Sample records for uniform spherically symmetric

  1. Plasma oscillations in spherical Gaussian shaped ultracold neutral plasma

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Chen, Tianxing; Lu, Ronghua, E-mail: lurh@siom.ac.cn; Guo, Li

    2016-04-15

    The collective plasma oscillations are investigated in ultracold neutral plasma with a non-uniform density profile. Instead of the plane configuration widely used, we derive the plasma oscillation equations with spherically symmetric distribution and Gaussian density profile. The damping of radial oscillation is found. The Tonks–Dattner resonances of the ultracold neutral plasma with an applied RF field are also calculated.

  2. Point symmetric design approach to a wide-field wide-wavelength cat's eye retro-reflector anastigmat

    NASA Astrophysics Data System (ADS)

    Liepmann, Till W.

    2009-08-01

    A point symmetric design approach for creating a practical cat's eye retro-reflector (CERR) anastigmat lens with a wide field of regard (FOR), uniform reflectance and wide wavelength range is described. An anastigmat design is presented that demonstrates the performance capability of the design approach. The lens design is diffraction limited in double pass at F/3, has a "working distance" between lens and reflector, wide wavelength range of operation, and uniform reflectivity over a 120 deg FOR. An anastigmat fabricated from the design is presented; however, the design approach is generally useful for any application requiring a high performance retro-reflector. The design uses only spherical surfaces, thereby avoiding the fabrication expense of aspheric surfaces.

  3. How Spherical Is a Cube (Gravitationally)?

    NASA Astrophysics Data System (ADS)

    Sanny, Jeff; Smith, David

    2015-02-01

    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.1,2 By integrating over ring elements of a spherical shell, we show that the gravitational force on a point mass outside the shell is the same as that of a particle with the same mass as the shell at its center. This derivation works for objects with spherical symmetry while depending on the fact that the gravitational force between two point masses varies inversely as the square of their separation.3 If these conditions are not met, then the problem becomes more difficult. In this paper, we remove the condition of spherical symmetry and examine the gravitational force between two uniform cubes.

  4. An instability of the standard model of cosmology creates the anomalous acceleration without dark energy

    NASA Astrophysics Data System (ADS)

    Smoller, Joel; Temple, Blake; Vogler, Zeke

    2017-11-01

    We identify the condition for smoothness at the centre of spherically symmetric solutions of Einstein's original equations without the cosmological constant or dark energy. We use this to derive a universal phase portrait which describes general, smooth, spherically symmetric solutions near the centre of symmetry when the pressure p=0. In this phase portrait, the critical k=0 Friedmann space-time appears as a saddle rest point which is unstable to spherical perturbations. This raises the question as to whether the Friedmann space-time is observable by redshift versus luminosity measurements looking outwards from any point. The unstable manifold of the saddle rest point corresponding to Friedmann describes the evolution of local uniformly expanding space-times whose accelerations closely mimic the effects of dark energy. A unique simple wave perturbation from the radiation epoch is shown to trigger the instability, match the accelerations of dark energy up to second order and distinguish the theory from dark energy at third order. In this sense, anomalous accelerations are not only consistent with Einstein's original theory of general relativity, but are a prediction of it without the cosmological constant or dark energy.

  5. An instability of the standard model of cosmology creates the anomalous acceleration without dark energy.

    PubMed

    Smoller, Joel; Temple, Blake; Vogler, Zeke

    2017-11-01

    We identify the condition for smoothness at the centre of spherically symmetric solutions of Einstein's original equations without the cosmological constant or dark energy. We use this to derive a universal phase portrait which describes general, smooth, spherically symmetric solutions near the centre of symmetry when the pressure p =0. In this phase portrait, the critical k =0 Friedmann space-time appears as a saddle rest point which is unstable to spherical perturbations. This raises the question as to whether the Friedmann space-time is observable by redshift versus luminosity measurements looking outwards from any point. The unstable manifold of the saddle rest point corresponding to Friedmann describes the evolution of local uniformly expanding space-times whose accelerations closely mimic the effects of dark energy. A unique simple wave perturbation from the radiation epoch is shown to trigger the instability, match the accelerations of dark energy up to second order and distinguish the theory from dark energy at third order. In this sense, anomalous accelerations are not only consistent with Einstein's original theory of general relativity, but are a prediction of it without the cosmological constant or dark energy.

  6. Time-dependent spherically symmetric accretion onto compact X-ray sources

    NASA Technical Reports Server (NTRS)

    Cowie, L. L.; Ostriker, J. P.; Stark, A. A.

    1978-01-01

    Analytical arguments and a numerical hydrodynamic code are used to investigate spherically symmetric accretion onto a compact object, in an attempt to provide some insight into gas flows heated by an outgoing X-ray flux. It is shown that preheating of spherically symmetric accretion flows by energetic radiation from an X-ray source results in time-dependent behavior for a much wider range of source parameters than was determined previously and that there are two distinct types of instability. The results are compared with observations of X-ray bursters and transients as well as with theories on quasars and active galactic nuclei that involve quasi-spherically symmetric accretion onto massive black holes. Models based on spherically symmetric accretion are found to be inconsistent with observations of bursters and transients.

  7. Vanishing Viscosity Approach to the Compressible Euler Equations for Transonic Nozzle and Spherically Symmetric Flows

    NASA Astrophysics Data System (ADS)

    Chen, Gui-Qiang G.; Schrecker, Matthew R. I.

    2018-04-01

    We are concerned with globally defined entropy solutions to the Euler equations for compressible fluid flows in transonic nozzles with general cross-sectional areas. Such nozzles include the de Laval nozzles and other more general nozzles whose cross-sectional area functions are allowed at the nozzle ends to be either zero (closed ends) or infinity (unbounded ends). To achieve this, in this paper, we develop a vanishing viscosity method to construct globally defined approximate solutions and then establish essential uniform estimates in weighted L p norms for the whole range of physical adiabatic exponents γ\\in (1, ∞) , so that the viscosity approximate solutions satisfy the general L p compensated compactness framework. The viscosity method is designed to incorporate artificial viscosity terms with the natural Dirichlet boundary conditions to ensure the uniform estimates. Then such estimates lead to both the convergence of the approximate solutions and the existence theory of globally defined finite-energy entropy solutions to the Euler equations for transonic flows that may have different end-states in the class of nozzles with general cross-sectional areas for all γ\\in (1, ∞) . The approach and techniques developed here apply to other problems with similar difficulties. In particular, we successfully apply them to construct globally defined spherically symmetric entropy solutions to the Euler equations for all γ\\in (1, ∞).

  8. Rotational excitation of symmetric top molecules by collisions with atoms: Close coupling, coupled states, and effective potential calculations for NH3-He

    NASA Technical Reports Server (NTRS)

    Green, S.

    1976-01-01

    The formalism for describing rotational excitation in collisions between symmetric top rigid rotors and spherical atoms is presented both within the accurate quantum close coupling framework and also the coupled states approximation of McGuire and Kouri and the effective potential approximation of Rabitz. Calculations are reported for thermal energy NH3-He collisions, treating NH3 as a rigid rotor and employing a uniform electron gas (Gordon-Kim) approximation for the intermolecular potential. Coupled states are found to be in nearly quantitative agreement with close coupling results while the effective potential method is found to be at least qualitatively correct. Modifications necessary to treat the inversion motion in NH3 are discussed.

  9. Defect Implosion Experiments (DIME) at OMEGA

    NASA Astrophysics Data System (ADS)

    Cobble, J. A.; Schmitt, M. J.; Tregillis, I. L.; Obrey, K. D.; Magelssen, G. R.; Wilke, M. D.; Glebov, V.; Marshall, F. J.; Kim, Y. H.; Bradley, P. A.; Batha, S. H.

    2010-11-01

    The Los Alamos DIME campaign involves perturbed spherical implosions, driven by 60 OMEGA beams with uniform, symmetrical illumination. D-T-filled CH-shell targets with equatorial-plane defects are designed to produce a non-spherical neutron burn region. The objectives of the DIME series are to observe the non-spherical burn with the neutron imaging system (NIS) and to simulate the physics of the neutron and x-ray production. We have demonstrated adequate neutron yield for NIS imaging with targets of diameter 860 μm. All targets are filled with 5 atm of DT. We used two separate shell thicknesses: 8 μm and 15 μm, thus testing both exploding pusher and ablative designs. Defect channel depth ranges from 0 -- 8 μm. Width is 20 -- 40 μm. Perfect targets have no defect. Numerical simulations predict enhanced x-ray emission, that is suggested by experiment. Results from a recent DIME campaign will be discussed.

  10. Spherically-symmetric solutions in general relativity using a tetrad-based approach

    NASA Astrophysics Data System (ADS)

    Kim, Do Young; Lasenby, Anthony N.; Hobson, Michael P.

    2018-03-01

    We present a tetrad-based method for solving the Einstein field equations for spherically-symmetric systems and compare it with the widely-used Lemaître-Tolman-Bondi (LTB) model. In particular, we focus on the issues of gauge ambiguity and the use of comoving versus `physical' coordinate systems. We also clarify the correspondences between the two approaches, and illustrate their differences by applying them to the classic examples of the Schwarzschild and Friedmann-Lemaître-Robertson-Walker spacetimes. We demonstrate that the tetrad-based method does not suffer from the gauge freedoms inherent to the LTB model, naturally accommodates non-uniform pressure and has a more transparent physical interpretation. We further apply our tetrad-based method to a generalised form of `Swiss cheese' model, which consists of an interior spherical region surrounded by a spherical shell of vacuum that is embedded in an exterior background universe. In general, we allow the fluid in the interior and exterior regions to support pressure, and do not demand that the interior region be compensated. We pay particular attention to the form of the solution in the intervening vacuum region and illustrate the validity of Birkhoff's theorem at both the metric and tetrad level. We then reconsider critically the original theoretical arguments underlying the so-called Rh = ct cosmological model, which has recently received considerable attention. These considerations in turn illustrate the interesting behaviour of a number of `horizons' in general cosmological models.

  11. Molecular theory for self assembling mixtures of patchy colloids and colloids with spherically symmetric attractions: The single patch case

    NASA Astrophysics Data System (ADS)

    Marshall, Bennett D.; Chapman, Walter G.

    2013-09-01

    In this work we develop a new theory to model self assembling mixtures of single patch colloids and colloids with spherically symmetric attractions. In the development of the theory we restrict the interactions such that there are short ranged attractions between patchy and spherically symmetric colloids, but patchy colloids do not attract patchy colloids and spherically symmetric colloids do not attract spherically symmetric colloids. This results in the temperature, density, and composition dependent reversible self assembly of the mixture into colloidal star molecules. This type of mixture has been recently synthesized by grafting of complimentary single stranded DNA [L. Feng, R. Dreyfus, R. Sha, N. C. Seeman, and P. M. Chaikin, Adv. Mater. 25(20), 2779-2783 (2013)], 10.1002/adma.201204864. As a quantitative test of the theory, we perform new monte carlo simulations to study the self assembly of these mixtures; theory and simulation are found to be in excellent agreement.

  12. Smoothed particle hydrodynamic simulations of expanding HII regions

    NASA Astrophysics Data System (ADS)

    Bisbas, Thomas G.

    2009-09-01

    This thesis deals with numerical simulations of expanding ionized regions, known as HII regions. We implement a new three dimensional algorithm in Smoothed Particle Hydrodynamics for including the dynamical effects of the interaction between ionizing radiation and the interstellar medium. This interaction plays a crucial role in star formation at all epochs. We study the influence of ionizing radiation in spherically symmetric clouds. In particular, we study the spherically symmetric expansion of an HII region inside a uniform-density, non-self-gravitating cloud. We examine the ability of our algorithm to reproduce the known theoretical solution and we find that the agreement is very good. We also study the spherically symmetric expansion inside a uniform-density, self-gravitating cloud. We propose a new differential equation of motion for the expanding shell that includes the effects of gravity. Comparing its numerical solution with the simulations, we find that the equation predicts the position of the shell accurately. We also study the expansion of an off-centre HII region inside a uniform-density, non- self-gravitating cloud. This results in an evolution known as the rocket effect, where the ionizing radiation pushes and accelerates the cloud away from the exciting star leading to its dispersal. During this evolution, cometary knots appear as a result of Rayleigh-Taylor and Vishniac instabilities. The knots are composed of a dense head with a conic tail behind them, a structure that points towards the ionizing source. Our simulations show that these knots are very reminiscent of the observed structures in planetary nebula, such as in the Helix nebula. The last part of this thesis is dedicated to the study of cores ionized by an exciting source which is placed outside and far away from them. The evolution of these cores is known as radiation driven compression (or implosion). We perform simulations and compare our findings with results of other workers and we find that they agree very well. Using stable Bonnor-Ebert spheres, we extend our study to modelling triggered star formation within these cores as they are overrun and compressed by the incident ionizing flux. We construct a parameter space diagram and we map regions where star formation is expected to be observed. All the above results indicate that the algorithm presented in this thesis works well for treating the propagation of ionizing radiation. This new algorithm provides the means to explore and evaluate the role of ionizing radiation in regulating the efficiency and statistics of star formation.

  13. Energy gain calculations in spherical IEC fusion systems using the BAFP code

    NASA Astrophysics Data System (ADS)

    Chacón, L.; Miley, G. H.; Barnes, D. C.; Knoll, D. A.

    1999-11-01

    The spherical IEC fusion concept takes advantage of the potential well generated by an inner spherical cathode (physical or virtual), biased negatively to several kV with respect to a concentric outer grounded boundary, to focus ions inwards and form a dense central core where fusion may occur. However, defocusing of the ion beams due to ion-ion collisions may prevent a satisfactory energy balance in the system. This research concentrates of spherically symmetric virtual cathode IEC devices, in which a spherical cloud of electrons, confined á la Penning trap, creates the ion-confining electrostatic well. A bounce-averaged Fokker-Planck model has been constructed to analyze the ion physics in ideal conditions (i.e., spherically uniform electrostatic well, no collisional interaction between ions and electrons, single ion species).(L. Chacon, D. C. Barnes, D. A. Knoll, 40^th) Annual Meeting of the APS Division of Plasma Physics, New Orleans, LA, Nov. 1998 Results will reproduce the phenomenology of previously published( W. Nevins, Phys. Plasmas), 2(10), 3804-3819 (1995) theoretical limits, and will show that, under some conditions, steady-state solutions with relatively high gains and small ion recirculation powers exist for the bounce-averaged Fokker-Planck transport equation. Variations in gain with parameter space will be presented.

  14. Single molecule diffusion and the solution of the spherically symmetric residence time equation.

    PubMed

    Agmon, Noam

    2011-06-16

    The residence time of a single dye molecule diffusing within a laser spot is propotional to the total number of photons emitted by it. With this application in mind, we solve the spherically symmetric "residence time equation" (RTE) to obtain the solution for the Laplace transform of the mean residence time (MRT) within a d-dimensional ball, as a function of the initial location of the particle and the observation time. The solutions for initial conditions of potential experimental interest, starting in the center, on the surface or uniformly within the ball, are explicitly presented. Special cases for dimensions 1, 2, and 3 are obtained, which can be Laplace inverted analytically for d = 1 and 3. In addition, the analytic short- and long-time asymptotic behaviors of the MRT are derived and compared with the exact solutions for d = 1, 2, and 3. As a demonstration of the simplification afforded by the RTE, the Appendix obtains the residence time distribution by solving the Feynman-Kac equation, from which the MRT is obtained by differentiation. Single-molecule diffusion experiments could be devised to test the results for the MRT presented in this work. © 2011 American Chemical Society

  15. Noncommutative spherically symmetric spacetimes at semiclassical order

    NASA Astrophysics Data System (ADS)

    Fritz, Christopher; Majid, Shahn

    2017-07-01

    Working within the recent formalism of Poisson-Riemannian geometry, we completely solve the case of generic spherically symmetric metric and spherically symmetric Poisson-bracket to find a unique answer for the quantum differential calculus, quantum metric and quantum Levi-Civita connection at semiclassical order O(λ) . Here λ is the deformation parameter, plausibly the Planck scale. We find that r, t, d r, d t are all forced to be central, i.e. undeformed at order λ, while for each value of r, t we are forced to have a fuzzy sphere of radius r with a unique differential calculus which is necessarily nonassociative at order λ2 . We give the spherically symmetric quantisation of the FLRW cosmology in detail and also recover a previous analysis for the Schwarzschild black hole, now showing that the quantum Ricci tensor for the latter vanishes at order λ. The quantum Laplace-Beltrami operator for spherically symmetric models turns out to be undeformed at order λ while more generally in Poisson-Riemannian geometry we show that it deforms to □f+λ2ωαβ(Ricγα-Sγα)(∇^βdf)γ+O(λ2) in terms of the classical Levi-Civita connection \\widehat\

  16. Perturbations of a close-earth satellite due to sunlight diffusely reflected from the earth. I - Uniform albedo

    NASA Technical Reports Server (NTRS)

    Lautman, D. A.

    1977-01-01

    A semianalytic method has been developed to calculate the radiation-pressure perturbations of a close-earth satellite due to sunlight reflected from the earth. The assumptions made are that the satellite is spherically symmetric and that the solar radiation is reflected from the earth according to Lambert's Law with uniform albedo. By using expressions for the components of the radiation-pressure force due to Lochry, the expressions for the perturbations of the elements were developed into series in the true anomaly. The perturbations within a given revolution can be obtained analytically by integrating with respect to v while holding all slowly varying quantities constant. The long-range perturbations are then obtained by accumulating the net perturbations at the end of each revolution.

  17. Analytical expression for a class of spherically symmetric solutions in Lorentz-breaking massive gravity

    NASA Astrophysics Data System (ADS)

    Li, Ping; Li, Xin-zhou; Xi, Ping

    2016-06-01

    We present a detailed study of the spherically symmetric solutions in Lorentz-breaking massive gravity. There is an undetermined function { F }(X,{w}1,{w}2,{w}3) in the action of Stückelberg fields {S}φ ={{{Λ }}}4\\int {{{d}}}4x\\sqrt{-g}{ F }, which should be resolved through physical means. In general relativity, the spherically symmetric solution to the Einstein equation is a benchmark and its massive deformation also plays a crucial role in Lorentz-breaking massive gravity. { F } will satisfy the constraint equation {T}01=0 from the spherically symmetric Einstein tensor {G}01=0, if we maintain that any reasonable physical theory should possess the spherically symmetric solutions. The Stückelberg field {φ }i is taken as a ‘hedgehog’ configuration {φ }i=φ (r){x}i/r, whose stability is guaranteed by the topological one. Under this ansätz, {T}01=0 is reduced to d{ F }=0. The functions { F } for d{ F }=0 form a commutative ring {R}{ F }. We obtain an expression of the solution to the functional differential equation with spherical symmetry if { F }\\in {R}{ F }. If { F }\\in {R}{ F } and \\partial { F }/\\partial X=0, the functions { F } form a subring {S}{ F }\\subset {R}{ F }. We show that the metric is Schwarzschild, Schwarzschild-AdS or Schwarzschild-dS if { F }\\in {S}{ F }. When { F }\\in {R}{ F } but { F }\

  18. A no-hair theorem for stars in Horndeski theories

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Lehébel, A.; Babichev, E.; Charmousis, C., E-mail: antoine.lehebel@th.u-psud.fr, E-mail: eugeny.babichev@th.u-psud.fr, E-mail: christos.charmousis@th.u-psud.fr

    We consider a generic scalar-tensor theory involving a shift-symmetric scalar field and minimally coupled matter fields. We prove that the Noether current associated with shift-symmetry vanishes in regular, spherically symmetric and static spacetimes. We use this fact to prove the absence of scalar hair for spherically symmetric and static stars in Horndeski and beyond theories. We carefully detail the validity of this no-hair theorem.

  19. Compact Process for the Preparation of Microfine Spherical High-Niobium-Containing TiAl Alloy Powders

    NASA Astrophysics Data System (ADS)

    Tong, J. B.; Lu, X.; Liu, C. C.; Wang, L. N.; Qu, X. H.

    2015-03-01

    High-Nb-containing TiAl alloys are a new generation of materials for high-temperature structural applications because of their superior high-temperature mechanical properties. The alloy powders can be widely used for additive manufacturing, thermal spraying, and powder metallurgy. Because of the difficulty of making microfine spherical alloy powders in quantity by conventional techniques, a compact method was proposed, which consisted of two-step ball milling of elemental powders and subsequent radio frequency (RF) argon plasma spheroidization. In comparison with conventional mechanical alloying techniques, the two-step milling process can be used to prepare alloy powders with uniform scale in a short milling time with no addition of process control agent. This makes the process effective and less contaminating. After RF argon plasma spheroidization, the powders produced exhibit good sphericity, and the number-average diameter is about 8.2 μm with a symmetric unimodal particle size distribution. The powders perform high composition homogeneity and contain predominately supersaturated α 2-Ti3Al phase. The oxygen and carbon contents of the spheroidized powder are 0.47% and 0.050%, respectively.

  20. The effects of atmospheric refraction on the accuracy of laser ranging systems

    NASA Technical Reports Server (NTRS)

    Zanter, D. L.; Gardner, C. S.; Rao, N. N.

    1976-01-01

    Correction formulas derived by Saastamoinen and Marini, and the ray traces through the refractivity profiles all assume a spherically symmetric refractivity profile. The errors introduced by this assumption were investigated by ray tracing through three-dimensional profiles. The results of this investigation indicate that the difference between ray traces through the spherically symmetric and three-dimensional profiles is approximately three centimeters at 10 deg and decreases to less than one half of a centimeter at 80 deg. If the accuracy desired in future laser ranging systems is less than a few centimeters, Saastamoinen and Marini's formulas must be altered to account for the fact that the refractivity profile is not spherically symmetric.

  1. On the information content of natural frequency spectra associated with different angular numbers. [acoustic velocity in vibrating fluid sphere model of earth structure

    NASA Technical Reports Server (NTRS)

    Barcilon, V.

    1978-01-01

    The problem of inferring the speed of sound in a contained spherically symmetric fluid solely from its natural frequencies of vibration is considered. An investigation of the case in which the data consist of the two spectra associated with the angular numbers 0 and 1, suggests the possibility that a one-parameter family of slowness profiles can be constructed. These profiles are compatible with the data, up to first order in the non-uniformity of the fluid. It is conjectured that for other angular numbers, the loss of information increases as the difference between them increases.

  2. Line and point defects in nonlinear anisotropic solids

    NASA Astrophysics Data System (ADS)

    Golgoon, Ashkan; Yavari, Arash

    2018-06-01

    In this paper, we present some analytical solutions for the stress fields of nonlinear anisotropic solids with distributed line and point defects. In particular, we determine the stress fields of (i) a parallel cylindrically symmetric distribution of screw dislocations in infinite orthotropic and monoclinic media, (ii) a cylindrically symmetric distribution of parallel wedge disclinations in an infinite orthotropic medium, (iii) a distribution of edge dislocations in an orthotropic medium, and (iv) a spherically symmetric distribution of point defects in a transversely isotropic spherical ball.

  3. Shock wave propagation in layered planetary embryos

    NASA Astrophysics Data System (ADS)

    Arkani-Hamed, Jafar; Ivanov, Boris A.

    2014-05-01

    The propagation of impact-induced shock wave inside a planetary embryo is investigated using the Hugoniot equations and a new scaling law, governing the particle velocity variations along a shock ray inside a spherical body. The scaling law is adopted to determine the impact heating of a growing embryo in its early stage when it is an undifferentiated and uniform body. The new scaling law, similar to other existing scaling laws, is not suitable for a large differentiated embryo consisting of a silicate mantle overlying an iron core. An algorithm is developed in this study on the basis of the ray theory in a spherically symmetric body which relates the shock parameters at the top of the core to those at the base of the mantle, thus enabling the adoption of scaling laws to estimate the impact heating of both the mantle and the core. The algorithm is applied to two embryo models: a simple two-layered model with a uniform mantle overlying a uniform core, and a model where the pre-shock density and acoustic velocity of the embryo are radially dependent. The former illustrates details of the particle velocity, shock pressure, and temperature increase behind the shock front in a 2D axisymmetric geometry. The latter provides a means to compare the results with those obtained by a hydrocode simulation. The agreement between the results of the two techniques in revealing the effects of the core-mantle boundary on the shock wave transmission across the boundary is encouraging.

  4. Sheet-like assemblies of spherical particles with point-symmetrical patches.

    PubMed

    Mani, Ethayaraja; Sanz, Eduardo; Roy, Soumyajit; Dijkstra, Marjolein; Groenewold, Jan; Kegel, Willem K

    2012-04-14

    We report a computational study on the spontaneous self-assembly of spherical particles into two-dimensional crystals. The experimental observation of such structures stabilized by spherical objects appeared paradoxical so far. We implement patchy interactions with the patches point-symmetrically (icosahedral and cubic) arranged on the surface of the particle. In these conditions, preference for self-assembly into sheet-like structures is observed. We explain our findings in terms of the inherent symmetry of the patches and the competition between binding energy and vibrational entropy. The simulation results explain why hollow spherical shells observed in some Keplerate-type polyoxometalates (POM) appear. Our results also provide an explanation for the experimentally observed layer-by-layer growth of apoferritin--a quasi-spherical protein.

  5. Method for preparing spherical thermoplastic particles of uniform size

    DOEpatents

    Day, J.R.

    1975-11-17

    Spherical particles of thermoplastic material of virtually uniform roundness and diameter are prepared by cutting monofilaments of a selected diameter into rod-like segments of a selected uniform length which are then heated in a viscous liquid to effect the formation of the spherical particles.

  6. Nonspherically Symmetric Collapse in Asymptotically AdS Spacetimes.

    PubMed

    Bantilan, Hans; Figueras, Pau; Kunesch, Markus; Romatschke, Paul

    2017-11-10

    We numerically simulate gravitational collapse in asymptotically anti-de Sitter spacetimes away from spherical symmetry. Starting from initial data sourced by a massless real scalar field, we solve the Einstein equations with a negative cosmological constant in five spacetime dimensions and obtain a family of nonspherically symmetric solutions, including those that form two distinct black holes on the axis. We find that these configurations collapse faster than spherically symmetric ones of the same mass and radial compactness. Similarly, they require less mass to collapse within a fixed time.

  7. Nonspherically Symmetric Collapse in Asymptotically AdS Spacetimes

    NASA Astrophysics Data System (ADS)

    Bantilan, Hans; Figueras, Pau; Kunesch, Markus; Romatschke, Paul

    2017-11-01

    We numerically simulate gravitational collapse in asymptotically anti-de Sitter spacetimes away from spherical symmetry. Starting from initial data sourced by a massless real scalar field, we solve the Einstein equations with a negative cosmological constant in five spacetime dimensions and obtain a family of nonspherically symmetric solutions, including those that form two distinct black holes on the axis. We find that these configurations collapse faster than spherically symmetric ones of the same mass and radial compactness. Similarly, they require less mass to collapse within a fixed time.

  8. A new two-metric theory of gravity with prior geometry

    NASA Technical Reports Server (NTRS)

    Lightman, A. P.; Lee, D. L.

    1972-01-01

    A theory is presented of gravity which has the same post-Newtonian (PN) as that of general relativity. The field equations, and a calculation of the PN limit of the theory are discussed along with the equations of stellar structure for static spherically symmetric stars. A special exterior spherically symmetric solution, time dependent solutions, conservations, and gravitational waves are analyzed.

  9. Sooting and disruption in spherically symmetrical combustion of decane droplets in air

    NASA Technical Reports Server (NTRS)

    Dryer, F. L.; Williams, F. A.; Haggard, J. B., Jr.; Shaw, B. D.

    1987-01-01

    The paper presents the results of experiments on the burning of individual 1-2 mm decane droplets in air at room temperature and atmospheric pressure. The NASA Lewis 2.2 s drop tower was used as well as a newly designed droplet-combustion apparatus that promotes nearly spherically symmetrical combustion. Unanticipated disruptions related to sooting behavior were encountered.

  10. Anomalous waterlike behavior in spherically-symmetric water models optimized with the relative entropy.

    PubMed

    Chaimovich, Aviel; Shell, M Scott

    2009-03-28

    Recent efforts have attempted to understand many of liquid water's anomalous properties in terms of effective spherically-symmetric pairwise molecular interactions entailing two characteristic length scales (so-called "core-softened" potentials). In this work, we examine the extent to which such simple descriptions of water are representative of the true underlying interactions by extracting coarse-grained potential functions that are optimized to reproduce the behavior of an all-atom model. To perform this optimization, we use a novel procedure based upon minimizing the relative entropy, a quantity that measures the extent to which a coarse-grained configurational ensemble overlaps with a reference all-atom one. We show that the optimized spherically-symmetric water models exhibit notable variations with the state conditions at which they were optimized, reflecting in particular the shifting accessibility of networked hydrogen bonding interactions. Moreover, we find that water's density and diffusivity anomalies are only reproduced when the effective coarse-grained potentials are allowed to vary with state. Our results therefore suggest that no state-independent spherically-symmetric potential can fully capture the interactions responsible for water's unique behavior; rather, the particular way in which the effective interactions vary with temperature and density contributes significantly to anomalous properties.

  11. A new approach to spherically symmetric junction surfaces and the matching of FLRW regions

    NASA Astrophysics Data System (ADS)

    Kirchner, U.

    2004-08-01

    We investigate timelike junctions (with surface layer) between spherically symmetric solutions of the Einstein-field equation. In contrast to previous investigations, this is done in a coordinate system in which the junction surface motion is absorbed in the metric, while all coordinates are continuous at the junction surface. The evolution equations for all relevant quantities are derived. We discuss the no-surface layer case (boundary surface) and study the behaviour for small surface energies. It is shown that one should expect cases in which the speed of light is reached within a finite proper time. We carefully discuss necessary and sufficient conditions for a possible matching of spherically symmetric sections. For timelike junctions between spherically symmetric spacetime sections we show explicitly that the time component of the Lanczos equation always reduces to an identity (independent of the surface equation of state). The results are applied to the matching of Friedmann Lemaître Robertson Walker (FLRW) models. We discuss 'vacuum bubbles' and closed open junctions in detail. As illustrations several numerical integration results are presented, some of them indicate that (observers comoving with) the junction surface can reach the speed of light within a finite time.

  12. Revealing Large-Scale Asymetries in the Winds of Hot, Luminous Stars Using Spectroscopy and Polarimetry

    NASA Astrophysics Data System (ADS)

    St-Louis, Nicole

    2015-08-01

    The winds of hot, luminous stars are known to show small but also large scale density structures. Ultimately, these departures from spherical symmetry are important for the understanding of the loss of angular momentum from the star and are crucial in determining its rotation rate. There are many observational signatures of these departures from a uniform and spherically symmetric outflow. This poster will present results from spectroscopic and polarimetric observations of Wolf-Rayet stars, the descendants of massive O stars, that reveal large-scale asymmetries in their winds and discuss what can be learned about the structure of these winds and about the the physical mechanism responsible for generating them. Very little is known about the rotation rates of these small, He-burning stars which are the direct progenitors of at least some supernova explosions. If enough angular momentum is retained in the core, some may also very well be the progenitors of long gamma-ray bursts.

  13. Time-resolved compression of a capsule with a cone to high density for fast-ignition laser fusion

    DOE PAGES

    Theobald, W.; Solodov, A. A.; Stoeckl, C.; ...

    2014-12-12

    The advent of high-intensity lasers enables us to recreate and study the behaviour of matter under the extreme densities and pressures that exist in many astrophysical objects. It may also enable us to develop a power source based on laser-driven nuclear fusion. Achieving such conditions usually requires a target that is highly uniform and spherically symmetric. Here we show that it is possible to generate high densities in a so-called fast-ignition target that consists of a thin shell whose spherical symmetry is interrupted by the inclusion of a metal cone. Using picosecond-time-resolved X-ray radiography, we show that we can achievemore » areal densities in excess of 300 mg cm -2 with a nanosecond-duration compression pulse -- the highest areal density ever reported for a cone-in-shell target. Such densities are high enough to stop MeV electrons, which is necessary for igniting the fuel with a subsequent picosecond pulse focused into the resulting plasma.« less

  14. Time-resolved compression of a capsule with a cone to high density for fast-ignition laser fusion.

    PubMed

    Theobald, W; Solodov, A A; Stoeckl, C; Anderson, K S; Beg, F N; Epstein, R; Fiksel, G; Giraldez, E M; Glebov, V Yu; Habara, H; Ivancic, S; Jarrott, L C; Marshall, F J; McKiernan, G; McLean, H S; Mileham, C; Nilson, P M; Patel, P K; Pérez, F; Sangster, T C; Santos, J J; Sawada, H; Shvydky, A; Stephens, R B; Wei, M S

    2014-12-12

    The advent of high-intensity lasers enables us to recreate and study the behaviour of matter under the extreme densities and pressures that exist in many astrophysical objects. It may also enable us to develop a power source based on laser-driven nuclear fusion. Achieving such conditions usually requires a target that is highly uniform and spherically symmetric. Here we show that it is possible to generate high densities in a so-called fast-ignition target that consists of a thin shell whose spherical symmetry is interrupted by the inclusion of a metal cone. Using picosecond-time-resolved X-ray radiography, we show that we can achieve areal densities in excess of 300 mg cm(-2) with a nanosecond-duration compression pulse--the highest areal density ever reported for a cone-in-shell target. Such densities are high enough to stop MeV electrons, which is necessary for igniting the fuel with a subsequent picosecond pulse focused into the resulting plasma.

  15. Static, free vibration and thermal analysis of composite plates and shells using a flat triangular shell element

    NASA Astrophysics Data System (ADS)

    Kapania, R. K.; Mohan, P.

    1996-09-01

    Finite element static, free vibration and thermal analysis of thin laminated plates and shells using a three noded triangular flat shell element is presented. The flat shell element is a combination of the Discrete Kirchhoff Theory (DKT) plate bending element and a membrane element derived from the Linear Strain Triangular (LST) element with a total of 18 degrees of freedom (3 translations and 3 rotations per node). Explicit formulations are used for the membrane, bending and membrane-bending coupling stiffness matrices and the thermal load vector. Due to a strong analogy between the induced strain caused by the thermal field and the strain induced in a structure due to an electric field the present formulation is readily applicable for the analysis of structures excited by surface bonded or embedded piezoelectric actuators. The results are presented for (i) static analysis of (a) simply supported square plates under doubly sinusoidal load and uniformly distributed load (b) simply supported spherical shells under a uniformly distributed load, (ii) free vibration analysis of (a) square cantilever plates, (b) skew cantilever plates and (c) simply supported spherical shells; (iii) Thermal deformation analysis of (a) simply supported square plates, (b) simply supported-clamped square plate and (c) simply supported spherical shells. A numerical example is also presented demonstrating the application of the present formulation to analyse a symmetrically laminated graphite/epoxy laminate excited by a layer of piezoelectric polyvinylidene flouride (PVDF). The results presented are in good agreement with those available in the literature.

  16. Controlling the shape of membrane protein polyhedra

    NASA Astrophysics Data System (ADS)

    Li, Di; Kahraman, Osman; Haselwandter, Christoph A.

    2017-03-01

    Membrane proteins and lipids can self-assemble into membrane protein polyhedral nanoparticles (MPPNs). MPPNs have a closed spherical surface and a polyhedral protein arrangement, and may offer a new route for structure determination of membrane proteins and targeted drug delivery. We develop here a general analytic model of how MPPN self-assembly depends on bilayer-protein interactions and lipid bilayer mechanical properties. We find that the bilayer-protein hydrophobic thickness mismatch is a key molecular control parameter for MPPN shape that can be used to bias MPPN self-assembly towards highly symmetric and uniform MPPN shapes. Our results suggest strategies for optimizing MPPN shape for structural studies of membrane proteins and targeted drug delivery.

  17. Initial boundary-value problem for the spherically symmetric Einstein equations with fluids with tangential pressure.

    PubMed

    Brito, Irene; Mena, Filipe C

    2017-08-01

    We prove that, for a given spherically symmetric fluid distribution with tangential pressure on an initial space-like hypersurface with a time-like boundary, there exists a unique, local in time solution to the Einstein equations in a neighbourhood of the boundary. As an application, we consider a particular elastic fluid interior matched to a vacuum exterior.

  18. Group analysis of dynamics equations of self-gravitating polytropic gas

    NASA Astrophysics Data System (ADS)

    Klebanov, I.; Panov, A.; Ivanov, S.; Maslova, O.

    2018-06-01

    The Lie algebras admitted by the dynamics equations of self-gravitating gas for an arbitrary equation of state and a polytropic gas are calculated. A spherically symmetric submodel is constructed for the case of a polytropic gas. The Lie algebras and the optimal system of subalgebras for a spherically symmetric submodel are computed. An invariant solution describing the steady motion is obtained.

  19. General Wahlquist metrics in all dimensions

    NASA Astrophysics Data System (ADS)

    Hinoue, Kazuki; Houri, Tsuyoshi; Rugina, Christina; Yasui, Yukinori

    2014-07-01

    It is shown that the Wahlquist metric, which is a stationary, axially symmetric perfect fluid solution with ρ +3p=const, admits a rank-2 generalized closed conformal Killing-Yano tensor with a skew-symmetric torsion. Taking advantage of the presence of such a tensor, we obtain a higher-dimensional generalization of the Wahlquist metric in arbitrary dimensions, including a family of vacuum black hole solutions with spherical horizon topology such as Schwarzschild-Tangherlini, Myers-Perry and higher-dimensional Kerr-NUT-(A)dS metrics and a family of static, spherically symmetric perfect fluid solutions in higher dimensions.

  20. Nonpolynomial Lagrangian approach to regular black holes

    NASA Astrophysics Data System (ADS)

    Colléaux, Aimeric; Chinaglia, Stefano; Zerbini, Sergio

    We present a review on Lagrangian models admitting spherically symmetric regular black holes (RBHs), and cosmological bounce solutions. Nonlinear electrodynamics, nonpolynomial gravity, and fluid approaches are explained in details. They consist respectively in a gauge invariant generalization of the Maxwell-Lagrangian, in modifications of the Einstein-Hilbert action via nonpolynomial curvature invariants, and finally in the reconstruction of density profiles able to cure the central singularity of black holes. The nonpolynomial gravity curvature invariants have the special property to be second-order and polynomial in the metric field, in spherically symmetric spacetimes. Along the way, other models and results are discussed, and some general properties that RBHs should satisfy are mentioned. A covariant Sakharov criterion for the absence of singularities in dynamical spherically symmetric spacetimes is also proposed and checked for some examples of such regular metric fields.

  1. Higher-dimensional gravitational collapse of perfect fluid spherically symmetric spacetime in f(R, T) gravity

    NASA Astrophysics Data System (ADS)

    Khan, Suhail; Khan, Muhammad Shoaib; Ali, Amjad

    2018-04-01

    In this paper, our aim is to study (n + 2)-dimensional collapse of perfect fluid spherically symmetric spacetime in the context of f(R, T) gravity. The matching conditions are acquired by considering a spherically symmetric non-static (n + 2)-dimensional metric in the inner region and Schwarzschild (n + 2)-dimensional metric in the outer region of the star. To solve the field equations for above settings in f(R, T) gravity, we choose the stress-energy tensor trace and the Ricci scalar as constants. It is observed that two physical horizons, namely, cosmological and black hole horizons appear as a consequence of this collapse. A singularity is also formed after the birth of both the horizons. It is also observed that the term f(R0, T0) slows down the collapsing process.

  2. Identification of black hole horizons using scalar curvature invariants

    NASA Astrophysics Data System (ADS)

    Coley, Alan; McNutt, David

    2018-01-01

    We introduce the concept of a geometric horizon, which is a surface distinguished by the vanishing of certain curvature invariants which characterize its special algebraic character. We motivate its use for the detection of the event horizon of a stationary black hole by providing a set of appropriate scalar polynomial curvature invariants that vanish on this surface. We extend this result by proving that a non-expanding horizon, which generalizes a Killing horizon, coincides with the geometric horizon. Finally, we consider the imploding spherically symmetric metrics and show that the geometric horizon identifies a unique quasi-local surface corresponding to the unique spherically symmetric marginally trapped tube, implying that the spherically symmetric dynamical black holes admit a geometric horizon. Based on these results, we propose a suite of conjectures concerning the application of geometric horizons to more general dynamical black hole scenarios.

  3. Hawking Radiation from a Spherically Symmetric Static Black Hole

    NASA Astrophysics Data System (ADS)

    Dai, Qian; Liu, Wenbiao

    2007-08-01

    The massive particles’ Hawking radiation from a spherically symmetric static black hole is investigated with Parikh-Wilczek method, Hamilton Jacobi method and Damour Ruffini’s method. When energy conservation is considered, the same result can be concluded that the radiation spectrum is not precisely thermal. The corrected spectrum is consistent to the underlying unitary quantum theory, which can be used to explain the information loss paradox possibly.

  4. Spherically symmetric analysis on open FLRW solution in non-linear massive gravity

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Chiang, Chien-I; Izumi, Keisuke; Chen, Pisin, E-mail: chienichiang@berkeley.edu, E-mail: izumi@phys.ntu.edu.tw, E-mail: chen@slac.stanford.edu

    2012-12-01

    We study non-linear massive gravity in the spherically symmetric context. Our main motivation is to investigate the effect of helicity-0 mode which remains elusive after analysis of cosmological perturbation around an open Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. The non-linear form of the effective energy-momentum tensor stemming from the mass term is derived for the spherically symmetric case. Only in the special case where the area of the two sphere is not deviated away from the FLRW universe, the effective energy momentum tensor becomes completely the same as that of cosmological constant. This opens a window for discriminating the non-linear massive gravity frommore » general relativity (GR). Indeed, by further solving these spherically symmetric gravitational equations of motion in vacuum to the linear order, we obtain a solution which has an arbitrary time-dependent parameter. In GR, this parameter is a constant and corresponds to the mass of a star. Our result means that Birkhoff's theorem no longer holds in the non-linear massive gravity and suggests that energy can probably be emitted superluminously (with infinite speed) on the self-accelerating background by the helicity-0 mode, which could be a potential plague of this theory.« less

  5. Constrained field theories on spherically symmetric spacetimes with horizons

    NASA Astrophysics Data System (ADS)

    Fernandes, Karan; Lahiri, Amitabha; Ghosh, Suman

    2017-02-01

    We apply the Dirac-Bergmann algorithm for the analysis of constraints to gauge theories defined on spherically symmetric black hole backgrounds. We find that the constraints for a given theory are modified on such spacetimes through the presence of additional contributions from the horizon. As a concrete example, we consider the Maxwell field on a black hole background, and determine the role of the horizon contributions on the dynamics of the theory.

  6. Linear clusters of galaxies - A999 and A1016

    NASA Astrophysics Data System (ADS)

    Chapman, G. N. F.; Geller, M. J.; Huchra, J. P.

    1987-09-01

    The authors have measured 44 new redshifts in A 999 and 40 in A 1016: these clusters are both "linear" according to Rood and Sastry (1971) and Struble and Rood (1982, 1984). With 20 cluster members in A 999 and 22 in A 1016, the authors can estimate the probability that these clusters are actually drawn from spherically symmetric distributions. By comparing the clusters with Monte Carlo King models, they find that A 999 is probably intrinsically spherically symmetric, but A 1016 is probably linear. The authors estimate that ⪆2% of a catalog of spherically symmetric clusters might be erroneously classified as linear. They use the data to estimate the virial masses for these systems. The authors reassess the cluster-galaxy alignment analysis of Adams, Strom, and Strom (1980) and examine the relationship between the luminosity and morphological type of the cluster members and the cluster itself.

  7. No hair theorem in quasi-dilaton massive gravity

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Wu, De-Jun; Zhou, Shuang-Yong

    We investigate the static, spherically symmetric black hole solutions in the quasi-dilaton model and its generalizations, which are scalar extended dRGT massive gravity with a shift symmetry. We show that, unlike generic scalar extended massive gravity models, these theories do not admit static, spherically symmetric black hole solutions until the theory parameters in the dRGT potential are fine-tuned. When fine-tuned, the geometry of the static, spherically symmetric black hole is necessarily that of general relativity and the quasi-dilaton field is constant across the spacetime. The fine-tuning and the no hair theorem apply to black holes with flat, anti-de Sitter ormore » de Sitter asymptotics. (C) 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP(3).« less

  8. Black hole and cosmos with multiple horizons and multiple singularities in vector-tensor theories

    NASA Astrophysics Data System (ADS)

    Gao, Changjun; Lu, Youjun; Yu, Shuang; Shen, You-Gen

    2018-05-01

    A stationary and spherically symmetric black hole (e.g., Reissner-Nordström black hole or Kerr-Newman black hole) has, at most, one singularity and two horizons. One horizon is the outer event horizon and the other is the inner Cauchy horizon. Can we construct static and spherically symmetric black hole solutions with N horizons and M singularities? The de Sitter cosmos has only one apparent horizon. Can we construct cosmos solutions with N horizons? In this article, we present the static and spherically symmetric black hole and cosmos solutions with N horizons and M singularities in the vector-tensor theories. Following these motivations, we also construct the black hole solutions with a firewall. The deviation of these black hole solutions from the usual ones can be potentially tested by future measurements of gravitational waves or the black hole continuum spectrum.

  9. No hair theorem in quasi-dilaton massive gravity

    DOE PAGES

    Wu, De-Jun; Zhou, Shuang-Yong

    2016-04-11

    We investigate the static, spherically symmetric black hole solutions in the quasi-dilaton model and its generalizations, which are scalar extended dRGT massive gravity with a shift symmetry. We show that, unlike generic scalar extended massive gravity models, these theories do not admit static, spherically symmetric black hole solutions until the theory parameters in the dRGT potential are fine-tuned. When fine-tuned, the geometry of the static, spherically symmetric black hole is necessarily that of general relativity and the quasi-dilaton field is constant across the spacetime. The fine-tuning and the no hair theorem apply to black holes with flat, anti-de Sitter ormore » de Sitter asymptotics. (C) 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP(3).« less

  10. Fractal continuum model for tracer transport in a porous medium.

    PubMed

    Herrera-Hernández, E C; Coronado, M; Hernández-Coronado, H

    2013-12-01

    A model based on the fractal continuum approach is proposed to describe tracer transport in fractal porous media. The original approach has been extended to treat tracer transport and to include systems with radial and uniform flow, which are cases of interest in geoscience. The models involve advection due to the fluid motion in the fractal continuum and dispersion whose mathematical expression is taken from percolation theory. The resulting advective-dispersive equations are numerically solved for continuous and for pulse tracer injection. The tracer profile and the tracer breakthrough curve are evaluated and analyzed in terms of the fractal parameters. It has been found in this work that anomalous transport frequently appears, and a condition on the fractal parameter values to predict when sub- or superdiffusion might be expected has been obtained. The fingerprints of fractality on the tracer breakthrough curve in the explored parameter window consist of an early tracer breakthrough and long tail curves for the spherical and uniform flow cases, and symmetric short tailed curves for the radial flow case.

  11. Coherent Backscattering in the Cross-Polarized Channel

    NASA Technical Reports Server (NTRS)

    Mischenko, Michael I.; Mackowski, Daniel W.

    2011-01-01

    We analyze the asymptotic behavior of the cross-polarized enhancement factor in the framework of the standard low-packing-density theory of coherent backscattering by discrete random media composed of spherically symmetric particles. It is shown that if the particles are strongly absorbing or if the smallest optical dimension of the particulate medium (i.e., the optical thickness of a plane-parallel slab or the optical diameter of a spherically symmetric volume) approaches zero, then the cross-polarized enhancement factor tends to its upper-limit value 2. This theoretical prediction is illustrated using direct computer solutions of the Maxwell equations for spherical volumes of discrete random medium.

  12. Cryogenic target formation using cold gas jets

    DOEpatents

    Hendricks, Charles D.

    1981-01-01

    A method and apparatus using cold gas jets for producing a substantially uniform layer of cryogenic materials on the inner surface of hollow spherical members having one or more layers, such as inertially imploded targets. By vaporizing and quickly refreezing cryogenic materials contained within a hollow spherical member, a uniform layer of the materials is formed on an inner surface of the spherical member. Basically the method involves directing cold gas jets onto a spherical member having one or more layers or shells and containing the cryogenic material, such as a deuterium-tritium (DT) mixture, to freeze the contained material, momentarily heating the spherical member so as to vaporize the contained material, and quickly refreezing the thus vaporized material forming a uniform layer of cryogenic material on an inner surface of the spherical member.

  13. Cryogenic target formation using cold gas jets

    DOEpatents

    Hendricks, Charles D. [Livermore, CA

    1980-02-26

    A method and apparatus using cold gas jets for producing a substantially uniform layer of cryogenic materials on the inner surface of hollow spherical members having one or more layers, such as inertially imploded targets. By vaporizing and quickly refreezing cryogenic materials contained within a hollow spherical member, a uniform layer of the materials is formed on an inner surface of the spherical member. Basically the method involves directing cold gas jets onto a spherical member having one or more layers or shells and containing the cryogenic material, such as a deuterium-tritium (DT) mixture, to freeze the contained material, momentarily heating the spherical member so as to vaporize the contained material, and quickly refreezing the thus vaporized material forming a uniform layer of cryogenic material on an inner surface of the spherical member.

  14. Asymmetrical Deterministic Lateral Displacement Gaps for Dual Functions of Enhanced Separation and Throughput of Red Blood Cells

    PubMed Central

    Zeming, Kerwin Kwek; Salafi, Thoriq; Chen, Chia-Hung; Zhang, Yong

    2016-01-01

    Deterministic lateral displacement (DLD) method for particle separation in microfluidic devices has been extensively used for particle separation in recent years due to its high resolution and robust separation. DLD has shown versatility for a wide spectrum of applications for sorting of micro particles such as parasites, blood cells to bacteria and DNA. DLD model is designed for spherical particles and efficient separation of blood cells is challenging due to non-uniform shape and size. Moreover, separation in sub-micron regime requires the gap size of DLD systems to be reduced which exponentially increases the device resistance, resulting in greatly reduced throughput. This paper shows how simple application of asymmetrical DLD gap-size by changing the ratio of lateral-gap (GL) to downstream-gap (GD) enables efficient separation of RBCs without greatly restricting throughput. This method reduces the need for challenging fabrication of DLD pillars and provides new insight to the current DLD model. The separation shows an increase in DLD critical diameter resolution (separate smaller particles) and increase selectivity for non-spherical RBCs. The RBCs separate better as compared to standard DLD model with symmetrical gap sizes. This method can be applied to separate non-spherical bacteria or sub-micron particles to enhance throughput and DLD resolution. PMID:26961061

  15. Asymmetrical Deterministic Lateral Displacement Gaps for Dual Functions of Enhanced Separation and Throughput of Red Blood Cells.

    PubMed

    Zeming, Kerwin Kwek; Salafi, Thoriq; Chen, Chia-Hung; Zhang, Yong

    2016-03-10

    Deterministic lateral displacement (DLD) method for particle separation in microfluidic devices has been extensively used for particle separation in recent years due to its high resolution and robust separation. DLD has shown versatility for a wide spectrum of applications for sorting of micro particles such as parasites, blood cells to bacteria and DNA. DLD model is designed for spherical particles and efficient separation of blood cells is challenging due to non-uniform shape and size. Moreover, separation in sub-micron regime requires the gap size of DLD systems to be reduced which exponentially increases the device resistance, resulting in greatly reduced throughput. This paper shows how simple application of asymmetrical DLD gap-size by changing the ratio of lateral-gap (GL) to downstream-gap (GD) enables efficient separation of RBCs without greatly restricting throughput. This method reduces the need for challenging fabrication of DLD pillars and provides new insight to the current DLD model. The separation shows an increase in DLD critical diameter resolution (separate smaller particles) and increase selectivity for non-spherical RBCs. The RBCs separate better as compared to standard DLD model with symmetrical gap sizes. This method can be applied to separate non-spherical bacteria or sub-micron particles to enhance throughput and DLD resolution.

  16. Gaussian statistics for palaeomagnetic vectors

    USGS Publications Warehouse

    Love, J.J.; Constable, C.G.

    2003-01-01

    With the aim of treating the statistics of palaeomagnetic directions and intensities jointly and consistently, we represent the mean and the variance of palaeomagnetic vectors, at a particular site and of a particular polarity, by a probability density function in a Cartesian three-space of orthogonal magnetic-field components consisting of a single (unimoda) non-zero mean, spherically-symmetrical (isotropic) Gaussian function. For palaeomagnetic data of mixed polarities, we consider a bimodal distribution consisting of a pair of such symmetrical Gaussian functions, with equal, but opposite, means and equal variances. For both the Gaussian and bi-Gaussian distributions, and in the spherical three-space of intensity, inclination, and declination, we obtain analytical expressions for the marginal density functions, the cumulative distributions, and the expected values and variances for each spherical coordinate (including the angle with respect to the axis of symmetry of the distributions). The mathematical expressions for the intensity and off-axis angle are closed-form and especially manageable, with the intensity distribution being Rayleigh-Rician. In the limit of small relative vectorial dispersion, the Gaussian (bi-Gaussian) directional distribution approaches a Fisher (Bingham) distribution and the intensity distribution approaches a normal distribution. In the opposite limit of large relative vectorial dispersion, the directional distributions approach a spherically-uniform distribution and the intensity distribution approaches a Maxwell distribution. We quantify biases in estimating the properties of the vector field resulting from the use of simple arithmetic averages, such as estimates of the intensity or the inclination of the mean vector, or the variances of these quantities. With the statistical framework developed here and using the maximum-likelihood method, which gives unbiased estimates in the limit of large data numbers, we demonstrate how to formulate the inverse problem, and how to estimate the mean and variance of the magnetic vector field, even when the data consist of mixed combinations of directions and intensities. We examine palaeomagnetic secular-variation data from Hawaii and Re??union, and although these two sites are on almost opposite latitudes, we find significant differences in the mean vector and differences in the local vectorial variances, with the Hawaiian data being particularly anisotropic. These observations are inconsistent with a description of the mean field as being a simple geocentric axial dipole and with secular variation being statistically symmetrical with respect to reflection through the equatorial plane. Finally, our analysis of palaeomagnetic acquisition data from the 1960 Kilauea flow in Hawaii and the Holocene Xitle flow in Mexico, is consistent with the widely held suspicion that directional data are more accurate than intensity data.

  17. Gaussian statistics for palaeomagnetic vectors

    NASA Astrophysics Data System (ADS)

    Love, J. J.; Constable, C. G.

    2003-03-01

    With the aim of treating the statistics of palaeomagnetic directions and intensities jointly and consistently, we represent the mean and the variance of palaeomagnetic vectors, at a particular site and of a particular polarity, by a probability density function in a Cartesian three-space of orthogonal magnetic-field components consisting of a single (unimodal) non-zero mean, spherically-symmetrical (isotropic) Gaussian function. For palaeomagnetic data of mixed polarities, we consider a bimodal distribution consisting of a pair of such symmetrical Gaussian functions, with equal, but opposite, means and equal variances. For both the Gaussian and bi-Gaussian distributions, and in the spherical three-space of intensity, inclination, and declination, we obtain analytical expressions for the marginal density functions, the cumulative distributions, and the expected values and variances for each spherical coordinate (including the angle with respect to the axis of symmetry of the distributions). The mathematical expressions for the intensity and off-axis angle are closed-form and especially manageable, with the intensity distribution being Rayleigh-Rician. In the limit of small relative vectorial dispersion, the Gaussian (bi-Gaussian) directional distribution approaches a Fisher (Bingham) distribution and the intensity distribution approaches a normal distribution. In the opposite limit of large relative vectorial dispersion, the directional distributions approach a spherically-uniform distribution and the intensity distribution approaches a Maxwell distribution. We quantify biases in estimating the properties of the vector field resulting from the use of simple arithmetic averages, such as estimates of the intensity or the inclination of the mean vector, or the variances of these quantities. With the statistical framework developed here and using the maximum-likelihood method, which gives unbiased estimates in the limit of large data numbers, we demonstrate how to formulate the inverse problem, and how to estimate the mean and variance of the magnetic vector field, even when the data consist of mixed combinations of directions and intensities. We examine palaeomagnetic secular-variation data from Hawaii and Réunion, and although these two sites are on almost opposite latitudes, we find significant differences in the mean vector and differences in the local vectorial variances, with the Hawaiian data being particularly anisotropic. These observations are inconsistent with a description of the mean field as being a simple geocentric axial dipole and with secular variation being statistically symmetrical with respect to reflection through the equatorial plane. Finally, our analysis of palaeomagnetic acquisition data from the 1960 Kilauea flow in Hawaii and the Holocene Xitle flow in Mexico, is consistent with the widely held suspicion that directional data are more accurate than intensity data.

  18. The appearance of highly relativistic, spherically symmetric stellar winds

    NASA Technical Reports Server (NTRS)

    Abramowicz, Marek A.; Novikov, Igor D.; Paczynski, Bohdan

    1991-01-01

    A nonluminous, steady state, spherically symmetric, relativistic wind, with the opacity dominated by electron scattering appears against a bright background as a dark circle with the radius rd. A luminous wind would appear as a bright spot with a radius rl = rd/2 pi gamma exp 3, where gamma is the Lorentz factor of the wind. The bright wind photosphere is convex for v equal to or less than 2c/3, and appears concave for higher outflow velocities.

  19. The Lifespan of a Class of Smooth Spherically Symmetric Solutions of the Compressible Euler Equations with Variable Entropy in Three Space Dimensions

    NASA Astrophysics Data System (ADS)

    Godin, Paul

    2005-09-01

    We consider smooth three-dimensional spherically symmetric Eulerian flows of ideal polytropic gases with variable entropy, whose initial data are obtained by adding a small smooth perturbation with compact support to a constant state. Under a natural assumption, we obtain precise information on the asymptotic behavior of their lifespan when the size of the initial perturbation tends to 0. This is achieved by the construction and estimate of a suitable approximate flow.

  20. Reconstruction of spherically symmetric objects from slit-imaged emission: limitations due to finite slit width

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Mueller, M.M.

    1979-11-01

    A simple method for reconstructing spherically symmetric objects from slit-imaged emission was recently described by Vest and Steel. Although this method is valid for infinitesimal slit widths and practically noise-free irradiance data, it is shown here that its validity does not extend to slits of practical width in the laser-fusion program. However, a method is given for reducing the Vest--Steel plots with practical apertures to obtain information on core diameter, shell diameter, and shell thickness.

  1. Cryogenic target formation using cold gas jets

    DOEpatents

    Hendricks, C.D.

    1980-02-26

    A method and apparatus using cold gas jets for producing a substantially uniform layer of cryogenic materials on the inner surface of hollow spherical members having one or more layers, such as inertially imploded targets are disclosed. By vaporizing and quickly refreezing cryogenic materials contained within a hollow spherical member, a uniform layer of the materials is formed on an inner surface of the spherical member. Basically the method involves directing cold gas jets onto a spherical member having one or more layers or shells and containing the cryogenic material, such as a deuterium-tritium (DT) mixture, to freeze the contained material, momentarily heating the spherical member so as to vaporize the contained material, and quickly refreezing the thus vaporized material forming a uniform layer of cryogenic material on an inner surface of the spherical member. 4 figs.

  2. Dynamics of aspherical dust grains in a cometary atmosphere: I. axially symmetric grains in a spherically symmetric atmosphere

    NASA Astrophysics Data System (ADS)

    Ivanovski, S. L.; Zakharov, V. V.; Della Corte, V.; Crifo, J.-F.; Rotundi, A.; Fulle, M.

    2017-01-01

    In-situ measurements of individual dust grain parameters in the immediate vicinity of a cometary nucleus are being carried by the Rosetta spacecraft at comet 67P/Churyumov-Gerasimenko. For the interpretations of these observational data, a model of dust grain motion as realistic as possible is requested. In particular, the results of the Stardust mission and analysis of samples of interplanetary dust have shown that these particles are highly aspherical, which should be taken into account in any credible model. The aim of the present work is to study the dynamics of ellipsoidal shape particles with various aspect ratios introduced in a spherically symmetric expanding gas flow and to reveal the possible differences in dynamics between spherical and aspherical particles. Their translational and rotational motion under influence of the gravity and of the aerodynamic force and torque is numerically integrated in a wide range of physical parameters values including those of comet 67P/Churyumov-Gerasimenko. The main distinctions of the dynamics of spherical and ellipsoidal particles are discussed. The aerodynamic characteristics of the ellipsoidal particles, and examples of their translational and rotational motion in the postulated gas flow are presented.

  3. Spherical aberration correction with threefold symmetric line currents.

    PubMed

    Hoque, Shahedul; Ito, Hiroyuki; Nishi, Ryuji; Takaoka, Akio; Munro, Eric

    2016-02-01

    It has been shown that N-fold symmetric line current (henceforth denoted as N-SYLC) produces 2N-pole magnetic fields. In this paper, a threefold symmetric line current (N3-SYLC in short) is proposed for correcting 3rd order spherical aberration of round lenses. N3-SYLC can be realized without using magnetic materials, which makes it free of the problems of hysteresis, inhomogeneity and saturation. We investigate theoretically the basic properties of an N3-SYLC configuration which can in principle be realized by simple wires. By optimizing the parameters of a system with beam energy of 5.5keV, the required excitation current for correcting 3rd order spherical aberration coefficient of 400 mm is less than 1AT, and the residual higher order aberrations can be kept sufficiently small to obtain beam size of less than 1 nm for initial slopes up to 5 mrad. Copyright © 2015 Elsevier B.V. All rights reserved.

