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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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

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.

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

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.

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.

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.

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.

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.

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.

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.

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…

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)

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.

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.

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.

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.

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

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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

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.

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.

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.

Radiatively driven relativistic spherical winds under relativistic radiative transfer

NASA Astrophysics Data System (ADS)

Fukue, J.

2018-05-01

We numerically investigate radiatively driven relativistic spherical winds from the central luminous object with mass M and luminosity L* under Newtonian gravity, special relativity, and relativistic radiative transfer. We solve both the relativistic radiative transfer equation and the relativistic hydrodynamical equations for spherically symmetric flows under the double-iteration processes, to obtain the intensity and velocity fields simultaneously. We found that the momentum-driven winds with scattering are quickly accelerated near the central object to reach the terminal speed. The results of numerical solutions are roughly fitted by a relation of \\dot{m}=0.7(Γ _*-1)\\tau _* β _* β _out^{-2.6}, where \\dot{m} is the mass-loss rate normalized by the critical one, Γ* the central luminosity normalized by the critical one, τ* the typical optical depth, β* the initial flow speed at the central core of radius R*, and βout the terminal speed normalized by the speed of light. This relation is close to the non-relativistic analytical solution, \\dot{m} = 2(Γ _*-1)\\tau _* β _* β _out^{-2}, which can be re-expressed as β _out^2/2 = (Γ _*-1)GM/c^2 R_*. That is, the present solution with small optical depth is similar to that of the radiatively driven free outflow. Furthermore, we found that the normalized luminosity (Eddington parameter) must be larger than unity for the relativistic spherical wind to blow off with intermediate or small optical depth, i.e. Γ _* ≳ \\sqrt{(1+β _out)^3/(1-β _out)}. We briefly investigate and discuss an isothermal wind.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

Multi-facet concentrator of solar setup for irradiating the objects placed in a target plane with solar light

DOEpatents

Lewandowski, Allan A.; Yampolskiy, Vladislav; Alekseev, Valerie; Son, Valentin

2001-01-01

According to the proposed invention, this technical result is achieved so that many-facet concentrator of a solar setup for exposure of objects, placed in a target plane, to the action of solar radiation containing a supporting frame and facets differing by that the facets of the concentrator are chosen with spherical focusing reflective surfaces of equal focal lengths and with selective coatings reflecting a desired spectral fraction of solar radiation, and are arranged on the supporting frame symmetrically with respect to the common axis of the concentrator, their optical axes being directed to the single point on the optical axis of the concentrator located before the nominal focus point of the concentrator and determining the position of arranging the target plane.

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.

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.

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

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.

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.

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.

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.

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

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

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.

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.

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.

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

Bozza, V.; Postiglione, A., E-mail: valboz@sa.infn.it, E-mail: postiglione@fis.uniroma3.it

The metric outside an isolated object made up of ordinary matter is bound to be the classical Schwarzschild vacuum solution of General Relativity. Nevertheless, some solutions are known (e.g. Morris-Thorne wormholes) that do not match Schwarzschild asymptotically. On a phenomenological point of view, gravitational lensing in metrics falling as 1/r{sup q} has recently attracted great interest. In this work, we explore the conditions on the source matter for constructing static spherically symmetric metrics exhibiting an arbitrary power-law as Newtonian limit. For such space-times we also derive the expressions of gravitational redshift and force on probe masses, which, together with lightmore » deflection, can be used in astrophysical searches of non-Schwarzschild objects made up of exotic matter. Interestingly, we prove that even a minimally coupled scalar field with a power-law potential can support non-Schwarzschild metrics with arbitrary asymptotic behaviour.« less

Relativistic jet models for the BL Lacertae object Mrk 421 during three epochs of observation

NASA Technical Reports Server (NTRS)

Mufson, S. L.; Hutter, D. J.; Kondo, Y.; Wisniewski, W. Z.

1988-01-01

Coordinated observation of the nearby BL Lacertae object Mrk 421 obtained during May 1980, January 1984, and March 1984 are described. These observations give a time-frozen picture of the continuous spectrum of Mrk 421 at X-ray, ultraviolet, optical, and radio wavelengths. The observed spectra have been fitted to an inhomogeneous relativistic jet model. In general, the models reproduce the data well. Many of the observed differences during the three epochs can be attributed to variations in the opening angle of the jet and in the angle that the jet makes to the line of sight. The jet models obtained here are compared with the homogeneous, spherically symmetric, synchrotron self-Compton models for this source. The models are also compared with the relativistic jet models obtained for other active galactic nuclei.

Gravitational perturbation of irregular bodies modeled with regular polyhedra

NASA Astrophysics Data System (ADS)

Venditti, Flaviane; Prado, Antonio

In this work the study of the dynamics around bodies with non-spherical shapes is considered. The gravitational field of an irregular body, meaning that the mass distribution is asymmetric, generates orbits around this body to perform different from a keplerian orbit. In this case, there is a perturbation on the gravitational field that must be analyzed. To know the gravitational force of an irregular object, first it is necessary to model this body, which is not an easy thing to do, considering that, usually, they are not symmetric figures. To better model the irregular objects, a combination of several geometric figures can be used, like parallelepipeds. This can be applied to asteroids, which are objects with non-spherical shapes. The disturbing force generated by these bodies can then be obtained as the sum of the force on each figure. Here the equation for the potential of a cube is considered (MacMillan, 1930), which makes it possible to have analytical results. The main idea is to build a body with several cubes, and having the gravitational potential of each cube, it is possible to obtain the total perturbation as the sum of the forces acting on each piece. This methodology can be very helpful on space missions to small bodies, because when a spacecraft is in the vicinity of an irregular body, the gravitational perturbation generated by its shape must be considered to compensate this effect.

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.

Hypergeometric Equation in Modeling Relativistic Isotropic Sphere

NASA Astrophysics Data System (ADS)

Thirukkanesh, S.; Ragel, F. C.

2014-04-01

We study the Einstein system of equations in static spherically symmetric spacetimes. We obtained classes of exact solutions to the Einstein system by transforming the condition for pressure isotropy to a hypergeometric equation choosing a rational form for one of the gravitational potentials. The solutions are given in simple form that is a desirable requisite to study the behavior of relativistic compact objects in detail. A physical analysis indicate that our models satisfy all the fundamental requirements of realistic star and match smoothly with the exterior Schwarzschild metric. The derived masses and densities are consistent with the previously reported experimental and theoretical studies describing strange stars. The models satisfy the standard energy conditions required by normal matter.

The scale of the Fourier transform: a point of view of the fractional Fourier transform

NASA Astrophysics Data System (ADS)

Jimenez, C. J.; Vilardy, J. M.; Salinas, S.; Mattos, L.; Torres, C. O.

2017-01-01

In this paper using the Fourier transform of order fractional, the ray transfer matrix for the symmetrical optical systems type ABCD and the formulae by Collins for the diffraction, we obtain explicitly the expression for scaled Fourier transform conventional; this result is the great importance in optical signal processing because it offers the possibility of scaling the size of output the Fourier distribution of the system, only by manipulating the distance of the diffraction object toward the thin lens, this research also emphasizes on practical limits when a finite spherical converging lens aperture is used. Digital simulation was carried out using the numerical platform of Matlab 7.1.

Design, Fabrication, Optical Testing, and Performance of Diamond Machined Aspheric Mirrors for Ground-Based Near-IR Astronomy

NASA Technical Reports Server (NTRS)

Ohl, Raymond G.; Mink, Ronald; Chambers, V. John; Connelly, Joseph A.; Mentzell, J. Eric; Tveekrem, June L.; Howard, Joseph M.; Preuss, Werner; Schroeder, Mechthild; Sohn, Alex;

Cosmic structures and gravitational waves in ghost-free scalar-tensor theories of gravity

NASA Astrophysics Data System (ADS)

Bartolo, Nicola; Karmakar, Purnendu; Matarrese, Sabino; Scomparin, Mattia

2018-05-01

We study cosmic structures in the quadratic Degenerate Higher Order Scalar Tensor (qDHOST) model, which has been proposed as the most general scalar-tensor theory (up to quadratic dependence on the covariant derivatives of the scalar field), which is not plagued by the presence of ghost instabilities. We then study a static, spherically symmetric object embedded in de Sitter space-time for the qDHOST model. This model exhibits breaking of the Vainshtein mechanism inside the cosmic structure and Schwarzschild-de Sitter space-time outside, where General Relativity (GR) can be recovered within the Vainshtein radius. We constrained the parameters of the qDHOST model by requiring the validity of the Vainshtein screening mechanism inside the cosmic structures and the consistency with the recently established bounds on gravitational wave speed from GW170817/GRB170817A event. We find that these two constraints rule out the same set of parameters, corresponding to the Lagrangians that are quadratic in second-order derivatives of the scalar field, for the shift symmetric qDHOST.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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].

Astrophysical and Cosmological Consequences of the Dynamical Localization of Gravity

NASA Astrophysics Data System (ADS)

Germani, Cristiano

2003-11-01

In this thesis I review cosmological and astrophysical exact models for Randall-Sundrum-type braneworlds and their physical implications. I present new insights and show their analogies with quantum theories via the holographic idea. In astrophysics I study the two fundamental models of a spherically symmetric static star and spherically symmetric collapsing objects. I show how matching for the pressure of a static star encodes braneworld effects. In addition I study the problem of the vacuum exterior conjecturing a uniqueness theorem. Furthermore I show that a collapsing dust cloud in the braneworld has a non-static exterior, in contrast to the General Relativistic case. This non-static behaviour is linked to the presence of a "surplus potential energy" that must be released, producing a non-zero flux of energy. Via holography this can be connected with the Hawking process, giving an indirect measure of the brane tension. In cosmology I investigate the generalization of the Randall-Sundrum-type model obtained by introducing the Gauss-Bonnet combination into the action. I elucidate the junction conditions necessary to study the brane model and obtain the cosmological dynamics, showing that, even in the thin shell limit for the brane, the Gauss-Bonnet term implies a non-trivial internal structure for the matter and geometry distributions. Independently of the gravitational theory used, I show how to derive the modified Friedman equation and how it is related to the black hole solution of the theory. Via holography I also show how to interpret quantum mechanically the mass of this black hole from a four-dimensional perspective in the simplest Randall-Sundrum-type scenario.

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.

The stability of nonlinear dynamos and the limited role of kinematic growth rates

NASA Astrophysics Data System (ADS)

Brandenburg, A.; Krause, F.; Meinel, R.; Moss, D.; Tuominen, I.

1989-04-01

The growth rate behavior of several kinematic dynamo models was investigated in the context of the observation that, as a rule, a magnetic field of a single symmetry dominates in the sun and other cosmic objects. For all dynamo models considered, it is shown that, as the dynamo numbers increase, the kinematic growth rates of fields of different parities are asymptotically equal, indicating that growth rates do not dominate the final state of the field. The possibility that the stability of different solutions of nonlinear dynamos determines the final state was then investigated. Dynamo models in spherical geometry were found in which both symmetric and antisymmetric solutions are stable. The kind of symmetry finally established depends in these cases on the initial conditions, i.e., on the history of the object. It is noted that the basic mechanism stabilizing or destabilizing different solutions is not well understood.

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.

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.

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.

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.

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.

Radiative acceleration in Schwarzschild space-times

NASA Astrophysics Data System (ADS)

Keane, A. J.; Barrett, R. K.; Simmons, J. F. L.

2001-03-01

We examine the radial motion of a material particle in the intense radiation field of a static spherically symmetric compact object with spherical emitting surface outside the Schwarzschild radius. This paper generalizes previous work which dealt with radial motion in the Thomson limit, where the radiation force is simply proportional to the radiative flux. In the general case the average time component of the 4-momentum transferred to the particle is not negligible compared with its rest mass. Consequently, we find that the frequency dependence of the radiation force owing to Compton scattering for highly energetic photons gives rise to an increase in the effective mass of the test particle. In this work we outline the effects of this frequency dependence and compare these with the results in the Thomson limit. We present the frequency dependent saturation velocity curves for a range of stellar luminosities and radiation frequencies and present the resulting phase-space diagrams corresponding to the radial test particle trajectories. In particular, the stable equilibrium points which exist in the Thomson limit are found to be absent in the general case.

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.

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

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.

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.

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)

An exact solution to the Einstein-Maxwell equations representing a nonspherical, highly charged object

NASA Astrophysics Data System (ADS)

Menon, Govind K.

The Reissner-Nordstrom solution possesses a naked singularity when e2 > m2, where m is the mass and e is the net charge of the system. Also, the singularity at r = 0 is repulsive (i.e., no timelike geodesics (neutral particles) can reach the singularity). These unusual properties of the Reissner-Nordstrom geometry are considered as an accident resulting from the highly symmetric nature of the space-time. Here we wish to generalize the condition of spherical symmetry to axial symmetry and to probe into the issues of naked singularity and gravitational repulsion. To do this, we must construct a nonspherical solution to the Einstein-Maxwell set of equations in the event that e2 > m2. The Erez-Rosen extension of the vacuum Schwarzschild solution to the non-spherical case gave one of the first physically significant solutions of the Einstein field equations. Nonvacuum extensions of the Erez-Rosen solution representing a non-spherical mass containing a very high net charge (i.e., when e2 > m2) will be discussed. The special case of spherical symmetry, as would be expected, results in the Reissner-Nordstrom solution. The search for the physical singularities involves the calculation of a nontrivial scalar constructed from the Riemann curvature tensor. As it turns out, the resulting geometry does indeed possess a naked singularity. In addition, the space-time also entertains gravitational repulsion. However, unlike the Reissner-Nordstrom solution, it has been found that all timelike geodesics are not necessarily repelled from the origin.

The effect of non-sphericity on mass and anisotropy measurements in dSph galaxies with Schwarzschild method

NASA Astrophysics Data System (ADS)

Kowalczyk, Klaudia; Łokas, Ewa L.; Valluri, Monica

2018-05-01

In our previous work we confirmed the reliability of the spherically symmetric Schwarzschild orbit-superposition method to recover the mass and velocity anisotropy profiles of spherical dwarf galaxies. Here, we investigate the effect of its application to intrinsically non-spherical objects. For this purpose we use a model of a dwarf spheroidal galaxy formed in a numerical simulation of a major merger of two discy dwarfs. The shape of the stellar component of the merger remnant is axisymmetric and prolate which allows us to identify and measure the bias caused by observing the spheroidal galaxy along different directions, especially the longest and shortest principal axis. The modelling is based on mock data generated from the remnant that are observationally available for dwarfs: projected positions and line-of-sight velocities of the stars. In order to obtain a reliable tool while keeping the number of parameters low we parametrize the total mass distribution as a radius-dependent mass-to-light ratio with just two free parameters we aim to constrain. Our study shows that if the total density profile is known, the true, radially increasing anisotropy profile can be well recovered for the observations along the longest axis whereas the data along the shortest axis lead to the inference of an incorrect, isotropic model. On the other hand, if the density profile is derived from the method as well, the anisotropy is always underestimated but the total mass profile is well recovered for the data along the shortest axis whereas for the longest axis the mass content is overestimated.

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.

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.

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.

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

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.

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.

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.

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

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.

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.

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

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.

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.

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.

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.

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

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.

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.

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

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.

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.

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.

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.

Gravitational properties of light: The emission of counter-propagating laser pulses from an atom

NASA Astrophysics Data System (ADS)

Rätzel, Dennis; Wilkens, Martin; Menzel, Ralf

2017-04-01

The gravitational field of a laser pulse, although not detectable at the moment, has a special feature which continues to attract attention; cause and effect propagate with the same speed, the speed of light. One particular result of this feature is that the gravitational field of an emitted laser pulse and the gravitational effect of the emitter's energy-momentum change are intimately entangled. In this article, a specific example of an emission process is considered: An atom, modeled as a point mass, emits two counter-propagating pulses. The corresponding curvature and the effect on massive and massless test particles is discussed. A comparison is made with the metric corresponding to a spherically symmetric massive object that isotropically emits radiation; the Vaidya metric.

