser extent by the liver, had longer circulation time in the blood, and higher accumulation in the tumors, compared with their spherical counterparts. The cellular uptake of PEGylated gold nanoparticles by a murine macrophage-like cell line as a function of geometry was examined. Compared to nanospheres, PEGylated gold nanorods were taken up to a lesser extent by macrophages. These studies point to the importance of gold nanoparticle geometry and surface properties on transport across biological barriers. PMID:21093587
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
Impact of contact lens zone geometry and ocular optics on bifocal retinal image quality
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
Do spherical tokamaks have a thermonuclear future?
NASA Astrophysics Data System (ADS)
Mirnov, S. V.
2012-12-01
This work has been initiated by the publication of a review by B.V.Kuteev et al., "Intense Fusion Neutron Sources" [Plasma Physics Reports 36, 281 (2010)]. It is stated that the key thesis of the above review that a spherical tokamak can be recommended for research neutron sources and for demonstration hybrid systems as an alternative to expensive "classical" tokamaks of the JET and ITER type is inconsistent. The analysis of the experimental material obtained during the last 10 years in the course of studies on the existing spherical tokamaks shows that the TIN-ST fusion neutron source spherical tokamak proposed by the authors of the review and intended, according to the authors' opinion, to replace "monsters" in view of its table-top dimensions (2 m3) and laboratory-level energetics cannot be transformed into any noticeable stationary megawatt-power neutron source competing with the existing classical tokamaks (in particular, with JET with its quasi-steady DT fusion power at a level of 5 MW). Namely, the maximum plasma current in the proposed tokamak will be not 3 MA, as the authors suppose erroneously, but, according to the present-day practice of spherical tokamaks, within 0.6-0.7 MA, which will lead to a reduction on the neutron flux by two to three orders of magnitude from the expected 5 MW. The possibility of the maintenance of the stationary process itself even in such a "weakened" spherical tokamak is very doubtful. The experience of the largest existing devices of this type (such as NSTX and MAST) has shown that they are incapable of operating even in a quasi-steady operating mode, because the discharge in them is spontaneously interrupted about 1 s after the beginning of the current pulse, although its expected duration is of up to 5 s. The nature of this phenomenon is the subject of further study of the physics of spherical tokamaks. This work deals with a critical analysis of the available experimental data concerning such tokamaks and a discussion of
Earthquake cycles in complex geometries
NASA Astrophysics Data System (ADS)
Romanet, Pierre; Bhat, Harsha; Madariaga, Raul
2016-04-01
Our understanding of earthquake cycles, from a modelling perspective, comes mainly from theoretical, and numerical, work on a single straight fault. However, natural fault systems are geometrically complex. Modelling complex fault geometry (bends, kinks and multiple faults) is in itself a challenge as it is computationally intensive. To overcome this difficulty, we appeal to the Fast Multipole Method which was developed in the context of modelling N-body problems. This method is then used to model the quasi-dynamic response of multiple faults, with complex geometries, that are governed by rate and state friction laws. Our preliminary findings tell us that when stress interaction between faults, due to complex geometry, is accounted then even strongly rate-weakening faults (a-b)<0 show a complex spectrum of slow slip and dynamic ruptures.
Conventionalism and integrable Weyl geometry
NASA Astrophysics Data System (ADS)
Pucheu, M. L.
2015-03-01
Since the appearance of Einstein's general relativity, gravitation has been associated to the space-time curvature. This theory introduced a geometrodynamic language which became a convenient tool to predict matter behaviour. However, the properties of space-time itself cannot be measurable by experiments. Taking Poincaré idea that the geometry of space-time is merely a convention, we show that the general theory of relativity can be completely reformulated in a more general setting, a generalization of Riemannian geometry, namely, the Weyl integrable geometry. The choice of this new mathematical language implies, among other things, that the path of particles and light rays should now correspond to Weylian geodesies. Such modification in the dynamic of bodies brings a new perception of physical phenomena that we will explore.
Frustrated Order on Extrinsic Geometries
Mbanga, Badel L.; Grason, Gregory M.; Santangelo, Christian D.
2012-01-03
We study, numerically and theoretically, defects in an anisotropic liquid that couple to the extrinsic geometry of a surface. Though the intrinsic geometry tends to confine topological defects to regions of large Gaussian curvature, extrinsic couplings tend to orient the order along the local direction of maximum or minimum bending. This additional frustration is generically unavoidable, and leads to complex ground-state thermodynamics. Using the catenoid as a prototype, we show, in contradistinction to the well-known effects of intrinsic geometry, that extrinsic curvature expels disclinations from the region of maximum curvature above a critical coupling threshold. On catenoids lacking an “inside-outside” symmetry, defects are expelled altogether above a critical neck size.
Quantum geometry and gravitational entropy
Simon, Joan; Balasubramanian, Vijay; Czech, Bart Iomiej; Larjo, Klaus; Marolf, Donald; Simon, Joan
2007-05-29
Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of asymptotically AdS_5 x S5 universes. In this sector we devise a"coarse-grained metric operator" whose eigenstates are well described by a single spacetime topology and geometry. We show that such half-BPS universes have a non-vanishing entropy if and only if the metric is singular, and that the entropy arises from coarse-graining the geometry. Finally, we use our entropy formula to find the most entropic spacetimes with fixed asymptotic moments beyond the global charges.
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.
Contact condition for the density profiles in spherical and cylindrical double layers
NASA Astrophysics Data System (ADS)
Silvestre-Alcantara, Whasington; Henderson, Douglas; Bari Bhuiyan, Lutful
2015-11-01
Exact sum rules involving the contact values of the density profiles and bulk osmotic pressure in spherical and cylindrical electric double layers are formulated. When the radius of curvature in these systems tends to infinity, the contact conditions reduce to the well-known contact condition in planar double layer due to Henderson, Blum, and Lebowitz (1979). However, unlike the latter relation, the contact conditions in the non-planar geometries are non-local, and require for their implementation full knowledge of the electrode-ion singlet distribution functions.
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.
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.
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.
Preparation and Evaluation of Two Apatites with Spherical Nanocrystal Morphology.
Zhang, Yali; Li, Qihong; Li, Xiaojie; Li, Yong; Wang, Chunhui; Zhao, Yantao; Song, Yingliang; Liu, Yanpu
2016-03-01
Spherical nanocrystal of apatite has been proved to be beneficial for osteoblast growth. Two apatites with spherical nanocrystal morphology were prepared in this study by chemical wet method and further sintering process. SEM exhibited that both apatites had spherical nanocrystal morphology. The crystal morphology and size was approaching to each other. XRD showed the apatites separately were hydroxyapatite and tricalcium phosphate phases. The cellular biocompatibility was evaluated by osteoblasts for these two spherical nanocrstal apatites. The MTT result indicated a higher cell proliferation rate for spherical tricalcium phosphate group. The ALP activity assay also strongly favored the tricalcium phosphate group. RT-PCR results indicated that Collagen I had a higher transcription level on the spherical tricalcium phosphate group. SEM results showed robust cell growth on the materials. It was concluded that the spherical nanophase tricalcium phosphate was superior to the cellular biocompatibility of spherical nanophase hydroxyapatite and the results were helpful in the manufacture of more suitable tissue engineering scaffolds.
Acoustic waves of different geometry in polydisperse bubble liquids: Theory and experiment
NASA Astrophysics Data System (ADS)
Nigmatulin, R. I.; Gubaidullin, D. A.; Fedorov, Yu. V.
2013-06-01
A mathematical model that determines the propagation of acoustic waves of different geometry in two-fraction mixtures of liquids with polydispersed gas bubbles of various compositions is presented. A unique dispersion relationship, which takes into account the propagation of the plane, spherical, and cylindrical perturbations in these mixtures, is derived. It is shown that the theoretical curves of the phase velocity and the damping factor agree well with the experimental data involving the resonant frequency range.
Confined H(1s) and H(2p) under different geometries
NASA Astrophysics Data System (ADS)
Micca Longo, G.; Longo, S.; Giordano, D.
2015-08-01
In this paper the diffusion Monte Carlo method is applied to the confined hydrogen atom with different confinement geometries. This approach is validated using the much studied spherical and cylindrical confinements and then applied to cubical and squared ones, for which data are not available, as new applications of the method relevant to solid state physics. The energy eigenvalues of the ground state and one low-lying excited state are reported as a function of the characteristic confinement length.
RSRM Propellant Grain Geometry Modification
NASA Technical Reports Server (NTRS)
Schorr, Andrew A.; Endicott, Joni B.; McCool, Alex (Technical Monitor)
2000-01-01
This document is composed of viewgraphs about the RSRM propellant grain geometry modification project, which hopes to improve personnel and system safety by modifying propellant grain geometry to improve structural factors of safety. Using techniques such as Finite Element Analysis to determine blend radii required to reduce localized stresses, and ballistic predictions to ensure that the ballistics, ignition transient and Block Model have not been adversely affected, the project hopes to build and test FSM-10 with a new design, and determine flight effectivity pending successful test evaluation.
Geometry, topology, and string theory
Varadarajan, Uday
2003-07-10
A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.
Geometry of generalized depolarizing channels
Burrell, Christian K.
2009-10-15
A generalized depolarizing channel acts on an N-dimensional quantum system to compress the 'Bloch ball' in N{sup 2}-1 directions; it has a corresponding compression vector. We investigate the geometry of these compression vectors and prove a conjecture of Dixit and Sudarshan [Phys. Rev. A 78, 032308 (2008)], namely, that when N=2{sup d} (i.e., the system consists of d qubits), and we work in the Pauli basis then the set of all compression vectors forms a simplex. We extend this result by investigating the geometry in other bases; in particular we find precisely when the set of all compression vectors forms a simplex.
Multiple Weather Regimes and Baroclinically Forced Spherical Resonance.
NASA Astrophysics Data System (ADS)
Yang, Shuting; Reinhold, Brian; Källén, Erland
1997-06-01
Systematically recurrent, geographically fixed weather regimes forced by a single isolated mountain in a two-layer, high-resolution, quasigeostrophic model modified for the sphere are found to be robust phenomena. While the climatological stationary wave is often confined to (or has maximum amplitude in) the region just downstream of the orography, giving the appearance of a wave train propagating into the Tropics, the regional maximum centers of low-frequency variance appear around the hemisphere, giving the appearance of zonal resonance or some type of zonally confined propagation. This result is not anticipated in light of Rossby wave dispersion theory on the sphere. On the other hand, baroclinic disturbances developing on a meridional temperature gradient of finite extent force subtropical and polar easterlies as well as a sharpened midlatitude westerly jet, which provides a zonal waveguide (by refraction and/or reflection) for the Rossby waves. These conditions are favorable for the establishment of multiple weather regimes. The baroclinicity of the atmosphere is then continuously forcing a mean state that favors forced zonal propagation, counteracting the meridional dispersion generated by the spherical geometry alone. These ideas suggest that the multiple-equilibria theories may be more applicable to the atmosphere than originally suggested by linear dispersion theory on the sphere. It may also help explain why channel models work as well as they do even for the largest scales.
Spherical Harmonic Solutions to the 3D Kobayashi Benchmark Suite
Brown, P.N.; Chang, B.; Hanebutte, U.R.
1999-12-29
Spherical harmonic solutions of order 5, 9 and 21 on spatial grids containing up to 3.3 million cells are presented for the Kobayashi benchmark suite. This suite of three problems with simple geometry of pure absorber with large void region was proposed by Professor Kobayashi at an OECD/NEA meeting in 1996. Each of the three problems contains a source, a void and a shield region. Problem 1 can best be described as a box in a box problem, where a source region is surrounded by a square void region which itself is embedded in a square shield region. Problems 2 and 3 represent a shield with a void duct. Problem 2 having a straight and problem 3 a dog leg shaped duct. A pure absorber and a 50% scattering case are considered for each of the three problems. The solutions have been obtained with Ardra, a scalable, parallel neutron transport code developed at Lawrence Livermore National Laboratory (LLNL). The Ardra code takes advantage of a two-level parallelization strategy, which combines message passing between processing nodes and thread based parallelism amongst processors on each node. All calculations were performed on the IBM ASCI Blue-Pacific computer at LLNL.
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.
BIPOLAR MAGNETIC SPOTS FROM DYNAMOS IN STRATIFIED SPHERICAL SHELL TURBULENCE
Jabbari, Sarah; Brandenburg, Axel; Kleeorin, Nathan; Mitra, Dhrubaditya; Rogachevskii, Igor
2015-06-01
Recent work by Mitra et al. (2014) has shown that in strongly stratified forced two-layer turbulence with helicity and corresponding large-scale dynamo action in the lower layer, and nonhelical turbulence in the upper, a magnetic field occurs in the upper layer in the form of sharply bounded bipolar magnetic spots. Here we extend this model to spherical wedge geometry covering the northern hemisphere up to 75° latitude and an azimuthal extent of 180°. The kinetic helicity and therefore also the large-scale magnetic field are strongest at low latitudes. For moderately strong stratification, several bipolar spots form that eventually fill the full longitudinal extent. At early times, the polarity of spots reflects the orientation of the underlying azimuthal field, as expected from Parker’s Ω-shaped flux loops. At late times their tilt changes such that there is a radial field of opposite orientation at different latitudes separated by about 10°. Our model demonstrates the spontaneous formation of spots of sizes much larger than the pressure scale height. Their tendency to produce filling factors close to unity is argued to be reminiscent of highly active stars. We confirm that strong stratification and strong scale separation are essential ingredients behind magnetic spot formation, which appears to be associated with downflows at larger depths.