  4. 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…

  5. Electron Optics for Biologists: Physical Origins of Spherical Aberrations

    ERIC Educational Resources Information Center

    Geissler, Peter; Zadunaisky, Jose

    1974-01-01

    Reports on the physical origins of spherical aberrations in axially symmetric electrostatic lenses to convey the essentials of electon optics to those who must think critically about the resolution of the electron microscope. (GS)

  6. Fiber-Supported Droplet Combustion Experiment-2

    NASA Technical Reports Server (NTRS)

    Colantonio, Renato O.

    1998-01-01

    A major portion of the energy produced in the world today comes from the burning of liquid hydrocarbon fuels in the form of droplets. Understanding the fundamental physical processes involved in droplet combustion is not only important in energy production but also in propulsion, in the mitigation of combustion-generated pollution, and in the control of the fire hazards associated with handling liquid combustibles. Microgravity makes spherically symmetric combustion possible, allowing investigators to easily validate their droplet models without the complicating effects of gravity. The Fiber-Supported Droplet Combustion (FSDC-2) investigation was conducted in the Microgravity Glovebox facility of the shuttles' Spacelab during the reflight of the Microgravity Science Laboratory (MSL- 1R) on STS-94 in July 1997. FSDC-2 studied fundamental phenomena related to liquid fuel droplet combustion in air. Pure fuels and mixtures of fuels were burned as isolated single and duo droplets with and without forced air convection. FSDC-2 is sponsored by the NASA Lewis Research Center, whose researchers are working in cooperation with several investigators from industry and academia. The rate at which a droplet burns is important in many commercial applications. The classical theory of droplet burning assumes that, for an isolated, spherically symmetric, single-fuel droplet, the gas-phase combustion processes are much faster than the droplet surface regression rate and that the liquid phase is at a uniform temperature equal to the boiling point. Recent, more advanced models predict that both the liquid and gas phases are unsteady during a substantial portion of the droplet's burning history, thus affecting the instantaneous and average burning rates, and that flame radiation is a dominant mechanism that can extinguish flames in a microgravity environment. FSDC-2 has provided well-defined, symmetric droplet burning data including radiative emissions to validate these theoretical models for heptane, decane, ethanol, and methanol fuels. Since most commercial combustion systems burn droplets in a convective environment, data were obtained without and with convective flow over the burning droplet (see the following photos).

  7. Light propagation in linearly perturbed ΛLTB models

    NASA Astrophysics Data System (ADS)

    Meyer, Sven; Bartelmann, Matthias

    2017-11-01

    We apply a generic formalism of light propagation to linearly perturbed spherically symmetric dust models including a cosmological constant. For a comoving observer on the central worldline, we derive the equation of geodesic deviation and perform a suitable spherical harmonic decomposition. This allows to map the abstract gauge-invariant perturbation variables to well-known quantities from weak gravitational lensing like convergence or cosmic shear. The resulting set of differential equations can effectively be solved by a Green's function approach leading to line-of-sight integrals sourced by the perturbation variables on the backward lightcone. The resulting spherical harmonic coefficients of the lensing observables are presented and the shear field is decomposed into its E- and B-modes. Results of this work are an essential tool to add information from linear structure formation to the analysis of spherically symmetric dust models with the purpose of testing the Copernican Principle with multiple cosmological probes.

  8. A symmetric integral identity for Bessel functions with applications to integral geometry

    NASA Astrophysics Data System (ADS)

    Salman, Yehonatan

    2017-12-01

    In the article of Kunyansky (Inverse Probl 23(1):373-383, 2007) a symmetric integral identity for Bessel functions of the first and second kind was proved in order to obtain an explicit inversion formula for the spherical mean transform where our data is given on the unit sphere in Rn . The aim of this paper is to prove an analogous symmetric integral identity in case where our data for the spherical mean transform is given on an ellipse E in R2 . For this, we will use the recent results obtained by Cohl and Volkmer (J Phys A Math Theor 45:355204, 2012) for the expansions into eigenfunctions of Bessel functions of the first and second kind in elliptical coordinates.

  9. ODF Maxima Extraction in Spherical Harmonic Representation via Analytical Search Space Reduction

    PubMed Central

    Aganj, Iman; Lenglet, Christophe; Sapiro, Guillermo

    2015-01-01

    By revealing complex fiber structure through the orientation distribution function (ODF), q-ball imaging has recently become a popular reconstruction technique in diffusion-weighted MRI. In this paper, we propose an analytical dimension reduction approach to ODF maxima extraction. We show that by expressing the ODF, or any antipodally symmetric spherical function, in the common fourth order real and symmetric spherical harmonic basis, the maxima of the two-dimensional ODF lie on an analytically derived one-dimensional space, from which we can detect the ODF maxima. This method reduces the computational complexity of the maxima detection, without compromising the accuracy. We demonstrate the performance of our technique on both artificial and human brain data. PMID:20879302

  10. Black hole evaporation in conformal gravity

    NASA Astrophysics Data System (ADS)

    Bambi, Cosimo; Modesto, Leonardo; Porey, Shiladitya; Rachwał, Lesław

    2017-09-01

    We study the formation and the evaporation of a spherically symmetric black hole in conformal gravity. From the collapse of a spherically symmetric thin shell of radiation, we find a singularity-free non-rotating black hole. This black hole has the same Hawking temperature as a Schwarzschild black hole with the same mass, and it completely evaporates either in a finite or in an infinite time, depending on the ensemble. We consider the analysis both in the canonical and in the micro-canonical statistical ensembles. Last, we discuss the corresponding Penrose diagram of this physical process.

  11. Effects of horizontal refractivity gradients on the accuracy of laser ranging to satellites

    NASA Technical Reports Server (NTRS)

    Gardner, C. S.

    1976-01-01

    Numerous formulas have been developed to partially correct laser ranging data for the effects of atmospheric refraction. All the formulas assume the atmospheric refractivity profile is spherically symmetric. The effects of horizontal refractivity gradients are investigated by ray tracing through spherically symmetric and three-dimensional refractivity profiles. The profiles are constructed from radiosonde data. The results indicate that the horizontal gradients introduce an rms error of approximately 3 cm when the satellite is near 10 deg elevation. The error decreases to a few millimeters near zenith.

  12. Topological geons with self-gravitating phantom scalar field

    NASA Astrophysics Data System (ADS)

    Kratovitch, P. V.; Potashov, I. M.; Tchemarina, Ju V.; Tsirulev, A. N.

    2017-12-01

    A topological geon is the quotient manifold M/Z 2 where M is a static spherically symmetric wormhole having the reflection symmetry with respect to its throat. We distinguish such asymptotically at solutions of the Einstein equations according to the form of the time-time metric function by using the quadrature formulas of the so-called inverse problem for self-gravitating spherically symmetric scalar fields. We distinguish three types of geon spacetimes and illustrate them by simple examples. We also study possible observational effects associated with bounded geodesic motion near topological geons.

  13. Black hole evaporation in conformal gravity

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Bambi, Cosimo; Rachwał, Lesław; Modesto, Leonardo

    We study the formation and the evaporation of a spherically symmetric black hole in conformal gravity. From the collapse of a spherically symmetric thin shell of radiation, we find a singularity-free non-rotating black hole. This black hole has the same Hawking temperature as a Schwarzschild black hole with the same mass, and it completely evaporates either in a finite or in an infinite time, depending on the ensemble. We consider the analysis both in the canonical and in the micro-canonical statistical ensembles. Last, we discuss the corresponding Penrose diagram of this physical process.

  14. Study of conformally flat polytropes with tilted congruence

    NASA Astrophysics Data System (ADS)

    Sharif, M.; Sadiq, Sobia

    This paper is aimed to study the modeling of spherically symmetric spacetime in the presence of anisotropic dissipative fluid configuration. This is accomplished for an observer moving relative to matter content using two cases of polytropic equation-of-state under conformally flat condition. We formulate the corresponding generalized Tolman-Oppenheimer-Volkoff equation, mass equation, as well as energy conditions for both cases. The conformally flat condition is imposed to find an expression for anisotropy which helps to study spherically symmetric polytropes. Finally, Tolman mass is used to analyze stability of the resulting models.

  15. Relativistic scattered-wave theory. II - Normalization and symmetrization. [of Dirac wavefunctions

    NASA Technical Reports Server (NTRS)

    Yang, C. Y.

    1978-01-01

    Formalisms for normalization and symmetrization of one-electron Dirac scattered-wave wavefunctions are presented. The normalization integral consists of one-dimensional radial integrals for the spherical regions and an analytic expression for the intersphere region. Symmetrization drastically reduces the size of the secular matrix to be solved. Examples for planar Pb2Se2 and tetrahedral Pd4 are discussed.

  16. Method to produce large, uniform hollow spherical shells

    DOEpatents

    Hendricks, C.D.

    1983-09-26

    The invention is a method to produce large uniform hollow spherical shells by (1) forming uniform size drops of heat decomposable or vaporizable material, (2) evaporating the drops to form dried particles, (3) coating the dried particles with a layer of shell forming material and (4) heating the composite particles to melt the outer layer and to decompose or vaporize the inner particle to form an expanding inner gas bubble. The expanding gas bubble forms the molten outer layer into a shell of relatively large diameter. By cycling the temperature and pressure on the molten shell, nonuniformities in wall thickness can be reduced. The method of the invention is utilized to produce large uniform spherical shells, in the millimeter to centimeter diameter size range, from a variety of materials and of high quality, including sphericity, concentricity and surface smoothness, for use as laser fusion or other inertial confinement fusion targets as well as other applications.

  17. Topics in electromagnetic, acoustic, and potential scattering theory

    NASA Astrophysics Data System (ADS)

    Nuntaplook, Umaporn

    With recent renewed interest in the classical topics of both acoustic and electromagnetic aspects for nano-technology, transformation optics, fiber optics, metamaterials with negative refractive indices, cloaking and invisibility, the topic of time-independent scattering theory in quantum mechanics is becoming a useful field to re-examine in the above contexts. One of the key areas of electromagnetic theory scattering of plane electromagnetic waves --- is based on the properties of the refractive indices in the various media. It transpires that the refractive index of a medium and the potential in quantum scattering theory are intimately related. In many cases, understanding such scattering in radially symmetric media is sufficient to gain insight into scattering in more complex media. Meeting the challenge of variable refractive indices and possibly complicated boundary conditions therefore requires accurate and efficient numerical methods, and where possible, analytic solutions to the radial equations from the governing scalar and vector wave equations (in acoustics and electromagnetic theory, respectively). Until relatively recently, researchers assumed a constant refractive index throughout the medium of interest. However, the most interesting and increasingly useful cases are those with non-constant refractive index profiles. In the majority of this dissertation the focus is on media with piecewise constant refractive indices in radially symmetric media. The method discussed is based on the solution of Maxwell's equations for scattering of plane electromagnetic waves from a dielectric (or "transparent") sphere in terms of the related Helmholtz equation. The main body of the dissertation (Chapters 2 and 3) is concerned with scattering from (i) a uniform spherical inhomogeneity embedded in an external medium with different properties, and (ii) a piecewise-uniform central inhomogeneity in the external medium. The latter results contain a natural generalization of the former (previously known) results. The link with time-independent quantum mechanical scattering, via morphology-dependent resonances (MDRs), is discussed in Chapter 2. This requires a generalization of the classical problem for scattering of a plane wave from a uniform spherically-symmetric inhomogeneity (in which the velocity of propagation is a function only of the radial coordinate r. i.e.. c = c(r)) to a piecewise-uniform inhomogeneity. In Chapter 3 the Jost-function formulation of potential scattering theory is used to solve the radial differential equation for scattering which can be converted into an integral equation corresponding via the Jost boundary conditions. The first two iterations for the zero angular momentum case l = 0 are provided for both two-layer and three-layer models. It is found that the iterative technique is most useful for long wavelengths and sufficiently small ratios of interior and exterior wavenumbers. Exact solutions are also provided for these cases. In Chapter 4 the time-independent quantum mechanical 'connection' is exploited further by generalizing previous work on a spherical well potential to the case where a delta 'function' potential is appended to the exterior of the well (for l ≠ 0). This corresponds to an idealization of the former approach to the case of a 'coated sphere'. The poles of the associated 'S-matrix' are important in this regard, since they correspond directly with the morphology-dependent resonances discussed in Chapter 2. These poles (for the l = 0 case, to compare with Nussenzveig's analysis) are tracked in the complex wavenumber plane as the strength of the delta function potential changes. Finally, a set of 4 Appendices is provided to clarify some of the connections between (i) the scattering of acoustic/electromagnetic waves from a penetrable/dielectric sphere and (ii) time-independent potential scattering theory in quantum mechanics. This, it is hoped, will be the subject of future work.

  18. Schwarzschild and Kerr solutions of Einstein's field equation: An Introduction

    NASA Astrophysics Data System (ADS)

    Heinicke, Christian; Hehl, Friedrich W.

    2015-12-01

    Starting from Newton's gravitational theory, we give a general introduction into the spherically symmetric solution of Einstein's vacuum field equation, the Schwarzschild(-Droste) solution, and into one specific stationary axially symmetric solution, the Kerr solution. The Schwarzschild solution is unique and its metric can be interpreted as the exterior gravitational field of a spherically symmetric mass. The Kerr solution is only unique if the multipole moments of its mass and its angular momentum take on prescribed values. Its metric can be interpreted as the exterior gravitational field of a suitably rotating mass distribution. Both solutions describe objects exhibiting an event horizon, a frontier of no return. The corresponding notion of a black hole is explained to some extent. Eventually, we present some generalizations of the Kerr solution.

  19. Averaged ratio between complementary profiles for evaluating shape distortions of map projections and spherical hierarchical tessellations

    NASA Astrophysics Data System (ADS)

    Yan, Jin; Song, Xiao; Gong, Guanghong

    2016-02-01

    We describe a metric named averaged ratio between complementary profiles to represent the distortion of map projections, and the shape regularity of spherical cells derived from map projections or non-map-projection methods. The properties and statistical characteristics of our metric are investigated. Our metric (1) is a variable of numerical equivalence to both scale component and angular deformation component of Tissot indicatrix, and avoids the invalidation when using Tissot indicatrix and derived differential calculus for evaluating non-map-projection based tessellations where mathematical formulae do not exist (e.g., direct spherical subdivisions), (2) exhibits simplicity (neither differential nor integral calculus) and uniformity in the form of calculations, (3) requires low computational cost, while maintaining high correlation with the results of differential calculus, (4) is a quasi-invariant under rotations, and (5) reflects the distortions of map projections, distortion of spherical cells, and the associated distortions of texels. As an indicator of quantitative evaluation, we investigated typical spherical tessellation methods, some variants of tessellation methods, and map projections. The tessellation methods we evaluated are based on map projections or direct spherical subdivisions. The evaluation involves commonly used Platonic polyhedrons, Catalan polyhedrons, etc. Quantitative analyses based on our metric of shape regularity and an essential metric of area uniformity implied that (1) Uniform Spherical Grids and its variant show good qualities in both area uniformity and shape regularity, and (2) Crusta, Unicube map, and a variant of Unicube map exhibit fairly acceptable degrees of area uniformity and shape regularity.

  20. Static models with conformal symmetry

    NASA Astrophysics Data System (ADS)

    Manjonjo, A. M.; Maharaj, S. D.; Moopanar, S.

    2018-02-01

    We study static spherically symmetric spacetimes with a spherical conformal symmetry and a nonstatic conformal factor associated with the conformal Killing field. With these assumptions we find an explicit relationship relating two metric components of the metric tensor field. This leads to the general solution of the Einstein field equations with a conformal symmetry in a static spherically symmetric spacetime. For perfect fluids we can find all metrics explicitly and show that the models always admit a barotropic equation of state. Contained within this class of spacetimes are the well known metrics of (interior) Schwarzschild, Tolman, Kuchowicz, Korkina and Orlyanskii, Patwardhan and Vaidya, and Buchdahl and Land. The isothermal metric of Saslaw et al also admits a conformal symmetry. For imperfect fluids an infinite family of exact solutions to the field equations can be generated.

  1. 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.

  2. A black hole with torsion in 5D Lovelock gravity

    NASA Astrophysics Data System (ADS)

    Cvetković, B.; Simić, D.

    2018-03-01

    We analyze static spherically symmetric solutions of five dimensional (5D) Lovelock gravity in the first order formulation. In the Riemannian sector, when torsion vanishes, the Boulware–Deser black hole represents a unique static spherically symmetric black hole solution for the generic choice of the Lagrangian parameters. We show that a special choice of the Lagrangian parameters, different from the Lovelock Chern–Simons gravity, leads to the existence of a static black hole solution with torsion, the metric of which is asymptotically anti-de Sitter (AdS). We calculate the conserved charges and thermodynamical quantities of this black hole solution.

  3. On the trajectories of null and timelike geodesics in different wormhole geometries

    NASA Astrophysics Data System (ADS)

    Mishra, Anuj; Chakraborty, Subenoy

    2018-05-01

    The paper deals with an extensive study of null and timelike geodesics in the background of wormhole geometries. Starting with a spherically symmetric spacetime, null geodesics are analyzed for the Morris-Thorne wormhole (WH) and photon spheres are examined in WH geometries. Both bounded and unbounded orbits are discussed for timelike geodesics. A similar analysis has been done for trajectories in a dynamic spherically symmetric WH and for a rotating WH. Finally, the invariant angle method of Rindler and Ishak has been used to calculate the angle between radial and tangential vectors at any point on the photon's trajectory.

  4. Generalized Vaidya spacetime for cubic gravity

    NASA Astrophysics Data System (ADS)

    Ruan, Shan-Ming

    2016-03-01

    We present a kind of generalized Vaidya solution of a new cubic gravity in five dimensions whose field equations in spherically symmetric spacetime are always second order like the Lovelock gravity. We also study the thermodynamics of its spherically symmetric apparent horizon and get its entropy expression and generalized Misner-Sharp energy. Finally, we present the first law and second law hold in this gravity. Although all the results are analogous to those in Lovelock gravity, we in fact introduce the contribution of a new cubic term in five dimensions where the cubic Lovelock term is just zero.

  5. New 2D dilaton gravity for nonsingular black holes

    NASA Astrophysics Data System (ADS)

    Kunstatter, Gabor; Maeda, Hideki; Taves, Tim

    2016-05-01

    We construct a two-dimensional action that is an extension of spherically symmetric Einstein-Lanczos-Lovelock (ELL) gravity. The action contains arbitrary functions of the areal radius and the norm squared of its gradient, but the field equations are second order and obey Birkhoff’s theorem. In complete analogy with spherically symmetric ELL gravity, the field equations admit the generalized Misner-Sharp mass as the first integral that determines the form of the vacuum solution. The arbitrary functions in the action allow for vacuum solutions that describe a larger class of interesting nonsingular black hole spacetimes than previously available.

  6. The classical D-type expansion of spherical H II regions

    NASA Astrophysics Data System (ADS)

    Williams, Robin J. R.; Bibas, Thomas G.; Haworth, Thomas J.; Mackey, Jonathan

    2018-06-01

    Recent numerical and analytic work has highlighted some shortcomings in our understanding of the dynamics of H II region expansion, especially at late times, when the H II region approaches pressure equilibrium with the ambient medium. Here we reconsider the idealized case of a constant radiation source in a uniform and spherically symmetric ambient medium, with an isothermal equation of state. A thick-shell solution is developed which captures the stalling of the ionization front and the decay of the leading shock to a weak compression wave as it escapes to large radii. An acoustic approximation is introduced to capture the late-time damped oscillations of the H II region about the stagnation radius. Putting these together, a matched asymptotic equation is derived for the radius of the ionization front which accounts for both the inertia of the expanding shell and the finite temperature of the ambient medium. The solution to this equation is shown to agree very well with the numerical solution at all times, and is superior to all previously published solutions. The matched asymptotic solution can also accurately model the variation of H II region radius for a time-varying radiation source.

  7. Astrophysical black holes in screened modified gravity

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Davis, Anne-Christine; Jha, Rahul; Muir, Jessica

    2014-08-01

    Chameleon, environmentally dependent dilaton, and symmetron gravity are three models of modified gravity in which the effects of the additional scalar degree of freedom are screened in dense environments. They have been extensively studied in laboratory, cosmological, and astrophysical contexts. In this paper, we present a preliminary investigation into whether additional constraints can be provided by studying these scalar fields around black holes. By looking at the properties of a static, spherically symmetric black hole, we find that the presence of a non-uniform matter distribution induces a non-constant scalar profile in chameleon and dilaton, but not necessarily symmetron gravity. Anmore » order of magnitude estimate shows that the effects of these profiles on in-falling test particles will be sub-leading compared to gravitational waves and hence observationally challenging to detect.« less

  8. Rotating-fluid experiments with an atmospheric general circulation model

    NASA Technical Reports Server (NTRS)

    Geisler, J. E.; Pitcher, E. J.; Malone, R. C.

    1983-01-01

    In order to determine features of rotating fluid flow that are dependent on the geometry, rotating annulus-type experiments are carried out with a numerical model in spherical coordinates. Rather than constructing and testing a model expressly for this purpose, it is found expedient to modify an existing general circulation model of the atmosphere by removing the model physics and replacing the lower boundary with a uniform surface. A regime diagram derived from these model experiments is presented; its major features are interpreted and contrasted with the major features of rotating annulus regime diagrams. Within the wave regime, a narrow region is found where one or two zonal wave numbers are dominant. The results reveal no upper symmetric regime; wave activity at low rotation rates is thought to be maintained by barotropic rather than baroclinic processes.

  9. Spherical aberration correction with an in-lens N-fold symmetric line currents model.

    PubMed

    Hoque, Shahedul; Ito, Hiroyuki; Nishi, Ryuji

    2018-04-01

    In our previous works, we have proposed N-SYLC (N-fold symmetric line currents) models for aberration correction. In this paper, we propose "in-lens N-SYLC" model, where N-SYLC overlaps rotationally symmetric lens. Such overlap is possible because N-SYLC is free of magnetic materials. We analytically prove that, if certain parameters of the model are optimized, an in-lens 3-SYLC (N = 3) doublet can correct 3rd order spherical aberration. By computer simulation, we show that the required excitation current for correction is less than 0.25 AT for beam energy 5 keV, and the beam size after correction is smaller than 1 nm at the corrector image plane for initial slope less than 4 mrad. Copyright © 2018 Elsevier B.V. All rights reserved.

  10. Line formation in winds with enhanced equatorial mass-loss rates and its application to the Wolf-Rayet star HD 50896

    NASA Technical Reports Server (NTRS)

    Rumpl, W. M.

    1980-01-01

    A model having a spherically symmetric velocity distribution with a higher density at the equatorial region was developed to simulate the UV spectrum of the Wolf-Rayet star HD 50896. The spectrum showed P Cygni-shaped profiles whose emissions are stronger than expected in a spherically symmetric stellar wind. The model was studied varying the inclination angle of the star-wind system and the polar to equatorial density ratios; it was shown that HD 50896 could possess a nonspherically symmetric wind and that its symmetry axis is inclined between 60 and 90 deg. It is possible that the velocity distribution of the wind could include an inner constant velocity plateau beyond which the wind accelerates to its terminal velocity as indicated by infrared continuum investigations.

  11. Solutions for the conductivity of multi-coated spheres and spherically symmetric inclusion problems

    NASA Astrophysics Data System (ADS)

    Pham, Duc Chinh

    2018-02-01

    Variational results on the macroscopic conductivity (thermal, electrical, etc.) of the multi-coated sphere assemblage have been used to derive the explicit expression of the respective field (thermal, electrical, etc.) within the spheres in d dimensions (d=2,3). A differential substitution approach has been developed to construct various explicit expressions or determining equations for the effective spherically symmetric inclusion problems, which include those with radially variable conductivity, different radially variable transverse and normal conductivities, and those involving imperfect interfaces, in d dimensions. When the volume proportion of the outermost spherical shell increases toward 1, one obtains the respective exact results for the most important specific cases: the dilute solutions for the compound inhomogeneities suspended in a major matrix phase. Those dilute solution results are also needed for other effective medium approximation schemes.

  12. Sound wave generation by a spherically symmetric outburst and AGN feedback in galaxy clusters

    NASA Astrophysics Data System (ADS)

    Tang, Xiaping; Churazov, Eugene

    2017-07-01

    We consider the evolution of an outburst in a uniform medium under spherical symmetry, having in mind active galactic nucleus feedback in the intracluster medium. For a given density and pressure of the medium, the spatial structure and energy partition at a given time tage (since the onset of the outburst) are fully determined by the total injected energy Einj and the duration tb of the outburst. We are particularly interested in the late phase evolution when the strong shock transforms into a sound wave. We studied the energy partition during such transition with different combinations of Einj and tb. For an instantaneous outburst with tb → 0, which corresponds to the extension of classic Sedov-Taylor solution with counter-pressure, the fraction of energy that can be carried away by sound waves is ≲12 per cent of Einj. As tb increases, the solution approaches the 'slow piston' limit, with the fraction of energy in sound waves approaching zero. We then repeat the simulations using radial density and temperature profiles measured in Perseus and M87/Virgo clusters. We find that the results with a uniform medium broadly reproduce an outburst in more realistic conditions once proper scaling is applied. We also develop techniques to map intrinsic properties of an outburst (Einj, tb and tage) to the observables like the Mach number of the shock and radii of the shock and ejecta. For the Perseus cluster and M87, the estimated (Einj, tb and tage) agree with numerical simulations tailored for these objects with 20-30 per cent accuracy.

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

    DOE PAGES

    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.

  14. The Morphology and Uniformity of Circumstellar OH/H2O Masers around OH/IR Stars

    NASA Astrophysics Data System (ADS)

    Felli, Derek Sean

    Even though low mass stars ( 8 solar masses), the more massive stars drive the chemical evolution of galaxies from which the next generation of stars and planets can form. Understanding mass loss of asymptotic giant branch stars contributes to our understanding of the chemical evolution of the galaxy, stellar populations, and star formation history. Stars with mass 8 solar masses go supernova. In both cases, these stars enrich their environments with elements heavier than simple hydrogen and helium molecules. While some general info about how stars die and form planetary nebulae are known, specific details are missing due to a lack of high-resolution observations and analysis of the intermediate stages. For example, we know that mass loss in stars creates morphologically diverse planetary nebulae, but we do not know the uniformity of these processes, and therefore lack detailed models to better predict how spherically symmetric stars form asymmetric nebulae. We have selected a specific group of late-stage stars and observed them at different scales to reveal the uniformity of mass loss through different layers close to the star. This includes observing nearby masers that trace the molecular shell structure around these stars. This study revealed detailed structure that was analyzed for uniformity to place constraints on how the mass loss processes behave in models. These results will feed into our ability to create more detailed models to better predict the chemical evolution of the next generation of stars and planets.

  15. Greybody factors for a spherically symmetric Einstein-Gauss-Bonnet-de Sitter black hole

    NASA Astrophysics Data System (ADS)

    Zhang, Cheng-Yong; Li, Peng-Cheng; Chen, Bin

    2018-02-01

    We study the greybody factors of the scalar fields in spherically symmetric Einstein-Gauss-Bonnet-de Sitter black holes in higher dimensions. We derive the greybody factors analytically for both minimally and nonminimally coupled scalar fields. Moreover, we discuss the dependence of the greybody factor on various parameters including the angular momentum number, the nonminimally coupling constant, the spacetime dimension, the cosmological constant, and the Gauss-Bonnet coefficient in detail. We find that the nonminimal coupling may suppress the greybody factor and the Gauss-Bonnet coupling could enhance it, but they both suppress the energy emission rate of Hawking radiation.

  16. Generic isolated horizons in loop quantum gravity

    NASA Astrophysics Data System (ADS)

    Beetle, Christopher; Engle, Jonathan

    2010-12-01

    Isolated horizons model equilibrium states of classical black holes. A detailed quantization, starting from a classical phase space restricted to spherically symmetric horizons, exists in the literature and has since been extended to axisymmetry. This paper extends the quantum theory to horizons of arbitrary shape. Surprisingly, the Hilbert space obtained by quantizing the full phase space of all generic horizons with a fixed area is identical to that originally found in spherical symmetry. The entropy of a large horizon remains one-quarter its area, with the Barbero-Immirzi parameter retaining its value from symmetric analyses. These results suggest a reinterpretation of the intrinsic quantum geometry of the horizon surface.

  17. Horizons versus singularities in spherically symmetric space-times

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Bronnikov, K. A.; Elizalde, E.; Odintsov, S. D.

    We discuss different kinds of Killing horizons possible in static, spherically symmetric configurations and recently classified as 'usual', 'naked', and 'truly naked' ones depending on the near-horizon behavior of transverse tidal forces acting on an extended body. We obtain the necessary conditions for the metric to be extensible beyond a horizon in terms of an arbitrary radial coordinate and show that all truly naked horizons, as well as many of those previously characterized as naked and even usual ones, do not admit an extension and therefore must be considered as singularities. Some examples are given, showing which kinds of mattermore » are able to create specific space-times with different kinds of horizons, including truly naked ones. Among them are fluids with negative pressure and scalar fields with a particular behavior of the potential. We also discuss horizons and singularities in Kantowski-Sachs spherically symmetric cosmologies and present horizon regularity conditions in terms of an arbitrary time coordinate and proper (synchronous) time. It turns out that horizons of orders 2 and higher occur in infinite proper times in the past or future, but one-way communication with regions beyond such horizons is still possible.« less

  18. Asymptotically flat black holes in Horndeski theory and beyond

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Babichev, E.; Charmousis, C.; Lehébel, A., E-mail: eugeny.babichev@th.u-psud.fr, E-mail: christos.charmousis@th.u-psud.fr, E-mail: antoine.lehebel@th.u-psud.fr

    We find spherically symmetric and static black holes in shift-symmetric Horndeski and beyond Horndeski theories. They are asymptotically flat and sourced by a non trivial static scalar field. The first class of solutions is constructed in such a way that the Noether current associated with shift symmetry vanishes, while the scalar field cannot be trivial. This in certain cases leads to hairy black hole solutions (for the quartic Horndeski Lagrangian), and in others to singular solutions (for a Gauss-Bonnet term). Additionally, we find the general spherically symmetric and static solutions for a pure quartic Lagrangian, the metric of which ismore » Schwarzschild. We show that under two requirements on the theory in question, any vacuum GR solution is also solution to the quartic theory. As an example, we show that a Kerr black hole with a non-trivial scalar field is an exact solution to these theories.« less

  19. Analytic Solution of the Problem of Additive Formation of an Inhomogeneous Elastic Spherical Body in an Arbitrary Nonstationary Central Force Field

    NASA Astrophysics Data System (ADS)

    Parshin, D. A.

    2017-09-01

    We study the processes of additive formation of spherically shaped rigid bodies due to the uniform accretion of additional matter to their surface in an arbitrary centrally symmetric force field. A special case of such a field can be the gravitational or electrostatic force field. We consider the elastic deformation of the formed body. The body is assumed to be isotropic with elasticmoduli arbitrarily varying along the radial coordinate.We assume that arbitrary initial circular stresses can arise in the additional material added to the body in the process of its formation. In the framework of linear mechanics of growing bodies, the mathematical model of the processes under study is constructed in the quasistatic approximation. The boundary value problems describing the development of stress-strain state of the object under study before the beginning of the process and during the entire process of its formation are posed. The closed analytic solutions of the posed problems are constructed by quadratures for some general types of material inhomogeneity. Important typical characteristics of the mechanical behavior of spherical bodies additively formed in the central force field are revealed. These characteristics substantially distinguish such bodies from the already completely composed bodies similar in dimensions and properties which are placed in the force field and are described by problems of mechanics of deformable solids in the classical statement disregarding the mechanical aspects of additive processes.

  20. Beyond Extreme Ultra Violet (BEUV) Radiation from Spherically symmetrical High-Z plasmas

    NASA Astrophysics Data System (ADS)

    Yoshida, Kensuke; Fujioka, Shinsuke; Higashiguchi, Takeshi; Ugomori, Teruyuki; Tanaka, Nozomi; Kawasaki, Masato; Suzuki, Yuhei; Suzuki, Chihiro; Tomita, Kentaro; Hirose, Ryouichi; Eshima, Takeo; Ohashi, Hayato; Nishikino, Masaharu; Scally, Enda; Nshimura, Hiroaki; Azechi, Hiroshi; O'Sullivan, Gerard

    2016-03-01

    Photo-lithography is a key technology for volume manufacture of high performance and compact semiconductor devices. Smaller and more complex structures can be fabricated by using shorter wavelength light in the photolithography. One of the most critical issues in development of the next generation photo-lithography is to increase energy conversion efficiency (CE) from laser to shorter wavelength light. Experimental database of beyond extreme ultraviolet (BEUV) radiation was obtained by using spherically symmetrical high-Z plasmas generated with spherically allocated laser beams. Absolute energy and spectra of BEUV light emitted from Tb, Gd, and Mo plasmas were measured with a absolutely calibrated BEUV calorimeter and a transmission grating spectrometer. 1.0 x 1012 W/cm2 is the optimal laser intensity to produced efficient BEUV light source plasmas with Tb and Gd targets. Maximum CE is achieved at 0.8% that is two times higher than the published CEs obtained with planar targets.

  1. Orthogonal fast spherical Bessel transform on uniform grid

    NASA Astrophysics Data System (ADS)

    Serov, Vladislav V.

    2017-07-01

    We propose an algorithm for the orthogonal fast discrete spherical Bessel transform on a uniform grid. Our approach is based upon the spherical Bessel transform factorization into the two subsequent orthogonal transforms, namely the fast Fourier transform and the orthogonal transform founded on the derivatives of the discrete Legendre orthogonal polynomials. The method utility is illustrated by its implementation for the problem of a two-atomic molecule in a time-dependent external field simulating the one utilized in the attosecond streaking technique.

  2. Fabrication of precision glass shells by joining glass rods

    DOEpatents

    Gac, Frank D.; Blake, Rodger D.; Day, Delbert E.; Haggerty, John S.

    1988-01-01

    A method for making uniform spherical shells. The present invention allows niform hollow spheres to be made by first making a void in a body of material. The material is heated so that the viscosity is sufficiently low so that the surface tension will transform the void into a bubble. The bubble is allowed to rise in the body until it is spherical. The excess material is removed from around the void to form a spherical shell with a uniform outside diameter.

  3. Interaction energy for a fullerene encapsulated in a carbon nanotorus

    NASA Astrophysics Data System (ADS)

    Sarapat, Pakhapoom; Baowan, Duangkamon; Hill, James M.

    2018-06-01

    The interaction energy of a fullerene symmetrically situated inside a carbon nanotorus is studied. For these non-bonded molecules, the main interaction originates from the van der Waals energy which is modelled by the 6-12 Lennard-Jones potential. Upon utilising the continuum approximation which assumes that there are infinitely many atoms that are uniformly distributed over the surfaces of the molecules, the total interaction energy between the two structures is obtained as a surface integral over the spherical and the toroidal surfaces. This analytical energy is employed to determine the most stable configuration of the torus encapsulating the fullerene. The results show that a torus with major radius around 20-22 Å and minor radius greater than 6.31 Å gives rise to the most stable arrangement. This study will pave the way for future developments in biomolecules design and drug delivery system.

  4. Observational signatures of spherically-symmetric black hole spacetimes

    NASA Astrophysics Data System (ADS)

    De Laurentis, Mariafelicia; Younsi, Ziri; Porth, Oliver; Mizuno, Yosuke; Fromm, Christian; Rezzolla, Luciano; Olivares, Hector

    2017-12-01

    A binary system composed of a supermassive black hole and a pulsar orbiting around it is studied. The motivation for this study arises from the fact that pulsar timing observations have proven to be a powerful tool in identifying physical features of the orbiting companion. In this study, taking into account a general spherically-symmetric metric, we present analytic calculations of the geodesic motion, and the possible deviations with respect to the standard Schwarzschild case of General Relativity. In particular, the advance at periastron is studied with the aim of identifying corrections to General Relativity. A discussion of the motion of a pulsar very close the supermassive central black hole in our Galaxy (Sgr A*) is reported.

  5. Non-Existence of Black Hole Solutionsfor a Spherically Symmetric, Static Einstein-Dirac-Maxwell System

    NASA Astrophysics Data System (ADS)

    Finster, Felix; Smoller, Joel; Yau, Shing-Tung

    We consider for j=1/2, 3/2,... a spherically symmetric, static system of (2j+1) Dirac particles, each having total angular momentum j. The Dirac particles interact via a classical gravitational and electromagnetic field. The Einstein-Dirac-Maxwell equations for this system are derived. It is shown that, under weak regularity conditions on the form of the horizon, the only black hole solutions of the EDM equations are the Reissner-Nordstrom solutions. In other words, the spinors must vanish identically. Applied to the gravitational collapse of a "cloud" of spin-1/2-particles to a black hole, our result indicates that the Dirac particles must eventually disappear inside the event horizon.

  6. Second order symmetry-preserving conservative Lagrangian scheme for compressible Euler equations in two-dimensional cylindrical coordinates

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Cheng, Juan, E-mail: cheng_juan@iapcm.ac.cn; Shu, Chi-Wang, E-mail: shu@dam.brown.edu

    In applications such as astrophysics and inertial confinement fusion, there are many three-dimensional cylindrical-symmetric multi-material problems which are usually simulated by Lagrangian schemes in the two-dimensional cylindrical coordinates. For this type of simulation, a critical issue for the schemes is to keep spherical symmetry in the cylindrical coordinate system if the original physical problem has this symmetry. In the past decades, several Lagrangian schemes with such symmetry property have been developed, but all of them are only first order accurate. In this paper, we develop a second order cell-centered Lagrangian scheme for solving compressible Euler equations in cylindrical coordinates, basedmore » on the control volume discretizations, which is designed to have uniformly second order accuracy and capability to preserve one-dimensional spherical symmetry in a two-dimensional cylindrical geometry when computed on an equal-angle-zoned initial grid. The scheme maintains several good properties such as conservation for mass, momentum and total energy, and the geometric conservation law. Several two-dimensional numerical examples in cylindrical coordinates are presented to demonstrate the good performance of the scheme in terms of accuracy, symmetry, non-oscillation and robustness. The advantage of higher order accuracy is demonstrated in these examples.« less

  7. Problems of Construction of Black Holes and Traversed Wormholes in Various Theories of Gravity

    NASA Astrophysics Data System (ADS)

    Karbanovski, Valeri; Kairov, Taimuraz.; Melehina, Olga

    In the framework of general relativity found new vacuum solutions [1,2] for the spherically symmetric non-static metrics as a constant source ("dynamic analog" gravitational radius), and a source in the form of time-dependent functions. In the latter case, the conditions for a smooth cross-linking with the original static metric. Within Post-Einstein theory of gravitation (PETG, [3]), is consider the variant with zero scalar curvature of space-time is considered. Found external solutions for spherically symmetric objects that allow a smooth stitching at distances slightly exceeding the gravitational radius of the source. We also show that in the studied approach the traversable vacuum wormholes can not be realized. In the theory of gravity with vacuum polarization (TGVP, [4]) built vacuum static spherically symmetric nonsingular solutions. At this the "polarization effects" appear only under the gravitational radius of the source. Also obtained metric describing the vacuum traversable wormhole. References begin{enumerate} Karbanovski V.V. et. al. - JETP, 2012, Vol. 115, No. 2, pp. 208-211. Karbanovski V.V. et. al. - JETP, 2012, Vol. 115, No. 4, pp. 733. Karbanovski V.V. et. al. - Class. Quantum Grav., 2012, Vol. 29, No. 6, 065007. Karbanovski V.V. et. al. - Acta Phys. Pol. B, 2011, Vol. 42, No.1, p. 171.

  8. The theory of spherically symmetric thin shells in conformal gravity

    NASA Astrophysics Data System (ADS)

    Berezin, Victor; Dokuchaev, Vyacheslav; Eroshenko, Yury

    The spherically symmetric thin shells are the nearest generalizations of the point-like particles. Moreover, they serve as the simple sources of the gravitational fields both in General Relativity and much more complex quadratic gravity theories. We are interested in the special and physically important case when all the quadratic in curvature tensor (Riemann tensor) and its contractions (Ricci tensor and scalar curvature) terms are present in the form of the square of Weyl tensor. By definition, the energy-momentum tensor of the thin shell is proportional to Diracs delta-function. We constructed the theory of the spherically symmetric thin shells for three types of gravitational theories with the shell: (1) General Relativity; (2) Pure conformal (Weyl) gravity where the gravitational part of the total Lagrangian is just the square of the Weyl tensor; (3) Weyl-Einstein gravity. The results are compared with these in General Relativity (Israel equations). We considered in detail the shells immersed in the vacuum. Some peculiar properties of such shells are found. In particular, for the traceless ( = massless) shell, it is shown that their dynamics cannot be derived from the matching conditions and, thus, is completely arbitrary. On the contrary, in the case of the Weyl-Einstein gravity, the trajectory of the same type of shell is completely restored even without knowledge of the outside solution.

  9. Particle in a Uniform Magnetic Field Under the Symmetric Gauge: The Eigenfunctions and the Time Evolution of Wave Packets

    ERIC Educational Resources Information Center

    de Brito, P. E.; Nazareno, H. N.

    2007-01-01

    In the present work we treat the problem of a particle in a uniform magnetic field along the symmetric gauge, so chosen since the wavefunctions present the required cylindrical symmetry. It is our understanding that by means of this work we can make a contribution to the teaching of the present subject, as well as encourage students to use…

  10. X-Ray Polarization from High Mass X-Ray Binaries

    NASA Technical Reports Server (NTRS)

    Kallman, T.; Dorodnitsyn, A.; Blondin, J.

    2015-01-01

    X-ray astronomy allows study of objects which may be associated with compact objects, i.e. neutron stars or black holes, and also may contain strong magnetic fields. Such objects are categorically non-spherical, and likely non-circular when projected on the sky. Polarization allows study of such geometric effects, and X-ray polarimetry is likely to become feasible for a significant number of sources in the future. A class of potential targets for future X-ray polarization observations is the high mass X-ray binaries (HMXBs), which consist of a compact object in orbit with an early type star. In this paper we show that X-ray polarization from HMXBs has a distinct signature which depends on the source inclination and orbital phase. The presence of the X-ray source displaced from the star creates linear polarization even if the primary wind is spherically symmetric whenever the system is viewed away from conjunction. Direct X-rays dilute this polarization whenever the X-ray source is not eclipsed; at mid-eclipse the net polarization is expected to be small or zero if the wind is circularly symmetric around the line of centers. Resonance line scattering increases the scattering fraction, often by large factors, over the energy band spanned by resonance lines. Real winds are not expected to be spherically symmetric, or circularly symmetric around the line of centers, owing to the combined effects of the compact object gravity and ionization on the wind hydrodynamics. A sample calculation shows that this creates polarization fractions ranging up to tens of percent at mid-eclipse.

  11. Exact solution of mean-field plus an extended T = 1 nuclear pairing Hamiltonian in the seniority-zero symmetric subspace

    NASA Astrophysics Data System (ADS)

    Pan, Feng; Ding, Xiaoxue; Launey, Kristina D.; Dai, Lianrong; Draayer, Jerry P.

    2018-05-01

    An extended pairing Hamiltonian that describes multi-pair interactions among isospin T = 1 and angular momentum J = 0 neutron-neutron, proton-proton, and neutron-proton pairs in a spherical mean field, such as the spherical shell model, is proposed based on the standard T = 1 pairing formalism. The advantage of the model lies in the fact that numerical solutions within the seniority-zero symmetric subspace can be obtained more easily and with less computational time than those calculated from the mean-field plus standard T = 1 pairing model. Thus, large-scale calculations within the seniority-zero symmetric subspace of the model is feasible. As an example of the application, the average neutron-proton interaction in even-even N ∼ Z nuclei that can be suitably described in the f5 pg9 shell is estimated in the present model, with a focus on the role of np-pairing correlations.

  12. Spherical aberration of an optical system and its influence on depth of focus.

    PubMed

    Mikš, Antonín; Pokorný, Petr

    2017-06-10

    This paper analyzes the influence of spherical aberration on the depth of focus of symmetrical optical systems for imaging of axial points. A calculation of a beam's caustics is discussed using ray equations in the image plane and considering longitudinal spherical aberration as well. Concurrently, the influence of aberration coefficients on extremes of such a curve is presented. Afterwards, conditions for aberration coefficients are derived if the Strehl definition should be the same in two symmetrically placed planes with respect to the paraxial image plane. Such conditions for optical systems with large aberrations are derived with the use of geometric-optical approximation where the gyration diameter of the beam in given planes of the optical system is evaluated. Therefore, one can calculate aberration coefficients in such a way that the optical system generates a beam of rays that has the gyration radius in a given interval smaller than the defined limit value. Moreover, one can calculate the maximal depth of focus of the optical system respecting the aforementioned conditions.

  13. Droplet Combustion and Soot Formation in Microgravity

    NASA Technical Reports Server (NTRS)

    Avedisian, C. Thomas

    1994-01-01

    One of the most complex processes involved in the combustion ot liquid fuels is the formation of soot. A well characterized flow field and simplified flame structure can improve considerably the understanding of soot formation processes. The simplest flame shape to analyze for a droplet is spherical with its associated one-dimensional flow field. It is a fundamental limit and the oldest and most often analyzed configuration of droplet combustion. Spherical symmetry in the droplet burning process will arise when there is no relative motion between the droplet and ambience or uneven heating around the droplet periphery, and buoyancy effects are negligible. The flame and droplet are then concentric with each other and there is no liquid circulation within the droplet. An understanding of the effect of soot on droplet combustion should therefore benefit from this simplified configuration. Soot formed during spherically symmetric droplet combustion, however, has only recently drawn attention and it appears to be one of the few aspects associated with droplet combustion which have not yet been thoroughly investigated. For this review, the broad subject of droplet combustion is narrowed considerably by restricting attention specifically to soot combined with spherically symmetric droplet burning processes that are promoted.

  14. On the inflation of poro-hyperelastic annuli

    NASA Astrophysics Data System (ADS)

    Selvadurai, A. P. S.; Suvorov, A. P.

    2017-10-01

    The paper presents the radially and spherically symmetric problems associated with the inflation of poro-hyperelastic regions. The theory of poro-hyperelasticity is a convenient framework for modelling the mechanical behaviour of highly deformable materials in which the pore space is saturated with fluids. Including the coupled mechanical responses of both the hyperelastic porous skeleton and the fluid is regarded as an important consideration for the application of the results, particularly to soft tissues encountered in biomechanical applications. The analytical solutions for radially and spherically symmetric problems involving annular domains are used to benchmark the accuracy of a standard computational approach. The paper also generates results applicable to the hyperelastic solutions when coupling is eliminated through the presence of a highly permeable pore structure.

  15. String solutions in spherically-symmetric f(R) gravity vacuum

    NASA Astrophysics Data System (ADS)

    Dil, Emre

    Dynamical evolution of the cosmic string in a spherically symmetric f(R) gravity vacuum is studied for a closed and straight string. We first set the background spacetime metric for a constant curvature scalar R = R0, and obtain the Killing fields for it. Using the standard gauge coordinates and constraints for both closed and straight strings, we present the equation of motions and find the solutions of them. We then analyze the dynamics of the string by studying the behavior of the string radius and periastron radius, with respect to both proper time and azimuthal angle, for various values of f(R) functions. Consequently, we conclude that the value of f(R) dramatically affects the closed string collapse time and the straight string angular deviation.

  16. Vacuum solutions around spherically symmetric and static objects in the Starobinsky model

    NASA Astrophysics Data System (ADS)

    ćıkıntoǧlu, Sercan

    2018-02-01

    The vacuum solutions around a spherically symmetric and static object in the Starobinsky model are studied with a perturbative approach. The differential equations for the components of the metric and the Ricci scalar are obtained and solved by using the method of matched asymptotic expansions. The presence of higher order terms in this gravity model leads to the formation of a boundary layer near the surface of the star allowing the accommodation of the extra boundary conditions on the Ricci scalar. Accordingly, the metric can be different from the Schwarzschild solution near the star depending on the value of the Ricci scalar at the surface of the star while matching the Schwarzschild metric far from the star.

  17. Particlelike solutions of the Einstein-Dirac equations

    NASA Astrophysics Data System (ADS)

    Finster, Felix; Smoller, Joel; Yau, Shing-Tung

    1999-05-01

    The coupled Einstein-Dirac equations for a static, spherically symmetric system of two fermions in a singlet spinor state are derived. Using numerical methods, we construct an infinite number of solitonlike solutions of these equations. The stability of the solutions is analyzed. For weak coupling (i.e., small rest mass of the fermions), all the solutions are linearly stable (with respect to spherically symmetric perturbations), whereas for stronger coupling, both stable and unstable solutions exist. For the physical interpretation, we discuss how the energy of the fermions and the (ADM) mass behave as functions of the rest mass of the fermions. Although gravitation is not renormalizable, our solutions of the Einstein-Dirac equations are regular and well behaved even for strong coupling.

  18. Connection between black-hole quasinormal modes and lensing in the strong deflection limit.

    PubMed

    Stefanov, Ivan Zh; Yazadjiev, Stoytcho S; Gyulchev, Galin G

    2010-06-25

    The purpose of the current Letter is to give some relations between gravitational lensing in the strong-deflection limit and the frequencies of the quasinormal modes of spherically symmetric, asymptotically flat black holes. On the one side, the relations obtained can give a physical interpretation of the strong-deflection limit parameters. On the other side, they also give an alternative method for the measurement of the frequencies of the quasinormal modes of spherically symmetric, asymptotically flat black holes. They could be applied to the localization of the sources of gravitational waves and could tell us what frequencies of the gravitational waves we could expect from a black hole acting simultaneously as a gravitational lens and a source of gravitational waves.

  19. EXACT RELATIVISTIC NEWTONIAN REPRESENTATION OF GRAVITATIONAL STATIC SPACETIME GEOMETRIES

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Ghosh, Shubhrangshu; Sarkar, Tamal; Bhadra, Arunava, E-mail: sghosh@jcbose.ac.in, E-mail: ta.sa.nbu@hotmail.com, E-mail: aru_bhadra@yahoo.com

    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 usefulmore » in studying a wide range of astrophysical phenomena, especially in strong field gravity.« less

  20. Irreducible structure, symmetry and average of Eshelby's tensor fields in isotropic elasticity

    NASA Astrophysics Data System (ADS)

    Zheng, Q.-S.; Zhao, Z.-H.; Du, D.-X.

    2006-02-01

    The strain field ɛ(x) in an infinitely large, homogenous, and isotropic elastic medium induced by a uniform eigenstrain ɛ0 in a domain ω depends linearly upon ɛ0 : ɛij(x)=Sijklω(x)ɛkl0. It has been a long-standing conjecture that the Eshelby's tensor field Sω(x) is uniform inside ω if and only if ω is ellipsoidally shaped. Because of the minor index symmetry Sijklω=Sjiklω=Sijlkω, Sω might have a maximum of 36 or nine independent components in three or two dimensions, respectively. In this paper, using the irreducible decomposition of Sω, we show that the isotropic part S of Sω vanishes outside ω and is uniform inside ω with the same value as the Eshelby's tensor S0 for 3D spherical or 2D circular domains. We further show that the anisotropic part Aω=Sω-S of Sω is characterized by a second- and a fourth-order deviatoric tensors and therefore have at maximum 14 or four independent components as characteristics of ω's geometry. Remarkably, the above irreducible structure of Sω is independent of ω's geometry (e.g., shape, orientation, connectedness, convexity, boundary smoothness, etc.). Interesting consequences have implication for a number of recently findings that, for example, both the values of Sω at the center of a 2D Cn(n⩾3,n≠4)-symmetric or 3D icosahedral ω and the average value of Sω over such a ω are equal to S0.

  1. A Geophysical Flow Experiment in a Compressible Critical Fluid

    NASA Technical Reports Server (NTRS)

    Hegseth, John; Garcia, Laudelino

    1996-01-01

    The first objective of this experiment is to build an experimental system in which, in analogy to a geophysical system, a compressible fluid in a spherical annulus becomes radially stratified in density through an A.C. electric field. When this density gradient is demonstrated, the system will be augmented so that the fluid can be driven by heating and rotation and tested in preparation for a microgravity experiment. This apparatus consists of a spherical capacitor filled with critical fluid in a temperature controlled environment. To make the fluid critical, the apparatus will be operated near the critical pressure, critical density, and critical temperature of the fluid. This will result in a highly compressible fluid because of the properties of the fluid near its critical point. A high voltage A.C. source applied across the capacitor will create a spherically symmetric central force because of the dielectric properties of the fluid in an electric field gradient. This central force will induce a spherically symmetric density gradient that is analogous to a geophysical fluid system. To generate such a density gradient the system must be small (approx. 1 inch diameter). This small cell will also be capable of driving the critical fluid by heating and rotation. Since a spherically symmetric density gradient can only be made in microgravity, another small cell, of the same geometry, will be built that uses incompressible fluid. The driving of the fluid by rotation and heating in these small cells will be developed. The resulting instabilities from the driving in these two systems will then be studied. The second objective is to study the pattern forming instabilities (bifurcations) resulting from the well controlled experimental conditions in the critical fluid cell. This experiment will come close to producing conditions that are geophysically similar and will be studied as the driving parameters are changed.

  2. Spherically symmetric vacuum in covariant F (T )=T +α/2 T2+O (Tγ) gravity theory

    NASA Astrophysics Data System (ADS)

    DeBenedictis, Andrew; Ilijić, Saša

    2016-12-01

    Recently, a fully covariant version of the theory of F (T ) torsion gravity has been introduced by M. Kršśák and E. Saridakis [Classical Quantum Gravity 33, 115009 (2016)]. In covariant F (T ) gravity, the Schwarzschild solution is not a vacuum solution for F (T )≠T , and therefore determining the spherically symmetric vacuum is an important open problem. Within the covariant framework, we perturbatively solve the spherically symmetric vacuum gravitational equations around the Schwarzschild solution for the scenario with F (T )=T +(α /2 )T2 , representing the dominant terms in theories governed by Lagrangians analytic in the torsion scalar. From this, we compute the perihelion shift correction to solar system planetary orbits as well as perturbative gravitational effects near neutron stars. This allows us to set an upper bound on the magnitude of the coupling constant, α , which governs deviations from general relativity. We find the bound on this nonlinear torsion coupling constant by specifically considering the uncertainty in the perihelion shift of Mercury. We also analyze a bound from a similar comparison with the periastron orbit of the binary pulsar PSR J0045-7319 as an independent check for consistency. Setting bounds on the dominant nonlinear coupling is important in determining if other effects in the Solar System or greater universe could be attributable to nonlinear torsion.

  3. Phase Behavior of Binary Blends of AB+AC Block Copolymers with compatible B and C blocks

    NASA Astrophysics Data System (ADS)

    Pryamitsyn, Victor; Ganesan, Venkat

    2012-02-01

    Recently the experimental studies of phase behavior of binary blends of PS-b-P2VP and PS-b-PHS demonstrated an interesting effect: blends of symmetric PS-b-P2VP and shorter symmetric (PS-b-PHS) formed cylindrical HEX and spherical BCC phases, while each pure component formed lamellas. The miscibility of P2VP and PHS is caused by the hydrogen bonding between P2VP and PHS,which can be described as a negative Flory ?-parameter between P2VP and PHS. We developed a theory of the microphase segregation of AB+AC blends of diblock copolymers based on strong stretching theory. The main result of our theory is that in the copolymer brush-like layer formed by longer B chain and shorter C chains, the attraction between B and shorter C chains causes relative stretching of short C chains and compression of longer B chains. The latter manifests in an excessive bending force towards the grafting surface (BC|AA interface). Such bending force causes a transition from a symmetric lamella phase to a HEX cylinder or BCC spherical phases with the BC phase being a ``matrix'' component. In a blend of asymmetric BCC sphere forming copolymers (where B and C segments are the minor components), such bending force may unfold BCC spherical phase to a HEX cylinder phase, or even highly uneven lamella phases.

  4. Stationary bound-state massive scalar field configurations supported by spherically symmetric compact reflecting stars

    NASA Astrophysics Data System (ADS)

    Hod, Shahar

    2017-12-01

    It has recently been demonstrated that asymptotically flat neutral reflecting stars are characterized by an intriguing no-hair property. In particular, it has been proved that these horizonless compact objects cannot support spatially regular static matter configurations made of scalar (spin-0) fields, vector (spin-1) fields and tensor (spin-2) fields. In the present paper we shall explicitly prove that spherically symmetric compact reflecting stars can support stationary (rather than static) bound-state massive scalar fields in their exterior spacetime regions. To this end, we solve analytically the Klein-Gordon wave equation for a linearized scalar field of mass μ and proper frequency ω in the curved background of a spherically symmetric compact reflecting star of mass M and radius R_{ {s}}. It is proved that the regime of existence of these stationary composed star-field configurations is characterized by the simple inequalities 1-2M/R_{ {s}}<(ω /μ )^2<1. Interestingly, in the regime M/R_{ {s}}≪ 1 of weakly self-gravitating stars we derive a remarkably compact analytical equation for the discrete spectrum {ω (M,R_{ {s}},μ )}^{n=∞}_{n=1} of resonant oscillation frequencies which characterize the stationary composed compact-reflecting-star-linearized-massive-scalar-field configurations. Finally, we verify the accuracy of the analytically derived resonance formula of the composed star-field configurations with direct numerical computations.

  5. Calculation of the fast ion tail distribution for a spherically symmetric hot spot

    NASA Astrophysics Data System (ADS)

    McDevitt, C. J.; Tang, X.-Z.; Guo, Z.; Berk, H. L.

    2014-10-01

    The fast ion tail for a spherically symmetric hot spot is computed via the solution of a simplified Fokker-Planck collision operator. Emphasis is placed on describing the energy scaling of the fast ion distribution function in the hot spot as well as the surrounding cold plasma throughout a broad range of collisionalities and temperatures. It is found that while the fast ion tail inside the hot spot is significantly depleted, leading to a reduction of the fusion yield in this region, a surplus of fast ions is observed in the neighboring cold plasma region. The presence of this surplus of fast ions in the neighboring cold region is shown to result in a partial recovery of the fusion yield lost in the hot spot.

  6. Constraining some Horndeski gravity theories

    NASA Astrophysics Data System (ADS)

    Bhattacharya, Sourav; Chakraborty, Sumanta

    2017-02-01

    We discuss two spherically symmetric solutions admitted by the Horndeski (or scalar-tensor) theory in the context of Solar System and astrophysical scenarios. One of these solutions is derived for Einstein-Gauss-Bonnet gravity, while the other originates from the coupling of the Gauss-Bonnet invariant with a scalar field. Specifically, we discuss the perihelion precession and the bending angle of light for these two different spherically symmetric spacetimes derived in Maeda and Dadhich [Phys. Rev. D 75, 044007 (2007), 10.1103/PhysRevD.75.044007] and Sotiriou and Zhou [Phys. Rev. D 90, 124063 (2014), 10.1103/PhysRevD.90.124063], respectively. The latter, in particular, applies only to black-hole spacetimes. We further delineate on the numerical bounds of relevant parameters of these theories from such computations.

  7. Spherically symmetric cosmological spacetimes with dust and radiation — numerical implementation

    NASA Astrophysics Data System (ADS)

    Lim, Woei Chet; Regis, Marco; Clarkson, Chris

    2013-10-01

    We present new numerical cosmological solutions of the Einstein Field Equations. The spacetime is spherically symmetric with a source of dust and radiation approximated as a perfect fluid. The dust and radiation are necessarily non-comoving due to the inhomogeneity of the spacetime. Such a model can be used to investigate non-linear general relativistic effects present during decoupling or big-bang nucleosynthesis, as well as for investigating void models of dark energy with isocurvature degrees of freedom. We describe the full evolution of the spacetime as well as the redshift and luminosity distance for a central observer. After demonstrating accuracy of the code, we consider a few example models, and demonstrate the sensitivity of the late time model to the degree of inhomogeneity of the initial radiation contrast.

  8. Spherically symmetric solutions and gravitational collapse in brane-worlds

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Heydari-Fard, Malihe; Sepangi, Hamid R., E-mail: heydarifard@qom.ac.ir, E-mail: hr-sepangi@sbu.ac.ir

    2009-02-15

    We consider spherically symmetric solutions within the context of brane-world theory without mirror symmetry or any form of junction conditions. For a constant curvature bulk, we obtain the modified Tolman-Oppenheimer-Volkoff (TOV) interior solutions in two cases where one is matched to a schwarzschild-de Sitter exterior while the other is consistent with an exterior solution whose structure can be used to explain the galaxy rotation curves without postulating dark matter. We also find the upper bound to the mass of a static brane-world star and show that the influence of the bulk effects on the interior solutions is small. Finally, wemore » investigate the gravitational collapse on the brane and show that the exterior of a collapsing star can be static in this scenario.« less

  9. Asymptotic behavior of dynamical variables and naked singularity formation in spherically symmetric gravitational collapse

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kawakami, Hayato; Mitsuda, Eiji; Nambu, Yasusada

    In considering the gravitational collapse of matter, it is an important problem to clarify what kind of conditions leads to the formation of naked singularity. For this purpose, we apply the 1+3 orthonormal frame formalism introduced by Uggla et al. to the spherically symmetric gravitational collapse of a perfect fluid. This formalism allows us to construct an autonomous system of evolution and constraint equations for scale-invariant dynamical variables normalized by the volume expansion rate of the timelike orthonormal frame vector. We investigate the asymptotic evolution of such dynamical variables towards the formation of a central singularity and present a conjecturemore » that the steep spatial gradient for the normalized density function is a characteristic of the naked singularity formation.« less

  10. Black hole evolution by spectral methods

    NASA Astrophysics Data System (ADS)

    Kidder, Lawrence E.; Scheel, Mark A.; Teukolsky, Saul A.; Carlson, Eric D.; Cook, Gregory B.