Nonminimal coupling for the gravitational and electromagnetic fields: Traversable electric wormholes

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

Balakin, Alexander B.; Zayats, Alexei E.; Lemos, Jose P. S.

2010-04-15

We discuss new exact solutions of a three-parameter nonminimal Einstein-Maxwell model. The solutions describe static spherically symmetric objects with and without center, supported by an electric field nonminimally coupled to gravity. We focus on a unique one-parameter model, which admits an exact solution for a traversable electrically charged wormhole connecting two universes, one asymptotically flat the other asymptotically de Sitter ones. The relation between the asymptotic mass and charge of the wormhole and its throat radius is analyzed. The wormhole solution found is thus a nonminimal realization of Wheeler's idea about charge without charge and shows that, if the worldmore » is somehow nonminimal in the coupling of gravity to electromagnetism, then wormhole appearance, or perhaps construction, is possible.« less

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Calculating observables in inhomogeneous cosmologies. Part I: general framework

NASA Astrophysics Data System (ADS)

Hellaby, Charles; Walters, Anthony

2018-02-01

We lay out a general framework for calculating the variation of a set of cosmological observables, down the past null cone of an arbitrarily placed observer, in a given arbitrary inhomogeneous metric. The observables include redshift, proper motions, area distance and redshift-space density. Of particular interest are observables that are zero in the spherically symmetric case, such as proper motions. The algorithm is based on the null geodesic equation and the geodesic deviation equation, and it is tailored to creating a practical numerical implementation. The algorithm provides a method for tracking which light rays connect moving objects to the observer at successive times. Our algorithm is applied to the particular case of the Szekeres metric. A numerical implementation has been created and some results will be presented in a subsequent paper. Future work will explore the range of possibilities.

Axial geometrical aberration correction up to 5th order with N-SYLC.

PubMed

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

2017-11-01

We present N-SYLC (N-fold symmetric line currents) models to correct 5th order axial geometrical aberrations in electron microscopes. In our previous paper, we showed that 3rd order spherical aberration can be corrected by 3-SYLC doublet. After that, mainly the 5th order aberrations remain to limit the resolution. In this paper, we extend the doublet to quadruplet models also including octupole and dodecapole fields for correcting these higher order aberrations, without introducing any new unwanted ones. We prove the validity of our models by analytical calculations. Also by computer simulations, we show that for beam energy of 5keV and initial angle 10mrad at the corrector object plane, beam size of less than 0.5nm is achieved at the corrector image plane. Copyright © 2017 Elsevier B.V. All rights reserved.

Elliptical-like orbits on a warped spandex fabric: A theoretical/experimental undergraduate research project

NASA Astrophysics Data System (ADS)

Middleton, Chad A.; Weller, Dannyl

2016-04-01

We present a theoretical and experimental analysis of the elliptical-like orbits of a marble rolling on a warped spandex fabric. We arrive at an expression describing the angular separation between successive apocenters, or equivalently successive pericenters, in both the small and large slope regimes. We find that a minimal angular separation of ˜197° is predicted for orbits with small radial distances when the surface is void of a central mass. We then show that for small radii and large central masses, when the orbiting marble is deep within the well, the angular separation between successive apocenters transitions to values greater than 360°. We lastly compare these expressions to those describing elliptical-like orbits about a static, spherically symmetric massive object in the presence of a constant vacuum energy, as described by general relativity.

Visible, invisible and trapped ghosts as sources of wormholes and black universes

NASA Astrophysics Data System (ADS)

Bolokhov, S. V.; Bronnikov, K. A.; Korolyov, P. A.; Skvortsova, M. V.

2016-02-01

We construct explicit examples of globally regular static, spherically symmetric solutions in general relativity with scalar and electromagnetic fields, describing traversable wormholes with flat and AdS asymptotics and regular black holes, in particular, black universes. (A black universe is a regular black hole with an expanding, asymptotically isotropic space-time beyond the horizon.) Such objects exist in the presence of scalar fields with negative kinetic energy (“phantoms”, or “ghosts”), which are not observed under usual physical conditions. To account for that, we consider what we call “trapped ghosts” (scalars whose kinetic energy is only negative in a strong-field region of space-time) and “invisible ghosts”, i.e., phantom scalar fields sufficiently rapidly decaying in the weak-field region. The resulting configurations contain different numbers of Killing horizons, from zero to four.

The correlation function of galaxy ellipticities produced by gravitational lensing

NASA Technical Reports Server (NTRS)

Miralda-Escude, Jordi

1991-01-01

The correlation of galaxy ellipticities produced by gravitational lensing is calculated as a function of the power spectrum of density fluctuations in the universe by generalizing an analytical method developed by Gunn (1967). The method is applied to a model where identical objects with spherically symmetric density profiles are randomly laid down in space, and to the cold dark matter model. The possibility of detecting this correlation is discussed. Although an ellipticity correlation can also be caused by an intrinsic alignment of the axes of galaxies belonging to a cluster or a supercluster, a method is suggested by which one type of correlation can be distinguished from another. The advantage of this ellipticity correlation is that it is one of the few astronomical observations that can directly probe large-scale mass fluctuations in the universe.

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.

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.

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.

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.

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.

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.

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.

Determining the Drag Coefficient of Rotational Symmetric Objects Falling through Liquids

ERIC Educational Resources Information Center

Houari, Ahmed

2012-01-01

I will propose here a kinematic approach for measuring the drag coefficient of rotational symmetric objects falling through liquids. For this, I will show that one can obtain a measurement of the drag coefficient of a rotational symmetric object by numerically solving the equation of motion describing its fall through a known liquid contained in a…

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.

Hot super-dense compact object with particular EoS

NASA Astrophysics Data System (ADS)

Tito, E. P.; Pavlov, V. I.

2018-03-01

We show the possibility of existence of a self-gravitating spherically-symmetric equilibrium configuration for a neutral matter with neutron-like density, small mass M ≪ M_{⊙}, and small radius R ≪ R_{⊙}. We incorporate the effects of both the special and general theories of relativity. Such object may be formed in a cosmic cataclysm, perhaps an exotic one. Since the base equations of hydrostatic equilibrium are completed by the equation of state (EoS) for the matter of the object, we offer a novel, interpolating experimental data from high-energy physics, EoS which permits the existence of such compact system of finite radius. This EoS model possesses a critical state characterized by density ρc and temperature Tc. For such an object, we derive a radial distribution for the super-dense matter in "liquid" phase using Tolman-Oppenheimer-Volkoff equations for hydrostatic equilibrium. We demonstrate that a stable configuration is indeed possible (only) for temperatures smaller than the critical one. We derive the mass-radius relation (adjusted for relativistic corrections) for such small (M ≪ M_{⊙}) super-dense compact objects. The results are within the constraints established by both heavy-ion collision experiments and theoretical studies of neutron-rich matter.

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.

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.

Increase in the energy density of the pinch plasma in 3D implosion of quasi-spherical wire arrays

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

Aleksandrov, V. V., E-mail: alexvv@triniti.ru; Gasilov, V. A.; Grabovski, E. V.

Results are presented from experimental studies of the characteristics of the soft X-ray (SXR) source formed in the implosion of quasi-spherical arrays made of tungsten wires and metalized kapron fibers. The experiments were carried out at the Angara-5-1 facility at currents of up to 3 MA. Analysis of the spatial distribution of hard X-ray emission with photon energies above 20 keV in the pinch images taken during the implosion of quasi-spherical tungsten wire arrays (QTWAs) showed that a compact quasi-spherical plasma object symmetric with respect to the array axis formed in the central region of the array. Using a diffractionmore » grazing incidence spectrograph, spectra of SXR emission with wavelengths of 20–400 Å from the central, axial, and peripheral regions of the emission source were measured with spatial resolutions along the array radius and height in the implosion of QTWAs. It is shown that the emission spectra of the SXR sources formed under the implosion of quasi-spherical and cylindrical tungsten wire arrays at currents of up to 3 MA have a maximum in the wavelength range of 50–150 Å. It is found that, during the implosion of a QTWA with a profiled linear mass, a redistribution of energy in the emission spectrum takes place, which indicates that, during 3D implosion, the energy of longitudinal motion of the array material additionally contributes to the radiation energy. It is also found that, at close masses of the arrays and close values of the current in the range of 2.4{sup −3} MA, the average energy density in the emission source formed during the implosion of a quasi-spherical wire array is larger by a factor of 7 than in the source formed during the implosion of a cylindrical wire array. The experimental data were compared with results of 3D simulations of plasma dynamics and radiation generation during the implosion of quasi-spherical wire arrays with a profiled mass by using the MARPLE-3D radiative magnetohydrodynamic code, developed at the Keldysh Institute of Applied Mathematics, Russian Academy of Sciences.« less

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.

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.

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.

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.

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

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.

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.

On the Problem of Deformed Spherical Systems in Modified Newtonian Dynamics

NASA Astrophysics Data System (ADS)

Ko, Chung-Ming

2016-04-01

Based on Newtonian dynamics, observations show that the luminous masses of astrophysical objects that are the size of a galaxy or larger are not enough to generate the measured motions which they supposedly determine. This is typically attributed to the existence of dark matter, which possesses mass but does not radiate (or absorb radiation). Alternatively, the mismatch can be explained if the underlying dynamics is not Newtonian. Within this conceptual scheme, Modified Newtonian Dynamics (MOND) is a successful theoretical paradigm. MOND is usually expressed in terms of a nonlinear Poisson equation, which is difficult to analyze for arbitrary matter distributions. We study the MONDian gravitational field generated by slightly non-spherically symmetric mass distributions based on the fact that both Newtonian and MONDian fields are conservative (which we refer to as the compatibility condition). As the non-relativistic version of MOND has two different formulations (AQUAL and QuMOND) and the compatibility condition can be expressed in two ways, there are four approaches to the problem in total. The method involves solving a suitably defined linear deformation potential, which generally depends on the choice of MOND interpolation function. However, for some specific form of the deformation potential, the solution is independent of the interpolation function.

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.

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.

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.

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.

Chameleon scalar fields in relativistic gravitational backgrounds

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

Tsujikawa, Shinji; Tamaki, Takashi; Tavakol, Reza, E-mail: shinji@rs.kagu.tus.ac.jp, E-mail: tamaki@gravity.phys.waseda.ac.jp, E-mail: r.tavakol@qmul.ac.uk

2009-05-15

We study the field profile of a scalar field {phi} that couples to a matter fluid (dubbed a chameleon field) in the relativistic gravitational background of a spherically symmetric spacetime. Employing a linear expansion in terms of the gravitational potential {Phi}{sub c} at the surface of a compact object with a constant density, we derive the thin-shell field profile both inside and outside the object, as well as the resulting effective coupling with matter, analytically. We also carry out numerical simulations for the class of inverse power-law potentials V({phi}) = M{sup 4+n}{phi}{sup -n} by employing the information provided by ourmore » analytical solutions to set the boundary conditions around the centre of the object and show that thin-shell solutions in fact exist if the gravitational potential {Phi}{sub c} is smaller than 0.3, which marginally covers the case of neutron stars. Thus the chameleon mechanism is present in the relativistic gravitational backgrounds, capable of reducing the effective coupling. Since thin-shell solutions are sensitive to the choice of boundary conditions, our analytic field profile is very helpful to provide appropriate boundary conditions for {Phi}{sub c}{approx}« less

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

Afonso, V.I.; Olmo, Gonzalo J.; Rubiera-Garcia, D., E-mail: viafonso@df.ufcg.edu.br, E-mail: gonzalo.olmo@uv.es, E-mail: drgarcia@fc.ul.pt

The existence of static, spherically symmetric, self-gravitating scalar field solutions in the context of Born-Infeld gravity is explored. Upon a combination of analytical approximations and numerical methods, the equations for a free scalar field (without a potential term) are solved, verifying that the solutions recover the predictions of General Relativity far from the center but finding important new effects in the central regions. We find two classes of objects depending on the ratio between the Schwarzschild radius and a length scale associated to the Born-Infeld theory: massive solutions have a wormhole structure, with their throat at r ≈ 2 Mmore » , while for the lighter configurations the topology is Euclidean. The total energy density of these solutions exhibits a solitonic profile with a maximum peaked away from the center, and located at the throat whenever a wormhole exists. The geodesic structure and curvature invariants are analyzed for the various configurations considered.« less

Black hole formation due to collapsing dark matter in a presence of dark energy in the brane-world scenario

NASA Astrophysics Data System (ADS)

Shah, Hasrat Hussain

In the last three to four decades, various programs have been studied in order to investigate the final fate of gravitational collapse of massive astronomical objects. In the theoretical context, Black Holes (BHs) are the consequence of final stage of the gravitational collapse. In this work, we investigated the gravitational collapse process of a spherically symmetric star constituted of dark matter (DM), ρM, and Dark Energy (DE), ρ in the context of the brane-world scenario. In our model, we discussed the anisotropy of the pressure in a fluid with Equation of State (EoS) pt = kρ and pr = lρ, (l + 2k < ‑1). We briefly discussed various cases of gravitational collapse and it is found that BH can be formed by the gravitational collapse in brane-world regime while in some cases there is only a naked singularity at their end state.

Recognition of 3-D symmetric objects from range images in automated assembly tasks

NASA Technical Reports Server (NTRS)

Alvertos, Nicolas; Dcunha, Ivan

1990-01-01

A new technique is presented for the three dimensional recognition of symmetric objects from range images. Beginning from the implicit representation of quadrics, a set of ten coefficients is determined for symmetric objects like spheres, cones, cylinders, ellipsoids, and parallelepipeds. Instead of using these ten coefficients trying to fit them to smooth surfaces (patches) based on the traditional way of determining curvatures, a new approach based on two dimensional geometry is used. For each symmetric object, a unique set of two dimensional curves is obtained from the various angles at which the object is intersected with a plane. Using the same ten coefficients obtained earlier and based on the discriminant method, each of these curves is classified as a parabola, circle, ellipse, or hyperbola. Each symmetric object is found to possess a unique set of these two dimensional curves whereby it can be differentiated from the others. It is shown that instead of using the three dimensional discriminant which involves evaluation of the rank of its matrix, it is sufficient to use the two dimensional discriminant which only requires three arithmetic operations.

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.

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.

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.

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.

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.

Kuiper Belt Objects of different sizes and average densities: thermal evolution scenarios and modern structure of matter

NASA Astrophysics Data System (ADS)

Shchuko, O. B.; Shchuko, S. D.; Kartashov, D.; Orosei, R.

2012-04-01

Thermal evolution of accretion-formed Kuiper Belt Objects (KBOs) with modern sizes from 200 to 2000 km and average densities from 1100 to 3200 kg/m3 has been studied by mathematical simulation methods. The values range of physical parameters of the accretion material and ultimate radionuclide content, securing KBO existence at present, have been found. The solid dust material of protosolar cloud fringe regions and fine-fractured H2O condensate in the form of amorphous ice are considered to have been the building matter for these objects. This material was represented by small dust particles of different chemical and mineralogical composition, embedded with radionuclides 238U, 235U, 232Th, 40K providing the sources of radiogenic heat. H2O condensate secured the presence of amorphous ice in the forming body's matter. Radiogenic heat leads to H2O phase transitions which define a body's interior matter differentiation. The radionuclide content at the initial time of the body formation determined the dynamically changing degree of the interior matter differentiation at different KBO depths for the whole period from the initial up to the present time. For the models of the celestial objects considered, the dynamically changing boundaries of spherically symmetric regions with different degree of matter differentiation have been determined.