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.
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.
Electromagnetic signatures of thin accretion disks in wormhole geometries
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.
Semiautomated inspection of superfinished spherical surfaces
Klingsporn, P.E.
1980-01-01
Lapping and polishing techniques are used at Bendix Kansas City to fabricate superfinished spherical metal surfaces. A laser-light reflection method has been developed for semiautomated inspection of the surfaces. The reflected and diffracted light intensity distributions from the spherical surface are measured with an array of photodetectors interfaced with a data sampler and a minicomputer programmed to distinguish between pits and scratches. For automated measurement, standard deviations for scratch width and depth are 3 and 0.3 ..mu..m (120 and 12 ..mu..in.), respectively, and for pit diameter and depth are 5.8 and 0.9 ..mu..m (230 and 36 ..mu..in.), respectively. A laser interferometric displacement measuring system interfaced with the computer is used for automated measurement of surface waviness.
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.
Limiting Temperatures of Spherical Shock Wave Implosion.
Liverts, Michael; Apazidis, Nicholas
2016-01-01
Spherical shock wave implosion in argon is studied both theoretically and experimentally. It is shown that as the strength of the converging shock increases the nonideal gas effects become dominant and govern the evolution of thermal and transport gas properties limiting the shock acceleration, lowering the gas adiabatic index and the achievable energy density at the focus. Accounting for multiple-level ionization, excitation, Coulomb interaction and radiation effects, the limiting equilibrium temperatures to be achieved during the shock implosion are estimated. Focal temperatures of the order of 30 000 K are measured in experiments where converging spherical shock waves are created using a conventional gas-dynamic shock tube facility. PMID:26799021
Testing the spherical evolution of cosmic voids
NASA Astrophysics Data System (ADS)
Demchenko, Vasiliy; Cai, Yan-Chuan; Heymans, Catherine; Peacock, John A.
2016-11-01
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-1 Mpc, 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.
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.
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.
Imaging with Spherically Bent Crystals or Reflectors
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.
Domínguez, Jorge Bouza; Bérubé-Lauzière, Yves
2011-01-01
We introduce a system of coupled time-dependent parabolic simplified spherical harmonic equations to model the propagation of both excitation and fluorescence light in biological tissues. We resort to a finite element approach to obtain the time-dependent profile of the excitation and the fluorescence light fields in the medium. We present results for cases involving two geometries in three-dimensions: a homogeneous cylinder with an embedded fluorescent inclusion and a realistically-shaped rodent with an embedded inclusion alike an organ filled with a fluorescent probe. For the cylindrical geometry, we show the differences in the time-dependent fluorescence response for a point-like, a spherical, and a spherically Gaussian distributed fluorescent inclusion. From our results, we conclude that the model is able to describe the time-dependent excitation and fluorescent light transfer in small geometries with high absorption coefficients and in nondiffusive domains, as may be found in small animal diffuse optical tomography (DOT) and fluorescence DOT imaging. PMID:21483606
Precursory singularities in spherical gravitational collapse
NASA Astrophysics Data System (ADS)
Lake, Kayll
1992-05-01
General conditions are developed for the formation of naked precursory ('shell-focusing') singularities in spherical gravitational collapse. These singularities owe their nakedness to the fact that the gravitational potential fails to be single valued prior to the onset of a true gravitational singularity. It is argued that they do not violate the spirit of cosmic censorship. Rather, they may well be an essentially generic feature of relativistic gravitational collapse.
Thermal deformations of a glass spherical satellite
NASA Astrophysics Data System (ADS)
Vasiliev, V. P.; Nenadovich, V. D.; Murashkin, V. V.; Sokolov, A. L.
2016-09-01
The effect of the kind of the reflecting coating of a glass spherical satellite on thermal deformations caused by the solar irradiation is considered. Two types of coating deposited on one of the hemispheres are considered: aluminum with a protective layer of bakelite varnish and interference dielectric coating for two orientations of the satellite orbit. Structures of a multilayer dielectric coating and technologies of its deposition are described.
Fast ion orbits in spherical tokamaks
Solano, E.R.
1995-07-20
In a spherical tokamak, the 1/R variation of the toroidal field is extreme, and for a given value of the safety factor a relatively low average toroidal field can be used, together with large plasma current and large plasma minor radius and elongation. The poloidal and toroidal fields are then of similar size. In consequence, the orbits of fast ions depart considerably from the guiding center orbits because of gyromotion in the small magnetic fields in the low field side.
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
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.
Wave equation on spherically symmetric Lorentzian metrics
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.
Spherical Cancer Models in Tumor Biology1
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
Spherical cloaking with homogeneous isotropic multilayered structures
NASA Astrophysics Data System (ADS)
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.
Spherical cloaking with homogeneous isotropic multilayered structures.
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
Modeling of thermal processes in spherical area
NASA Astrophysics Data System (ADS)
Demyanchenko, O.; Lyashenko, V.
2016-10-01
In this paper a mathematical model of the temperature field in spherical area with complex conditions of heat exchange with the environment is considered. The solution of the nonlinear initial boundary value problem is reduced to the solution of the nonlinear integral equation of Fredholm type respect to spatial coordinates and Volterra with the kernel in the form of the Green's function on the time coordinate.
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.
On Recurrence Formulae of Solid Spherical Monogenics
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.
Numerical simulation of spherical plasma focus diode
NASA Astrophysics Data System (ADS)
Jiang, W.; Masugata, K.; Yatsui, K.
1995-06-01
A self-magnetically insulated, three-dimensionally-focused ion-beam diode, spherical plasma focus diode (SPFD), is studied by numerical simulation using a two-dimensional, electromagnetic, relativistic particle-in-cell computer code. The calculated results of the diode impedance, the ion-current efficiency, and the focusing characteristics of the ion beam are presented. These results, except the data of the ion-beam current, are in good agreement with the experimental results.
Low Ekman Number Dynamos in Cartesian Geometry
NASA Astrophysics Data System (ADS)
Stellmach, S.; Hansen, U.
2002-12-01
Fully self consistent 3d dynamo simulations in spherical geometry have become an important part of geomagnetic research during the last years. The parameter range accesible for these models is quite limited and far away from the values estimated for the Earth's core. Especially viscous effects are overestimated by many orders of magnitude in all models published today. In view of these difficulties, we use a plane layer dynamo model which is computationally less demanding to study dynamo processes in the regime of low viscosity. The calculations we present employ Ekman numbers in the range E=10-4-5 x 10-6 without using parameterizations such as hyperdiffusion. Full inertia with Pr=1 is included where Pr denotes the Prandtl number. We find subcritical dynamos which remain stable for two magnetic decay times and an example of an initially stable subcritical dynamo which starts to decay after more than one magnetic diffusion time. For both supercritical and subcritical cases, the force balances are analyzed in detail. We show that at low Ekman number the leading order force balance in our calculations is between Coriolis, buoyancy, pressure and Lorentz forces while both inertial and viscous forces are small in the bulk of the layer. The resulting flow is strongly influenced by the Taylor-Proudman effect and dominated by small scale structures. In the range of investigated Ekman numbers, the dominating length scales decrease with decreasing E. Although Taylor's constraint is not satisfied in the entire domain we find that the spatial mean value of the normalized Taylor integrals decreases with decreasing Ekman number.
Turbulent shear flow in a rapidly rotating spherical annulus
NASA Astrophysics Data System (ADS)
Zimmerman, Daniel S.
This dissertation presents experimental measurements of torque, wall shear stress, pressure, and velocity in the boundary-driven turbulent flow of water between concentric, independently rotating spheres, commonly known as spherical Couette flow. The spheres' radius ratio is 0.35, geometrically similar to that of Earth's core. The measurements are performed at unprecedented Reynolds number for this geometry, as high as fifty-six million. The role of rapid overall rotation on the turbulence is investigated. A number of different turbulent flow states are possible, selected by the Rossby number, a dimensionless measure of the differential rotation. In certain ranges of the Rossby number near state borders, bistable co-existence of states is possible. In these ranges the flow undergoes intermittent transitions between neighboring states. At fixed Rossby number, the flow properties vary with Reynolds number in a way similar to that of other turbulent flows. At most parameters investigated, the large scales of the turbulent flow are characterized by system-wide spatial and temporal correlations that co-exist with intense broadband velocity fluctuations. Some of these wave-like motions are identifiable as inertial modes. All waves are consistent with slowly drifting large scale patterns of vorticity, which include Rossby waves and inertial modes as a subset. The observed waves are generally very energetic, and imply significant inhomogeneity in the turbulent flow. Increasing rapidity of rotation as the Ekman number is lowered intensifies those waves identified as inertial modes with respect to other velocity fluctuations. The turbulent scaling of the torque on inner sphere is a focus of this dissertation. The Rossby-number dependence of the torque is complicated. We normalize the torque at a given Reynolds number in the rotating states by that when the outer sphere is stationary. We find that this normalized quantity can be considered a Rossby-dependent friction factor
Quantum corrected spherical collapse: A phenomenological framework
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.
Nematic order on curved spherical spaces
NASA Astrophysics Data System (ADS)
Fernandez-Nieves, Alberto; Lopez-Leon, Teresa; Devaiah, Sharan; Pairam, Ekapop
2010-03-01
When nematic liquid crystals are confined to spherical shells, complex defect structures emerge. These structures are characterized by a varying number of point defects and disclination lines, depending on the elastic energy of the liquid crystal, the thickness of the shell, and the boundary conditions for the director at the confining spheres. Topology establishes restrictions that must be fulfilled, but it is the energy landscape that ultimately determines the final state of the system. By using double emulsion droplets, we can experimentally address this fascinating interplay between topology and energy. We find a wealth of defect structures in our shells and propose that the shell thickness inhomogeneity is the key parameter enabling the broad range of configurations we observe; these include long-time predicted configurations, as well as new structures and transitions between them that where never considered before. In addition, we hope to extend our studies to non-spherical surfaces, such as the torus and higher-genus surfaces. For this purpose, we have recently generated toroidal droplets and have studied their hydrodynamic stability. On these closed surfaces, the nature of the defect structure is expected to be qualitatively different from that of the spherical case.
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.
RF experiments on spherical torus plasmas
Majeski, R.; Menard, J.; Batchelor, D.; Bigelow, T.; Carter, M. D.; Finkenthal, M.; Jaeger, E. F.; Jones, B.; Kaita, R.; Mau, T. K.
1999-09-20
Experimental operations are about to begin on the next generation of spherical torus (ST) devices-the National Spherical Torus eXperiment (NSTX) in the U.S. and the Mega-Amp Spherical Torus (MAST) in the U.K. The application of RF heating and current drive to these high beta, compact confinement devices is a challenging problem. The initial focus for NSTX had been on the High Harmonic Fast Wave (HHFW) regime. Although modeling of HHFW heating and current drive has been performed at ORNL, UCSD, MIT, and PPPL, there are few experiments in this frequency range. In conventional tokamaks, the DIII-D experiments at the 5{sup th}-7{sup th} cyclotron harmonic are the closest approach to the HHFW regime. In an ST, the only RF heating experiments to date have been performed at the 15{sup th} harmonic on the Current Drive eXperiment-Upgrade (CDX-U) at PPPL. General features of HHFW heating and current drive and the degree to which experimental confirmation of these features is available will be discussed. (c) 1999 American Institute of Physics.
Next Step Spherical Torus Design Studies
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.
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.
Scaling Relationships for Spherical Polymer Brushes Revisited.
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
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…
LOGO Based Instruction in Geometry.
ERIC Educational Resources Information Center
Yusuf, Mian Muhammad
The objective of this pretest-posttest Quasi-Experimental Design study was to determine the effects of LOGO Based Instruction (LBI) compared to instruction by teacher lecture and pencil-and-paper activities on: (1) students' understanding of the concepts of point, ray, line, and line segment; (2) students' attitudes toward learning geometry,…
Exploring Bundling Theory with Geometry
ERIC Educational Resources Information Center
Eckalbar, John C.
2006-01-01
The author shows how instructors might successfully introduce students in principles and intermediate microeconomic theory classes to the topic of bundling (i.e., the selling of two or more goods as a package, rather than separately). It is surprising how much students can learn using only the tools of high school geometry. To be specific, one can…
General Relativity: Geometry Meets Physics
ERIC Educational Resources Information Center
Thomsen, Dietrick E.
1975-01-01
Observing the relationship of general relativity and the geometry of space-time, the author questions whether the rest of physics has geometrical explanations. As a partial answer he discusses current research on subatomic particles employing geometric transformations, and cites the existence of geometrical definitions of physical quantities such…
Teaching Geometry According to Euclid.