    2000-10-01

    Current methods of evolving a spacetime containing one or more black holes are plagued by instabilities that prohibit long-term evolution. Some of these instabilities may be due to the numerical method used, traditionally finite differencing. In this paper, we explore the use of a pseudospectral collocation (PSC) method for the evolution of a spherically symmetric black hole spacetime in one dimension using a hyperbolic formulation of Einstein's equations. We demonstrate that our PSC method is able to evolve a spherically symmetric black hole spacetime forever without enforcing constraints, even if we add dynamics via a Klein-Gordon scalar field. We find that, in contrast with finite-differencing methods, black hole excision is a trivial operation using PSC applied to a hyperbolic formulation of Einstein's equations. We discuss the extension of this method to three spatial dimensions.

  11. An analytical study of the free and forced vibration response of a ribbed plate with free boundary conditions

    NASA Astrophysics Data System (ADS)

    Lin, Tian Ran; Zhang, Kai

    2018-05-01

    An analytical study to predict the vibration response of a ribbed plate with free boundary conditions is presented. The analytical solution was derived using a double cosine integral transform technique and then utilized to study the free and forced vibration of the ribbed plate, as well as the effect of the rib on the modal response of the uniform plate. It is shown that in addition to the three zero-frequency rigid body modes of the plate, the vibration modes of the uniform plate can be classified into four mode groups according to the symmetric properties of the plate with respect to the two orthogonal middle lines parallel to the plate edges. The four mode groups correspond to a double symmetric group, a double anti-symmetric group and two symmetric/anti-symmetric groups. Whilst the inclusion of the rib to the plate is shown to cause distortion to the distribution of vibration modes, most modes can still be traced back to the original modes of the uniform plate. Both the mass and stiffness of the rib are shown to affect the modal vibration of the uniform plate, whereby a dominant effect from the rib mass leads to a decrease in the modal frequency of the plate, whereas a dominant effect from the rib stiffness leads to an increase in plate modal frequency. When the stiffened rib behaves as an effective boundary to the plate vibration, an original plate mode becomes a pair of degenerate modes, whereby one mode has a higher frequency and the other mode has a lower frequency than that of the original mode.

  12. Dynamic stability of rolling particles between elastic plates

    NASA Astrophysics Data System (ADS)

    Guzev, Mikhail; Dmitriev, Aleksandr; Dyskin, Arcady; Pasternak, Elena

    2017-04-01

    Mechanical behaviour of a large class of engineering materials from granular materials and interlocking structures to damaged rock and fragmented rock masses is controlled by rotations of the constituents leading to the necessity to introduce internal rotations and rotational degrees of freedom into the constitutive laws. An important (and underappreciated) factor in these cases is the shape of rotating elements as it imposes, in the presence of compressive stress, kinematic constraints that provide additional resistance to rotations. (Despite the universal acknowledgement that the particles in geomaterial and concrete are far from being spherical, the vast majority of models, from the Cosserat continuum to the very recent are still based on spherical or circular elements, e.g. [1]). In the presence of high compressive loading the combination of rotation and non-sphericity of the constituents produces qualitatively new effects: the effect of apparent negative stiffness and a possibility of instability [2]. In order to simplify the analysis we investigate the stability of interacting rotating particles is a sympathetic oscillator [3]. A modified model of the oscillating system, given their rods slide without friction relative to each other was proposed in [4]. An important property of the system is the possibility of bifurcations depending on the distance between the suspension points. Here we study the stability of two linearly - interacting oscillators in a uniform gravity field. The simplest models pertinent to the analysis of stability of such systems is a system of two linked oscillators (masses on rods) with a modification that allows the rods to intersect and slide without friction relative to each other thus providing a simplified modelling of 3D situations. We demonstrate that the analysis of the system trajectories is the most convenient in a 2D parametric space which is generated by the initial relative distance between the masses and the potential energy of the oscillator normalised by the spring's effective energy. We found that the system has symmetrical and asymmetrical equilibrium solutions. In the dynamical case, the asymmetric solutions ensue when the system is deviated from its symmetrical equilibrium. We point out a few features of the global dynamics of the system: 1) at the symmetric equilibrium, the stability region of the sympathetic oscillators does not intersect the stability region of the modified oscillator system below the horizontal suspension line; 2) at the asymmetric equilibrium, the stability region of the sympathetic oscillators intersect the stability region of the modified oscillator system below the suspension line. References [1] Kun, F., I. Varga, S. Lennartz-Sassinek & I.G. Main, 2014. Rupture cascades in a discrete element model of a porous sedimentary rock. Phys. Rev. Lett. 112, 065501. [2] Dyskin, A.V. & E. Pasternak, 2012. Mechanical effect of rotating non-spherical particles on failure in compression. Phil. Mag. 92, 3451-3473. [3] A. Sommerfeld, Vorlesungen uber Theoretische Physik, Band 1: Mechanik, Verlag Harri Deutsch, Thun, 1994. [4] P. Ramachandran, S. G. Krishna, Y. M. Ram, Instability of a constrained pendulum system, Am. J. Phys. 79 (4) (2011) 395-400.

  13. Global Resolution of the Physical Vacuum Singularity for Three-Dimensional Isentropic Inviscid Flows with Damping in Spherically Symmetric Motions

    NASA Astrophysics Data System (ADS)

    Zeng, Huihui

    2017-10-01

    For the gas-vacuum interface problem with physical singularity and the sound speed being {C^{{1}/{2}}}-Hölder continuous near vacuum boundaries of the isentropic compressible Euler equations with damping, the global existence of smooth solutions and the convergence to Barenblatt self-similar solutions of the corresponding porous media equation are proved in this paper for spherically symmetric motions in three dimensions; this is done by overcoming the analytical difficulties caused by the coordinate's singularity near the center of symmetry, and the physical vacuum singularity to which standard methods of symmetric hyperbolic systems do not apply. Various weights are identified to resolve the singularity near the vacuum boundary and the center of symmetry globally in time. The results obtained here contribute to the theory of global solutions to vacuum boundary problems of compressible inviscid fluids, for which the currently available results are mainly for the local-in-time well-posedness theory, and also to the theory of global smooth solutions of dissipative hyperbolic systems which fail to be strictly hyperbolic.

  14. Klein–Gordon equation in curved space-time

    NASA Astrophysics Data System (ADS)

    Lehn, R. D.; Chabysheva, S. S.; Hiller, J. R.

    2018-07-01

    We report the methods and results of a computational physics project on the solution of the relativistic Klein–Gordon equation for a light particle gravitationally bound to a heavy central mass. The gravitational interaction is prescribed by the metric of a spherically symmetric space-time. Metrics are considered for an impenetrable sphere, a soft sphere of uniform density, and a soft sphere with a linear transition from constant to zero density; in each case the radius of the central mass is chosen to be sufficient to avoid any event horizon. The solutions are obtained numerically and compared with nonrelativistic Coulomb-type solutions, both directly and in perturbation theory, to study the general-relativistic corrections to the quantum solutions for a 1/r potential. The density profile with a linear transition is chosen to avoid singularities in the wave equation that can be caused by a discontinuous derivative of the density. This project should be of interest to instructors and students of computational physics at the graduate and advanced undergraduate levels.

  15. Physical interpretation of Jeans instability in quantum plasmas

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Akbari-Moghanjoughi, M.; International Centre for Advanced Studies in Physical Sciences and Institute for Theoretical Physics, Ruhr University Bochum, D-44780 Bochum

    2014-08-15

    In this paper, we use the quantum hydrodynamics and its hydrostatic limit to investigate the newly posed problem of Jeans instability in quantum plasmas from a different point of view in connection with the well-known Chandrasekhar mass-limit on highly collapsed degenerate stellar configurations. It is shown that the hydrodynamic stability of a spherically symmetric uniform quantum plasma with a given fixed mass is achieved by increase in its mass-density or decrease in the radius under the action of gravity. It is also remarked that for masses beyond the limiting Jeans-mass, the plasma becomes completely unstable and the gravitational collapse wouldmore » proceed forever. This limiting mass is found to depend strongly on the composition of the quantum plasma and the atomic-number of the constituent ions, where it is observed that heavier elements rather destabilize the quantum plasma hydrodynamically. It is also shown that the Chandrasekhar mass-limit for white dwarf stars can be directly obtained from the hydrostatic limit of our model.« less

  16. Generalized power-spectrum Larmor formula for an extended charged particle embedded in a harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Marengo, Edwin A.; Khodja, Mohamed R.

    2006-09-01

    The nonrelativistic Larmor radiation formula, giving the power radiated by an accelerated charged point particle, is generalized for a spatially extended particle in the context of the classical charged harmonic oscillator. The particle is modeled as a spherically symmetric rigid charge distribution that possesses both translational and spinning degrees of freedom. The power spectrum obtained exhibits a structure that depends on the form factor of the particle, but reduces, in the limit of an infinitesimally small particle and for the charge distributions considered, to Larmor’s familiar result. It is found that for finite-duration small-enough accelerations as well as perpetual uniform accelerations the power spectrum of the spatially extended particle reduces to that of a point particle. It is also found that when the acceleration is violent or the size parameter of the particle is very large compared to the wavelength of the emitted radiation the power spectrum is highly suppressed. Possible applications are discussed.

  17. High-energy Electron Scattering and the Charge Distributions of Selected Nuclei

    DOE R&D Accomplishments Database

    Hahn, B.; Ravenhall, D. G.; Hofstadter, R.

    1955-10-01

    Experimental results are presented of electron scattering by Ca, V, Co, In, Sb, Hf, Ta, W, Au, Bi, Th, and U, at 183 Mev and (for some of the elements) at 153 Mev. For those nuclei for which asphericity and inelastic scattering are absent or unimportant, i.e., Ca, V, Co, In, Sb, Au, and Bi, a partial wave analysis of the Dirac equation has been performed in which the nuclei are represented by static, spherically symmetric charge distributions. Smoothed uniform charge distributions have been assumed; these are characterized by a constant charge density in the central region of the nucleus, with a smoothed-our surface. Essentially two parameters can be determined, related to the radium and to the surface thickness. An examination of the Au experiments show that the functional forms of the surface are not important, and that the charge density in the central regions is probably fairly flat, although it cannot be determined very accurately.

  18. Validation of Spherically Symmetric Inversion by Use of a Tomographically Reconstructed Three-Dimensional Electron Density of the Solar Corona

    NASA Technical Reports Server (NTRS)

    Wang, Tongjiang; Davila, Joseph M.

    2014-01-01

    Determining the coronal electron density by the inversion of white-light polarized brightness (pB) measurements by coronagraphs is a classic problem in solar physics. An inversion technique based on the spherically symmetric geometry (spherically symmetric inversion, SSI) was developed in the 1950s and has been widely applied to interpret various observations. However, to date there is no study of the uncertainty estimation of this method. We here present the detailed assessment of this method using a three-dimensional (3D) electron density in the corona from 1.5 to 4 solar radius as a model, which is reconstructed by a tomography method from STEREO/COR1 observations during the solar minimum in February 2008 (Carrington Rotation, CR 2066).We first show in theory and observation that the spherically symmetric polynomial approximation (SSPA) method and the Van de Hulst inversion technique are equivalent. Then we assess the SSPA method using synthesized pB images from the 3D density model, and find that the SSPA density values are close to the model inputs for the streamer core near the plane of the sky (POS) with differences generally smaller than about a factor of two; the former has the lower peak but extends more in both longitudinal and latitudinal directions than the latter. We estimate that the SSPA method may resolve the coronal density structure near the POS with angular resolution in longitude of about 50 deg. Our results confirm the suggestion that the SSI method is applicable to the solar minimum streamer (belt), as stated in some previous studies. In addition, we demonstrate that the SSPA method can be used to reconstruct the 3D coronal density, roughly in agreement with the reconstruction by tomography for a period of low solar activity (CR 2066). We suggest that the SSI method is complementary to the 3D tomographic technique in some cases, given that the development of the latter is still an ongoing research effort.

  19. Horizon Quantum Mechanics: Spherically Symmetric and Rotating Sources

    NASA Astrophysics Data System (ADS)

    Casadio, Roberto; Giugno, Andrea; Giusti, Andrea; Micu, Octavian

    2018-04-01

    The Horizon Quantum Mechanics is an approach that allows one to analyse the gravitational radius of spherically symmetric systems and compute the probability that a given quantum state is a black hole. We first review the (global) formalism and show how it reproduces a gravitationally inspired GUP relation. This results leads to unacceptably large fluctuations in the horizon size of astrophysical black holes if one insists in describing them as (smeared) central singularities. On the other hand, if they are extended systems, like in the corpuscular models, no such issue arises and one can in fact extend the formalism to include asymptotic mass and angular momentum with the harmonic model of rotating corpuscular black holes. The Horizon Quantum Mechanics then shows that, in simple configurations, the appearance of the inner horizon is suppressed and extremal (macroscopic) geometries seem disfavoured.

  20. Massive graviton geons

    NASA Astrophysics Data System (ADS)

    Aoki, Katsuki; Maeda, Kei-ichi; Misonoh, Yosuke; Okawa, Hirotada

    2018-02-01

    We find vacuum solutions such that massive gravitons are confined in a local spacetime region by their gravitational energy in asymptotically flat spacetimes in the context of the bigravity theory. We call such self-gravitating objects massive graviton geons. The basic equations can be reduced to the Schrödinger-Poisson equations with the tensor "wave function" in the Newtonian limit. We obtain a nonspherically symmetric solution with j =2 , ℓ=0 as well as a spherically symmetric solution with j =0 , ℓ=2 in this system where j is the total angular momentum quantum number and ℓ is the orbital angular momentum quantum number, respectively. The energy eigenvalue of the Schrödinger equation in the nonspherical solution is smaller than that in the spherical solution. We then study the perturbative stability of the spherical solution and find that there is an unstable mode in the quadrupole mode perturbations which may be interpreted as the transition mode to the nonspherical solution. The results suggest that the nonspherically symmetric solution is the ground state of the massive graviton geon. The massive graviton geons may decay in time due to emissions of gravitational waves but this timescale can be quite long when the massive gravitons are nonrelativistic and then the geons can be long-lived. We also argue possible prospects of the massive graviton geons: applications to the ultralight dark matter scenario, nonlinear (in)stability of the Minkowski spacetime, and a quantum transition of the spacetime.

  1. Holographic Spherically Symmetric Metrics

    NASA Astrophysics Data System (ADS)

    Petri, Michael

    The holographic principle (HP) conjectures, that the maximum number of degrees of freedom of any realistic physical system is proportional to the system's boundary area. The HP has its roots in the study of black holes. It has recently been applied to cosmological solutions. In this article we apply the HP to spherically symmetric static space-times. We find that any regular spherically symmetric object saturating the HP is subject to tight constraints on the (interior) metric, energy-density, temperature and entropy-density. Whenever gravity can be described by a metric theory, gravity is macroscopically scale invariant and the laws of thermodynamics hold locally and globally, the (interior) metric of a regular holographic object is uniquely determined up to a constant factor and the interior matter-state must follow well defined scaling relations. When the metric theory of gravity is general relativity, the interior matter has an overall string equation of state (EOS) and a unique total energy-density. Thus the holographic metric derived in this article can serve as simple interior 4D realization of Mathur's string fuzzball proposal. Some properties of the holographic metric and its possible experimental verification are discussed. The geodesics of the holographic metric describe an isotropically expanding (or contracting) universe with a nearly homogeneous matter-distribution within the local Hubble volume. Due to the overall string EOS the active gravitational mass-density is zero, resulting in a coasting expansion with Ht = 1, which is compatible with the recent GRB-data.

  2. Electromagnetic Fields of a Uniform Sphere in a Uniform Conducting Medium with Application to Dipole Sources

    DTIC Science & Technology

    1991-09-01

    12b. DISTRIBUTION CODE Approved for public release; distribution is unlimited. 13. ABSTRACT (Maximum 200 words) Vector spherical harmonic expansions are...electric and magnetic field vectors from E rand B - r alone. Genural expressions are given relating the scattered field expansion coefficients to the source...Prescnbed by ANSI Std. Z39-18 29W-102 NCSC TR 426-90 CONTENTS Pag o INTRODUCTION 1 BACKGROUND 1 ANGULAR MOMENTUM OPERATOR AND VECTOR SPHERICAL

  3. METHOD OF MAKING SPHERICAL ACTINIDE CARBIDE

    DOEpatents

    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)

  4. Dynamic Snap-Through of Thermally Buckled Structures by a Reduced Order Method

    NASA Technical Reports Server (NTRS)

    Przekop, Adam; Rizzi, Stephen A.

    2007-01-01

    The goal of this investigation is to further develop nonlinear modal numerical simulation methods for application to geometrically nonlinear response of structures exposed to combined high intensity random pressure fluctuations and thermal loadings. The study is conducted on a flat aluminum beam, which permits a comparison of results obtained by a reduced-order analysis with those obtained from a numerically intensive simulation in physical degrees-of-freedom. A uniformly distributed thermal loading is first applied to investigate the dynamic instability associated with thermal buckling. A uniformly distributed random loading is added to investigate the combined thermal-acoustic response. In the latter case, three types of response characteristics are considered, namely: (i) small amplitude vibration around one of the two stable buckling equilibrium positions, (ii) intermittent snap-through response between the two equilibrium positions, and (iii) persistent snap-through response between the two equilibrium positions. For the reduced-order analysis, four categories of modal basis functions are identified including those having symmetric transverse, anti-symmetric transverse, symmetric in-plane, and anti-symmetric in-plane displacements. The effect of basis selection on the quality of results is investigated for the dynamic thermal buckling and combined thermal-acoustic response. It is found that despite symmetric geometry, loading, and boundary conditions, the anti-symmetric transverse and symmetric in-plane modes must be included in the basis as they participate in the snap-through behavior.

  5. Effects of visual cues of object density on perception and anticipatory control of dexterous manipulation.

    PubMed

    Crajé, Céline; Santello, Marco; Gordon, Andrew M

    2013-01-01

    Anticipatory force planning during grasping is based on visual cues about the object's physical properties and sensorimotor memories of previous actions with grasped objects. Vision can be used to estimate object mass based on the object size to identify and recall sensorimotor memories of previously manipulated objects. It is not known whether subjects can use density cues to identify the object's center of mass (CM) and create compensatory moments in an anticipatory fashion during initial object lifts to prevent tilt. We asked subjects (n = 8) to estimate CM location of visually symmetric objects of uniform densities (plastic or brass, symmetric CM) and non-uniform densities (mixture of plastic and brass, asymmetric CM). We then asked whether subjects can use density cues to scale fingertip forces when lifting the visually symmetric objects of uniform and non-uniform densities. Subjects were able to accurately estimate an object's center of mass based on visual density cues. When the mass distribution was uniform, subjects could scale their fingertip forces in an anticipatory fashion based on the estimation. However, despite their ability to explicitly estimate CM location when object density was non-uniform, subjects were unable to scale their fingertip forces to create a compensatory moment and prevent tilt on initial lifts. Hefting object parts in the hand before the experiment did not affect this ability. This suggests a dichotomy between the ability to accurately identify the object's CM location for objects with non-uniform density cues and the ability to utilize this information to correctly scale their fingertip forces. These results are discussed in the context of possible neural mechanisms underlying sensorimotor integration linking visual cues and anticipatory control of grasping.

  6. HEAT TRANSFER MEANS

    DOEpatents

    Fraas, A.P.; Wislicenus, G.F.

    1961-07-11

    A heat exchanger is adapted to unifomly cool a spherical surface. Equations for the design of a spherical heat exchanger hav~g tubes with a uniform center-to-center spining are given. The heat exchanger is illustrated in connection with a liquid-fueled reactor.

  7. Plasma coating of nanoparticles in the presence of an external electric field

    NASA Astrophysics Data System (ADS)

    Ebadi, Zahra; Pourali, Nima; Mohammadzadeh, Hosein

    2018-04-01

    Film deposition onto nanoparticles by low-pressure plasma in the presence of an external electric field is studied numerically. The plasma discharge fluid model along with surface deposition and heating models for nanoparticles, as well as a dynamics model considering the motion of nanoparticles, are employed for this study. The results of the simulation show that applying external field during the process increases the uniformity of the film deposited onto nanoparticles and leads to that nanoparticles grow in a spherical shape. Increase in film uniformity and particles sphericity is related to particle dynamics that is controlled by parameters of the external field like frequency and amplitude. The results of this work can be helpful to produce spherical core-shell nanoparticles in nanomaterial industry.

  8. A tensor formulation of the equation of transfer for spherically symmetric flows. [radiative transfer in seven dimensional Riemannian space

    NASA Technical Reports Server (NTRS)

    Haisch, B. M.

    1976-01-01

    A tensor formulation of the equation of radiative transfer is derived in a seven-dimensional Riemannian space such that the resulting equation constitutes a divergence in any coordinate system. After being transformed to a spherically symmetric comoving coordinate system, the transfer equation contains partial derivatives in angle and frequency, as well as optical depth due to the effects of aberration and the Doppler shift. However, by virtue of the divergence form of this equation, the divergence theorem may be applied to yield a numerical differencing scheme which is expected to be stable and to conserve luminosity. It is shown that the equation of transfer derived by this method in a Lagrangian coordinate system may be reduced to that given by Castor (1972), although it is, of course, desirable to leave the equation in divergence form.

  9. Bopp-Podolsky black holes and the no-hair theorem

    NASA Astrophysics Data System (ADS)

    Cuzinatto, R. R.; de Melo, C. A. M.; Medeiros, L. G.; Pimentel, B. M.; Pompeia, P. J.

    2018-01-01

    Bopp-Podolsky electrodynamics is generalized to curved space-times. The equations of motion are written for the case of static spherically symmetric black holes and their exterior solutions are analyzed using Bekenstein's method. It is shown that the solutions split up into two parts, namely a non-homogeneous (asymptotically massless) regime and a homogeneous (asymptotically massive) sector which is null outside the event horizon. In addition, in the simplest approach to Bopp-Podolsky black holes, the non-homogeneous solutions are found to be Maxwell's solutions leading to a Reissner-Nordström black hole. It is also demonstrated that the only exterior solution consistent with the weak and null energy conditions is the Maxwell one. Thus, in the light of the energy conditions, it is concluded that only Maxwell modes propagate outside the horizon and, therefore, the no-hair theorem is satisfied in the case of Bopp-Podolsky fields in spherically symmetric space-times.

  10. Spherically symmetric vacuum solutions arising from trace dynamics modifications to gravitation

    NASA Astrophysics Data System (ADS)

    Adler, Stephen L.; Ramazanoğlu, Fethi M.

    2015-12-01

    We derive the equations governing static, spherically symmetric vacuum solutions to the Einstein equations, as modified by the frame-dependent effective action (derived from trace dynamics) that gives an alternative explanation of the origin of "dark energy". We give analytic and numerical results for the solutions of these equations, first in polar coordinates, and then in isotropic coordinates. General features of the static case are that: (i) there is no horizon, since g00 is nonvanishing for finite values of the polar radius, and only vanishes (in isotropic coordinates) at the internal singularity, (ii) the Ricci scalar R vanishes identically, and (iii) there is a physical singularity at cosmological distances. The large distance singularity may be an artifact of the static restriction, since we find that the behavior at large distances is altered in a time-dependent solution using the McVittie Ansatz.

  11. Generalized transformations and coordinates for static spherically symmetric general relativity

    NASA Astrophysics Data System (ADS)

    Hill, James M.; O'Leary, Joseph

    2018-04-01

    We examine a static, spherically symmetric solution of the empty space field equations of general relativity with a non-orthogonal line element which gives rise to an opportunity that does not occur in the standard derivations of the Schwarzschild solution. In these derivations, convenient coordinate transformations and dynamical assumptions inevitably lead to the Schwarzschild solution. By relaxing these conditions, a new solution possibility arises and the resulting formalism embraces the Schwarzschild solution as a special case. The new solution avoids the coordinate singularity associated with the Schwarzschild solution and is achieved by obtaining a more suitable coordinate chart. The solution embodies two arbitrary constants, one of which can be identified as the Newtonian gravitational potential using the weak field limit. The additional arbitrary constant gives rise to a situation that allows for generalizations of the Eddington-Finkelstein transformation and the Kruskal-Szekeres coordinates.

  12. On the stability of soliton and hairy black hole solutions of 𝔰𝔲(N) Einstein-Yang-Mills theory with a negative cosmological constant

    NASA Astrophysics Data System (ADS)

    Baxter, J. Erik; Winstanley, Elizabeth

    2016-02-01

    We investigate the stability of spherically symmetric, purely magnetic, soliton and black hole solutions of four-dimensional 𝔰𝔲(N) Einstein-Yang-Mills theory with a negative cosmological constant Λ. These solutions are described by N - 1 magnetic gauge field functions ωj. We consider linear, spherically symmetric, perturbations of these solutions. The perturbations decouple into two sectors, known as the sphaleronic and gravitational sectors. For any N, there are no instabilities in the sphaleronic sector if all the magnetic gauge field functions ωj have no zeros and satisfy a set of N - 1 inequalities. In the gravitational sector, we prove that there are solutions which have no instabilities in a neighbourhood of stable embedded 𝔰𝔲(2) solutions, provided the magnitude of the cosmological constant |" separators=" Λ | is sufficiently large.

  13. Spherically symmetric charged black holes in f(R) gravitational theories

    NASA Astrophysics Data System (ADS)

    Nashed, G. G. L.

    2018-01-01

    In this study, we have derived electric and magnetic spherically symmetric black holes for the class f(R)=R+ζ R2 without assuming any restrictions on the Ricci scalar. These black holes asymptotically behave as the de Sitter spacetime under certain constrains. We have shown that the magnetic charge contributes in the metric spacetime similarly to the electric charge. The most interesting feature of some of these black holes is the fact that the Cauchy horizon is not identical to the event horizon. We have calculated the invariants of Ricci and Kretschmann scalars to investigate the nature of singularities of such black holes. Also, we have calculated the conserved quantities to match the constants of integration with the physical quantities. Finally, the thermodynamical quantities, like Hawking temperature, entropy, etc., have been evaluated and the validity of the first law of thermodynamics has been verified.

  14. The Gross–Pitaevskii equations of a static and spherically symmetric condensate of gravitons

    NASA Astrophysics Data System (ADS)

    Cunillera, Francesc; Germani, Cristiano

    2018-05-01

    In this paper we consider the Dvali and Gómez assumption that the end state of a gravitational collapse is a Bose–Einstein condensate of gravitons. We then construct the two Gross–Pitaevskii equations for a static and spherically symmetric configuration of the condensate. These two equations correspond to the constrained minimisation of the gravitational Hamiltonian with respect to the redshift and the Newtonian potential, per given number of gravitons. We find that the effective geometry of the condensate is the one of a gravastar (a de Sitter star) with a sub-Planckian cosmological constant, for masses larger than the Planck scale. Thus, a condensate corresponding to a semiclassical black hole, is always quantum and weakly coupled. Finally, we obtain that the boundary of our gravastar, although it is not the location of a horizon, corresponds to the Schwarzschild radius.

  15. Hydrodynamic Stability of Multicomponent Droplet Gasification in Reduced Gravity

    NASA Technical Reports Server (NTRS)

    Aharon, I.; Shaw, B. D.

    1995-01-01

    This investigation addresses the problem of hydrodynamic stability of a two-component droplet undergoing spherically-symmetrical gasification. The droplet components are assumed to have characteristic liquid species diffusion times that are large relative to characteristic droplet surface regression times. The problem is formulated as a linear stability analysis, with a goal of predicting when spherically-symmetric droplet gasification can be expected to be hydrodynamically unstable from surface-tension gradients acting along the surface of a droplet which result from perturbations. It is found that for the conditions assumed in this paper (quasisteady gas phase, no initial droplet temperature gradients, diffusion-dominated gasification), surface tension gradients do not play a role in the stability characteristics. In addition, all perturbations are predicted to decay such that droplets were hydrodynamically stable. Conditions are identified, however, that deserve more analysis as they may lead to hydrodynamic instabilities driven by capillary effects.

  16. Generalized transformations and coordinates for static spherically symmetric general relativity.

    PubMed

    Hill, James M; O'Leary, Joseph

    2018-04-01

    We examine a static, spherically symmetric solution of the empty space field equations of general relativity with a non-orthogonal line element which gives rise to an opportunity that does not occur in the standard derivations of the Schwarzschild solution. In these derivations, convenient coordinate transformations and dynamical assumptions inevitably lead to the Schwarzschild solution. By relaxing these conditions, a new solution possibility arises and the resulting formalism embraces the Schwarzschild solution as a special case. The new solution avoids the coordinate singularity associated with the Schwarzschild solution and is achieved by obtaining a more suitable coordinate chart. The solution embodies two arbitrary constants, one of which can be identified as the Newtonian gravitational potential using the weak field limit. The additional arbitrary constant gives rise to a situation that allows for generalizations of the Eddington-Finkelstein transformation and the Kruskal-Szekeres coordinates.

  17. Generalized transformations and coordinates for static spherically symmetric general relativity

    PubMed Central

    2018-01-01

    We examine a static, spherically symmetric solution of the empty space field equations of general relativity with a non-orthogonal line element which gives rise to an opportunity that does not occur in the standard derivations of the Schwarzschild solution. In these derivations, convenient coordinate transformations and dynamical assumptions inevitably lead to the Schwarzschild solution. By relaxing these conditions, a new solution possibility arises and the resulting formalism embraces the Schwarzschild solution as a special case. The new solution avoids the coordinate singularity associated with the Schwarzschild solution and is achieved by obtaining a more suitable coordinate chart. The solution embodies two arbitrary constants, one of which can be identified as the Newtonian gravitational potential using the weak field limit. The additional arbitrary constant gives rise to a situation that allows for generalizations of the Eddington–Finkelstein transformation and the Kruskal–Szekeres coordinates. PMID:29765624

  18. Spherically Symmetric Gravitational Collapse of a Dust Cloud in Third-Order Lovelock Gravity

    NASA Astrophysics Data System (ADS)

    Zhou, Kang; Yang, Zhan-Ying; Zou, De-Cheng; Yue, Rui-Hong

    We investigate the spherically symmetric gravitational collapse of an incoherent dust cloud by considering a LTB-type spacetime in third-order Lovelock Gravity without cosmological constant, and give three families of LTB-like solutions which separately corresponding to hyperbolic, parabolic and elliptic. Notice that the contribution of high-order curvature corrections have a profound influence on the nature of the singularity, and the global structure of spacetime changes drastically from the analogous general relativistic case. Interestingly, the presence of high order Lovelock terms leads to the formation of massive, naked and timelike singularities in the 7D spacetime, which is disallowed in general relativity. Moveover, we point out that the naked singularities in the 7D case may be gravitational weak therefore may not be a serious threat to the cosmic censorship hypothesis, while the naked singularities in the D ≥ 8 inhomogeneous collapse violate the cosmic censorship hypothesis seriously.

  19. Winds from T Tauri stars. I - Spherically symmetric models

    NASA Technical Reports Server (NTRS)

    Hartmann, Lee; Avrett, Eugene H.; Loeser, Rudolf; Calvet, Nuria

    1990-01-01

    Line fluxes and profiles are computed for a sequence of spherically symmetric T Tauri wind models. The calculations indicate that the H-alpha emission of T Tauri stars arises in an extended and probably turbulent circumstellar envelope at temperatures above about 8000 K. The models predict that Mg II resonance line emission should be strongly correlated with H-alpha fluxes; observed Mg II/H-alpha ratios are inconsistent with the models unless extinction corrections have been underestimated. The models predict that most of the Ca II resonance line and IR triplet emission arises in dense layers close to the star rather than in the wind. H-alpha emission levels suggest mass loss rates of about 10 to the -8th solar mass/yr for most T Tauri stars, in reasonable agreement with independent analysis of forbidden emission lines. These results should be useful for interpreting observed line profiles in terms of wind densities, temperatures, and velocity fields.

  20. Global solutions to physical vacuum problem of non-isentropic viscous gaseous stars and nonlinear asymptotic stability of stationary solutions

    NASA Astrophysics Data System (ADS)

    Hong, Guangyi; Luo, Tao; Zhu, Changjiang

    2018-07-01

    This paper is concerned with spherically symmetric motions of non-isentropic viscous gaseous stars with self-gravitation. When the stationary entropy S ‾ (x) is spherically symmetric and satisfies a suitable smallness condition, the existence and properties of the stationary solutions are obtained for 6/5 < γ < 2 with weaker constraints upon S ‾ (x) compared with the one in [26], where γ is the adiabatic exponent. The global existence of strong solutions capturing the physical vacuum singularity that the sound speed is C 1/2 -Hölder continuous across the vacuum boundary to a simplified system for non-isentropic viscous flow with self-gravitation and the nonlinear asymptotic stability of the stationary solution are proved when 4/3 < γ < 2 with the detailed convergence rates, motivated by the results and analysis of the nonlinear asymptotic stability of Lane-Emden solutions for isentropic flows in [29,30].

  1. Existence and uniqueness of weak solutions of the compressible spherically symmetric Navier-Stokes equations

    NASA Astrophysics Data System (ADS)

    Huang, Xiangdi

    2017-02-01

    One of the most influential fundamental tools in harmonic analysis is the Riesz transforms. It maps Lp functions to Lp functions for any p ∈ (1 , ∞) which plays an important role in singular operators. As an application in fluid dynamics, the norm equivalence between ‖∇u‖Lp and ‖ div u ‖ Lp +‖ curl u ‖ Lp is well established for p ∈ (1 , ∞). However, since Riesz operators sent bounded functions only to BMO functions, there is no hope to bound ‖∇u‖L∞ in terms of ‖ div u ‖ L∞ +‖ curl u ‖ L∞. As pointed out by Hoff (2006) [11], this is the main obstacle to obtain uniqueness of weak solutions for isentropic compressible flows. Fortunately, based on new observations, see Lemma 2.2, we derive an exact estimate for ‖∇u‖L∞ ≤ (2 + 1 / N)‖ div u ‖ L∞ for any N-dimensional radially symmetric vector functions u. As a direct application, we give an affirmative answer to the open problem of uniqueness of some weak solutions to the compressible spherically symmetric flows in a bounded ball.

  2. Information theory lateral density distribution for Earth inferred from global gravity field

    NASA Technical Reports Server (NTRS)

    Rubincam, D. P.

    1981-01-01

    Information Theory Inference, better known as the Maximum Entropy Method, was used to infer the lateral density distribution inside the Earth. The approach assumed that the Earth consists of indistinguishable Maxwell-Boltzmann particles populating infinitesimal volume elements, and followed the standard methods of statistical mechanics (maximizing the entropy function). The GEM 10B spherical harmonic gravity field coefficients, complete to degree and order 36, were used as constraints on the lateral density distribution. The spherically symmetric part of the density distribution was assumed to be known. The lateral density variation was assumed to be small compared to the spherically symmetric part. The resulting information theory density distribution for the cases of no crust removed, 30 km of compensated crust removed, and 30 km of uncompensated crust removed all gave broad density anomalies extending deep into the mantle, but with the density contrasts being the greatest towards the surface (typically + or 0.004 g cm 3 in the first two cases and + or - 0.04 g cm 3 in the third). None of the density distributions resemble classical organized convection cells. The information theory approach may have use in choosing Standard Earth Models, but, the inclusion of seismic data into the approach appears difficult.

  3. Linear perturbations in spherically symmetric dust cosmologies including a cosmological constant

    NASA Astrophysics Data System (ADS)

    Meyer, Sven; Bartelmann, Matthias

    2017-12-01

    We study the dynamical behaviour of gauge-invariant linear perturbations in spherically symmetric dust cosmologies including a cosmological constant. In contrast to spatially homogeneous FLRW models, the reduced degree of spatial symmetry causes a non-trivial dynamical coupling of gauge-invariant quantities already at first order perturbation theory and the strength and influence of this coupling on the spacetime evolution is investigated here. We present results on the underlying dynamical equations augmented by a cosmological constant and integrate them numerically. We also present a method to derive cosmologically relevant initial variables for this setup. Estimates of angular power spectra for each metric variable are computed and evaluated on the central observer's past null cone. By comparing the full evolution to the freely evolved initial profiles, the coupling strength will be determined for a best fit radially inhomogeneous patch obtained in previous works (see [1]). We find that coupling effects are not noticeable within the cosmic variance limit and can therefore safely be neglected for a relevant cosmological scenario. On the contrary, we find very strong coupling effects in a best fit spherical void model matching the distance redshift relation of SNe which is in accordance with previous findings using parametric void models.

  4. Dynamos in asymptotic-giant-branch stars as the origin of magnetic fields shaping planetary nebulae.

    PubMed

    Blackman, E G; Frank, A; Markiel, J A; Thomas, J H; Van Horn, H M

    2001-01-25

    Planetary nebulae are thought to be formed when a slow wind from the progenitor giant star is overtaken by a subsequent fast wind generated as the star enters its white dwarf stage. A shock forms near the boundary between the winds, creating the relatively dense shell characteristic of a planetary nebula. A spherically symmetric wind will produce a spherically symmetric shell, yet over half of known planetary nebulae are not spherical; rather, they are elliptical or bipolar in shape. A magnetic field could launch and collimate a bipolar outflow, but the origin of such a field has hitherto been unclear, and some previous work has even suggested that a field could not be generated. Here we show that an asymptotic-giant-branch (AGB) star can indeed generate a strong magnetic field, having as its origin a dynamo at the interface between the rapidly rotating core and the more slowly rotating envelope of the star. The fields are strong enough to shape the bipolar outflows that produce the observed bipolar planetary nebulae. Magnetic braking of the stellar core during this process may also explain the puzzlingly slow rotation of most white dwarf stars.

  5. An axion-like scalar field environment effect on binary black hole merger

    NASA Astrophysics Data System (ADS)

    Yang, Qing; Ji, Li-Wei; Hu, Bin; Cao, Zhou-Jian; Cai, Rong-Gen

    2018-06-01

    The environment, such as an accretion disk, could modify the signal of the gravitational wave from astrophysical black hole binaries. In this article, we model the matter field around intermediate-mass binary black holes by means of an axion-like scalar field and investigate their joint evolution. In detail, we consider equal mass binary black holes surrounded by a shell of axion-like scalar field both in spherically symmetric and non-spherically symmetric cases, and with different strengths of the scalar field. Our result shows that the environmental scalar field could essentially modify the dynamics. Firstly, in the spherically symmetric case, with increase of the scalar field strength, the number of circular orbits for the binary black hole is reduced. This means that the scalar field could significantly accelerate the merger process. Secondly, once the scalar field strength exceeds a certain critical value, the scalar field could collapse into a third black hole with its mass being larger than that of the binary. Consequently, the new black hole that collapses from the environmental scalar field could accrete the binary promptly and the binary collides head-on with each other. In this process, there is almost no quadrupole signal produced, and, consequently, the gravitational wave is greatly suppressed. Thirdly, when the scalar field strength is relatively smaller than the critical value, the black hole orbit could develop eccentricity through accretion of the scalar field. Fourthly, during the initial stage of the inspiral, the gravitational attractive force from the axion-like scalar field could induce a sudden turn in the binary orbits, hence resulting in a transient wiggle in the gravitational waveform. Finally, in the non-spherical case, the scalar field could gravitationally attract the binary moving toward the center of mass for the scalar field and slow down the merger process.

  6. Conical singularities and the Vainshtein screening in full GLPV theories

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kase, Ryotaro; Tsujikawa, Shinji; Felice, Antonio De, E-mail: r.kase@rs.tus.ac.jp, E-mail: shinji@rs.kagu.tus.ac.jp, E-mail: antonio.defelice@yukawa.kyoto-u.ac.jp

    In Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories, it is known that the conical singularity arises at the center of a spherically symmetric body (r = 0) in the case where the parameter α{sub H}4 characterizing the deviation from the Horndeski Lagrangian L{sub 4} approaches a non-zero constant as r → 0. We derive spherically symmetric solutions around the center in full GLPV theories and show that the GLPV Lagrangian L{sub 5} does not modify the divergent property of the Ricci scalar R induced by the non-zero α{sub H}4. Provided that α{sub H}4 = 0, curvature scalar quantities can remain finite at r = 0 even in the presence of L{sub 5}more » beyond the Horndeski domain. For the theories in which the scalar field φ is directly coupled to R, we also obtain spherically symmetric solutions inside/outside the body to study whether the fifth force mediated by φ can be screened by non-linear field self-interactions. We find that there is one specific model of GLPV theories in which the effect of L{sub 5} vanishes in the equations of motion. We also show that, depending on the sign of a L{sub 5}-dependent term in the field equation, the model can be compatible with solar-system constraints under the Vainshtein mechanism or it is plagued by the problem of a divergence of the field derivative in high-density regions.« less

  7. A Programming Language Supporting First-Class Parallel Environments

    DTIC Science & Technology

    1989-01-01

    Symmetric Lisp later in the thesis. 1.5.1.2 Procedures as Data - Comparison with Lisp Classical Lisp[48, 54] has been altered and extended in many ways... manangement problems. A resource manager controls access to one or more resources shared by concurrently executing processes. Database transaction systems...symmetric languages are related to languages based on more classical models? 3. What are the kinds of uniformity that the symmetric model supports and what

  8. Numerical modeling of melt flows in vertical Bridgman configuration affected by a rotating heat field

    NASA Astrophysics Data System (ADS)

    Kokh, K. A.; Popov, V. N.; Kokh, A. E.; Krasin, B. A.; Nepomnyaschikh, A. I.

    2007-05-01

    In this work, the numerical modeling of convection in a vertical Bridgman system under the influence of a rotating heat field was studied. First results show that changing of the heating from an axi-symmetric to a non-symmetric non-stationary configuration results in an increase in the convective flow and thus led to an increase of the melt uniformity because the convective cell is occupying almost the entire melt domain. Experimental growth of polycrystalline silicon under such special conditions provided ingots with improved texture and uniformity of electronic properties.

  9. Watermarking on 3D mesh based on spherical wavelet transform.

    PubMed

    Jin, Jian-Qiu; Dai, Min-Ya; Bao, Hu-Jun; Peng, Qun-Sheng

    2004-03-01

    In this paper we propose a robust watermarking algorithm for 3D mesh. The algorithm is based on spherical wavelet transform. Our basic idea is to decompose the original mesh into a series of details at different scales by using spherical wavelet transform; the watermark is then embedded into the different levels of details. The embedding process includes: global sphere parameterization, spherical uniform sampling, spherical wavelet forward transform, embedding watermark, spherical wavelet inverse transform, and at last resampling the mesh watermarked to recover the topological connectivity of the original model. Experiments showed that our algorithm can improve the capacity of the watermark and the robustness of watermarking against attacks.

  10. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Karbanovski, V. V., E-mail: Karbanovski_V_V@mail.ru; Sorokin, O. M.; Nesterova, M. I.

    The system of the spherical-symmetric vacuum equations of the General Relativity Theory is considered. The general solution to a problem representing two classes of line elements with arbitrary functions g{sub 00} and g{sub 22} is obtained. The properties of the found solutions are analyzed.

  11. Dyadosphere bending of light

    NASA Astrophysics Data System (ADS)

    De Lorenci, V. A.; Figueiredo, N.; Fliche, H. H.; Novello, M.

    2001-04-01

    In the context of the static and spherically symmetric solution of a charged compact object, we present the expression for the bending of light in the region just outside the event horizon - the dyadosphere - where vacuum polarization effects are taken into account.

  12. ECCENTRIC ROLLING OF POWDER AND BONDING AGENT INTO SPHERICAL PELLETS

    DOEpatents

    Patton, G. Jr.; Zirinsky, S.

    1961-06-01

    A machine is described for pelletizing powder and bonding agent into spherical pellets of high density and uniform size. In this device, the material to be compacted is added to a flat circular pan which is moved in a circular orbit in a horizontal plane about an axis displaced from that of the pan's central axis without rotating the pan about its central axis. This movement causes the material contained therein to roll around the outside wall of the container and build up pellets of uniform shape, size, and density.

  13. Impact-generated dust clouds around planetary satellites: asymmetry effects

    NASA Astrophysics Data System (ADS)

    Sremčević, Miodrag; Krivov, Alexander V.; Spahn, Frank

    2003-06-01

    In a companion paper (Krivov et al., Impact-generated dust clouds around planetary satellites: spherically symmetric case, Planet. Space. Sci. 2003, 51, 251-269) an analytic model of an impact-generated, steady-state, spherically symmetric dust cloud around an atmosphereless planetary satellite (or planet - Mercury, Pluto) has been developed. This paper lifts the assumption of spherical symmetry and focuses on the asymmetry effects that result from the motion of the parent body through an isotropic field of impactors. As in the spherically symmetric case, we first consider the dust production from the surface and then derive a general phase-space distribution function of the ensemble of ejected dust motes. All quantities of interest, such as particle number densities and fluxes, can be obtained by integrating this phase-space distribution function. As an example, we calculate an asymmetric distribution of dust number density in a cloud. It is found that the deviation from the symmetric case can be accurately described by a cosine function of the colatitude measured from the apex of the satellite motion. This property of the asymmetry is rather robust. It is shown that even an extremely asymmetric dust production at the surface, when nearly all dust is ejected from the leading hemisphere, turns rapidly into the cosine modulation of the number density at distances larger than a few satellite radii. The amplitude of the modulation depends on the ratio of the moon orbital velocity to the speed of impactors and on the initial angular distribution of the ejecta. Furthermore, regardless of the functional form of the initial angular distribution, the number density distribution of the dust cloud is only sensitive to the mean ejecta angle. When the mean angle is small - ejection close to the normal of the surface - the initial dust production asymmetry remains persistent even far from the satellite, but when this angle is larger than about 45°, the asymmetry coefficient drops very rapidly with the increasing distance. The dependence of the asymmetric number density on other parameters is very weak. On the whole, our results provide necessary theoretical guidelines for a dedicated quest of asymmetries in the dust detector data, both those obtained by the Galileo dust detector around the Galilean satellites of Jupiter and those expected from the Cassini dust experiment around outer Saturnian moons.

  14. Nonlinear structure formation in flat cosmological models

    NASA Technical Reports Server (NTRS)

    Martel, Hugo

    1995-01-01

    This paper describes the formation of nonlinear structure in flat (zero curvature) Friedmann cosmological models. We consider models with two components: the usual nonrelativistic component that evolves under gravity and eventually forms the large-scale structure of the universe, and a uniform dark matter component that does not clump under gravity, and whose energy density varies with the scale factor a(t) like a(t)(sup -n), where n is a free parameter. Each model is characterized by two parameters: the exponent n and the present density parameter Omega(sub 0) of the nonrelativistic component. The linear perturbation equations are derived and solved for these models, for the three different cases n = 3, n is greater than 3, and n is less than 3. The case n = 3 is relevant to model with massive neutrinos. The presence of the uniform component strongly reduces the growth of the perturbation compared with the Einstein-de Sitter model. We show that the Meszaros effect (suppression of growth at high redshift) holds not only for n = 4, radiation-dominated models, but for all models with n is greater than 3. This essentially rules out any such model. For the case n is less than 3, we numerically integrate the perturbation equations from the big bang to the present, for 620 different models with various values of Omega(sub 0) and n. Using these solutions, we show that the function f(Omega(sub 0), n) = (a/delta(sub +))d(delta)(sub +)/da, which enters in the relationship between the present density contrast delta(sub 0) and peculiar velocity field u(sub 0) is essentially independent of n. We derive approximate solutions for the second-order perturbation equations. These second-order solutions are tested against the exact solutions and the Zel'dovich approximation for spherically symmetric perturbations in the marginally nonlinear regime (the absolute value of delta is less than or approximately 1). The second-order and Zel'dovich solutions have comparable accuracy, significantly higher than the accuracy of the linear solutions. We then investigate the dependence of the delta(sub 0) - u(sub 0) relationship upon the value of n in the nonlinear regime using the second-order solutions for marginally nonlinear, general perturbations, and the exact solutions for strongly nonlinear, spherically symmetric perturbations. In both cases, we find that the delta(sub 0) - u(sub 0) relationship remains independent of n. We speculate that this result extends to strongly nonlinear, general perturbations as well. This eliminates any hope to determine the presence of the uniform component or the value of n using dynamical methods. Finally, we compute the nonlinear evolution of the skewness of the distribution of values of delta, assuming Gaussian initial conditions. We find that the skewness is not only independent of n, but also of Omega(sub 0). Thus the skewness cannot be used to discriminate among various models with Gaussian initial conditions. However, it can be used for testing the Gaussianity of the initial conditions themselves. We conclude that the uniform component leaves no observable signature in the present large-scale structure of the universe. To determine its presence and nature, we must investigate the relationship between the past and present universe, using redshift-dependent tests.

  15. Manipulating femtosecond laser interactions in bulk glass and thin-film with spatial light modulation (Conference Presentation)

    NASA Astrophysics Data System (ADS)

    Alimohammadian, Ehsan; Ho, Stephen; Ertorer, Erden; Gherghe, Sebastian; Li, Jianzhao; Herman, Peter R.

    2017-03-01

    Spatial Light Modulators (SLM) are emerging as a power tool for laser beam shaping whereby digitally addressed phase shifts can impose computer-generated hologram patterns on incoming laser light. SLM provide several additional advantages with ultrashort-pulsed lasers in controlling the shape of both surface and internal interactions with materials. Inside transparent materials, nonlinear optical effects can confine strong absorption only to the focal volume, extend dissipation over long filament tracks, or reach below diffraction-limited spot sizes. Hence, SLM beam shaping has been widely adopted for laser material processing applications that include parallel structuring, filamentation, fiber Bragg grating formation and optical aberration correction. This paper reports on a range of SLM applications we have studied in femtosecond processing of transparent glasses and thin films. Laser phase-fronts were tailored by the SLM to compensate for spherical surface aberration, and to further address the nonlinear interactions that interplay between Kerr-lens self-focusing and plasma defocusing effects over shallow and deep focusing inside the glass. Limits of strong and weak focusing were examined around the respective formation of low-loss optical waveguides and long uniform filament tracks. Further, we have employed the SLM for beam patterning inside thin film, exploring the limits of phase noise, resolution and fringe contrast during interferometric intra-film structuring. Femtosecond laser pulses of 200 fs pulse duration and 515 nm wavelength were shaped by a phase-only LCOS-SLM (Hamamatsu X10468-04). By imposing radial phase profiles, axicon, grating and beam splitting gratings, volume shape control of filament diameter, length, and uniformity as well as simultaneous formation of multiple filaments has been demonstrated. Similarly, competing effects of spherical surface aberration, self-focusing, and plasma de-focusing were studied and delineated to enable formation of low-loss optical waveguides over shallow and deep focusing conditions. Lastly, SLM beam shaping has been successfully extended to interferometric processing inside thin transparent film, enabling the arbitrary formation of uniform or non-uniform, symmetric or asymmetric patterns of flexible shape on nano-scale dimensions without phase-noise degradation by the SLM patterning. We present quantized structuring of thin films by a single laser pulse, demonstrating λ/2nfilm layer ejection control, blister formation, nano-cavities, and film colouring. Closed intra-film nanochannels with high aspect ratio (20:1) have been formed inside 3.5 um thick silica, opening new prospects for sub-cellular studies and lab-in-film concepts that integrate on CMOS silicon technologies.

  16. Image reconstruction in cone-beam CT with a spherical detector using the BPF algorithm

    NASA Astrophysics Data System (ADS)

    Zuo, Nianming; Zou, Yu; Jiang, Tianzi; Pan, Xiaochuan

    2006-03-01

    Both flat-panel detectors and cylindrical detectors have been used in CT systems for data acquisition. The cylindrical detector generally offers a sampling of a transverse image plane more uniformly than does a flat-panel detector. However, in the longitudinal dimension, the cylindrical and flat-panel detectors offer similar sampling of the image space. In this work, we investigate a detector of spherical shape, which can yield uniform sampling of the 3D image space because the solid angle subtended by each individual detector bin remains unchanged. We have extended the backprojection-filtration (BPF) algorithm, which we have developed previously for cone-beam CT, to reconstruct images in cone-beam CT with a spherical detector. We also conduct computer-simulation studies to validate the extended BPF algorithm. Quantitative results in these numerical studies indicate that accurate images can be obtained from data acquired with a spherical detector by use of our extended BPF cone-beam algorithms.

  17. Ladder Operators for Some Spherically Symmetric Potentials in Quantum Mechanics

    ERIC Educational Resources Information Center

    Newmarch, J. D.; Golding, R. M.

    1978-01-01

    The energy levels of the free field, Coulomb potential, and the three-dimensional harmonic oscillator are found using the Dirac operator formalism by the construction of suitable ladder operators. The degeneracy of each level is also discussed. (Author/GA)

  18. Toroidal configurations of perfect fluid in the Reissner-Nordström-(anti-)de Sitter spacetimes

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kucáková, Hana; Slaný, Petr; Stuchlík, Zdenĕk, E-mail: hana.kucakova@centrum.cz, E-mail: petr.slany@fpf.slu.cz, E-mail: zdenek.stuchlik@fpf.slu.cz

    Influence of cosmological constant on toroidal fluid configurations around charged spherically symmetric black holes and naked singularities is demostrated by study of perfect-fluid tori with uniform distribution of specific angular momentum orbiting in the Reissner-Nordström-(anti-)de Sitter spacetimes. Toroidal configurations are allowed only in the spacetimes admitting existence of stable circular geodesics. Configurations with marginally closed equipotential (equipressure) surfaces crossing itself in a cusp allow accretion (through the inner cusp) and/or excretion (through the outer cusp) of matter from the toroidal configuration. Detailed classification of the Reissner-Nordström-(anti-)de Sitter spacetimes according to properties of the marginally stable tori is given. It ismore » demonstrated that in the Reissner-Nordström-de Sitter naked-singularity spacetimes an interesting phenomenon of doubled tori can exist enabling exchange of matter between two tori in both inward and outward directions. In naked-singularity spacetimes the accretion onto the central singularity is impossible due to existence of a potential barrier.« less

  19. Second rank direction cosine spherical tensor operators and the nuclear electric quadrupole hyperfine structure Hamiltonian of rotating molecules

    NASA Astrophysics Data System (ADS)

    di Lauro, C.

    2018-03-01

    Transformations of vector or tensor properties from a space-fixed to a molecule-fixed axis system are often required in the study of rotating molecules. Spherical components λμ,ν of a first rank irreducible tensor can be obtained from the direction cosines between the two axis systems, and a second rank tensor with spherical components λμ,ν(2) can be built from the direct product λ × λ. It is shown that the treatment of the interaction between molecular rotation and the electric quadrupole of a nucleus is greatly simplified, if the coefficients in the axis-system transformation of the gradient of the electric field of the outer charges at the coupled nucleus are arranged as spherical components λμ,ν(2). Then the reduced matrix elements of the field gradient operators in a symmetric top eigenfunction basis, including their dependence on the molecule-fixed z-angular momentum component k, can be determined from the knowledge of those of λ(2) . The hyperfine structure Hamiltonian Hq is expressed as the sum of terms characterized each by a value of the molecule-fixed index ν, whose matrix elements obey the rule Δk = ν. Some of these terms may vanish because of molecular symmetry, and the specific cases of linear and symmetric top molecules, orthorhombic molecules, and molecules with symmetry lower than orthorhombic are considered. Each ν-term consists of a contraction of the rotational tensor λ(2) and the nuclear quadrupole tensor in the space-fixed frame, and its matrix elements in the rotation-nuclear spin coupled representation can be determined by the standard spherical tensor methods.

  20. Effects of cell geometry on reversible vesicular transport

    NASA Astrophysics Data System (ADS)

    Karamched, Bhargav R.; Bressloff, Paul C.

    2017-02-01

    A major question in cell biology concerns the biophysical mechanism underlying delivery of newly synthesized macromolecules to specific targets within a cell. A recent modeling paper investigated this phenomenon in the context of vesicular delivery to en passant synapses in neurons (Bressloff and Levien 2015 Phys. Rev. Lett.). It was shown how reversibility in vesicular delivery to synapses could play a crucial role in achieving uniformity in the distribution of resources throughout an axon, which is consistent with experimental observations in C. elegans and Drosophila. In this work we generalize the previous model by investigating steady-state vesicular distributions on a Cayley tree, a disk, and a sphere. We show that for irreversible transport on a tree, branching increases the rate of decay of the steady-state distribution of vesicles. On the other hand, the steady-state profiles for reversible transport are similar to the 1D case. In the case of higher-dimensional geometries, we consider two distinct types of radially-symmetric microtubular network: (i) a continuum and (ii) a discrete set. In the continuum case, we model the motor-cargo dynamics using a phenomenologically-based advection-diffusion equation in polar (2D) and spherical (3D) coordinates. On the other-hand, in the discrete case, we derive the population model from a stochastic model of a single motor switching between ballistic motion and diffusion. For all of the geometries we find that reversibility in vesicular delivery to target sites allows for a more uniform distribution of vesicles, provided that cargo-carrying motors are not significantly slowed by their cargo. In each case we characterize the loss of uniformity as a function of the dispersion in velocities.

  1. Flow Separation Ahead of a Blunt Axially Symmetric Body at Mach Numbers 1.76 to 2.10

    NASA Technical Reports Server (NTRS)

    Moeckel, W E

    1951-01-01

    The pressure distribution and drag were determined for a spherical-nosed axially symmetric body with thin projecting rods at Mach numbers of 1.76, 1.93, and 2.10. The upstream projection distance of the rods was varied over a wide range to study changes in the character of the flow separation and to determine the variation of drag and pressure distribution with tip projection. Drag coefficients between 0.18 and 0.30 were obtained for most tip projections at each Mach number.

  2. Trading spaces: building three-dimensional nets from two-dimensional tilings

    PubMed Central

    Castle, Toen; Evans, Myfanwy E.; Hyde, Stephen T.; Ramsden, Stuart; Robins, Vanessa

    2012-01-01

    We construct some examples of finite and infinite crystalline three-dimensional nets derived from symmetric reticulations of homogeneous two-dimensional spaces: elliptic (S2), Euclidean (E2) and hyperbolic (H2) space. Those reticulations are edges and vertices of simple spherical, planar and hyperbolic tilings. We show that various projections of the simplest symmetric tilings of those spaces into three-dimensional Euclidean space lead to topologically and geometrically complex patterns, including multiple interwoven nets and tangled nets that are otherwise difficult to generate ab initio in three dimensions. PMID:24098839

  3. Rigid rotators. [deriving the time-independent energy states associated with rotational motions of the molecule

    NASA Technical Reports Server (NTRS)

    1976-01-01

    The two-particle, steady-state Schroedinger equation is transformed to center of mass and internuclear distance vector coordinates, leading to the free particle wave equation for the kinetic energy motion of the molecule and a decoupled wave equation for a single particle of reduced mass moving in a spherical potential field. The latter describes the vibrational and rotational energy modes of the diatomic molecule. For fixed internuclear distance, this becomes the equation of rigid rotator motion. The classical partition function for the rotator is derived and compared with the quantum expression. Molecular symmetry effects are developed from the generalized Pauli principle that the steady-state wave function of any system of fundamental particles must be antisymmetric. Nuclear spin and spin quantum functions are introduced and ortho- and para-states of rotators, along with their degeneracies, are defined. Effects of nuclear spin on entropy are deduced. Next, rigid polyatomic rotators are considered and the partition function for this case is derived. The patterns of rotational energy levels for nonlinear molecules are discussed for the spherical symmetric top, for the prolate symmetric top, for the oblate symmetric top, and for the asymmetric top. Finally, the equilibrium energy and specific heat of rigid rotators are derived.

  4. The role of β-effect and a uniform current on tropical cyclone intensity

    NASA Astrophysics Data System (ADS)

    Duan, Yihong; Wu, Rongsheng; Yu, Hui; Liang, Xudong; Chan, Johnny C. L.

    2004-02-01

    A limited-area primitive equation model is used to study the role of the β-effect and a uniform current on tropical cyclone (TC) intensity. It is found that TC intensity is reduced in a non-quiescent environment compared with the case of no uniform current. On an f-plane, the rate of intensification of a tropical cyclone is larger than that of the uniform flow. A TC on a β-plane intensifies slower than one on an f-plane. The main physical characteristic that distinguishes the experiments is the asymmetric thermodynamic (including convective) and dynamic structures present when either a uniform flow or β-effect is introduced. But a fairly symmetric TC structure is simulated on an f-plane. The magnitude of the warm core and the associated subsidence are found to be responsible for such simulated intensity changes. On an f-plane, the convection tends to be symmetric, which results in strong upper-level convergence near the center and hence strong forced subsidence and a very warm core. On the other hand, horizontal advection of temperature cancels part of the adiabatic heating and results in less warming of the core, and hence the TC is not as intense. This advective process is due to the tilt of the vortex as a result of the β-effect. A similar situation occurs in the presence of a uniform flow. Thus, the asymmetric horizontal advection of temperature plays an important role in the temperature distribution. Dynamically, the asymmetric angular momentum (AM) flux is very small on an f-plane throughout the troposphere. However, the total AM exports at the upper levels for a TC either on a β-plane or with a uniform flow environment are larger because of an increase of the asymmetric as well as symmetric AM export on the plane at radii >450 km, and hence there is a lesser intensification.