Stealth configurations in vector-tensor theories of gravity

NASA Astrophysics Data System (ADS)

Chagoya, Javier; Tasinato, Gianmassimo

2018-01-01

Studying the physics of compact objects in modified theories of gravity is important for understanding how future observations can test alternatives to General Relativity. We consider a subset of vector-tensor Galileon theories of gravity characterized by new symmetries, which can prevent the propagation of the vector longitudinal polarization, even in absence of Abelian gauge invariance. We investigate new spherically symmetric and slowly rotating solutions for these systems, including an arbitrary matter Lagrangian. We show that, under certain conditions, there always exist stealth configurations whose geometry coincides with solutions of Einstein gravity coupled with the additional matter. Such solutions have a non-trivial profile for the vector field, characterized by independent integration constants, which extends to asymptotic infinity. We interpret our findings in terms of the symmetries and features of the original vector-tensor action, and on the number of degrees of freedom that it propagates. These results are important to eventually describe gravitationally bound configurations in modified theories of gravity, such as black holes and neutron stars, including realistic matter fields forming or surrounding the object.

Verlinde's emergent gravity versus MOND and the case of dwarf spheroidals

NASA Astrophysics Data System (ADS)

Diez-Tejedor, Alberto; Gonzalez-Morales, Alma X.; Niz, Gustavo

2018-06-01

In a recent paper, Erik Verlinde has developed the interesting possibility that space-time and gravity may emerge from the entangled structure of an underlying microscopic theory. In this picture, dark matter arises as a response to the standard model of particle physics from the delocalized degrees of freedom that build up the dark energy component of the Universe. Dark matter physics is then regulated by a characteristic acceleration scale a0, identified with the radius of the (quasi)-de Sitter universe we inhabit. For a point particle matter source, or outside an extended spherically symmetric object, MOND's empirical fitting formula is recovered. However, Verlinde's theory critically departs from MOND when considering the inner structure of galaxies, differing by a factor of 2 at the centre of a regular massive body. For illustration, we use the eight classical dwarf spheroidal satellites of the Milky Way. These objects are perfect testbeds for the model given their approximate spherical symmetry, measured kinematics, and identified missing mass. We show that, without the assumption of a maximal deformation, Verlinde's theory can fit the velocity dispersion profile in dwarf spheroidals with no further need of an extra dark particle component. If a maximal deformation is considered, the theory leads to mass-to-light ratios that are marginally larger than expected from stellar population and formation history studies. We also compare our results with the recent phenomenological interpolating MOND function of McGaugh et al., and find a departure that, for these galaxies, is consistent with the scatter in current observations.

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.

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

Publicly Available Geosynchronous (GEO) Space Object Catalog for Future Space Situational Awareness (SSA) Studies

NASA Astrophysics Data System (ADS)

Koblick, D. C.; Shankar, P.; Xu, S.

Previously, there have been many commercial proposals and extensive academic studies regarding ground and space based sensors to assist a space surveillance network in obtaining metric observations of satellites and debris near Geosynchronous Earth Orbit (GEO). Most use physics based models for geometric constraints, lighting, and tasker/scheduler operations of sensor architectures. Under similar physics modeling assumptions, the space object catalog is often different due to proprietary standards and datasets. Lack of catalog commonality between studies creates barriers and difficulty comparing performance benefits of sensor trades. To solve this problem, we have constructed a future GEO space catalog from publicly available datasets and literature. The annual number of new payloads and rocket bodies is drawn from a Poisson distribution while the growth of the current GEO catalog is bootstrapped from the historical payload, upper stage, and debris data. We adopt a spherically symmetric explosion model and couple it with the NASA standard breakup model to simulate explosions of payloads and rocket bodies as they are the primary drivers of the debris population growth. The cumulative number of fragments follow a power-law distribution. Result from 1,000 random catalog growth simulations indicates that the GEO space object population in the year 2050 will include over 3,600 objects, nearly half of which are debris greater than 10 cm spherical diameter. The number of rocket bodies and dead payloads is projected to nearly double over the next 33 years. For comparison, the current Air Force Space Command catalog snapshot contains fewer than 50 pieces of debris and coarse Radar Cross Section (RCS) estimates which include: small, medium, and large. The current catalog may be sufficient for conjunction studies, but not for analyzing future sensor system performance. The 2050 GEO projected catalog will be available online for commercial/academic research and development.

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.

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.

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.

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.

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.

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

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.…

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.

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

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.

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

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

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.

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.

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

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

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.

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.

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

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.

Topography measurements of high NA aspherical microlenses by digital holographic microscopy with spherical illumination

NASA Astrophysics Data System (ADS)

Józwik, Michal; Mikuła, Marta; Kozacki, Tomasz; Kostencka, Julianna; Gorecki, Christophe

2017-06-01

In this contribution, we propose a method of digital holographic microscopy (DHM) that enables measurement of high numerical aperture spherical and aspherical microstructures of both concave and convex shapes. The proposed method utilizes reflection of the spherical illumination beam from the object surface and the interference with a spherical reference beam of the similar curvature. In this case, the NA of DHM is fully utilized for illumination and imaging of the reflected object beam. Thus, the system allows capturing the phase coming from larger areas of the quasi-spherical object and, therefore, offers possibility of high accuracy characterization of its surface even in the areas of high inclination. The proposed measurement procedure allows determining all parameters required for the accurate shape recovery: the location of the object focus point and the positions of the illumination and reference point sources. The utility of the method is demonstrated with characterization of surface of high NA focusing objects. The accuracy is firstly verified by characterization of a known reference sphere with low error of sphericity. Then, the method is applied for shape measurement of spherical and aspheric microlenses. The results provide a full-field reconstruction of high NA topography with resolution in the nanometer range. The surface sphericity is evaluated by the deviation from the best fitted sphere or asphere, and the important parameters of the measured microlens: e.g.: radius of curvature and conic constant.

Design for an aberration corrected scanning electron microscope using miniature electron mirrors.

PubMed

Dohi, Hideto; Kruit, Pieter

2018-06-01

Resolution of scanning electron microscopes (SEMs) is determined by aberrations of the objective lens. It is well known that both spherical and chromatic aberrations can be compensated by placing a 90-degree bending magnet and an electron mirror in the beam path before the objective lens. Nevertheless, this approach has not led to wide use of these aberration correctors, partly because aberrations of the bending magnet can be a serious problem. A mirror corrector with two mirrors placed perpendicularly to the optic axis of an SEM and facing each other is proposed. As a result, only small-angle magnetic deflection is necessary to guide the electron beam around the top mirror to the bottom mirror and around the bottom mirror to the objective lens. The deflection angle, in the order of 50 mrad, is sufficiently small to avoid deflection aberrations. In addition, lateral dispersion at the sample plane can be avoided by making the deflection fields symmetric. Such a corrector system is only possible if the incoming beam can pass the top mirror at a distance in the order of millimeters, without being disturbed by the electric fields of electrodes of the mirror. It is proposed that condition can be satisfied with micro-scale electron optical elements fabricated by using MEMS technology. In the proposed corrector system, the micro-mirrors have to provide the exact negative spherical and chromatic aberrations for correcting the aberration of the objective lens. This exact tuning is accomplished by variable magnification between the micro-mirrors and the objective lens using an additional transfer lens. Extensive optical calculations are reported. Aberrations of the micro-mirrors were analyzed by numerical calculation. Dispersion and aberrations of the deflectors were calculated by using an analytical field model. Combination aberrations caused by the off-axis position of dispersive rays in the mirrors and objective lens were also analyzed. It is concluded that the proposed corrector system will be a promising candidate for simple and low-cost aberration correction in low-voltage SEMs. Copyright © 2018 Elsevier B.V. All rights reserved.

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

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.

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*.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

The Combination of Spherical Photogrammetry and UAV for 3D Modeling

NASA Astrophysics Data System (ADS)

Ihsanudin, T.; Affriani, A. R.

2017-12-01

The complete of 3D models required the object that was recorded from both side and top. If the object recorded from above, then the object from the side can not be covered, and if the objects recorded from the side, it can not be covered from the top. Recording of objects from the side using spherical photogrammetry method and from the top using UAV method. The merge of both models using a conform transformation, by bringing the spherical photogrammetry coordinates system to the UAV model. The object of this research is Ratu Boko temple, Sleman, Yogyakarta. The spherical photogrammetry recording was performed by rotating the camera in 360° angle on the entire area of the temple. The area consists of 12 stations. The UAV method uses a drone with flight attitude of 20 meters. The merge of the both models produced the completeness of the temple model from the top and side.

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.

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.

Relativistic model for anisotropic strange stars

NASA Astrophysics Data System (ADS)

Deb, Debabrata; Chowdhury, Sourav Roy; Ray, Saibal; Rahaman, Farook; Guha, B. K.

2017-12-01

In this article, we attempt to find a singularity free solution of Einstein's field equations for compact stellar objects, precisely strange (quark) stars, considering Schwarzschild metric as the exterior spacetime. To this end, we consider that the stellar object is spherically symmetric, static and anisotropic in nature and follows the density profile given by Mak and Harko (2002) , which satisfies all the physical conditions. To investigate different properties of the ultra-dense strange stars we have employed the MIT bag model for the quark matter. Our investigation displays an interesting feature that the anisotropy of compact stars increases with the radial coordinate and attains its maximum value at the surface which seems an inherent property for the singularity free anisotropic compact stellar objects. In this connection we also perform several tests for physical features of the proposed model and show that these are reasonably acceptable within certain range. Further, we find that the model is consistent with the energy conditions and the compact stellar structure is stable with the validity of the TOV equation and Herrera cracking concept. For the masses below the maximum mass point in mass vs radius curve the typical behavior achieved within the framework of general relativity. We have calculated the maximum mass and radius of the strange stars for the three finite values of bag constant Bg.

Design and analysis of aspherical multilayer imaging X-ray microscope

NASA Technical Reports Server (NTRS)

Shealy, David L.; Jiang, WU; Hoover, Richard B.

1991-01-01

Spherical Schwarzschild microscopes for soft X-ray applications in microscopy and projection lithography employ two concentric spherical mirrors that are configured such that the third-order spherical aberration and coma are zero. Based on incoherent, sine-wave MTF calculations, the object-plane resolution of a magnification-factor-20 microscope is presently analyzed as a function of object height and numerical aperture of the primary for several spherical Schwarzschild, conic, and aspherical two-mirror microscope configurations.

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.

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.

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.

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.

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)

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

Pre-Big Bang Bubbles from the Gravitational Instability of Generic String Vacua

NASA Astrophysics Data System (ADS)

Buonanno, A.; Damour, T.; Veneziano, G.

1998-06-01

We formulate the basic postulate of pre-big bang cosmology as one of 'asymptotic past triviality', by which we mean that the initial state is a generic perturbative solution of the tree-level low-energy effective action. Each such singular space-like hypersurface of gravitational collapse becomes, in the string-frame metric, the usual big-bang t = 0 hypersurface, i.e. the place of birth of a baby Friedmann universe after a period of dilaton-driven inflation. Specializing to the spherically-symmetric case, we review and reinterpret previous work on the subject, and propose a simple, scale-invariant criterion for collapse/inflation in terms of asymptotic data at past null infinity. Those data should determine whether, when, and where collapse/inflation occurs, and, when it does, fix its characteristics, including anisotropies on the big bang hypersurface whose imprint could have survived till now. Using Bayesian probability concepts, we finally attempt to answer some fine-tuning objections recently moved to the pre-gib bang scenario.

Anisotropic strange star with Tolman V potential

NASA Astrophysics Data System (ADS)

Shee, Dibyendu; Deb, Debabrata; Ghosh, Shounak; Ray, Saibal; Guha, B. K.

In this paper, we present a strange stellar model using Tolman V-type metric potential employing simplest form of the MIT bag equation of state (EOS) for the quark matter. We consider that the stellar system is spherically symmetric, compact and made of an anisotropic fluid. Choosing different values of n we obtain exact solutions of the Einstein field equations and finally conclude that for a specific value of the parameter n = 1/2, we find physically acceptable features of the stellar object. Further, we conduct different physical tests, viz., the energy condition, generalized Tolman-Oppeheimer-Volkoff (TOV) equation, Herrera’s cracking concept, etc., to confirm the physical validity of the presented model. Matching conditions provide expressions for different constants whereas maximization of the anisotropy parameter provides bag constant. By using the observed data of several compact stars, we derive exact values of some of the physical parameters and exhibit their features in tabular form. It is to note that our predicted value of the bag constant satisfies the report of CERN-SPS and RHIC.

Generalized formulation of the interactions between soft spheres

NASA Astrophysics Data System (ADS)

Alonso-Marroquín, F.; McNamara, S.

2014-10-01

The goal of this paper is to identify the most general formulation that consistently links the different degrees of freedom in a contact between spherical soft particles. These contact laws have two parts: a set of "generalized contact velocities" that characterize the relative motion of the two particles, and a set of "generalized contact forces" that characterize the interparticle forces. One well known constraint on contact models is that the contact velocities must be objective. This requirement fixes the number of linearly independent contact velocities. We also present a previously unnoticed (in this context) constraint, namely, that the velocities and forces must be related in such a way that the stiffness matrix is symmetric. This constraint also places restrictions on the coupling between the contact forces. Within our generalized contact model, we discuss the expression for rolling velocity that need to be used in the calculation of rolling resistance, and the risk or producing perpetual mobile when other expressions of rolling velocity are using instead.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

How does the Structure of Spherical Dark Matter Halos Affect the Types of Orbits in Disk Galaxies?

NASA Astrophysics Data System (ADS)

Zotos, Euaggelos E.

The main objective of this work is to determine the character of orbits of stars moving in the meridional (R,z) plane of an axially symmetric time-independent disk galaxy model with a central massive nucleus and an additional spherical dark matter halo component. In particular, we try to reveal the influence of the scale length of the dark matter halo on the different families of orbits of stars, by monitoring how the percentage of chaotic orbits, as well as the percentages of orbits of the main regular resonant families evolve when this parameter varies. The smaller alignment index (SALI) was computed by numerically integrating the equations of motion as well as the variational equations to extensive samples of orbits in order to distinguish safely bet ween ordered and chaotic motion. In addition, a method based on the concept of spectral dynamics that utilizes the Fourier transform of the time series of each coordinate is used to identify the various families of regular orbits and also to recognize the secondary resonances that bifurcate from them. Our numerical computations reveal that when the dark matter halo is highly concentrated, that is when the scale length has low values the vast majority of star orbits move in regular orbits, while on the oth er hand in less concentrated dark matter halos the percentage of chaos increases significantly. We also compared our results with early related work.

The Zulu Ditransitive Verb Phrase

ERIC Educational Resources Information Center

Adams, Nikki

2010-01-01

In this dissertation, several related aspects of arguments to ditransitive verbs are explored. The aim is to discover in what ways certain asymmetries in what is frequently referred to as a "symmetric object" language are interconnected while still allowing the other symmetric object behavior. These asymmetries are: (1) The requirement that the…

Sphericity determination using resonant ultrasound spectroscopy

DOEpatents

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

1994-01-01

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

Sphericity determination using resonant ultrasound spectroscopy

DOEpatents

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

1994-10-18

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

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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, ∞).

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.

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.

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.

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

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.

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

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.

The analysis of crystallographic symmetry types in finite groups

NASA Astrophysics Data System (ADS)

Sani, Atikah Mohd; Sarmin, Nor Haniza; Adam, Nooraishikin; Zamri, Siti Norziahidayu Amzee

2014-06-01

Undeniably, it is human nature to prefer objects which are considered beautiful. Most consider beautiful as perfection, hence they try to create objects which are perfectly balance in shape and patterns. This creates a whole different kind of art, the kind that requires an object to be symmetrical. This leads to the study of symmetrical objects and pattern. Even mathematicians and ethnomathematicians are very interested with the essence of symmetry. One of these studies were conducted on the Malay traditional triaxial weaving culture. The patterns derived from this technique are symmetrical and this allows for further research. In this paper, the 17 symmetry types in a plane, known as the wallpaper groups, are studied and discussed. The wallpaper groups will then be applied to the triaxial patterns of food cover in Malaysia.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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)

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.

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.