ERIC Educational Resources Information Center
Hartshorne, Robin
2000-01-01
This essay contains some reflections and questions arising from encounters with the text of Euclid's Elements. The reflections arise out of the teaching of a course in Euclidean and non-Euclidean geometry to undergraduates. It is concluded that teachers of such courses should read Euclid and ask questions, then teach a course on Euclid and later…
Analogical Reasoning in Geometry Education
ERIC Educational Resources Information Center
Magdas, Ioana
2015-01-01
The analogical reasoning isn't used only in mathematics but also in everyday life. In this article we approach the analogical reasoning in Geometry Education. The novelty of this article is a classification of geometrical analogies by reasoning type and their exemplification. Our classification includes: analogies for understanding and setting a…
Foucault pendulum through basic geometry
NASA Astrophysics Data System (ADS)
von Bergmann, Jens; von Bergmann, HsingChi
2007-10-01
We provide a thorough explanation of the Foucault pendulum that utilizes its underlying geometry on a level suitable for science students not necessarily familiar with calculus. We also explain how the geometrically understood Foucault pendulum can serve as a prototype for more advanced phenomena in physics known as Berry's phase or geometric phases.
Spectral geometry of symplectic spinors
NASA Astrophysics Data System (ADS)
Vassilevich, Dmitri
2015-10-01
Symplectic spinors form an infinite-rank vector bundle. Dirac operators on this bundle were constructed recently by Habermann, K. ["The Dirac operator on symplectic spinors," Ann. Global Anal. Geom. 13, 155-168 (1995)]. Here we study the spectral geometry aspects of these operators. In particular, we define the associated distance function and compute the heat trace asymptotics.
Exploring Fractal Geometry with Children.
ERIC Educational Resources Information Center
Vacc, Nancy Nesbitt
1999-01-01
Heightens the awareness of elementary school teachers, teacher educators, and teacher-education researchers of possible applications of fractal geometry with children and, subsequently, initiates discussion about the appropriateness of including this new mathematics in the elementary curriculum. Presents activities for exploring children's…
Differential geometry meets the cell.
Marshall, Wallace F
2013-07-18
A new study by Terasaki et al. highlights the role of physical forces in biological form by showing that connections between stacked endoplasmic reticulum cisternae have a shape well known in classical differential geometry, the helicoid, and that this shape is a predictable consequence of membrane physics.
Instructional Identities of Geometry Students
ERIC Educational Resources Information Center
Aaron, Wendy Rose; Herbst, Patricio
2012-01-01
We inspect the hypothesis that geometry students may be oriented toward how they expect that the teacher will evaluate them as students or otherwise oriented to how they expect that their work will give them opportunities to do mathematics. The results reported here are based on a mixed-methods analysis of twenty-two interviews with high school…
Physiological optics and physical geometry.
Hyder, D J
2001-09-01
Hermann von Helmholtz's distinction between "pure intuitive" and "physical" geometry must be counted as the most influential of his many contributions to the philosophy of science. In a series of papers from the 1860s and 70s, Helmholtz argued against Kant's claim that our knowledge of Euclidean geometry was an a priori condition for empirical knowledge. He claimed that geometrical propositions could be meaningful only if they were taken to concern the behaviors of physical bodies used in measurement, from which it followed that it was posterior to our acquaintance with this behavior. This paper argues that Helmholtz's understanding of geometry was fundamentally shaped by his work in sense-physiology, above all on the continuum of colors. For in the course of that research, Helmholtz was forced to realize that the color-space had no inherent metrical structure. The latter was a product of axiomatic definitions of color-addition and the empirical results of such additions. Helmholtz's development of these views is explained with detailed reference to the competing work of the mathematician Hermann Grassmann and that of the young James Clerk Maxwell. It is this separation between 1) essential properties of a continuum, 2) supplementary axioms concerning distance-measurement, and 3) the behaviors of the physical apparatus used to realize the axioms, which is definitive of Helmholtz's arguments concerning geometry.
Noncommutative geometry inspired entropic inflation
NASA Astrophysics Data System (ADS)
Nozari, Kourosh; Akhshabi, Siamak
2011-06-01
Recently Verlinde proposed that gravity can be described as an emergent phenomena arising from changes in the information associated with the positions of material bodies. By using noncommutative geometry as a way to describe the microscopic microstructure of quantum spacetime, we derive modified Friedmann equation in this setup and study the entropic force modifications to the inflationary dynamics of early universe.
Math Sense: Algebra and Geometry.
ERIC Educational Resources Information Center
Howett, Jerry
This book is designed to help students gain the range of math skills they need to succeed in life, work, and on standardized tests; overcome math anxiety; discover math as interesting and purposeful; and develop good number sense. Topics covered in this book include algebra and geometry. Lessons are organized around four strands: (1) skill lessons…
Signature geometry and quantum engineering
NASA Astrophysics Data System (ADS)
Samociuk, Stefan
2013-09-01
As the operating frequency of electromagnetic based devices increase, physical design geometry is playing an ever more important role. Evidence is considered in support of a relationship between the dimensionality of primitive geometric forms, such as transistors, and corresponding electromagnetic coupling efficiency. The industry of electronics is defined as the construction of devices by the patterning of primitive forms to physical materials. Examples are given to show the evolution of these primitives, down to nano scales, are requiring exacting geometry and three dimensional content. Consideration of microwave monolithic integrated circuits,(MMIC), photonics and metamaterials,(MM), support this trend and also add new requirements of strict geometric periodicity and multiplicity. Signature geometries,(SG), are characterized by distinctive attributes and examples are given. The transcendent form transcode algorithm, (TTA) is introduced as a multi dimensional SG and its use in designing photonic integrated circuits and metamaterials is discussed . A creative commons licensed research database, TRANSFORM, containing TTA geometries in OASIS file formats is described. An experimental methodology for using the database is given. Multidimensional SG and extraction of three dimensional cross sections as primitive forms is discussed as a foundation for quantum engineering and the exploitation of phenomena other than the electromagnetic.
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
Coupling spectral elements and modes in a spherical Earth: an extension to the `sandwich' case
NASA Astrophysics Data System (ADS)
Capdeville, Y.; To, A.; Romanowicz, B.
2003-07-01
We present an extension to the coupling scheme of the spectral element method (SEM) with a normal-mode solution in spherical geometry. This extension allows us to consider a thin spherical shell of spectral elements between two modal solutions above and below. The SEM is based on a high-order variational formulation in space and a second-order explicit scheme in time. It combines the geometrical flexibility of the classical finite-element method with the exponential convergence rate associated with spectral techniques. In the inner sphere and outer shell, the solution is sought in terms of a modal solution in the frequency domain after expansion on the spherical harmonics basis. The SEM has been shown to obtain excellent accuracy in solving the wave equation in complex media but is still numerically expensive for the whole Earth for high-frequency simulations. On the other hand, modal solutions are well known and numerically cheap in spherically symmetric models. By combining these two methods we take advantage of both, allowing high-frequency simulations in global Earth models with 3-D structure in a limited depth range. Within the spectral element method, the coupling is introduced via a dynamic interface operator, a Dirichlet-to-Neumann operator which can be explicitly constructed in the frequency and generalized spherical harmonics domain using modal solutions in the inner sphere and outer shell. The presence of the source and receivers in the top modal solution shell requires some special treatment. The accuracy of the method is checked against the mode summation method in simple spherically symmetric models and shows very good agreement for all type of waves, including diffracted waves travelling on the coupling boundary. A first simulation in a 3-D D''-layer model based on the tomographic model SAW24b16 is presented up to a corner frequency of 1/12 s. The comparison with data shows surprisingly good results for the 3-D model even when the observed waveform
Geometry-induced rigidity in nonspherical pressurized elastic shells.
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. PMID:23083245
Geometry-induced rigidity in nonspherical pressurized elastic shells.
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.
Stringy differential geometry, beyond Riemann
NASA Astrophysics Data System (ADS)
Jeon, Imtak; Lee, Kanghoon; Park, Jeong-Hyuck
2011-08-01
While the fundamental object in Riemannian geometry is a metric, closed string theories call for us to put a two-form gauge field and a scalar dilaton on an equal footing with the metric. Here we propose a novel differential geometry that treats the three objects in a unified manner, manifests not only diffeomorphism and one-form gauge symmetry but also O(D,D) T-duality, and enables us to rewrite the known low energy effective action of them as a single term. Further, we develop a corresponding vielbein formalism and gauge the internal symmetry that is given by a direct product of two local Lorentz groups, SO(1,D-1)×SŌ(1,D-1). We comment that the notion of cosmological constant naturally changes.
Geometry-invariant resonant cavities
Liberal, I.; Mahmoud, A. M.; Engheta, N.
2016-01-01
Resonant cavities are one of the basic building blocks in various disciplines of science and technology, with numerous applications ranging from abstract theoretical modelling to everyday life devices. The eigenfrequencies of conventional cavities are a function of their geometry, and, thus, the size and shape of a resonant cavity is selected to operate at a specific frequency. Here we demonstrate theoretically the existence of geometry-invariant resonant cavities, that is, resonators whose eigenfrequencies are invariant with respect to geometrical deformations of their external boundaries. This effect is obtained by exploiting the unusual properties of zero-index metamaterials, such as epsilon-near-zero media, which enable decoupling of the temporal and spatial field variations in the lossless limit. This new class of resonators may inspire alternative design concepts, and it might lead to the first generation of deformable resonant devices. PMID:27010103
Hyperbolic geometry for colour metrics.
Farup, Ivar
2014-05-19
It is well established from both colour difference and colour order perpectives that the colour space cannot be Euclidean. In spite of this, most colour spaces still in use today are Euclidean, and the best Euclidean colour metrics are performing comparably to state-of-the-art non-Euclidean metrics. In this paper, it is shown that a transformation from Euclidean to hyperbolic geometry (i.e., constant negative curvature) for the chromatic plane can significantly improve the performance of Euclidean colour metrics to the point where they are statistically significantly better than state-of-the-art non-Euclidean metrics on standard data sets. The resulting hyperbolic geometry nicely models both qualitatively and quantitatively the hue super-importance phenomenon observed in colour order systems.
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.
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.
Transport of barrel and spherical shaped colloids in unsaturated porous media.
Knappenberger, Thorsten; Aramrak, Surachet; Flury, Markus
2015-09-01
Model colloids are usually spherical, but natural colloids have irregular geometries. Transport experiments of spherical colloids may not reflect the transport characteristics of natural colloids in porous media. We investigated saturated and unsaturated transport of colloids with spherical and angular shapes under steady-state, flow conditions. A pulse of negatively-charged colloids was introduced into a silica sand column at three different effective water saturations (Se = 0.31, 0.45, and 1.0). Colloids were introduced under high ionic strength of [106]mM to cause attachment to the secondary energy minimum and later released by changing the pore water to low ionic strength. After the experiment, sand was sampled from different depths (0, -4, and -11 cm) for scanning electron microscopy (SEM) analysis and colloid extraction. Water saturation affected colloid transport with more retention under low than under high saturation. Colloids were retained and released from a secondary energy minimum with more angular-shaped colloids being retained and released. Colloids extracted from the sand revealed highest colloid deposition in the top layer and decreasing deposition with depth. Pore straining and grain-grain wedging dominated colloid retention.
Expansion of arbitrary electromagnetic fields in terms of vector spherical wave functions.
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
Gottardi, Luciano
2007-01-15
We report the results of a detailed numerical analysis of a real resonant spherical gravitational wave antenna operating with six resonant two-mode capacitive transducers read out by superconducting quantum interference devices (SQUID) amplifiers. We derive a set of equations to describe the electromechanical dynamics of the detector. The model takes into account the effect of all the noise sources present in each transducer chain: the thermal noise associated with the mechanical resonators, the thermal noise from the superconducting impedance matching transformer, the backaction noise, and the additive current noise of the SQUID amplifier. Asymmetries in the detector signal-to-noise ratio and bandwidth, coming from considering the transducers not as pointlike objects but as a sensor with physically defined geometry and dimension, are also investigated. We calculate the sensitivity for an ultracryogenic, 30 ton, 2 m in diameter, spherical detector with optimal and nonoptimal impedance matching of the electrical readout scheme to the mechanical modes. The results of the analysis are useful not only to optimize existing smaller mass spherical detector like MiniGrail, in Leiden, but also as a technological guideline for future massive detectors. Furthermore we calculate the antenna patterns when the sphere operates with one, three, and six transducers. The sky coverage for two detectors based in The Netherlands and Brazil and operating in coincidence is also estimated. Finally, we describe and numerically verify a calibration and filtering procedure useful for diagnostic and detection purposes in analogy with existing resonant bar detectors.
Transport of barrel and spherical shaped colloids in unsaturated porous media.
Knappenberger, Thorsten; Aramrak, Surachet; Flury, Markus
2015-09-01
Model colloids are usually spherical, but natural colloids have irregular geometries. Transport experiments of spherical colloids may not reflect the transport characteristics of natural colloids in porous media. We investigated saturated and unsaturated transport of colloids with spherical and angular shapes under steady-state, flow conditions. A pulse of negatively-charged colloids was introduced into a silica sand column at three different effective water saturations (Se = 0.31, 0.45, and 1.0). Colloids were introduced under high ionic strength of [106]mM to cause attachment to the secondary energy minimum and later released by changing the pore water to low ionic strength. After the experiment, sand was sampled from different depths (0, -4, and -11 cm) for scanning electron microscopy (SEM) analysis and colloid extraction. Water saturation affected colloid transport with more retention under low than under high saturation. Colloids were retained and released from a secondary energy minimum with more angular-shaped colloids being retained and released. Colloids extracted from the sand revealed highest colloid deposition in the top layer and decreasing deposition with depth. Pore straining and grain-grain wedging dominated colloid retention. PMID:26275396
Expansion of arbitrary electromagnetic fields in terms of vector spherical wave functions.
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.