  5. Far Field Boundary Conditions for Underwater Explosions

    DTIC Science & Technology

    1994-12-22

    NSWCDDfTR-94/20 CHAPTER 1 INTRODUCTION A factor controlling the computational resources required to model an underwater explo- sion is the extent of...NSWCDD/TRI-94/20 SPHERICAL SHOCKS The explosion of a spherical TNT charge in a uniform water environment is modeled in spherical coordinates. The TNT is...described using a JWL equation of state while the water is modeled using a modified Tait equation of state.6 The TNT is assumed to combust

  6. Apparatus for irradiating a continuously flowing stream of fluid. [For neutron activation analysis

    DOEpatents

    Speir, L.G.; Adams, E.L.

    1982-05-13

    An apparatus for irradiating a continuously flowing stream of fluid is disclosed. The apparatus consists of a housing having a spherical cavity and a spherical moderator containing a radiation source positioned within the spherical cavity. The spherical moderator is of lesser diameter than the spherical cavity so as to define a spherical annular volume around the moderator. The housing includes fluid intake and output conduits which open onto the spherical cavity at diametrically opposite positions. Fluid flows through the cavity around the spherical moderator and is uniformly irradiated due to the 4..pi.. radiation geometry. The irradiation source, for example a /sup 252/Cf neutron source, is removable from the spherical moderator through a radial bore which extends outwardly to an opening on the outside of the housing. The radiation source may be routinely removed without interrupting the flow of fluid or breaching the containment of the fluid.

  7. Apparatus for irradiating a continuously flowing stream of fluid

    DOEpatents

    Speir, Leslie G.; Adams, Edwin L.

    1984-01-01

    An apparatus for irradiating a continuously flowing stream of fluid is diosed. The apparatus consists of a housing having a spherical cavity and a spherical moderator containing a radiation source positioned within the spherical cavity. The spherical moderator is of lesser diameter than the spherical cavity so as to define a spherical annular volume around the moderator. The housing includes fluid intake and output conduits which open onto the spherical cavity at diametrically opposite positions. Fluid flows through the cavity around the spherical moderator and is uniformly irradiated due to the 4.pi. radiation geometry. The irradiation source, for example a .sup.252 CF neutron source, is removable from the spherical moderator through a radial bore which extends outwardly to an opening on the outside of the housing. The radiation source may be routinely removed without interrupting the flow of fluid or breaching the containment of the fluid.

  8. Formation of spherical-shaped GaN and InN quantum dots on curved SiN/Si surface.

    PubMed

    Choi, Ilgyu; Lee, Hyunjoong; Lee, Cheul-Ro; Jeong, Kwang-Un; Kim, Jin Soo

    2018-08-03

    This paper reports the formation of GaN and InN quantum dots (QDs) with symmetric spherical shapes, grown on SiN/Si(111). Spherical QDs are grown by modulating initial growth behavior via gallium and indium droplets functioning as nucleation sites for QDs. Field-emission scanning electron microscope (FE-SEM) images show that GaN and InN QDs are formed on curved SiN/Si(111) instead of on a flat surface similar to balls on a latex mattress. This is considerably different from the structural properties of In(Ga)As QDs grown on GaAs or InP. In addition, considering the shape of the other III-V semiconductor QDs, the QDs in this study are very close to the ideal shape of zero-dimensional nanostructures. Transmission-electron microscope images show the formation of symmetric GaN and InN QDs with a round shape, agreeing well with the FE-SEM results. Compared to other III-V semiconductor QDs, the unique structural properties of Si-based GaN and InN QDs are strongly related to the modulation in the initial nucleation characteristics due to the presence of droplets, the degree of lattice mismatch between GaN or InN and SiN/Si(111), and the melt-back etching phenomenon.

  9. Critical phenomena in the general spherically symmetric Einstein-Yang-Mills system

    NASA Astrophysics Data System (ADS)

    Maliborski, Maciej; Rinne, Oliver

    2018-02-01

    We study critical behavior in gravitational collapse of a general spherically symmetric Yang-Mills field coupled to the Einstein equations. Unlike the magnetic ansatz used in previous numerical work, the general Yang-Mills connection has two degrees of freedom in spherical symmetry. This fact changes the phenomenology of critical collapse dramatically. The magnetic sector features both type I and type II critical collapse, with universal critical solutions. In contrast, in the general system type I disappears and the critical behavior at the threshold between dispersal and black hole formation is always type II. We obtain values of the mass scaling and echoing exponents close to those observed in the magnetic sector, however we find some indications that the critical solution differs from the purely magnetic discretely self-similar attractor and exact self-similarity and universality might be lost. The additional "type III" critical phenomenon in the magnetic sector, where black holes form on both sides of the threshold but the Yang-Mills potential is in different vacuum states and there is a mass gap, also disappears in the general system. We support our dynamical numerical simulations with calculations in linear perturbation theory; for instance, we compute quasi-normal modes of the unstable attractor (the Bartnik-McKinnon soliton) in type I collapse in the magnetic sector.

  10. Spherically symmetric conformal gravity and ''gravitational bubbles''

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Berezin, V.A.; Dokuchaev, V.I.; Eroshenko, Yu.N., E-mail: berezin@inr.ac.ru, E-mail: dokuchaev@inr.ac.ru, E-mail: eroshenko@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-timesmore » (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.« less

  11. Newton gauge cosmological perturbations for static spherically symmetric modifications of the de Sitter metric

    NASA Astrophysics Data System (ADS)

    Santa Vélez, Camilo; Enea Romano, Antonio

    2018-05-01

    Static coordinates can be convenient to solve the vacuum Einstein's equations in presence of spherical symmetry, but for cosmological applications comoving coordinates are more suitable to describe an expanding Universe, especially in the framework of cosmological perturbation theory (CPT). Using CPT we develop a method to transform static spherically symmetric (SSS) modifications of the de Sitter solution from static coordinates to the Newton gauge. We test the method with the Schwarzschild de Sitter (SDS) metric and then derive general expressions for the Bardeen's potentials for a class of SSS metrics obtained by adding to the de Sitter metric a term linear in the mass and proportional to a general function of the radius. Using the gauge invariance of the Bardeen's potentials we then obtain a gauge invariant definition of the turn around radius. We apply the method to an SSS solution of the Brans-Dicke theory, confirming the results obtained independently by solving the perturbation equations in the Newton gauge. The Bardeen's potentials are then derived for new SSS metrics involving logarithmic, power law and exponential modifications of the de Sitter metric. We also apply the method to SSS metrics which give flat rotation curves, computing the radial energy density profile in comoving coordinates in presence of a cosmological constant.

  12. Interior of black holes and information recovery

    NASA Astrophysics Data System (ADS)

    Kawai, Hikaru; Yokokura, Yuki

    2016-02-01

    We analyze time evolution of a spherically symmetric collapsing matter from a point of view that black holes evaporate by nature. We first consider a spherical thin shell that falls in the metric of an evaporating Schwarzschild black hole of which the radius a (t ) decreases in time. The important point is that the shell can never reach a (t ) but it approaches a (t )-a (t )d/a (t ) d t . This situation holds at any radius because the motion of a shell in a spherically symmetric system is not affected by the outside. In this way, we find that the collapsing matter evaporates without forming a horizon. Nevertheless, a Hawking-like radiation is created in the metric, and the object looks the same as a conventional black hole from the outside. We then discuss how the information of the matter is recovered. We also consider a black hole that is adiabatically grown in the heat bath and obtain the interior metric. We show that it is the self-consistent solution of Gμ ν=8 π G ⟨Tμ ν⟩ and that the four-dimensional Weyl anomaly induces the radiation and a strong angular pressure. Finally, we analyze the internal structures of the charged and the slowly rotating black holes.

  13. A Fast and Accurate Method of Radiation Hydrodynamics Calculation in Spherical Symmetry

    NASA Astrophysics Data System (ADS)

    Stamer, Torsten; Inutsuka, Shu-ichiro

    2018-06-01

    We develop a new numerical scheme for solving the radiative transfer equation in a spherically symmetric system. This scheme does not rely on any kind of diffusion approximation, and it is accurate for optically thin, thick, and intermediate systems. In the limit of a homogeneously distributed extinction coefficient, our method is very accurate and exceptionally fast. We combine this fast method with a slower but more generally applicable method to describe realistic problems. We perform various test calculations, including a simplified protostellar collapse simulation. We also discuss possible future improvements.

  14. Total Internal Reflection Ultrasonic Sensor for Detection of Subsurface Flaws: Proof of Concept

    DTIC Science & Technology

    2010-01-01

    34 Tv001 Ve group (ray) velocity of the elastic wave X1, X2, X3 crystallographic coordinates x, y, z Descartes ’ coordinates tied to the transducer y0...TeO2 prism. 1.2.1. Orientation of directions and planes of interest with respect to Descartes ’ and Spherical coordinates. 1.2.2. Reflection of the...spect to Descartes ’ and Spherical coordi- nates. , (1.2.1) lili uuv Γ=ρ 2 where ρ is the crystal density and the symmetrical second rank Christoffel

  15. High energy neutron dosimeter

    DOEpatents

    Sun, Rai Ko S.F.

    1994-01-01

    A device for measuring dose equivalents in neutron radiation fields. The device includes nested symmetrical hemispheres (forming spheres) of different neutron moderating materials that allow the measurement of dose equivalents from 0.025 eV to past 1 GeV. The layers of moderating material surround a spherical neutron counter. The neutron counter is connected by an electrical cable to an electrical sensing means which interprets the signal from the neutron counter in the center of the moderating spheres. The spherical shape of the device allows for accurate measurement of dose equivalents regardless of its positioning.

  16. Solution of an eigenvalue problem for the Laplace operator on a spherical surface. M.S. Thesis - Maryland Univ.

    NASA Technical Reports Server (NTRS)

    Walden, H.

    1974-01-01

    Methods for obtaining approximate solutions for the fundamental eigenvalue of the Laplace-Beltrami operator (also referred to as the membrane eigenvalue problem for the vibration equation) on the unit spherical surface are developed. Two specific types of spherical surface domains are considered: (1) the interior of a spherical triangle, i.e., the region bounded by arcs of three great circles, and (2) the exterior of a great circle arc extending for less than pi radians on the sphere (a spherical surface with a slit). In both cases, zero boundary conditions are imposed. In order to solve the resulting second-order elliptic partial differential equations in two independent variables, a finite difference approximation is derived. The symmetric (generally five-point) finite difference equations that develop are written in matrix form and then solved by the iterative method of point successive overrelaxation. Upon convergence of this iterative method, the fundamental eigenvalue is approximated by iteration utilizing the power method as applied to the finite Rayleigh quotient.

  17. Simulating The Prompt Electromagnetic Pulse In 3D Using Vector Spherical Harmonics

    NASA Astrophysics Data System (ADS)

    Friedman, Alex; Cohen, Bruce I.; Eng, Chester D.; Farmer, William A.; Grote, David P.; Kruger, Hans W.; Larson, David J.

    2017-10-01

    We describe a new, efficient code for simulating the prompt electromagnetic pulse. In SHEMP (``Spherical Harmonic EMP''), we extend to 3-D the methods pioneered in C. Longmire's CHAP code. The geomagnetic field and air density are consistent with CHAP's assumed spherical symmetry only for narrow domains of influence about the line of sight, limiting validity to very early times. Also, we seek to model inherently 3-D situations. In CHAP and our own CHAP-lite, the independent coordinates are r (the distance from the source) and τ = t-r/c; the pulse varies slowly with r at fixed τ, so a coarse radial grid suffices. We add non-spherically-symmetric physics via a vector spherical harmonic decomposition. For each (l,m) harmonic, the radial equation is similar to that in CHAP and CHAP-lite. We present our methodology and results on model problems. This work was performed under the auspices of the U.S. DOE by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

  18. The Coupling of Gravity to Spin and Electromagnetism

    NASA Astrophysics Data System (ADS)

    Finster, Felix; Smoller, Joel; Yau, Shing-Tung

    The coupled Einstein-Dirac-Maxwell equations are considered for a static, spherically symmetric system of two fermions in a singlet spinor state. Stable soliton-like solutions are shown to exist, and we discuss the regularizing effect of gravity from a Feynman diagram point of view.

  19. Rovibrational states of Wigner molecules in spherically symmetric confining potentials

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Cioslowski, Jerzy

    2016-08-07

    The strong-localization limit of three-dimensional Wigner molecules, in which repulsively interacting particles are confined by a weak spherically symmetric potential, is investigated. An explicit prescription for computation of rovibrational wavefunctions and energies that are asymptotically exact at this limit is presented. The prescription is valid for systems with arbitrary angularly-independent interparticle and confining potentials, including those involving Coulombic and screened (i.e., Yukawa/Debye) interactions. The necessary derivations are greatly simplified by explicit constructions of the Eckart frame and the parity-adapted primitive wavefunctions. The performance of the new formalism is illustrated with the three- and four-electron harmonium atoms at their strong-correlation limits.more » In particular, the involvement of vibrational modes with the E symmetry is readily pinpointed as the origin of the “anomalous” weak-confinement behavior of the {sup 1}S{sub +} state of the four-electron species that is absent in its {sup 1}D{sub +} companion of the strong-confinement regime.« less

  20. Dyons and dyonic black holes in su (N ) Einstein-Yang-Mills theory in anti-de Sitter spacetime

    NASA Astrophysics Data System (ADS)

    Shepherd, Ben L.; Winstanley, Elizabeth

    2016-03-01

    We present new spherically symmetric, dyonic soliton and black hole solutions of the su (N ) Einstein-Yang-Mills equations in four-dimensional asymptotically anti-de Sitter spacetime. The gauge field has nontrivial electric and magnetic components and is described by N -1 magnetic gauge field functions and N -1 electric gauge field functions. We explore the phase space of solutions in detail for su (2 ) and su (3 ) gauge groups. Combinations of the electric gauge field functions are monotonic and have no zeros; in general the magnetic gauge field functions may have zeros. The phase space of solutions is extremely rich, and we find solutions in which the magnetic gauge field functions have more than fifty zeros. Of particular interest are solutions for which the magnetic gauge field functions have no zeros, which exist when the negative cosmological constant has sufficiently large magnitude. We conjecture that at least some of these nodeless solutions may be stable under linear, spherically symmetric, perturbations.

  1. RESONATORS. MODES: Modes of a plano - spherical laser resonator with the Gaussian gain distribution of the active medium

    NASA Astrophysics Data System (ADS)

    Malyutin, A. A.

    2007-03-01

    Modes of a laser with plano-spherical degenerate and nondegenerate resonators are calculated upon diode pumping producing the Gaussian gain distribution in the active medium. Axially symmetric and off-axis pumpings are considered. It is shown that in the first case the lowest Hermite-Gaussian mode is excited with the largest weight both in the degenerate and nondegenerate resonator if the pump level is sufficiently high or the characteristic size wg of the amplifying region greatly exceeds the mode radius w0. The high-order Ince-Gaussian modes are excited upon weak off-axis pumping in the nondegenerate resonator both in the absence and presence of the symmetry of the gain distribution with respect to the resonator axis. It is found that when the level of off-axis symmetric pumping of the resonator is high enough, modes with the parameters of the TEM00 mode periodically propagating over a closed path in the resonator can exist. The explanation of this effect is given.

  2. Static black hole solutions with a self-interacting conformally coupled scalar field

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Dotti, Gustavo; Gleiser, Reinaldo J.; Martinez, Cristian

    2008-05-15

    We study static, spherically symmetric black hole solutions of the Einstein equations with a positive cosmological constant and a conformally coupled self-interacting scalar field. Exact solutions for this model found by Martinez, Troncoso, and Zanelli were subsequently shown to be unstable under linear gravitational perturbations, with modes that diverge arbitrarily fast. We find that the moduli space of static, spherically symmetric solutions that have a regular horizon--and satisfy the weak and dominant energy conditions outside the horizon--is a singular subset of a two-dimensional space parametrized by the horizon radius and the value of the scalar field at the horizon. Themore » singularity of this space of solutions provides an explanation for the instability of the Martinez, Troncoso, and Zanelli spacetimes and leads to the conclusion that, if we include stability as a criterion, there are no physically acceptable black hole solutions for this system that contain a cosmological horizon in the exterior of its event horizon.« less

  3. Vaporization of irradiated droplets

    NASA Astrophysics Data System (ADS)

    Armstrong, R. L.; O'Rourke, P. J.; Zardecki, A.

    1986-11-01

    The vaporization of a spherically symmetric liquid droplet subject to a high-intensity laser flux is investigated on the basis of a hydrodynamic description of the system composed of the vapor and ambient gas. In the limit of the convective vaporization, the boundary conditions at the fluid-gas interface are formulated by using the notion of a Knudsen layer in which translational equilibrium is established. This leads to approximate jump conditions at the interface. For homogeneous energy deposition, the hydrodynamic equations are solved numerically with the aid of the CON1D computer code (``CON1D: A computer program for calculating spherically symmetric droplet combustion,'' Los Alamos National Laboratory Report No. LA-10269-MS, December, 1984), based on the implict continuous-fluid Eulerian (ICE) [J. Comput. Phys. 8, 197 (1971)] and arbitrary Lagrangian-Eulerian (ALE) [J. Comput. Phys. 14, 1227 (1974)] numerical mehtods. The solutions exhibit the existence of two shock waves propagating in opposite directions with respect to the contact discontinuity surface that separates the ambient gas and vapor.

  4. Improved Bounds on Nonluminous Matter in Solar Orbit

    NASA Technical Reports Server (NTRS)

    Anderson, John D.; Lau, Eunice L.; Krisher, Timothy P.; Dicus, Duane A.; Rosenbaum, Doris C.; Teplitz, Vigdor L.

    1995-01-01

    We improve, using a larger set of observations including Voyager 2 Neptune flyby data, previous bounds on the amount of dark matter (DM) trapped in a spherically symmetric distribution about the Sun. We bound DM by noting that such a distribution would increase the effective mass of the Sun as seen by the outer planets and by finding the uncertainty in that effective mass for Uranus and Neptune in fits to the JPL developmental ephemeris residuals, including optical data and those two planets' Voyager 2 flybys. We extend our previous procedure by fitting more parameters of the developmental ephamerides. In addition, we present here the values for Pioneer 10, Pioneer 11, Voyager 1, and Voyager 2 Jupiter-ranging normal points (and incorporate these data as well). Our principal result is to limit DM in spherically symmetric distributions in orbit about the Sun interior to Neptune's orbit to less than Earth mass and interior to Uranus's orbit to about 1/6 of Earth's mass.

  5. Investigation of the Wave Propagation of Vector Modes of Light in a Spherically Symmetric Refractive Index Profile

    NASA Astrophysics Data System (ADS)

    Pozderac, Preston; Leary, Cody

    We investigated the solutions to the Helmholtz equation in the case of a spherically symmetric refractive index using three different methods. The first method involves solving the Helmholtz equation for a step index profile and applying further constraints contained in Maxwell's equations. Utilizing these equations, we can simultaneously solve for the electric and magnetic fields as well as the allowed energies of photons propagating in this system. The second method applies a perturbative correction to these energies, which surfaces when deriving a Helmholtz type equation in a medium with an inhomogeneous refractive index. Applying first order perturbation theory, we examine how the correction term affects the energy of the photon. In the third method, we investigate the effects of the above perturbation upon solutions to the scalar Helmholtz equation, which are separable with respect to its polarization and spatial degrees of freedom. This work provides insights into the vector field structure of a photon guided by a glass microsphere.

  6. Uniform convergence of multigrid V-cycle iterations for indefinite and nonsymmetric problems

    NASA Technical Reports Server (NTRS)

    Bramble, James H.; Kwak, Do Y.; Pasciak, Joseph E.

    1993-01-01

    In this paper, we present an analysis of a multigrid method for nonsymmetric and/or indefinite elliptic problems. In this multigrid method various types of smoothers may be used. One type of smoother which we consider is defined in terms of an associated symmetric problem and includes point and line, Jacobi, and Gauss-Seidel iterations. We also study smoothers based entirely on the original operator. One is based on the normal form, that is, the product of the operator and its transpose. Other smoothers studied include point and line, Jacobi, and Gauss-Seidel. We show that the uniform estimates for symmetric positive definite problems carry over to these algorithms. More precisely, the multigrid iteration for the nonsymmetric and/or indefinite problem is shown to converge at a uniform rate provided that the coarsest grid in the multilevel iteration is sufficiently fine (but not depending on the number of multigrid levels).

  7. Modelling of influence of spherical aberration coefficients on depth of focus of optical systems

    NASA Astrophysics Data System (ADS)

    Pokorný, Petr; Šmejkal, Filip; Kulmon, Pavel; Mikš, Antonín.; Novák, Jiří; Novák, Pavel

    2017-06-01

    This contribution describes how to model the influence of spherical aberration coefficients on the depth of focus of optical systems. Analytical formulas for the calculation of beam's caustics are presented. The conditions for aberration coefficients are derived for two cases when we require that either the Strehl definition or the gyration radius should be the identical in two symmetrically placed planes with respect to the paraxial image plane. One can calculate the maximum depth of focus and the minimum diameter of the circle of confusion of the optical system corresponding to chosen conditions. This contribution helps to understand how spherical aberration may affect the depth of focus and how to design such an optical system with the required depth of focus. One can perform computer modelling and design of the optical system and its spherical aberration in order to achieve the required depth of focus.

  8. Rotational dynamics with geometric algebra

    NASA Technical Reports Server (NTRS)

    Hestenes, D.

    1983-01-01

    A new spinor formulation of rotational dynamics is developed. A general theorem is established reducing the theory of the symmetric top to that of the spherical top. The classical problems of Lagrange and Poinsot are treated in detail, along with a modern application to the theory of magnetic resonance.

  9. Effect of Particle Morphology on the Reactivity of Explosively Dispersed Titanium Particles

    NASA Astrophysics Data System (ADS)

    Frost, David L.; Cairns, Malcolm; Goroshin, Samuel; Zhang, Fan

    2009-12-01

    The effect of particle morphology on the reaction of titanium (Ti) particles explosively dispersed during the detonation of either cylindrical or spherical charges has been investigated experimentally. The explosive charges consisted of packed beds of Ti particles saturated with nitromethane. The reaction behaviour of irregularly-shaped Ti particles in three size ranges is compared with tests with spherical Ti particles. The particle reaction is strongly dependent on particle morphology, e.g., 95 μm spherical Ti particles failed to ignite (in cylinders up to 49 mm in dia), whereas similarly sized irregular Ti particles readily ignited. For irregular particles, the uniformity of ignition on the particle cloud surface was almost independent of particle size, but depended on charge diameter. As the charge diameter was reduced, ignition in the conically expanding particle cloud occurred only at isolated spots or bands. For spherical charges, whereas large irregular Ti particles ignited promptly and uniformly throughout the particle cloud, the smallest particles dispersed nonuniformly and ignition occurred at isolated locations after a delay. Hence the charge geometry, as well as particle morphology, influences the reaction behaviour of the particles.

  10. A platonic solid templating Archimedean solid: an unprecedented nanometre-sized Ag37 cluster

    NASA Astrophysics Data System (ADS)

    Li, Xiao-Yu; Su, Hai-Feng; Yu, Kai; Tan, Yuan-Zhi; Wang, Xing-Po; Zhao, Ya-Qin; Sun, Di; Zheng, Lan-Sun

    2015-04-01

    The spontaneous formation of discrete spherical nanosized molecules is prevalent in nature, but the authentic structural mimicry of such highly symmetric polyhedra from edge sharing of regular polygons has remained elusive. Here we present a novel ball-shaped {(HNEt3)[Ag37S4(SC6H4tBu)24(CF3COO)6(H2O)12]} cluster (1) that is assembled via a one-pot process from polymeric {(HNEt3)2[Ag10(SC6H4tBu)12]}n and CF3COOAg. Single crystal X-ray analysis confirmed that 1 is a Td symmetric spherical molecule with a [Ag36(SC6H4tBu)24] anion shell enwrapping a AgS4 tetrahedron. The shell topology of 1 belongs to one of 13 Archimedean solids, a truncated tetrahedron with four edge-shared hexagons and trigons, which are supported by a AgS4 Platonic solid in the core. Interestingly, the cluster emits green luminescence centered at 515 nm at room temperature. Our investigations have provided a promising synthetic protocol for a high-nuclearity silver cluster based on underlying geometrical principles.The spontaneous formation of discrete spherical nanosized molecules is prevalent in nature, but the authentic structural mimicry of such highly symmetric polyhedra from edge sharing of regular polygons has remained elusive. Here we present a novel ball-shaped {(HNEt3)[Ag37S4(SC6H4tBu)24(CF3COO)6(H2O)12]} cluster (1) that is assembled via a one-pot process from polymeric {(HNEt3)2[Ag10(SC6H4tBu)12]}n and CF3COOAg. Single crystal X-ray analysis confirmed that 1 is a Td symmetric spherical molecule with a [Ag36(SC6H4tBu)24] anion shell enwrapping a AgS4 tetrahedron. The shell topology of 1 belongs to one of 13 Archimedean solids, a truncated tetrahedron with four edge-shared hexagons and trigons, which are supported by a AgS4 Platonic solid in the core. Interestingly, the cluster emits green luminescence centered at 515 nm at room temperature. Our investigations have provided a promising synthetic protocol for a high-nuclearity silver cluster based on underlying geometrical principles. Electronic supplementary information (ESI) available: detailed synthesis procedure, tables, crystal data in CIF files, IR data, TGA results and powder X-ray diffractogram for 1. CCDC 1042228. See DOI: 10.1039/c5nr01222h

  11. MPI-AMRVAC 2.0 for Solar and Astrophysical Applications

    NASA Astrophysics Data System (ADS)

    Xia, C.; Teunissen, J.; El Mellah, I.; Chané, E.; Keppens, R.

    2018-02-01

    We report on the development of MPI-AMRVAC version 2.0, which is an open-source framework for parallel, grid-adaptive simulations of hydrodynamic and magnetohydrodynamic (MHD) astrophysical applications. The framework now supports radial grid stretching in combination with adaptive mesh refinement (AMR). The advantages of this combined approach are demonstrated with one-dimensional, two-dimensional, and three-dimensional examples of spherically symmetric Bondi accretion, steady planar Bondi–Hoyle–Lyttleton flows, and wind accretion in supergiant X-ray binaries. Another improvement is support for the generic splitting of any background magnetic field. We present several tests relevant for solar physics applications to demonstrate the advantages of field splitting on accuracy and robustness in extremely low-plasma β environments: a static magnetic flux rope, a magnetic null-point, and magnetic reconnection in a current sheet with either uniform or anomalous resistivity. Our implementation for treating anisotropic thermal conduction in multi-dimensional MHD applications is also described, which generalizes the original slope-limited symmetric scheme from two to three dimensions. We perform ring diffusion tests that demonstrate its accuracy and robustness, and show that it prevents the unphysical thermal flux present in traditional schemes. The improved parallel scaling of the code is demonstrated with three-dimensional AMR simulations of solar coronal rain, which show satisfactory strong scaling up to 2000 cores. Other framework improvements are also reported: the modernization and reorganization into a library, the handling of automatic regression tests, the use of inline/online Doxygen documentation, and a new future-proof data format for input/output.

  12. Diagnostics for PLX-alpha

    NASA Astrophysics Data System (ADS)

    Gilmore, Mark; Hsu, Scott

    2015-11-01

    The goal of the Plasma Liner eXperiment PLX-alpha at Los Alamos National Laboratory is to establish the viability of creating a spherically imploding plasma liner for MIF and HED applications, using a spherical array of supersonic plasma jets launched by innovative contoured-gap coaxial plasma guns. PLX- α experiments will focus in particular on establishing the ram pressure and uniformity scalings of partial and fully spherical plasma liners. In order to characterize these parameters experimentally, a suite of diagnostics is planned, including multi-camera fast imaging, a 16-channel visible interferometer (upgraded from 8 channels) with reconfigurable, fiber-coupled front end, and visible and VUV high-resolution and survey spectroscopy. Tomographic reconstruction and data fusion techniques will be used in conjunction with interferometry, imaging, and synthetic diagnostics from modeling to characterize liner uniformity in 3D. Diagnostic and data analysis design, implementation, and status will be presented. Supported by the Advanced Research Projects Agency - Energy - U.S. Department of Energy.

  13. Dynamic Snap-Through of Thin-Walled Structures by a Reduced Order Method

    NASA Technical Reports Server (NTRS)

    Przekop, Adam; Rizzi, Stephen A.

    2006-01-01

    The goal of this investigation is to further develop nonlinear modal numerical simulation methods for application to geometrically nonlinear response of structures exposed to combined high intensity random pressure fluctuations and thermal loadings. The study is conducted on a flat aluminum beam, which permits a comparison of results obtained by a reduced-order analysis with those obtained from a numerically intensive simulation in physical degrees-of-freedom. A uniformly distributed thermal loading is first applied to investigate the dynamic instability associated with thermal buckling. A uniformly distributed random loading is added to investigate the combined thermal-acoustic response. In the latter case, three types of response characteristics are considered, namely: (i) small amplitude vibration around one of the two stable buckling equilibrium positions, (ii) intermittent snap-through response between the two equilibrium positions, and (iii) persistent snap-through response between the two equilibrium positions. For the reduced order analysis, four categories of modal basis functions are identified including those having symmetric transverse (ST), anti-symmetric transverse (AT), symmetric in-plane (SI), and anti-symmetric in-plane (AI) displacements. The effect of basis selection on the quality of results is investigated for the dynamic thermal buckling and combined thermal-acoustic response. It is found that despite symmetric geometry, loading, and boundary conditions, the AT and SI modes must be included in the basis as they participate in the snap-through behavior.

  14. Fully Characterizing Axially Symmetric Szekeres Models with Three Data Sets

    NASA Astrophysics Data System (ADS)

    Célérier, Marie-Nöelle Mishra, Priti; Singh, Tejinder P.

    2015-01-01

    Inhomogeneous exact solutions of General Relativity with zero cosmological constant have been used in the literature to challenge the ΛCDM model. From one patch Lemaître-Tolman-Bondi (LTB) models to axially symmetric quasi-spherical Szekeres (QSS) Swiss-cheese models, some of them are able to reproduce to a good accuracy the cosmological data. It has been shown in the literature that a zero Λ LTB model with a central observer can be fully determined by two data sets. We demonstrate that an axially symmetric zero Λ QSS model with an observer located at the origin can be fully reconstructed from three data sets, number counts, luminosity distance and redshift drift. This is a first step towards a future demonstration involving five data sets and the most general Szekeres model.

  15. An Exact Solution of Einstein-Maxwell Gravity Coupled to a Scalar Field

    NASA Technical Reports Server (NTRS)

    Turyshev, S. G.

    1995-01-01

    The general solution to low-energy string theory representing static spherically symmetric solution of the Einstein-Maxwell gravity with a massless scalar field has been found. Some of the partial cases appear to coincide with known solutions to black holes, naked singularities, and gravity and electromagnetic fields.

  16. Circular dichroism in photo-single-ionization of unoriented atoms.

    PubMed

    Feagin, James M

    2002-01-28

    We predict circular dichroism in photo-single-ionization angular distributions from spherically symmetric atomic states if the ionized electron is detected using two-slit interferometry. We demonstrate that the resulting electron interference pattern captures phase information on quadrupole corrections to the photoionization amplitude lost in conventional angular distributions.

  17. Nakedly singular non-vacuum gravitating equilibrium states

    NASA Astrophysics Data System (ADS)

    Woszczyna, Andrzej; Kutschera, Marek; Kubis, Sebastian; Czaja, Wojciech; Plaszczyk, Piotr; Golda, Zdzisław A.

    2016-01-01

    Non-vacuum static spherically symmetric spacetimes with central point-like repulsive gravity sources are investigated. Both the symmetries of spacetime and the degree of irregularity of curvature invariants, are the same as for the Schwarzschild case. The equilibrium configurations are modelled using the neutron star polytrope equation of state.

  18. Hairy black hole solutions in U(1) gauge-invariant scalar-vector-tensor theories

    NASA Astrophysics Data System (ADS)

    Heisenberg, Lavinia; Tsujikawa, Shinji

    2018-05-01

    In U (1) gauge-invariant scalar-vector-tensor theories with second-order equations of motion, we study the properties of black holes (BH) on a static and spherically symmetric background. In shift-symmetric theories invariant under the shift of scalar ϕ → ϕ + c, we show the existence of new hairy BH solutions where a cubic-order scalar-vector interaction gives rise to a scalar hair manifesting itself around the event horizon. In the presence of a quartic-order interaction besides the cubic coupling, there are also regular BH solutions endowed with scalar and vector hairs.

  19. Almost commuting self-adjoint matrices: The real and self-dual cases

    NASA Astrophysics Data System (ADS)

    Loring, Terry A.; Sørensen, Adam P. W.

    2016-08-01

    We show that a pair of almost commuting self-adjoint, symmetric matrices is close to a pair of commuting self-adjoint, symmetric matrices (in a uniform way). Moreover, we prove that the same holds with self-dual in place of symmetric and also for paths of self-adjoint matrices. Since a symmetric, self-adjoint matrix is real, we get a real version of Huaxin Lin’s famous theorem on almost commuting matrices. Similarly, the self-dual case gives a version for matrices over the quaternions. To prove these results, we develop a theory of semiprojectivity for real C*-algebras and also examine various definitions of low-rank for real C*-algebras.

  20. High energy neutron dosimeter

    DOEpatents

    Rai, K.S.F.

    1994-01-11

    A device for measuring dose equivalents in neutron radiation fields is described. The device includes nested symmetrical hemispheres (forming spheres) of different neutron moderating materials that allow the measurement of dose equivalents from 0.025 eV to past 1 GeV. The layers of moderating material surround a spherical neutron counter. The neutron counter is connected by an electrical cable to an electrical sensing means which interprets the signal from the neutron counter in the center of the moderating spheres. The spherical shape of the device allows for accurate measurement of dose equivalents regardless of its positioning. 2 figures.

  1. On some transonic aspects of general relativistic spherical accretion on to Schwarzschild black holes

    NASA Astrophysics Data System (ADS)

    Das, Tapas K.

    2002-03-01

    The equations governing general relativistic, spherically symmetric, hydrodynamic accretion of polytropic fluid on to black holes are solved in the Schwarzschild metric to investigate some of the transonic properties of the flow. Only stationary solutions are discussed. For such accretion, it has been shown that real physical sonic points may form even for flow with γ<4/3or γ>5/3. The behaviour of some flow variables in the close vicinity of the event horizon is studied as a function of specific energy and the polytropic index of the flow.

  2. Study of the geodesic equations of a spherical symmetric spacetime in conformal Weyl gravity

    NASA Astrophysics Data System (ADS)

    Hoseini, Bahareh; Saffari, Reza; Soroushfar, Saheb

    2017-03-01

    A set of analytic solutions of the geodesic equation in a spherical conformal spacetime is presented. Solutions of this geodesics can be expressed in terms of the Weierstrass \\wp function and the Kleinian σ function. Using conserved energy and angular momentum we can characterize the different orbits. Also, considering parametric diagrams and effective potentials, we plot some possible orbits. Moreover, with the help of analytical solutions, we investigate the light deflection for such an escape orbit. Finally, by using periastron advance we get to an upper bound for magnitude of γ.

  3. The Geophysical Fluid Flow Cell Experiment

    NASA Technical Reports Server (NTRS)

    Hart, J. E.; Ohlsen, D.; Kittleman, S.; Borhani, N.; Leslie, F.; Miller, T.

    1999-01-01

    The Geophysical Fluid Flow Cell (GFFC) experiment performed visualizations of thermal convection in a rotating differentially heated spherical shell of fluid. In these experiments dielectric polarization forces are used to generate a radially directed buoyancy force. This enables the laboratory simulation of a number of geophysically and astrophysically important situations in which sphericity and rotation both impose strong constraints on global scale fluid motions. During USML-2 a large set of experiments with spherically symmetric heating were carried out. These enabled the determination of critical points for the transition to various forms of nonaxisymmetric convection and, for highly turbulent flows, the transition latitudes separating the different modes of motion. This paper presents a first analysis of these experiments as well as data on the general performance of the instrument during the USML-2 flight.

  4. Synthetic approaches to construct viral capsid-like spherical nanomaterials.

    PubMed

    Matsuura, Kazunori

    2018-06-06

    This feature article describes recent progress in synthetic strategies to construct viral capsid-like spherical nanomaterials using the self-assembly of peptides and/or proteins. By mimicking the self-assembly of spherical viral capsids and clathrin, trigonal peptide conjugates bearing β-sheet-forming peptides, glutathiones, or coiled-coil-forming peptides were developed to construct viral capsid-like particles. β-Annulus peptides from tomato bushy stunt virus self-assembled into viral capsid-like nanocapsules with a size of 30-50 nm, which could encapsulate various guest molecules and be decorated with different molecules on their surface. Rationally designed fusion proteins bearing symmetric assembling units afforded precise viral capsid-like polyhedral assemblies. These synthetic approaches to construct artificial viruses could become useful guidelines to develop novel drug carriers, vaccine platforms, nanotemplates and nanoreactors.

  5. Optical realization of optimal symmetric real state quantum cloning machine

    NASA Astrophysics Data System (ADS)

    Hu, Gui-Yu; Zhang, Wen-Hai; Ye, Liu

    2010-01-01

    We present an experimentally uniform linear optical scheme to implement the optimal 1→2 symmetric and optimal 1→3 symmetric economical real state quantum cloning machine of the polarization state of the single photon. This scheme requires single-photon sources and two-photon polarization entangled state as input states. It also involves linear optical elements and three-photon coincidence. Then we consider the realistic realization of the scheme by using the parametric down-conversion as photon resources. It is shown that under certain condition, the scheme is feasible by current experimental technology.

  6. Method and apparatus for uniformly concentrating solar flux for photovoltaic applications

    DOEpatents

    Jorgensen, Gary J.; Carasso, Meir; Wendelin, Timothy J.; Lewandowski, Allan A.

    1992-01-01

    A dish reflector and method for concentrating moderate solar flux uniformly on a target plane on a solar cell array, the dish having a stepped reflective surface that is characterized by a plurality of ring-like segments arranged about a common axis, and each segment having a concave spherical configuration.

  7. 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.

  8. How do stars form

    NASA Astrophysics Data System (ADS)

    Tscharnuter, W. M.

    1980-02-01

    Modes and model concept of star formation are reviewed, beginning with the theory of Kant (1755), via Newton's exact mathematical formulation of the laws of motion, his recognition of the universal validity of general gravitation, to modern concepts and hypotheses. Axisymmetric and spherically symmetric collapse models are discussed, and the origin of double and multiple star systems is examined.

  9. Mid-Infrared Interferometry on Spectral Lines. II. Continuum (Dust) Emission Around IRC +10216 and VY Canis Majoris

    NASA Astrophysics Data System (ADS)

    Monnier, J. D.; Danchi, W. C.; Hale, D. S.; Lipman, E. A.; Tuthill, P. G.; Townes, C. H.

    2000-11-01

    The University of California Berkeley Infrared Spatial Interferometer has measured the mid-infrared visibilities of the carbon star IRC +10216 and the red supergiant VY CMa. The dust shells around these sources have been previously shown to be time variable, and these new data are used to probe the evolution of the dust shells on a decade timescale, complementing contemporaneous studies at other wavelengths. Self-consistent, spherically symmetric models at maximum and minimum light both show the inner radius of the IRC +10216 dust shell to be much larger (150 mas) than expected from the dust-condensation temperature, implying that dust production has slowed or stopped in recent years. Apparently, dust does not form every pulsational cycle (638 days), and these mid-infrared results are consistent with recent near-infrared imaging, which indicates little or no new dust production in the last 3 yr. Spherically symmetric models failed to fit recent VY CMa data, implying that emission from the inner dust shell is highly asymmetric and/or time variable.

  10. On the number of light rings in curved spacetimes of ultra-compact objects

    NASA Astrophysics Data System (ADS)

    Hod, Shahar

    2018-01-01

    In a very interesting paper, Cunha, Berti, and Herdeiro have recently claimed that ultra-compact objects, self-gravitating horizonless solutions of the Einstein field equations which have a light ring, must possess at least two (and, in general, an even number of) light rings, of which the inner one is stable. In the present compact paper we explicitly prove that, while this intriguing theorem is generally true, there is an important exception in the presence of degenerate light rings which, in the spherically symmetric static case, are characterized by the simple dimensionless relation 8 πrγ2 (ρ +pT) = 1 [here rγ is the radius of the light ring and { ρ ,pT } are respectively the energy density and tangential pressure of the matter fields]. Ultra-compact objects which belong to this unique family can have an odd number of light rings. As a concrete example, we show that spherically symmetric constant density stars with dimensionless compactness M / R = 1 / 3 possess only one light ring which, interestingly, is shown to be unstable.

  11. Conserved charges of black holes in Weyl and Einstein-Gauss-Bonnet gravities

    NASA Astrophysics Data System (ADS)

    Peng, Jun-Jin

    2014-11-01

    An off-shell generalization of the Abbott-Deser-Tekin (ADT) conserved charge was recently proposed by Kim et al. They achieved this by introducing off-shell Noether currents and potentials. In this paper, we construct the crucial off-shell Noether current by the variation of the Bianchi identity for the expression of EOM, with the help of the property of Killing vector. Our Noether current, which contains an additional term that is just one half of the Lie derivative of a surface term with respect to the Killing vector, takes a different form in comparison with the one in their work. Then we employ the generalized formulation to calculate the quasi-local conserved charges for the most general charged spherically symmetric and the dyonic rotating black holes with AdS asymptotics in four-dimensional conformal Weyl gravity, as well as the charged spherically symmetric black holes in arbitrary dimensional Einstein-Gauss-Bonnet gravity coupled to Maxwell or nonlinear electrodynamics in AdS spacetime. Our results confirm those obtained through other methods in the literature.

  12. Multi-domain boundary element method for axi-symmetric layered linear acoustic systems

    NASA Astrophysics Data System (ADS)

    Reiter, Paul; Ziegelwanger, Harald

    2017-12-01

    Homogeneous porous materials like rock wool or synthetic foam are the main tool for acoustic absorption. The conventional absorbing structure for sound-proofing consists of one or multiple absorbers placed in front of a rigid wall, with or without air-gaps in between. Various models exist to describe these so called multi-layered acoustic systems mathematically for incoming plane waves. However, there is no efficient method to calculate the sound field in a half space above a multi layered acoustic system for an incoming spherical wave. In this work, an axi-symmetric multi-domain boundary element method (BEM) for absorbing multi layered acoustic systems and incoming spherical waves is introduced. In the proposed BEM formulation, a complex wave number is used to model absorbing materials as a fluid and a coordinate transformation is introduced which simplifies singular integrals of the conventional BEM to non-singular radial and angular integrals. The radial and angular part are integrated analytically and numerically, respectively. The output of the method can be interpreted as a numerical half space Green's function for grounds consisting of layered materials.

  13. Radial accretion flows on static spherically symmetric black holes

    NASA Astrophysics Data System (ADS)

    Chaverra, Eliana; Sarbach, Olivier

    2015-08-01

    We analyze the steady radial accretion of matter into a nonrotating black hole. Neglecting the self-gravity of the accreting matter, we consider a rather general class of static, spherically symmetric and asymptotically flat background spacetimes with a regular horizon. In addition to the Schwarzschild metric, this class contains certain deformation of it, which could arise in alternative gravity theories or from solutions of the classical Einstein equations in the presence of external matter fields. Modeling the ambient matter surrounding the black hole by a relativistic perfect fluid, we reformulate the accretion problem as a dynamical system, and under rather general assumptions on the fluid equation of state, we determine the local and global qualitative behavior of its phase flow. Based on our analysis and generalizing previous work by Michel, we prove that for any given positive particle density number at infinity, there exists a unique radial, steady-state accretion flow which is regular at the horizon. We determine the physical parameters of the flow, including its accretion and compression rates, and discuss their dependency on the background metric.

  14. Collapsing shells and black holes: a quantum analysis

    NASA Astrophysics Data System (ADS)

    Leal, P.; Bernardini, A. E.; Bertolami, O.

    2018-06-01

    The quantization of a spherically symmetric null shells is performed and extended to the framework of phase-space noncommutative (NC) quantum mechanics. This shell is considered to be inside a black hole event horizon. The encountered properties are investigated making use of the Israel junction conditions on the shell, considering that it is the boundary between two spherically symmetric spacetimes. Using this method, and considering two different Kantowski–Sachs spacetimes as a representation for the Schwarzschild spacetime, the relevant quantities on the shell are computed, such as its stress-energy tensor and the action for the whole spacetime. From the obtained action, the Wheeler–deWitt equation is deduced in order to provide the quantum framework for the system. Solutions for the wave function of the system are found on both the commutative and NC scenarios. It is shown that, on the commutative version, the wave function has a purely oscillatory behavior in the interior of the shell. In the NC setting, it is shown that the wave function vanishes at the singularity, as well as, at the event horizon of the black hole.

  15. Effect of Particle Morphology on the Reactivity of Explosively Dispersed Titanium Particles

    NASA Astrophysics Data System (ADS)

    Frost, David; Cairns, Malcolm; Goroshin, Samuel; Zhang, Fan

    2009-06-01

    The effect of particle morphology on the reaction of titanium (Ti) particles explosively dispersed during the detonation of either cylindrical or spherical charges has been investigated experimentally. The explosive charges consisted of packed beds of Ti particles saturated with nitromethane. The reaction behavior of irregularly-shaped Ti particles in three size ranges is compared with tests with spherical Ti particles. The particle reaction is strongly dependent on particle morphology, e.g., 95 μm spherical Ti particles failed to ignite (in cylinders up to 49 mm in dia), whereas similarly sized irregular Ti particles readily ignited. For irregular particles, the uniformity of ignition on the particle cloud surface was almost independent of particle size, but depended on charge diameter. As the charge diameter was reduced, ignition in the conically expanding particle cloud occurred only at isolated spots or bands. For spherical charges, although large irregular Ti particles ignited promptly and uniformly throughout the particle cloud, the smallest particles dispersed nonuniformly and ignition occurred at isolated locations. In general, particle ignition is a competition between particle heating (which is influenced by particle morphology, size, number density and the local thermodynamic history) and expansion cooling of the products.

  16. Symmetric tops in combined electric fields: Conditional quasisolvability via the quantum Hamilton-Jacobi theory

    NASA Astrophysics Data System (ADS)

    Schatz, Konrad; Friedrich, Bretislav; Becker, Simon; Schmidt, Burkhard

    2018-05-01

    We make use of the quantum Hamilton-Jacobi (QHJ) theory to investigate conditional quasisolvability of the quantum symmetric top subject to combined electric fields (symmetric top pendulum). We derive the conditions of quasisolvability of the time-independent Schrödinger equation as well as the corresponding finite sets of exact analytic solutions. We do so for this prototypical trigonometric system as well as for its anti-isospectral hyperbolic counterpart. An examination of the algebraic and numerical spectra of these two systems reveals mutually closely related patterns. The QHJ approach allows us to retrieve the closed-form solutions for the spherical and planar pendula and the Razavy system that had been obtained in our earlier work via supersymmetric quantum mechanics as well as to find a cornucopia of additional exact analytic solutions.

  17. Spherical Macroporous Carbon Nanotube Particles with Ultrahigh Sulfur Loading for Lithium-Sulfur Battery Cathodes.

    PubMed

    Gueon, Donghee; Hwang, Jeong Tae; Yang, Seung Bo; Cho, Eunkyung; Sohn, Kwonnam; Yang, Doo-Kyung; Moon, Jun Hyuk

    2018-01-23

    A carbon host capable of effective and uniform sulfur loading is the key for lithium-sulfur batteries (LSBs). Despite the application of porous carbon materials of various morphologies, the carbon hosts capable of uniformly impregnating highly active sulfur is still challenging. To address this issue, we demonstrate a hierarchical pore-structured CNT particle host containing spherical macropores of several hundred nanometers. The macropore CNT particles (M-CNTPs) are prepared by drying the aerosol droplets in which CNTs and polymer particles are dispersed. The spherical macropore greatly improves the penetration of sulfur into the carbon host in the melt diffusion of sulfur. In addition, the formation of macropores greatly develops the volume of the micropore between CNT strands. As a result, we uniformly impregnate 70 wt % sulfur without sulfur residue. The S-M-CNTP cathode shows a highly reversible capacity of 1343 mA h g -1 at a current density of 0.2 C even at a high sulfur content of 70 wt %. Upon a 10-fold current density increase, a high capacity retention of 74% is observed. These cathodes have a higher sulfur content than those of conventional CNT hosts but nevertheless exhibit excellent performance. Our CNTPs and pore control technology will advance the commercialization of CNT hosts for LSBs.

  18. Path planning and parameter optimization of uniform removal in active feed polishing

    NASA Astrophysics Data System (ADS)

    Liu, Jian; Wang, Shaozhi; Zhang, Chunlei; Zhang, Linghua; Chen, Huanan

    2015-06-01

    A high-quality ultrasmooth surface is demanded in short-wave optical systems. However, the existing polishing methods have difficulties meeting the requirement on spherical or aspheric surfaces. As a new kind of small tool polishing method, active feed polishing (AFP) could attain a surface roughness of less than 0.3 nm (RMS) on spherical elements, although AFP may magnify the residual figure error or mid-frequency error. The purpose of this work is to propose an effective algorithm to realize uniform removal of the surface in the processing. At first, the principle of the AFP and the mechanism of the polishing machine are introduced. In order to maintain the processed figure error, a variable pitch spiral path planning algorithm and the dwell time-solving model are proposed. For suppressing the possible mid-frequency error, the uniformity of the synthesis tool path, which is generated by an arbitrary point at the polishing tool bottom, is analyzed and evaluated, and the angular velocity ratio of the tool spinning motion to the revolution motion is optimized. Finally, an experiment is conducted on a convex spherical surface and an ultrasmooth surface is finally acquired. In conclusion, a high-quality ultrasmooth surface can be successfully obtained with little degradation of the figure and mid-frequency errors by the algorithm.

  19. Discontinuous Galerkin finite element methods for radiative transfer in spherical symmetry

    NASA Astrophysics Data System (ADS)

    Kitzmann, D.; Bolte, J.; Patzer, A. B. C.

    2016-11-01

    The discontinuous Galerkin finite element method (DG-FEM) is successfully applied to treat a broad variety of transport problems numerically. In this work, we use the full capacity of the DG-FEM to solve the radiative transfer equation in spherical symmetry. We present a discontinuous Galerkin method to directly solve the spherically symmetric radiative transfer equation as a two-dimensional problem. The transport equation in spherical atmospheres is more complicated than in the plane-parallel case owing to the appearance of an additional derivative with respect to the polar angle. The DG-FEM formalism allows for the exact integration of arbitrarily complex scattering phase functions, independent of the angular mesh resolution. We show that the discontinuous Galerkin method is able to describe accurately the radiative transfer in extended atmospheres and to capture discontinuities or complex scattering behaviour which might be present in the solution of certain radiative transfer tasks and can, therefore, cause severe numerical problems for other radiative transfer solution methods.

  20. Nonlinear elastic inclusions in isotropic solids.

    PubMed

    Yavari, Arash; Goriely, Alain

    2013-12-08

    We introduce a geometric framework to calculate the residual stress fields and deformations of nonlinear solids with inclusions and eigenstrains. Inclusions are regions in a body with different reference configurations from the body itself and can be described by distributed eigenstrains. Geometrically, the eigenstrains define a Riemannian 3-manifold in which the body is stress-free by construction. The problem of residual stress calculation is then reduced to finding a mapping from the Riemannian material manifold to the ambient Euclidean space. Using this construction, we find the residual stress fields of three model systems with spherical and cylindrical symmetries in both incompressible and compressible isotropic elastic solids. In particular, we consider a finite spherical ball with a spherical inclusion with uniform pure dilatational eigenstrain and we show that the stress in the inclusion is uniform and hydrostatic. We also show how singularities in the stress distribution emerge as a consequence of a mismatch between radial and circumferential eigenstrains at the centre of a sphere or the axis of a cylinder.

  1. Nonlinear elastic inclusions in isotropic solids

    PubMed Central

    Yavari, Arash; Goriely, Alain

    2013-01-01

    We introduce a geometric framework to calculate the residual stress fields and deformations of nonlinear solids with inclusions and eigenstrains. Inclusions are regions in a body with different reference configurations from the body itself and can be described by distributed eigenstrains. Geometrically, the eigenstrains define a Riemannian 3-manifold in which the body is stress-free by construction. The problem of residual stress calculation is then reduced to finding a mapping from the Riemannian material manifold to the ambient Euclidean space. Using this construction, we find the residual stress fields of three model systems with spherical and cylindrical symmetries in both incompressible and compressible isotropic elastic solids. In particular, we consider a finite spherical ball with a spherical inclusion with uniform pure dilatational eigenstrain and we show that the stress in the inclusion is uniform and hydrostatic. We also show how singularities in the stress distribution emerge as a consequence of a mismatch between radial and circumferential eigenstrains at the centre of a sphere or the axis of a cylinder. PMID:24353470

  2. A fully automatic, threshold-based segmentation method for the estimation of the Metabolic Tumor Volume from PET images: validation on 3D printed anthropomorphic oncological lesions

    NASA Astrophysics Data System (ADS)

    Gallivanone, F.; Interlenghi, M.; Canervari, C.; Castiglioni, I.

    2016-01-01

    18F-Fluorodeoxyglucose (18F-FDG) Positron Emission Tomography (PET) is a standard functional diagnostic technique to in vivo image cancer. Different quantitative paramters can be extracted from PET images and used as in vivo cancer biomarkers. Between PET biomarkers Metabolic Tumor Volume (MTV) has gained an important role in particular considering the development of patient-personalized radiotherapy treatment for non-homogeneous dose delivery. Different imaging processing methods have been developed to define MTV. The different proposed PET segmentation strategies were validated in ideal condition (e.g. in spherical objects with uniform radioactivity concentration), while the majority of cancer lesions doesn't fulfill these requirements. In this context, this work has a twofold objective: 1) to implement and optimize a fully automatic, threshold-based segmentation method for the estimation of MTV, feasible in clinical practice 2) to develop a strategy to obtain anthropomorphic phantoms, including non-spherical and non-uniform objects, miming realistic oncological patient conditions. The developed PET segmentation algorithm combines an automatic threshold-based algorithm for the definition of MTV and a k-means clustering algorithm for the estimation of the background. The method is based on parameters always available in clinical studies and was calibrated using NEMA IQ Phantom. Validation of the method was performed both in ideal (e.g. in spherical objects with uniform radioactivity concentration) and non-ideal (e.g. in non-spherical objects with a non-uniform radioactivity concentration) conditions. The strategy to obtain a phantom with synthetic realistic lesions (e.g. with irregular shape and a non-homogeneous uptake) consisted into the combined use of standard anthropomorphic phantoms commercially and irregular molds generated using 3D printer technology and filled with a radioactive chromatic alginate. The proposed segmentation algorithm was feasible in a clinical context and showed a good accuracy both in ideal and in realistic conditions.

  3. Global strong solutions to radial symmetric compressible Navier-Stokes equations with free boundary

    NASA Astrophysics Data System (ADS)

    Li, Hai-liang; Zhang, Xingwei

    2016-12-01

    In this paper, we consider the two-dimensional barotropic compressible Navier-Stokes equations with stress free boundary condition imposed on the free surface. As the viscosity coefficients satisfies μ (ρ) = 2 μ, λ (ρ) =ρβ, β > 1, we establish the existence of global strong solution for arbitrarily large spherical symmetric initial data even if the density vanishes across the free boundary. In particular, we show that the density is strictly positive and bounded from the above and below in any finite time if the initial density is strictly positive, and the free boundary propagates along the particle path and expand outwards at an algebraic rate.

  4. Are Singularities Integral to General Theory of Relativity?

    NASA Astrophysics Data System (ADS)

    Krori, K.; Dutta, S.

    2011-11-01

    Since the 1960s the general relativists have been deeply obsessed with the possibilities of GTR singularities - blackhole as well as cosmological singularities. Senovilla, for the first time, followed by others, showed that there are cylindrically symmetric cosmological space-times which are free of singularities. On the other hand, Krori et al. have presently shown that spherically symmetric cosmological space-times - which later reduce to FRW space-times may also be free of singularities. Besides, Mitra has in the mean-time come forward with some realistic calculations which seem to rule out the possibility of a blackhole singularity. So whether singularities are integral to GTR seems to come under a shadow.

  5. 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.

  6. Optimization of spherical facets for parabolic solar concentrators

    NASA Technical Reports Server (NTRS)

    White, J. E.; Erikson, R. J.; Sturgis, J. D.; Elfe, T. B.

    1986-01-01

    Solar concentrator designs which employ deployable hexagonal panels are being developed for space power systems. An offset optical configuration has been developed which offers significant system level advantages over previously proposed collector designs for space applications. Optical analyses have been performed which show offset reflector intercept factors to be only slightly lower than those for symmetric reflectors with the same slope error. Fluxes on the receiver walls are asymmetric but manageable by varying the tilt angle of the receiver. Greater producibility is achieved by subdividing the hexagonal panels into triangular mirror facets of spherical contour. Optical analysis has been performed upon these to yield near-optimum sizes and radii.

  7. Methods of and apparatus for recording images occurring just prior to a rapid, random event

    DOEpatents

    Kelley, Edward F.

    1994-01-01

    An apparatus and a method are disclosed for recording images of events in a medium wherein the images that are recorded are of conditions existing just prior to and during the occurrence of an event that triggers recording of these images. The apparatus and method use an optical delay path that employs a spherical focusing mirror facing a circular array of flat return mirrors around a central flat mirror. The image is reflected in a symmetric pattern which balances astigmatism which is created by the spherical mirror. Delays on the order of hundreds of nanoseconds are possible.

  8. Theoretical regime diagrams for thermally driven flows in a beta-plane channel. [in atmosphere

    NASA Technical Reports Server (NTRS)

    Geisler, J. E.; Fowlis, W. W.

    1979-01-01

    It is noted that thermally driven flows in rotating laboratory containers with cylindrical geometry can be axially symmetric or wavelike depending on the experimental parameters. In anticipation that rotating fluid experiments might soon be done in spherical shell geometry, Barcilon's model has been extended to a beta-plane channel in order to gain a rough understanding of the effects of rotating spherical geometry. An incompressible fluid version of the Charney (1947) model of baroclinic instability, modified to include Ekman pumping at rigid horizontal boundaries is used. With this model, stability boundaries are mapped out for individual zonal wavenumbers in the parameter space used by Barcilon.

  9. Coupled macrospins: Mode dynamics in symmetric and asymmetric vertices

    NASA Astrophysics Data System (ADS)

    Bang, Wonbae; Jungfleisch, Matthias B.; Montoncello, Federico; Farmer, Barry W.; Lapa, Pavel N.; Hoffmann, Axel; Giovannini, Loris; De Long, Lance E.; Ketterson, John B.

    2018-05-01

    We report the microwave response of symmetric and asymmetric threefold clusters with nearly contacting segments that can serve as the node in a Kagome artificial spin ice lattice. The structures are patterned on a coplanar waveguide and consist of elongated and nearly-contacting ellipses with uniform thickness. Branches of the ferromagnetic resonance spectra display mode softening that correlates well with the calculations, whereas agreement between the measured and simulated static magnetization is more qualitative.

  10. Coupled macrospins: Mode dynamics in symmetric and asymmetric vertices

    DOE PAGES

    Bang, Wonbae; Jungfleisch, Matthias B.; Montoncello, Federico; ...

    2017-12-29

    We report the microwave response of symmetric and asymmetric threefold clusters with nearly contacting segments that can serve as the node in a Kagome artificial spin ice lattice. The structures are patterned on a coplanar waveguide and consist of elongated and nearly-contacting ellipses with uniform thickness. Branches of the ferromagnetic resonance spectra display mode softening that correlates well with the calculations, whereas agreement between the measured and simulated static magnetization is more qualitative.

  11. Spherical Pendulum Small Oscillations for Slewing Crane Motion

    PubMed Central

    Perig, Alexander V.; Stadnik, Alexander N.; Deriglazov, Alexander I.