Symmetric Objects Become Special in Perception Because of Generic Computations in Neurons

PubMed Central

Pramod, R. T.

2017-01-01

Symmetry is a salient visual property: It is easy to detect and influences perceptual phenomena from segmentation to recognition. Yet researchers know little about its neural basis. Using recordings from single neurons in monkey IT cortex, we asked whether symmetry—being an emergent property—induces nonlinear interactions between object parts. Remarkably, we found no such deviation: Whole-object responses were always the sum of responses to the object’s parts, regardless of symmetry. The only defining characteristic of symmetric objects was that they were more distinctive compared with asymmetric objects. This was a consequence of neurons preferring the same part across locations within an object. Just as mixing diverse paints produces a homogeneous overall color, adding heterogeneous parts within an asymmetric object renders it indistinct. In contrast, adding identical parts within a symmetric object renders it distinct. This distinctiveness systematically predicted human symmetry judgments, and it explains many previous observations about symmetry perception. Thus, symmetry becomes special in perception despite being driven by generic computations at the level of single neurons. PMID:29219748

Role of pressure anisotropy on relativistic compact stars

NASA Astrophysics Data System (ADS)

Maurya, S. K.; Banerjee, Ayan; Hansraj, Sudan

2018-02-01

We investigate a compact spherically symmetric relativistic body with anisotropic particle pressure profiles. The distribution possesses characteristics relevant to modeling compact stars within the framework of general relativity. For this purpose, we consider a spatial metric potential of Korkina and Orlyanskii [Ukr. Phys. J. 36, 885 (1991)] type in order to solve the Einstein field equations. An additional prescription we make is that the pressure anisotropy parameter takes the functional form proposed by Lake [Phys. Rev. D 67, 104015 (2003), 10.1103/PhysRevD.67.104015]. Specifying these two geometric quantities allows for further analysis to be carried out in determining unknown constants and obtaining a limit of the mass-radius diagram, which adequately describes compact strange star candidates like Her X-1 and SMC X-1. Using the anisotropic Tolman-Oppenheimer-Volkoff equations, we explore the hydrostatic equilibrium and the stability of such compact objects. Then, we investigate other physical features of this model, such as the energy conditions, speeds of sound, and compactness of the star, in detail and show that our results satisfy all the required elementary conditions for a physically acceptable stellar model. The results obtained are useful in analyzing the stability of other anisotropic compact objects like white dwarfs, neutron stars, and gravastars.

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.

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.

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.

Design of almost symmetric orthogonal wavelet filter bank via direct optimization.

PubMed

Murugesan, Selvaraaju; Tay, David B H

2012-05-01

It is a well-known fact that (compact-support) dyadic wavelets [based on the two channel filter banks (FBs)] cannot be simultaneously orthogonal and symmetric. Although orthogonal wavelets have the energy preservation property, biorthogonal wavelets are preferred in image processing applications because of their symmetric property. In this paper, a novel method is presented for the design of almost symmetric orthogonal wavelet FB. Orthogonality is structurally imposed by using the unnormalized lattice structure, and this leads to an objective function, which is relatively simple to optimize. The designed filters have good frequency response, flat group delay, almost symmetric filter coefficients, and symmetric wavelet function.

Multiwavelength digital holography with wavelength-multiplexed holograms and arbitrary symmetric phase shifts.

PubMed

Tahara, Tatsuki; Otani, Reo; Omae, Kaito; Gotohda, Takuya; Arai, Yasuhiko; Takaki, Yasuhiro

2017-05-15

We propose multiwavelength in-line digital holography with wavelength-multiplexed phase-shifted holograms and arbitrary symmetric phase shifts. We use phase-shifting interferometry selectively extracting wavelength information to reconstruct multiwavelength object waves separately from wavelength-multiplexed monochromatic images. The proposed technique obtains systems of equations for real and imaginary parts of multiwavelength object waves from the holograms by introducing arbitrary symmetric phase shifts. Then, the technique derives each complex amplitude distribution of each object wave selectively and analytically by solving the two systems of equations. We formulate the algorithm in the case of an arbitrary number of wavelengths and confirm its validity numerically and experimentally in the cases where the number of wavelengths is two and three.

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.

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.

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

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.

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.

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).

Network Analysis of Rat Spatial Cognition: Behaviorally-Established Symmetry in a Physically Asymmetrical Environment

PubMed Central

Eilam, David; Portugali, Juval; Blumenfeld-Lieberthal, Efrat

2012-01-01

Background We set out to solve two inherent problems in the study of animal spatial cognition (i) What is a “place”?; and (ii) whether behaviors that are not revealed as differing by one methodology could be revealed as different when analyzed using a different approach. Methodology We applied network analysis to scrutinize spatial behavior of rats tested in either a symmetrical or asymmetrical layout of 4, 8, or 12 objects placed along the perimeter of a round arena. We considered locations as the units of the network (nodes), and passes between locations as the links within the network. Principal Findings While there were only minor activity differences between rats tested in the symmetrical or asymmetrical object layouts, network analysis revealed substantial differences. Viewing ‘location’ as a cluster of stopping coordinates, the key locations (large clusters of stopping coordinates) were at the objects in both layouts with 4 objects. However, in the asymmetrical layout with 4 objects, additional key locations were spaced by the rats between the objects, forming symmetry among the key locations. It was as if the rats had behaviorally imposed symmetry on the physically asymmetrical environment. Based on a previous finding that wayfinding is easier in symmetrical environments, we suggest that when the physical attributes of the environment were not symmetrical, the rats established a symmetric layout of key locations, thereby acquiring a more legible environment despite its complex physical structure. Conclusions and Significance The present study adds a behavioral definition for “location”, a term that so far has been mostly discussed according to its physical attributes or neurobiological correlates (e.g. - place and grid neurons). Moreover, network analysis enabled the assessment of the importance of a location, even when that location did not display any distinctive physical properties. PMID:22815808

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.

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

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

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.

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.

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.

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.

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.

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.

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.

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

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.

Does space-time torsion determine the minimum mass of gravitating particles?

NASA Astrophysics Data System (ADS)

Böhmer, Christian G.; Burikham, Piyabut; Harko, Tiberiu; Lake, Matthew J.

2018-03-01

We derive upper and lower limits for the mass-radius ratio of spin-fluid spheres in Einstein-Cartan theory, with matter satisfying a linear barotropic equation of state, and in the presence of a cosmological constant. Adopting a spherically symmetric interior geometry, we obtain the generalized continuity and Tolman-Oppenheimer-Volkoff equations for a Weyssenhoff spin fluid in hydrostatic equilibrium, expressed in terms of the effective mass, density and pressure, all of which contain additional contributions from the spin. The generalized Buchdahl inequality, which remains valid at any point in the interior, is obtained, and general theoretical limits for the maximum and minimum mass-radius ratios are derived. As an application of our results we obtain gravitational red shift bounds for compact spin-fluid objects, which may (in principle) be used for observational tests of Einstein-Cartan theory in an astrophysical context. We also briefly consider applications of the torsion-induced minimum mass to the spin-generalized strong gravity model for baryons/mesons, and show that the existence of quantum spin imposes a lower bound for spinning particles, which almost exactly reproduces the electron mass.

Does space-time torsion determine the minimum mass of gravitating particles?

PubMed

Böhmer, Christian G; Burikham, Piyabut; Harko, Tiberiu; Lake, Matthew J

2018-01-01

We derive upper and lower limits for the mass-radius ratio of spin-fluid spheres in Einstein-Cartan theory, with matter satisfying a linear barotropic equation of state, and in the presence of a cosmological constant. Adopting a spherically symmetric interior geometry, we obtain the generalized continuity and Tolman-Oppenheimer-Volkoff equations for a Weyssenhoff spin fluid in hydrostatic equilibrium, expressed in terms of the effective mass, density and pressure, all of which contain additional contributions from the spin. The generalized Buchdahl inequality, which remains valid at any point in the interior, is obtained, and general theoretical limits for the maximum and minimum mass-radius ratios are derived. As an application of our results we obtain gravitational red shift bounds for compact spin-fluid objects, which may (in principle) be used for observational tests of Einstein-Cartan theory in an astrophysical context. We also briefly consider applications of the torsion-induced minimum mass to the spin-generalized strong gravity model for baryons/mesons, and show that the existence of quantum spin imposes a lower bound for spinning particles, which almost exactly reproduces the electron mass.

Towards a second law for Lovelock theories

NASA Astrophysics Data System (ADS)

Bhattacharyya, Sayantani; Haehl, Felix M.; Kundu, Nilay; Loganayagam, R.; Rangamani, Mukund

2017-03-01

In classical general relativity described by Einstein-Hilbert gravity, black holes behave as thermodynamic objects. In particular, the laws of black hole mechanics can be interpreted as laws of thermodynamics. The first law of black hole mechanics extends to higher derivative theories via the Noether charge construction of Wald. One also expects the statement of the second law, which in Einstein-Hilbert theory owes to Hawking's area theorem, to extend to higher derivative theories. To argue for this however one needs a notion of entropy for dynamical black holes, which the Noether charge construction does not provide. We propose such an entropy function for the family of Lovelock theories, treating the higher derivative terms as perturbations to the Einstein-Hilbert theory. Working around a dynamical black hole solution, and making no assumptions about the amplitude of departure from equilibrium, we construct a candidate entropy functional valid to all orders in the low energy effective field theory. This entropy functional satisfies a second law, modulo a certain subtle boundary term, which deserves further investigation in non-spherically symmetric situations.

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).

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.

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

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.

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.

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.

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.

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.

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.

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.

The ALMA View of the OMC1 Explosion in Orion

NASA Astrophysics Data System (ADS)

Bally, John; Ginsburg, Adam; Arce, Hector; Eisner, Josh; Youngblood, Allison; Zapata, Luis; Zinnecker, Hans

2017-03-01

Most massive stars form in dense clusters where gravitational interactions with other stars may be common. The two nearest forming massive stars, the BN object and Source I, located behind the Orion Nebula, were ejected with velocities of ˜29 and ˜13 km s-1 about 500 years ago by such interactions. This event generated an explosion in the gas. New ALMA observations show in unprecedented detail, a roughly spherically symmetric distribution of over a hundred 12CO J = 2-1 streamers with velocities extending from V LSR = -150 to +145 km s-1. The streamer radial velocities increase (or decrease) linearly with projected distance from the explosion center, forming a “Hubble Flow” confined to within 50″ of the explosion center. They point toward the high proper-motion, shock-excited H2 and [Fe II] “fingertips” and lower-velocity CO in the H2 wakes comprising Orion's “fingers.” In some directions, the H2 “fingers” extend more than a factor of two farther from the ejection center than the CO streamers. Such deviations from spherical symmetry may be caused by ejecta running into dense gas or the dynamics of the N-body interaction that ejected the stars and produced the explosion. This ˜1048 erg event may have been powered by the release of gravitational potential energy associated with the formation of a compact binary or a protostellar merger. Orion may be the prototype for a new class of stellar explosiozn responsible for luminous infrared transients in nearby galaxies.

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.

X ray microscope assembly and alignment support and advanced x ray microscope design and analysis

NASA Technical Reports Server (NTRS)

Shealy, David L.

1991-01-01

Considerable efforts have been devoted recently to the design, analysis, fabrication, and testing of spherical Schwarzschild microscopes for soft x ray application in microscopy and projection lithography. The spherical Schwarzschild microscope consists of two concentric spherical mirrors configured such that the third order spherical aberration and coma are zero. Since multilayers are used on the mirror substrates for x ray applications, it is desirable to have only two reflecting surfaces in a microscope. In order to reduce microscope aberrations and increase the field of view, generalized mirror surface profiles have been considered in this investigation. Based on incoherent and sine wave modulation transfer function (MTF) calculations, the object plane resolution of a microscope has been analyzed as a function of the object height and numerical aperture (NA) of the primary for several spherical Schwarzschild, conic, and aspherical head reflecting two mirror microscope configurations.

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.

Unsupervised object segmentation with a hybrid graph model (HGM).

PubMed

Liu, Guangcan; Lin, Zhouchen; Yu, Yong; Tang, Xiaoou

2010-05-01

In this work, we address the problem of performing class-specific unsupervised object segmentation, i.e., automatic segmentation without annotated training images. Object segmentation can be regarded as a special data clustering problem where both class-specific information and local texture/color similarities have to be considered. To this end, we propose a hybrid graph model (HGM) that can make effective use of both symmetric and asymmetric relationship among samples. The vertices of a hybrid graph represent the samples and are connected by directed edges and/or undirected ones, which represent the asymmetric and/or symmetric relationship between them, respectively. When applied to object segmentation, vertices are superpixels, the asymmetric relationship is the conditional dependence of occurrence, and the symmetric relationship is the color/texture similarity. By combining the Markov chain formed by the directed subgraph and the minimal cut of the undirected subgraph, the object boundaries can be determined for each image. Using the HGM, we can conveniently achieve simultaneous segmentation and recognition by integrating both top-down and bottom-up information into a unified process. Experiments on 42 object classes (9,415 images in total) show promising results.

Accretion onto a charged Kiselev black hole

NASA Astrophysics Data System (ADS)

Abbas, G.; Ditta, A.

2018-04-01

Accretion of matter onto a compact is one of the interesting astrophysical processes. Here, we study the accretion of matter onto a charged Kiselev black hole. The problem of static and spherically symmetric accretion of a polytropic fluid is explored for the analytic solution of equations of motion. We have investigated the necessary conditions for existence of the critical flow points and the mass accretion rate. Finally, we discuss the polytropic gas accretion in detail. It has been found that in the accretion process the quintessence and charge parameters play a dominant role.

Extended Reissner-Nordström solutions sourced by dynamical torsion

NASA Astrophysics Data System (ADS)

Cembranos, Jose A. R.; Valcarcel, Jorge Gigante

2018-04-01

We find a new exact vacuum solution in the framework of the Poincaré Gauge field theory with massive torsion. In this model, torsion operates as an independent field and introduces corrections to the vacuum structure present in General Relativity. The new static and spherically symmetric configuration shows a Reissner-Nordström-like geometry characterized by a spin charge. It extends the known massless torsion solution to the massive case. The corresponding Reissner-Nordström-de Sitter solution is also compatible with a cosmological constant and additional U (1) gauge fields.

Fermions tunnelling from the charged dilatonic black holes

NASA Astrophysics Data System (ADS)

Chen, De-You; Jiang, Qing-Quan; Zu, Xiao-Tao

2008-10-01

Kerner and Mann's recent work shows that for an uncharged and non-rotating black hole its Hawking temperature can be correctly derived by fermions tunnelling from its horizons. In this paper, our main work is to improve the analysis to deal with charged fermion tunnelling from the general dilatonic black holes, specifically including the charged, spherically symmetric dilatonic black hole, the rotating Einstein Maxwell dilaton axion (EMDA) black hole and the rotating Kaluza Klein (KK) black hole. As a result, the correct Hawking temperatures are well recovered by charged fermions tunnelling from these black holes.

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

Cembranos, Jose A.R.; Valcarcel, Jorge Gigante, E-mail: cembra@fis.ucm.es, E-mail: jorgegigante@ucm.es

We derive a new exact static and spherically symmetric vacuum solution in the framework of the Poincaré gauge field theory with dynamical massless torsion. This theory is built in such a form that allows to recover General Relativity when the first Bianchi identity of the model is fulfilled by the total curvature. The solution shows a Reissner-Nordström type geometry with a Coulomb-like curvature provided by the torsion field. It is also shown the existence of a generalized Reissner-Nordström-de Sitter solution when additional electromagnetic fields and/or a cosmological constant are coupled to gravity.

An integral condition for core-collapse supernova explosions

DOE PAGES

Murphy, Jeremiah W.; Dolence, Joshua C.