Augmentation of Radiation Intensity in Quasi-Spherical Double Liner/Dynamic Hohlraum
NASA Astrophysics Data System (ADS)
Zakharov, S. V.; Smirnov, V. P.
2006-01-01
To increase the conversion efficiency of magnetic energy to radiation in Double Liner/Dynamic-Hohlraum and to approach closer to the ignition conditions we proposed the concept of implosion of a quasi-spherical double liner. The almost spherical implosion can be realized with a special mass distribution in liners. Axial cumulating of liner kinetic energy and more efficient radiation energy confinement allow augmentation of radiation intensity on the capsule with respect to cylindrical case under the same driver conditions. A controllable mass redistribution inside the nested external liner allows significant reduction and correction of distortions produced by the Rayleigh-Taylor instability. A phenomenon of energy confinement and enhancement of radiation intensity is considered and compared with the cylindrical case. On the basis of the developed physical model of non-LTE plasma using the RMHD code ZETA the dynamics of quasi-spherical Double Liner/Dynamic-Hohlraum and generation of radiation in two-dimensional geometry is examined and liner configuration is optimized.
Augmentation of Radiation Intensity in Quasi-Spherical Double Liner/Dynamic Hohlraum
Zakharov, S.V.; Smirnov, V.P.
2006-01-05
To increase the conversion efficiency of magnetic energy to radiation in Double Liner/Dynamic-Hohlraum and to approach closer to the ignition conditions we proposed the concept of implosion of a quasi-spherical double liner. The almost spherical implosion can be realized with a special mass distribution in liners. Axial cumulating of liner kinetic energy and more efficient radiation energy confinement allow augmentation of radiation intensity on the capsule with respect to cylindrical case under the same driver conditions. A controllable mass redistribution inside the nested external liner allows significant reduction and correction of distortions produced by the Rayleigh-Taylor instability. A phenomenon of energy confinement and enhancement of radiation intensity is considered and compared with the cylindrical case. On the basis of the developed physical model of non-LTE plasma using the RMHD code ZETA the dynamics of quasi-spherical Double Liner/Dynamic-Hohlraum and generation of radiation in two-dimensional geometry is examined and liner configuration is optimized.
Geometry Dependence of Stellarator Turbulence
H.E. Mynick, P. Xanthopoulos and A.H. Boozer
2009-08-10
Using the nonlinear gyrokinetic code package GENE/GIST, we study the turbulent transport in a broad family of stellarator designs, to understand the geometry-dependence of the microturbulence. By using a set of flux tubes on a given flux surface, we construct a picture of the 2D structure of the microturbulence over that surface, and relate this to relevant geometric quantities, such as the curvature, local shear, and effective potential in the Schrodinger-like equation governing linear drift modes.
NASA Astrophysics Data System (ADS)
Mignone, A.
2014-08-01
High-order reconstruction schemes for the solution of hyperbolic conservation laws in orthogonal curvilinear coordinates are revised in the finite volume approach. The formulation employs a piecewise polynomial approximation to the zone-average values to reconstruct left and right interface states from within a computational zone to arbitrary order of accuracy by inverting a Vandermonde-like linear system of equations with spatially varying coefficients. The approach is general and can be used on uniform and non-uniform meshes although explicit expressions are derived for polynomials from second to fifth degree in cylindrical and spherical geometries with uniform grid spacing. It is shown that, in regions of large curvature, the resulting expressions differ considerably from their Cartesian counterparts and that the lack of such corrections can severely degrade the accuracy of the solution close to the coordinate origin. Limiting techniques and monotonicity constraints are revised for conventional reconstruction schemes, namely, the piecewise linear method (PLM), third-order weighted essentially non-oscillatory (WENO) scheme and the piecewise parabolic method (PPM). The performance of the improved reconstruction schemes is investigated in a number of selected numerical benchmarks involving the solution of both scalar and systems of nonlinear equations (such as the equations of gas dynamics and magnetohydrodynamics) in cylindrical and spherical geometries in one and two dimensions. Results confirm that the proposed approach yields considerably smaller errors, higher convergence rates and it avoid spurious numerical effects at a symmetry axis.
Design of spherical symmetric gradient index lenses
NASA Astrophysics Data System (ADS)
Miñano, Juan C.; Grabovičkić, Dejan; Benítez, Pablo; González, Juan C.; Santamaría, Asunción
2012-10-01
Spherical symmetric refractive index distributions also known as Gradient Index lenses such as the Maxwell-Fish-Eye (MFE), the Luneburg or the Eaton lenses have always played an important role in Optics. The recent development of the technique called Transformation Optics has renewed the interest in these gradient index lenses. For instance, Perfect Imaging within the Wave Optics framework has recently been proved using the MFE distribution. We review here the design problem of these lenses, classify them in two groups (Luneburg moveable-limits and fixed-limits type), and establish a new design techniques for each type of problem.
Spherical Combustion Layer in a TNT Explosion
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.
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
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
Charged radial infall for spherical central bodies
NASA Astrophysics Data System (ADS)
Franklin, J.; Morton-Park, F.
2010-12-01
A massive, charged, spherical body can be neutralized by attracting particles of opposite charge. We calculate the time it takes to neutralize such a body using Newtonian and relativistic mechanics and the "forced" trajectories of general relativity. We compare the classical and (special) relativistic times and find that the special relativistic neutralization time is longer. A comparison of these times with the general relativistic result is not as direct. We offer the final calculation as a demonstration of dynamics in the general relativistic setting, highlighting the structural similarity of this problem with the other two cases.
Compressive sensing with a spherical microphone array.
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.
Orbit propagation in Minkowskian geometry
NASA Astrophysics Data System (ADS)
Roa, Javier; Peláez, Jesús
2015-09-01
The geometry of hyperbolic orbits suggests that Minkowskian geometry, and not Euclidean, may provide the most adequate description of the motion. This idea is explored in order to derive a new regularized formulation for propagating arbitrarily perturbed hyperbolic orbits. The mathematical foundations underlying Minkowski space-time are exploited to describe hyperbolic orbits. Hypercomplex numbers are introduced to define the rotations, vectors, and metrics in the problem: the evolution of the eccentricity vector is described on the Minkowski plane in terms of hyperbolic numbers, and the orbital plane is described on the inertial reference using quaternions. A set of eight orbital elements is introduced, namely a time-element, the components of the eccentricity vector in , the semimajor axis, and the components of the quaternion defining the orbital plane. The resulting formulation provides a deep insight into the geometry of hyperbolic orbits. The performance of the formulation in long-term propagations is studied. The orbits of four hyperbolic comets are integrated and the accuracy of the solution is compared to other regularized formulations. The resulting formulation improves the stability of the integration process and it is not affected by the perihelion passage. It provides a level of accuracy that may not be reached by the compared formulations, at the cost of increasing the computational time.
NASA 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.
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.
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
Two-fluid simulations of driven reconnection in the mega-ampere spherical tokamak
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.
Effect of conductor geometry on source localization: Implications for epilepsy studies
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.
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. Multisource 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.
Network geometry with flavor: From complexity to quantum geometry
NASA Astrophysics Data System (ADS)
Bianconi, Ginestra; Rahmede, Christoph
2016-03-01
Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d -dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s =-1 ,0 ,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d . In d =1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d >1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t . Interestingly the NGF remains fully classical but
Network geometry with flavor: From complexity to quantum geometry.
Bianconi, Ginestra; Rahmede, Christoph
2016-03-01
Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d-dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s=-1,0,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d. In d=1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d>1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t. Interestingly the NGF remains fully classical but its
Network geometry with flavor: From complexity to quantum geometry.
Bianconi, Ginestra; Rahmede, Christoph
2016-03-01
Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d-dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s=-1,0,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d. In d=1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d>1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t. Interestingly the NGF remains fully classical but its
Acoustic geometry through perturbation of mass accretion rate: radial flow in static spacetimes
NASA Astrophysics Data System (ADS)
Ananda, Deepika B.; Bhattacharya, Sourav; Das, Tapas K.
2015-09-01
In this work we present an alternative derivation of the general relativistic acoustic analogue geometry by perturbing the mass accretion rate or flux of an ideal fluid flowing radially in a general static and spherically symmetric spacetime. To the best of our knowledge, this has so far been done in non-relativistic scenario. The resulting causal structure of the two dimensional acoustic geometry is qualitatively similar to that one derives via the perturbation of the velocity potential. Using this, we then briefly discuss the stability issues by studying the wave configurations generated by the perturbation of the mass accretion rate, and formally demonstrate the stability of the accretion process. This is in qualitative agreement with earlier results on stability, established via study of wave configurations generated by the perturbation of velocity potential, by using the acoustic geometry associated with it. We further discuss explicit examples of the Schwarzschild and Rindler spacetimes.
The effects of arcjet thruster operating condition constrictor geometry on the plasma plume
NASA Technical Reports Server (NTRS)
Carney, Lynnette M.; Sankovic, John M.
1989-01-01
Measurements of plasma number density and electron temperature were obtained in the plumes of lab arcjet thrusters using electrostatic probes of both spherical and cylindrical geometry. The two arcjet thrusters used had different constrictor and/or nozzle geometries and operated on mixtures of nitrogen, hydrogen, and ammonia to simulate the decomposition products of hydrazine and ammonia. An increase in the measured electron density was observed for both geometries with increasing arc power at a constant mass flow rate and with increasing mass flow rate at a constant arc current. For a given operating condition, the electron number density decreased exponentially off centerline and followed an inverse distance squared relationship along the thrust axis. Typical measured electron temperatures ranged from 0.1 to 0.2 eV.
The effects of arcjet operating condition and constrictor geometry on the plasma plume
NASA Technical Reports Server (NTRS)
Carney, Lynnette M.; Sankovic, John M.
1989-01-01
Measurements of plasma number density and electron temperature were obtained in the plumes of lab arcjet thrusters using electrostatic probes of both spherical and cylindrical geometry. The two arcjet thrusters used had different constrictor and/or nozzle geometries and operated on mixtures of nitrogen, hydrogen, and ammonia to simulate the decomposition products of hydrazine and ammonia. An increase in the measured electron density was observed for both geometries with increasing arc power at a constant mass flow rate and with increasing mass flow rate at a constant arc current. For a given operating condition, the electron number density decreased exponentially off centerline and followed an inverse distance squared relationship along the thrust axis. Typical measured electron temperatures ranged from 0.1 to 0.2 eV.
Multi-element spherical shell generation
NASA Technical Reports Server (NTRS)
Morrison, Andrew D. (Inventor)
1990-01-01
A nozzle assembly in a multi-element spherical shell generation system includes first and second side-by-side spaced apart nozzles and a web portion extending between and connecting the nozzles. The first nozzle has an inner orifice adapted to discharge a first filler material and an outer annular orifice separated from and defined in concentric relation about the inner orifice and adapted to discharge a first shell material. The second nozzle has an inner orifice adapted to discharge a second filler material and an outer annular orifice separated from and defined in concentric relation about the inner orifice and adapted to discharge a second shell material. A multi-element spherical shell can be formed through employment of the nozzle assembly by merger with one another after discharge from the outer orifices of the nozzles of a pair of adjacent annular streams of liquid or molten shell wall material of different compositions and encapsulation by the mixed shell wall materials of a common encapsulated core fluids also simultaneously discharged by the inner orifices nozzles. On the other hand, the pair of encapsulating streams of shell wall material can be of the same materials which merge together and encapsulate core fluids of different compositions which will merge together after discharge from the nozzles.
Rayleigh scattering of a spherical sound wave.
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.
Spherically symmetric conformal gravity and ''gravitational bubbles''
Berezin, V.A.; Dokuchaev, V.I.; Eroshenko, Yu.N. E-mail: dokuchaev@inr.ac.ru
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.
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.
Clusters of polyhedra in spherical confinement.
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
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).
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.
Variational extensions of the mean spherical approximation
NASA Astrophysics Data System (ADS)
Blum, L.; Ubriaco, M.
2000-04-01
In a previous work we have proposed a method to study complex systems with objects of arbitrary size. For certain specific forms of the atomic and molecular interactions, surprisingly simple and accurate theories (The Variational Mean Spherical Scaling Approximation, VMSSA) [(Velazquez, Blum J. Chem. Phys. 110 (1990) 10 931; Blum, Velazquez, J. Quantum Chem. (Theochem), in press)] can be obtained. The basic idea is that if the interactions can be expressed in a rapidly converging sum of (complex) exponentials, then the Ornstein-Zernike equation (OZ) has an analytical solution. This analytical solution is used to construct a robust interpolation scheme, the variation mean spherical scaling approximation (VMSSA). The Helmholtz excess free energy Δ A=Δ E- TΔ S is then written as a function of a scaling matrix Γ. Both the excess energy Δ E( Γ) and the excess entropy Δ S( Γ) will be functionals of Γ. In previous work of this series the form of this functional was found for the two- (Blum, Herrera, Mol. Phys. 96 (1999) 821) and three-exponential closures of the OZ equation (Blum, J. Stat. Phys., submitted for publication). In this paper we extend this to M Yukawas, a complete basis set: We obtain a solution for the one-component case and give a closed-form expression for the MSA excess entropy, which is also the VMSSA entropy.
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.