    2014-01-01

    The present paper focuses on the Lagrange mechanics-based description of small oscillations of a spherical pendulum with a uniformly rotating suspension center. The analytical solution of the natural frequencies' problem has been derived for the case of uniform rotation of a crane boom. The payload paths have been found in the inertial reference frame fixed on earth and in the noninertial reference frame, which is connected with the rotating crane boom. The numerical amplitude-frequency characteristics of the relative payload motion have been found. The mechanical interpretation of the terms in Lagrange equations has been outlined. The analytical expression and numerical estimation for cable tension force have been proposed. The numerical computational results, which correlate very accurately with the experimental observations, have been shown. PMID:24526891

  12. Detection of defects on apple using B-spline lighting correction method

    NASA Astrophysics Data System (ADS)

    Li, Jiangbo; Huang, Wenqian; Guo, Zhiming

    To effectively extract defective areas in fruits, the uneven intensity distribution that was produced by the lighting system or by part of the vision system in the image must be corrected. A methodology was used to convert non-uniform intensity distribution on spherical objects into a uniform intensity distribution. A basically plane image with the defective area having a lower gray level than this plane was obtained by using proposed algorithms. Then, the defective areas can be easily extracted by a global threshold value. The experimental results with a 94.0% classification rate based on 100 apple images showed that the proposed algorithm was simple and effective. This proposed method can be applied to other spherical fruits.

  13. A new treatment of the albedo radiation pressure in the case of a uniform albedo and of a spherical satellite

    NASA Technical Reports Server (NTRS)

    Borderies, Nicole; Longaretti, Pierre-Yves

    1990-01-01

    The purpose of this paper is to present a model for the radiation pressure acceleration of a spherical satellite, due to the radiation reflected by a planet with a uniform albedo. A particular choice of variables allows one to reduce the surface integrals over the lit portion of the planet visible to the satellite to one-dimensional integrals. Exact analytical expressions are found for the integrals corresponding to the case where the spacecraft does not 'see' the terminator. The other integrals can be computer either numerically, or analytical in an approximate form. The results are compared with those of Lochry (1966). The model is applied to Magellan, a spacecraft orbiting Venus.

  14. Global structure of static spherically symmetric solutions surrounded by quintessence

    NASA Astrophysics Data System (ADS)

    Cruz, Miguel; Ganguly, Apratim; Gannouji, Radouane; Leon, Genly; Saridakis, Emmanuel N.

    2017-06-01

    We investigate all static spherically symmetric solutions in the context of general relativity surrounded by a minimally-coupled quintessence field, using dynamical system analysis. Applying the 1  +  1  +  2 formalism and introducing suitable normalized variables involving the Gaussian curvature, we were able to reformulate the field equations as first order differential equations. In the case of a massless canonical scalar field we recovered all known black hole results, such as the Fisher solution, and we found that apart from the Schwarzschild solution all other solutions are naked singularities. Additionally, we identified the symmetric phase space which corresponds to the white hole part of the solution and in the case of a phantom field, we were able to extract the conditions for the existence of wormholes and define all possible classes of solutions such as cold black holes, singular spacetimes and wormholes such as the Ellis wormhole, for example. For an exponential potential, we found that the black hole solution which is asymptotically flat is unique and it is the Schwarzschild spacetime, while all other solutions are naked singularities. Furthermore, we found solutions connecting to a white hole through a maximum radius, and not a minimum radius (throat) such as wormhole solutions, therefore violating the flare-out condition. Finally, we have found a necessary and sufficient condition on the form of the potential to have an asymptotically AdS spacetime along with a necessary condition for the existence of asymptotically flat black holes.

  15. Equatorial symmetry of Boussinesq convective solutions in a rotating spherical shell allowing rotation of the inner and outer spheres

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kimura, Keiji; Takehiro, Shin-ichi; Yamada, Michio

    2014-08-15

    We investigate properties of convective solutions of the Boussinesq thermal convection in a moderately rotating spherical shell allowing the respective rotation of the inner and outer spheres due to the viscous torque of the fluid. The ratio of the inner and outer radii of the spheres, the Prandtl number, and the Taylor number are fixed to 0.4, 1, and 500{sup 2}, respectively. The Rayleigh number is varied from 2.6 × 10{sup 4} to 3.4 × 10{sup 4}. In this parameter range, the behaviours of obtained asymptotic convective solutions are almost similar to those in the system whose inner and outermore » spheres are restricted to rotate with the same constant angular velocity, although the difference is found in the transition process to chaotic solutions. The convective solution changes from an equatorially symmetric quasi-periodic one to an equatorially symmetric chaotic one, and further to an equatorially asymmetric chaotic one, as the Rayleigh number is increased. This is in contrast to the transition in the system whose inner and outer spheres are assumed to rotate with the same constant angular velocity, where the convective solution changes from an equatorially symmetric quasi-periodic one, to an equatorially asymmetric quasi-periodic one, and to equatorially asymmetric chaotic one. The inner sphere rotates in the retrograde direction on average in the parameter range; however, it sometimes undergoes the prograde rotation when the convective solution becomes chaotic.« less

  16. Test-particle motion in the nonsymmetric gravitation theory

    NASA Astrophysics Data System (ADS)

    Moffat, J. W.

    1987-06-01

    A derivation of the motion of test particles in the nonsymmetric gravitational theory (NGT) is given using the field equations in the presence of matter. The motion of the particle is governed by the Christoffel symbols, which are formed from the symmetric part of the fundamental tensor gμν, as well as by a tensorial piece determined by the skew part of the contracted curvature tensor Rμν. Given the energy-momentum tensor for a perfect fluid and the definition of a test particle in the NGT, the equations of motion follow from the conservation laws. The tensorial piece in the equations of motion describes a new force in nature that acts on the conserved charge in a body. Particles that carry this new charge do not follow geodesic world lines in the NGT, whereas photons do satisfy geodesic equations of motion and the equivalence principle of general relativity. Astronomical predictions, based on the exact static, spherically symmetric solution of the field equations in a vacuum and the test-particle equations of motion, are derived in detail. The maximally extended coordinates that remove the event-horizon singularities in the static, spherically symmetric solution are presented. It is shown how an inward radially falling test particle can be prevented from forming an event horizon for a value greater than a specified critical value of the source charge. If a test particle does fall through an event horizon, then it must continue to fall until it reaches the singularity at r=0.

  17. Numerical Solution of the Problem of the Expansion of the Universe in the Schwarzschild Metric

    NASA Astrophysics Data System (ADS)

    Vasenin, I. M.; Goiko, V. L.

    2018-02-01

    The statement and solution of the problem of the expansion of the Universe in nonstationary spherically-symmetric coordinates in the Schwarzschild metric are considered without pressure taken into account. The observational data of astronomers investigating the rates of recession of distant stars are explained on the basis of the obtained solutions.

  18. Accretion of a relativistic, collisionless kinetic gas into a Schwarzschild black hole

    NASA Astrophysics Data System (ADS)

    Rioseco, Paola; Sarbach, Olivier

    2017-05-01

    We provide a systematic study for the accretion of a collisionless, relativistic kinetic gas into a nonrotating black hole. To this end, we first solve the relativistic Liouville equation on a Schwarzschild background spacetime. The most general solution for the distribution function is given in terms of appropriate symplectic coordinates on the cotangent bundle, and the associated observables, including the particle current density and stress energy-momentum tensor, are determined. Next, we explore the case where the flow is steady-state and spherically symmetric. Assuming that in the asymptotic region the gas is described by an equilibrium distribution function, we determine the relevant parameters of the accretion flow as a function of the particle density and the temperature of the gas at infinity. In particular, we find that in the low temperature limit the tangential pressure at the horizon is about an order of magnitude larger than the radial one, showing explicitly that a collisionless gas, despite exerting kinetic pressure, behaves very differently than an isotropic perfect fluid, and providing a partial explanation for the known fact that the accretion rate is much lower than in the hydrodynamic case of Bondi-Michel accretion. Finally, we establish the asymptotic stability of the steady-state spherical flows by proving pointwise convergence results which show that a large class of (possibly nonstationary and nonspherical) initial conditions for the distribution function lead to solutions of the Liouville equation which relax in time to a steady-state, spherically symmetric configuration.

  19. Space Telescope Imaging Spectrograph Spectroscopy of the Central 14 pc OF NGC 3998: Evidence for an Inflow

    NASA Astrophysics Data System (ADS)

    Devereux, Nick

    2011-02-01

    Prior imaging of the lenticular galaxy, NGC 3998, with the Hubble Space Telescope revealed a small, highly inclined, nuclear ionized gas disk, the kinematics of which indicate the presence of a 270 million solar mass black hole. Plausible kinematic models are used to constrain the size of the broad emission line region (BELR) in NGC 3998 by modeling the shape of the broad Hα, Hβ, and Hγ emission line profiles. The analysis indicates that the BELR is large with an outer radius ~7 pc, regardless of whether the kinematic model is represented by an accretion disk or a spherically symmetric inflow. The electron temperature in the BELR is <= 28,800 K consistent with photoionization by the active galactic nucleus (AGN). Indeed, the AGN is able to sustain the ionization of the BELR, albeit with a high covering factor ranging between 20% and 100% depending on the spectral energy distribution adopted for the AGN. The high covering factor favors a spherical distribution for the gas as opposed to a thin disk. If the gas density is >=7 × 103 cm-3 as indicated by the broad forbidden [S II] emission line ratio, then interpreting the broad Hα emission line in terms of a steady state spherically symmetric inflow leads to a rate <= 6.5 × 10-2 M sun yr-1 which exceeds the inflow requirement to explain the X-ray luminosity in terms of a radiatively inefficient inflow by a factor of <=18.

  20. Brownian motion and thermophoresis effects on Peristaltic slip flow of a MHD nanofluid in a symmetric/asymmetric channel

    NASA Astrophysics Data System (ADS)

    Sucharitha, G.; Sreenadh, S.; Lakshminarayana, P.; Sushma, K.

    2017-11-01

    The slip and heat transfer effects on MHD peristaltic transport of a nanofluid in a non-uniform symmetric/asymmetric channel have studied under the assumptions of elongated wave length and negligible Reynolds number. From the simplified governing equations, the closed form solutions for velocity, stream function, temperature and concentrations are obtained. Also dual solutions are discussed for symmetric and asymmetric channel cases. The effects of important physical parameters are explained graphically. The slip parameter decreases the fluid velocity in middle of the channel whereas it increases the velocity at the channel walls. Temperature and concentration are decreasing and increasing functions of radiation parameter respectively. Moreover, velocity, temperature and concentrations are high in symmetric channel when compared with asymmetric channel.

  1. Black holes and stars in Horndeski theory

    NASA Astrophysics Data System (ADS)

    Babichev, Eugeny; Charmousis, Christos; Lehébel, Antoine

    2016-08-01

    We review black hole and star solutions for Horndeski theory. For non-shift symmetric theories, black holes involve a Kaluza-Klein reduction of higher dimensional Lovelock solutions. On the other hand, for shift symmetric theories of Horndeski and beyond Horndeski, black holes involve two classes of solutions: those that include, at the level of the action, a linear coupling to the Gauss-Bonnet term and those that involve time dependence in the galileon field. We analyze the latter class in detail for a specific subclass of Horndeski theory, discussing the general solution of a static and spherically symmetric spacetime. We then discuss stability issues, slowly rotating solutions as well as black holes coupled to matter. The latter case involves a conformally coupled scalar field as well as an electromagnetic field and the (primary) hair black holes thus obtained. We review and discuss the recent results on neutron stars in Horndeski theories.

  2. Uniform batch processing using microwaves

    NASA Technical Reports Server (NTRS)

    Barmatz, Martin B. (Inventor); Jackson, Henry W. (Inventor)

    2000-01-01

    A microwave oven and microwave heating method generates microwaves within a cavity in a predetermined mode such that there is a known region of uniform microwave field. Samples placed in the region will then be heated in a relatively identical manner. Where perturbations induced by the samples are significant, samples are arranged in a symmetrical distribution so that the cumulative perturbation at each sample location is the same.

  3. Elastic field of a spherical inclusion with non-uniform eigenfields in second strain gradient elasticity

    NASA Astrophysics Data System (ADS)

    Delfani, M. R.; Latifi Shahandashti, M.

    2017-09-01

    In this paper, within the complete form of Mindlin's second strain gradient theory, the elastic field of an isolated spherical inclusion embedded in an infinitely extended homogeneous isotropic medium due to a non-uniform distribution of eigenfields is determined. These eigenfields, in addition to eigenstrain, comprise eigen double and eigen triple strains. After the derivation of a closed-form expression for Green's function associated with the problem, two different cases of non-uniform distribution of the eigenfields are considered as follows: (i) radial distribution, i.e. the distributions of the eigenfields are functions of only the radial distance of points from the centre of inclusion, and (ii) polynomial distribution, i.e. the distributions of the eigenfields are polynomial functions in the Cartesian coordinates of points. While the obtained solution for the elastic field of the latter case takes the form of an infinite series, the solution to the former case is represented in a closed form. Moreover, Eshelby's tensors associated with the two mentioned cases are obtained.

  4. In-flight performance of the Faint Object Camera of the Hubble Space Telescope

    NASA Technical Reports Server (NTRS)

    Greenfield, P.; Paresce, F.; Baxter, D.; Hodge, P.; Hook, R.; Jakobsen, P.; Jedrzejewski, R.; Nota, A.; Sparks, W. B.; Towers, N.

    1991-01-01

    An overview of the Faint Object Camera and its performance to date is presented. In particular, the detector's efficiency, the spatial uniformity of response, distortion characteristics, detector and sky background, detector linearity, spectrography, and operation are discussed. The effect of the severe spherical aberration of the telescope's primary mirror on the camera's point spread function is reviewed, as well as the impact it has on the camera's general performance. The scientific implications of the performance and the spherical aberration are outlined, with emphasis on possible remedies for spherical aberration, hardware remedies, and stellar population studies.

  5. Apparatus and method for generating swirling flow

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Haden, Robert E.; Lorentz, Donald G.

    An apparatus and method for generating a swirl is disclosed that is used to induce an axi-symmetric swirling flow to an incoming flow. The disclosed subject matter induces a uniform and axi-symmetric swirl, circumferentially around a discharge location, thus imparting a more accurate, repeatable, continuous, and controllable swirl and mixing condition of interest. Moreover, the disclosed subject matter performs the swirl injection at a lower pressure drop in comparison to a more traditional methods and devices.

  6. Spontaneous spherical symmetry breaking in atomic confinement

    NASA Astrophysics Data System (ADS)

    Sveshnikov, Konstantin; Tolokonnikov, Andrey

    2017-07-01

    The effect of spontaneous breaking of initial SO(3) symmetry is shown to be possible for an H-like atom in the ground state, when it is confined in a spherical box under general boundary conditions of "not going out" through the box surface (i.e. third kind or Robin's ones), for a wide range of physically reasonable values of system parameters. The most novel and nontrivial result, which has not been reported previously, is that such an effect takes place not only for attractive, but also for repulsive interactions of atomic electrons with the cavity environment. Moreover, in the limit of a large box size R ≫ aB the regime of an atom, soaring over a plane with boundary condition of "not going out", is reproduced, rather than a spherically symmetric configuration, which would be expected on the basis of the initial SO(3) symmetry of the problem.

  7. The influence of ozone and aerosols on the brightness and color of the twilight sky

    NASA Technical Reports Server (NTRS)

    Adams, C. N.; Plass, G. N.; Kattawar, G. W.

    1974-01-01

    The radiance and color of the twilight sky are calculated for single scattered radiation with the use of spherically symmetric models of the earth's atmosphere. Spherical geometry is used throughout the calculations with no plane-parallel approximations. Refraction effects are taken into account through fine subdivision of the atmosphere into spherical shells of fixed index of refraction. Snell's law of refraction is used to calculate a new direction of travel each time that a photon traverses the interface between layers. Five different models of the atmosphere were used: a pure molecular scattering atmosphere; molecular atmosphere plus ozone absorption; and three models with aerosol concentrations of one, three, and ten times normal together with molecular scattering and ozone absorption. The results of the calculations are shown for various observation positions and local viewing angles in the solar plane for wavelengths in the range from 0.40 to 0.75 micron.

  8. The influence of ozone and aerosols on the brightness and color of the twilight zone

    NASA Technical Reports Server (NTRS)

    Adams, C. N.; Plass, G. N.; Kattawar, G. W.

    1973-01-01

    The radiance and color of the twilight sky are calculated for single scattered radiation with the use of spherically symmetric models of the earth's atmosphere. Spherical geometry is used throughout the calculations with no plane parallel approximations. Refraction effects are taken into account through fine subdivision of the atmosphere into spherical shells of fixed index of refraction. Shell's law of refraction is used to calculate a direction of travel each time that a photon traverses the interface between layers. Five different models of the atmosphere were used: a pure molecular scattering atmosphere; molecular atmosphere plus ozone absorption; and three models with aerosol concentrations of 1, 3, and 10 times normal together with molecular scattering and ozone absorption. The results of the calculations are shown for various observation positions and local viewing angles in the solar plane for wavelengths in the range of 0.40 microns to 0.75 microns.

  9. Unconditional security of a three state quantum key distribution protocol.

    PubMed

    Boileau, J-C; Tamaki, K; Batuwantudawe, J; Laflamme, R; Renes, J M

    2005-02-04

    Quantum key distribution (QKD) protocols are cryptographic techniques with security based only on the laws of quantum mechanics. Two prominent QKD schemes are the Bennett-Brassard 1984 and Bennett 1992 protocols that use four and two quantum states, respectively. In 2000, Phoenix et al. proposed a new family of three-state protocols that offers advantages over the previous schemes. Until now, an error rate threshold for security of the symmetric trine spherical code QKD protocol has been shown only for the trivial intercept-resend eavesdropping strategy. In this Letter, we prove the unconditional security of the trine spherical code QKD protocol, demonstrating its security up to a bit error rate of 9.81%. We also discuss how this proof applies to a version of the trine spherical code QKD protocol where the error rate is evaluated from the number of inconclusive events.

  10. Dual-phase-shift spherical Fizeau interferometer for reduction of noise due to internally scattered light

    NASA Astrophysics Data System (ADS)

    Kumagai, Toshiki; Hibino, Kenichi; Nagaike, Yasunari

    2017-03-01

    Internally scattered light in a Fizeau interferometer is generated from dust, defects, imperfect coating of the optical components, and multiple reflections inside the collimator lens. It produces additional noise fringes in the observed interference image and degrades the repeatability of the phase measurement. A method to reduce the phase measurement error is proposed, in which the test surface is mechanically translated between each phase measurement in addition to an ordinary phase shift of the reference surface. It is shown that a linear combination of several measured phases at different test surface positions can reduce the phase errors caused by the scattered light. The combination can also compensate for the nonuniformity of the phase shift that occurs in spherical tests. A symmetric sampling of the phase measurements can cancel the additional primary spherical aberrations that occur when the test surface is out of the null position of the confocal configuration.

  11. Symmetric flows for compressible heat-conducting fluids with temperature dependent viscosity coefficients

    NASA Astrophysics Data System (ADS)

    Wan, Ling; Wang, Tao

    2017-06-01

    We consider the Navier-Stokes equations for compressible heat-conducting ideal polytropic gases in a bounded annular domain when the viscosity and thermal conductivity coefficients are general smooth functions of temperature. A global-in-time, spherically or cylindrically symmetric, classical solution to the initial boundary value problem is shown to exist uniquely and converge exponentially to the constant state as the time tends to infinity under certain assumptions on the initial data and the adiabatic exponent γ. The initial data can be large if γ is sufficiently close to 1. These results are of Nishida-Smoller type and extend the work (Liu et al. (2014) [16]) restricted to the one-dimensional flows.

  12. A Generalization of the Einstein-Maxwell Equations

    NASA Astrophysics Data System (ADS)

    Cotton, Fredrick

    2016-03-01

    The proposed modifications of the Einstein-Maxwell equations include: (1) the addition of a scalar term to the electromagnetic side of the equation rather than to the gravitational side, (2) the introduction of a 4-dimensional, nonlinear electromagnetic constitutive tensor and (3) the addition of curvature terms arising from the non-metric components of a general symmetric connection. The scalar term is defined by the condition that a spherically symmetric particle be force-free and mathematically well-behaved everywhere. The constitutive tensor introduces two auxiliary fields which describe the particle structure. The additional curvature terms couple both to particle solutions and to electromagnetic and gravitational wave solutions. http://sites.google.com/site/fwcotton/em-30.pdf

  13. Computer simulation of schlieren images of rotationally symmetric plasma systems: a simple method.

    PubMed

    Noll, R; Haas, C R; Weikl, B; Herziger, G

    1986-03-01

    Schlieren techniques are commonly used methods for quantitative analysis of cylindrical or spherical index of refraction profiles. Many schlieren objects, however, are characterized by more complex geometries, so we have investigated the more general case of noncylindrical, rotationally symmetric distributions of index of refraction n(r,z). Assuming straight ray paths in the schlieren object we have calculated 2-D beam deviation profiles. It is shown that experimental schlieren images of the noncylindrical plasma generated by a plasma focus device can be simulated with these deviation profiles. The computer simulation allows a quantitative analysis of these schlieren images, which yields, for example, the plasma parameters, electron density, and electron density gradients.

  14. On approximately symmetric informationally complete positive operator-valued measures and related systems of quantum states

    NASA Astrophysics Data System (ADS)

    Klappenecker, Andreas; Rötteler, Martin; Shparlinski, Igor E.; Winterhof, Arne

    2005-08-01

    We address the problem of constructing positive operator-valued measures (POVMs) in finite dimension n consisting of n2 operators of rank one which have an inner product close to uniform. This is motivated by the related question of constructing symmetric informationally complete POVMs (SIC-POVMs) for which the inner products are perfectly uniform. However, SIC-POVMs are notoriously hard to construct and, despite some success of constructing them numerically, there is no analytic construction known. We present two constructions of approximate versions of SIC-POVMs, where a small deviation from uniformity of the inner products is allowed. The first construction is based on selecting vectors from a maximal collection of mutually unbiased bases and works whenever the dimension of the system is a prime power. The second construction is based on perturbing the matrix elements of a subset of mutually unbiased bases. Moreover, we construct vector systems in Cn which are almost orthogonal and which might turn out to be useful for quantum computation. Our constructions are based on results of analytic number theory.

  15. Regular and chaotic dynamics of non-spherical bodies. Zeldovich's pancakes and emission of very long gravitational waves

    NASA Astrophysics Data System (ADS)

    Bisnovatyi-Kogan, G. S.; Tsupko, O. Yu.

    2015-10-01

    > In this paper we review a recently developed approximate method for investigation of dynamics of compressible ellipsoidal figures. Collapse and subsequent behaviour are described by a system of ordinary differential equations for time evolution of semi-axes of a uniformly rotating, three-axis, uniform-density ellipsoid. First, we apply this approach to investigate dynamic stability of non-spherical bodies. We solve the equations that describe, in a simplified way, the Newtonian dynamics of a self-gravitating non-rotating spheroidal body. We find that, after loss of stability, a contraction to a singularity occurs only in a pure spherical collapse, and deviations from spherical symmetry prevent the contraction to the singularity through a stabilizing action of nonlinear non-spherical oscillations. The development of instability leads to the formation of a regularly or chaotically oscillating body, in which dynamical motion prevents the formation of the singularity. We find regions of chaotic and regular pulsations by constructing a Poincaré diagram. A real collapse occurs after damping of the oscillations because of energy losses, shock wave formation or viscosity. We use our approach to investigate approximately the first stages of collapse during the large scale structure formation. The theory of this process started from ideas of Ya. B. Zeldovich, concerning the formation of strongly non-spherical structures during nonlinear stages of the development of gravitational instability, known as `Zeldovich's pancakes'. In this paper the collapse of non-collisional dark matter and the formation of pancake structures are investigated approximately. Violent relaxation, mass and angular momentum losses are taken into account phenomenologically. We estimate an emission of very long gravitational waves during the collapse, and discuss the possibility of gravitational lensing and polarization of the cosmic microwave background by these waves.

  16. The dynamics of domain walls and strings

    NASA Technical Reports Server (NTRS)

    Gregory, Ruth; Haws, David; Garfinkle, David

    1989-01-01

    The leading order finite-width corrections to the equation of motion describing the motion of a domain wall are derived. The regime in which this equation of motion is invalid is discussed. Spherically and cylindrically symmetric solutions to this equation of motion are found. A misconception that has arisen in recent years regarding the rigidity (or otherwise) of cosmic strings is also clarified.

  17. Hawking radiation from a Reissner-Nordstroem black hole with a global monopole via covariant anomalies and effective action

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Gangopadhyay, Sunandan

    2008-08-15

    We adopt the covariant anomaly cancellation method as well as the effective action approach to obtain the Hawking radiation from the Reissner-Nordstroem blackhole with a global monopole falling in the class of the most general spherically symmetric charged blackhole ({radical}(-g){ne}1), using only covariant boundary conditions at the event horizon.

  18. Static and Dynamic Traversable Wormholes

    NASA Astrophysics Data System (ADS)

    Adamiak, Jaroslaw P.

    2008-09-01

    The aim of this work is to discuss the effects found in static and dynamic wormholes that occur as a solution of Einstein equations in general relativity. The ground is prepared by presentation of faster than light effects, then the focus is narrowed to Morris-Thorne framework for a static spherically symmetric wormhole. Two types of dynamic worm-holes, evolving and rotating, are considered.

  19. Fate of inhomogeneity in Schwarzschild-deSitter space-time

    NASA Astrophysics Data System (ADS)

    Nambu, Yasusada

    1994-03-01

    We investigate the global structure of the space-time with a spherically symmetric inhomogeneity using a metric junction, and classify all possible types. We found that a motion with a negative gravitational mass is possible although the energy condition of the matter is not violated. Using the result, formation of black hole and worm hole during the inflationary era is discussed.

  20. Noncontractible hyperloops in gauge models with Higgs fields in the fundamental representation

    NASA Astrophysics Data System (ADS)

    Burzlaff, Jürgen

    1984-11-01

    We study finite-energy configurations in SO( N) gauge theories with Higgs fields in the fundamental representation. For all winding numbers, noncontractible hyperloops are constructed. The corresponding energy density is spherically symmetric, and the configuration with maximal energy on each hyperloop can be determined. Noncontractible hyperloops with an arbitrary winding number for SU(2) gauge theory are also given.

  1. Quantum Entanglement in Optical Lattice Systems

    DTIC Science & Technology

    2015-02-18

    Zitterbewegung oscillation was first predicted by Schroedinger in 1930 for relativistic Dirac electrons where it arises from the interference...magnetic gradient. The gradient affected the Rabi cycling rate, leading to a phase winding along the long axis of the cigar -shaped BEC. While the single...approach is applicable to spherically symmetric, strictly two- dimensional, strictly one-dimensional, cigar -shaped, and pancake-shaped traps and has

  2. Acceleration of a Static Observer Near the Event Horizon of a Static Isolated Black Hole.

    ERIC Educational Resources Information Center

    Doughty, Noel A.

    1981-01-01

    Compares the magnitude of the proper acceleration of a static observer in a static, isolated, spherically symmetric space-time region with the Newtonian result including the situation in the interior of a perfect-fluid star. This provides a simple physical interpretation of surface gravity and illustrates the global nature of the event horizon.…

  3. Spherically symmetric Einstein-aether perfect fluid models

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Coley, Alan A.; Latta, Joey; Leon, Genly

    We investigate spherically symmetric cosmological models in Einstein-aether theory with a tilted (non-comoving) perfect fluid source. We use a 1+3 frame formalism and adopt the comoving aether gauge to derive the evolution equations, which form a well-posed system of first order partial differential equations in two variables. We then introduce normalized variables. The formalism is particularly well-suited for numerical computations and the study of the qualitative properties of the models, which are also solutions of Horava gravity. We study the local stability of the equilibrium points of the resulting dynamical system corresponding to physically realistic inhomogeneous cosmological models and astrophysicalmore » objects with values for the parameters which are consistent with current constraints. In particular, we consider dust models in (β−) normalized variables and derive a reduced (closed) evolution system and we obtain the general evolution equations for the spatially homogeneous Kantowski-Sachs models using appropriate bounded normalized variables. We then analyse these models, with special emphasis on the future asymptotic behaviour for different values of the parameters. Finally, we investigate static models for a mixture of a (necessarily non-tilted) perfect fluid with a barotropic equations of state and a scalar field.« less

  4. No regularity singularities exist at points of general relativistic shock wave interaction between shocks from different characteristic families.

    PubMed

    Reintjes, Moritz; Temple, Blake

    2015-05-08

    We give a constructive proof that coordinate transformations exist which raise the regularity of the gravitational metric tensor from C 0,1 to C 1,1 in a neighbourhood of points of shock wave collision in general relativity. The proof applies to collisions between shock waves coming from different characteristic families, in spherically symmetric spacetimes. Our result here implies that spacetime is locally inertial and corrects an error in our earlier Proc. R. Soc. A publication, which led us to the false conclusion that such coordinate transformations, which smooth the metric to C 1,1 , cannot exist. Thus, our result implies that regularity singularities (a type of mild singularity introduced in our Proc. R. Soc. A paper) do not exist at points of interacting shock waves from different families in spherically symmetric spacetimes. Our result generalizes Israel's celebrated 1966 paper to the case of such shock wave interactions but our proof strategy differs fundamentally from that used by Israel and is an extension of the strategy outlined in our original Proc. R. Soc. A publication. Whether regularity singularities exist in more complicated shock wave solutions of the Einstein-Euler equations remains open.

  5. No regularity singularities exist at points of general relativistic shock wave interaction between shocks from different characteristic families

    PubMed Central

    Reintjes, Moritz; Temple, Blake

    2015-01-01

    We give a constructive proof that coordinate transformations exist which raise the regularity of the gravitational metric tensor from C0,1 to C1,1 in a neighbourhood of points of shock wave collision in general relativity. The proof applies to collisions between shock waves coming from different characteristic families, in spherically symmetric spacetimes. Our result here implies that spacetime is locally inertial and corrects an error in our earlier Proc. R. Soc. A publication, which led us to the false conclusion that such coordinate transformations, which smooth the metric to C1,1, cannot exist. Thus, our result implies that regularity singularities (a type of mild singularity introduced in our Proc. R. Soc. A paper) do not exist at points of interacting shock waves from different families in spherically symmetric spacetimes. Our result generalizes Israel's celebrated 1966 paper to the case of such shock wave interactions but our proof strategy differs fundamentally from that used by Israel and is an extension of the strategy outlined in our original Proc. R. Soc. A publication. Whether regularity singularities exist in more complicated shock wave solutions of the Einstein–Euler equations remains open. PMID:27547092

  6. Science Support for Space-Based Droplet Combustion: Drop Tower Experiments and Detailed Numerical Modeling

    NASA Technical Reports Server (NTRS)

    Marchese, Anthony J.; Dryer, Frederick L.

    1997-01-01

    This program supports the engineering design, data analysis, and data interpretation requirements for the study of initially single component, spherically symmetric, isolated droplet combustion studies. Experimental emphasis is on the study of simple alcohols (methanol, ethanol) and alkanes (n-heptane, n-decane) as fuels with time dependent measurements of drop size, flame-stand-off, liquid-phase composition, and finally, extinction. Experiments have included bench-scale studies at Princeton, studies in the 2.2 and 5.18 drop towers at NASA-LeRC, and both the Fiber Supported Droplet Combustion (FSDC-1, FSDC-2) and the free Droplet Combustion Experiment (DCE) studies aboard the shuttle. Test matrix and data interpretation are performed through spherically-symmetric, time-dependent numerical computations which embody detailed sub-models for physical and chemical processes. The computed burning rate, flame stand-off, and extinction diameter are compared with the respective measurements for each individual experiment. In particular, the data from FSDC-1 and subsequent space-based experiments provide the opportunity to compare all three types of data simultaneously with the computed parameters. Recent numerical efforts are extending the computational tools to consider time dependent, axisymmetric 2-dimensional reactive flow situations.

  7. Distorting general relativity: gravity's rainbow and f(R) theories at work

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Garattini, Remo, E-mail: Remo.Garattini@unibg.it

    2013-06-01

    We compute the Zero Point Energy in a spherically symmetric background combining the high energy distortion of Gravity's Rainbow with the modification induced by a f(R) theory. Here f(R) is a generic analytic function of the Ricci curvature scalar R in 4D and in 3D. The explicit calculation is performed for a Schwarzschild metric. Due to the spherically symmetric property of the Schwarzschild metric we can compare the effects of the modification induced by a f(R) theory in 4D and in 3D. We find that the final effect of the combined theory is to have finite quantities that shift themore » Zero Point Energy. In this context we setup a Sturm-Liouville problem with the cosmological constant considered as the associated eigenvalue. The eigenvalue equation is a reformulation of the Wheeler-DeWitt equation which is analyzed by means of a variational approach based on gaussian trial functionals. With the help of a canonical decomposition, we find that the relevant contribution to one loop is given by the graviton quantum fluctuations around the given background. A final discussion on the connection of our result with the observed cosmological constant is also reported.« less

  8. Quasinormal modes, bifurcations, and nonuniqueness of charged scalar-tensor black holes

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Doneva, Daniela D.; Theoretical Astrophysics, Eberhard-Karls University of Tuebingen, Tuebingen 72076; Yazadjiev, Stoytcho S.

    In the present paper, we study the scalar sector of the quasinormal modes of charged general relativistic, static, and spherically symmetric black holes coupled to nonlinear electrodynamics and embedded in a class of scalar-tensor theories. We find that for a certain domain of the parametric space, there exists unstable quasinormal modes. The presence of instabilities implies the existence of scalar-tensor black holes with primary hair that bifurcate from the embedded general relativistic black-hole solutions at critical values of the parameters corresponding to the static zero modes. We prove that such scalar-tensor black holes really exist by solving the full systemmore » of scalar-tensor field equations for the static, spherically symmetric case. The obtained solutions for the hairy black holes are nonunique, and they are in one-to-one correspondence with the bounded states of the potential governing the linear perturbations of the scalar field. The stability of the nonunique hairy black holes is also examined, and we find that the solutions for which the scalar field has zeros are unstable against radial perturbations. The paper ends with a discussion of possible formulations of a new classification conjecture.« less

  9. Weak-field limit of Kaluza-Klein models with spherically symmetric static scalar field: observational constraints

    NASA Astrophysics Data System (ADS)

    Zhuk, Alexander; Chopovsky, Alexey; Fakhr, Seyed Hossein; Shulga, Valerii; Wei, Han

    2017-11-01

    In a multidimensional Kaluza-Klein model with Ricci-flat internal space, we study the gravitational field in the weak-field limit. This field is created by two coupled sources. First, this is a point-like massive body which has a dust-like equation of state in the external space and an arbitrary parameter Ω of equation of state in the internal space. The second source is a static spherically symmetric massive scalar field centered at the origin where the point-like massive body is. The found perturbed metric coefficients are used to calculate the parameterized post-Newtonian (PPN) parameter γ . We define under which conditions γ can be very close to unity in accordance with the relativistic gravitational tests in the solar system. This can take place for both massive or massless scalar fields. For example, to have γ ≈ 1 in the solar system, the mass of scalar field should be μ ≳ 5.05× 10^{-49}g ˜ 2.83× 10^{-16}eV. In all cases, we arrive at the same conclusion that to be in agreement with the relativistic gravitational tests, the gravitating mass should have tension: Ω = - 1/2.

  10. Existence and stability of circular orbits in general static and spherically symmetric spacetimes

    NASA Astrophysics Data System (ADS)

    Jia, Junji; Liu, Jiawei; Liu, Xionghui; Mo, Zhongyou; Pang, Xiankai; Wang, Yaoguang; Yang, Nan

    2018-02-01

    The existence and stability of circular orbits (CO) in static and spherically symmetric (SSS) spacetime are important because of their practical and potential usefulness. In this paper, using the fixed point method, we first prove a necessary and sufficient condition on the metric function for the existence of timelike COs in SSS spacetimes. After analyzing the asymptotic behavior of the metric, we then show that asymptotic flat SSS spacetime that corresponds to a negative Newtonian potential at large r will always allow the existence of CO. The stability of the CO in a general SSS spacetime is then studied using the Lyapunov exponent method. Two sufficient conditions on the (in)stability of the COs are obtained. For null geodesics, a sufficient condition on the metric function for the (in)stability of null CO is also obtained. We then illustrate one powerful application of these results by showing that three SSS spacetimes whose metric function is not completely known will allow the existence of timelike and/or null COs. We also used our results to assert the existence and (in)stabilities of a number of known SSS metrics.

  11. Wormholes minimally violating the null energy condition

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Bouhmadi-López, Mariam; Lobo, Francisco S N; Martín-Moruno, Prado, E-mail: mariam.bouhmadi@ehu.es, E-mail: fslobo@fc.ul.pt, E-mail: pmmoruno@fc.ul.pt

    2014-11-01

    We consider novel wormhole solutions supported by a matter content that minimally violates the null energy condition. More specifically, we consider an equation of state in which the sum of the energy density and radial pressure is proportional to a constant with a value smaller than that of the inverse area characterising the system, i.e., the area of the wormhole mouth. This approach is motivated by a recently proposed cosmological event, denoted {sup t}he little sibling of the big rip{sup ,} where the Hubble rate and the scale factor blow up but the cosmic derivative of the Hubble rate doesmore » not [1]. By using the cut-and-paste approach, we match interior spherically symmetric wormhole solutions to an exterior Schwarzschild geometry, and analyse the stability of the thin-shell to linearized spherically symmetric perturbations around static solutions, by choosing suitable properties for the exotic material residing on the junction interface radius. Furthermore, we also consider an inhomogeneous generalization of the equation of state considered above and analyse the respective stability regions. In particular, we obtain a specific wormhole solution with an asymptotic behaviour corresponding to a global monopole.« less

  12. Quintic quasi-topological gravity

    NASA Astrophysics Data System (ADS)

    Cisterna, Adolfo; Guajardo, Luis; Hassaïne, Mokhtar; Oliva, Julio

    2017-04-01

    We construct a quintic quasi-topological gravity in five dimensions, i.e. a theory with a Lagrangian containing {\\mathcal{R}}^5 terms and whose field equations are of second order on spherically (hyperbolic or planar) symmetric spacetimes. These theories have recently received attention since when formulated on asymptotically AdS spacetimes might provide for gravity duals of a broad class of CFTs. For simplicity we focus on five dimensions. We show that this theory fulfils a Birkhoff's Theorem as it is the case in Lovelock gravity and therefore, for generic values of the couplings, there is no s-wave propagating mode. We prove that the spherically symmetric solution is determined by a quintic algebraic polynomial equation which resembles Wheeler's polynomial of Lovelock gravity. For the black hole solutions we compute the temperature, mass and entropy and show that the first law of black holes thermodynamics is fulfilled. Besides of being of fourth order in general, we show that the field equations, when linearized around AdS are of second order, and therefore the theory does not propagate ghosts around this background. Besides the class of theories originally introduced in arXiv:1003.4773, the general geometric structure of these Lagrangians remains an open problem.

  13. The correlation function for density perturbations in an expanding universe. I - Linear theory

    NASA Technical Reports Server (NTRS)

    Mcclelland, J.; Silk, J.

    1977-01-01

    The evolution of the two-point correlation function for adiabatic density perturbations in the early universe is studied. Analytical solutions are obtained for the evolution of linearized spherically symmetric adiabatic density perturbations and the two-point correlation function for these perturbations in the radiation-dominated portion of the early universe. The results are then extended to the regime after decoupling. It is found that: (1) adiabatic spherically symmetric perturbations comparable in scale with the maximum Jeans length would survive the radiation-dominated regime; (2) irregular fluctuations are smoothed out up to the scale of the maximum Jeans length in the radiation era, but regular fluctuations might survive on smaller scales; (3) in general, the only surviving structures for irregularly shaped adiabatic density perturbations of arbitrary but finite scale in the radiation regime are the size of or larger than the maximum Jeans length in that regime; (4) infinite plane waves with a wavelength smaller than the maximum Jeans length but larger than the critical dissipative damping scale could survive the radiation regime; and (5) black holes would also survive the radiation regime and might accrete sufficient mass after decoupling to nucleate the formation of galaxies.

  14. Combustion of two-component miscible droplets in reduced gravity

    NASA Technical Reports Server (NTRS)

    Shaw, Benjamin D.; Aharon, Israel; Gage, James W.; Jenkins, Andrew J.; Kahoe, Thomas J.

    1995-01-01

    This research focuses on the combustion of binary miscible droplets initially in the mm size range. Experiments are performed using the NASA Lewis 2.2 sec drop tower in Cleveland, Ohio, where mixtures of alkanes and/or alcohols are studied. The fuel components are selected to have significantly different volatilities. Initial oxygen mole fractions from about 0.15-0.5 and initial pressures from 0.2-2 atm are employed. Different inerts are used (He, CO2, Ar, N2) to change burning rates and sooting behaviors. Objectives are to observe the following: (1) Transient droplet diameters (including three-staged combustion behaviors and microexplosion; (2) Transient flow behaviors (sudden flame contraction, luminosity, extinction); and (3) Behaviors of observable soot particles. theoretical and computational research in support of this program has also been undertaken. This research includes analytical studies to determine the effects of small but nonzero gravitational levels on droplet gasification, analytical studies of hydrodynamic stability of spherically-symmetrical droplet gasification (to address the question as to whether spherically-symmetrical droplet gasification may be destabilized from capillary, i.e., Marangoni effects), and computational modeling of effects of capillary stresses on droplet gasification.

  15. New definition of complexity for self-gravitating fluid distributions: The spherically symmetric, static case

    NASA Astrophysics Data System (ADS)

    Herrera, L.

    2018-02-01

    We put forward a new definition of complexity, for static and spherically symmetric self-gravitating systems, based on a quantity, hereafter referred to as complexity factor, that appears in the orthogonal splitting of the Riemann tensor, in the context of general relativity. We start by assuming that the homogeneous (in the energy density) fluid, with isotropic pressure is endowed with minimal complexity. For this kind of fluid distribution, the value of complexity factor is zero. So, the rationale behind our proposal for the definition of complexity factor stems from the fact that it measures the departure, in the value of the active gravitational mass (Tolman mass), with respect to its value for a zero complexity system. Such departure is produced by a specific combination of energy density inhomogeneity and pressure anisotropy. Thus, zero complexity factor may also be found in self-gravitating systems with inhomogeneous energy density and anisotropic pressure, provided the effects of these two factors, on the complexity factor, cancel each other. Some exact interior solutions to the Einstein equations satisfying the zero complexity criterium are found, and prospective applications of this newly defined concept, to the study of the structure and evolution of compact objects, are discussed.

  16. Bending of Light in Modified Gravity at Large Distances

    NASA Technical Reports Server (NTRS)

    Sultana, Joseph; Kazanas, Demosthenes

    2012-01-01

    We discuss the bending of light in a recent model for gravity at large distances containing a Rindler type acceleration proposed by Grumiller. We consider the static, spherically symmetric metric with cosmological constant and Rindler-like term 2ar presented in this model, and we use the procedure by Rindler and Ishak. to obtain the bending angle of light in this metric. Earlier work on light bending in this model by Carloni, Grumiller, and Preis, using the method normally employed for asymptotically flat space-times, led to a conflicting result (caused by the Rindler-like term in the metric) of a bending angle that increases with the distance of closest approach r(sub 0) of the light ray from the centrally concentrated spherically symmetric matter distribution. However, when using the alternative approach for light bending in nonasymptotically flat space-times, we show that the linear Rindler-like term produces a small correction to the general relativistic result that is inversely proportional to r(sub 0). This will in turn affect the bounds on Rindler acceleration obtained earlier from light bending and casts doubts on the nature of the linear term 2ar in the metric

  17. On the Effective Thermal Conductivity of Porous Packed Beds with Uniform Spherical Particles

    NASA Technical Reports Server (NTRS)

    Kandula, Max

    2010-01-01

    Point contact models for the effective thermal conductivity of porous media with uniform spherical inclusions have been briefly reviewed. The model of Zehner and Schlunder (1970) has been further validated with recent experimental data over a broad range of conductivity ratio from 8 to 1200 and over a range of solids fraction up to about 0.8. The comparisons further confirm the validity of Zehner-Schlunder model, known to be applicable for conductivity ratios less than about 2000, above which area contact between the particles becomes significant. This validation of the Zehner-Schlunder model has implications for its use in the prediction of the effective thermal conductivity of water frost (with conductivity ratio around 100) which arises in many important areas of technology.

  18. Porous poly-ether ether ketone (PEEK) manufactured by a novel powder route using near-spherical salt bead porogens: characterisation and mechanical properties.

    PubMed

    Siddiq, Abdur R; Kennedy, Andrew R

    2015-02-01

    Porous PEEK structures with approximately 85% open porosity have been made using PEEK-OPTIMA® powder and a particulate leaching technique using porous, near-spherical, sodium chloride beads. A novel manufacturing approach is presented and compared with a traditional dry mixing method. Irrespective of the method used, the use of near-spherical beads with a fairly narrow size range results in uniform pore structures. However the integration, by tapping, of fine PEEK into a pre-existing network salt beads, followed by compaction and "sintering", produces porous structures with excellent repeatability and homogeneity of density; more uniform pore and strut sizes; an improved and predictable level of connectivity via the formation of "windows" between the cells; faster salt removal rates and lower levels of residual salt. Although tapped samples show a compressive yield stress >1 MPa and stiffness >30 MPa for samples with 84% porosity, the presence of windows in the cell walls means that tapped structures show lower strengths and lower stiffnesses than equivalent structures made by mixing. Copyright © 2014 Elsevier B.V. All rights reserved.

  19. On the determination of the electromagnetic field upon scattering by a small inhomogeneous spherical object

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Shalashov, A. G., E-mail: ags@appl.sci-nnov.ru; Gospodchikov, E. D.

    An efficient and fairly simple method of solving the problem of the incidence of a plane electromagnetic wave on an inhomogeneous object with specified spherically symmetric distributions of its electric permittivity and magnetic permeability is presented. The fields inside the object and the integrated scattering and absorption cross sections are found by assuming the object to be small compared to the vacuum wavelength. Since no constraints are imposed on the scales of the fields inside the object, the method is suitable for investigating complex cases, including those associated with the local amplification and absorption of the electromagnetic field in inhomogeneousmore » resonant media.« less

  20. Photoacoustic Effect Generated from an Expanding Spherical Source

    NASA Astrophysics Data System (ADS)

    Bai, Wenyu; Diebold, Gerald J.

    2018-02-01

    Although the photoacoustic effect is typically generated by amplitude-modulated continuous or pulsed radiation, the form of the wave equation for pressure that governs the generation of sound indicates that optical sources moving in an absorbing fluid can produce sound as well. Here, the characteristics of the acoustic wave produced by a radially symmetric Gaussian source expanding outwardly from the origin are found. The unique feature of the photoacoustic effect from the spherical source is a trailing compressive wave that arises from reflection of an inwardly propagating component of the wave. Similar to the one-dimensional geometry, an unbounded amplification effect is found for the Gaussian source expanding at the sound speed.

  1. Effects of particle packing on the sintered microstructure

    NASA Astrophysics Data System (ADS)

    Barringer, E. A.; Bowen, H. K.

    1988-04-01

    The sintering process is shown to be critically dependent on particle-packing density and porosity uniformity. Sintering experiments were conducted on compacts consisting of monodisperse, spherical TiO2 particles. Densification kinetics and microstructure evolution for two initial packing densities, 55% and 69% of theoretical, were investigated. The lower-density compacts sintered rapidly to theoretical density, yet improved particle-packing density and uniformity significantly enhanced densification.

  2. Region Spherical Harmonic Magnetic Modeling from Near-Surface and Satellite-Altitude Anomlaies

    NASA Technical Reports Server (NTRS)

    Kim, Hyung Rae; von Frese, Ralph R. B.; Taylor, Patrick T.

    2013-01-01

    The compiled near-surface data and satellite crustal magnetic measured data are modeled with a regionally concentrated spherical harmonic presentation technique over Australia and Antarctica. Global crustal magnetic anomaly studies have used a spherical harmonic analysis to represent the Earth's magnetic crustal field. This global approach, however is best applied where the data are uniformly distributed over the entire Earth. Satellite observations generally meet this requirement, but unequally distributed data cannot be easily adapted in global modeling. Even for the satellite observations, due to the errors spread over the globe, data smoothing is inevitable in the global spherical harmonic presentations. In addition, global high-resolution modeling requires a great number of global spherical harmonic coefficients for the regional presentation of crustal magnetic anomalies, whereas a lesser number of localized spherical coefficients will satisfy. We compared methods in both global and regional approaches and for a case where the errors were propagated outside the region of interest. For observations from the upcoming Swarm constellation, the regional modeling will allow the production a lesser number of spherical coefficients that are relevant to the region of interest

  3. Spherical cows in dark matter indirect detection

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Bernal, Nicolás; Necib, Lina; Slatyer, Tracy R., E-mail: nicolas.bernal@uan.edu.co, E-mail: lnecib@mit.edu, E-mail: tslatyer@mit.edu

    2016-12-01

    Dark matter (DM) halos have long been known to be triaxial, but in studies of possible annihilation and decay signals they are often treated as approximately spherical. In this work, we examine the asymmetry of potential indirect detection signals of DM annihilation and decay, exploiting the large statistics of the hydrodynamic simulation Illustris. We carefully investigate the effects of the baryons on the sphericity of annihilation and decay signals for both the case where the observer is at 8.5 kpc from the center of the halo (exemplified in the case of Milky Way-like halos), and for an observer situated wellmore » outside the halo. In the case of Galactic signals, we find that both annihilation and decay signals are expected to be quite symmetric, with axis ratios very different from 1 occurring rarely. In the case of extragalactic signals, while decay signals are still preferentially spherical, the axis ratio for annihilation signals has a much flatter distribution, with elongated profiles appearing frequently. Many of these elongated profiles are due to large subhalos and/or recent mergers. Comparing to gamma-ray emission from the Milky Way and X-ray maps of clusters, we find that the gamma-ray background appears less spherical/more elongated than the expected DM signal from the large majority of halos, and the Galactic gamma ray excess appears very spherical, while the X-ray data would be difficult to distinguish from a DM signal by elongation/sphericity measurements alone.« less

  4. Spherical cows in dark matter indirect detection

    NASA Astrophysics Data System (ADS)

    Bernal, Nicolás; Necib, Lina; Slatyer, Tracy R.

    2016-12-01

    Dark matter (DM) halos have long been known to be triaxial, but in studies of possible annihilation and decay signals they are often treated as approximately spherical. In this work, we examine the asymmetry of potential indirect detection signals of DM annihilation and decay, exploiting the large statistics of the hydrodynamic simulation Illustris. We carefully investigate the effects of the baryons on the sphericity of annihilation and decay signals for both the case where the observer is at 8.5 kpc from the center of the halo (exemplified in the case of Milky Way-like halos), and for an observer situated well outside the halo. In the case of Galactic signals, we find that both annihilation and decay signals are expected to be quite symmetric, with axis ratios very different from 1 occurring rarely. In the case of extragalactic signals, while decay signals are still preferentially spherical, the axis ratio for annihilation signals has a much flatter distribution, with elongated profiles appearing frequently. Many of these elongated profiles are due to large subhalos and/or recent mergers. Comparing to gamma-ray emission from the Milky Way and X-ray maps of clusters, we find that the gamma-ray background appears less spherical/more elongated than the expected DM signal from the large majority of halos, and the Galactic gamma ray excess appears very spherical, while the X-ray data would be difficult to distinguish from a DM signal by elongation/sphericity measurements alone.

  5. Systematic analysis of hot Yb* isotopes using the energy density formalism

    NASA Astrophysics Data System (ADS)

    Jain, Deepika; Sharma, Manoj K.; Rajni; Kumar, Raj; Gupta, Raj K.

    2014-10-01

    A systematic study of the spin-orbit density interaction potential is carried out, with spherical as well as deformed choices of nuclei, for a variety of near-symmetric and asymmetric colliding nuclei leading to various isotopes of the compound nucleus Yb*, using the semiclassical extended Thomas-Fermi formulation (ETF) of the Skyrme energy density formalism (SEDF). We observe that the spin-orbit density interaction barrier height ( and barrier position ( increase systematically with the increase in number of neutrons in both the projectile and target, for spherical systems. On allowing deformation effects with optimum orientations, the barrier-height increases by a large order of magnitude, as compared to the spherical case, in going from 156Yb* to 172Yb* nuclear systems formed via near-symmetric Ni+Mo or asymmetric O+Sm colliding nuclei, except that for the oblate-shaped nuclei, the is the highest and shifts towards a smaller (compact) interaction radius. The temperature does not change the behavior of spin-orbit density dependent ( and independent ( interaction potentials, except for some minor changes in the magnitude. The orientation degree of freedom also plays an important role in modifying the barrier characteristics and hence produces a large effect on the fusion cross section. The fusion excitation function of the compound nuclei 160, 164Yb* formed in different incoming channels, show clearly that the new forces GSkI and KDE0v1 respond better than the old SIII force. Among the first two, KDE0v1 seems to perform better. The fusion cross-sections are also predicted for a few other isotopes of Yb*.

  6. A Noise Removal Method for Uniform Circular Arrays in Complex Underwater Noise Environments with Low SNR

    PubMed Central

    Xia, Huijun; Yang, Kunde; Ma, Yuanliang; Wang, Yong; Liu, Yaxiong

    2017-01-01

    Generally, many beamforming methods are derived under the assumption of white noise. In practice, the actual underwater ambient noise is complex. As a result, the noise removal capacity of the beamforming method may be deteriorated considerably. Furthermore, in underwater environment with extremely low signal-to-noise ratio (SNR), the performances of the beamforming method may be deteriorated. To tackle these problems, a noise removal method for uniform circular array (UCA) is proposed to remove the received noise and improve the SNR in complex noise environments with low SNR. First, the symmetrical noise sources are defined and the spatial correlation of the symmetrical noise sources is calculated. Then, based on the preceding results, the noise covariance matrix is decomposed into symmetrical and asymmetrical components. Analysis indicates that the symmetrical component only affect the real part of the noise covariance matrix. Consequently, the delay-and-sum (DAS) beamforming is performed by using the imaginary part of the covariance matrix to remove the symmetrical component. However, the noise removal method causes two problems. First, the proposed method produces a false target. Second, the proposed method would seriously suppress the signal when it is located in some directions. To solve the first problem, two methods to reconstruct the signal covariance matrix are presented: based on the estimation of signal variance and based on the constrained optimization algorithm. To solve the second problem, we can design the array configuration and select the suitable working frequency. Theoretical analysis and experimental results are included to demonstrate that the proposed methods are particularly effective in complex noise environments with low SNR. The proposed method can be extended to any array. PMID:28598386

  7. Radiative Heat Loss Measurements During Microgravity Droplet Combustion in a Slow Convective Flow

    NASA Technical Reports Server (NTRS)

    Hicks, Michael C.; Kaib, Nathan; Easton, John; Nayagam, Vedha; Williams, Forman A.

    2003-01-01

    Radiative heat loss from burning droplets in a slow convective flow under microgravity conditions is measured using a broad-band (0.6 to 40 microns) radiometer. In addition, backlit images of the droplet as well as color images of the flame were obtained using CCD cameras to estimate the burning rates and the flame dimensions, respectively. Tests were carried out in air at atmospheric pressure using n-heptane and methanol fuels with imposed forced flow velocities varied from 0 to 10 centimeters per second and initial droplet diameters varied from 1 to 3 millimeters. Slow convective flows were generated using three different experimental configurations in three different facilities in preparation for the proposed International Space Station droplet experiments. In the 2.2 Second Drop-Tower Facility a droplet supported on the leading edge of a quartz fiber is placed within a flow tunnel supplied by compressed air. In the Zero-Gravity Facility (five-second drop tower) a tethered droplet is translated in a quiescent ambient atmosphere to establish a uniform flow field around the droplet. In the KC 135 aircraft an electric fan was used to draw a uniform flow past a tethered droplet. Experimental results show that the burn rate increases and the overall flame size decreases with increases in forced-flow velocities over the range of flow velocities and droplet sizes tested. The total radiative heat loss rate, Q(sub r), decreases as the imposed flow velocity increases with the spherically symmetric combustion having the highest values. These observations are in contrast to the trends observed for gas-jet flames in microgravity, but consistent with the observations during flame spread over solid fuels where the burning rate is coupled to the forced flow as here.

  8. Sound Source Localization Using Non-Conformal Surface Sound Field Transformation Based on Spherical Harmonic Wave Decomposition

    PubMed Central

    Zhang, Lanyue; Ding, Dandan; Yang, Desen; Wang, Jia; Shi, Jie

    2017-01-01

    Spherical microphone arrays have been paid increasing attention for their ability to locate a sound source with arbitrary incident angle in three-dimensional space. Low-frequency sound sources are usually located by using spherical near-field acoustic holography. The reconstruction surface and holography surface are conformal surfaces in the conventional sound field transformation based on generalized Fourier transform. When the sound source is on the cylindrical surface, it is difficult to locate by using spherical surface conformal transform. The non-conformal sound field transformation by making a transfer matrix based on spherical harmonic wave decomposition is proposed in this paper, which can achieve the transformation of a spherical surface into a cylindrical surface by using spherical array data. The theoretical expressions of the proposed method are deduced, and the performance of the method is simulated. Moreover, the experiment of sound source localization by using a spherical array with randomly and uniformly distributed elements is carried out. Results show that the non-conformal surface sound field transformation from a spherical surface to a cylindrical surface is realized by using the proposed method. The localization deviation is around 0.01 m, and the resolution is around 0.3 m. The application of the spherical array is extended, and the localization ability of the spherical array is improved. PMID:28489065

  9. Study of modulation property to incident laser by surface micro-defects on KH2PO4 crystal

    NASA Astrophysics Data System (ADS)

    Chen, Ming-Jun; Cheng, Jian; Li, Ming-Quan; Xiao, Yong

    2012-06-01

    KH2PO4 crystal is a crucial optical component of inertial confinement fusion. Modulation of an incident laser by surface micro-defects will induce the growth of surface damage, which largely restricts the enhancement of the laser induced damage threshold. The modulation of an incident laser by using different kinds of surface defects are simulated by employing the three-dimensional finite-difference time-domain method. The results indicate that after the modulation of surface defects, the light intensity distribution inside the crystal is badly distorted, with the light intensity enhanced symmetrically. The relations between modulation properties and defect geometries (e.g., width, morphology, and depth of defects) are quite different for different defects. The modulation action is most obvious when the width of surface defects reaches 1.064 μm. For defects with smooth morphology, such as spherical pits, the degree of modulation is the smallest and the light intensity distribution seems relatively uniform. The degree of modulation increases rapidly with the increase of the depth of surface defects and becomes stable when the depth reaches a critical value. The critical depth is 1.064 μm for cuboid pits and radial cracks, while for ellipsoidal pits the value depends on both the width and the length of the defects.

  10. Observational Appearance and Spectrum of Black-Hole Winds

    NASA Astrophysics Data System (ADS)

    Fukue, Jun; Iino, Eriko

    2010-12-01

    We examine the observational appearance of an optically thick, spherically symmetric, relativistic wind (a black-hole wind), focusing our attention on the emerging spectrum. In a relativistic flow, the apparent optical depth becomes small (large) in the downstream (upstream) direction due to the Lorentz-Fitzgerald contraction. As a result, the location of the apparent photosphere of the wind is remarkably modified, and there appears a relativistic limb-darkening (center-brightening) effect, where the comoving temperature distribution of the apparent photosphere is enhanced (reduced) at the center (in the limb). In addition, due to the usual Doppler boost, the observed temperature distribution is greatly changed. These relativistic effects modify the expected spectrum. When the wind speed is subrelativistic, the observed temperature distribution is almost uniform, and the spectra of the black-hole wind are blackbody-like. When the wind speed becomes relativistic, on the other hand, the observed temperature distribution, Tobs, exhibits a power-law nature of Tobs ∝ r-1, where r is the distance from the disk center, and the observed spectra Sν become a modified blackbody, which has a power-law part of Sν ∝ ν, where ν is the frequency. We briefly examine the effects of the spatial variation of the wind speed and the mass-loss rate.

  11. Hydrodynamical models of cometary H II regions

    NASA Astrophysics Data System (ADS)

    Steggles, H. G.; Hoare, M. G.; Pittard, J. M.

    2017-04-01

    We have modelled the evolution of cometary H II regions produced by zero-age main-sequence stars of O and B spectral types, which are driving strong winds and are born off-centre from spherically symmetric cores with power-law (α = 2) density slopes. A model parameter grid was produced that spans stellar mass, age and core density. Exploring this parameter space, we investigated limb-brightening, a feature commonly seen in cometary H II regions. We found that stars with mass M⋆ ≥ 12 M⊙ produce this feature. Our models have a cavity bounded by a contact discontinuity separating hot shocked wind and ionized ambient gas that is similar in size to the surrounding H II region. Because of early pressure confinement, we did not see shocks outside of the contact discontinuity for stars with M⋆ ≤ 40 M⊙, but the cavities were found to continue to grow. The cavity size in each model plateaus as the H II region stagnates. The spectral energy distributions of our models are similar to those from identical stars evolving in uniform density fields. The turn-over frequency is slightly lower in our power-law models as a result of a higher proportion of low-density gas covered by the H II regions.