2017-01-10

Here, we derive an integral condition for core-collapse supernova (CCSN) explosions and use it to construct a new diagnostic of explodability. The fundamental challenge in CCSN theory is to explain how a stalled accretion shock revives to explode a star. In this manuscript, we assume that the shock revival is initiated by the delayed-neutrino mechanism and derive an integral condition for spherically symmetric shock expansion, v s > 0. One of the most useful one-dimensional explosion conditions is the neutrino luminosity and mass-accretion rate (more » $${L}_{\

Effect of the Diurnal Atmospheric Bulge on Satellite Accelerations

NASA Technical Reports Server (NTRS)

Wyatt, Stanley P.

1961-01-01

Formulas are developed to express the secular acceleration of a satellite on passing through an atmosphere which bulges in the sunward direction and in which the scale height increases with height, these two properties of the high atmosphere having previously been established from satellite observations. Comparison of the new formulas with those for a spherically symmetric atmosphere of constant scale height indicates that deduced atmospheric densities may be systematically incorrect by up to 50 or 60 percent at heights of 500 to 600 km when the earlier and simpler equations are used.

Anisotropic extension of Finch and Skea stellar model

NASA Astrophysics Data System (ADS)

Sharma, Ranjan; Das, Shyam; Thirukkanesh, S.

2017-12-01

In this paper, the spacetime geometry of Finch and Skea [Class. Quantum Gravity 6:467, 1989] has been utilized to obtain closed-form solutions for a spherically symmetric anisotropic matter distribution. By examining its physical admissibility, we have shown that the class of solutions can be used as viable models for observed pulsars. In particular, a specific class of solutions can be used as an `anisotropic switch' to examine the impact of anisotropy on the gross physical properties of a stellar configuration. Accordingly, the mass-radius relationship has been analyzed.

Solutions of Boltzmann`s Equation for Mono-energetic Neutrons in an Infinite Homogeneous Medium

DOE R&D Accomplishments Database

Wigner, E. P.

1943-11-30

Boltzman's equation is solved for the case of monoenergetic neutrons created by a plane or point source in an infinite medium which has spherically symmetric scattering. The customary solution of the diffusion equation appears to be multiplied by a constant factor which is smaller than 1. In addition to this term the total neutron density contains another term which is important in the neighborhood of the source. It varies as 1/r{sup 2} in the neighborhood of a point source. (auth)

Noncommutative wormhole solutions in F(T, T𝒢) gravity

NASA Astrophysics Data System (ADS)

Sharif, M.; Nazir, Kanwal

2017-04-01

This paper is devoted to the study of static spherically symmetric wormhole solutions along with noncommutative geometry in the background of F(T, T𝒢) gravity. We assume a nonzero redshift function as well as two well-known models of this gravity and discuss the behavior of null/weak energy conditions graphically. We conclude that there does not exist any physically acceptable wormhole solution for the first model, but there is a chance to develop physically acceptable wormhole solution in a particular region for the second model.

Upper bounds on quantum uncertainty products and complexity measures

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

Guerrero, Angel; Sanchez-Moreno, Pablo; Dehesa, Jesus S.

The position-momentum Shannon and Renyi uncertainty products of general quantum systems are shown to be bounded not only from below (through the known uncertainty relations), but also from above in terms of the Heisenberg-Kennard product . Moreover, the Cramer-Rao, Fisher-Shannon, and Lopez-Ruiz, Mancini, and Calbet shape measures of complexity (whose lower bounds have been recently found) are also bounded from above. The improvement of these bounds for systems subject to spherically symmetric potentials is also explicitly given. Finally, applications to hydrogenic and oscillator-like systems are done.

Evaluating nuclear physics inputs in core-collapse supernova models

NASA Astrophysics Data System (ADS)

Lentz, E.; Hix, W. R.; Baird, M. L.; Messer, O. E. B.; Mezzacappa, A.

Core-collapse supernova models depend on the details of the nuclear and weak interaction physics inputs just as they depend on the details of the macroscopic physics (transport, hydrodynamics, etc.), numerical methods, and progenitors. We present preliminary results from our ongoing comparison studies of nuclear and weak interaction physics inputs to core collapse supernova models using the spherically-symmetric, general relativistic, neutrino radiation hydrodynamics code Agile-Boltztran. We focus on comparisons of the effects of the nuclear EoS and the effects of improving the opacities, particularly neutrino--nucleon interactions.

Particle-like solutions of the Einstein-Dirac-Maxwell equations

NASA Astrophysics Data System (ADS)

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

1999-08-01

We consider the coupled Einstein-Dirac-Maxwell equations for a static, spherically symmetric system of two fermions in a singlet spinor state. Soliton-like solutions are constructed numerically. The stability and the properties of the ground state solutions are discussed for different values of the electromagnetic coupling constant. We find solutions even when the electromagnetic coupling is so strong that the total interaction is repulsive in the Newtonian limit. Our solutions are regular and well-behaved; this shows that the combined electromagnetic and gravitational self-interaction of the Dirac particles is finite.

Universal instability of hairy black holes in Lovelock-Galileon theories in D dimensions

NASA Astrophysics Data System (ADS)

Takahashi, Kazufumi; Suyama, Teruaki; Kobayashi, Tsutomu

2016-03-01

We analyze spherically symmetric black hole solutions with time-dependent scalar hair in a class of Lovelock-Galileon theories, which are the scalar-tensor theories with second-order field equations in arbitrary dimensions. We first show that known black hole solutions in five dimensions are always plagued by the ghost/gradient instability in the vicinity of the horizon. We then generalize such black hole solutions to higher dimensions and show that the same instability found in five dimensions appears universally in any number of dimensions.

Escape of gravitational radiation from the field of massive bodies

NASA Technical Reports Server (NTRS)

Price, Richard H.; Pullin, Jorge; Kundu, Prasun K.

1993-01-01

We consider a compact source of gravitational waves of frequency omega in or near a massive spherically symmetric distribution of matter or a black hole. Recent calculations have led to apparently contradictory results for the influence of the massive body on the propagation of the waves. We show here that the results are in fact consistent and in agreement with the 'standard' viewpoint in which the high-frequency compact source produces the radiation as if in a flat background, and the background curvature affects the propagation of these waves.

On numerical solution of the Schrödinger equation: the shooting method revisited

NASA Astrophysics Data System (ADS)

Indjin, D.; Todorović, G.; Milanović, V.; Ikonić, Z.

1995-09-01

An alternative formulation of the "shooting" method for a numerical solution of the Schrödinger equation is described for cases of general asymmetric one-dimensional potential (planar geometry), and spherically symmetric potential. The method relies on matching the asymptotic wavefunctions and the potential core region wavefunctions, in course of finding bound states energies. It is demonstrated in the examples of Morse and Kratzer potentials, where a high accuracy of the calculated eigenvalues is found, together with a considerable saving of the computation time.

A fixed energy fixed angle inverse scattering in interior transmission problem

NASA Astrophysics Data System (ADS)

Chen, Lung-Hui

2017-06-01

We study the inverse acoustic scattering problem in mathematical physics. The problem is to recover the index of refraction in an inhomogeneous medium by measuring the scattered wave fields in the far field. We transform the problem to the interior transmission problem in the study of the Helmholtz equation. We find an inverse uniqueness on the scatterer with a knowledge of a fixed interior transmission eigenvalue. By examining the solution in a series of spherical harmonics in the far field, we can determine uniquely the perturbation source for the radially symmetric perturbations.

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.

Thermal invisibility based on scattering cancellation and mantle cloaking

PubMed Central

Farhat, M.; Chen, P.-Y.; Bagci, H.; Amra, C.; Guenneau, S.; Alù, A.

2015-01-01

We theoretically and numerically analyze thermal invisibility based on the concept of scattering cancellation and mantle cloaking. We show that a small object can be made completely invisible to heat diffusion waves, by tailoring the heat conductivity of the spherical shell enclosing the object. This means that the thermal scattering from the object is suppressed, and the heat flow outside the object and the cloak made of these spherical shells behaves as if the object is not present. Thermal invisibility may open new vistas in hiding hot spots in infrared thermography, military furtivity, and electronics heating reduction. PMID:25928664

Symmetrical and overloaded effect of diffusion in information filtering

NASA Astrophysics Data System (ADS)

Zhu, Xuzhen; Tian, Hui; Chen, Guilin; Cai, Shimin

2017-10-01

In physical dynamics, mass diffusion theory has been applied to design effective information filtering models on bipartite network. In previous works, researchers unilaterally believe objects' similarities are determined by single directional mass diffusion from the collected object to the uncollected, meanwhile, inadvertently ignore adverse influence of diffusion overload. It in some extent veils the essence of diffusion in physical dynamics and hurts the recommendation accuracy and diversity. After delicate investigation, we argue that symmetrical diffusion effectively discloses essence of mass diffusion, and high diffusion overload should be published. Accordingly, in this paper, we propose an symmetrical and overload penalized diffusion based model (SOPD), which shows excellent performances in extensive experiments on benchmark datasets Movielens and Netflix.

Dynamic response of sand particles impacted by a rigid spherical object

NASA Astrophysics Data System (ADS)

Youplao, P.; Takita, A.; Nasbey, H.; Yupapin, P. P.; Fujii, Y.

2018-06-01

A method for measuring the dynamic impact responses that acting on a spherical object while dropping and colliding with dried sand, such as the velocity, displacement, acceleration, and resultant force, is presented and discussed. In the experiment, a Michelson-type laser interferometer is employed to obtain the velocity of the spherical stainless steel object. Then the obtained time velocity profile is used to calculate the acceleration, the displacement, and the inertial force acting on the observed sand particles. Furthermore, a high-speed camera is employed to observe the behavior of the sand during the collision. From the experimental results with the sampling interval for frequencies calculation of 1 ms, the combined standard uncertainty in the instantaneous value of the impact force acts on the observed object is obtained and approximated to 0.49 N, which is related to a corresponding 4.07% of the maximum value at 12.05 N of the impact force.

Physically Based Modeling and Simulation with Dynamic Spherical Volumetric Simplex Splines

PubMed Central

Tan, Yunhao; Hua, Jing; Qin, Hong

2009-01-01

In this paper, we present a novel computational modeling and simulation framework based on dynamic spherical volumetric simplex splines. The framework can handle the modeling and simulation of genus-zero objects with real physical properties. In this framework, we first develop an accurate and efficient algorithm to reconstruct the high-fidelity digital model of a real-world object with spherical volumetric simplex splines which can represent with accuracy geometric, material, and other properties of the object simultaneously. With the tight coupling of Lagrangian mechanics, the dynamic volumetric simplex splines representing the object can accurately simulate its physical behavior because it can unify the geometric and material properties in the simulation. The visualization can be directly computed from the object’s geometric or physical representation based on the dynamic spherical volumetric simplex splines during simulation without interpolation or resampling. We have applied the framework for biomechanic simulation of brain deformations, such as brain shifting during the surgery and brain injury under blunt impact. We have compared our simulation results with the ground truth obtained through intra-operative magnetic resonance imaging and the real biomechanic experiments. The evaluations demonstrate the excellent performance of our new technique. PMID:20161636

Stability and Instability of the Sub-extremal Reissner-Nordström Black Hole Interior for the Einstein-Maxwell-Klein-Gordon Equations in Spherical Symmetry

NASA Astrophysics Data System (ADS)

Van de Moortel, Maxime

2018-05-01

We show non-linear stability and instability results in spherical symmetry for the interior of a charged black hole—approaching a sub-extremal Reissner-Nordström background fast enough—in presence of a massive and charged scalar field, motivated by the strong cosmic censorship conjecture in that setting: 1. Stability We prove that spherically symmetric characteristic initial data to the Einstein-Maxwell-Klein-Gordon equations approaching a Reissner-Nordström background with a sufficiently decaying polynomial decay rate on the event horizon gives rise to a space-time possessing a Cauchy horizon in a neighbourhood of time-like infinity. Moreover, if the decay is even stronger, we prove that the space-time metric admits a continuous extension to the Cauchy horizon. This generalizes the celebrated stability result of Dafermos for Einstein-Maxwell-real-scalar-field in spherical symmetry. 2. Instability We prove that for the class of space-times considered in the stability part, whose scalar field in addition obeys a polynomial averaged- L 2 (consistent) lower bound on the event horizon, the scalar field obeys an integrated lower bound transversally to the Cauchy horizon. As a consequence we prove that the non-degenerate energy is infinite on any null surface crossing the Cauchy horizon and the curvature of a geodesic vector field blows up at the Cauchy horizon near time-like infinity. This generalizes an instability result due to Luk and Oh for Einstein-Maxwell-real-scalar-field in spherical symmetry. This instability of the black hole interior can also be viewed as a step towards the resolution of the C 2 strong cosmic censorship conjecture for one-ended asymptotically flat initial data.

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.

Entanglement of heavy quark impurities and generalized gravitational entropy

NASA Astrophysics Data System (ADS)

Kumar, S. Prem; Silvani, Dorian

2018-01-01

We calculate the contribution from non-conformal heavy quark sources to the entanglement entropy (EE) of a spherical region in N=4 SUSY Yang-Mills theory. We apply the generalized gravitational entropy method to non-conformal probe D-brane embeddings in AdS5×S5, dual to pointlike impurities exhibiting flows between quarks in large-rank tensor representations and the fundamental representation. For the D5-brane embedding which describes the screening of fundamental quarks in the UV to the antisymmetric tensor representation in the IR, the EE excess decreases non-monotonically towards its IR asymptotic value, tracking the qualitative behaviour of the one-point function of static fields sourced by the impurity. We also examine two classes of D3-brane embeddings, one which connects a symmetric representation source in the UV to fundamental quarks in the IR, and a second category which yields the symmetric representation source on the Coulomb branch. The EE excess for the former increases from the UV to the IR, whilst decreasing and becoming negative for the latter. In all cases, the probe free energy on hyperbolic space with β = 2 π increases monotonically towards the IR, supporting its interpretation as a relative entropy. We identify universal corrections, depending logarithmically on the VEV, for the symmetric representation on the Coulomb branch.

Instantons for vacuum decay at finite temperature in the thin wall limit

NASA Astrophysics Data System (ADS)

Garriga, Jaume

1994-05-01

In N+1 dimensions, false vacuum decay at zero temperature is dominated by the O(N+1)-symmetric instanton, a sphere of radius R0, whereas at temperatures T>>R-10, the decay is dominated by a ``cylindrical'' (static) O(N)-symmetric instanton. We study the transition between these two regimes in the thin wall approximation. Taking an O(N)-symmetric ansatz for the instantons, we show that for N=2 and N=3 new periodic solutions exist in a finite temperature range in the neighborhood of T~R-10. However, these solutions have a higher action than the spherical or the cylindrical one. This suggests that there is a sudden change (a first order transition) in the derivative of the nucleation rate at a certain temperature T*, when the static instanton starts dominating. For N=1, on the other hand, the new solutions are dominant and they smoothly interpolate between the zero temperature instanton and the high temperature one, so the transition is of second order. The determinantal prefactors corresponding to the ``cylindrical'' instantons are discussed, and it is pointed out that the entropic contributions from massless excitations corresponding to deformations of the domain wall give rise to an exponential enhancement of the nucleation rate for T>>R-10.

Decoherence and Determinism in a One-Dimensional Cloud-Chamber Model

NASA Astrophysics Data System (ADS)

Sparenberg, Jean-Marc; Gaspard, David

2018-03-01

The hypothesis (Sparenberg et al. in EPJ Web Conf 58:01016, [1]. https://doi.org/10.1051/epjconf/20135801016) that the particular linear tracks appearing in the measurement of a spherically-emitting radioactive source in a cloud chamber are determined by the (random) positions of atoms or molecules inside the chamber is further explored in the framework of a recently established one-dimensional model (Carlone et al. Comm Comput Phys 18:247, [2]. https://doi.org/10.4208/cicp.270814.311214a). In this model, meshes of localized spins 1/2 play the role of the cloud-chamber atoms and the spherical wave is replaced by a linear superposition of two wave packets moving from the origin to the left and to the right, evolving deterministically according to the Schrödinger equation. We first revisit these results using a time-dependent approach, where the wave packets impinge on a symmetric two-sided detector. We discuss the evolution of the wave function in the configuration space and stress the interest of a non-symmetric detector in a quantum-measurement perspective. Next we use a time-independent approach to study the scattering of a plane wave on a single-sided detector. Preliminary results are obtained, analytically for the single-spin case and numerically for up to 8 spins. They show that the spin-excitation probabilities are sometimes very sensitive to the parameters of the model, which corroborates the idea that the measurement result could be determined by the atom positions. The possible origin of decoherence and entropy increase in future models is finally discussed.