Preparation of nanoporous titania spherical nanoparticles
NASA Astrophysics Data System (ADS)
Shiba, Kota; Sato, Soh; Matsushita, Takayuki; Ogawa, Makoto
2013-03-01
Preparation of nanoporous titania particles from well-defined titania-octadecylamine (titania-ODA) hybrid spherical particles with 450 nm in size, which were prepared by the method reported previously (Chem. Commun., 2009, pp. 6851-6853 [39]; RSC Adv., 2012, vol. 2, pp. 1343-1349 [40]), was studied. ODA was removed by solvent extraction with acidic ethanol to obtain nanoporous titania particles and subsequent calcination led to the formation of nanoporous titania particles with the nanopore size ranging from 2 to 4 nm depending on the calcination temperature. The as-synthesized titania was amorphous and was transformed into anatase (at around 300 °C) and rutile (at around 600 °C) by the heat treatment. The phase transition behavior was discussed in comparison with that of as-synthesized titania-ODA particles without ODA removal. Spherical particles of titania-ODA hybrids with 70 nm in size were also transformed into nanoporous titania particles composed of anatase crystallites by the washing and calcination at 500 °C for 1 h.
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.
Understanding pop-ins in spherical nanoindentation
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.
Clusters of polyhedra in spherical confinement
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
Spherical Stellarators and Stellarator-Hybrids
NASA Astrophysics Data System (ADS)
Moroz, P. E.
1997-11-01
Stellarators are typically the large aspect ratio devices, A ≈ 7-10, and the lowest-A stellarators ever built have A ≈ 5. Following the increasing interest in very compact tokamak devices, called Spherical Tokamaks (ST), an interest has also emerged recently in very compact stellarator devices with A <= 3.5, as their attractiveness for fusion is being demonstrated [1-4]. These stellarators have been called, in analogy with the ST, the Spherical Stellarators (SS). The SS devices have a number of unique features and benefit from the strong bootstrap current. The SS concept shows a path to a compact, high-β, and steady-state fusion reactor, which can be relatively simple and inexpensive. We will report on the latest results obtained, discuss various types of coil configurations advantageous for the SS, and present results of the first round of configuration optimization. Applications to ST devices [5] and new results for stellarator-spheromak hybrids [6] will be presented as well. [1] P.E. Moroz, Phys. Rev. Lett. 77, 651 (1996); [2] P.E. Moroz, Phys. Plasmas 3, 3055 (1996); [3] P.E. Moroz, D.B. Batchelor et al., Fusion Tech. 30, 1347 (1996); [4] P.E. Moroz, Plasma Phys. Reports 23, 502 (1997); [5] P.E. Moroz, Nucl. Fusion 37, No. 7 (1997); [6] P.E. Moroz, Sherwood Fus. Theor. Conf., Madison, 3C31 (1997). *Supported by DOE Grant No. DE-FG02-97ER54395.
Initial assessments of ignition spherical torus
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.
Understanding pop-ins in spherical nanoindentation
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.
Understanding pop-ins in spherical nanoindentation
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
Quasi-spherical direct drive fusion.
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.
Spherical aggregates composed of gold nanoparticles
NASA Astrophysics Data System (ADS)
Chen, Chi-Chang; Kuo, Ping-Lin; Cheng, Yu-Chen
2009-02-01
Alkylated triethylenetetramine (C12E3) was synthesized and used as both a reductant in the preparation of gold nanoparticles by the reduction of HAuCl4 and a stabilizer in the subsequent self-assembly of the gold nanoparticles. In acidic aqueous solution, spherical aggregates (with a diameter of about 202 ± 22 nm) of gold nanoparticles (with the mean diameter of ~18.7 nm) were formed. The anion-induced ammonium adsorption of the alkylated amines on the gold nanoparticles was considered to provide the electrostatic repulsion and steric hindrance between the gold nanoparticles, which constituted the barrier that prevented the individual particles from coagulating. However, as the amino groups became deprotonated with increasing pH, the ammonium adsorption was weakened, and the amino groups were desorbed from the gold surface, resulting in discrete gold particles. The results indicate that the morphology of the reduced gold nanoparticles is controllable through pH-'tunable' aggregation under the mediation of the amino groups of alkylated amine to create spherical microstructures.
Measuring Shell Resonances of Spherical Acoustic Resonators
NASA Astrophysics Data System (ADS)
Truong, D.; Sparasci, F.; Foltête, E.; Ouisse, M.; Pitre, L.
2011-01-01
Coupling between the gas and shell is a concern in the experiment used at LNE-CNAM to determine the Boltzmann constant k B by an acoustic method. As the walls of real resonators are not perfectly rigid, some perturbations occur in the frequency range of the acoustic resonances measured within helium gas contained in the cavity. As a contribution for a better understanding of this phenomenon, an experiment to measure the shell modes of the spherical resonators is in use in this laboratory. A work in progress to assess these modes using a hammer blow method together with modal analysis is reported here. The study is carried out with an air-filled, copper-walled, half-liter quasi-spherical resonator in the frequency range from 1 Hz to 20 kHz. Results show that the shell modes expand into multiple resonances of similar modal shape, including the "breathing" mode. The observations reported in other studies of shell perturbations at other frequencies than the breathing frequency are confirmed.
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…
A Whirlwind Tour of Computational Geometry.
ERIC Educational Resources Information Center
Graham, Ron; Yao, Frances
1990-01-01
Described is computational geometry which used concepts and results from classical geometry, topology, combinatorics, as well as standard algorithmic techniques such as sorting and searching, graph manipulations, and linear programing. Also included are special techniques and paradigms. (KR)
Optimizing solar-cell grid geometry
NASA Technical Reports Server (NTRS)
Crossley, A. P.
1969-01-01
Trade-off analysis and mathematical expressions calculate optimum grid geometry in terms of various cell parameters. Determination of the grid geometry provides proper balance between grid resistance and cell output to optimize the energy conversion process.
Interaction between two spherical particles in a nematic liquid crystal.
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 Q(ij) 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 approximately 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 less than or approximately equal 10R0, which is stronger than the dipole-dipole repulsion (approximately D-3 ) expected theoretically as an asymptotic behavior for large D.
Forces and fluctuations in planar, spherical and tubular membranes
NASA Astrophysics Data System (ADS)
Barbetta, Camilla
2010-11-01
Lipid membranes constitute very particular materials: on the one hand, they break very easily under microscopical stretching; on the other hand, they are extremely flexible, presenting deformations even at small scales. Consequently, a piece of membrane has an area excess relative to its optically resolvable area, also called projected area. From a mechanical point of view, we can thus identify three tensions associated to lipid membranes: the mechanical effective tension τ, associated to an increase in the projected area and to the flattening of the fluctuations; the tension sigma, associated to the microscopical area of the membrane and thus non measurable, but commonly used in theoretical predictions; and its macroscopical counterpart measured through the fluctuation spectrum, r. Up to now, the equality between these quantities was taken for granted when analyzing experimental data. In this dissertation, we have studied, using the projected stress tensor, whether and under which conditions it is justified to assume τ = sigma. We studied three geometries (planar, spherical and cylindrical) and obtained the relation τ approx sigma - sigma_0, where sigma_0 is a constant depending only on the membrane's high frequency cutoff and on the temperature. Accordingly, we conclude that neglecting the difference between τ and sigma is justifiable only to membranes under large tensions: in the case of small tensions, corrections must be taken into account. We have studied the implications of this result to the interpretation of experiments involving membrane nanotubes. Regarding r, we have questioned a former demonstration concerning its equality with τ. Finally, the force fluctuation for planar membranes and membrane nanotubes was quantified for the first time.
The Geometry of Quasar Outflows
NASA Astrophysics Data System (ADS)
Ganguly, Rajib
2012-10-01
Quasar outflows are important for understanding the accretion and growth processes of the central black hole, but also potentially play a role in feedback to the galaxy, halting star formation and infall of gas. A big uncertainty lies in the geometry and density of these outflows, especially as a function of ionization and velocity. We aim to tackle this using the archival COS M grating spectra of 266 quasars. We separate the geometry of outflows into two parts: the solid angle subtended around the black hole, and the distance of the outflow from the central engine. Large numbers of quasars with high resolution spectra are required for each aspect of this statistical investigation. First, we will determine which/how many absorption-line systems are intrinsic through both partial covering methods and statistical assessments. Second, we will consider the incidence of intrinsic absorbers as a function of quasar property {e.g., radio-loudness, SED shape, black hole mass, bolometric luminosity}. This will reveal what determines the solid angle. This can only be done at moderate redshifts where quasars with a larger range of properties are observable, and hence requires HST/COS. Third, we will use the wide range of diagnostic lines to constrain the physical conditions of the absorbers. We will target the CIII*1175 complex and apply photoionization models to constrain the densities and ionization parameters. This will provide the largest set yet of intrinsic absorbers with systematic distance constraints. In tandem with the solid angles, this work will inform models regarding the geometry of quasar outflows.
The geometry of musical chords.
Tymoczko, Dmitri
2006-07-01
A musical chord can be represented as a point in a geometrical space called an orbifold. Line segments represent mappings from the notes of one chord to those of another. Composers in a wide range of styles have exploited the non-Euclidean geometry of these spaces, typically by using short line segments between structurally similar chords. Such line segments exist only when chords are nearly symmetrical under translation, reflection, or permutation. Paradigmatically consonant and dissonant chords possess different near-symmetries and suggest different musical uses.
Worldsheet geometries of ambitwistor string
NASA Astrophysics Data System (ADS)
Ohmori, Kantaro
2015-06-01
Mason and Skinner proposed the ambitwistor string theory which directly reproduces the formulas for the amplitudes of massless particles proposed by Cachazo, He and Yuan. In this paper we discuss geometries of the moduli space of worldsheets associated to the bosonic or the RNS ambitwistor string. Further, we investigate the factorization properties of the amplitudes when an internal momentum is near on-shell in the abstract CFT language. Along the way, we propose the existence of the ambitwistor strings with three or four fermionic worldsheet currents.
Ooguri, Hirosi; Yamazaki, Masahito
2009-04-24
We show how the smooth geometry of Calabi-Yau manifolds emerges from the thermodynamic limit of the statistical mechanical model of crystal melting defined in our previous paper. In particular, the thermodynamic partition function of molten crystals is shown to be equal to the classical limit of the partition function of the topological string theory by relating the Ronkin function of the characteristic polynomial of the crystal melting model to the holomorphic 3-form on the corresponding Calabi-Yau manifold. PMID:19518695
Exceptional geometry and Borcherds superalgebras
NASA Astrophysics Data System (ADS)
Palmkvist, Jakob
2015-11-01
We study generalized diffeomorphisms in exceptional geometry with U-duality group E n( n) from an algebraic point of view. By extending the Lie algebra {e}_n to an infinite-dimensional Borcherds superalgebra, involving also the extension to {e}_{n+1} , the generalized Lie derivatives can be expressed in a simple way, and the expressions take the same form for any n ≤ 7. The closure of the transformations then follows from the Jacobi identity and the grading of {e}_{n+1} with respect to {e}_n.
Theory of diffusion-influenced reactions in complex geometries.
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.
The role of pore geometry in single nanoparticle detection
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.
The role of pore geometry in single nanoparticle detection
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
Theory of diffusion-influenced reactions in complex geometries.
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
Application of spherical gratings in synchrotron radiation spectroscopy
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.
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.
Bending stresses in spherically hollow ball bearing and fatigue experiments
NASA Technical Reports Server (NTRS)
Nypan, L. J.; Coe, H. H.; Parker, R. J.
1975-01-01
Spherically hollow balls of 21.7, 50.0, and 56.5 percent mass reduction were operated in ball bearings and in a five-ball fatigue tester with differing outcomes. Available theoretical and experimental treatments of stresses in spherically hollow balls are reviewed and compared. Bending stresses are estimated for these spherically hollow balls to better understand the differences in ball bearing and fatigue test experience.
Bending stresses in spherically hollow ball bearing and fatigue experiments
NASA Technical Reports Server (NTRS)
Nypan, L. J.; Coe, H. H.; Parker, R. J.
1975-01-01
Spherically hollow balls of 21.7, 50.0 and 56.5 per cent mass reduction have been operated in ball bearings and in a 5-ball fatigue tester with differing outcomes. Available theoretical and experimental treatments of stresses in spherically hollow balls are reviewed and compared. Bending stresses are estimated for these spherically hollow balls to better understand the differences in ball bearing and fatigue test experience.
Teaching Geometry: An Experiential and Artistic Approach.
ERIC Educational Resources Information Center
Ogletree, Earl J.
The view that geometry should be taught at every grade level is promoted. Primary and elementary school children are thought to rarely have any direct experience with geometry, except on an incidental basis. Children are supposed to be able to learn geometry rather easily, so long as the method and content are adapted to their development and…
Preservice Primary School Teachers' Elementary Geometry Knowledge
ERIC Educational Resources Information Center
Marchis, Iuliana
2012-01-01
Geometrical notions and properties occur in real-world problems, thus Geometry has an important place in school Mathematics curricula. Primary school curricula lays the foundation of Geometry knowledge, pupils learn Geometry notions and properties by exploring their environment. Thus it is very important that primary school teachers have a good…
Geometry in the Early Years: A Commentary
ERIC Educational Resources Information Center
Dindyal, Jaguthsing
2015-01-01
The primary goal of this paper is to provide a commentary on the teaching and learning of geometry in the early years of schooling with the set of papers in this issue as a guiding factor. It is structured around issues about geometry education of young learners, such as: what should we teach in geometry and why; representation of geometrical…
Engaging All Students with "Impossible Geometry"
ERIC Educational Resources Information Center
Wiest, Lynda R.; Ayebo, Abraham; Dornoo, Michael D.