  12. Uniform electron gases. III. Low-density gases on three-dimensional spheres.

    PubMed

    Agboola, Davids; Knol, Anneke L; Gill, Peter M W; Loos, Pierre-François

    2015-08-28

    By combining variational Monte Carlo (VMC) and complete-basis-set limit Hartree-Fock (HF) calculations, we have obtained near-exact correlation energies for low-density same-spin electrons on a three-dimensional sphere (3-sphere), i.e., the surface of a four-dimensional ball. In the VMC calculations, we compare the efficacies of two types of one-electron basis functions for these strongly correlated systems and analyze the energy convergence with respect to the quality of the Jastrow factor. The HF calculations employ spherical Gaussian functions (SGFs) which are the curved-space analogs of Cartesian Gaussian functions. At low densities, the electrons become relatively localized into Wigner crystals, and the natural SGF centers are found by solving the Thomson problem (i.e., the minimum-energy arrangement of n point charges) on the 3-sphere for various values of n. We have found 11 special values of n whose Thomson sites are equivalent. Three of these are the vertices of four-dimensional Platonic solids - the hyper-tetrahedron (n = 5), the hyper-octahedron (n = 8), and the 24-cell (n = 24) - and a fourth is a highly symmetric structure (n = 13) which has not previously been reported. By calculating the harmonic frequencies of the electrons around their equilibrium positions, we also find the first-order vibrational corrections to the Thomson energy.

  13. Measuring the Distribution and Excitation of Cometary CH3OH Using ALMA

    NASA Astrophysics Data System (ADS)

    Cordiner, M. A.; Charnley, S. B.; Mumma, M. J.; Bockelée-Morvan, D.; Biver, N.; Villanueva, G.; Paganini, L.; Milam, S. N.; Remijan, A. J.; Lis, D. C.; Crovisier, J.; Boissier, J.; Kuan, Y.-J.; Coulson, I. M.

    2016-10-01

    The Atacama Large Millimeter/submillimeter Array (ALMA) was used to obtain measurements of spatially and spectrally resolved CH3OH emission from comet C/2012 K1 (PanSTARRS) on 28-29 June 2014. Detection of 12-14 emission lines of CH3OH on each day permitted the derivation of spatially-resolved rotational temperature profiles (averaged along the line of sight), for the innermost 5000 km of the coma. On each day, the CH3OH distribution was centrally peaked and approximately consistent with spherically symmetric, uniform outflow. The azimuthally-averaged CH3OH rotational temperature (T rot) as a function of sky-projected nucleocentric distance (ρ), fell by about 40 K between ρ= 0 and 2500 km on 28 June, whereas on 29 June, T rot fell by about 50 K between ρ =0 km and 1500 km. A remarkable (~50 K) rise in T rot at ρ = 1500-2500 km on 29 June was not present on 28 June. The observed variations in CH3OH rotational temperature are interpreted primarily as a result of variations in the coma kinetic temperature due to adiabatic cooling, and heating through Solar irradiation, but collisional and radiative non-LTE excitation processes also play a role.

  14. Solutions to horava gravity.

    PubMed

    Lü, H; Mei, Jianwei; Pope, C N

    2009-08-28

    Recently Horava proposed a nonrelativistic renormalizable theory of gravitation, which reduces to Einstein's general relativity at large distances, and that may provide a candidate for a UV completion of Einstein's theory. In this Letter, we derive the full set of equations of motion, and then we obtain spherically symmetric solutions and discuss their properties. We also obtain solutions for the Friedmann-Lemaître-Robertson-Walker cosmological metric.

  15. Asymptotically flat, stable black hole solutions in Einstein-Yang-Mills-Chern-Simons theory.

    PubMed

    Brihaye, Yves; Radu, Eugen; Tchrakian, D H

    2011-02-18

    We construct finite mass, asymptotically flat black hole solutions in d=5 Einstein-Yang-Mills-Chern-Simons theory. Our results indicate the existence of a second order phase transition between Reissner-Nordström solutions and the non-Abelian black holes which generically are thermodynamically preferred. Some of the non-Abelian configurations are also stable under linear, spherically symmetric perturbations.

  16. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Krasheninnikov, S. I.

    The equations of motion of a dust grain with non-spherical shape in plasma are generalized by incorporating the effects associated with propeller-like features of the grain's shape. For the grain shape close to rotationally symmetric, the stability of “stationary” (in terms of variables used in the grain dynamic equations) solutions are considered. It is found that propeller-like features of the grain's shape can crucially alter stability of such “stationary” states.

  17. The interaction of Dirac particles with non-abelian gauge fields and gravity - bound states

    NASA Astrophysics Data System (ADS)

    Finster, Felix; Smoller, Joel; Yau, Shing-Tung

    2000-09-01

    We consider a spherically symmetric, static system of a Dirac particle interacting with classical gravity and an SU(2) Yang-Mills field. The corresponding Einstein-Dirac-Yang-Mills equations are derived. Using numerical methods, we find different types of soliton-like solutions of these equations and discuss their properties. Some of these solutions are stable even for arbitrarily weak gravitational coupling.

  18. Singularity-free solutions for anisotropic charged fluids with Chaplygin equation of state

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Rahaman, Farook; Ray, Saibal; Jafry, Abdul Kayum

    2010-11-15

    We extend the Krori-Barua analysis of the static, spherically symmetric, Einstein-Maxwell field equations and consider charged fluid sources with anisotropic stresses. The inclusion of a new variable (tangential pressure) allows the use of a nonlinear, Chaplygin-type equation of state with coefficients fixed by the matching conditions at the boundary of the source. Some physical features are briefly discussed.

  19. Equilibium and Stability of Spherical Vlasov Systems

    NASA Astrophysics Data System (ADS)

    Barnes, D. C.; Chacon, L.; Finn, J. M.

    2002-04-01

    Collisionless systems with inverse square interaction potentials and possible background confining potentials are considered for the case of spherical symmetry and in the Vlasov limit. The equilibrium is the most general, with single-particle distribution function dependence on both total energy E and total angular momentum L. A new formulation of the full integral-equation stability problem is developed. For a general spherical harmonic perturbation potential, the 3D stability problem is reduced to a 2D problem in an arbitrary central plane of motion, then to a small number of coupled 1D problems involving only the radius. Normal modes depend only on the total mode number l, as is shown directly by this new formulation, with all m degenerate. This method has been used for the Coulomb (repulsive) case.[1] An equilibrium family with uniform central (electron) density is found, and the low-frequency response computed to show that these solutions may provide stable confinement of a massive second (ion) species. These methods may be applied to a particle bunch in the beam frame, and some stability results appropriate to this case are presented. Application to the gravitational (attractive) case is also described, and some initial analytic results are presented. [1] D. C. Barnes, L. Chacón, J. M. Finn, “Equilibrium and Low-frequency Stability of a Uniform Density, Collisionless, Spherical Vlasov System,” submitted to Phys. of Plasmas (2002).

  20. Effects of beam irregularity on uniform scanning

    NASA Astrophysics Data System (ADS)

    Kim, Chang Hyeuk; Jang, Sea duk; Yang, Tae-Keun

    2016-09-01

    An active scanning beam delivery method has many advantages in particle beam applications. For the beam is to be successfully delivered to the target volume by using the active scanning technique, the dose uniformity must be considered and should be at least 2.5% in the case of therapy application. During beam irradiation, many beam parameters affect the 2-dimensional uniformity at the target layer. A basic assumption in the beam irradiation planning stage is that the shape of the beam is symmetric and follows a Gaussian distribution. In this study, a pure Gaussian-shaped beam distribution was distorted by adding parasitic Gaussian distribution. An appropriate uniform scanning condition was deduced by using a quantitative analysis based on the gamma value of the distorted beam and 2-dimensional uniformities.

  1. YASEIS: Yet Another computer program to calculate synthetic SEISmograms for a spherically multi-layered Earth model

    NASA Astrophysics Data System (ADS)

    Ma, Yanlu

    2013-04-01

    Although most researches focus on the lateral heterogeneity of 3D Earth nowadays, a spherically multi-layered model where the parameters depend only on depth still represents a good first order approximation of real Earth. Such 1D models could be used as starting models for seismic tomographic inversion or as background model where the source mechanisms are inverted. The problem of wave propagation in a spherically layered model had been solved theoretically long time ago (Takeuchi and Saito, 1972). The existing computer programs such as Mineos (developed by G. Master, J. Woodhouse and F. Gilbert), Gemini (Friederich and Dalkolmo 1995), DSM (Kawai et. al. 2006) and QSSP (Wang 1999) tackled the computational aspects of the problem. A new simple and fast program for computing the Green's function of a stack of spherical dissipative layers is presented here. The analytical solutions within each homogeneous spherical layer are joined through the continuous boundary conditions and propagated from the center of model up to the level of source depth. Another solution is built by propagating downwardly from the free surface of model to the source level. The final solution is then constructed in frequency domain from the previous two solutions to satisfy the discontinuities of displacements and stresses at the source level which are required by the focal mechanism. The numerical instability in the propagator approach is solved by complementing the matrix propagating with an orthonormalization procedure (Wang 1999). Another unstable difficulty due to the high attenuation in the upper mantle low velocity zone is overcome by switching the bases of solutions from the spherical Bessel functions to the spherical Hankel functions when necessary. We compared the synthetic seismograms obtained from the new program YASEIS with those computed by Gemini and QSSP. In the range of near distances, the synthetics by a reflectivity code for the horizontally layers are also compared with those from YASEIS. Finally the static displacements in the source region are computed by choosing a very small frequency value in YASEIS which is designed for computing the dynamic response, and compared with the results in a homogeneous half-space model (Okada 1992). [1] Friederich, W. and J. Dalkolmo (1995). Complete synthetic seismograms for a spherically symmetric Earth a numerical computation of the Green's function in the frequency domain, Geophys. J. Int., vol. 122, 537-550. [2] Kawai, K., N. Takeuchi, and R.J. Geller (2006). Complete synthetic seismograms up to 2Hz for transversely isotropic spherically symmetric media, Geophys. J. Int., vol. 164, 411-424. [3] Okada, Y. (1992). Internal deformation due to shear and tensile faults in a half space, Bull. Seismol. Soc. Am., vol. 82, no. 2, 1018-1040. [4] Takeuchi, H. and M. Saito (1972). Seismic surface waves, Methods in computational physics, vol. II, 217-295. [5] Wang, R. (1999). A simple orthonormalization method for stable and efficient computation of Green's functions, Bull. Seismol. Soc. Am., vol. 89, no. 3, 733-741.

  2. Sonochemical synthesis of silica particles and their size control

    NASA Astrophysics Data System (ADS)

    Kim, Hwa-Min; Lee, Chang-Hyun; Kim, Bonghwan

    2016-09-01

    Using an ultrasound-assisted sol-gel method, we successfully synthesized very uniformly shaped, monodisperse, and size-controlled spherical silica particles from a mixture of ethanol, water, and tetraethyl orthosilicate in the presence of ammonia as catalyst, at room temperature. The diameters of the silica particles were distributed in the range from 40 to 400 nm; their morphology was well characterized by scanning electron microscopy. The silica particle size could be adjusted by choosing suitable concentrations of ammonium hydroxide and water, which in turn determined the nucleation and growth rates of the particles during the reaction. This sonochemical-based silica synthesis offers an alternative way to produce spherical silica particles in a relatively short reaction time. Thus, we suggest that this simple, low-cost, and efficient method of preparing uniform silica particles of various sizes will have practical and wide-ranging industrial applicability.

  3. Reconstructing matter profiles of spherically compensated cosmic regions in ΛCDM cosmology

    NASA Astrophysics Data System (ADS)

    de Fromont, Paul; Alimi, Jean-Michel

    2018-02-01

    The absence of a physically motivated model for large-scale profiles of cosmic voids limits our ability to extract valuable cosmological information from their study. In this paper, we address this problem by introducing the spherically compensated cosmic regions, named CoSpheres. Such cosmic regions are identified around local extrema in the density field and admit a unique compensation radius R1 where the internal spherical mass is exactly compensated. Their origin is studied by extending the standard peak model and implementing the compensation condition. Since the compensation radius evolves as the Universe itself, R1(t) ∝ a(t), CoSpheres behave as bubble Universes with fixed comoving volume. Using the spherical collapse model, we reconstruct their profiles with a very high accuracy until z = 0 in N-body simulations. CoSpheres are symmetrically defined and reconstructed for both central maximum (seeding haloes and galaxies) and minimum (identified with cosmic voids). We show that the full non-linear dynamics can be solved analytically around this particular compensation radius, providing useful predictions for cosmology. This formalism highlights original correlations between local extremum and their large-scale cosmic environment. The statistical properties of these spherically compensated cosmic regions and the possibilities to constrain efficiently both cosmology and gravity will be investigated in companion papers.

  4. Theoretical and experimental analysis of the electromechanical behavior of a compact spherical loudspeaker array for directivity control.

    PubMed

    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.

  5. Method for producing solid or hollow spherical particles of chosen chemical composition and of uniform size

    DOEpatents

    Hendricks, Charles D.

    1988-01-01

    A method is provided for producing commercially large quantities of high melting temperature solid or hollow spherical particles of a predetermined chemical composition and having a uniform and controlled size distribution. An end (18, 50, 90) of a solid or hollow rod (20, 48, 88) of the material is rendered molten by a laser beam (14, 44, 82). Because of this, there is no possibility of the molten rod material becoming contaminated with extraneous material. In various aspects of the invention, an electric field is applied to the molten rod end (18, 90), and/or the molten rod end (50, 90) is vibrated. In a further aspect of the invention, a high-frequency component is added to the electric field applied to the molten end of the rod (90). By controlling the internal pressure of the rod, the rate at which the rod is introduced into the laser beam, the environment of the process, the vibration amplitude and frequency of the molten rod end, the electric field intensity applied to the molten rod end, and the frequency and intensity of the component added to the electric field, the uniformity and size distribution of the solid or hollow spherical particles (122) produced by the inventive method is controlled. The polarity of the electric field applied to the molten rod end can be chosen to eliminate backstreaming electrons, which tend to produce run-away heating in the rod, from the process.

  6. Elastic Solutions in a Semi-Infinite Solid with an Ellipsoidal Inclusion

    DTIC Science & Technology

    1990-01-25

    the free surface has been solved for a spherical inclusion with pure dilatational eigenstrain ( stress free transformation strain ) ( Mindlin and Cheng...1950B ), an ellipsoidal inclusion with pure dilatational eigenstrains ( Seo and Mura, 1979 ) and a cuboidal inclusion with uniform eigenstrains ...solution of a half-space under normal surface traction on the full space solution due to a cuboidal inclusion and its image with the uniform eigenstrains

  7. Measurement of the azimuthal dependence of cross-polarized lidar returns and its relation to optical depth.

    PubMed

    Roy, Nathalie; Roy, Gilles; Bissonnette, Luc R; Simard, Jean-Robert

    2004-05-01

    We measure with a gated intensified CCD camera the cross-polarized backscattered light from a linearly polarized laser beam penetrating a cloud made of spherical particles. In accordance with previously published results we observe a clear azimuthal pattern in the recorded images. We show that the pattern is symmetrical, that it originates from second-order scattering, and that higher-order scattering causes blurring that increases with optical depth. We also find that the contrast in the symmetrical features can be related to measurement of the optical depth. Moreover, when the blurring contributions are identified and subtracted, the resulting pattern provides a pure second-order scattering measurement that can be used for retrieval of droplet size.

  8. Generalized quasitopological gravity

    NASA Astrophysics Data System (ADS)

    Hennigar, Robie A.; KubizÅák, David; Mann, Robert B.

    2017-05-01

    We construct the most general, to cubic order in curvature, theory of gravity whose (most general) static spherically symmetric vacuum solutions are fully described by a single field equation. The theory possesses the following remarkable properties: (i) It has a well-defined Einstein gravity limit, (ii) it admits "Schwarzschild-like" solutions characterized by a single metric function, (iii) on maximally symmetric backgrounds it propagates the same degrees of freedom as Einstein's gravity, and (iv) Lovelock and quasitopological gravities, as well as the recently developed Einsteinian cubic gravity [Bueno and Cano Phys. Rev. D 94, 104005 (2016)., 10.1103/PhysRevD.94.104005] in four dimensions, are recovered as special cases. We perform a brief analysis of asymptotically flat black holes in this theory and study their thermodynamics.

  9. Simulation of hydrodynamically interacting particles near a no-slip boundary

    NASA Astrophysics Data System (ADS)

    Swan, James W.; Brady, John F.

    2007-11-01

    The dynamics of spherical particles near a single plane wall are computed using an extension of the Stokesian dynamics method that includes long-range many-body and pairwise lubrication interactions between the spheres and the wall in Stokes flow. Extra care is taken to ensure that the mobility and resistance tensors are symmetric, positive, and definite—something which is ineluctable for particles in low-Reynolds-number flows. We discuss why two previous simulation methods for particles near a plane wall, one using multipole expansions and the other using the Rotne-Prager tensor, fail to produce symmetric resistance and mobility tensors. Additionally, we offer some insight on how the Stokesian dynamics paradigm might be extended to study the dynamics of particles in any confining geometry.

  10. Symmetry breaking, Josephson oscillation and self-trapping in a self-bound three-dimensional quantum ball.

    PubMed

    Adhikari, S K

    2017-11-22

    We study spontaneous symmetry breaking (SSB), Josephson oscillation, and self-trapping in a stable, mobile, three-dimensional matter-wave spherical quantum ball self-bound by attractive two-body and repulsive three-body interactions. The SSB is realized by a parity-symmetric (a) one-dimensional (1D) double-well potential or (b) a 1D Gaussian potential, both along the z axis and no potential along the x and y axes. In the presence of each of these potentials, the symmetric ground state dynamically evolves into a doubly-degenerate SSB ground state. If the SSB ground state in the double well, predominantly located in the first well (z > 0), is given a small displacement, the quantum ball oscillates with a self-trapping in the first well. For a medium displacement one encounters an asymmetric Josephson oscillation. The asymmetric oscillation is a consequence of SSB. The study is performed by a variational and a numerical solution of a non-linear mean-field model with 1D parity-symmetric perturbations.

  11. A computationally tractable version of the collective model

    NASA Astrophysics Data System (ADS)

    Rowe, D. J.

    2004-05-01

    A computationally tractable version of the Bohr-Mottelson collective model is presented which makes it possible to diagonalize realistic collective models and obtain convergent results in relatively small appropriately chosen subspaces of the collective model Hilbert space. Special features of the proposed model are that it makes use of the beta wave functions given analytically by the softened-beta version of the Wilets-Jean model, proposed by Elliott et al., and a simple algorithm for computing SO(5)⊃SO(3) spherical harmonics. The latter has much in common with the methods of Chacon, Moshinsky, and Sharp but is conceptually and computationally simpler. Results are presented for collective models ranging from the spherical vibrator to the Wilets-Jean and axially symmetric rotor-vibrator models.

  12. Tradeoff between insensitivity to depth-induced spherical aberration and resolution of 3D fluorescence imaging due to the use of wavefront encoding with a radially symmetric phase mask

    NASA Astrophysics Data System (ADS)

    Doblas, Ana; Dutta, Ananya; Saavedra, Genaro; Preza, Chrysanthe

    2018-02-01

    Previously, a wavefront encoded (WFE) imaging system implemented using a squared cubic (SQUBIC) phase mask has been verified to reduce the sensitivity of the imaging system to spherical aberration (SA). The strength of the SQUBIC phase mask and, as consequence, the performance of the WFE system are controlled by a design parameter, A. Although the higher the A-value, the more tolerant the WFE system is to SA, this is accomplished at the expense of the effective imaging resolution. In this contribution, we investigate this tradeoff in order to find an optimal A-value to balance the effect of SA and loss of resolution.

  13. Effect of polarization forces on carbon deposition on a non-spherical nanoparticle. Monte Carlo simulations [Effect of polarization forces on atom deposition on a non-spherical nanoparticle. Monte Carlo simulations

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Nemchinsky, V.; Khrabry, A.

    Trajectories of a polarizable species (atoms or molecules) in the vicinity of a negatively charged nanoparticle (at a floating potential) are considered. The atoms are pulled into regions of strong electric field by polarization forces. The polarization increases the deposition rate of the atoms and molecules at the nanoparticle. The effect of the non-spherical shape of the nanoparticle is investigated by the Monte Carlo method. The shape of the non-spherical nanoparticle is approximated by an ellipsoid. The total deposition rate and its flux density distribution along the nanoparticle surface are calculated. As a result, it is shown that the fluxmore » density is not uniform along the surface. It is maximal at the nanoparticle tips.« less

  14. Effect of polarization forces on carbon deposition on a non-spherical nanoparticle. Monte Carlo simulations [Effect of polarization forces on atom deposition on a non-spherical nanoparticle. Monte Carlo simulations

    DOE PAGES

    Nemchinsky, V.; Khrabry, A.

    2018-02-01

    Trajectories of a polarizable species (atoms or molecules) in the vicinity of a negatively charged nanoparticle (at a floating potential) are considered. The atoms are pulled into regions of strong electric field by polarization forces. The polarization increases the deposition rate of the atoms and molecules at the nanoparticle. The effect of the non-spherical shape of the nanoparticle is investigated by the Monte Carlo method. The shape of the non-spherical nanoparticle is approximated by an ellipsoid. The total deposition rate and its flux density distribution along the nanoparticle surface are calculated. As a result, it is shown that the fluxmore » density is not uniform along the surface. It is maximal at the nanoparticle tips.« less

  15. Steady axisymmetric vortex flows with swirl and shear

    NASA Astrophysics Data System (ADS)

    Elcrat, Alan R.; Fornberg, Bengt; Miller, Kenneth G.

    A general procedure is presented for computing axisymmetric swirling vortices which are steady with respect to an inviscid flow that is either uniform at infinity or includes shear. We consider cases both with and without a spherical obstacle. Choices of numerical parameters are given which yield vortex rings with swirl, attached vortices with swirl analogous to spherical vortices found by Moffatt, tubes of vorticity extending to infinity and Beltrami flows. When there is a spherical obstacle we have found multiple solutions for each set of parameters. Flows are found by numerically solving the Bragg-Hawthorne equation using a non-Newton-based iterative procedure which is robust in its dependence on an initial guess.

  16. The PLX- α project: demonstrating the viability of spherically imploding plasma liners as an MIF driver

    NASA Astrophysics Data System (ADS)

    Hsu, S. C.; Witherspoon, F. D.; Cassibry, J. T.; Gilmore, M.; Samulyak, R.; Stoltz, P.; the PLX-α Team

    2015-11-01

    Under ARPA-E's ALPHA program, the Plasma Liner Experiment-ALPHA (PLX- α) project aims to demonstrate the viability and scalability of spherically imploding plasma liners as a standoff, high-implosion-velocity magneto-inertial-fusion (MIF) driver that is potentially compatible with both low- and high- β targets. The project has three major objectives: (a) advancing existing contoured-gap coaxial-gun technology to achieve higher operational reliability/precision and better control/reproducibility of plasma-jet properties and profiles; (2) conducting ~ π / 2 -solid-angle plasma-liner experiments with 9 guns to demonstrate (along with extrapolations from modeling) that the jet-merging process leads to Mach-number degradation and liner uniformity that are acceptable for MIF; and (3) conducting 4 π experiments with up to 60 guns to demonstrate the formation of an imploding spherical plasma liner for the first time, and to provide empirical ram-pressure and uniformity scaling data for benchmarking our codes and informing us whether the scalings justify further development beyond ALPHA. This talk will provide an overview of the PLX- α project as well as key research results to date. Supported by ARPA-E's ALPHA program; original PLX construction supported by DOE Fusion Energy Sciences.

  17. Matrix eigenvalue method for free-oscillations modelling of spherical elastic bodies

    NASA Astrophysics Data System (ADS)

    Zábranová, E.; Hanyk, L.; Matyska, C.

    2017-11-01

    Deformations and changes of the gravitational potential of pre-stressed self-gravitating elastic bodies caused by free oscillations are described by means of the momentum and Poisson equations and the constitutive relation. For spherically symmetric bodies, the equations and boundary conditions are transformed into ordinary differential equations of the second order by the spherical harmonic decomposition and further discretized by highly accurate pseudospectral difference schemes on Chebyshev grids; we pay special attention to the conditions at the centre of the models. We thus obtain a series of matrix eigenvalue problems for eigenfrequencies and eigenfunctions of the free oscillations. Accuracy of the presented numerical approach is tested by means of the Rayleigh quotients calculated for the eigenfrequencies up to 500 mHz. Both the modal frequencies and eigenfunctions are benchmarked against the output from the Mineos software package based on shooting methods. The presented technique is a promising alternative to widely used methods because it is stable and with a good capability up to high frequencies.

  18. Spherical aberration correction in a scanning transmission electron microscope using a sculpted thin film.

    PubMed

    Shiloh, Roy; Remez, Roei; Lu, Peng-Han; Jin, Lei; Lereah, Yossi; Tavabi, Amir H; Dunin-Borkowski, Rafal E; Arie, Ady

    2018-06-01

    Nearly eighty years ago, Scherzer showed that rotationally symmetric, charge-free, static electron lenses are limited by an unavoidable, positive spherical aberration. Following a long struggle, a major breakthrough in the spatial resolution of electron microscopes was reached two decades ago by abandoning the first of these conditions, with the successful development of multipole aberration correctors. Here, we use a refractive silicon nitride thin film to tackle the second of Scherzer's constraints and demonstrate an alternative method for correcting spherical aberration in a scanning transmission electron microscope. We reveal features in Si and Cu samples that cannot be resolved in an uncorrected microscope. Our thin film corrector can be implemented as an immediate low cost upgrade to existing electron microscopes without re-engineering of the electron column or complicated operation protocols and can be extended to the correction of additional aberrations. Copyright © 2018 The Authors. Published by Elsevier B.V. All rights reserved.

  19. Receiving sensitivity and transmitting voltage response of a fluid loaded spherical piezoelectric transducer with an elastic coating.

    PubMed

    George, Jineesh; Ebenezer, D D; Bhattacharyya, S K

    2010-10-01

    A method is presented to determine the response of a spherical acoustic transducer that consists of a fluid-filled piezoelectric sphere with an elastic coating embedded in infinite fluid to electrical and plane-wave acoustic excitations. The exact spherically symmetric, linear, differential, governing equations are used for the interior and exterior fluids, and elastic and piezoelectric materials. Under acoustic excitation and open circuit boundary condition, the equation governing the piezoelectric sphere is homogeneous and the solution is expressed in terms of Bessel functions. Under electrical excitation, the equation governing the piezoelectric sphere is inhomogeneous and the complementary solution is expressed in terms of Bessel functions and the particular integral is expressed in terms of a power series. Numerical results are presented to illustrate the effect of dimensions of the piezoelectric sphere, fluid loading, elastic coating and internal material losses on the open-circuit receiving sensitivity and transmitting voltage response of the transducer.

  20. Probing crustal structures from neutron star compactness

    NASA Astrophysics Data System (ADS)

    Sotani, Hajime; Iida, Kei; Oyamatsu, Kazuhiro

    2017-10-01

    With various sets of the parameters that characterize the equation of state (EOS) of nuclear matter, we systematically examine the thickness of a neutron star crust and of the pasta phases contained therein. Then, with respect to the thickness of the phase of spherical nuclei, the thickness of the cylindrical phase and the crust thickness, we successfully derive fitting formulas that express the ratio of each thickness to the star's radius as a function of the star's compactness, the incompressibility of symmetric nuclear matter and the density dependence of the symmetry energy. In particular, we find that the thickness of the phase of spherical nuclei has such a strong dependence on the stellar compactness as the crust thickness, but both of them show a much weaker dependence on the EOS parameters. Thus, via determination of the compactness, the thickness of the phase of spherical nuclei as well as the crust thickness can be constrained reasonably, even if the EOS parameters remain to be well-determined.

  1. Magnetic Inertial Confinement Fusion (MICF)

    NASA Astrophysics Data System (ADS)

    Miao, Feng; Zheng, Xianjun; Deng, Baiquan; Liu, Wei; Ou, Wei; Huang, Yi

    2016-11-01

    Based on the similarity in models of the early Sun and the 3-D common focal region of the micro-pinch in X-pinch experiments, a novel hybrid fusion configuration by continuous focusing of multiple Z-pinched plasma beams on spatially symmetric plasma is proposed. By replacing gravity with Lorentz force with subsequent centripetal spherical pinch, the beam-target fusion reactivity is enhanced in a quasi-spherical converging region, thus achieving MICF. An assessment, presented here, suggests that a practical fusion power source could be achieved using deuterium alone. Plasma instabilities can be suppressed by fast rotation resulting from an asymmetric tangential torsion in the spherical focal region of this configuration. Mathematical equivalence with the Sun allows the development of appropriate equations for the focal region of MICF, which are solved numerically to provide density, temperature and pressure distributions that produce net fusion energy output. An analysis of MICF physics and a preliminary experimental demonstration of a single beam are also carried out. supported by National Natural Science Foundation of China (Nos. 11374217 and 11176020)

  2. Geometric multiaxial representation of N -qubit mixed symmetric separable states

    NASA Astrophysics Data System (ADS)

    SP, Suma; Sirsi, Swarnamala; Hegde, Subramanya; Bharath, Karthik

    2017-08-01

    The study of N -qubit mixed symmetric separable states is a longstanding challenging problem as no unique separability criterion exists. In this regard, we take up the N -qubit mixed symmetric separable states for a detailed study as these states are of experimental importance and offer an elegant mathematical analysis since the dimension of the Hilbert space is reduced from 2N to N +1 . Since there exists a one-to-one correspondence between the spin-j system and an N -qubit symmetric state, we employ Fano statistical tensor parameters for the parametrization of the spin-density matrix. Further, we use a geometric multiaxial representation (MAR) of the density matrix to characterize the mixed symmetric separable states. Since the separability problem is NP-hard, we choose to study it in the continuum limit where mixed symmetric separable states are characterized by the P -distribution function λ (θ ,ϕ ) . We show that the N -qubit mixed symmetric separable states can be visualized as a uniaxial system if the distribution function is independent of θ and ϕ . We further choose a distribution function to be the most general positive function on a sphere and observe that the statistical tensor parameters characterizing the N -qubit symmetric system are the expansion coefficients of the distribution function. As an example for the discrete case, we investigate the MAR of a uniformly weighted two-qubit mixed symmetric separable state. We also observe that there exists a correspondence between the separability and classicality of states.

  3. A template-free method for stable CuO hollow microspheres fabricated from a metal organic framework (HKUST-1).

    PubMed

    Zhang, Suoying; Liu, Hong; Liu, Pengfei; Yang, Zhuhong; Feng, Xin; Huo, Fengwei; Lu, Xiaohua

    2015-06-07

    Uniform CuO hollow microspheres were successfully achieved from a non-uniform metal organic framework by using a template-free method. The process mechanism has been revealed to be spherical aggregation and Ostwald ripening. When tested in CO oxidation and heat treatment, these assembled microspheres exhibited an excellent catalytic performance and show a much better stability than the inherited hollow structure from MOFs.

  4. Geodetic precession or dragging of inertial frames

    NASA Technical Reports Server (NTRS)

    Ashby, Neil; Shahid-Saless, Bahman

    1989-01-01

    In General Relativity, the Principle of General Covariance allows one to describe phenomena by means of any convenient choice of coordinate system. Here, it is shown that the geodetic precession of a gyroscope orbiting a spherically symmetric, nonrotating mass can be recast as a Lense-Thirring frame-dragging effect, in an appropriately chosen coordinate frame whose origin falls freely along with the gyroscope and whose spatial coordinate axes point in fixed directions.

  5. Can mixed star-plus-wormhole systems mimic black holes?

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Dzhunushaliev, Vladimir; Folomeev, Vladimir; Kleihaus, Burkhard

    We consider mixed strongly gravitating configurations consisting of a wormhole threaded by two types of ordinary matter. For such systems, the possibility of obtaining static spherically symmetric solutions describing compact massive central objects enclosed by high-redshift surfaces (black-hole-like configurations) is studied. Using the standard thin accretion disk model, we exhibit potentially observable differences allowing to distinguish the mixed systems from ordinary black holes with the same masses.

  6. Transparency of an instantaneously created electron-positron-photon plasma

    NASA Astrophysics Data System (ADS)

    Bégué, D.; Vereshchagin, G. V.

    2014-03-01

    The problem of the expansion of a relativistic plasma generated when a large amount of energy is released in a small volume has been considered by many authors. We use the analytical solution of Bisnovatyi-Kogan and Murzina for the spherically symmetric relativistic expansion. The light curves and the spectra from transparency of an electron-positron-photon plasma are obtained. We compare our results with the work of Goodman.

  7. Compact Transducers and Arrays

    DTIC Science & Technology

    2005-05-01

    Batra A, Priya S, Uchino K, Markley D, Newnham RE, Hofmann HF, "Energy harvesting using a piezoelectric "cymbal" transducer in dynamic environment...transducers, the flexural vibration of the metal shell causes an extensional vibration of the piezoelectric ceramic, or vice versa. Cymbal elements are...34On Axi-Symmetrical Vibrations of Shallow Spherical Shells," Quart. Appl. Math, 13 279 (1950). 19.R.S. Woollett, "Theory of the Piezoelectric Flexural

  8. Sound wave generation by a spherically symmetric outburst and AGN feedback in galaxy clusters II: impact of thermal conduction.

    NASA Astrophysics Data System (ADS)

    Tang, Xiaping; Churazov, Eugene

    2018-04-01

    We analyze the impact of thermal conduction on the appearance of a shock-heated gas shell which is produced when a spherically symmetric outburst of a supermassive black hole inflates bubbles of relativistic plasma at the center of a galaxy cluster. The presence of the hot and low-density shell can be used as an ancillary indicator for a high rate of energy release during the outburst, which is required to drive strong shocks into the gas. Here we show that conduction can effectively erase such shell, unless the diffusion of electrons is heavily suppressed. We conclude that a more robust proxy to the energy release rate is the ratio between the shock radius and bubble radius. We also revisited the issue of sound waves dissipation induced by thermal conduction in a scenario, where characteristic wavelength of the sound wave is set by the total energy of the outburst. For a fiducial short outburst model, the dissipation length does not exceed the cooling radius in a typical cluster, provided that the conduction is suppressed by a factor not larger than ˜100. For quasi-continuous energy injection neither the shock-heated shell nor the outgoing sound wave are important and the role of conduction is subdominant.

  9. Mode-sum regularization of ⟨ϕ2⟩ in the angular-splitting method

    NASA Astrophysics Data System (ADS)

    Levi, Adam; Ori, Amos

    2016-08-01

    The computation of the renormalized stress-energy tensor or ⟨ϕ2⟩ren in curved spacetime is a challenging task, at both the conceptual and technical levels. Recently we developed a new approach to compute such renormalized quantities in asymptotically flat curved spacetimes, based on the point-splitting procedure. Our approach requires the spacetime to admit some symmetry. We already implemented this approach to compute ⟨ϕ2⟩ren in a stationary spacetime using t splitting, namely splitting in the time-translation direction. Here we present the angular-splitting version of this approach, aimed for computing renormalized quantities in a general (possibly dynamical) spherically symmetric spacetime. To illustrate how the angular-splitting method works, we use it here to compute ⟨ϕ2⟩ren for a quantum massless scalar field in Schwarzschild background, in various quantum states (Boulware, Unruh, and Hartle-Hawking states). We find excellent agreement with the results obtained from the t -splitting variant and also with other methods. Our main goal in pursuing this new mode-sum approach was to enable the computation of the renormalized stress-energy tensor in a dynamical spherically symmetric background, e.g. an evaporating black hole. The angular-splitting variant presented here is most suitable to this purpose.

  10. Test-particle dynamics in general spherically symmetric black hole spacetimes

    NASA Astrophysics Data System (ADS)

    De Laurentis, Mariafelicia; Younsi, Ziri; Porth, Oliver; Mizuno, Yosuke; Rezzolla, Luciano

    2018-05-01

    To date, the most precise tests of general relativity have been achieved through pulsar timing, albeit in the weak-field regime. Since pulsars are some of the most precise and stable "clocks" in the Universe, present observational efforts are focused on detecting pulsars in the vicinity of supermassive black holes (most notably in the Galactic Centre), enabling pulsar timing to be used as an extremely precise probe of strong-field gravity. In this paper, a mathematical framework to describe test-particle dynamics in general black-hole spacetimes is presented and subsequently used to study a binary system comprising a pulsar orbiting a black hole. In particular, taking into account the parameterization of a general spherically symmetric black-hole metric, general analytic expressions for both the advance of the periastron and for the orbital period of a massive test particle are derived. Furthermore, these expressions are applied to four representative cases of solutions arising in both general relativity and in alternative theories of gravity. Finally, this framework is applied to the Galactic center S -stars and four distinct pulsar toy models. It is shown that by adopting a fully general-relativistic description of test-particle motion which is independent of any particular theory of gravity, observations of pulsars can help impose better constraints on alternative theories of gravity than is presently possible.

  11. On equatorially symmetric and antisymmetric geomagnetic secular variation timescales

    NASA Astrophysics Data System (ADS)

    Amit, Hagay; Coutelier, Maélie; Christensen, Ulrich R.

    2018-03-01

    It has been suggested that the secular variation (SV) timescales of the geomagnetic field vary as 1 / ℓ (where ℓ is the spherical harmonic degree), except for the dipole. Here we propose that the same scaling law applies for SV timescales defined for different symmetry classes of the geomagnetic field and SV. We decompose the field and its SV into symmetric and antisymmetric parts and show in geomagnetic field models and numerical dynamo simulations that the corresponding SV timescales also vary as 1 / ℓ , again except for the dipole. The time-average antisymmetric/symmetric SV timescales are larger/smaller than the total, respectively. The difference in SV timescales between these two symmetry classes is probably due to different degrees of alignment of the core flow with different magnetic field structures at the core-mantle boundary. The symmetric dipole SV timescale in the recent geomagnetic field and in long-term time-averages from numerical dynamos is below the extrapolated 1 / ℓ curve, whereas before ∼ 1965 the geomagnetic dipole tilt was rather steady and the symmetric dipole SV timescale exceeded the extrapolated 1 / ℓ curve. We hypothesize that the period of nearly steady geomagnetic dipole tilt between 1810-1965 was anomalous for the geodynamo. Overall, the deviation of the dipole SV timescales from the 1 / ℓ curves may indicate that magnetic diffusion contributes to the dipole SV more than it does for higher degrees.

  12. Dissolution of spherical cap CO2 bubbles attached to flat surfaces in air-saturated water

    NASA Astrophysics Data System (ADS)

    Peñas, Pablo; Parrales, Miguel A.; Rodriguez-Rodriguez, Javier

    2014-11-01

    Bubbles attached to flat surfaces immersed in quiescent liquid environments often display a spherical cap (SC) shape. Their dissolution is a phenomenon commonly observed experimentally. Modelling these bubbles as fully spherical may lead to an inaccurate estimate of the bubble dissolution rate. We develop a theoretical model for the diffusion-driven dissolution or growth of such multi-component SC gas bubbles under constant pressure and temperature conditions. Provided the contact angle of the bubble with the surface is large, the concentration gradients in the liquid may be approximated as spherically symmetric. The area available for mass transfer depends on the instantaneous bubble contact angle, whose dynamics is computed from the adhesion hysteresis model [Hong et al., Langmuir, vol. 27, 6890-6896 (2011)]. Numerical simulations and experimental measurements on the dissolution of SC CO2 bubbles immersed in air-saturated water support the validity of our model. We verify that contact line pinning slows down the dissolution rate, and the fact that any bubble immersed in a saturated gas-liquid solution eventually attains a final equilibrium size. Funded by the Spanish Ministry of Economy and Competitiveness through Grant DPI2011-28356-C03-0.

  13. New phase method of measuring particle size with laser Doppler radar

    NASA Astrophysics Data System (ADS)

    Zemlianskii, Vladimir M.

    1996-06-01

    A vast field of non-contact metrology, vibrometry, dynamics and microdynamics problems solved on the basis of laser Doppler method resulted in the development of great variety of laser Doppler radar (LDR). In coherent LDR few beams with various polarization are generally adopted, that are directed at the zone of measurement, through which the probing air stream moves. Studies of various coherent LDR demonstrated that polarization-phase effects of scattering can in some cases considerably effect on the signal-to-noise ratio of the Doppler signal. On the other side using phase effects can simultaneous measurement of size and velocity of spherical particles. New possibilities for improving the accuracy of measuring spherical particles' sizes come to light when application is made in coherent LDR of two waves- probing and one out of the types of symmetrical reception of scattered radiation, during which phase-conjugate signals are formed. The theoretical analysis on the basis of the scattering theory showed, that in symmetrical reception of scattered radiation with respect to the planes OXZ and OYZ output signal of the photoreceiver contains two high- frequency signal components, which in relation to parameters of the probing and size, can either be in phase or antiphase. Results of numerical modeling are presented: amplitude of high frequency signal, coefficient of phase and polarization matching of mixed waves, the depths of photocurrent modulation and also signal's phase in relation to the angle between the probing beams. Phase method of determining particle's sizes based on the use of two wavelengths probing and symmetrical reception of scattered radiation in which conditions for the formation of phase conjugated high-frequency signals are satisfied is presented.

  14. A New Code for Calculating Post-seismic Displacements as Well as Geoid and Gravity Changes on a Layered Visco-Elastic Spherical Earth

    NASA Astrophysics Data System (ADS)

    Gao, Shanghua; Fu, Guangyu; Liu, Tai; Zhang, Guoqing

    2017-03-01

    Tanaka et al. (Geophys J Int 164:273-289, 2006, Geophys J Int 170:1031-1052, 2007) proposed the spherical dislocation theory (SDT) in a spherically symmetric, self-gravitating visco-elastic earth model. However, to date there have been no reports on easily adopted, widely used software that utilizes Tanaka's theory. In this study we introduce a new code to compute post-seismic deformations (PSD), including displacements as well as Geoid and gravity changes, caused by a seismic source at any position. This new code is based on the above-mentioned SDT. The code consists of two parts. The first part is the numerical frame of the dislocation Green function (DGF), which contains a set of two-dimensional discrete numerical frames of DGFs on a symmetric earth model. The second part is an integration function, which performs bi-quadratic spline interpolation operations on the frame of DGFs. The inputs are the information on the seismic fault models and the information on the observation points. After the user prepares the inputs in a file with given format, the code will automatically compute the PSD. As an example, we use the new code to calculate the co-seismic displacements caused by the Tohoku-Oki Mw 9.0 earthquake. We compare the result with observations and the result from a full-elastic SDT, and we found that the Root Mean Square error between the calculated and observed results is 7.4 cm. This verifies the suitability of our new code. Finally, we discuss several issues that require attention when using the code, which should be helpful for users.

  15. New Constraints on the Geometry and Kinematics of Matter Surrounding the Accretion Flow in X-Ray Binaries from Chandra High-Energy Transmission Grating X-Ray Spectroscopy

    NASA Technical Reports Server (NTRS)

    Tzanavaris, P.; Yaqoob, T.

    2018-01-01

    The narrow, neutral Fe Ka fluorescence emission line in X-ray binaries (XRBs) is a powerful probe of the geometry, kinematics, and Fe abundance of matter around the accretion flow. In a recent study it has been claimed, using Chandra High-Energy Transmission Grating (HETG) spectra for a sample of XRBs, that the circumnuclear material is consistent with a solar-abundance, uniform, spherical distribution. It was also claimed that the Fe Ka line was unresolved in all cases by the HETG. However, these conclusions were based on ad hoc models that did not attempt to relate the global column density to the Fe Ka line emission. We revisit the sample and test a self-consistent model of a uniform, spherical X-ray reprocessor against HETG spectra from 56 observations of 14 Galactic XRBs. We find that the model is ruled out in 13/14 sources because a variable Fe abundance is required. In two sources a spherical distribution is viable, but with nonsolar Fe abundance. We also applied a solar-abundance Compton-thick reflection model, which can account for the spectra that are inconsistent with a spherical model, but spectra with a broader bandpass are required to better constrain model parameters. We also robustly measured the velocity width of the Fe Ka line and found FWHM values of up to approx. 5000 km/s. Only in some spectra was the Fe Ka line unresolved by the HETG.

  16. Experiment to Form and Characterize a Section of a Spherically Imploding Plasma Liner

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Hsu, S. C.; Langendorf, S. J.; Yates, K. C.

    Here, we describe an experiment to form and characterize a section of a spherically imploding plasma liner by merging six supersonic plasma jets that are launched by newly designed contoured-gap coaxial plasma guns. This experiment is a prelude to forming a fully spherical imploding plasma liner using many dozens of plasma guns, as a standoff driver for plasma-jet-driven magneto-inertial fusion. The objectives of the six-jet experiments are to assess the evolution and scalings of liner Mach number and uniformity, which are important metrics for spherically imploding plasma liners to compress magnetized target plasmas to fusion conditions. Lastly, this article describesmore » the design of the coaxial plasma guns, experimental characterization of the plasma jets, six-jet experimental setup and diagnostics, initial diagnostic data from three- and six-jet experiments, and the high-level objectives of associated numerical modeling.« less

  17. Experiment to Form and Characterize a Section of a Spherically Imploding Plasma Liner

    DOE PAGES

    Hsu, S. C.; Langendorf, S. J.; Yates, K. C.; ...

    2017-12-18

    Here, we describe an experiment to form and characterize a section of a spherically imploding plasma liner by merging six supersonic plasma jets that are launched by newly designed contoured-gap coaxial plasma guns. This experiment is a prelude to forming a fully spherical imploding plasma liner using many dozens of plasma guns, as a standoff driver for plasma-jet-driven magneto-inertial fusion. The objectives of the six-jet experiments are to assess the evolution and scalings of liner Mach number and uniformity, which are important metrics for spherically imploding plasma liners to compress magnetized target plasmas to fusion conditions. Lastly, this article describesmore » the design of the coaxial plasma guns, experimental characterization of the plasma jets, six-jet experimental setup and diagnostics, initial diagnostic data from three- and six-jet experiments, and the high-level objectives of associated numerical modeling.« less

  18. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Suzuki, Akihiro; Maeda, Keiichi; Shigeyama, Toshikazu

    A two-dimensional special relativistic radiation-hydrodynamics code is developed and applied to numerical simulations of supernova shock breakout in bipolar explosions of a blue supergiant. Our calculations successfully simulate the dynamical evolution of a blast wave in the star and its emergence from the surface. Results of the model with spherical energy deposition show a good agreement with previous simulations. Furthermore, we calculate several models with bipolar energy deposition and compare their results with the spherically symmetric model. The bolometric light curves of the shock breakout emission are calculated by a ray-tracing method. Our radiation-hydrodynamic models indicate that the early partmore » of the shock breakout emission can be used to probe the geometry of the blast wave produced as a result of the gravitational collapse of the iron core.« less

  19. Gravity fields of the solar system

    NASA Technical Reports Server (NTRS)

    Zendell, A.; Brown, R. D.; Vincent, S.

    1975-01-01

    The most frequently used formulations of the gravitational field are discussed and a standard set of models for the gravity fields of the earth, moon, sun, and other massive bodies in the solar system are defined. The formulas are presented in standard forms, some with instructions for conversion. A point-source or inverse-square model, which represents the external potential of a spherically symmetrical mass distribution by a mathematical point mass without physical dimensions, is considered. An oblate spheroid model is presented, accompanied by an introduction to zonal harmonics. This spheroid model is generalized and forms the basis for a number of the spherical harmonic models which were developed for the earth and moon. The triaxial ellipsoid model is also presented. These models and their application to space missions are discussed.

  20. Nonlinear anomalous diffusion equation and fractal dimension: exact generalized Gaussian solution.

    PubMed

    Pedron, I T; Mendes, R S; Malacarne, L C; Lenzi, E K

    2002-04-01

    In this work we incorporate, in a unified way, two anomalous behaviors, the power law and stretched exponential ones, by considering the radial dependence of the N-dimensional nonlinear diffusion equation partial differential rho/ partial differential t=nabla.(Knablarho(nu))-nabla.(muFrho)-alpharho, where K=Dr(-theta), nu, theta, mu, and D are real parameters, F is the external force, and alpha is a time-dependent source. This equation unifies the O'Shaughnessy-Procaccia anomalous diffusion equation on fractals (nu=1) and the spherical anomalous diffusion for porous media (theta=0). An exact spherical symmetric solution of this nonlinear Fokker-Planck equation is obtained, leading to a large class of anomalous behaviors. Stationary solutions for this Fokker-Planck-like equation are also discussed by introducing an effective potential.

  1. Thermally generated magnetic fields in laser-driven compressions and explosions

    NASA Technical Reports Server (NTRS)

    Tidman, D. A.

    1975-01-01

    The evolution of thermally generated magnetic fields in a plasma undergoing a nearly spherically symmetric adiabatic compression or expansion is calculated. The analysis is applied to obtain approximate results for the development of magnetic fields in laser-driven compression and explosion of a pellet of nuclear fuel. Localized sources, such as those occurring at composition boundaries in structured pellets or at shock fronts, give stronger fields than those deriving from smoothly distributed asymmetries. Although these fields may approach 10 million G in the late stages of compression, this is not expected to present difficulties for the compression process. Assuming ignition of a nuclear explosion occurs, the sources become much stronger, and values of approximately 10 billion G are obtained at tamper boundaries assuming a 20% departure from spherical symmetry during the explosion.

  2. Nonsymmetric dynamical thin-shell wormhole in Robinson-Trautman class

    NASA Astrophysics Data System (ADS)

    Svítek, O.; Tahamtan, T.

    2018-02-01

    The thin-shell wormhole created using the Darmois-Israel formalism applied to Robinson-Trautman family of spacetimes is presented. The stress energy tensor created on the throat is interpreted in terms of two dust streams and it is shown that asymptotically this wormhole settles to the Schwarzschild wormhole with a throat located at the position of the horizon. This behavior shows a nonlinear stability (within the Robinson-Trautman class) of this spherically symmetric wormhole. The gravitational radiation emitted by the Robinson-Trautman wormhole during the transition to spherical symmetry is indistinguishable from that of the corresponding black hole Robinson-Trautman spacetime. Subsequently, we show that the higher-dimensional generalization of Robinson-Trautman geometry offers a possibility of constructing wormholes without the need to violate the energy conditions for matter induced on the throat.

  3. Hollow spherical shell manufacture

    DOEpatents

    O'Holleran, T.P.

    1991-11-26

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

  4. Hollow spherical shell manufacture

    DOEpatents

    O'Holleran, Thomas P.

    1991-01-01

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

  5. Static black holes with back reaction from vacuum energy

    NASA Astrophysics Data System (ADS)

    Ho, Pei-Ming; Matsuo, Yoshinori

    2018-03-01

    We study spherically symmetric static solutions to the semi-classical Einstein equation sourced by the vacuum energy of quantum fields in the curved space-time of the same solution. We found solutions that are small deformations of the Schwarzschild metric for distant observers, but without horizon. Instead of being a robust feature of objects with high densities, the horizon is sensitive to the energy–momentum tensor in the near-horizon region.

  6. Exact vacuum solution to conformal Weyl gravity and galactic rotation curves

    NASA Technical Reports Server (NTRS)

    Mannheim, Philip D.; Kazanas, Demosthenes

    1989-01-01

    The complete, exact exterior solution for a static, spherically symmetric source in locally conformal invariant Weyl gravity is presented. The solution includes the familiar exterior Schwarzschild solution as a special case and contains an extra gravitational potential term which grows linearly with distance. The obtained solution provides a potential explanation for observed galactic rotation curves without the need for dark matter. The solution also has some interesting implications for cosmology.

  7. Faraday Wave Turbulence on a Spherical Liquid Shell

    NASA Technical Reports Server (NTRS)

    Holt, R. Glynn; Trinh, Eugene H.

    1996-01-01

    Millimeter-radius liquid shells are acoustically levitated in an ultrasonic field. Capillary waves are observed on the shells. At low energies (minimal acoustic amplitude, thick shell) a resonance is observed between the symmetric and antisymmetric thin film oscillation modes. At high energies (high acoustic pressure, thin shell) the shell becomes fully covered with high-amplitude waves. Temporal spectra of scattered light from the shell in this regime exhibit a power-law decay indicative of turbulence.

  8. Design of light guide sleeve on hyperspectral imaging system for skin diagnosis

    NASA Astrophysics Data System (ADS)

    Yan, Yung-Jhe; Chang, Chao-Hsin; Huang, Ting-Wei; Chiang, Hou-Chi; Wu, Jeng-Fu; Ou-Yang, Mang

    2017-08-01

    A hyperspectral imaging system is proposed for early study of skin diagnosis. A stable and high hyperspectral image quality is important for analysis. Therefore, a light guide sleeve (LGS) was designed for the embedded on a hyperspectral imaging system. It provides a uniform light source on the object plane with the determined distance. Furthermore, it can shield the ambient light from entering the system and increasing noise. For the purpose of producing a uniform light source, the LGS device was designed in the symmetrical double-layered structure. It has light cut structures to adjust distribution of rays between two layers and has the Lambertian surface in the front-end to promote output uniformity. In the simulation of the design, the uniformity of illuminance was about 91.7%. In the measurement of the actual light guide sleeve, the uniformity of illuminance was about 92.5%.

  9. Primordial black holes in linear and non-linear regimes

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Allahyari, Alireza; Abolhasani, Ali Akbar; Firouzjaee, Javad T., E-mail: allahyari@physics.sharif.edu, E-mail: j.taghizadeh.f@ipm.ir

    We revisit the formation of primordial black holes (PBHs) in the radiation-dominated era for both linear and non-linear regimes, elaborating on the concept of an apparent horizon. Contrary to the expectation from vacuum models, we argue that in a cosmological setting a density fluctuation with a high density does not always collapse to a black hole. To this end, we first elaborate on the perturbation theory for spherically symmetric space times in the linear regime. Thereby, we introduce two gauges. This allows to introduce a well defined gauge-invariant quantity for the expansion of null geodesics. Using this quantity, we arguemore » that PBHs do not form in the linear regime irrespective of the density of the background. Finally, we consider the formation of PBHs in non-linear regimes, adopting the spherical collapse picture. In this picture, over-densities are modeled by closed FRW models in the radiation-dominated era. The difference of our approach is that we start by finding an exact solution for a closed radiation-dominated universe. This yields exact results for turn-around time and radius. It is important that we take the initial conditions from the linear perturbation theory. Additionally, instead of using uniform Hubble gauge condition, both density and velocity perturbations are admitted in this approach. Thereby, the matching condition will impose an important constraint on the initial velocity perturbations δ {sup h} {sub 0} = −δ{sub 0}/2. This can be extended to higher orders. Using this constraint, we find that the apparent horizon of a PBH forms when δ > 3 at turn-around time. The corrections also appear from the third order. Moreover, a PBH forms when its apparent horizon is outside the sound horizon at the re-entry time. Applying this condition, we infer that the threshold value of the density perturbations at horizon re-entry should be larger than δ {sub th} > 0.7.« less

  10. Communication requirements of sparse Cholesky factorization with nested dissection ordering

    NASA Technical Reports Server (NTRS)

    Naik, Vijay K.; Patrick, Merrell L.

    1989-01-01

    Load distribution schemes for minimizing the communication requirements of the Cholesky factorization of dense and sparse, symmetric, positive definite matrices on multiprocessor systems are presented. The total data traffic in factoring an n x n sparse symmetric positive definite matrix representing an n-vertex regular two-dimensional grid graph using n exp alpha, alpha not greater than 1, processors are shown to be O(n exp 1 + alpha/2). It is O(n), when n exp alpha, alpha not smaller than 1, processors are used. Under the conditions of uniform load distribution, these results are shown to be asymptotically optimal.

  11. Fresnel cup reflector directs maximum energy from light source

    NASA Technical Reports Server (NTRS)

    Laue, E. G.; Youngberg, C. L.

    1964-01-01

    To minimize shielding and overheating, a composite Fresnel cup reflector design directs the maximum energy from a light source. It consists of a uniformly ellipsoidal end surface and an extension comprising a series of confocal ellipsoidal and concentric spherical surfaces.

  12. Gaussian Beam Intensity Flattener

    NASA Technical Reports Server (NTRS)

    Griffin, DeVon W.

    1998-01-01

    The goal of this investigation was to use commercial elements and extend the correction to a 1/e(sup 2) diameter of 3 mm over long propagation distances. Shafer discussed the use of spherical elements to generate a uniform beam to the 1/e diameter.

  13. Boundary Layer Flow Control with a One Atmosphere Uniform Glow Discharge Surface Plasma

    NASA Technical Reports Server (NTRS)

    Roth, J. Reece; Sherman, Daniel M.; Wilkinson, Stephen P.

    1998-01-01

    Low speed wind tunnel data have been acquired for planar panels covered by a uniform, glow-discharge surface plasma in atmospheric pressure air known as the One Atmosphere Uniform Glow Discharge Plasma (OAUGDP). Streamwise and spanwise arrays of flush, plasma-generating surface electrodes have been studied in laminar, transitional, and fully turbulent boundary layer flow. Plasma between symmetric streamwise electrode strips caused large increases in panel drag, whereas asymmetric spanwise electrode configurations produced a significant thrust. Smoke wire flow visualization and mean velocity diagnostics show the primary cause of the phenomena to be a combination of mass transport and vortical structures induced by strong paraelectric ElectroHydroDynamic (EHD) body forces on the flow.

  14. Configurational entropy as a lifetime predictor and pattern discriminator for oscillons

    NASA Astrophysics Data System (ADS)

    Gleiser, Marcelo; Stephens, Michelle; Sowinski, Damian

    2018-05-01

    Oscillons are long-lived, spherically symmetric, attractor scalar field configurations that emerge as certain field configurations evolve in time. It has been known for many years that there is a direct correlation between the initial configuration's shape and the resulting oscillon lifetime: a shape memory. In this paper, we use an information-entropic measure of spatial complexity known as differential configurational entropy (DCE) to obtain estimates of oscillon lifetimes in scalar field theories with symmetric and asymmetric double-well potentials. The time-dependent DCE is built from the Fourier transform of the two-point correlation function of the energy density of the scalar field configuration. We obtain a scaling law correlating oscillon lifetimes and measures obtained from its evolving DCE. For the symmetric double well, for example, we show that we can apply DCE to predict an oscillon's lifetime with an average accuracy of 6% or better. We also show that the DCE acts as a pattern discriminator, able to distinguish initial configurations that evolve into long-lived oscillons from other nonperturbative short-lived fluctuations.

  15. Weyl metrics and wormholes

    NASA Astrophysics Data System (ADS)

    Gibbons, Gary W.; Volkov, Mikhail S.

    2017-05-01

    We study solutions obtained via applying dualities and complexifications to the vacuum Weyl metrics generated by massive rods and by point masses. Rescaling them and extending to complex parameter values yields axially symmetric vacuum solutions containing singularities along circles that can be viewed as singular matter sources. These solutions have wormhole topology with several asymptotic regions interconnected by throats and their sources can be viewed as thin rings of negative tension encircling the throats. For a particular value of the ring tension the geometry becomes exactly flat although the topology remains non-trivial, so that the rings literally produce holes in flat space. To create a single ring wormhole of one metre radius one needs a negative energy equivalent to the mass of Jupiter. Further duality transformations dress the rings with the scalar field, either conventional or phantom. This gives rise to large classes of static, axially symmetric solutions, presumably including all previously known solutions for a gravity-coupled massless scalar field, as for example the spherically symmetric Bronnikov-Ellis wormholes with phantom scalar. The multi-wormholes contain infinite struts everywhere at the symmetry axes, apart from solutions with locally flat geometry.

  16. Micro-scale blood particulate dynamics using a non-uniform rational B-spline-based isogeometric analysis.

    PubMed

    Chivukula, V; Mousel, J; Lu, J; Vigmostad, S

    2014-12-01

    The current research presents a novel method in which blood particulates - biconcave red blood cells (RBCs) and spherical cells are modeled using isogeometric analysis, specifically Non-Uniform Rational B-Splines (NURBS) in 3-D. The use of NURBS ensures that even with a coarse representation, the geometry of the blood particulates maintains an accurate description when subjected to large deformations. The fundamental advantage of this method is the coupling of the geometrical description and the stress analysis of the cell membrane into a single, unified framework. Details on the modeling approach, implementation of boundary conditions and the membrane mechanics analysis using isogeometric modeling are presented, along with validation cases for spherical and biconcave cells. Using NURBS - based isogeometric analysis, the behavior of individual cells in fluid flow is presented and analyzed in different flow regimes using as few as 176 elements for a spherical cell and 220 elements for a biconcave RBC. This work provides a framework for modeling a large number of 3-D deformable biological cells, each with its own geometric description and membrane properties. To the best knowledge of the authors, this is the first application of the NURBS - based isogeometric analysis to model and simulate blood particulates in flow in 3D. Copyright © 2014 John Wiley & Sons, Ltd.