Dynamics of a spherically symmetric inhomogeneous coupled dark energy model with coupling term proportional to non relatvistic matter

NASA Astrophysics Data System (ADS)

Izquierdo, Germán; Blanquet-Jaramillo, Roberto C.; Sussman, Roberto A.

2018-01-01

The quasi-local scalar variables approach is applied to a spherically symmetric inhomogeneous Lemaître-Tolman-Bondi metric containing a mixture of non-relativistic cold dark matter and coupled dark energy with constant equation of state. The quasi-local coupling term considered is proportional to the quasi-local cold dark matter energy density and a quasi-local Hubble factor-like scalar via a coupling constant α . The autonomous numerical system obtained from the evolution equations is classified for different choices of the free parameters: the adiabatic constant of the dark energy w and α . The presence of a past attractor in a non-physical region of the energy densities phase-space of the system makes the coupling term non physical when the energy flows from the matter to the dark energy in order to avoid negative values of the dark energy density in the past. On the other hand, if the energy flux goes from dark energy to dark matter, the past attractor lies in a physical region. The system is also numerically solved for some interesting initial profiles leading to different configurations: an ever expanding mixture, a scenario where the dark energy is completely consumed by the non-relativistic matter by means of the coupling term, a scenario where the dark energy disappears in the inner layers while the outer layers expand as a mixture of both sources, and, finally, a structure formation toy model scenario, where the inner shells containing the mixture collapse while the outer shells expand.

Quantum dot properties in the multiband envelope-function approximation using boundary conditions based upon first-principles quantum calculations

NASA Astrophysics Data System (ADS)

Flory, Curt A.; Musgrave, Charles B.; Zhang, Zhiyong

2008-05-01

A number of physical processes involving quantum dots depend critically upon the “evanescent” electron eigenstate wave function that extends outside of the material surface into the surrounding region. These processes include electron tunneling through quantum dots, as well as interactions between multiple quantum dot structures. In order to unambiguously determine these evanescent fields, appropriate boundary conditions have been developed to connect the electronic solutions interior to the semiconductor quantum dot to exterior vacuum solutions. In standard envelope function theory, the interior wave function consists of products of band edge and envelope functions, and both must be considered when matching to the external solution. While the envelope functions satisfy tractable equations, the band edge functions are generally not known. In this work, symmetry arguments in the spherically symmetric approximation are used in conjunction with the known qualitative behavior of bonding and antibonding orbitals to catalog the behavior of the band edge functions at the unit cell boundary. This physical approximation allows consolidation of the influence of the band edge functions to two simple surface parameters that are incorporated into the boundary conditions and are straightforwardly computed by using numerical first-principles quantum techniques. These new boundary conditions are employed to analyze an isolated spherically symmetric semiconductor quantum dot in vacuum within the analytical model of Sercel and Vahala [Phys. Rev. Lett. 65, 239 (1990); Phys. Rev. B 42, 3690 (1990)]. Results are obtained for quantum dots made of GaAs and InP, which are compared with ab initio calculations that have appeared in the literature.

Assessment of exposure to electromagnetic fields from wireless computer networks (wi-fi) in schools; results of laboratory measurements.

PubMed

Peyman, A; Khalid, M; Calderon, C; Addison, D; Mee, T; Maslanyj, M; Mann, S

2011-06-01

Laboratory measurements have been carried out with examples of Wi-Fi devices used in UK schools to evaluate the radiofrequency power densities around them and the total emitted powers. Unlike previous studies, a 20 MHz bandwidth signal analyzer was used, enabling the whole Wi-Fi signal to be captured and monitored. The radiation patterns of the laptops had certain similarities, including a minimum toward the torso of the user and two maxima symmetrically opposed across a vertical plane bisecting the screen and keyboard. The maxima would have resulted from separate antennas mounted behind the top left and right corners of the laptop screens. The patterns for access points were more symmetrical with generally higher power densities at a given distance. The spherically-integrated radiated power (IRP) ranged from 5 to 17 mW for 15 laptops in the 2.45 GHz band and from 1 to 16 mW for eight laptops in the 5 GHz band. For practical reasons and because access points are generally wall-mounted with beams directed into the rooms, their powers were integrated over a hemisphere. These ranged from 3 to 28 mW for 12 access points at 2.4 GHz and from 3 to 29 mW for six access points at 5 GHz. In addition to the spherical measurements of IRP, power densities were measured at distances of 0.5 m and greater from the devices, and consistent with the low radiated powers, these were all much lower than the ICNIRP reference level.

NOTE: An innovative phantom for quantitative and qualitative investigation of advanced x-ray imaging technologies

NASA Astrophysics Data System (ADS)

Chiarot, C. B.; Siewerdsen, J. H.; Haycocks, T.; Moseley, D. J.; Jaffray, D. A.

2005-11-01

Development, characterization, and quality assurance of advanced x-ray imaging technologies require phantoms that are quantitative and well suited to such modalities. This note reports on the design, construction, and use of an innovative phantom developed for advanced imaging technologies (e.g., multi-detector CT and the numerous applications of flat-panel detectors in dual-energy imaging, tomosynthesis, and cone-beam CT) in diagnostic and image-guided procedures. The design addresses shortcomings of existing phantoms by incorporating criteria satisfied by no other single phantom: (1) inserts are fully 3D—spherically symmetric rather than cylindrical; (2) modules are quantitative, presenting objects of known size and contrast for quality assurance and image quality investigation; (3) features are incorporated in ideal and semi-realistic (anthropomorphic) contexts; and (4) the phantom allows devices to be inserted and manipulated in an accessible module (right lung). The phantom consists of five primary modules: (1) head, featuring contrast-detail spheres approximate to brain lesions; (2) left lung, featuring contrast-detail spheres approximate to lung modules; (3) right lung, an accessible hull in which devices may be placed and manipulated; (4) liver, featuring conrast-detail spheres approximate to metastases; and (5) abdomen/pelvis, featuring simulated kidneys, colon, rectum, bladder, and prostate. The phantom represents a two-fold evolution in design philosophy—from 2D (cylindrically symmetric) to fully 3D, and from exclusively qualitative or quantitative to a design accommodating quantitative study within an anatomical context. It has proven a valuable tool in investigations throughout our institution, including low-dose CT, dual-energy radiography, and cone-beam CT for image-guided radiation therapy and surgery.

Towards Relaxing the Spherical Solar Radiation Pressure Model for Accurate Orbit Predictions

NASA Astrophysics Data System (ADS)

Lachut, M.; Bennett, J.

2016-09-01

The well-known cannonball model has been used ubiquitously to capture the effects of atmospheric drag and solar radiation pressure on satellites and/or space debris for decades. While it lends itself naturally to spherical objects, its validity in the case of non-spherical objects has been debated heavily for years throughout the space situational awareness community. One of the leading motivations to improve orbit predictions by relaxing the spherical assumption, is the ongoing demand for more robust and reliable conjunction assessments. In this study, we explore the orbit propagation of a flat plate in a near-GEO orbit under the influence of solar radiation pressure, using a Lambertian BRDF model. Consequently, this approach will account for the spin rate and orientation of the object, which is typically determined in practice using a light curve analysis. Here, simulations will be performed which systematically reduces the spin rate to demonstrate the point at which the spherical model no longer describes the orbital elements of the spinning plate. Further understanding of this threshold would provide insight into when a higher fidelity model should be used, thus resulting in improved orbit propagations. Therefore, the work presented here is of particular interest to organizations and researchers that maintain their own catalog, and/or perform conjunction analyses.

Meissner effect for axially symmetric charged black holes

NASA Astrophysics Data System (ADS)

Gürlebeck, Norman; Scholtz, Martin

2018-04-01

In our previous work [N. Gürlebeck and M. Scholtz, Phys. Rev. D 95, 064010 (2017), 10.1103/PhysRevD.95.064010], we have shown that electric and magnetic fields are expelled from the horizons of extremal, stationary and axially symmetric uncharged black holes; this is called the Meissner effect for black holes. Here, we generalize this result in several directions. First, we allow that the black hole carries charge, which requires a generalization of the definition of the Meissner effect. Next, we introduce the notion of almost isolated horizons, which is weaker than the usual notion of isolated horizons, since the geometry of the former is not necessarily completely time independent. Moreover, we allow the horizon to be pierced by strings, thereby violating the usual assumption on the spherical topology made in the definition of the weakly isolated horizon. Finally, we spell out in detail all assumptions entering the proof and show that the Meissner effect is an inherent property of black holes even in full nonlinear theory.

Conformally symmetric traversable wormholes

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

Boehmer, Christian G.; Harko, Tiberiu; Lobo, Francisco S. N.

2007-10-15

Exact solutions of traversable wormholes are found under the assumption of spherical symmetry and the existence of a nonstatic conformal symmetry, which presents a more systematic approach in searching for exact wormhole solutions. In this work, a wide variety of solutions are deduced by considering choices for the form function, a specific linear equation of state relating the energy density and the pressure anisotropy, and various phantom wormhole geometries are explored. A large class of solutions impose that the spatial distribution of the exotic matter is restricted to the throat neighborhood, with a cutoff of the stress-energy tensor at amore » finite junction interface, although asymptotically flat exact solutions are also found. Using the 'volume integral quantifier', it is found that the conformally symmetric phantom wormhole geometries may, in principle, be constructed by infinitesimally small amounts of averaged null energy condition violating matter. Considering the tidal acceleration traversability conditions for the phantom wormhole geometry, specific wormhole dimensions and the traversal velocity are also deduced.« less

Rings of non-spherical, axisymmetric bodies

NASA Astrophysics Data System (ADS)

Gupta, Akash; Nadkarni-Ghosh, Sharvari; Sharma, Ishan

2018-01-01

We investigate the dynamical behavior of rings around bodies whose shapes depart considerably from that of a sphere. To this end, we have developed a new self-gravitating discrete element N-body code, and employed a local simulation method to simulate a patch of the ring. The central body is modeled as a symmetric (oblate or prolate) ellipsoid, or defined through the characteristic frequencies (circular, vertical, epicyclic) that represent its gravitational field. Through our simulations we explore how a ring's behavior - characterized by dynamical properties like impact frequency, granular temperature, number density, vertical thickness and radial width - varies with the changing gravitational potential of the central body. We also contrast properties of rings about large central bodies (e.g. Saturn) with those of smaller ones (e.g. Chariklo). Finally, we investigate how the characteristic frequencies of a central body, restricted to being a solid of revolution with an equatorial plane of symmetry, affect the ring dynamics. The latter process may be employed to qualitatively understand the dynamics of rings about any symmetric solid of revolution.

Capsule Shimming Developments for National Ignition Facility (NIF) Hohlraum Asymmetry Experiments

DOE PAGES

Rice, Neal G.; Vu, M.; Kong, C.; ...

2017-12-20

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

On the existence of topological dyons and dyonic black holes in anti-de Sitter Einstein-Yang-Mills theories with compact semisimple gauge groups

NASA Astrophysics Data System (ADS)

Baxter, J. Erik

2018-05-01

Here we study the global existence of "hairy" dyonic black hole and dyon solutions to four-dimensional, anti-de Sitter Einstein-Yang-Mills theories for a general simply connected and semisimple gauge group G, for the so-called topologically symmetric systems, concentrating here on the regular case. We generalise here cases in the literature which considered purely magnetic spherically symmetric solutions for a general gauge group and topological dyonic solutions for s u (N ) . We are able to establish the global existence of non-trivial solutions to all such systems, both near existing embedded solutions and as |Λ| → ∞. In particular, we can identify non-trivial solutions where the gauge field functions have no zeroes, which in the s u (N ) case proved important to stability. We believe that these are the most general analytically proven solutions in 4D anti-de Sitter Einstein-Yang-Mills systems to date.

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.

Charging of nonspherical macroparticles in a plasma

NASA Astrophysics Data System (ADS)

Holgate, J. T.; Coppins, M.

2016-03-01

The current theories of macroparticle charging in a plasma are limited to spheres, and are unsuitable for the multitude of nonspherical objects existing in astrophysical, atmospheric, laboratory, and fusion plasmas. This paper extends the most widely used spherical charging theory, orbit motion limited theory, to spheroids and, as such, provides a comprehensive study of the charging of nonspherical objects in a plasma. The spherical charging theory is shown to be a reasonable approximation for a considerable range of spheroids. However, the electric potential of highly elongated spheroids can be almost twice the spherical value. Furthermore, the total charge on the spheroids increases by a significantly larger factor than their potential.

The ALMA View of the OMC1 Explosion in Orion

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

Bally, John; Youngblood, Allison; Ginsburg, Adam

Most massive stars form in dense clusters where gravitational interactions with other stars may be common. The two nearest forming massive stars, the BN object and Source I, located behind the Orion Nebula, were ejected with velocities of ∼29 and ∼13 km s{sup −1} about 500 years ago by such interactions. This event generated an explosion in the gas. New ALMA observations show in unprecedented detail, a roughly spherically symmetric distribution of over a hundred {sup 12}CO J = 2−1 streamers with velocities extending from V {sub LSR} = −150 to +145 km s{sup −1}. The streamer radial velocities increasemore » (or decrease) linearly with projected distance from the explosion center, forming a “Hubble Flow” confined to within 50″ of the explosion center. They point toward the high proper-motion, shock-excited H{sub 2} and [Fe ii] “fingertips” and lower-velocity CO in the H{sub 2} wakes comprising Orion's “fingers.” In some directions, the H{sub 2} “fingers” extend more than a factor of two farther from the ejection center than the CO streamers. Such deviations from spherical symmetry may be caused by ejecta running into dense gas or the dynamics of the N -body interaction that ejected the stars and produced the explosion. This ∼10{sup 48} erg event may have been powered by the release of gravitational potential energy associated with the formation of a compact binary or a protostellar merger. Orion may be the prototype for a new class of stellar explosiozn responsible for luminous infrared transients in nearby galaxies.« less

The nature of spherical collapse and a study of black hole dynamics

NASA Astrophysics Data System (ADS)

Nampalliwar, Sourabh

Gravitational waves and singularities are two of the most significant predictions of General Relativity. Binary systems are the most promising sources of gravitational waves that are expected to be detected with the current ground-based and upcoming space-based gravitational wave detectors. During the merger of binary compact objects, an important stage is the plunge. A small part of the gravitational waveform, it marks the end of early inspiral and determines the quasinormal ringing (QNR) of the final product of the merger. It is also the part of the waveform where most of the gravitational energy is released. But, unlike early inspiral and late ringdown, it is poorly understood in terms of phenomenology. This thesis introduces a novel approach combining the Fourier domain Green's function in the particle perturbation approximation and a simple model to understand this crucial stage. The resulting understanding is successful in explaining QNR for a Schwarzschild black hole and opens a new approach to understanding binary inspiral. It holds the promise of a much improved understanding, and improved efficiency in making astrophysical estimates of gravitational wave source strength. Singularities are known to be the ultimate fate of all massive stars undergoing gravitational collapse. The cosmic censorship hypothesis predicts that all these singularities are generically covered by event horizons, i.e., all collapsing stars, if they result in a singularity, end up as black holes. Although several theoretical examples of non-hidden (naked) singularities have been found, the question of the genericity of naked singularities is far from settled. This thesis presents a study of the causal structure of spherically symmetric models of dust collapse and its perturbations to investigate the genericity of naked singularities.