2010-01-01
Geometry is an area in which Australian students performed particularly poorly on the 2007 Trends in International Mathematics and Science Study (TIMSS). One innovative area of recreational geometry that has rich potential to engage and challenge a wide variety of students is "impossible geometry." An impossible geometric object is a…
Geometry: Career Related Units. Teacher's Edition.
ERIC Educational Resources Information Center
Pierro, Mike; And Others
Using six geometry units as resource units, the document explores 22 math-related careers. The authors intend the document to provide senior high school students with career orientation and exploration experiences while they learn geometry skills. The units are to be considered as a part of a geometry course, not a course by themselves. The six…
A spherical joint piston design for high speed diesel engines
Wiczynski, P.D.; Mielke, S.; Conrow, R.
1996-09-01
A spherical joint piston and connecting rod have been developed through design proof-of-concept. The spherical joint allows piston rotation. The benefits of a rotating, symmetrical piston are: mechanical and thermal load symmetry, improved ring sealing and lubrication, and reduced bearing loads, scuffing, clearances and oil consumption. The assembly includes a squeeze cast, fiber reinforced aluminum spherical joint piston. Reinforcement is located in the piston bowl and skirt. The connecting rod consists of a spherical small end positioned on an elliptical cross-sectioned shank blended into a conventional big end. The assembly has operated at cylinder pressures exceeding of 24 MPa.
Circle of least confusion of a spherical reflector.
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
Characteristic Matrices for Spherical Shell Photonic Systems
NASA Technical Reports Server (NTRS)
Fuller, Kirk A.; Smith, David D.
2004-01-01
We establish a parallel between the transfer matrix used in the study of plane-parallel photonic structures and the matrix characterizing transfer of partial waves in concentric spheres. We derive explicit expressions for the elements of the transfer matrix for concentric spherical layers, and from those expressions derive the scattering coefficients of a multilayered sphere. The transfer matrices are 4x4 block diagonal with only four independent elements. Matrix elements for the case of TM waves are related to those for the case of TE waves through simple interchange and multiplicative constants. In analogy with plane parallel layers, the transfer matrix for concentric multilayers is simply the product of the transfer matrices of the individual layers.
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.
Preparing spherical lignin from rice husk.
Zhang, Hongxi; Zhao, Xu; Ding, Xuefeng; Lei, Hong; Wang, Zichen
2013-08-01
Lignin is one of the important branched amorphous polymers, which generally has the irregular and fractal morphology. The preparation of regular sphere of lignin needs long steps and special conditions. In this study, the regular sphere of lignin can be simply prepared from rice husk (RH) under certain conditions. Namely, RH is mixed with 35% ethanol aqueous solution in the proportion of 1:10 (g:mL), non-isothermally heated to 493 K and kept for 5 h. After filtration and air-drying at room temperature, the regular lignin sphere with the diameter of 100-400 nm is obtained. The regular sphere of lignin has the potential utilization in fields such as reactive functional materials, photo sensing materials and surface active materials in cosmetics. The mechanism of formation of the regular spherical lignin is proposed and discussed in this paper.
Simple spherical ablative-implosion model
Mayer, F.J.; Steele, J.T.; Larsen, J.T.
1980-06-23
A simple model of the ablative implosion of a high-aspect-ratio (shell radius to shell thickness ratio) spherical shell is described. The model is similar in spirit to Rosenbluth's snowplow model. The scaling of the implosion time was determined in terms of the ablation pressure and the shell parameters such as diameter, wall thickness, and shell density, and compared these to complete hydrodynamic code calculations. The energy transfer efficiency from ablation pressure to shell implosion kinetic energy was examined and found to be very efficient. It may be possible to attach a simple heat-transport calculation to our implosion model to describe the laser-driven ablation-implosion process. The model may be useful for determining other energy driven (e.g., ion beam) implosion scaling.
Spherical wave scattering by slender bodies.
Van Nhieu, M T
1993-01-01
The problem of the scattering of a spherical acoustic wave by rigid slender bodies of revolution is investigated theoretically from a formalism based on the matched asymptotic expansion method. It is an extension of a formulation that was originally derived for incident plane waves with the so-called slender-body approximation. Simple and practical formulas are obtained for the scattered pressure in the near- and far-fields: they are valid at low and medium frequencies when the reduced wavenumber Ka is less or of the order of unity. Computations of the monostatic and bistatic angular distributions for a spheroid are presented to illustrate the sensitivity of the scattered field with respect to the distance source and observation point.
The semipermeability of simple spherical virus capsids.
Durham, A C; Witz, J; Bancroft, J B
1984-02-01
Hydrogen-ion titration curves are reported for tomato bushy stunt virus, two strains of cowpea chlorotic mottle virus, and turnip crinkle virus, with particular attention to the hysteresis loops associated with the swelling and contraction of virions. There appears to be an archetypal shape of hysteresis loops, which is shared by viruses in several groups, suggestive of many intermediate states in the swelling of any one particle. In contrast, eggplant mosaic virus behaves as if its protein capsid is impermeable to small ions in mild conditions; its cation-binding sites were revealed by treatment with high concentrations of salt or urea, or at raised temperatures. Putting these observations together with the fact that a spherical virus capsid is a closed, holey, charged surface leads to a theory of titration hysteresis: its key feature is that the protein capsids of simple viruses are inherently semipermeable, with many of the ion-handling properties usually attributed only to complex lipid membranes.
On dynamic gas ablation from spherical galaxies
NASA Astrophysics Data System (ADS)
Nepveu, M.
1981-05-01
Two-dimensional, time dependent gas dynamic calculations are presented on the transonic motion of galaxies through a cluster medium. Lea and De Young's (1976) calculations are extended to include violent behavior in the center. On time scales of 10 to the 8th yr, galaxies in clusters can already lose a significant fraction of their gaseous content (up to 50% has been found in the calculations). This dynamic ablation occurs through rarefaction rather than shock heating. Explosions in spherical galaxies become effective as mechanisms for gas removal only if the galaxy moves with respect to its surroundings. Speculations are made on stripping of spiral galaxies (moving head-on in a cluster); the Gunn and Gott (1972) stripping formula is put to doubt. A method is suggested to obtain information on the state of motion of field galaxies.
Spherical explosion with a central energy source
NASA Astrophysics Data System (ADS)
Masuyama, Miyu; Shigeyama, Toshikazu; Tsuboki, Yoichiro
2016-04-01
We present a novel semi-analytic solution that describes the propagation of a spherical blast wave driven by a central energy source. The initial density profile has a power-law function of the distance from the center and the energy is injected only into the central region at a rate given by a power-law function of time. This solution is composed of three regions separated by the contact surface and the shock front. The innermost region is assumed to be uniform and the outside of the contact surface includes the shocked matter described by self-similar solutions. We analytically derive the applicable range of parameters of this solution from requirements needed to satisfy the boundary conditions. We perform numerical simulations for flows with various values of parameters, some of which reside out of the thus-derived applicable range, and compare the results with the semi-analytic solutions.
Nonlinear axisymmetric liquid currents in spherical annuli
NASA Technical Reports Server (NTRS)
Astafyeva, N. M.; Vvedenskaya, N. D.; Yavorskaya, I. M.
1978-01-01
A numerical analysis of non-linear axisymmetric viscous flows in spherical annuli of different gap sizes is presented. Only inner sphere was supposed to rotate at a constant angular velocity. The streamlines, lines of constant angular velocity, kinetic energy spectra, and spectra of velocity components are obtained. A total kinetic energy and torque needed to rotate the inner sphere are calculated as functions of Re for different gap sizes. In small-gap annulus nonuniqueness of steady solutions of Navier-Stokes equations is established and regions of different flow regime existences are found. Numerical solutions in a wide-gap annulus and experimental results are used in conclusions about flow stability in the considered range of Re. The comparison of experimental and numerical results shows close qualitative and quantitative agreement.
Noether currents of charged spherical black holes
NASA Astrophysics Data System (ADS)
Ashworth, M. C.; Hayward, Sean A.
2000-09-01
We calculate the Noether currents and charges for the Einstein-Maxwell theory using a version of the Wald approach. In spherical symmetry, the choice of time can be taken as the Kodama vector. For the static case, the resulting combined Einstein-Maxwell charge is just the mass of the black hole. Using either a classically defined entropy or the Iyer-Wald selection rules, the entropy is found to be just a quarter of the area of the trapping horizon. We propose identifying the combined Noether charge as an energy associated with the Kodama time. For the extremal black hole case, we discuss the problem of Wald's rescaling of the surface gravity to define the entropy.
Sound field inside acoustically levitated spherical drop
NASA Astrophysics Data System (ADS)
Xie, W. J.; Wei, B.
2007-05-01
The sound field inside an acoustically levitated small spherical water drop (radius of 1mm) is studied under different incident sound pressures (amplitude p0=2735-5643Pa). The transmitted pressure ptr in the drop shows a plane standing wave, which varies mainly in the vertical direction, and distributes almost uniformly in the horizontal direction. The maximum of ptr is always located at the lowermost point of the levitated drop. Whereas the secondary maximum appears at the uppermost point if the incident pressure amplitude p0 is higher than an intermediate value (3044Pa), in which there exists a pressure nodal surface in the drop interior. The value of the maximum ptr lies in a narrow range of 2489-3173Pa, which has a lower limit of 2489Pa when p0=3044Pa. The secondary maximum of ptr is rather small and only remarkable at high incident pressures.
Implications of nonlinearity for spherically symmetric accretion
NASA Astrophysics Data System (ADS)
Sen, Sourav; Ray, Arnab K.
2014-03-01
We subject the steady solutions of a spherically symmetric accretion flow to a time-dependent radial perturbation. The equation of the perturbation includes nonlinearity up to any arbitrary order and bears a form that is very similar to the metric equation of an analogue acoustic black hole. Casting the perturbation as a standing wave on subsonic solutions, and maintaining nonlinearity in it up to the second order, we get the time dependence of the perturbation in the form of a Liénard system. A dynamical systems analysis of the Liénard system reveals a saddle point in real time, with the implication that instabilities will develop in the accreting system when the perturbation is extended into the nonlinear regime. The instability of initial subsonic states also adversely affects the temporal evolution of the flow toward a final and stable transonic state.
Spark Plasma Sintering of Titanium Spherical Particles
NASA Astrophysics Data System (ADS)
Abedi, Mohammad; Moskovskikh, Dmitry O.; Rogachev, Alexander S.; Mukasyan, Alexander S.
2016-10-01
The densification kinetics for sintering of titanium spherical particles under two different experimental schemes, i.e., current-assisted and current-insulated were investigated. It was shown that measurable densification rate differences between the two schemes are recognized only for the preheating stage. For current-assisted experiments, consolidation starts at lower temperatures than for current-insulated samples. Also at high heating rates, the change of sample porosity all through the preheating stage is higher for current-assisted conditions, while at relatively low heating rates ( i.e., less than 100 K/min) they are comparable. All through the isothermal sintering stage, at a temperature of 1073 K (800 °C), the shrinkage rates are comparable for both experimental schemes within the measurement accuracy. The explanation of the observed effects within the framework of conventional sintering theory is also provided.
Gravitational vacuum polarization around static spherical stars
Hiscock, W.A.
1988-04-15
The gravitational vacuum polarization of conformally coupled quantum fields in the spacetime of a uniform-density, static, spherical star is studied using the approximation developed by Page, Brown, and Ottewill. Approximate vacuum stress-energy tensors are calculated for conformal massless scalar, spinor, and vector fields; in the case of vector fields, both dimensionally regularized and zeta-function results are given. Explicit algebraic forms for the stress-energy tensors are given for the interior of the star and for the exterior Schwarzschild region. If the vacuum stress energy is to be conserved and have the correct trace anomaly at the surface of the star, it is necessary that there be distributional terms in the vacuum stress energy at the surface. The nature and magnitude of these terms are determined. The semiclassical Einstein equations are solved in the exterior region of the star to first order in (h/2..pi..), and the first quantum corrections to Kepler's third law are found.
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.
Stability of Spherical Vesicles in Electric Fields
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
Collective excitations of spherical semiconductor nanoparticles
NASA Astrophysics Data System (ADS)
Moradi, Afshin
2016-10-01
In this article, we study the dispersion properties of bulk and surface electrostatic oscillations of a spherical quantum electron-hole semiconductor plasma as a simple model of a semiconductor nanoparticle. We derive general dispersion relation for both bulk and surface modes, using quantum hydrodynamic theory (including the electrons and holes quantum recoil effects, quantum statistical pressures of the plasma species, as well as exchange and correlation effects) in conjunction with Poisson’s equation and appropriate boundary conditions. We show that for the arbitrary value of angular quantum number {\\ell }≥slant 1 there are only two surface plasmon modes, but two infinite series of bulk modes for {\\ell }≥slant 0 that owe their existence to the curvature of the interface. We use the typical values of GaAs semiconductor to compute the bulk and surface mode frequencies for different value of {\\ell }.
Spark Plasma Sintering of Titanium Spherical Particles
NASA Astrophysics Data System (ADS)
Abedi, Mohammad; Moskovskikh, Dmitry O.; Rogachev, Alexander S.; Mukasyan, Alexander S.