  17. New Horizons in Thermodynamics

    NASA Astrophysics Data System (ADS)

    Hayward, Geoffrey Gordon

    1991-02-01

    This thesis collects five papers which treat the theory of horizon thermodynamics and its applications to cosmology. In the first paper I consider general, spherically symmetric spacetimes with cosmological and black hole horizons. I find that a state of thermal equilibrium may exist in classical manifolds with two horizons so long as a matter distribution is present. I calculate the Euclidean action for non-classical manifolds with and without boundary and relate it to the grand canonical weighting factor. I find that the mean thermal energy of the cosmological horizon is negative. In the second paper I derive the first law of thermodynamics for bounded, static, spherically symmetric spacetimes which include a matter distribution and either a black hole or cosmological horizon. I calculate heat capacities associated with matter/horizon systems and find that they may be positive or negative depending on the matter configuration. I discuss the case in which the cosmological constant is allowed to vary and conclude that the Hawking/Coleman mechanisms for explaining the low value of the cosmological constant are not well formulated. In the third paper, co-authored by Jorma Louko, we analyze variational principles for non-smooth metrics. These principles give insight to the problem of constructing minisuperspace path integrals in horizon statistical mechanics and quantum cosmology. We demonstrate that smoothness conditions can be derived from the variational principle as equations of motion. We suggest a new prescription for minisuperspace path integrals on the manifold | D times S^2. In the fourth paper, I examine the contribution of the horizon energy density to black hole temperature. I show the existence of positive heat capacity solutions in the small mass regime. In the fifth paper, co-authored by Diego Pavon we investigate the role of primordial black holes in the very early universe under SU(3) times SU(2) times U (1), SU(5), and their supersymmetric counterparts. Three of the four theories predict a phase in which black holes and radiation are of comparable energy density. The fourth theory, SU(5), predicts a radiation dominated model from the Planck era onward. In the concluding general discussion I show how generalized laws of thermodynamics can be related to variations of the classical gravitational action. These laws apply even for non-static, non-spherically symmetric spacetimes.

  18. Simple analysis of scattering data with the Ornstein-Zernike equation

    NASA Astrophysics Data System (ADS)

    Kats, E. I.; Muratov, A. R.

    2018-01-01

    In this paper we propose and explore a method of analysis of the scattering experimental data for uniform liquidlike systems. In our pragmatic approach we are not trying to introduce by hands an artificial small parameter to work out a perturbation theory with respect to the known results, e.g., for hard spheres or sticky hard spheres (all the more that in the agreement with the notorious Landau statement, there is no physical small parameter for liquids). Instead of it being guided by the experimental data we are solving the Ornstein-Zernike equation with a trial (variational) form of the interparticle interaction potential. To find all needed correlation functions this variational input is iterated numerically to satisfy the Ornstein-Zernike equation supplemented by a closure relation. Our method is developed for spherically symmetric scattering objects, and our numeric code is written for such a case. However, it can be extended (at the expense of more involved computations and a larger amount of required experimental input information) for nonspherical particles. What is important for our approach is that it is sufficient to know experimental data in a relatively narrow range of the scattering wave vectors (q ) to compute the static structure factor in a much broader range of q . We illustrate by a few model and real experimental examples of the x-ray and neutron scattering data how the approach works.

  19. Attractor mechanism as a distillation procedure

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Levay, Peter; Szalay, Szilard

    2010-07-15

    In a recent paper it was shown that for double extremal static spherical symmetric BPS black hole solutions in the STU model the well-known process of moduli stabilization at the horizon can be recast in a form of a distillation procedure of a three-qubit entangled state of a Greenberger-Horne-Zeilinger type. By studying the full flow in moduli space in this paper we investigate this distillation procedure in more detail. We introduce a three-qubit state with amplitudes depending on the conserved charges, the warp factor, and the moduli. We show that for the recently discovered non-BPS solutions it is possible tomore » see how the distillation procedure unfolds itself as we approach the horizon. For the non-BPS seed solutions at the asymptotically Minkowski region we are starting with a three-qubit state having seven nonequal nonvanishing amplitudes and finally at the horizon we get a Greenberger-Horne-Zeilinger state with merely four nonvanishing ones with equal magnitudes. The magnitude of the surviving nonvanishing amplitudes is proportional to the macroscopic black hole entropy. A systematic study of such attractor states shows that their properties reflect the structure of the fake superpotential. We also demonstrate that when starting with the very special values for the moduli corresponding to flat directions the uniform structure at the horizon deteriorates due to errors generalizing the usual bit flips acting on the qubits of the attractor states.« less

  20. General post-Minkowskian expansion and application of the phase function

    NASA Astrophysics Data System (ADS)

    Qin, Cheng-Gang; Shao, Cheng-Gang

    2017-07-01

    The phase function is a useful tool to study all observations of space missions, since it can give all the information about light propagation in a gravitational field. For the extreme accuracy of the modern space missions, a precise relativistic modeling of observations is required. So, we develop a recursive procedure enabling us to expand the phase function into a perturbative series of ascending powers of the Newtonian gravitational constant. Any n th-order perturbation of the phase function can be determined by the integral along the straight line connecting two point events. To illustrate the result, we carry out the calculation of the phase function outside a static, spherically symmetric body up to the order of G2. Then, we develop a precise relativistic model that is able to calculate the phase function and the derivatives of the phase function in the gravitational field of rotating and uniformly moving bodies. This model allows the computing of the Doppler, radio science, and astrometric observables of the space missions in the Solar System. With the development of space technology, the relativistic corrections due to the motion of a planet's spin must be considered in the high-precision space missions in the near future. As an example, we give the estimates of the relativistic corrections on the observables about the space missions TianQin and BEACON.

  1. Charged perfect fluid tori in strong central gravitational and dipolar magnetic fields

    NASA Astrophysics Data System (ADS)

    Kovář, Jiří; Slaný, Petr; Cremaschini, Claudio; Stuchlík, Zdeněk; Karas, Vladimír; Trova, Audrey

    2016-06-01

    We study electrically charged perfect fluid toroidal structures encircling a spherically symmetric gravitating object with Schwarzschild spacetime geometry and endowed with a dipole magnetic field. The work represents a direct continuation of our previous general-relativistic studies of electrically charged fluid in the approximation of zero conductivity, which formed tori around a Reissner-Nordström black hole or a Schwarzschild black hole equipped with a test electric charge and immersed in an asymptotically uniform magnetic field. After a general introduction of the zero-conductivity charged fluid model, we discuss a variety of possible topologies of the toroidal fluid configurations. Along with the charged equatorial tori forming interesting coupled configurations, we demonstrate the existence of the off-equatorial tori, for which the dipole type of magnetic field seems to be necessary. We focus on orbiting structures with constant specific angular momentum and on those in permanent rigid rotation. We stress that the general analytical treatment developed in our previous works is enriched here by the integrated form of the pressure equations. To put our work into an astrophysical context, we identify the central object with an idealization of a nonrotating magnetic neutron star. Constraining ranges of its parameters and also parameters of the circling fluid, we discuss a possible relevance of the studied toroidal structures, presenting along with their topology also pressure, density, temperature and charge profiles.

  2. Uniform electron gases. III. Low-density gases on three-dimensional spheres

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Agboola, Davids; Knol, Anneke L.; Gill, Peter M. W., E-mail: peter.gill@anu.edu.au

    2015-08-28

    By combining variational Monte Carlo (VMC) and complete-basis-set limit Hartree-Fock (HF) calculations, we have obtained near-exact correlation energies for low-density same-spin electrons on a three-dimensional sphere (3-sphere), i.e., the surface of a four-dimensional ball. In the VMC calculations, we compare the efficacies of two types of one-electron basis functions for these strongly correlated systems and analyze the energy convergence with respect to the quality of the Jastrow factor. The HF calculations employ spherical Gaussian functions (SGFs) which are the curved-space analogs of Cartesian Gaussian functions. At low densities, the electrons become relatively localized into Wigner crystals, and the natural SGFmore » centers are found by solving the Thomson problem (i.e., the minimum-energy arrangement of n point charges) on the 3-sphere for various values of n. We have found 11 special values of n whose Thomson sites are equivalent. Three of these are the vertices of four-dimensional Platonic solids — the hyper-tetrahedron (n = 5), the hyper-octahedron (n = 8), and the 24-cell (n = 24) — and a fourth is a highly symmetric structure (n = 13) which has not previously been reported. By calculating the harmonic frequencies of the electrons around their equilibrium positions, we also find the first-order vibrational corrections to the Thomson energy.« less

  3. Accurate thermodynamics for short-ranged truncations of Coulomb interactions in site-site molecular models

    NASA Astrophysics Data System (ADS)

    Rodgers, Jocelyn M.; Weeks, John D.

    2009-12-01

    Coulomb interactions are present in a wide variety of all-atom force fields. Spherical truncations of these interactions permit fast simulations but are problematic due to their incorrect thermodynamics. Herein we demonstrate that simple analytical corrections for the thermodynamics of uniform truncated systems are possible. In particular, results for the simple point charge/extended (SPC/E) water model treated with spherically truncated Coulomb interactions suggested by local molecular field theory [J. M. Rodgers and J. D. Weeks, Proc. Natl. Acad. Sci. U.S.A. 105, 19136 (2008)] are presented. We extend the results developed by Chandler [J. Chem. Phys. 65, 2925 (1976)] so that we may treat the thermodynamics of mixtures of flexible charged and uncharged molecules simulated with spherical truncations. We show that the energy and pressure of spherically truncated bulk SPC/E water are easily corrected using exact second-moment-like conditions on long-ranged structure. Furthermore, applying the pressure correction as an external pressure removes the density errors observed by other research groups in NPT simulations of spherically truncated bulk species.

  4. Asymptotic theory of intermediate- and high-degree solar acoustic oscillations

    NASA Technical Reports Server (NTRS)

    Brodsky, M.; Vorontsov, S. V.

    1993-01-01

    A second-order asymptotic approximation is developed for adiabatic nonradial p-modes of a spherically symmetric star. The exact solutions of adiabatic oscillations are assumed in the outermost layers, where the asymptotic description becomes invalid, which results in a eigenfrequency equation with model-dependent surface phase shift. For lower degree modes, the phase shift is a function of frequency alone; for high-degree modes, its dependence on the degree is explicitly taken into account.

  5. Exact solution of equations for proton localization in neutron star matter

    NASA Astrophysics Data System (ADS)

    Kubis, Sebastian; Wójcik, Włodzimierz

    2015-11-01

    The rigorous treatment of proton localization phenomenon in asymmetric nuclear matter is presented. The solution of proton wave function and neutron background distribution is found by the use of the extended Thomas-Fermi approach. The minimum of energy is obtained in the Wigner-Seitz approximation of a spherically symmetric cell. The analysis of four different nuclear models suggests that the proton localization is likely to take place in the interior of a neutron star.

  6. On the stability of dyons and dyonic black holes in Einstein-Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Nolan, Brien C.; Winstanley, Elizabeth

    2016-02-01

    We investigate the stability of four-dimensional dyonic soliton and black hole solutions of {su}(2) Einstein-Yang-Mills theory in anti-de Sitter space. We prove that, in a neighbourhood of the embedded trivial (Schwarzschild-)anti-de Sitter solution, there exist non-trivial dyonic soliton and black hole solutions of the field equations which are stable under linear, spherically symmetric, perturbations of the metric and non-Abelian gauge field.

  7. Information Theory and the Earth's Density Distribution

    NASA Technical Reports Server (NTRS)

    Rubincam, D. P.

    1979-01-01

    An argument for using the information theory approach as an inference technique in solid earth geophysics. A spherically symmetric density distribution is derived as an example of the method. A simple model of the earth plus knowledge of its mass and moment of inertia lead to a density distribution which was surprisingly close to the optimum distribution. Future directions for the information theory approach in solid earth geophysics as well as its strengths and weaknesses are discussed.

  8. The NIF x-ray spectrometer calibration campaign at Omega.

    PubMed

    Pérez, F; Kemp, G E; Regan, S P; Barrios, M A; Pino, J; Scott, H; Ayers, S; Chen, H; Emig, J; Colvin, J D; Bedzyk, M; Shoup, M J; Agliata, A; Yaakobi, B; Marshall, F J; Hamilton, R A; Jaquez, J; Farrell, M; Nikroo, A; Fournier, K B

    2014-11-01

    The calibration campaign of the National Ignition Facility X-ray Spectrometer (NXS) was carried out at the Omega laser facility. Spherically symmetric, laser-driven, millimeter-scale x-ray sources of K-shell and L-shell emission from various mid-Z elements were designed for the 2-18 keV energy range of the NXS. The absolute spectral brightness was measured by two calibrated spectrometers. We compare the measured performance of the target design to radiation hydrodynamics simulations.

  9. An Alternative Treatment of Heat Flow for Charge Transport in Semiconductor Devices (Postprint)

    DTIC Science & Technology

    2010-07-01

    is tantamount to treating them as ideal gases. A three-dimensional ideal Fermi gas is spherically symmetric in momentum space, and its distribution in...the first mo- ment of the Boltzmann equation using the momentum relax- ation time and effective mass approximations.13 Neglecting any magnetic field and...where the integral is over all momentum vectors k, v is electron velocity, k is the momentum relaxation time, and kf denotes the gradient in momentum

  10. Black holes in loop quantum gravity: the complete space-time.

    PubMed

    Gambini, Rodolfo; Pullin, Jorge

    2008-10-17

    We consider the quantization of the complete extension of the Schwarzschild space-time using spherically symmetric loop quantum gravity. We find an exact solution corresponding to the semiclassical theory. The singularity is eliminated but the space-time still contains a horizon. Although the solution is known partially numerically and therefore a proper global analysis is not possible, a global structure akin to a singularity-free Reissner-Nordström space-time including a Cauchy horizon is suggested.

  11. Static solutions for fourth order gravity

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Nelson, William

    2010-11-15

    The Lichnerowicz and Israel theorems are extended to higher order theories of gravity. In particular it is shown that Schwarzschild is the unique spherically symmetric, static, asymptotically flat, black-hole solution, provided the spatial curvature is less than the quantum gravity scale outside the horizon. It is then shown that in the presence of matter (satisfying certain positivity requirements), the only static and asymptotically flat solutions of general relativity that are also solutions of higher order gravity are the vacuum solutions.

  12. A Deep Chandra Observation of the Distant Galaxy Cluster MS 1137.5+6625

    NASA Astrophysics Data System (ADS)

    Grego, Laura; Vrtilek, J. M.; Van Speybroeck, Leon; David, Laurence P.; Forman, William; Carlstrom, John E.; Reese, Erik D.; Joy, Marshall K.

    2004-06-01

    We present results from a deep Chandra observation of MS 1137.5+66, a distant (z=0.783) and massive cluster of galaxies. Only a few similarly massive clusters are currently known at such high redshifts; accordingly, this observation provides much needed information on the dynamical state of these rare systems. The cluster appears both regular and symmetric in the X-ray image. However, our analysis of the spectral and spatial X-ray data in conjunction with interferometric Sunyaev-Zel'dovich effect data and published deep optical imaging suggests that the cluster has a fairly complex structure. The angular diameter distance we calculate from the Chandra and Sunyaev-Zel'dovich effect data assuming an isothermal, spherically symmetric cluster implies a low value for the Hubble constant for which we explore possible explanations.

  13. Renormalization Group scale-setting in astrophysical systems

    NASA Astrophysics Data System (ADS)

    Domazet, Silvije; Štefančić, Hrvoje

    2011-09-01

    A more general scale-setting procedure for General Relativity with Renormalization Group corrections is proposed. Theoretical aspects of the scale-setting procedure and the interpretation of the Renormalization Group running scale are discussed. The procedure is elaborated for several highly symmetric systems with matter in the form of an ideal fluid and for two models of running of the Newton coupling and the cosmological term. For a static spherically symmetric system with the matter obeying the polytropic equation of state the running scale-setting is performed analytically. The obtained result for the running scale matches the Ansatz introduced in a recent paper by Rodrigues, Letelier and Shapiro which provides an excellent explanation of rotation curves for a number of galaxies. A systematic explanation of the galaxy rotation curves using the scale-setting procedure introduced in this Letter is identified as an important future goal.

  14. Wormholes with fluid sources: A no-go theorem and new examples

    NASA Astrophysics Data System (ADS)

    Bronnikov, K. A.; Baleevskikh, K. A.; Skvortsova, M. V.

    2017-12-01

    For static, spherically symmetric space-times in general relativity (GR), a no-go theorem is proved: it excludes the existence of wormholes with flat and/or anti-de Sitter asymptotic regions on both sides of the throat if the source matter is isotropic, i.e., the radial and tangential pressures coincide. It explains why in all previous attempts to build such solutions it was necessary to introduce boundaries with thin shells that manifestly violate the isotropy of matter. Under a simple assumption on the behavior of the spherical radius r (x ), we obtain a number of examples of wormholes with isotropic matter and one or both de Sitter asymptotic regions, allowed by the no-go theorem. We also obtain twice asymptotically flat wormholes with anisotropic matter, both symmetric and asymmetric with respect to the throat, under the assumption that the scalar curvature is zero. These solutions may be on equal grounds interpreted as those of GR with a traceless stress-energy tensor and as vacuum solutions in a brane world. For such wormholes, the traversability conditions and gravitational lensing properties are briefly discussed. As a byproduct, we obtain twice asymptotically flat regular black hole solutions with up to four Killing horizons. As another byproduct, we point out intersection points in families of integral curves for the function A (x )=gt t, parametrized by its values on the throat.

  15. Radially Symmetric Motions of Nonlinearly Viscoelastic Bodies Under Live Loads

    NASA Astrophysics Data System (ADS)

    Stepanov, Alexey B.; Antman, Stuart S.

    2017-12-01

    This paper treats radially symmetric motions of nonlinearly viscoelastic circular-cylindrical and spherical shells subjected to the live loads of centrifugal force and (time-dependent) hydrostatic pressures. The governing equations are exact versions of those for 3-dimensional continuum mechanics (so shell does not connote an approximate via some shell theory). These motions are governed by quasilinear third-order parabolic-hyperbolic equations having but one independent spatial variable. The principal part of such a partial differential equation is determined by a general family of nonlinear constitutive equations. The presence of strains in two orthogonal directions requires a careful treatment of constitutive restrictions that are physically natural and support the analysis. The interaction of geometrically exact formulations, the compatible use of general constitutive equations for material response, and the presence of live loads show how these factors play crucial roles in the behavior of solutions. In particular, for different kinds of live loads there are thresholds separating materials that produce qualitatively different dynamical behavior. The analysis (using classical methods) covers infinite-time blowup for cylindrical shells subject to centrifugal forces, infinite-time blowup for cylindrical shells subject to steady and time-dependent hydrostatic pressures, finite-time blowup for spherical shells subject to steady and time-dependent hydrostatic pressures, and the preclusion of total compression. This paper concludes with a sketch (using some modern methods) of the existence of regular solutions until the time of blowup.

  16. Complete affine connection in the causal boundary: static, spherically symmetric spacetimes

    NASA Astrophysics Data System (ADS)

    Harris, Steven (Stacey) G.

    2017-02-01

    The boundary at I^+, future null infinity, for a standard static, spherically symmetric spactime is examined for possible linear connections. Two independent methods are employed, one for treating I^+ as the future causal boundary, and one for treating it as a conformal boundary (the latter is subsumed in the former, which is of greater generality). Both methods provide the same result: a constellation of various possible connections, depending on an arbitrary choice of a certain function, a sort of gauge freedom in obtaining a natural connection on I^+; choosing that function to be constant (for instance) results in a complete connection. Treating I^+ as part of the future causal boundary, the method is to impute affine connections on null hypersurfaces going out to I^+, in terms of a transverse vector field on each null hypersurface (there is much gauge freedom on choice of the transverse vector fields). Treating I^+ as part of a conformal boundary, the method is to make a choice of conformal factor that makes the boundary totally geodesic in the enveloping manifold (there is much gauge freedom in choice of that conformal factor). Similar examination is made of other boundaries, such as timelike infinity and timelike and spacelike singularities. These are much simpler, as they admit a unique connection from a similar limiting process (i.e., no gauge freedom); and that connection is complete.

  17. Dissipative dark matter halos: The steady state solution. II.

    NASA Astrophysics Data System (ADS)

    Foot, R.

    2018-05-01

    Within the mirror dark matter model and dissipative dark matter models in general, halos around galaxies with active star formation (including spirals and gas-rich dwarfs) are dynamical: they expand and contract in response to heating and cooling processes. Ordinary type II supernovae (SNe) can provide the dominant heat source, which is possible if kinetic mixing interaction exists with strength ɛ ˜10-9- 10-10 . Dissipative dark matter halos can be modeled as a fluid governed by Euler's equations. Around sufficiently isolated and unperturbed galaxies the halo can relax to a steady state configuration, where heating and cooling rates locally balance and hydrostatic equilibrium prevails. These steady state conditions can be solved to derive the physical properties, including the halo density and temperature profiles, for model galaxies. Here, we consider idealized spherically symmetric galaxies within the mirror dark particle model, as in our earlier paper [Phys. Rev. D 97, 043012 (2018), 10.1103/PhysRevD.97.043012], but we assume that the local halo heating in the SN vicinity dominates over radiative sources. With this assumption, physically interesting steady state solutions arise which we compute for a representative range of model galaxies. The end result is a rather simple description of the dark matter halo around idealized spherically symmetric systems, characterized in principle by only one parameter, with physical properties that closely resemble the empirical properties of disk galaxies.

  18. Fully quantal calculation of H{sub 2} translation-rotation states in the (p-H{sub 2}){sub 2}@5{sup 12}6{sup 4} clathrate hydrate inclusion compound

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Felker, Peter M., E-mail: felker@chem.ucla.edu

    2014-11-14

    The quantal translation-rotation (TR) states of the (p-H{sub 2}){sub 2}@5{sup 12}6{sup 4} clathrate hydrate inclusion compound have been computed. The ten-dimensional problem (in the rigid-cage and rigid-H{sub 2} approximation) is solved by first approximating the H{sub 2} moieties as spherically symmetric and solving for their 6D translational eigenstates. These are then combined with H{sub 2} free rotational states in a product basis that is used to diagonalize the full TR hamiltonian. The computed low-energy eigenstates have translational components that are essentially identical to the 6D translational eigenstates and rotational components that are 99.9% composed of rotationally unexcited H{sub 2} moieties.more » In other words, TR coupling is minimal for the low-energy states of the species. The low-energy level structure is found to be substantially more congested than that of the more tightly packed (p-H{sub 2}){sub 4}@5{sup 12}6{sup 4} clathrate species. The level structure is also shown to be understandable in terms of a model of (H{sub 2}){sub 2} as a semirigid diatomic species consisting of two spherically symmetric H{sub 2} pseudo-atoms.« less

  19. Measuring Symmetry, Asymmetry and Randomness in Neural Network Connectivity

    PubMed Central

    Esposito, Umberto; Giugliano, Michele; van Rossum, Mark; Vasilaki, Eleni

    2014-01-01

    Cognitive functions are stored in the connectome, the wiring diagram of the brain, which exhibits non-random features, so-called motifs. In this work, we focus on bidirectional, symmetric motifs, i.e. two neurons that project to each other via connections of equal strength, and unidirectional, non-symmetric motifs, i.e. within a pair of neurons only one neuron projects to the other. We hypothesise that such motifs have been shaped via activity dependent synaptic plasticity processes. As a consequence, learning moves the distribution of the synaptic connections away from randomness. Our aim is to provide a global, macroscopic, single parameter characterisation of the statistical occurrence of bidirectional and unidirectional motifs. To this end we define a symmetry measure that does not require any a priori thresholding of the weights or knowledge of their maximal value. We calculate its mean and variance for random uniform or Gaussian distributions, which allows us to introduce a confidence measure of how significantly symmetric or asymmetric a specific configuration is, i.e. how likely it is that the configuration is the result of chance. We demonstrate the discriminatory power of our symmetry measure by inspecting the eigenvalues of different types of connectivity matrices. We show that a Gaussian weight distribution biases the connectivity motifs to more symmetric configurations than a uniform distribution and that introducing a random synaptic pruning, mimicking developmental regulation in synaptogenesis, biases the connectivity motifs to more asymmetric configurations, regardless of the distribution. We expect that our work will benefit the computational modelling community, by providing a systematic way to characterise symmetry and asymmetry in network structures. Further, our symmetry measure will be of use to electrophysiologists that investigate symmetry of network connectivity. PMID:25006663

  20. Measuring symmetry, asymmetry and randomness in neural network connectivity.

    PubMed

    Esposito, Umberto; Giugliano, Michele; van Rossum, Mark; Vasilaki, Eleni

    2014-01-01

    Cognitive functions are stored in the connectome, the wiring diagram of the brain, which exhibits non-random features, so-called motifs. In this work, we focus on bidirectional, symmetric motifs, i.e. two neurons that project to each other via connections of equal strength, and unidirectional, non-symmetric motifs, i.e. within a pair of neurons only one neuron projects to the other. We hypothesise that such motifs have been shaped via activity dependent synaptic plasticity processes. As a consequence, learning moves the distribution of the synaptic connections away from randomness. Our aim is to provide a global, macroscopic, single parameter characterisation of the statistical occurrence of bidirectional and unidirectional motifs. To this end we define a symmetry measure that does not require any a priori thresholding of the weights or knowledge of their maximal value. We calculate its mean and variance for random uniform or Gaussian distributions, which allows us to introduce a confidence measure of how significantly symmetric or asymmetric a specific configuration is, i.e. how likely it is that the configuration is the result of chance. We demonstrate the discriminatory power of our symmetry measure by inspecting the eigenvalues of different types of connectivity matrices. We show that a Gaussian weight distribution biases the connectivity motifs to more symmetric configurations than a uniform distribution and that introducing a random synaptic pruning, mimicking developmental regulation in synaptogenesis, biases the connectivity motifs to more asymmetric configurations, regardless of the distribution. We expect that our work will benefit the computational modelling community, by providing a systematic way to characterise symmetry and asymmetry in network structures. Further, our symmetry measure will be of use to electrophysiologists that investigate symmetry of network connectivity.

  1. New Constraints on the Geometry and Kinematics of Matter Surrounding the Accretion Flow in X-Ray Binaries from Chandra High-energy Transmission Grating X-Ray Spectroscopy

    NASA Astrophysics Data System (ADS)

    Tzanavaris, P.; Yaqoob, T.

    2018-03-01

    The narrow, neutral Fe Kα fluorescence emission line in X-ray binaries (XRBs) is a powerful probe of the geometry, kinematics, and Fe abundance of matter around the accretion flow. In a recent study it has been claimed, using Chandra High-Energy Transmission Grating (HETG) spectra for a sample of XRBs, that the circumnuclear material is consistent with a solar-abundance, uniform, spherical distribution. It was also claimed that the Fe Kα line was unresolved in all cases by the HETG. However, these conclusions were based on ad hoc models that did not attempt to relate the global column density to the Fe Kα line emission. We revisit the sample and test a self-consistent model of a uniform, spherical X-ray reprocessor against HETG spectra from 56 observations of 14 Galactic XRBs. We find that the model is ruled out in 13/14 sources because a variable Fe abundance is required. In two sources a spherical distribution is viable, but with nonsolar Fe abundance. We also applied a solar-abundance Compton-thick reflection model, which can account for the spectra that are inconsistent with a spherical model, but spectra with a broader bandpass are required to better constrain model parameters. We also robustly measured the velocity width of the Fe Kα line and found FWHM values of up to ∼5000 km s‑1. Only in some spectra was the Fe Kα line unresolved by the HETG.

  2. Interfacial effect on physical properties of composite media: Interfacial volume fraction with non-spherical hard-core-soft-shell-structured particles.

    PubMed

    Xu, Wenxiang; Duan, Qinglin; Ma, Huaifa; Chen, Wen; Chen, Huisu

    2015-11-02

    Interfaces are known to be crucial in a variety of fields and the interfacial volume fraction dramatically affects physical properties of composite media. However, it is an open problem with great significance how to determine the interfacial property in composite media with inclusions of complex geometry. By the stereological theory and the nearest-surface distribution functions, we first propose a theoretical framework to symmetrically present the interfacial volume fraction. In order to verify the interesting generalization, we simulate three-phase composite media by employing hard-core-soft-shell structures composed of hard mono-/polydisperse non-spherical particles, soft interfaces, and matrix. We numerically derive the interfacial volume fraction by a Monte Carlo integration scheme. With the theoretical and numerical results, we find that the interfacial volume fraction is strongly dependent on the so-called geometric size factor and sphericity characterizing the geometric shape in spite of anisotropic particle types. As a significant interfacial property, the present theoretical contribution can be further drawn into predicting the effective transport properties of composite materials.

  3. Interfacial effect on physical properties of composite media: Interfacial volume fraction with non-spherical hard-core-soft-shell-structured particles

    PubMed Central

    Xu, Wenxiang; Duan, Qinglin; Ma, Huaifa; Chen, Wen; Chen, Huisu

    2015-01-01

    Interfaces are known to be crucial in a variety of fields and the interfacial volume fraction dramatically affects physical properties of composite media. However, it is an open problem with great significance how to determine the interfacial property in composite media with inclusions of complex geometry. By the stereological theory and the nearest-surface distribution functions, we first propose a theoretical framework to symmetrically present the interfacial volume fraction. In order to verify the interesting generalization, we simulate three-phase composite media by employing hard-core-soft-shell structures composed of hard mono-/polydisperse non-spherical particles, soft interfaces, and matrix. We numerically derive the interfacial volume fraction by a Monte Carlo integration scheme. With the theoretical and numerical results, we find that the interfacial volume fraction is strongly dependent on the so-called geometric size factor and sphericity characterizing the geometric shape in spite of anisotropic particle types. As a significant interfacial property, the present theoretical contribution can be further drawn into predicting the effective transport properties of composite materials. PMID:26522701

  4. Diffusion-mediated dephasing in the dipole field around a single spherical magnetic object.

    PubMed

    Buschle, Lukas R; Kurz, Felix T; Kampf, Thomas; Triphan, Simon M F; Schlemmer, Heinz-Peter; Ziener, Christian Herbert

    2015-11-01

    In this work, the time evolution of the free induction decay caused by the local dipole field of a spherical magnetic perturber is analyzed. The complicated treatment of the diffusion process is replaced by the strong-collision-approximation that allows a determination of the free induction decay in dependence of the underlying microscopic tissue parameters such as diffusion coefficient, sphere radius and susceptibility difference. The interplay between susceptibility- and diffusion-mediated effects yields several dephasing regimes of which, so far, only the classical regimes of motional narrowing and static dephasing for dominant and negligible diffusion, respectively, were extensively examined. Due to the asymmetric form of the dipole field for spherical objects, the free induction decay exhibits a complex component in contradiction to the cylindrical case, where the symmetric local dipole field only causes a purely real induction decay. Knowledge of the shape of the corresponding frequency distribution is necessary for the evaluation of more sophisticated pulse sequences and a detailed understanding of the off-resonance distribution allows improved quantification of transverse relaxation. Copyright © 2015 Elsevier Inc. All rights reserved.

  5. Acoustic manipulation of active spherical carriers: Generation of negative radiation force

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Rajabi, Majid, E-mail: majid_rajabi@iust.ac.ir; Mojahed, Alireza

    2016-09-15

    This paper examines theoretically a novel mechanism of generating negative (pulling) radiation force for acoustic manipulation of spherical carriers equipped with piezoelectric actuators in its inner surface. In this mechanism, the spherical particle is handled by common plane progressive monochromatic acoustic waves instead of zero-/higher- order Bessel beams or standing waves field. The handling strategy is based on applying a spatially uniform harmonic electrical voltage at the piezoelectric actuator with the same frequency of handling acoustic waves, in order to change the radiation force effect from repulsive (away from source) to attractive (toward source). This study may be considered asmore » a start point for development of contact-free precise handling and entrapment technology of active carriers which are essential in many engineering and medicine applications.« less

  6. Spectral stability of unitary network models

    NASA Astrophysics Data System (ADS)

    Asch, Joachim; Bourget, Olivier; Joye, Alain

    2015-08-01

    We review various unitary network models used in quantum computing, spectral analysis or condensed matter physics and establish relationships between them. We show that symmetric one-dimensional quantum walks are universal, as are CMV matrices. We prove spectral stability and propagation properties for general asymptotically uniform models by means of unitary Mourre theory.

  7. Spherical cows in the sky with fab four

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kaloper, Nemanja; Sandora, McCullen, E-mail: kaloper@physics.ucdavis.edu, E-mail: mesandora@ucdavis.edu

    2014-05-01

    We explore spherically symmetric static solutions in a subclass of unitary scalar-tensor theories of gravity, called the 'Fab Four' models. The weak field large distance solutions may be phenomenologically viable, but only if the Gauss-Bonnet term is negligible. Only in this limit will the Vainshtein mechanism work consistently. Further, classical constraints and unitarity bounds constrain the models quite tightly. Nevertheless, in the limits where the range of individual terms at large scales is respectively Kinetic Braiding, Horndeski, and Gauss-Bonnet, the horizon scale effects may occur while the theory satisfies Solar system constraints and, marginally, unitarity bounds. On the other hand,more » to bring the cutoff down to below a millimeter constrains all the couplings scales such that 'Fab Fours' can't be heard outside of the Solar system.« less

  8. Numerical study of spherical Taylor-Couette flow

    NASA Technical Reports Server (NTRS)

    Yang, R.-J.

    1989-01-01

    A new technique to simulate Taylor vortices in a spherical gap between a rotating inner sphere and a stationary outer one has been developed and tested. Paths leading to zero-, one-, and two-vortex flows are designed heuristically. Fictitious symmetric boundaries near the equator are imposed, and the choice of the location of the fictitious boundaries is determined by either one- or two-vortex flow being stimulated. The imposition of one or two fictitious boundaries during the initial calculation generates the state suitable for one-or two-vortex flow to exist. After removing the fictitious boundaries, the flow settles down into its own attractor. Using this method, the three steady flow modes can be simulated by using a half domain. The technique can converge to desired flows very fast, and its results show excellent agreement with experimental ones.

  9. Outwardly Propagating Flames at Elevated Pressures

    NASA Technical Reports Server (NTRS)

    Law, C. K.; Rozenchan, G.; Tse, S. D.; Zhu, D. L.

    2001-01-01

    Spherical, outwardly-propagating flames of CH4-O2-inert and H2-O2-inert mixtures were experimentally studied in a high pressure apparatus. Stretch-free flame speeds and Markstein lengths were extracted for a wide range of pressures and equivalence ratios for spherically-symmetric, smooth flamefronts and compared to numerical computations with detailed chemistry and transport, as well as existing data in the literature. Wrinkle development was examined for propagating flames that were unstable under our experimental conditions. Hydrodynamic cells developed for most H2-air and CH4-air flames at elevated pressures, while thermal-diffusive instabilities were also observed for lean and near-stoichiometric hydrogen flames at pressures above atmospheric. Strategies in suppressing or delaying the onset of cell formation have been assessed. Buoyancy effects affected sufficiently off-stoichiometric CH4 mixtures at high pressures.

  10. Equilibrium location for spherical DNA and toroidal cyclodextrin

    NASA Astrophysics Data System (ADS)

    Sarapat, Pakhapoom; Baowan, Duangkamon; Hill, James M.

    2018-05-01

    Cyclodextrin comprises a ring structure composed of glucose molecules with an ability to form complexes of certain substances within its central cavity. The compound can be utilised for various applications including food, textiles, cosmetics, pharmaceutics, and gene delivery. In gene transfer, the possibility of forming complexes depends upon the interaction energy between cyclodextrin and DNA molecules which here are modelled as a torus and a sphere, respectively. Our proposed model is derived using the continuum approximation together with the Lennard-Jones potential, and the total interaction energy is obtained by integrating over both the spherical and toroidal surfaces. The results suggest that the DNA prefers to be symmetrically situated about 1.2 Å above the centre of the cyclodextrin to minimise its energy. Furthermore, an optimal configuration can be determined for any given size of torus and sphere.

  11. Preparation of ultra-fine powders from polysaccharide-coated solid lipid nanoparticles and nanostructured lipid carriers by innovative nano spray drying technology.

    PubMed

    Wang, Taoran; Hu, Qiaobin; Zhou, Mingyong; Xue, Jingyi; Luo, Yangchao

    2016-09-10

    In this study, five polysaccharides were applied as natural polymeric coating materials to prepare solid lipid nanoparticles (SLN) and nanostructure lipid carriers (NLC), and then the obtained lipid colloidal particles were transformed to solid powders by the innovative nano spray drying technology. The feasibility and suitability of this new technology to generate ultra-fine lipid powder particles were evaluated and the formulation was optimized. The spray dried SLN powder exhibited the aggregated and irregular shape and dimension, but small, uniform, well-separated spherical powder particles of was obtained from NLC. The optimal formulation of NLC was prepared by a 20-30% oleic acid content with carrageenan or pectin as coating material. Therefore, nano spray drying technology has a potential application to produce uniform, spherical, and sub-microscale lipid powder particles when the formulation of lipid delivery system is appropriately designed. Copyright © 2016 Elsevier B.V. All rights reserved.

  12. Development of a radio frequency ion source with multi-helicon plasma injectors for neutral beam injection system of Versatile Experiment Spherical Torus

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Choe, Kyumin; Jung, Bongki; Chung, Kyoung-Jae, E-mail: jkjlsh1@snu.ac.kr

    2014-02-15

    Despite of high plasma density, helicon plasma has not yet been applied to a large area ion source such as a driver for neutral beam injection (NBI) system due to intrinsically poor plasma uniformity in the discharge region. In this study, a radio-frequency (RF) ion source with multi-helicon plasma injectors for high plasma density with good uniformity has been designed and constructed for the NBI system of Versatile Experiment Spherical Torus at Seoul National University. The ion source consists of a rectangular plasma expansion chamber (120 × 120 × 120 mm{sup 3}), four helicon plasma injectors with annular permanent magnetsmore » and RF power system. Main feature of the source is downstream plasma confinement in the cusp magnetic field configuration which is generated by arranging polarities of permanent magnets in the helicon plasma injectors. In this paper, detailed design of the multi-helicon plasma injector and plasma characteristics of the ion source are presented.« less

  13. Development of a radio frequency ion source with multi-helicon plasma injectors for neutral beam injection system of Versatile Experiment Spherical Torus

    NASA Astrophysics Data System (ADS)

    Choe, Kyumin; Jung, Bongki; Chung, Kyoung-Jae; Hwang, Y. S.

    2014-02-01

    Despite of high plasma density, helicon plasma has not yet been applied to a large area ion source such as a driver for neutral beam injection (NBI) system due to intrinsically poor plasma uniformity in the discharge region. In this study, a radio-frequency (RF) ion source with multi-helicon plasma injectors for high plasma density with good uniformity has been designed and constructed for the NBI system of Versatile Experiment Spherical Torus at Seoul National University. The ion source consists of a rectangular plasma expansion chamber (120 × 120 × 120 mm3), four helicon plasma injectors with annular permanent magnets and RF power system. Main feature of the source is downstream plasma confinement in the cusp magnetic field configuration which is generated by arranging polarities of permanent magnets in the helicon plasma injectors. In this paper, detailed design of the multi-helicon plasma injector and plasma characteristics of the ion source are presented.

  14. Development of a radio frequency ion source with multi-helicon plasma injectors for neutral beam injection system of Versatile Experiment Spherical Torus.

    PubMed

    Choe, Kyumin; Jung, Bongki; Chung, Kyoung-Jae; Hwang, Y S

    2014-02-01

    Despite of high plasma density, helicon plasma has not yet been applied to a large area ion source such as a driver for neutral beam injection (NBI) system due to intrinsically poor plasma uniformity in the discharge region. In this study, a radio-frequency (RF) ion source with multi-helicon plasma injectors for high plasma density with good uniformity has been designed and constructed for the NBI system of Versatile Experiment Spherical Torus at Seoul National University. The ion source consists of a rectangular plasma expansion chamber (120 × 120 × 120 mm(3)), four helicon plasma injectors with annular permanent magnets and RF power system. Main feature of the source is downstream plasma confinement in the cusp magnetic field configuration which is generated by arranging polarities of permanent magnets in the helicon plasma injectors. In this paper, detailed design of the multi-helicon plasma injector and plasma characteristics of the ion source are presented.

  15. Diffusion-controlled reactions: hydrodynamic interaction between charged, uniformly reactive spherical reactants.

    PubMed

    Allison, Stuart

    2006-12-28

    In this work, different models of hydrodynamic interaction (HI) are examined in the diffusion-controlled reaction between uniformly reactive charged spherical particles. In addition to Oseen "stick" and "slip" models of HI, one is considered that accounts for the disturbance of fluid flow by the ions around one reactive partner as they interact with a neighboring reactive species. This interaction is closely related to the "electrophoretic effect" in electrokinetics and can be described by a fairly simple electrophoretic, or E-tensor. These models are applied to the electron-transfer quenching reaction of Ru(bpy)3(2+) and methyl viologen (MV2+) over a wide range of NaCl concentrations (Chiorboli, C. et al., J. Phys. Chem. 1988, 92, 156). The back reaction is also considered. From a comparison of the salt dependence of the model and experimental rates, it is concluded that the "E-tensor" model works best and ignoring HI altogether works worst. The Oseen "stick" and "slip" models fall between these.

  16. Synthesis of water dispersible boron core silica shell (B@SiO2) nanoparticles

    NASA Astrophysics Data System (ADS)

    Walton, Nathan I.; Gao, Zhe; Eygeris, Yulia; Ghandehari, Hamidreza; Zharov, Ilya

    2018-04-01

    Water dispersible boron nanoparticles have great potential as materials for boron neutron capture therapy of cancer and magnetic resonance imaging, if they are prepared on a large scale with uniform size and shape and hydrophilic modifiable surface. We report the first method to prepare spherical, monodisperse, water dispersible boron core silica shell nanoparticles (B@SiO2 NPs) suitable for aforementioned biomedical applications. In this method, 40 nm elemental boron nanoparticles, easily prepared by mechanical milling and carrying 10-undecenoic acid surface ligands, are hydrosilylated using triethoxysilane, followed by base-catalyzed hydrolysis of tetraethoxysilane, which forms a 10-nm silica shell around the boron core. This simple two-step process converts irregularly shaped hydrophobic boron particles into the spherically shaped uniform nanoparticles. The B@SiO2 NPs are dispersible in water and the silica shell surface can be modified with primary amines that allow for the attachment of a fluorophore and, potentially, of targeting moieties. [Figure not available: see fulltext.

  17. An analytical model for the evolution of the coldest component of the Boomerang Nebula

    NASA Astrophysics Data System (ADS)

    Bohigas, J.

    2017-04-01

    The most striking feature of the Boomerang Nebula is a large nearly spherical cloud where the temperature is close to 2 K. At its inner and outer boundaries, this cloud is expanding at velocities close to 35 and 180 km s-1. The cloud surrounds an asymptotic giant branch (AGB) star and a smaller bipolar molecular cloud, expanding much more slowly. The ultracold spherical cloud has been and still is expanding into a rarefied medium, since there is no trace of a shock wave. This ultracold cloud is modelled using the analytical solution for a power-driven expansion of a spherically symmetric cloud, followed by an adiabatic expansion phase, both into a vacuum. Assuming that the cloud is at a distance of 1500 pc, the present temperature and velocity profile are reproduced with a model where the cloud has an energy close to 8.5 × 1046 erg per solar mass and was ejected 1000 yr ago. In this model, the power-driven phase lasts for ˜10 yr and half of the energy is injected in less than a year. The general features of this model, are amenable with what is found in other spherical shells surrounding AGB stars, the small amount of mass lost by massive OH/IR stars and evolutionary models indicating that there may be extremely high and abrupt mass-loss phases in AGB stars. The energy and time-scale suggest that the ejection of the cold spherical cloud was an intermediate luminosity transient.

  18. Structure of spherical electric double layers with fully asymmetric electrolytes: a systematic study by Monte Carlo simulations and density functional theory.

    PubMed

    Patra, Chandra N

    2014-11-14

    A systematic investigation of the spherical electric double layers with the electrolytes having size as well as charge asymmetry is carried out using density functional theory and Monte Carlo simulations. The system is considered within the primitive model, where the macroion is a structureless hard spherical colloid, the small ions as charged hard spheres of different size, and the solvent is represented as a dielectric continuum. The present theory approximates the hard sphere part of the one particle correlation function using a weighted density approach whereas a perturbation expansion around the uniform fluid is applied to evaluate the ionic contribution. The theory is in quantitative agreement with Monte Carlo simulation for the density and the mean electrostatic potential profiles over a wide range of electrolyte concentrations, surface charge densities, valence of small ions, and macroion sizes. The theory provides distinctive evidence of charge and size correlations within the electrode-electrolyte interface in spherical geometry.

  19. Ultraviolet excitation of remote phosphor with symmetrical illumination used in dual-sided liquid-crystal display.

    PubMed

    Huang, Hsin-Tao; Tsai, Chuang-Chuang; Huang, Yi-Pai

    2010-08-01

    The UV-excited flat lighting (UFL) technique differs from conventional fluorescent lamp or LED illumination. It involves using a remote phosphor film to convert the wavelength of UV light to visible light, achieving high brightness and planar and uniform illumination. In particular, UFL can accomplish compact size, low power consumption, and symmetrical dual-sided illumination. Additionally, UFL utilizes a thermal radiation mechanism to release the large amount of heat that is generated upon illumination without thermal accumulation. These characteristics of the UFL technique can motivate a wide range of lighting applications in thin-film transistor LCD backlighting or general lighting.

  20. Interplay between geometry and flow distribution in an airway tree.

    PubMed

    Mauroy, B; Filoche, M; Andrade, J S; Sapoval, B

    2003-04-11

    Uniform flow distribution in a symmetric volume can be realized through a symmetric branched tree. It is shown here, however, by 3D numerical simulation of the Navier-Stokes equations, that the flow partitioning can be highly sensitive to deviations from exact symmetry if inertial effects are present. The flow asymmetry is quantified and found to depend on the Reynolds number. Moreover, for a given Reynolds number, we show that the flow distribution depends on the aspect ratio of the branching elements as well as their angular arrangement. Our results indicate that physiological variability should be severely restricted in order to ensure adequate fluid distribution through a tree.

  1. Four-mirror extreme ultraviolet (EUV) lithography projection system

    DOEpatents

    Cohen, Simon J; Jeong, Hwan J; Shafer, David R

    2000-01-01

    The invention is directed to a four-mirror catoptric projection system for extreme ultraviolet (EUV) lithography to transfer a pattern from a reflective reticle to a wafer substrate. In order along the light path followed by light from the reticle to the wafer substrate, the system includes a dominantly hyperbolic convex mirror, a dominantly elliptical concave mirror, spherical convex mirror, and spherical concave mirror. The reticle and wafer substrate are positioned along the system's optical axis on opposite sides of the mirrors. The hyperbolic and elliptical mirrors are positioned on the same side of the system's optical axis as the reticle, and are relatively large in diameter as they are positioned on the high magnification side of the system. The hyperbolic and elliptical mirrors are relatively far off the optical axis and hence they have significant aspherical components in their curvatures. The convex spherical mirror is positioned on the optical axis, and has a substantially or perfectly spherical shape. The spherical concave mirror is positioned substantially on the opposite side of the optical axis from the hyperbolic and elliptical mirrors. Because it is positioned off-axis to a degree, the spherical concave mirror has some asphericity to counter aberrations. The spherical concave mirror forms a relatively large, uniform field on the wafer substrate. The mirrors can be tilted or decentered slightly to achieve further increase in the field size.

  2. Solution of Eshelby's inclusion problem with a bounded domain and Eshelby's tensor for a spherical inclusion in a finite spherical matrix based on a simplified strain gradient elasticity theory

    NASA Astrophysics Data System (ADS)

    Gao, X.-L.; Ma, H. M.

    2010-05-01

    A solution for Eshelby's inclusion problem of a finite homogeneous isotropic elastic body containing an inclusion prescribed with a uniform eigenstrain and a uniform eigenstrain gradient is derived in a general form using a simplified strain gradient elasticity theory (SSGET). An extended Betti's reciprocal theorem and an extended Somigliana's identity based on the SSGET are proposed and utilized to solve the finite-domain inclusion problem. The solution for the disturbed displacement field is expressed in terms of the Green's function for an infinite three-dimensional elastic body in the SSGET. It contains a volume integral term and a surface integral term. The former is the same as that for the infinite-domain inclusion problem based on the SSGET, while the latter represents the boundary effect. The solution reduces to that of the infinite-domain inclusion problem when the boundary effect is not considered. The problem of a spherical inclusion embedded concentrically in a finite spherical elastic body is analytically solved by applying the general solution, with the Eshelby tensor and its volume average obtained in closed forms. This Eshelby tensor depends on the position, inclusion size, matrix size, and material length scale parameter, and, as a result, can capture the inclusion size and boundary effects, unlike existing Eshelby tensors. It reduces to the classical Eshelby tensor for the spherical inclusion in an infinite matrix if both the strain gradient and boundary effects are suppressed. Numerical results quantitatively show that the inclusion size effect can be quite large when the inclusion is very small and that the boundary effect can dominate when the inclusion volume fraction is very high. However, the inclusion size effect is diminishing as the inclusion becomes large enough, and the boundary effect is vanishing as the inclusion volume fraction gets sufficiently low.

  3. Non-local currents and the structure of eigenstates in planar discrete systems with local symmetries

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Röntgen, M., E-mail: mroentge@physnet.uni-hamburg.de; Morfonios, C.V., E-mail: christian.morfonios@physnet.uni-hamburg.de; Diakonos, F.K., E-mail: fdiakono@phys.uoa.gr

    Local symmetries are spatial symmetries present in a subdomain of a complex system. By using and extending a framework of so-called non-local currents that has been established recently, we show that one can gain knowledge about the structure of eigenstates in locally symmetric setups through a Kirchhoff-type law for the non-local currents. The framework is applicable to all discrete planar Schrödinger setups, including those with non-uniform connectivity. Conditions for spatially constant non-local currents are derived and we explore two types of locally symmetric subsystems in detail, closed-loops and one-dimensional open ended chains. We find these systems to support locally similarmore » or even locally symmetric eigenstates. - Highlights: • We extend the framework of non-local currents to discrete planar systems. • Structural information about the eigenstates is gained. • Conditions for the constancy of non-local currents are derived. • We use the framework to design two types of example systems featuring locally symmetric eigenstates.« less

  4. Numerical relativity and the early Universe

    NASA Astrophysics Data System (ADS)

    Mironov, Sergey

    2016-10-01

    We consider numerical simulations in general relativity in ADM formalism with cosmological ansatz for the metric. This ansatz is convenient for investigations of the Universe creation in laboratory with Galileons. Here we consider toy model for the software: spherically symmetric scalar field minimally coupled to the gravity with asymmetric double well potential. We studied the dependence of radius of critical bubble on the parameters of the theory. It demonstrates the wide applicability of thin-wall approximation. We did not find any kind of stable bubble solution.

  5. Chameleon stars

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Dzhunushaliev, Vladimir; Institute of Physicotechnical Problems and Material Science of the NAS of the Kyrgyz Republic, 265 a, Chui Street, Bishkek, 720071; Folomeev, Vladimir

    2011-10-15

    We consider a gravitating spherically symmetric configuration consisting of a scalar field nonminimally coupled to ordinary matter in the form of a perfect fluid. For this system we find static, regular, asymptotically flat solutions for both relativistic and nonrelativistic cases. It is shown that the presence of the nonminimal interaction leads to substantial changes both in the radial matter distribution of the star and in the star's total mass. A simple stability test indicates that, for the choice of parameters used in the paper, the solutions are unstable.

  6. An inverse method using toroidal mode data

    USGS Publications Warehouse

    Willis, C.

    1986-01-01

    The author presents a numerical method for calculating the density and S-wave velocity in the upper mantle of a spherically symmetric, non-rotating Earth which consists of a perfect elastic, isotropic material. The data comes from the periods of the toroidal oscillations. She tests the method on a smoothed version of model A. The error in the reconstruction is less than 1%. The effects of perturbations in the eigenvalues are studied and she finds that the final model is sensitive to errors in the data.

  7. Viscous-shock-layer solutions for turbulent flow of radiating gas mixtures in chemical equilibrium

    NASA Technical Reports Server (NTRS)

    Anderson, E. C.; Moss, J. N.

    1975-01-01

    The viscous-shock-layer equations for hypersonic laminar and turbulent flows of radiating or nonradiating gas mixtures in chemical equilibrium are presented for two-dimensional and axially-symmetric flow fields. Solutions were obtained using an implicit finite-difference scheme and results are presented for hypersonic flow over spherically-blunted cone configurations at freestream conditions representative of entry into the atmosphere of Venus. These data are compared with solutions obtained using other methods of analysis.

  8. Viscous shock layer solutions for turbulent flow of radiating gas mixtures in chemical equilibrium

    NASA Technical Reports Server (NTRS)

    Anderson, E. C.; Moss, J. N.

    1975-01-01

    The viscous shock layer equations for hypersonic laminar and turbulent flows of radiating or nonradiating gas mixtures in chemical equilibrium are presented for two-dimensional and axially symmetric flow fields. Solutions are obtained using an implicit finite difference scheme and results are presented for hypersonic flow over spherically blunted cone configurations at free stream conditions representative of entry into the atmosphere of Venus. These data are compared with solutions obtained using other methods of analysis.

  9. Gravitation: Foundations and Frontiers

    NASA Astrophysics Data System (ADS)

    Padmanabhan, T.

    2010-01-01

    1. Special relativity; 2. Scalar and electromagnetic fields in special relativity; 3. Gravity and spacetime geometry: the inescapable connection; 4. Metric tensor, geodesics and covariant derivative; 5. Curvature of spacetime; 6. Einstein's field equations and gravitational dynamics; 7. Spherically symmetric geometry; 8. Black holes; 9. Gravitational waves; 10. Relativistic cosmology; 11. Differential forms and exterior calculus; 12. Hamiltonian structure of general relativity; 13. Evolution of cosmological perturbations; 14. Quantum field theory in curved spacetime; 15. Gravity in higher and lower dimensions; 16. Gravity as an emergent phenomenon; Notes; Index.

  10. General Relativity

    NASA Astrophysics Data System (ADS)

    Hobson, M. P.; Efstathiou, G. P.; Lasenby, A. N.

    2006-02-01

    1. The spacetime of special relativity; 2. Manifolds and coordinates; 3. Vector calculus on manifolds; 4. Tensor calculus on manifolds; 5. Special relativity revisited; 6. Electromagnetism; 7. The equivalence principle and spacetime curvature; 8. The gravitational field equations; 9. The Schwarzschild geometry; 10. Experimental tests of general relativity; 11. Schwarzschild black holes; 12. Further spherically-symmetric geometries; 13. The Kerr geometry; 14. The Friedmann-Robertson-Walker geometry; 15. Cosmological models; 16. Inflationary cosmology; 17. Linearised general relativity; 18. Gravitational waves; 19. A variational approach to general relativity.

  11. Hawking temperature of rotating charged black strings from tunneling

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Ahmed, Jamil; Saifullah, K., E-mail: jamil_051@yahoo.com, E-mail: saifullah@qau.edu.pk

    2011-11-01

    Thermal radiations from spherically symmetric black holes have been studied from the point of view of quantum tunneling. In this paper we extend this approach to study radiation of fermions from charged and rotating black strings. Using WKB approximation and Hamilton-Jacobi method we work out the tunneling probabilities of incoming and outgoing fermions and find the correct Hawking temperature for these objects. We show that in appropriate limits the results reduce to those for the uncharged and non-rotating black strings.

  12. Soft black hole absorption rates as conservation laws

    DOE PAGES

    Avery, Steven G.; Schwab, Burkhard U. W.

    2017-04-10

    The absorption rate of low-energy, or soft, electromagnetic radiation by spherically symmetric black holes in arbitrary dimensions is shown to be fixed by conservation of energy and large gauge transformations. Here, we interpret this result as the explicit realization of the Hawking-Perry-Strominger Ward identity for large gauge transformations in the background of a non-evaporating black hole. Along the way we rederive and extend our previous analytic results regarding the absorption rate for the minimal scalar and the photon.

  13. Caustics for spherical waves

    DOE PAGES

    de Rham, Claudia; Motohashi, Hayato

    2017-03-07

    We study the development of caustics in shift-symmetric scalar field theories by focusing on simple waves with an S O ( p ) -symmetry in an arbitrary number of space dimensions. We show that the pure Galileon, the DBI–Galileon, and the extreme-relativistic Galileon naturally emerge as the unique set of caustic-free theories, highlighting a link between the caustic-free condition for simple S O ( p ) -waves and the existence of either a global Galilean symmetry or a global (extreme-)relativistic Galilean symmetry.

  14. Revisiting the analogue of the Jebsen-Birkhoff theorem in Brans-Dicke gravity

    NASA Astrophysics Data System (ADS)

    Faraoni, Valerio; Hammad, Fayçal; Cardini, Adriana M.; Gobeil, Thomas

    2018-04-01

    We report the explicit form of the general static, spherically symmetric, and asymptotically flat solution of vacuum Brans-Dicke gravity in the Jordan frame, assuming that the Brans-Dicke scalar field has no singularities or zeros (except possibly for a central singularity). This general solution is conformal to the Fisher-Wyman geometry of Einstein theory and its nature depends on a scalar charge parameter. Apart from the Schwarzschild black hole, only wormhole throats and central naked singularities are possible.

  15. Quasicrystalline structures and uses thereof

    DOEpatents

    Steinhardt, Paul J; Chaikin, Paul Michael; Man, Weining

    2013-12-03

    This invention relates generally to the field of quasicrystalline structures. In preferred embodiments, the stopgap structure is more spherically symmetric than periodic structures facilitating the formation of stopgaps in nearly all directions because of higher rotational symmetries. More particularly, the invention relates to the use of quasicrystalline structures for optical, mechanical, electrical and magnetic purposes. In some embodiments, the invention relates to manipulating, controlling, modulating and directing waves including electromagnetic, sound, spin, and surface waves, for pre-selected range of wavelengths propagating in multiple directions.

  16. Quasicrystalline structures and uses thereof

    DOEpatents

    Steinhardt, Paul Joseph [Princeton, NJ; Chaikin, Paul Michael [New York, NY; Man, Weining [San Francisco, CA

    2011-11-22

    This invention relates generally to the field of quasicrystalline structures. In preferred embodiments, the stopgap structure is more spherically symmetric than periodic structures facilitating the formation of stopgaps in nearly all directions because of higher rotational symmetries. More particularly, the invention relates to the use of quasicrystalline structures for optical, mechanical, electrical and magnetic purposes. In some embodiments, the invention relates to manipulating, controlling, modulating and directing waves including electromagnetic, sound, spin, and surface waves, for a pre-selected range of wavelengths propagating in multiple directions.

  17. Quasicrystalline structures and uses thereof

    DOEpatents

    Steinhardt, Paul Joseph; Chaikin, Paul Michael; Man, Weining

    2017-02-14

    This invention relates generally to the field of quasicrystalline structures. In preferred embodiments, the stopgap structure is more spherically symmetric than periodic structures facilitating the formation of stopgaps in nearly all directions because of higher rotational symmetries. More particularly, the invention relates to the use of quasicrystalline structures for optical, mechanical, electrical and magnetic purposes. In some embodiments, the invention relates to manipulating, controlling, modulating and directing waves including electromagnetic, sound, spin, and surface waves, for pre-selected range of wavelengths propagating in multiple directions.

  18. Limiting assumptions in molecular modeling: electrostatics.

    PubMed

    Marshall, Garland R

    2013-02-01

    Molecular mechanics attempts to represent intermolecular interactions in terms of classical physics. Initial efforts assumed a point charge located at the atom center and coulombic interactions. It is been recognized over multiple decades that simply representing electrostatics with a charge on each atom failed to reproduce the electrostatic potential surrounding a molecule as estimated by quantum mechanics. Molecular orbitals are not spherically symmetrical, an implicit assumption of monopole electrostatics. This perspective reviews recent evidence that requires use of multipole electrostatics and polarizability in molecular modeling.

  19. The Bach equations in spin-coefficient form

    NASA Astrophysics Data System (ADS)

    Forbes, Hamish

    2018-06-01

    Conformal gravity theories are defined by field equations that determine only the conformal structure of the spacetime manifold. The Bach equations represent an early example of such a theory, we present them here in component form in terms of spin- and boost-weighted spin-coefficients using the compacted spin-coefficient formalism. These equations can be used as an efficient alternative to the standard tensor form. As a simple application we solve the Bach equations for pp-wave and static spherically symmetric spacetimes.

  20. SU(2) Yang-Mills solitons in R2 gravity

    NASA Astrophysics Data System (ADS)

    Perapechka, I.; Shnir, Ya.

    2018-05-01

    We construct new family of spherically symmetric regular solutions of SU (2) Yang-Mills theory coupled to pure R2 gravity. The particle-like field configurations possess non-integer non-Abelian magnetic charge. A discussion of the main properties of the solutions and their differences from the usual Bartnik-McKinnon solitons in the asymptotically flat case is presented. It is shown that there is continuous family of linearly stable non-trivial solutions in which the gauge field has no nodes.

  1. Toroidal marginally outer trapped surfaces in closed Friedmann-Lemaître-Robertson-Walker spacetimes: Stability and isoperimetric inequalities

    NASA Astrophysics Data System (ADS)

    Mach, Patryk; Xie, Naqing

    2017-10-01

    We investigate toroidal marginally outer trapped surfaces (MOTS) and marginally outer trapped tubes (MOTT) in closed Friedmann-Lemaître-Robertson-Walker (FLRW) geometries. They are constructed by embedding constant mean curvature (CMC) Clifford tori in a FLRW spacetime. This construction is used to assess the quality of certain isoperimetric inequalities, recently proved in axial symmetry. Similarly to spherically symmetric MOTS existing in FLRW spacetimes, the toroidal ones are also unstable.

  2. Stability of thin shell wormholes with a modified Chaplygin gas in Einstein-Hoffman-Born-Infeld theory

    NASA Astrophysics Data System (ADS)

    Eid, A.