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.

Avoidance of singularities in asymptotically safe Quantum Einstein Gravity

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

Kofinas, Georgios; Zarikas, Vasilios; Department of Physics, Aristotle University of Thessaloniki,54124 Thessaloniki

2015-10-30

New general spherically symmetric solutions have been derived with a cosmological “constant” Λ as a source. This Λ term is not constant but it satisfies the properties of the asymptotically safe gravity at the ultraviolet fixed point. The importance of these solutions comes from the fact that they may describe the near to the centre region of black hole spacetimes as this is modified by the Renormalization Group scaling behaviour of the fields. The consistent set of field equations which respect the Bianchi identities is derived and solved. One of the solutions (with conventional sign of temporal-radial metric components) ismore » timelike geodesically complete, and although there is still a curvature divergent origin, this is never approachable by an infalling massive particle which is reflected at a finite distance due to the repulsive origin. Another family of solutions (of both signatures) range from a finite radius outwards, they cannot be extended to the centre of spherical symmetry, and the curvature invariants are finite at the minimum radius.« less

Avoidance of singularities in asymptotically safe Quantum Einstein Gravity

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

Kofinas, Georgios; Zarikas, Vasilios, E-mail: gkofinas@aegean.gr, E-mail: vzarikas@teilam.gr

2015-10-01

New general spherically symmetric solutions have been derived with a cosmological ''constant'' Λ as a source. This Λ term is not constant but it satisfies the properties of the asymptotically safe gravity at the ultraviolet fixed point. The importance of these solutions comes from the fact that they may describe the near to the centre region of black hole spacetimes as this is modified by the Renormalization Group scaling behaviour of the fields. The consistent set of field equations which respect the Bianchi identities is derived and solved. One of the solutions (with conventional sign of temporal-radial metric components) ismore » timelike geodesically complete, and although there is still a curvature divergent origin, this is never approachable by an infalling massive particle which is reflected at a finite distance due to the repulsive origin. Another family of solutions (of both signatures) range from a finite radius outwards, they cannot be extended to the centre of spherical symmetry, and the curvature invariants are finite at the minimum radius.« less

Dispersion of gravitational waves in cold spherical interstellar medium

NASA Astrophysics Data System (ADS)

Barta, Dániel; Vasúth, Mátyás

We investigate the propagation of locally plane, small-amplitude, monochromatic gravitational waves (GWs) through cold compressible interstellar gas in order to provide a more accurate picture of expected waveforms for direct detection. The quasi-isothermal gas is concentrated in a spherical symmetric cloud held together by self-gravitation. Gravitational waves can be treated as linearized perturbations on the background inner Schwarzschild spacetime. The perturbed quantities lead to the field equations governing the gas dynamics and describe the interaction of gravitational waves with matter. We have shown that the transport equation of these amplitudes provides numerical solutions for the frequency-alteration. The decrease in frequency is driven by the energy dissipating process of GW-matter interactions. The decrease is significantly smaller than the magnitude of the original frequency and too small to be detectable by present second-generation and planned third-generation detectors. It exhibits a power-law relationship between original and decreased frequencies. The frequency deviation was examined particularly for the transient signal GW150914.

Optimized preparation of in situ forming microparticles for the parenteral delivery of vinpocetine.

PubMed

Li, Jizhong; Chen, Fei; Hu, Chanjuan; He, Ling; Yan, Keshu; Zhou, Liying; Pan, Weisan

2008-06-01

A spherical symmetric design-response surface methodology was applied to optimize the preparation of vinpocetine-loaded poly(D,L-lactide-co-glycolide) PLGA in situ forming microparticles (ISM system). The influence of the ratio of PLGA to vinpocetine (w/w), the concentration of Tween 80 (w/v) and the volume of propylene glycol on the burst release, medium particle diameter and size distribution was evaluated. Scan electron microscopy of the optimized in situ microparticles exhibited spherical shape, and vinpocetine-loading mainly inside the microparticles. The data showed that the release of vinpocetine from in situ microparticles in vitro and in vivo lasted about 40 d. In vivo pharmacokinetic characteristics of the optimized in situ microparticles was assessed after they were intramuscularly injected into rats. HPLC method was used to determine the plasma concentration of vinpocetine. The absolute bioavailability of vinpocetine in the microparticles was 27.6% in rats, which suggested that PLGA in situ microparticles were a valuable system for the delivery of vinpocetine.

Wave equations in conformal gravity

NASA Astrophysics Data System (ADS)

Du, Juan-Juan; Wang, Xue-Jing; He, You-Biao; Yang, Si-Jiang; Li, Zhong-Heng

2018-05-01

We study the wave equation governing massless fields of all spins (s = 0, 1 2, 1, 3 2 and 2) in the most general spherical symmetric metric of conformal gravity. The equation is separable, the solution of the angular part is a spin-weighted spherical harmonic, and the radial wave function may be expressed in terms of solutions of the Heun equation which has four regular singular points. We also consider various special cases of the metric and find that the angular wave functions are the same for all cases, the actual shape of the metric functions affects only the radial wave function. It is interesting to note that each radial equation can be transformed into a known ordinary differential equation (i.e. Heun equation, or confluent Heun equation, or hypergeometric equation). The results show that there are analytic solutions for all the wave equations of massless spin fields in the spacetimes of conformal gravity. This is amazing because exact solutions are few and far between for other spacetimes.

On the Theory of Type 1 X-Ray Bursts: The Energetics of Bursts and the Nuclear Fuel Reservoir in the Envelope

NASA Technical Reports Server (NTRS)

Fujimoto, Masayuki Y.; Sztajno, Mirek; Lewin, Walter H. G.; Vanparadijs, Jan

1986-01-01

The observed properties of type 1 X-ray bursts from 4U/MXB 1636-53 and those of models of thermonuclear flashes on accreting neutron stars are compared. Ways to explain variations in the burst recurrence properties without an apparent correlation with the accretion rate, including the rapid succession of bursts at intervals 10 min are discussed. The strongest X-ray bursts, which occur after a very long interval, are well described by thermonuclear flash models with simple accumulation of accreted fuel, and a spherically symmetric structure in the burning shell. The majority of observed bursts, however, occur after much shorter intervals, and radiate much smaller amounts of energy, by a factor of up to 10 times that predicted by the spherical models. An ignition mechanism of the bursts is proposed in terms of elemental mixing and dissipative heating associated with hydrodynamical instabilities in the neutron star envelope caused by angular momentum carried inward by accreted gas.

ME(SSY)**2: Monte Carlo Code for Star Cluster Simulations

NASA Astrophysics Data System (ADS)

Freitag, Marc Dewi

2013-02-01

ME(SSY)**2 stands for “Monte-carlo Experiments with Spherically SYmmetric Stellar SYstems." This code simulates the long term evolution of spherical clusters of stars; it was devised specifically to treat dense galactic nuclei. It is based on the pioneering Monte Carlo scheme proposed by Hénon in the 70's and includes all relevant physical ingredients (2-body relaxation, stellar mass spectrum, collisions, tidal disruption, ldots). It is basically a Monte Carlo resolution of the Fokker-Planck equation. It can cope with any stellar mass spectrum or velocity distribution. Being a particle-based method, it also allows one to take stellar collisions into account in a very realistic way. This unique code, featuring most important physical processes, allows million particle simulations, spanning a Hubble time, in a few CPU days on standard personal computers and provides a wealth of data only rivalized by N-body simulations. The current version of the software requires the use of routines from the "Numerical Recipes in Fortran 77" (http://www.nrbook.com/a/bookfpdf.php).

Theoretical study of symmetry of flux onto a capsule

NASA Astrophysics Data System (ADS)

Duan, Hao; Wu, Changshu; Pei, Wenbing; Zou, Shiyang

2015-09-01

An analytic model to describe the flux asymmetry onto a capsule based on the viewfactor approximation is developed and verified with numerical simulations. By using a nested spheres technique to represent the various sources of flux asymmetry, the model can treat spherically and cylindrically symmetric hohlraums, e.g., cylinder, elliptic, and rugby. This approach includes the more realistic case of frequency-dependent flux asymmetry compared with the more standard frequency-integrated or single-frequency approaches [D. W. Phillion and S. M. Pollaine, Phys. Plasmas 1, 2963 (1994)]. Correspondingly, the approach can be used to assess x-ray preheat asymmetry generated from localized laser absorption in the high-Z hohlraum wall. For spherical hohlraums with 4, 6, or 8 laser entrance holes (LEHs), an optimal configuration of LEHs, laser spot placement, and angle-of-incidence of the single-ringed laser beams is defined. An analogy between minimizing the flux asymmetry onto a capsule and the Thomson problem of point charge placement on a sphere for minimized energy is shown.

Electromagnetic fields and torque for a rotating gyroscope with a superconducting shield

NASA Technical Reports Server (NTRS)

Ebner, C.; Sung, C. C.

1975-01-01

In a proposed experiment, a measurement is to be made of the angular precession of a rotating superconducting gyroscope for the purpose of testing different general-relativity theories. For various reasons having to do with the design of the experiment, the superconducting shield surrounding the gyroscope is not spherically symmetric and produces a torque. There are two distinct features of the shield which lead to a torque on the gyroscope. First, its shape is a sphere intersected by a plane. If the angular momentum of the gyroscope is not parallel to the rotational symmetry axis of the shield, there is a torque which is calculated. Second, there are small holes in the spherical portion of the shield. The earth's field can penetrate through these holes and give an additional torque which is also calculated. In the actual experiment, these torques must be accurately known or made very small in order to obtain meaningful results. The present calculation is sufficiently general for application over a wide range of experimental design parameters.

Measurement of poloidal velocity on the National Spherical Torus Experiment (invited).

PubMed

Bell, Ronald E; Feder, Russell

2010-10-01

A diagnostic suite has been developed to measure the impurity poloidal flow using charge exchange recombination spectroscopy on the National Spherical Torus Experiment. Toroidal and poloidal viewing systems measure all the quantities required to determine the radial electric field. Two sets of up/down symmetric poloidal views are used to measure both the active emission in the plane of the neutral heating beams and the background emission in a radial plane away from the neutral beams. Differential velocity measurements isolate the line-integrated poloidal velocity from apparent flows due to the energy-dependent charge exchange cross section. Six f/1.8 spectrometers measure 276 spectra to obtain 75 active and 63 background channels every 10 ms. The local measurements from a similar midplane toroidal viewing system are mapped into two dimensions to allow the inversion of poloidal line-integrated measurements to obtain local poloidal velocity profiles. The radial resolution after inversion is 0.6-1.8 cm from the plasma edge to the center.

Theoretical study of symmetry of flux onto a capsule

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

Duan, Hao; Wu, Changshu; Zou, Shiyang, E-mail: duan-hao@iapcm.ac.cn

2015-09-15

An analytic model to describe the flux asymmetry onto a capsule based on the viewfactor approximation is developed and verified with numerical simulations. By using a nested spheres technique to represent the various sources of flux asymmetry, the model can treat spherically and cylindrically symmetric hohlraums, e.g., cylinder, elliptic, and rugby. This approach includes the more realistic case of frequency-dependent flux asymmetry compared with the more standard frequency-integrated or single-frequency approaches [D. W. Phillion and S. M. Pollaine, Phys. Plasmas 1, 2963 (1994)]. Correspondingly, the approach can be used to assess x-ray preheat asymmetry generated from localized laser absorption inmore » the high-Z hohlraum wall. For spherical hohlraums with 4, 6, or 8 laser entrance holes (LEHs), an optimal configuration of LEHs, laser spot placement, and angle-of-incidence of the single-ringed laser beams is defined. An analogy between minimizing the flux asymmetry onto a capsule and the Thomson problem of point charge placement on a sphere for minimized energy is shown.« less

Formation of a new archetypal Metal-Organic Framework from a simple monatomic liquid

NASA Astrophysics Data System (ADS)

Metere, Alfredo; Oleynikov, Peter; Dzugutov, Mikhail; O'Keeffe, Michael

2014-12-01

We report a molecular-dynamics simulation of a single-component system of particles interacting via a spherically symmetric potential that is found to form, upon cooling from a liquid state, a low-density porous crystalline phase. Its structure analysis demonstrates that the crystal can be described by a net with a topology that belongs to the class of topologies characteristic of the Metal-Organic Frameworks (MOFs). The observed net is new, and it is now included in the Reticular Chemistry Structure Resource database. The observation that a net topology characteristic of MOF crystals, which are known to be formed by a coordination-driven self-assembly process, can be reproduced by a thermodynamically stable configuration of a simple single-component system of particles opens a possibility of using these models in studies of MOF nets. It also indicates that structures with MOF topology, as well as other low-density porous crystalline structures can possibly be produced in colloidal systems of spherical particles, with an appropriate tuning of interparticle interaction.

Nonequilibrium phase transitions of sheared colloidal microphases: Results from dynamical density functional theory

NASA Astrophysics Data System (ADS)

Stopper, Daniel; Roth, Roland

2018-06-01

By means of classical density functional theory and its dynamical extension, we consider a colloidal fluid with spherically symmetric competing interactions, which are well known to exhibit a rich bulk phase behavior. This includes complex three-dimensional periodically ordered cluster phases such as lamellae, two-dimensional hexagonally packed cylinders, gyroid structures, or spherical micelles. While the bulk phase behavior has been studied extensively in earlier work, in this paper we focus on such structures confined between planar repulsive walls under shear flow. For sufficiently high shear rates, we observe that microphase separation can become fully suppressed. For lower shear rates, however, we find that, e.g., the gyroid structure undergoes a kinetic phase transition to a hexagonally packed cylindrical phase, which is found experimentally and theoretically in amphiphilic block copolymer systems. As such, besides the known similarities between the latter and colloidal systems regarding the equilibrium phase behavior, our work reveals further intriguing nonequilibrium relations between copolymer melts and colloidal fluids with competing interactions.

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

Influence of Non-spherical Initial Stellar Structure on the Core-Collapse Supernova Mechanism

NASA Astrophysics Data System (ADS)

Couch, Sean M.

I review the state of investigation into the impact that nonspherical stellar progenitor structure has on the core-collapse supernova mechanism. Although modeling stellar evolution relies on 1D spherically symmetric calculations, massive stars are not truly spherical. In the stellar evolution codes, this fact is accounted for by "fixes" such as mixing length theory and attendant modifications. Of particular relevance to the supernova mechanism, the Si- and O-burning shells surrounding the iron core at the point of collapse can be violently convective, with convective speeds of hundreds of km s-1. It has recently been shown by a number of groups that the presence of nonspherical perturbations in the layers surrounding the collapsing iron core can have a favorable impact on the likelihood for shock revival and explosion via the neutrino heating mechanism. This is due in large part to the strengthening of turbulence behind the stalled shock due to the presence of finite amplitude seed perturbations to speed the growth of convection which drives the post-shock turbulence. Efforts are now underway to simulate the final minutes of stellar evolution to core-collapse in 3D with the aim to generate realistic multidimensional initial conditions for use in simulations of the supernova mechanism.

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.

Critical radiation fluxes and luminosities of black holes and relativistic stars

NASA Technical Reports Server (NTRS)

Lamb, Frederick K.; Miller, M. Coleman

1995-01-01

The critial luminosity at which the outward force of radiation balances the inward force of gravity plays an important role in many astrophysical systems. We present expressions for the radiation force on particles with arbitrary cross sections and analyze the radiation field produced by radiating matter, such as a disk, ring, boundary layer, or stellar surface, that rotates slowly around a slowly rotating gravitating mass. We then use these results to investigate the critical radiation flux and, where possible, the critical luminosity of such a system in genral relativity. We demonstrate that if the radiation source is axisymmetric and emission is back-front symmetric with repect to the local direction of motion of the radiating matter, as seen in the comoving frame, then the radial component of the radiation flux and the diagonal components of the radiation stress-energy tensor outside the source are the same, to first order in the rotation rates, as they would be if the radiation source and gravitating mass were not rotating. We argue that the critical radiation flux for matter at rest in the locally nonrotating frame is often satisfactory as an astrophysical benchmark flux and show that if this benchmark is adopted, many of the complications potentially introduced by rotation of the radiation source and the gravitating mass are avoided. We show that if the radiation field in the absence of rotation would be spherically symmetric and the opacity is independent of frequency and direction, one can define a critical luminosity for the system that is independent of frequency and direction, one can define a critical luminosity for the system that is independent of the spectrum and angular size of the radiation source and is unaffected by rotation of the source and mass and orbital motion of the matter, to first order. Finally, we analyze the conditions under which the maximum possible luminosity of a star or black hole powered by steady spherically symmetric radial accretion is the same in general relativity as in the Newtonian limit.