2016-07-01
The densification kinetics for sintering of titanium spherical particles under two different experimental schemes, i.e., current-assisted and current-insulated were investigated. It was shown that measurable densification rate differences between the two schemes are recognized only for the preheating stage. For current-assisted experiments, consolidation starts at lower temperatures than for current-insulated samples. Also at high heating rates, the change of sample porosity all through the preheating stage is higher for current-assisted conditions, while at relatively low heating rates (i.e., less than 100 K/min) they are comparable. All through the isothermal sintering stage, at a temperature of 1073 K (800 °C), the shrinkage rates are comparable for both experimental schemes within the measurement accuracy. The explanation of the observed effects within the framework of conventional sintering theory is also provided.
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.
Geometry of modified Newtonian dynamics
NASA Astrophysics Data System (ADS)
Skordis, Constantinos; Zlosnik, Tom
2012-02-01
Modified Newtonian dynamics is an empirical modification to Poisson’s equation which has had success in accounting for the “gravitational field” Φ in a variety of astrophysical systems. The field Φ may be interpreted in terms of the weak-field limit of a variety of spacetime geometries. Here we consider three of these geometries in a more comprehensive manner and look at the effect on timelike and null geodesics. In particular we consider the aquadratic Lagrangian (AQUAL) theory, tensor-vector-scalar (TeVeS) theory and generalized Einstein-aether theory. We uncover a number of novel features, some of which are specific to the theory considered while others are generic. In the case of AQUAL and TeVeS theories, the spacetime exhibits an excess (AQUAL) or deficit TeVeS solid angle akin to the case of a Barriola-Vilenkin global monopole. In the case of generalized Einstein-aether, a disformal symmetry of the action emerges in the limit of ∇→Φ→0. Finally, in all theories studied, massive particles can never reach spatial infinity while photons can do so only after experiencing infinite redshift.
Quanta of geometry: noncommutative aspects.
Chamseddine, Ali H; Connes, Alain; Mukhanov, Viatcheslav
2015-03-01
In the construction of spectral manifolds in noncommutative geometry, a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of real scalar fields naturally appears and implies, by equality with the index formula, the quantization of the volume. We first show that this condition implies that the manifold decomposes into disconnected spheres, which will represent quanta of geometry. We then refine the condition by involving the real structure and two types of geometric quanta, and show that connected spin manifolds with large quantized volume are then obtained as solutions. The two algebras M_{2}(H) and M_{4}(C) are obtained, which are the exact constituents of the standard model. Using the two maps from M_{4} to S^{4} the four-manifold is built out of a very large number of the two kinds of spheres of Planckian volume. We give several physical applications of this scheme such as quantization of the cosmological constant, mimetic dark matter, and area quantization of black holes. PMID:25793795
Turbine engine variable geometry device
NASA Technical Reports Server (NTRS)
Rogo, Casimir (Inventor); Lenz, Herman N. (Inventor)
1985-01-01
A variable geometry device for use with the turbine nozzle of a turbine engine of the type having a support housing and a combustion chamber contained within the support housing. A pair of spaced walls in the support housing define an annular and radially extending nozzle passageway. The outer end of the nozzle passageway is open to the combustion chamber while the inner end of the nozzle passageway is open to one or more turbine stages. A plurality of circumferentially spaced nozzle vanes are mounted to one of the spaced walls and protrude across the nozzle passageway. An annular opening is formed around the opposite spaced wall and an annular ring is axially slidably mounted within the opening. A motor is operatively connected to this ring and, upon actuation, axially displaces the ring within the nozzle passageway. In addition, the ring includes a plurality of circumferentially spaced slots which register with the nozzle vanes so that the vane geometry remains the same despite axial displacement of the ring.
Interactive rendering of dynamic geometry.
Ponchio, Federico; Hormann, Kai
2008-01-01
Fluid simulations typically produce complex three-dimensional (3D) isosurfaces whose geometry and topology change over time. The standard way of representing such "dynamic geometry" is by a set of isosurfaces that are extracted individually at certain time steps. An alternative strategy is to represent the whole sequence as a four-dimensional (4D) tetrahedral mesh. The iso-surface at a specific time step can then be computed by intersecting the tetrahedral mesh with a 3D hyperplane. This not only allows the animation of the surface continuously over time without having to worry about the topological changes, but also enables simplification algorithms to exploit temporal coherence. We show how to interactively render such 4D tetrahedral meshes by improving previous GPU-accelerated techniques and building an out-of-core multi-resolution structure based on quadric error simplification. As a second application, we apply our framework to time-varying surfaces that result from morphing one triangle mesh into another. PMID:18467764
Geometry and the quantum: basics
NASA Astrophysics Data System (ADS)
Chamseddine, Ali H.; Connes, Alain; Mukhanov, Viatcheslav
2014-12-01
Motivated by the construction of spectral manifolds in noncommutative geometry, we introduce a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. This commutation relation appears in two versions, one sided and two sided. It implies the quantization of the volume. In the one-sided case it implies that the manifold decomposes into a disconnected sum of spheres which will represent quanta of geometry. The two sided version in dimension 4 predicts the two algebras M 2(ℍ) and M 4(ℂ) which are the algebraic constituents of the Standard Model of particle physics. This taken together with the non-commutative algebra of functions allows one to reconstruct, using the spectral action, the Lagrangian of gravity coupled with the Standard Model. We show that any connected Riemannian Spin 4-manifold with quantized volume > 4 (in suitable units) appears as an irreducible representation of the two-sided commutation relations in dimension 4 and that these representations give a seductive model of the "particle picture" for a theory of quantum gravity in which both the Einstein geometric standpoint and the Standard Model emerge from Quantum Mechanics. Physical applications of this quantization scheme will follow in a separate publication.
Neuronal activity controls transsynaptic geometry
Glebov, Oleg O.; Cox, Susan; Humphreys, Lawrence; Burrone, Juan
2016-01-01
The neuronal synapse is comprised of several distinct zones, including presynaptic vesicle zone (SVZ), active zone (AZ) and postsynaptic density (PSD). While correct relative positioning of these zones is believed to be essential for synaptic function, the mechanisms controlling their mutual localization remain unexplored. Here, we employ high-throughput quantitative confocal imaging, super-resolution and electron microscopy to visualize organization of synaptic subdomains in hippocampal neurons. Silencing of neuronal activity leads to reversible reorganization of the synaptic geometry, resulting in a increased overlap between immunostained AZ and PSD markers; in contrast, the SVZ-AZ spatial coupling is decreased. Bayesian blinking and bleaching (3B) reconstruction reveals that the distance between the AZ-PSD distance is decreased by 30 nm, while electron microscopy shows that the width of the synaptic cleft is decreased by 1.1 nm. Our findings show that multiple aspects of synaptic geometry are dynamically controlled by neuronal activity and suggest mutual repositioning of synaptic components as a potential novel mechanism contributing to the homeostatic forms of synaptic plasticity. PMID:26951792
Alternative cosmology from cusp geometries
NASA Astrophysics Data System (ADS)
Rosa, Reinaldo; Herbin Stalder Díaz, Diego
We study an alternative geometrical approach on the problem of classical cosmological singularity. It is based on a generalized function f(x,y)=x(2+y^2=(1-z)z^n) which consists of a cusped projected coupled isosurface. Such a projected geometry is computed and analized into the context of Friedmann singularity-free cosmology where a pre-big bang scenario is considered. Assuming that the mechanism of cusp formation is described by non-linear oscillations of a pre- big bang extended very high energy density field (>3x10^{94} kg/m^3$), we show that the action under the gravitational field follows a tautochrone of revolution, understood here as the primary projected geometry that alternatively replaces the Friedmann singularity in the standard big bang theory. As shown here this new approach allows us to interpret the nature of both matter and dark energy from first geometric principles [1]. [1] Rosa et al. DOI: 10.1063/1.4756991
Fuzzy Logic for Incidence Geometry
2016-01-01
The paper presents a mathematical framework for approximate geometric reasoning with extended objects in the context of Geography, in which all entities and their relationships are described by human language. These entities could be labelled by commonly used names of landmarks, water areas, and so forth. Unlike single points that are given in Cartesian coordinates, these geographic entities are extended in space and often loosely defined, but people easily perform spatial reasoning with extended geographic objects “as if they were points.” Unfortunately, up to date, geographic information systems (GIS) miss the capability of geometric reasoning with extended objects. The aim of the paper is to present a mathematical apparatus for approximate geometric reasoning with extended objects that is usable in GIS. In the paper we discuss the fuzzy logic (Aliev and Tserkovny, 2011) as a reasoning system for geometry of extended objects, as well as a basis for fuzzification of the axioms of incidence geometry. The same fuzzy logic was used for fuzzification of Euclid's first postulate. Fuzzy equivalence relation “extended lines sameness” is introduced. For its approximation we also utilize a fuzzy conditional inference, which is based on proposed fuzzy “degree of indiscernibility” and “discernibility measure” of extended points. PMID:27689133
Weyl gravity and Cartan geometry
NASA Astrophysics Data System (ADS)
Attard, J.; François, J.; Lazzarini, S.
2016-04-01
We point out that the Cartan geometry known as the second-order conformal structure provides a natural differential geometric framework underlying gauge theories of conformal gravity. We are concerned with two theories: the first one is the associated Yang-Mills-like Lagrangian, while the second, inspired by [1], is a slightly more general one that relaxes the conformal Cartan geometry. The corresponding gauge symmetry is treated within the Becchi-Rouet-Stora-Tyutin language. We show that the Weyl gauge potential is a spurious degree of freedom, analogous to a Stueckelberg field, that can be eliminated through the dressing field method. We derive sets of field equations for both the studied Lagrangians. For the second one, they constrain the gauge field to be the "normal conformal Cartan connection.''Finally, we provide in a Lagrangian framework a justification of the identification, in dimension 4, of the Bach tensor with the Yang-Mills current of the normal conformal Cartan connection, as proved in [2].
Target Detection Using Fractal Geometry
NASA Technical Reports Server (NTRS)
Fuller, J. Joseph
1991-01-01
The concepts and theory of fractal geometry were applied to the problem of segmenting a 256 x 256 pixel image so that manmade objects could be extracted from natural backgrounds. The two most important measurements necessary to extract these manmade objects were fractal dimension and lacunarity. Provision was made to pass the manmade portion to a lookup table for subsequent identification. A computer program was written to construct cloud backgrounds of fractal dimensions which were allowed to vary between 2.2 and 2.8. Images of three model space targets were combined with these backgrounds to provide a data set for testing the validity of the approach. Once the data set was constructed, computer programs were written to extract estimates of the fractal dimension and lacunarity on 4 x 4 pixel subsets of the image. It was shown that for clouds of fractal dimension 2.7 or less, appropriate thresholding on fractal dimension and lacunarity yielded a 64 x 64 edge-detected image with all or most of the cloud background removed. These images were enhanced by an erosion and dilation to provide the final image passed to the lookup table. While the ultimate goal was to pass the final image to a neural network for identification, this work shows the applicability of fractal geometry to the problems of image segmentation, edge detection and separating a target of interest from a natural background.
Chemistry as a diagnostic of prestellar core geometry
NASA Astrophysics Data System (ADS)
Tritsis, A.; Tassis, K.; Willacy, K.
2016-05-01
We present a new method for assessing the intrinsic 3D shape of prestellar cores from molecular column densities. We have employed hydrodynamic simulations of contracting, isothermal cores considering three intrinsic geometries: spherical, cylindrical/filamentary and disc-like. We have coupled our hydrodynamic simulations with non-equilibrium chemistry. We find that (a) when cores are observed very elongated (i.e. for aspect ratios ≤0.15) the intrinsic 3D geometry can be probed by their 2D molecular emission maps, since these exhibit significant qualitative morphological differences between cylindrical and disc-like cores. Specifically, if a disc-like core is observed as a filamentary object in dust emission, then it will be observed as two parallel filaments in N2H+; (b) for cores with higher aspect ratios (i.e. 0.15-0.9) we define a metric Δ that quantifies whether a molecular column density profile is centrally peaked, depressed or flat. We have identified one molecule (CN) for which Δ as a function of the aspect ratio probes the 3D geometry of the core; and (c) for cores with almost circular projections (i.e. for aspect ratios ˜1), we have identified three molecules (OH, CO and H2CO) that can be used to probe the intrinsic 3D shape by close inspection of their molecular column density radial profiles. We alter the temperature and the cosmic ray ionization rate and demonstrate that our method is robust against the choice of parameters.
Pasqual, Alexander Mattioli; Herzog, Philippe; Arruda, José Roberto de França
2010-12-01
Sound directivity control is made possible by a compact array of independent loudspeakers operating at the same frequency range. The drivers are usually distributed over a sphere-like frame according to a Platonic solid geometry to obtain a highly symmetrical configuration. The radiation pattern of spherical loudspeaker arrays has been predicted from the surface velocity pattern by approximating the drivers membranes as rigid vibrating spherical caps, although a rigorous assessment of this model has not been provided so far. Many aspects concerning compact array electromechanics remain unclear, such as the effects on the acoustical performance of the drivers interaction inside the array cavity, or the fact that voltages rather than velocities are controlled in practice. This work presents a detailed investigation of the electromechanical behavior of spherical loudspeaker arrays. Simulation results are shown to agree with laser vibrometer measurements and experimental sound power data obtained for a 12-driver spherical array prototype at low frequencies, whereas the non-rigid body motion and the first cavity eigenfrequency yield a discrepancy between theoretical and experimental results at high frequencies. Finally, although the internal acoustic coupling affects the drivers vibration in the low-frequency range, it does not play an important role on the radiated sound power.