    2017-11-01

    In the framework of Darmois-Israel formalism, the dynamics of motion equations of spherically symmetric thin shell wormholes that are supported by a modified Chaplygin gas in Einstein-Hoffman-Born-Infeld theory are constructed. The stability analysis of a thin shell wormhole is also discussed using a linearized radial perturbation around static solutions at the wormhole throat. The existence of stable static solutions depends on the value of some parameters of dynamical shell.

  3. Anisotropic solutions by gravitational decoupling

    NASA Astrophysics Data System (ADS)

    Ovalle, J.; Casadio, R.; da Rocha, R.; Sotomayor, A.

    2018-02-01

    We investigate the extension of isotropic interior solutions for static self-gravitating systems to include the effects of anisotropic spherically symmetric gravitational sources by means of the gravitational decoupling realised via the minimal geometric deformation approach. In particular, the matching conditions at the surface of the star with the outer Schwarzschild space-time are studied in great detail, and we describe how to generate, from a single physically acceptable isotropic solution, new families of anisotropic solutions whose physical acceptability is also inherited from their isotropic parent.

  4. An instability in neutron stars at birth

    NASA Technical Reports Server (NTRS)

    Burrows, Adam; Fryxell, Bruce A.

    1992-01-01

    Calculations with a two-dimensional hydrodynamic simulation show that a generic Raleigh-Taylor-like instability occurs in the mantles of nascent neutron stars, that it is possibly violent, and that the standard spherically symmetric models of neutron star birth and supernova explosion may be inadequate. Whether this 'convective' instability is pivotal to the supernova mechanism, pulsar nagnetic fields, or a host of other important issues that attend stellar collapse remains to be seen, but its existence promises to modify all questions concerning this most energetic of astronomical phenomena.

  5. Gravitational field of a concentrated mass in Jordan—Brans—Dicke theory

    NASA Astrophysics Data System (ADS)

    Arutyunyan, G. G.; Papoyan, V. V.

    1994-04-01

    The problem of determining the gravitational field of a static, spherically symmetric, self-gravitating object is formulated. The small number of physically applicable exact solutions of the equations in Jordan—Brans—Dicke theory is augmented with new exact solutions describing the external gravitational field of the given body. Once a solution has been found, it can be rewritten in modified curvature, homogeneous, and other coordinates by appropriate gauging. In a special case the solution coincides with the well-known Schwarzschild solution.

  6. Soft black hole absorption rates as conservation laws

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Avery, Steven G.; Schwab, Burkhard U. W.

    The absorption rate of low-energy, or soft, electromagnetic radiation by spherically symmetric black holes in arbitrary dimensions is shown to be fixed by conservation of energy and large gauge transformations. Here, we interpret this result as the explicit realization of the Hawking-Perry-Strominger Ward identity for large gauge transformations in the background of a non-evaporating black hole. Along the way we rederive and extend our previous analytic results regarding the absorption rate for the minimal scalar and the photon.

  7. NEUTRON ENERGY LEVELS IN A DIFFUSE POTENTIAL

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Ghosh, A.; Sil, N.C.

    1960-06-01

    The energy eigenvalues of neutrons within the nucleus for a spherically symmetrical potential V(r) = --V/sub 0/STAl + exp{(r-- R)/a}!/sup -1/ are investigated by following a new method of Lanczos for solving the differential equation. The s- and p-state energy levels are calculated for atomic mass 200 with the values of parameters adopted by Feshbach et al. in their calculation of the neutron strength function with a similar potential. The results of the calculation agree closely with those of Malenka. (auth)

  8. Addendum to ''Thin-shell wormholes supported by ordinary matter in Einstein-Gauss-Bonnet gravity''

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Simeone, Claudio

    2011-04-15

    Thin-shell wormholes are constructed starting from the exotic branch of the Wiltshire spherically symmetric solution of Einstein-Gauss-Bonnet gravity. The energy-momentum tensor of the shell is studied, and it is shown that configurations supported by matter satisfying the energy conditions exist for certain values of the parameters. Differing from the previous result associated with the normal branch of the Wiltshire solution, this is achieved for small positive values of the Gauss-Bonnet parameter and for vanishing charge.

  9. Classical dynamics on curved Snyder space

    NASA Astrophysics Data System (ADS)

    Ivetić, B.; Meljanac, S.; Mignemi, S.

    2014-05-01

    We study the classical dynamics of a particle in nonrelativistic Snyder-de Sitter space. We show that for spherically symmetric systems, parameterizing the solutions in terms of an auxiliary time variable, which is a function only of the physical time and of the energy and angular momentum of the particles, one can reduce the problem to the equivalent one in classical mechanics. We also discuss a relativistic extension of these results, and a generalization to the case in which the algebra is realized in flat space.

  10. Fabrication and Characterization of Nanoenergetic Hollow Spherical Hexanitrostibene (HNS) Derivatives.

    PubMed

    Cao, Xiong; Deng, Peng; Hu, Shuangqi; Ren, Lijun; Li, Xiaoxia; Xiao, Peng; Liu, Yu

    2018-05-16

    The spherization of nanoenergetic materials is the best way to improve the sensitivity and increase loading densities and detonation properties for weapons and ammunition, but the preparation of spherical nanoenergetic materials with high regularization, uniform size and monodispersity is still a challenge. In this paper, nanoenergetic hollow spherical hexanitrostibene (HNS) derivatives were fabricated via a one-pot copolymerization strategy, which is based on the reaction of HNS and piperazine in acetonitrile solution. Characterization results indicated the as-prepared reaction nanoenergetic products were HNS-derived oligomers, where a free radical copolymerization reaction process was inferred. The hollow sphere structure of the HNS derivatives was characterized by scanning electron microscopy (SEM), transmission electron microscope (TEM), and synchrotron radiation X-ray imaging technology. The properties of the nanoenergetic hollow spherical derivatives, including thermal decomposition and sensitivity are discussed in detail. Sensitivity studies showed that the nanoenergetic derivatives exhibited lower impact, friction and spark sensitivity than raw HNS. Thermogravimetric-differential scanning calorimeter (TG-DSC) results showed that continuous exothermic decomposition occurred in the whole temperature range, which indicated that nanoenergetic derivatives have a unique role in thermal applications. Therefore, nanoenergetic hollow spherical HNS derivatives could provide a new way to modify the properties of certain energetic compounds and fabricate spherical nanomaterials to improve the charge configuration.

  11. Evacuated optical structure comprising optical bench mounted to sidewall of vacuum chamber in a manner which inhibits deflection and rotation of the optical bench

    DOEpatents

    Bowers, Joel M.

    1994-01-01

    An improved evacuated optical structure is disclosed comprising an optical bench mounted in a vacuum vessel in a manner which inhibits transmission of movement of the vacuum vessel to the optical bench, yet provides a compact and economical structure. The vacuum vessel is mounted, through a sidewall thereof, to a support wall at four symmetrically positioned and spaced apart areas, each of which comprises a symmetrically positioned group of mounting structures passing through the sidewall of the vacuum vessel. The optical bench is pivotally secured to the vacuum vessel by four symmetrically spaced apart bolts and spherical bearings, each of which is centrally positioned within one of the four symmetrically positioned groups of vacuum vessel mounting structures. Cover plates and o-ring seals are further provided to seal the vacuum vessel mounting structures from the interior of the vacuum vessel, and venting bores are provided to vent trapped gases in the bores used to secure the cover plates and o-rings to the vacuum vessel. Provision for detecting leaks in the mounting structures from the rear surface of the vacuum vessel sidewall facing the support wall are also provided. Deflection to the optical bench within the vacuum vessel is further minimized by tuning the structure for a resonant frequency of at least 100 Hertz.

  12. Evacuated optical structure comprising optical bench mounted to sidewall of vacuum chamber in a manner which inhibits deflection and rotation of the optical bench

    DOEpatents

    Bowers, J.M.

    1994-04-19

    An improved evacuated optical structure is disclosed comprising an optical bench mounted in a vacuum vessel in a manner which inhibits transmission of movement of the vacuum vessel to the optical bench, yet provides a compact and economical structure. The vacuum vessel is mounted, through a sidewall thereof, to a support wall at four symmetrically positioned and spaced apart areas, each of which comprises a symmetrically positioned group of mounting structures passing through the sidewall of the vacuum vessel. The optical bench is pivotally secured to the vacuum vessel by four symmetrically spaced apart bolts and spherical bearings, each of which is centrally positioned within one of the four symmetrically positioned groups of vacuum vessel mounting structures. Cover plates and o-ring seals are further provided to seal the vacuum vessel mounting structures from the interior of the vacuum vessel, and venting bores are provided to vent trapped gases in the bores used to secure the cover plates and o-rings to the vacuum vessel. Provision for detecting leaks in the mounting structures from the rear surface of the vacuum vessel sidewall facing the support wall are also provided. Deflection to the optical bench within the vacuum vessel is further minimized by tuning the structure for a resonant frequency of at least 100 Hertz. 10 figures.

  13. Quantum dynamics in phase space: Moyal trajectories 2

    NASA Astrophysics Data System (ADS)

    Braunss, G.

    2013-01-01

    Continuing a previous paper [G. Braunss, J. Phys. A: Math. Theor. 43, 025302 (2010), 10.1088/1751-8113/43/2/025302] where we had calculated ℏ2-approximations of quantum phase space viz. Moyal trajectories of examples with one and two degrees of freedom, we present in this paper the calculation of ℏ2-approximations for four examples: a two-dimensional Toda chain, the radially symmetric Schwarzschild field, and two examples with three degrees of freedom, the latter being the nonrelativistic spherically Coulomb potential and the relativistic cylinder symmetrical Coulomb potential with a magnetic field H. We show in particular that an ℏ2-approximation of the nonrelativistic Coulomb field has no singularity at the origin (r = 0) whereas the classical trajectories are singular at r = 0. In the third example, we show in particular that for an arbitrary function γ(H, z) the expression β ≡ pz + γ(H, z) is classically (ℏ = 0) a constant of motion, whereas for ℏ ≠ 0 this holds only if γ(H, z) is an arbitrary polynomial of second order in z. This statement is shown to extend correspondingly to a cylinder symmetrical Schwarzschild field with a magnetic field. We exhibit in detail a number of properties of the radially symmetric Schwarzschild field. We exhibit finally the problems of the nonintegrable Hénon-Heiles Hamiltonian and give a short review of the regular Hilbert space representation of Moyal operators.

  14. Ignition of deuterium-trtium fuel targets

    DOEpatents

    Musinski, Donald L.; Mruzek, Michael T.

    1991-01-01

    A method of igniting a deuterium-tritium ICF fuel target to obtain fuel burn in which the fuel target initially includes a hollow spherical shell having a frozen layer of DT material at substantially uniform thickness and cryogenic temperature around the interior surface of the shell. The target is permitted to free-fall through a target chamber having walls heated by successive target ignitions, so that the target is uniformly heated during free-fall to at least partially melt the frozen fuel layer and form a liquid single-phase layer or a mixed liquid/solid bi-phase layer of substantially uniform thickness around the interior shell surface. The falling target is then illuminated from exteriorly of the chamber while the fuel layer is at substantially uniformly single or bi-phase so as to ignite the fuel layer and release energy therefrom.

  15. Ignition of deuterium-tritium fuel targets

    DOEpatents

    Musinski, D.L.; Mruzek, M.T.

    1991-08-27

    Disclosed is a method of igniting a deuterium-tritium ICF fuel target to obtain fuel burn in which the fuel target initially includes a hollow spherical shell having a frozen layer of DT material at substantially uniform thickness and cryogenic temperature around the interior surface of the shell. The target is permitted to free-fall through a target chamber having walls heated by successive target ignitions, so that the target is uniformly heated during free-fall to at least partially melt the frozen fuel layer and form a liquid single-phase layer or a mixed liquid/solid bi-phase layer of substantially uniform thickness around the interior shell surface. The falling target is then illuminated from exteriorly of the chamber while the fuel layer is at substantially uniformly single or bi-phase so as to ignite the fuel layer and release energy therefrom. 5 figures.

  16. The Role of Parametric Assumptions in Adaptive Bayesian Estimation

    ERIC Educational Resources Information Center

    Alcala-Quintana, Rocio; Garcia-Perez, Miguel A.

    2004-01-01

    Variants of adaptive Bayesian procedures for estimating the 5% point on a psychometric function were studied by simulation. Bias and standard error were the criteria to evaluate performance. The results indicated a superiority of (a) uniform priors, (b) model likelihood functions that are odd symmetric about threshold and that have parameter…

  17. Numerical MHD study for plasmoid instability in uniform resistivity

    NASA Astrophysics Data System (ADS)

    Shimizu, Tohru; Kondoh, Koji; Zenitani, Seiji

    2017-11-01

    The plasmoid instability (PI) caused in uniform resistivity is numerically studied with a MHD numerical code of HLLD scheme. It is shown that the PI observed in numerical studies may often include numerical (non-physical) tearing instability caused by the numerical dissipations. By increasing the numerical resolutions, the numerical tearing instability gradually disappears and the physical tearing instability remains. Hence, the convergence of the numerical results is observed. Note that the reconnection rate observed in the numerical tearing instability can be higher than that of the physical tearing instability. On the other hand, regardless of the numerical and physical tearing instabilities, the tearing instability can be classified into symmetric and asymmetric tearing instability. The symmetric tearing instability tends to occur when the thinning of current sheet is stopped by the physical or numerical dissipations, often resulting in the drastic changes in plasmoid chain's structure and its activity. In this paper, by eliminating the numerical tearing instability, we could not specify the critical Lundquist number Sc beyond which PI is fully developed. It suggests that Sc does not exist, at least around S = 105.

  18. Chebyshev collocation approach for vibration analysis of functionally graded porous beams based on third-order shear deformation theory

    NASA Astrophysics Data System (ADS)

    Wattanasakulpong, Nuttawit; Chaikittiratana, Arisara; Pornpeerakeat, Sacharuck

    2018-06-01

    In this paper, vibration analysis of functionally graded porous beams is carried out using the third-order shear deformation theory. The beams have uniform and non-uniform porosity distributions across their thickness and both ends are supported by rotational and translational springs. The material properties of the beams such as elastic moduli and mass density can be related to the porosity and mass coefficient utilizing the typical mechanical features of open-cell metal foams. The Chebyshev collocation method is applied to solve the governing equations derived from Hamilton's principle, which is used in order to obtain the accurate natural frequencies for the vibration problem of beams with various general and elastic boundary conditions. Based on the numerical experiments, it is revealed that the natural frequencies of the beams with asymmetric and non-uniform porosity distributions are higher than those of other beams with uniform and symmetric porosity distributions.

  19. Spherical Lu2O2S:Eu3+ micro/nano-structure: Controlled synthesis and luminescence properties

    NASA Astrophysics Data System (ADS)

    Zhang, Bowen; Zou, Haifeng; Dai, Yunzhi; Guan, Hongxia; Song, Yanhua; Zheng, Keyan; Zhou, Xiuqing; Shi, Zhan; Sheng, Ye

    2017-02-01

    Monodisperse and uniform Lu2O2S:Eu3+ luminescent spheres have been successfully synthesized through a facile hydrothermal method followed by a subsequent calcination process. The sizes of the spheres can be tuned in the range of 65 nm-295 nm by only changing the pH value of the system. It is indicated that the luminescence properties of the spherical phosphors were strongly influenced by size of the spheres. Such a size-sensitive luminescence property was interpreted from the structures of the spheres, including the degree of crystallinity, band gap energy, crystal field symmetry around Eu3+. We expected that this study not only can provide important information for size-controlled synthesis of spherical phosphors, but also can give a reference for exploration of size-dependent luminescence.

  20. Fabricating the spherical and flake silver powder used for the optoelectronic devices

    NASA Astrophysics Data System (ADS)

    Ju, Wei; Ma, Wangjing; Zhang, Fangzhi; Chen, Yixiang; Xie, Jinpeng

    2018-01-01

    The spherical and flake silver powder with different particle size for the optoelectronic devices was partly prepared by using chemical reduction and ball milling method, and charactered by scanning electron microscope (SEM), X-ray diffraction (XRD), laser particle size analyzer and thermo-gravimetric(TG) analyzer. The particle size of three series of spherical silver powder fabricated by chemical reduction is about 1.5μm, 1μm and 0.6μm, respectively; after being mechanical milling, the particle size of flake silver powder with high flaky rate is about 10μm, 6μm and 2μm respectively. Thermo gravimetric (TG) and XRD analyses showed that the silver powders have high purity and crystalline, and then the laser particle size and SEM analyses showed that the silver powders has good uniformity.

  1. IRAS observations of R Coronae Borealis - Detection and study of a fossil shell

    NASA Technical Reports Server (NTRS)

    Gillett, F. C.; Backman, D. E.; Beichman, C.; Neugebauer, G.

    1986-01-01

    IRAS observations of the extreme hydrogen-deficient supergiant R CrB are presented and discussed. The star is surrounded by an enormous cool dust cloud which is tentatively identified as a fossil remnant of the hydrogen-rich envelope of the star. The angular extent of the emission corresponds to a linear extent of 8 pc, 20 times larger than the largest previously known shell around a late-type star. The radiating material is distributed very symmetrically over a wide range of radial distances from the star. The dust temperature is nearly constant throughout the extended shell. The total mass in the shell is about 0.3 solar mass. The ejection process appears to have occurred in a spherically symmetric fashion with a nearly constant mass loss rate and expansion velocity over a period of about 150,000 yr, terminating about 26,000 yr ago.

  2. Temporal and spatial foliations of spacetimes.

    NASA Astrophysics Data System (ADS)

    Herold, H.

    For the solution of initial-value problems in numerical relativity usually the (3+1) splitting of Einstein's equations is employed. An important part of this splitting is the choice of the temporal gauge condition. In order to estimate the quality of time-evolution schemes, different time slicings of given well-known spherically symmetric spacetimes have been studied. Besides the maximal slicing condition the harmonic slicing prescription has been used to calculate temporal foliations of the Schwarzschild and the Oppenheimer-Snyder spacetime. Additionally, the author has studied a recently proposed, geometrically motivated spatial gauge condition, which is defined by considering the foliations of the three-dimensional space-like hypersurfaces by 2-surfaces of constant mean extrinsic curvature. Apart from the equations for the shift vector, which can be derived for this gauge condition, he has investigated such spatial foliations for well-known stationary axially symmetric spacetimes, namely for the Kerr metric and for numerically determined solutions for rapidly rotating neutron stars.

  3. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Rice, Neal G.; Vu, M.; Kong, C.

    Capsule drive in National Ignition Facility (NIF) indirect drive implosions is generated by x-ray illumination from cylindrical hohlraums. The cylindrical hohlraum geometry is axially symmetric but not spherically symmetric causing capsule-fuel drive asymmetries. We hypothesize that fabricating capsules asymmetric in wall thickness (shimmed) may compensate for drive asymmetries and improve implosion symmetry. Simulations suggest that for high compression implosions Legendre mode P 4 hohlraum flux asymmetries are the most detrimental to implosion performance. General Atomics has developed a diamond turning method to form a GDP capsule outer surface to a Legendre mode P 4 profile. The P 4 shape requiresmore » full capsule surface coverage. Thus, in order to avoid tool-lathe interference flipping the capsule part way through the machining process is required. This flipping process risks misalignment of the capsule causing a vertical step feature on the capsule surface. Recent trials have proven this step feature height can be minimized to ~0.25 µm.« less

  4. Black hole hair formation in shift-symmetric generalised scalar-tensor gravity

    NASA Astrophysics Data System (ADS)

    Benkel, Robert; Sotiriou, Thomas P.; Witek, Helvi

    2017-03-01

    A linear coupling between a scalar field and the Gauss-Bonnet invariant is the only known interaction term between a scalar and the metric that: respects shift symmetry; does not lead to higher order equations; inevitably introduces black hole hair in asymptotically flat, 4-dimensional spacetimes. Here we focus on the simplest theory that includes such a term and we explore the dynamical formation of scalar hair. In particular, we work in the decoupling limit that neglects the backreaction of the scalar onto the metric and evolve the scalar configuration numerically in the background of a Schwarzschild black hole and a collapsing dust star described by the Oppenheimer-Snyder solution. For all types of initial data that we consider, the scalar relaxes at late times to the known, static, analytic configuration that is associated with a hairy, spherically symmetric black hole. This suggests that the corresponding black hole solutions are indeed endpoints of collapse.

  5. A purely Lagrangian method for computing linearly-perturbed flows in spherical geometry

    NASA Astrophysics Data System (ADS)

    Jaouen, Stéphane

    2007-07-01

    In many physical applications, one wishes to control the development of multi-dimensional instabilities around a one-dimensional (1D) complex flow. For predicting the growth rates of these perturbations, a general numerical approach is viable which consists in solving simultaneously the one-dimensional equations and their linearized form for three-dimensional perturbations. In Clarisse et al. [J.-M. Clarisse, S. Jaouen, P.-A. Raviart, A Godunov-type method in Lagrangian coordinates for computing linearly-perturbed planar-symmetric flows of gas dynamics, J. Comp. Phys. 198 (2004) 80-105], a class of Godunov-type schemes for planar-symmetric flows of gas dynamics has been proposed. Pursuing this effort, we extend these results to spherically symmetric flows. A new method to derive the Lagrangian perturbation equations, based on the canonical form of systems of conservation laws with zero entropy flux [B. Després, Lagrangian systems of conservation laws. Invariance properties of Lagrangian systems of conservation laws, approximate Riemann solvers and the entropy condition, Numer. Math. 89 (2001) 99-134; B. Després, C. Mazeran, Lagrangian gas dynamics in two dimensions and Lagrangian systems, Arch. Rational Mech. Anal. 178 (2005) 327-372] is also described. It leads to many advantages. First of all, many physical problems we are interested in enter this formalism (gas dynamics, two-temperature plasma equations, ideal magnetohydrodynamics, etc.) whatever is the geometry. Secondly, a class of numerical entropic schemes is available for the basic flow [11]. Last, linearizing and devising numerical schemes for the perturbed flow is straightforward. The numerical capabilities of these methods are illustrated on three test cases of increasing difficulties and we show that - due to its simplicity and its low computational cost - the Linear Perturbations Code (LPC) is a powerful tool to understand and predict the development of hydrodynamic instabilities in the linear regime.

  6. Tensioning device for a stretched membrane collector

    DOEpatents

    Murphy, Lawrence M.

    1984-01-01

    Disclosed is a solar concentrating collector comprising an elastic membrane member for concentrating sunlight, a frame for holding the membrane member in plane and in tension, and a tensioning means for varying the tension of the membrane member. The tensioning means is disposed at the frame and is adapted to releasably attach the membrane member thereto. The tensioning means is also adapted to uniformly and symmetrically subject the membrane member to stretching forces such that membrane stresses produced thereby are distributed uniformly over a thickness of the membrane member and reciprocal twisting moments are substantially prevented from acting about said frame.

  7. Tensioning device for a stretched membrane collector

    DOEpatents

    Murphy, L.M.

    1984-01-01

    Disclosed is a solar concentrating collector comprising an elestic membrane member for concentrating sunlight, a frame for holding the membrane member in plane and in tension, and a tensioning means for varying the tension of the membrane member. The tensioning means is disposed at the frame and is adapted to releasably attach the membrane member thereto. The tensioning means is also adapted to uniformly and symmetrically subject the membrane member to stretching forces such that membrane stresses produced thereby are distributed uniformly over a thickness of the membrane member and reciprocal twisting moments are substantially prevented from acting about said frame.

  8. Nonimaging reflectors for efficient uniform illumination.

    PubMed

    Gordon, J M; Kashin, P; Rabl, A

    1992-10-01

    Nonimaging reflectors that are an extension of the design principle that was developed for compound parabolic concentrator type devices are proposed for illumination applications. The optical designs presented offer maximal lighting efficiency while they retain sharp angular control of the radiation and highly uniform flux densities on distant target planes. Our results are presented for symmetrical configurations in two dimensions (troughlike reflectors) for flat and for tubular sources. For fields of view of practical interest (half-angle in the 30-60 degrees range), these devices can achieve minimum-tomaximum intensity ratios of 0.7, while they remain compact and incur low reflective losses.

  9. A Layered Searchable Encryption Scheme with Functional Components Independent of Encryption Methods

    PubMed Central

    Luo, Guangchun; Qin, Ke

    2014-01-01

    Searchable encryption technique enables the users to securely store and search their documents over the remote semitrusted server, which is especially suitable for protecting sensitive data in the cloud. However, various settings (based on symmetric or asymmetric encryption) and functionalities (ranked keyword query, range query, phrase query, etc.) are often realized by different methods with different searchable structures that are generally not compatible with each other, which limits the scope of application and hinders the functional extensions. We prove that asymmetric searchable structure could be converted to symmetric structure, and functions could be modeled separately apart from the core searchable structure. Based on this observation, we propose a layered searchable encryption (LSE) scheme, which provides compatibility, flexibility, and security for various settings and functionalities. In this scheme, the outputs of the core searchable component based on either symmetric or asymmetric setting are converted to some uniform mappings, which are then transmitted to loosely coupled functional components to further filter the results. In such a way, all functional components could directly support both symmetric and asymmetric settings. Based on LSE, we propose two representative and novel constructions for ranked keyword query (previously only available in symmetric scheme) and range query (previously only available in asymmetric scheme). PMID:24719565

  10. Investigating tunneling process of atom exposed in circularly polarized strong-laser field

    NASA Astrophysics Data System (ADS)

    Yuan, MingHu; Xin, PeiPei; Chu, TianShu; Liu, HongPing

    2017-03-01

    We propose a method for studying the tunneling process by analyzing the instantaneous ionization rate of a circularly polarized laser. A numerical calculation shows that, for an atom exposed to a long laser pulse, if its initial electronic state wave function is non-spherical symmetric, the delayed phase shift of the ionization rate vs the laser cycle period in real time in the region close to the peak intensity of the laser pulse can be used to probe the tunneling time. In this region, an obvious time delay phase shift of more than 190 attoseconds is observed. Further study shows that the atom has a longer tunneling time in the ionization under a shorter wavelength laser pulse. In our method, a Wigner rotation technique is employed to numerically solve the time-dependent Schrödinger equation of a single-active electron in a three-dimensional spherical coordinate system.

  11. Relativistic compact stars with charged anisotropic matter

    NASA Astrophysics Data System (ADS)

    Maurya, S. K.; Banerjee, Ayan; Channuie, Phongpichit

    2018-05-01

    In this article, we perform a detailed theoretical analysis of new exact solutions with anisotropic fluid distribution of matter for compact objects subject to hydrostatic equilibrium. We present a family solution to the Einstein-Maxwell equations describing a spherically symmetric, static distribution of a fluid with pressure anisotropy. We implement an embedding class one condition to obtain a relation between the metric functions. We generalize the properties of a spherical star with hydrostatic equilibrium using the generalised Tolman-Oppenheimer-Volkoff (TOV) equation. We match the interior solution to an exterior Reissner-Nordström one, and study the energy conditions, speed of sound, and mass-radius relation of the star. We also show that the obtained solutions are compatible with observational data for the compact object Her X-1. Regarding our results, the physical behaviour of the present model may serve for the modeling of ultra compact objects.

  12. Dynamics and universal scaling law in geometrically-controlled sessile drop evaporation

    PubMed Central

    Sáenz, P. J.; Wray, A. W.; Che, Z.; Matar, O. K.; Valluri, P.; Kim, J.; Sefiane, K.

    2017-01-01

    The evaporation of a liquid drop on a solid substrate is a remarkably common phenomenon. Yet, the complexity of the underlying mechanisms has constrained previous studies to spherically symmetric configurations. Here we investigate well-defined, non-spherical evaporating drops of pure liquids and binary mixtures. We deduce a universal scaling law for the evaporation rate valid for any shape and demonstrate that more curved regions lead to preferential localized depositions in particle-laden drops. Furthermore, geometry induces well-defined flow structures within the drop that change according to the driving mechanism. In the case of binary mixtures, geometry dictates the spatial segregation of the more volatile component as it is depleted. Our results suggest that the drop geometry can be exploited to prescribe the particle deposition and evaporative dynamics of pure drops and the mixing characteristics of multicomponent drops, which may be of interest to a wide range of industrial and scientific applications. PMID:28294114

  13. Self-assembled fibre optoelectronics with discrete translational symmetry

    PubMed Central

    Rein, Michael; Levy, Etgar; Gumennik, Alexander; Abouraddy, Ayman F.; Joannopoulos, John; Fink, Yoel

    2016-01-01

    Fibres with electronic and photonic properties are essential building blocks for functional fabrics with system level attributes. The scalability of thermal fibre drawing approach offers access to large device quantities, while constraining the devices to be translational symmetric. Lifting this symmetry to create discrete devices in fibres will increase their utility. Here, we draw, from a macroscopic preform, fibres that have three parallel internal non-contacting continuous domains; a semiconducting glass between two conductors. We then heat the fibre and generate a capillary fluid instability, resulting in the selective transformation of the cylindrical semiconducting domain into discrete spheres while keeping the conductive domains unchanged. The cylindrical-to-spherical expansion bridges the continuous conducting domains to create ∼104 self-assembled, electrically contacted and entirely packaged discrete spherical devices per metre of fibre. The photodetection and Mie resonance dependent response are measured by illuminating the fibre while connecting its ends to an electrical readout. PMID:27698454

  14. Derivative matrices of a skew ray for spherical boundary surfaces and their applications in system analysis and design.

    PubMed

    Lin, Psang Dain

    2014-05-10

    In a previous paper [Appl. Opt.52, 4151 (2013)], we presented the first- and second-order derivatives of a ray for a flat boundary surface to design prisms. In this paper, that scheme is extended to determine the Jacobian and Hessian matrices of a skew ray as it is reflected/refracted at a spherical boundary surface. The validity of the proposed approach as an analysis and design tool is demonstrated using an axis-symmetrical system for illustration purpose. It is found that these two matrices can provide the search direction used by existing gradient-based schemes to minimize the merit function during the optimization stage of the optical system design process. It is also possible to make the optical system designs more automatic, if the image defects can be extracted from the Jacobian and Hessian matrices of a skew ray.

  15. An Improved Computational Technique for Calculating Electromagnetic Forces and Power Absorptions Generated in Spherical and Deformed Body in Levitation Melting Devices

    NASA Technical Reports Server (NTRS)

    Zong, Jin-Ho; Szekely, Julian; Schwartz, Elliot

    1992-01-01

    An improved computational technique for calculating the electromagnetic force field, the power absorption and the deformation of an electromagnetically levitated metal sample is described. The technique is based on the volume integral method, but represents a substantial refinement; the coordinate transformation employed allows the efficient treatment of a broad class of rotationally symmetrical bodies. Computed results are presented to represent the behavior of levitation melted metal samples in a multi-coil, multi-frequency levitation unit to be used in microgravity experiments. The theoretical predictions are compared with both analytical solutions and with the results or previous computational efforts for the spherical samples and the agreement has been very good. The treatment of problems involving deformed surfaces and actually predicting the deformed shape of the specimens breaks new ground and should be the major usefulness of the proposed method.

  16. Static spherical wormhole models in f (R, T) gravity

    NASA Astrophysics Data System (ADS)

    Yousaf, Z.; Ilyas, M.; Zaeem-ul-Haq Bhatti, M.

    2017-06-01

    This paper explores the possibility of the existence of wormhole geometries coupled with relativistic matter configurations by taking a particular model of f(R,T) gravity (where T is the trace of energy-momentum tensor). For this purpose, we take the static form of spherically symmetric spacetime and after assuming a specific form of matter and combinations of shape function, the validity of energy conditions is checked. We have discussed our results through graphical representation and studied the equilibrium background of wormhole models by taking an anisotropic fluid. The extra curvature quantities coming from f(R,T) gravity could be interpreted as a gravitational entity supporting these non-standard astrophysical wormhole models. We have shown that in the context of anisotropic fluid and R+α R^2+λ T gravity, wormhole models could possibly exist in few zones in the space of parameters without the need for exotic matter.

  17. Self-assembled fibre optoelectronics with discrete translational symmetry.

    PubMed

    Rein, Michael; Levy, Etgar; Gumennik, Alexander; Abouraddy, Ayman F; Joannopoulos, John; Fink, Yoel

    2016-10-04

    Fibres with electronic and photonic properties are essential building blocks for functional fabrics with system level attributes. The scalability of thermal fibre drawing approach offers access to large device quantities, while constraining the devices to be translational symmetric. Lifting this symmetry to create discrete devices in fibres will increase their utility. Here, we draw, from a macroscopic preform, fibres that have three parallel internal non-contacting continuous domains; a semiconducting glass between two conductors. We then heat the fibre and generate a capillary fluid instability, resulting in the selective transformation of the cylindrical semiconducting domain into discrete spheres while keeping the conductive domains unchanged. The cylindrical-to-spherical expansion bridges the continuous conducting domains to create ∼10 4 self-assembled, electrically contacted and entirely packaged discrete spherical devices per metre of fibre. The photodetection and Mie resonance dependent response are measured by illuminating the fibre while connecting its ends to an electrical readout.

  18. Primordial inhomogeneities in the expanding universe. II - General features of spherical models at late times

    NASA Technical Reports Server (NTRS)

    Olson, D. W.; Silk, J.

    1979-01-01

    This paper studies the density profile that forms around a spherically symmetric bound central core immersed in a homogeneous-background k = 0 or k = -1 Friedmann-Robertson-Walker cosmological model, with zero pressure. Although the density profile in the linearized regime is almost arbitrary, in the nonlinear regime certain universal features of the density profile are obtained that are independent of the details of the initial conditions. The formation of 'halos' ('holes') with densities greater than (less than) the average cosmological density is discussed. It is shown that in most regions 'halos' form, and universal values are obtained for the slope of the ln (density)-ln (radius) profile in those 'halos' at late times, independently of the shape of the initial density profile. Restrictions are derived on where it is possible for 'holes' to exist at late times and on how such 'holes' must have evolved.

  19. Dynamics and universal scaling law in geometrically-controlled sessile drop evaporation.

    PubMed

    Sáenz, P J; Wray, A W; Che, Z; Matar, O K; Valluri, P; Kim, J; Sefiane, K

    2017-03-15

    The evaporation of a liquid drop on a solid substrate is a remarkably common phenomenon. Yet, the complexity of the underlying mechanisms has constrained previous studies to spherically symmetric configurations. Here we investigate well-defined, non-spherical evaporating drops of pure liquids and binary mixtures. We deduce a universal scaling law for the evaporation rate valid for any shape and demonstrate that more curved regions lead to preferential localized depositions in particle-laden drops. Furthermore, geometry induces well-defined flow structures within the drop that change according to the driving mechanism. In the case of binary mixtures, geometry dictates the spatial segregation of the more volatile component as it is depleted. Our results suggest that the drop geometry can be exploited to prescribe the particle deposition and evaporative dynamics of pure drops and the mixing characteristics of multicomponent drops, which may be of interest to a wide range of industrial and scientific applications.

  20. Initial system design method for non-rotationally symmetric systems based on Gaussian brackets and Nodal aberration theory.

    PubMed

    Zhong, Yi; Gross, Herbert

    2017-05-01

    Freeform surfaces play important roles in improving the imaging performance of off-axis optical systems. However, for some systems with high requirements in specifications, the structure of the freeform surfaces could be very complicated and the number of freeform surfaces could be large. That brings challenges in fabrication and increases the cost. Therefore, to achieve a good initial system with minimum aberrations and reasonable structure before implementing freeform surfaces is essential for optical designers. The already existing initial system design methods are limited to certain types of systems. A universal tool or method to achieve a good initial system efficiently is very important. In this paper, based on the Nodal aberration theory and the system design method using Gaussian Brackets, the initial system design method is extended from rotationally symmetric systems to general non-rotationally symmetric systems. The design steps are introduced and on this basis, two off-axis three-mirror systems are pre-designed using spherical shape surfaces. The primary aberrations are minimized using the nonlinear least-squares solver. This work provides insight and guidance for initial system design of off-axis mirror systems.

  1. Weyl metrics and wormholes

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Gibbons, Gary W.; Volkov, Mikhail S., E-mail: gwg1@cam.ac.uk, E-mail: volkov@lmpt.univ-tours.fr

    We study solutions obtained via applying dualities and complexifications to the vacuum Weyl metrics generated by massive rods and by point masses. Rescaling them and extending to complex parameter values yields axially symmetric vacuum solutions containing singularities along circles that can be viewed as singular matter sources. These solutions have wormhole topology with several asymptotic regions interconnected by throats and their sources can be viewed as thin rings of negative tension encircling the throats. For a particular value of the ring tension the geometry becomes exactly flat although the topology remains non-trivial, so that the rings literally produce holes inmore » flat space. To create a single ring wormhole of one metre radius one needs a negative energy equivalent to the mass of Jupiter. Further duality transformations dress the rings with the scalar field, either conventional or phantom. This gives rise to large classes of static, axially symmetric solutions, presumably including all previously known solutions for a gravity-coupled massless scalar field, as for example the spherically symmetric Bronnikov-Ellis wormholes with phantom scalar. The multi-wormholes contain infinite struts everywhere at the symmetry axes, apart from solutions with locally flat geometry.« less

  2. Studies of Flame Structure in Microgravity

    NASA Technical Reports Server (NTRS)

    Law, C. K.; Sung, C. J.; Zhu, D. L.

    1997-01-01

    The present research endeavor is concerned with gaining fundamental understanding of the configuration, structure, and dynamics of laminar premixed and diffusion flames under conditions of negligible effects of gravity. Of particular interest is the potential to establish and hence study the properties of spherically- and cylindrically-symmetric flames and their response to external forces not related to gravity. For example, in an earlier experimental study of the burner-stabilized cylindrical premixed flames, the possibility of flame stabilization through flow divergence was established, while the resulting one-dimensional, adiabatic, stretchless flame also allowed an accurate means of determining the laminar flame speeds of combustible mixtures. We have recently extended our studies of the flame structure in microgravity along the following directions: (1) Analysis of the dynamics of spherical premixed flames; (2) Analysis of the spreading of cylindrical diffusion flames; (3) Experimental observation of an interesting dual luminous zone structure of a steady-state, microbuoyancy, spherical diffusion flame of air burning in a hydrogen/methane mixture environment, and its subsequent quantification through computational simulation with detailed chemistry and transport; (4) Experimental quantification of the unsteady growth of a spherical diffusion flame; and (5) Computational simulation of stretched, diffusionally-imbalanced premixed flames near and beyond the conventional limits of flammability, and the substantiation of the concept of extended limits of flammability. Motivation and results of these investigations are individually discussed.

  3. Thermodynamics phase transition and Hawking radiation of the Schwarzschild black hole with quintessence-like matter and a deficit solid angle

    NASA Astrophysics Data System (ADS)

    Rodrigue, Kamiko Kouemeni Jean; Saleh, Mahamat; Thomas, Bouetou Bouetou; Kofane, Timoleon Crepin

    2018-05-01

    In this paper, we investigate the thermodynamics and Hawking radiation of Schwarzschild black hole with quintessence-like matter and deficit solid angle. From the metric of the black hole, we derive the expressions of temperature and specific heat using the laws of black hole thermodynamics. Using the null geodesics method and Parikh-Wilczeck tunneling method, we derive the expressions of Boltzmann factor and the change of Bekenstein-Hawking entropy for the black hole. The behaviors of the temperature, specific heat, Boltzmann factor and the change of Bekenstein entropy versus the deficit solid angle (ɛ 2) and the density of static spherically symmetric quintessence-like matter (ρ 0) were explicitly plotted. The results show that, when the deficit solid angle (ɛ 2) and the density of static spherically symmetric quintessence-like matter at r=1 (ρ 0) vanish (ρ 0=ɛ =0), these four thermodynamics quantities are reduced to those obtained for the simple case of Schwarzschild black hole. For low entropies, the presence of quintessence-like matter induces a first order phase transition of the black hole and for the higher values of the entropies, we observe the second order phase transition. When increasing ρ 0, the transition points are shifted to lower entropies. The same thing is observed when increasing ɛ 2. In the absence of quintessence-like matter (ρ 0=0), these transition phenomena disappear. Moreover the rate of radiation decreases when increasing ρ 0 or (ɛ ^2).

  4. Self-similar cosmological solutions with dark energy. I. Formulation and asymptotic analysis

    NASA Astrophysics Data System (ADS)

    Harada, Tomohiro; Maeda, Hideki; Carr, B. J.

    2008-01-01

    Based on the asymptotic analysis of ordinary differential equations, we classify all spherically symmetric self-similar solutions to the Einstein equations which are asymptotically Friedmann at large distances and contain a perfect fluid with equation of state p=(γ-1)μ with 0<γ<2/3. This corresponds to a “dark energy” fluid and the Friedmann solution is accelerated in this case due to antigravity. This extends the previous analysis of spherically symmetric self-similar solutions for fluids with positive pressure (γ>1). However, in the latter case there is an additional parameter associated with the weak discontinuity at the sonic point and the solutions are only asymptotically “quasi-Friedmann,” in the sense that they exhibit an angle deficit at large distances. In the 0<γ<2/3 case, there is no sonic point and there exists a one-parameter family of solutions which are genuinely asymptotically Friedmann at large distances. We find eight classes of asymptotic behavior: Friedmann or quasi-Friedmann or quasistatic or constant-velocity at large distances, quasi-Friedmann or positive-mass singular or negative-mass singular at small distances, and quasi-Kantowski-Sachs at intermediate distances. The self-similar asymptotically quasistatic and quasi-Kantowski-Sachs solutions are analytically extendible and of great cosmological interest. We also investigate their conformal diagrams. The results of the present analysis are utilized in an accompanying paper to obtain and physically interpret numerical solutions.

  5. Self-similar cosmological solutions with dark energy. I. Formulation and asymptotic analysis

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Harada, Tomohiro; Maeda, Hideki; Centro de Estudios Cientificos

    2008-01-15

    Based on the asymptotic analysis of ordinary differential equations, we classify all spherically symmetric self-similar solutions to the Einstein equations which are asymptotically Friedmann at large distances and contain a perfect fluid with equation of state p=({gamma}-1){mu} with 0<{gamma}<2/3. This corresponds to a 'dark energy' fluid and the Friedmann solution is accelerated in this case due to antigravity. This extends the previous analysis of spherically symmetric self-similar solutions for fluids with positive pressure ({gamma}>1). However, in the latter case there is an additional parameter associated with the weak discontinuity at the sonic point and the solutions are only asymptotically 'quasi-Friedmann',more » in the sense that they exhibit an angle deficit at large distances. In the 0<{gamma}<2/3 case, there is no sonic point and there exists a one-parameter family of solutions which are genuinely asymptotically Friedmann at large distances. We find eight classes of asymptotic behavior: Friedmann or quasi-Friedmann or quasistatic or constant-velocity at large distances, quasi-Friedmann or positive-mass singular or negative-mass singular at small distances, and quasi-Kantowski-Sachs at intermediate distances. The self-similar asymptotically quasistatic and quasi-Kantowski-Sachs solutions are analytically extendible and of great cosmological interest. We also investigate their conformal diagrams. The results of the present analysis are utilized in an accompanying paper to obtain and physically interpret numerical solutions.« less

  6. Self assembled linear polymeric chains with tuneable semiflexibility using isotropic interactions.

    PubMed

    Abraham, Alex; Chatterji, Apratim

    2018-04-21

    We propose a two-body spherically symmetric (isotropic) potential such that particles interacting by the potential self-assemble into linear semiflexible polymeric chains without branching. By suitable control of the potential parameters, we can control the persistence length of the polymer and can even introduce a controlled number of branches. Thus we show how to achieve effective directional interactions starting from spherically symmetric potentials. The self-assembled polymers have an exponential distribution of chain lengths akin to what is observed for worm-like micellar systems. On increasing particle density, the polymeric chains self-organize to an ordered line-hexagonal phase where every chain is surrounded by six parallel chains, the transition is first order. On further increase in monomer density, the order is destroyed and we get a branched gel-like phase. This potential can be used to model semi-flexible equilibrium polymers with tunable semiflexibility and excluded volume. The use of the potential is computationally cheap and hence can be used to simulate and probe equilibrium polymer dynamics with long chains. The potential also gives a plausible method of tuning colloidal interactions in experiments such that one can obtain self-assembling polymeric chains made up of colloids and probe polymer dynamics using an optical microscope. Furthermore, we show how a modified potential leads to the observation of an intermediate nematic phase of self-assembled chains in between the low density disordered phase and the line-ordered hexagonal phase.

  7. The Computation of Global Viscoelastic Co- and Post-seismic Displacement in a Realistic Earth Model by Straightforward Numerical Inverse Laplace Integration

    NASA Astrophysics Data System (ADS)

    Tang, H.; Sun, W.

    2016-12-01

    The theoretical computation of dislocation theory in a given earth model is necessary in the explanation of observations of the co- and post-seismic deformation of earthquakes. For this purpose, computation theories based on layered or pure half space [Okada, 1985; Okubo, 1992; Wang et al., 2006] and on spherically symmetric earth [Piersanti et al., 1995; Pollitz, 1997; Sabadini & Vermeersen, 1997; Wang, 1999] have been proposed. It is indicated that the compressibility, curvature and the continuous variation of the radial structure of Earth should be simultaneously taken into account for modern high precision displacement-based observations like GPS. Therefore, Tanaka et al. [2006; 2007] computed global displacement and gravity variation by combining the reciprocity theorem (RPT) [Okubo, 1993] and numerical inverse Laplace integration (NIL) instead of the normal mode method [Peltier, 1974]. Without using RPT, we follow the straightforward numerical integration of co-seismic deformation given by Sun et al. [1996] to present a straightforward numerical inverse Laplace integration method (SNIL). This method is used to compute the co- and post-seismic displacement of point dislocations buried in a spherically symmetric, self-gravitating viscoelastic and multilayered earth model and is easy to extended to the application of geoid and gravity. Comparing with pre-existing method, this method is relatively more straightforward and time-saving, mainly because we sum associated Legendre polynomials and dislocation love numbers before using Riemann-Merlin formula to implement SNIL.

  8. A no-short scalar hair theorem for rotating Kerr black holes

    NASA Astrophysics Data System (ADS)

    Hod, Shahar

    2016-06-01

    If a black hole has hair, how short can this hair be? A partial answer to this intriguing question was recently provided by the ‘no-short hair’ theorem which asserts that the external fields of a spherically symmetric electrically neutral hairy black-hole configuration must extend beyond the null circular geodesic which characterizes the corresponding black-hole spacetime. One naturally wonders whether the no-short hair inequality {r}{hair}\\gt {r}{null} is a generic property of all electrically neutral hairy black-hole spacetimes. In this paper we provide evidence that the answer to this interesting question may be positive. In particular, we prove that the recently discovered cloudy Kerr black-hole spacetimes—non-spherically symmetric non-static black holes which support linearized massive scalar fields in their exterior regions—also respect this no-short hair lower bound. Specifically, we analytically derive the lower bound {r}{field}/{r}+\\gt {r}+/{r}- on the effective lengths of the external bound-state massive scalar clouds (here {r}{field} is the peak location of the stationary bound-state scalar fields and r ± are the horizon radii of the black hole). Remarkably, this lower bound is universal in the sense that it is independent of the physical parameters (proper mass and angular harmonic indices) of the exterior scalar fields. Our results suggest that the lower bound {r}{hair}\\gt {r}{null} may be a general property of asymptotically flat electrically neutral hairy black-hole configurations.

  9. Self assembled linear polymeric chains with tuneable semiflexibility using isotropic interactions

    NASA Astrophysics Data System (ADS)

    Abraham, Alex; Chatterji, Apratim

    2018-04-01

    We propose a two-body spherically symmetric (isotropic) potential such that particles interacting by the potential self-assemble into linear semiflexible polymeric chains without branching. By suitable control of the potential parameters, we can control the persistence length of the polymer and can even introduce a controlled number of branches. Thus we show how to achieve effective directional interactions starting from spherically symmetric potentials. The self-assembled polymers have an exponential distribution of chain lengths akin to what is observed for worm-like micellar systems. On increasing particle density, the polymeric chains self-organize to an ordered line-hexagonal phase where every chain is surrounded by six parallel chains, the transition is first order. On further increase in monomer density, the order is destroyed and we get a branched gel-like phase. This potential can be used to model semi-flexible equilibrium polymers with tunable semiflexibility and excluded volume. The use of the potential is computationally cheap and hence can be used to simulate and probe equilibrium polymer dynamics with long chains. The potential also gives a plausible method of tuning colloidal interactions in experiments such that one can obtain self-assembling polymeric chains made up of colloids and probe polymer dynamics using an optical microscope. Furthermore, we show how a modified potential leads to the observation of an intermediate nematic phase of self-assembled chains in between the low density disordered phase and the line-ordered hexagonal phase.

  10. Local conditions separating expansion from collapse in spherically symmetric models with anisotropic pressures

    NASA Astrophysics Data System (ADS)

    Mimoso, José P.; Le Delliou, Morgan; Mena, Filipe C.

    2013-08-01

    We investigate spherically symmetric spacetimes with an anisotropic fluid and discuss the existence and stability of a separating shell dividing expanding and collapsing regions. We resort to a 3+1 splitting and obtain gauge invariant conditions relating intrinsic spacetime quantities to properties of the matter source. We find that the separating shell is defined by a generalization of the Tolman-Oppenheimer-Volkoff equilibrium condition. The latter establishes a balance between the pressure gradients, both isotropic and anisotropic, and the strength of the fields induced by the Misner-Sharp mass inside the separating shell and by the pressure fluxes. This defines a local equilibrium condition, but conveys also a nonlocal character given the definition of the Misner-Sharp mass. By the same token, it is also a generalized thermodynamical equation of state as usually interpreted for the perfect fluid case, which now has the novel feature of involving both the isotropic and the anisotropic stresses. We have cast the governing equations in terms of local, gauge invariant quantities that are revealing of the role played by the anisotropic pressures and inhomogeneous electric part of the Weyl tensor. We analyze a particular solution with dust and radiation that provides an illustration of our conditions. In addition, our gauge invariant formalism not only encompasses the cracking process from Herrera and co-workers but also reveals transparently the interplay and importance of the shear and of the anisotropic stresses.

  11. Self-gravitating black hole scalar wigs

    NASA Astrophysics Data System (ADS)

    Barranco, Juan; Bernal, Argelia; Degollado, Juan Carlos; Diez-Tejedor, Alberto; Megevand, Miguel; Núñez, Darío; Sarbach, Olivier

    2017-07-01

    It has long been known that no static, spherically symmetric, asymptotically flat Klein-Gordon scalar field configuration surrounding a nonrotating black hole can exist in general relativity. In a series of previous papers, we proved that, at the effective level, this no-hair theorem can be circumvented by relaxing the staticity assumption: for appropriate model parameters, there are quasibound scalar field configurations living on a fixed Schwarzschild background which, although not being strictly static, have a larger lifetime than the age of the universe. This situation arises when the mass of the scalar field distribution is much smaller than the black hole mass, and following the analogies with the hair in the literature we dubbed these long-lived field configurations wigs. Here we extend our previous work to include the gravitational backreaction produced by the scalar wigs. We derive new approximate solutions of the spherically symmetric Einstein-Klein-Gordon system which represent self-gravitating scalar wigs surrounding black holes. These configurations interpolate between boson star configurations and Schwarzschild black holes dressed with the long-lived scalar test field distributions discussed in previous papers. Nonlinear numerical evolutions of initial data sets extracted from our approximate solutions support the validity of our approach. Arbitrarily large lifetimes are still possible, although for the parameter space that we analyze in this paper they seem to decay faster than the quasibound states. Finally, we speculate about the possibility that these configurations could describe the innermost regions of dark matter halos.

  12. Non-singular black holes and the limiting curvature mechanism: a Hamiltonian perspective

    NASA Astrophysics Data System (ADS)

    Ben Achour, J.; Lamy, F.; Liu, H.; Noui, K.

    2018-05-01

    We revisit the non-singular black hole solution in (extended) mimetic gravity with a limiting curvature from a Hamiltonian point of view. We introduce a parameterization of the phase space which allows us to describe fully the Hamiltonian structure of the theory. We write down the equations of motion that we solve in the regime deep inside the black hole, and we recover that the black hole has no singularity, due to the limiting curvature mechanism. Then, we study the relation between such black holes and effective polymer black holes which have been introduced in the context of loop quantum gravity. As expected, contrary to what happens in the cosmological sector, mimetic gravity with a limiting curvature fails to reproduce the usual effective dynamics of spherically symmetric loop quantum gravity which are generically not covariant. Nonetheless, we exhibit a theory in the class of extended mimetic gravity whose dynamics reproduces the general shape of the effective corrections of spherically symmetric polymer models, but in an undeformed covariant manner. These covariant effective corrections are found to be always metric dependent, i.e. within the bar mu-scheme, underlying the importance of this ingredient for inhomogeneous polymer models. In that respect, extended mimetic gravity can be viewed as an effective covariant theory which naturally implements a covariant notion of point wise holonomy-like corrections. The difference between the mimetic and polymer Hamiltonian formulations provides us with a guide to understand the deformation of covariance in inhomogeneous polymer models.

  13. Natural convection in symmetrically heated vertical parallel plates with discrete heat sources

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Manca, O.; Nardini, S.; Naso, V.

    Laminar air natural convection in a symmetrically heated vertical channel with uniform flush-mounted discrete heat sources has been experimentally investigated. The effects of heated strips location and of their number are pointed out in terms of the maximum wall temperatures. A flow visualization in the entrance region of the channel was carried out and air temperatures and velocities in two cross sections have been measured. Dimensionless local heat transfer coefficients have been evaluated and monomial correlations among relevant parameters have bee derived in the local Rayleigh number range 10--10{sup 6}. Channel Nusselt number has been correlated in a polynomial formmore » in terms of channel Rayleigh number.« less

  14. Development of response models for the Earth Radiation Budget Experiment (ERBE) sensors. Part 2: Analysis of the ERBE integrating sphere ground calibration

    NASA Technical Reports Server (NTRS)

    Halyo, Nesim; Taylor, Deborah B.

    1987-01-01

    An explicit solution of the spectral radiance leaving an arbitrary point on the wall of a spherical cavity with diffuse reflectivity is obtained. The solution is applicable to spheres with an arbitrary number of openings of any size and shape, an arbitrary number of light sources with possible non-diffuse characteristics, a non-uniform sphere wall temperature distribution, non-uniform and non-diffuse sphere wall emissivity and non-uniform but diffuse sphere wall spectral reflectivity. A general measurement equation describing the output of a sensor with a given field of view, angular and spectral response measuring the sphere output is obtained. The results are applied to the Earth Radiation Budget Experiment (ERBE) integrating sphere. The sphere wall radiance uniformity, loading effects and non-uniform wall temperature effects are investigated. It is shown that using appropriate interpretation and processing, a high-accuracy short-wave calibration of the ERBE sensors can be achieved.

  15. Optical design of soft multifocal contact lens with uniform optical power in center-distance zone with optimized NURBS.

    PubMed

    Vu, Lien T; Chen, Chao-Chang A; Yu, Chia-Wei

    2018-02-05

    This study aims to develop a new optical design method of soft multifocal contact lens (CLs) to obtain uniform optical power in large center-distance zone with optimized Non-Uniform Rational B-spline (NURBS). For the anterior surface profiles of CLs, the NURBS design curves are optimized to match given optical power distributions. Then, the NURBS in the center-distance zones are fitted in the corresponding spherical/aspheric curves for both data points and their centers of curvature to achieve the uniform power. Four cases of soft CLs have been manufactured by casting in shell molds by injection molding and then measured to verify the design specifications. Results of power profiles of these CLs are concord with the given clinical requirements of uniform powers in larger center-distance zone. The developed optical design method has been verified for multifocal CLs design and can be further applied for production of soft multifocal CLs.

  16. The elastic field induced by a hemispherical inclusion in the half-space

    NASA Astrophysics Data System (ADS)

    Wu, Linzhi

    2003-06-01

    The elastic field induced by a hekispherical inclusion with uniform eigenstrains in a semi-infinite elastic medium is solved by using the Green's function method and series expansion technique. The exact solutions are presented for the displacement and stress fields which can be expressed by complete elliptic integrals of the first, second, and third kinds and hypergeometric functions. The present method can be used to determine the corresponding elastic fields when the shape of the inclusion is a spherical crown or a spherical segment. Finally, numerical results are given for the displacement and stress fields along the axis of symmetry ( x 3-axis).

  17. Radiatively-suppressed spherical accretion under relativistic radiative transfer

    NASA Astrophysics Data System (ADS)

    Fukue, Jun

    2018-03-01

    We numerically examine radiatively-suppressed relativistic spherical accretion flows on to a central object with mass M under Newtonian gravity and special relativity. We simultaneously solve both the relativistic radiative transfer equation and the relativistic hydrodynamical equations for spherically symmetric flows under the double iteration process in the case of the intermediate optical depth. We find that the accretion flow is suppressed, compared with the freefall case in the nonrelativistic regime. For example, in the case of accretion on to a luminous core with accretion luminosity L*, the freefall velocity v normalized by the speed of light c under the radiative force in the nonrelativistic regime is β (\\hat{r}) = v/c = -√{(1-Γ _*)/(\\hat{r}+1-Γ _*)}, where Γ* (≡ L*/LE, LE being the Eddington luminosity) is the Eddington parameter and \\hat{r} (= r/rS, rS being the Schwarzschild radius) the normalized radius, whereas the infall speed at the central core is ˜0.7β(1), irrespective of the mass-accretion rate. This is due to the relativistic effect; the comoving flux is enhanced by the advective flux. We briefly examine and discuss an isothermal case, where the emission takes place in the entire space.

  18. Two-dimensional symmetry breaking of fluid density distribution in closed nanoslits.

    PubMed

    Berim, Gersh O; Ruckenstein, Eli

    2008-01-14

    Stable and metastable fluid density distributions (FDDs) in a closed nanoslit between two identical parallel solid walls have been identified on the basis of a nonlocal canonical ensemble density functional theory. Similar to Monte Carlo simulations, periodicity of the FDD in one of the lateral (parallel to the walls surfaces) directions, denoted as the x direction, was assumed. In the other lateral direction, y direction, the FDD was considered uniform. It was found that depending on the average fluid density in the slit, both uniform as well as nonuniform FDDs in the x direction can occur. The uniform FDDs are either symmetric or asymmetric about the middle plane between walls; the latter FDD being the consequence of a symmetry breaking across the slit. The nonuniform FDDs in the x direction occur either in the form of a bump on a thin liquid film covering the walls or as a liquid bridge between those walls and provide symmetry breaking in the x direction. For small and large average densities, the stable state is uniform in the x direction and is symmetric about the middle plane between walls. In the intermediate range of the average density and depending on the length L(x) of the FDD period, the stable state can be represented either by a FDD, which is uniform in the x direction and asymmetric about the middle of the slit (small values of L(x)), or by a bump- and bridgelike FDD for intermediate and large values of L(x), respectively. These results are in agreement with the Monte Carlo simulations performed earlier by other authors. Because the free energy of the stable state decreases monotonically with increasing L(x), one can conclude that the real period is very large (infinite) and that for the values of the parameters employed, a single bridge of finite length over the entire slit is generated.

  19. Collisionless relaxation in spiral galaxy models

    NASA Technical Reports Server (NTRS)

    Hohl, F.

    1974-01-01

    The increase in random kinetic energy of stars by rapidly fluctuating gravitational fields (collisionless or violent relaxation) in disk galaxy models is investigated for three interaction potentials of the stars corresponding to (1) point stars, (2) rod stars of length 2 kpc, and (3) uniform density spherical stars of radius 2 kpc. To stabilize the galaxy against the large scale bar forming instability, a fixed field corresponding to a central core or halo component of stars was added with the stars containing at most 20 percent of the total mass of the galaxy. Considerable heating occurred for both the point stars and the rod stars, whereas the use of spherical stars resulted in a very low heating rate. The use of spherical stars with the resulting low heating rate will be desirable for the study of large scale galactic stability or density wave propagation, since collective heating effects will no longer mask the phenomena under study.

  20. Analytical functions for beta and gamma absorbed fractions of iodine-131 in spherical and ellipsoidal volumes.

    PubMed

    Mowlavi, Ali Asghar; Fornasier, Maria Rossa; Mirzaei, Mohammd; Bregant, Paola; de Denaro, Mario

    2014-10-01

    The beta and gamma absorbed fractions in organs and tissues are the important key factors of radionuclide internal dosimetry based on Medical Internal Radiation Dose (MIRD) approach. The aim of this study is to find suitable analytical functions for beta and gamma absorbed fractions in spherical and ellipsoidal volumes with a uniform distribution of iodine-131 radionuclide. MCNPX code has been used to calculate the energy absorption from beta and gamma rays of iodine-131 uniformly distributed inside different ellipsoids and spheres, and then the absorbed fractions have been evaluated. We have found the fit parameters of a suitable analytical function for the beta absorbed fraction, depending on a generalized radius for ellipsoid based on the radius of sphere, and a linear fit function for the gamma absorbed fraction. The analytical functions that we obtained from fitting process in Monte Carlo data can be used for obtaining the absorbed fractions of iodine-131 beta and gamma rays for any volume of the thyroid lobe. Moreover, our results for the spheres are in good agreement with the results of MIRD and other scientific literatures.

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