Differential Geometry Based Multiscale Models
Wei, Guo-Wei
2010-01-01
Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atom-istic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier–Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson–Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson–Nernst–Planck equations that
Differential geometry based multiscale models.
Wei, Guo-Wei
2010-08-01
Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atomistic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier-Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson-Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson-Nernst-Planck equations that are
Differential geometry based multiscale models.
Wei, Guo-Wei
2010-08-01
Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atomistic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier-Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson-Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson-Nernst-Planck equations that are
NASA Astrophysics Data System (ADS)
Bulanov, Stepan; Maksimchuk, Anatoly; Zhidkov, Alexei
2009-11-01
We report on the analytic and computer simulation study of a relativistic spherical wake wave. Such a wave in the breaking regime, traveling towards the center is able to reflect and focus the incoming radiation and up-shifting its frequency. The reflected and focused electromagnetic pulse can have such high intensity, that it is able to create e^+e^- pairs via Schwinger process.
Interactive graphics for geometry modeling
NASA Technical Reports Server (NTRS)
Wozny, M. J.
1984-01-01
An interactive vector capability to create geometry and a raster color shaded rendering capability to sample and verify interim geometric design steps through color snapshots is described. The development is outlined of the underlying methodology which facilitates computer aided engineering and design. At present, raster systems cannot match the interactivity and line-drawing capability of refresh vector systems. Consequently, an intermediate step in mechanical design is used to create objects interactively on the vector display and then scan convert the wireframe model to render it as a color shaded object on a raster display. Several algorithms are presented for rendering such objects. Superquadric solid primitive extend the class of primitives normally used in solid modelers.
Quantum gauge theories from geometry
NASA Astrophysics Data System (ADS)
Galehouse, Daniel C.
2006-03-01
Geometrical theories have been developed to describe quantum interacting particles with full mathematical covariance. They possess a sophisticated gauge structure that derives from the fundamental properties of the geometry. These theories are all implicitly quantized and come in three known types: Weyl, non-compactified Kaluza-Klein, and, as presented here, Dirac. The spin one-half particle is a conformal wave in an eight dimensional Riemannian space. The coordinates transform locally as spinors and project into space time to give the known gravitational and electromagnetic forces. The gauge structure of the weak interactions appears as well, as in this space the electron transforms into a neutrino under hyper-rotations. The possibility of including the strong interactions and the corresponding gauge system is discussed.
Noncommutative Geometry and Basic Physics
NASA Astrophysics Data System (ADS)
Kastler, Daniel
Alain Connes' noncommutative geometry, started in 1982 [0], widely developed in 1994 as expounded in his book at this date [0] (it has grown meanwhile) is a systematic quantization of mathematics parallel to the quantization of physics effected in the twenties.This theory widens the scope of mathematics in a manner congenial to physics, reorganizes the existing ("classical") mathematics of which it produces an hitherto unsuspected unification, and provides basic physics (the synthesis of elementary particles and gravitation) with a programme of renewal which has thus far achieved a clarification of the classical (tree-level) aspects of a new synthesis of the (Euclidean) standard model with gravitation [32],[33]: this is the subject of the present lectures - with the inherent tentative prediction of the Higgs mass.
Local geometry of isoscalar surfaces.
Dopazo, César; Martín, Jesús; Hierro, Juan
2007-11-01
An inert dynamically passive scalar in a constant density fluid forced by a statistically homogeneous field of turbulence has been investigated using the results of a 256(3) grid direct numerical simulation. Mixing characteristics are characterized in terms of either principal curvatures or mean and Gauss curvatures. The most probable small-scale scalar geometries are flat and tilelike isosurfaces. Preliminary correlations between flow and scalar small-scale structures associate highly curved saddle points with large-strain regions and elliptic points with vorticity-dominated zones. The concavity of the scalar profiles along the isosurface normal coordinate xn correlates well with negative mean curvatures, Gauss curvatures displaying any sign, which correspond to scalar minima, tiles, or saddle points; on the other hand, convexity along xn is associated with positive mean curvatures, Gauss curvatures ranging from negative to positive signs, featuring maxima, tiles, or saddle points; inflection points along xn correlate well with small values of the mean curvature and zero or negative values of kg, corresponding to plane isosurfaces or saddle points with curvatures of equal and opposite signs. Small values of the scalar gradient are associated with elliptic points, either concave or convex (kg>0) , for both concave and convex scalar profiles along xn. Large values of the scalar gradient (or, equivalently, scalar fluctuation dissipation rates) are generally connected with small values of the Gauss curvature (either flat or moderate-curvature tilelike local geometries), with both concave and convex scalar profiles along xn equally probable. Vortical local flow structures correlate well with small and moderate values of the scalar gradient, while strain-dominated regions are associated with large values. PMID:18233765
Geometry of discrete quantum computing
NASA Astrophysics Data System (ADS)
Hanson, Andrew J.; Ortiz, Gerardo; Sabry, Amr; Tai, Yu-Tsung
2013-05-01
Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2n infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any real-world resources, and, if we have the idea of physical law as some kind of computational algorithm of the universe, we would be compelled to alter our descriptions of physics to be consistent with computable numbers. Our purpose here is to examine the geometric implications of using finite fields Fp and finite complexified fields \\mathbf {F}_{p^2} (based on primes p congruent to 3 (mod4)) as the basis for computations in a theory of discrete quantum computing, which would therefore become a computable theory. Because the states of a discrete n-qubit system are in principle enumerable, we are able to determine the proportions of entangled and unentangled states. In particular, we extend the Hopf fibration that defines the irreducible state space of conventional continuous n-qubit theories (which is the complex projective space \\mathbf {CP}^{2^{n}-1}) to an analogous discrete geometry in which the Hopf circle for any n is found to be a discrete set of p + 1 points. The tally of unit-length n-qubit states is given, and reduced via the generalized Hopf fibration to \\mathbf {DCP}^{2^{n}-1}, the discrete analogue of the complex projective space, which has p^{2^{n}-1} (p-1)\\,\\prod _{k=1}^{n-1} ( p^{2^{k}}+1) irreducible states. Using a measure of entanglement, the purity, we explore the entanglement features of discrete quantum states and find that the n-qubit states based on the complexified field \\mathbf {F}_{p^2} have pn(p - 1)n unentangled states (the product of the tally for a single qubit) with purity 1, and they have pn + 1(p - 1)(p + 1)n - 1 maximally entangled states with purity zero.
Changing the Structure Boundary Geometry
Karasev, Viktor; Dzlieva, Elena; Ivanov, Artyom
2008-09-07
Analysis of previously obtained results shows that hexagonal crystal lattice is the dominant type of ordering, in particular, in striated glow discharges. We explore the possibility for changing the dust distribution in horizontal cross sections of relatively highly ordered structures in a glow-discharge. Presuming that boundary geometry can affect dust distribution, we used cylindrical coolers held at 0 deg. C and placed against a striation containing a structure, to change the geometry of its outer boundary. By varying the number of coolers, their positions, and their separations from the tube wall, azimuthally asymmetric thermophoretic forces can be used to form polygonal boundaries and vary the angles between their segments (in a horizontal cross section). The corner in the structure's boundary of 60 deg. stimulates formation of hexagonal cells. The structure between the supported parallel boundaries is also characterized by stable hexagonal ordering. We found that a single linear boundary segment does not give rise to any sizable domain, but generates a lattice extending from the boundary (without edge defects). A square lattice can be formed by setting the angle equal to 90 deg. . However, angles of 45 deg. and 135 deg. turned out easier to form. Square lattice was created by forming a near-135 deg. corner with four coolers. It was noted that no grain ordering is observed in the region adjacent to corners of angles smaller than 30 deg. , which do not promote ordering into cells of any shape. Thus, manipulation of a structure boundary can be used to change dust distribution, create structures free of the ubiquitous edge defects that destroy orientation order, and probably change the crystal lattice type.
Digital breast tomosynthesis geometry calibration
NASA Astrophysics Data System (ADS)
Wang, Xinying; Mainprize, James G.; Kempston, Michael P.; Mawdsley, Gordon E.; Yaffe, Martin J.
2007-03-01
Digital Breast Tomosynthesis (DBT) is a 3D x-ray technique for imaging the breast. The x-ray tube, mounted on a gantry, moves in an arc over a limited angular range around the breast while 7-15 images are acquired over a period of a few seconds. A reconstruction algorithm is used to create a 3D volume dataset from the projection images. This procedure reduces the effects of tissue superposition, often responsible for degrading the quality of projection mammograms. This may help improve sensitivity of cancer detection, while reducing the number of false positive results. For DBT, images are acquired at a set of gantry rotation angles. The image reconstruction process requires several geometrical factors associated with image acquisition to be known accurately, however, vibration, encoder inaccuracy, the effects of gravity on the gantry arm and manufacturing tolerances can produce deviations from the desired acquisition geometry. Unlike cone-beam CT, in which a complete dataset is acquired (500+ projections over 180°), tomosynthesis reconstruction is challenging in that the angular range is narrow (typically from 20°-45°) and there are fewer projection images (~7-15). With such a limited dataset, reconstruction is very sensitive to geometric alignment. Uncertainties in factors such as detector tilt, gantry angle, focal spot location, source-detector distance and source-pivot distance can produce several artifacts in the reconstructed volume. To accurately and efficiently calculate the location and angles of orientation of critical components of the system in DBT geometry, a suitable phantom is required. We have designed a calibration phantom for tomosynthesis and developed software for accurate measurement of the geometric parameters of a DBT system. These have been tested both by simulation and experiment. We will present estimates of the precision available with this technique for a prototype DBT system.
NASA Astrophysics Data System (ADS)
Kuhfittig, P. K. F.
2016-07-01
When Morris and Thorne first proposed the possible existence of traversable wormholes, they adopted the following strategy: maintain complete control over the geometry, thereby leaving open the determination of the stress-energy tensor. In this paper we determine this tensor by starting with a noncommutative-geometry background and assuming that the static and spherically symmetric spacetime admits conformal motions. This had been established in a previous collaboration with Rahaman et al. using a slightly different approach. Accordingly, the main purpose of this paper is to show that the wormhole obtained can be made stable to linearized radial perturbations.
Assessment of and Improvements to Acoustic Velocimetry in Flows in Core-like Geometries
NASA Astrophysics Data System (ADS)
Mautino, A. R.; Adams, M. M.; Stone, D.; Triana, S. A.; Lathrop, D. P.; Lekic, V.
2015-12-01
Rapidly rotating fluid flows are found in a wide variety of geophysical and astrophysical contexts, including the Earth's outer core. The dynamics of such flows can be studied experimentally at conditions inaccessible to computational modeling. However, accurately measuring the mean and time-varying flows noninvasively presents a technical challenge, particularly in opaque liquids. In this study, we tackle the problem of mapping zonal flow profiles in spherical Couette flows, shear flows in a core-like geometry. These rotating flows induce shifts and splittings in the spectrum of the acoustically resonant fluid-filled cavity. The azimuthal component of flow can be estimated from the spectra of the acoustic modes, using inversion procedures adapted from Helioseismology. Here, we present a technique for reconstructing the mean velocity field using modal analysis by way of the Finite Element Method, which is used to compute the forward model accurately, taking into account structural geometries associated with the experimental setups, such as shafts and axles. Accurate forward modeling is crucial for reliable mode identification, and we demonstrate that it allows us to identify many more modes than is possible when using the spherically symmetric approximation. We model flow geometry as a superposition of low order basis flow patterns, each of which affects mode frequency splittings and shifts through advection and Coriolis forces.
Systematic Calibration for a Backpacked Spherical Photogrammetry Imaging System
NASA Astrophysics Data System (ADS)
Rau, J. Y.; Su, B. W.; Hsiao, K. W.; Jhan, J. P.
2016-06-01
A spherical camera can observe the environment for almost 720 degrees' field of view in one shoot, which is useful for augmented reality, environment documentation, or mobile mapping applications. This paper aims to develop a spherical photogrammetry imaging system for the purpose of 3D measurement through a backpacked mobile mapping system (MMS). The used equipment contains a Ladybug-5 spherical camera, a tactical grade positioning and orientation system (POS), i.e. SPAN-CPT, and an odometer, etc. This research aims to directly apply photogrammetric space intersection technique for 3D mapping from a spherical image stereo-pair. For this purpose, several systematic calibration procedures are required, including lens distortion calibration, relative orientation calibration, boresight calibration for direct georeferencing, and spherical image calibration. The lens distortion is serious on the ladybug-5 camera's original 6 images. Meanwhile, for spherical image mosaicking from these original 6 images, we propose the use of their relative orientation and correct their lens distortion at the same time. However, the constructed spherical image still contains systematic error, which will reduce the 3D measurement accuracy. Later for direct georeferencing purpose, we need to establish a ground control field for boresight/lever-arm calibration. Then, we can apply the calibrated parameters to obtain the exterior orientation parameters (EOPs) of all spherical images. In the end, the 3D positioning accuracy after space intersection will be evaluated, including EOPs obtained by structure from motion method.