Effect of Central Mass Concentration on the Formation of Nuclear Spirals in Barred Galaxies

NASA Astrophysics Data System (ADS)

Thakur, Parijat; Ann, H. B.; Jiang, Ing-Guey

2009-03-01

We have performed smoothed particle hydrodynamics simulations to study the response of the central kiloparsec region of a gaseous disk to the imposition of nonaxisymmetric bar potentials. The model galaxies are composed of three axisymmetric components (halo, disk, and bulge) and a nonaxisymmetric bar. These components are assumed to be invariant in time in the frame corotating with the bar. The potential of spherical γ-models of Dehnen is adopted for the bulge component whose density varies as r -γ near the center and r -4 at larger radii and, hence, possesses a central density core for γ = 0 and cusps for γ>0. Since the central mass concentration of the model galaxies increases with the cusp parameter γ, we have examined here the effect of the central mass concentration by varying the cusp parameter γ on the mechanism responsible for the formation of the symmetric two-armed nuclear spirals in barred galaxies. Our simulations show that the symmetric two-armed nuclear spirals are formed by hydrodynamic spiral shocks driven by the gravitational torque of the bar for the models with γ = 0 and 0.5. On the other hand, the symmetric two-armed nuclear spirals in the models with γ = 1 and 1.5 are explained by gas density waves. Thus, we conclude that the mechanism responsible for the formation of symmetric two-armed nuclear spirals in barred galaxies changes from hydrodynamic shocks to gas density waves as the central mass concentration increases from γ = 0 to 1.5.

Quantum dynamics in phase space: Moyal trajectories 2

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

Braunss, G.

Continuing a previous paper [G. Braunss, J. Phys. A: Math. Theor. 43, 025302 (2010)] where we had calculated Planck-Constant-Over-Two-Pi {sup 2}-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 Planck-Constant-Over-Two-Pi {sup 2}-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 Planck-Constant-Over-Two-Pi {sup 2}-approximation of the nonrelativisticmore » 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 {gamma}(H, z) the expression {beta}{identical_to}p{sub z}+{gamma}(H, z) is classically ( Planck-Constant-Over-Two-Pi = 0) a constant of motion, whereas for Planck-Constant-Over-Two-Pi {ne} 0 this holds only if {gamma}(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 Henon-Heiles Hamiltonian and give a short review of the regular Hilbert space representation of Moyal operators.« less

Explaining the progenitors of peculiar type Ia supernovae

NASA Astrophysics Data System (ADS)

Das, Upasana; Mukhopadhyay, Banibrata

2015-01-01

Type Ia supernovae (SneIa) are believed to be triggered in white dwarfs having mass close to the Chandrasekhar limit of 1.44 M⊙. However, observations of several peculiar, highly under- and over-luminous SNeIa argue for exploding masses widely different from this limit. The over-luminous SNeIa, e.g. SN 2003fg, SN 2006gz, SN 2007if, SN 2009dc, seem to invoke super-Chandrasekhar white dwarf progenitors, having mass 2.1-2.8 M⊙. While, the under-luminous SNeIa, e.g. SN 1991bg, SN 1997cn, SN 1998de, SN 1999by, seem to favor sub-Chandrasekhar explosion scenarios. In order to explain the existence of super-Chandrasekhar white dwarfs, we have exploited the enormous potential of magnetic fields, which can affect the structure and properties of the underlying white dwarf in a variety of ways. We have progressed from a simplistic to more rigorous and self-consistent models in the following sequence - spherically symmetric Newtonian model with a constant central magnetic field; spherically symmetric general relativistic model with varying magnetic field and finally, a model including self-consistent departure from spherical symmetry obtained from general relativistic magnetohydrodynamic (GRMHD) simulations. Here we particularly present the results of the GRMHD simulations, whereby we have constructed equilibrium models of strongly magnetized, static, white dwarfs. Interestingly, we find that significantly super-Chandrasekhar white dwarfs are obtained for many possible field configurations, namely, poloidal, toroidal and mixed. Further, due to the inclusion of deformation in the white dwarf structure caused by a strong magnetic field, super-Chandrasekhar white dwarfs are obtained for relatively lower magnetic field strengths compared to that in the simplistic model. Finally, driven by the aim to establish a unification theory of under- and over-luminous SNeIa, we have shown that a modification of Einstein's theory of gravity leads to both significantly sub- and super-Chandrasekhar limiting masses, determined by a single model parameter. Explosions of these sub- and super-Chandrasekhar limiting mass white dwarfs can explain both the peculiar, under- and over-luminous SNeIa respectively.

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

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

Bose-Einstein correlations in Si + Al and Si + Au collisions at 14.6A GeV/c

NASA Technical Reports Server (NTRS)

Abbott, T.; Akiba, Y.; Beavis, D.; Bloomer, M. A.; Bond, P. D.; Chasman, C.; Chen, Z.; Chu, Y. Y.; Cole, B. A.; Costales, J. B.

1992-01-01

The E802 Spectrometer at the Brookhaven Alternating Gradient Synchrotron has been used to measure the correlation in relative momentum between like-sign pions emitted in central Si + Al and Si + Au collisions at 14.6A GeV/c. Data are presented in terms of the correlation function for both identified pi(-) and pi(+) pairs near the nucleon-nucleon center-of-mass rapidity. All parametrizations of the correlation function are consistent with a spherically symmetric source of rms radius 3.5 +/- 0.4 fm and lifetime fm/c.

Optical instruments

NASA Technical Reports Server (NTRS)

Abel, I. R. (Inventor)

1974-01-01

A wide angle, low focal ratio, high resolution, catoptric, image plane scanner is described. The scanner includes the following features: (1) a reflective improvement on the Schmidt principle, (2) a polar line scanner in which all field elements are brought to and corrected on axis, and (3) a scanner arrangement in which the aperture stop of the system is imaged at the center of curvature of a spherical primary mirror. The system scans are a large radial angle and an extremely high rate of speed with relatively small scanning mirrors. Because the system is symmetrical about the optical axis, the obscuration is independent of the scan angle.

On the motion of hairy black holes in Einstein-Maxwell-dilaton theories

NASA Astrophysics Data System (ADS)

Julié, Félix-Louis

2018-01-01

Starting from the static, spherically symmetric black hole solutions in massless Einstein-Maxwell-dilaton (EMD) theories, we build a "skeleton" action, that is, we phenomenologically replace black holes by an appropriate effective point particle action, which is well suited to the formal treatment of the many-body problem in EMD theories. We find that, depending crucially on the value of their scalar cosmological environment, black holes can undergo steep "scalarization" transitions, inducing large deviations to the general relativistic two-body dynamics, as shown, for example, when computing the first post-Keplerian Lagrangian of EMD theories.

Self-similar perturbations of a Friedmann universe

NASA Technical Reports Server (NTRS)

Carr, Bernard J.; Yahil, Amos

1990-01-01

The present analysis of spherically symmetric self-similar solutions to the Einstein equations gives attention to those solutions that are asymptotically k = 0 Friedmann at large z values, and possess finite but perturbed density at the origin. Such solutions represent nonlinear density fluctuations which grow at the same rate as the universe's particle horizon. The overdense solutions span only a narrow range of parameters, and resemble static isothermal gas spheres just within the sonic point; the underdense solutions may have arbitrarily low density at the origin while exhibiting a unique relationship between amplitude and scale. Their relevance to large-scale void formation is considered.

Inhomogeneity-induced cosmic acceleration in a dust universe

NASA Astrophysics Data System (ADS)

Chuang, Chia-Hsun; Gu, Je-An; Hwang, W.-Y. P.

2008-09-01

It is the common consensus that the expansion of a universe always slows down if the gravity provided by the energy sources therein is attractive and accordingly one needs to invoke dark energy as a source of anti-gravity for understanding the cosmic acceleration. To examine this point we find counterexamples for a spherically symmetric dust fluid described by the Lemaître Tolman Bondi solution without singularity. Thus, the validity of this naive consensus is indeed doubtful and the effects of inhomogeneities should be restudied. These counter-intuitive examples open a new perspective on the understanding of the evolution of our universe.

Large-scale deformed QRPA calculations of the gamma-ray strength function based on a Gogny force

NASA Astrophysics Data System (ADS)

Martini, M.; Goriely, S.; Hilaire, S.; Péru, S.; Minato, F.

2016-01-01

The dipole excitations of nuclei play an important role in nuclear astrophysics processes in connection with the photoabsorption and the radiative neutron capture that take place in stellar environment. We present here the results of a large-scale axially-symmetric deformed QRPA calculation of the γ-ray strength function based on the finite-range Gogny force. The newly determined γ-ray strength is compared with experimental photoabsorption data for spherical as well as deformed nuclei. Predictions of γ-ray strength functions and Maxwellian-averaged neutron capture rates for Sn isotopes are also discussed.

Test Equal Bending by Gravity for Space and Time

NASA Astrophysics Data System (ADS)

Sweetser, Douglas

2009-05-01

For the simplest problem of gravity - a static, non-rotating, spherically symmetric source - the solution for spacetime bending around the Sun should be evenly split between time and space. That is true to first order in M/R, and confirmed by experiment. At second order, general relativity predicts different amounts of contribution from time and space without a physical justification. I show an exponential metric is consistent with light bending to first order, measurably different at second order. All terms to all orders show equal contributions from space and time. Beautiful minimalism is Nature's way.

Traversable wormholes without exotic matter in multimetric repulsive gravity

NASA Astrophysics Data System (ADS)

Hohmann, Manuel

2014-04-01

We present a static, spherically symmetric, traversable wormhole solution to multimetric gravity which is sustained by only nonexotic matter, i.e., matter which satisfies all energy conditions. The possibility of this solution arises from the fact that under certain conditions the multimetric gravitational field equations reduce to the Einstein equations, but with a negative effective gravitational constant. We show that the Arnowitt-Deser-Misner mass of this wormhole vanishes, so that it appears massless to observers in the asymptotically flat spacetime. We finally speculate on the feasibility of creating and maintaining this type of wormhole by an advanced civilization.

Membrane paradigm of black holes in Chern-Simons modified gravity

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

Zhao, Tian-Yi; Wang, Towe, E-mail: zhaotianyi5566@foxmail.com, E-mail: twang@phy.ecnu.edu.cn

2016-06-01

The membrane paradigm of black hole is studied in the Chern-Simons modified gravity. Derived with the action principle a la Parikh-Wilczek, the stress tensor of membrane manifests a rich structure arising from the Chern-Simons term. The membrane stress tensor, if related to the bulk stress tensor in a special form, obeys the low-dimensional fluid continuity equation and the Navier-Stokes equation. This paradigm is applied to spherically symmetric static geometries, and in particular, the Schwarzschild black hole, which is a solution of a large class of dynamical Chern-Simons gravity.

Accretion onto some well-known regular black holes

NASA Astrophysics Data System (ADS)

Jawad, Abdul; Shahzad, M. Umair

2016-03-01

In this work, we discuss the accretion onto static spherically symmetric regular black holes for specific choices of the equation of state parameter. The underlying regular black holes are charged regular black holes using the Fermi-Dirac distribution, logistic distribution, nonlinear electrodynamics, respectively, and Kehagias-Sftesos asymptotically flat regular black holes. We obtain the critical radius, critical speed, and squared sound speed during the accretion process near the regular black holes. We also study the behavior of radial velocity, energy density, and the rate of change of the mass for each of the regular black holes.

Simulations of star-forming molecular clouds: observational predictions

NASA Astrophysics Data System (ADS)

Zhang, Shangjia; Hartmann, Lee; Kuznetsova, Aleksandra; Abelardo Zamora, Manuel

2018-01-01

Observations of protostellar molecular cloud cores can be used to test theories of star formation. However, observational results can be biased because of limited information: (a) only two spatial dimensions and one velocity dimension can be measured, (b) and cores generally are not spherically symmetric. We use numerical simulations of the formation and collapse of molecular gas with sink particles to make observational predictions. We use the radiative transfer code LIME to predict CO and NH3 channel maps. We find reasonable agreement with observed velocity structures and gradients but occasional large differences depending on viewing angle.

A special class of solutions in F( R)-gravity

NASA Astrophysics Data System (ADS)

Calzà, Marco; Rinaldi, Massimiliano; Sebastiani, Lorenzo

2018-03-01

We consider a special class of vacuum F( R)-modified gravity models. The form of their Lagrangian is such that the field equations are trivially satisfied when the Ricci scalar is constant. There are many interesting F( R)-models for inflation and dark energy that fall in this class. However, little is known outside the domain of cosmology therefore we aim to explore the class of solutions that are static and spherically symmetric. After some general considerations, we investigate in more detail black hole solutions, traversable wormhole metrics and, finally, configurations that can match the anomalous rotation curves of galaxies.

Analytic solutions in nonlinear massive gravity.

PubMed

Koyama, Kazuya; Niz, Gustavo; Tasinato, Gianmassimo

2011-09-23

We study spherically symmetric solutions in a covariant massive gravity model, which is a candidate for a ghost-free nonlinear completion of the Fierz-Pauli theory. There is a branch of solutions that exhibits the Vainshtein mechanism, recovering general relativity below a Vainshtein radius given by (r(g)m(2))(1/3), where m is the graviton mass and r(g) is the Schwarzschild radius of a matter source. Another branch of exact solutions exists, corresponding to de Sitter-Schwarzschild spacetimes where the curvature scale of de Sitter space is proportional to the mass squared of the graviton.

Development of 3D out-of-plane SU-8 microlenses using modified micromolding in capillaries (MIMIC) technology

NASA Astrophysics Data System (ADS)

Llobera, A.; Wilke, R.; Johnson, D. W.; Büttgenbach, S.

2006-04-01

This paper describes a modification of the standard MIMIC technology, solving its main drawbacks, to define arrays of spherical or ellipsoidal microlenses. Perfectly symmetrical meniscuses have been obtained by using a XP SU-8 NO-2 layer beneath the PDMS mold. Moreover, the photostructurable properties of this polymer allow obtaining self-alignment structures for adequate fiber optics positioning. Microchannels ended with these meniscuses have been filled with standard SU-8 to obtain 3D microlenses. Agreement between theory and experimental results allows confirming the validity of the proposed technology.

The non-radiating component of the field generated by a finite monochromatic scalar source distribution

NASA Astrophysics Data System (ADS)

Hoenders, Bernhard J.; Ferwerda, Hedzer A.

1998-09-01

We separate the field generated by a spherically symmetric bounded scalar monochromatic source into a radiative and non-radiative part. The non-radiative part is obtained by projecting the total field on the space spanned by the non-radiating inhomogeneous modes, i.e. the modes which satisfy the inhomogeneous wave equation. Using residue techniques, introduced by Cauchy, we obtain an explicit analytical expression for the non-radiating component. We also identify the part of the source distribution which corresponds to this non-radiating part. The analysis is based on the scalar wave equation.

On the control of a robot ball using two omniwheels

NASA Astrophysics Data System (ADS)

Ivanov, Alexander P.

2015-07-01

We discuss the dynamics of a balanced body of spherical shape on a rough plane, controlled by the movement of a built-in shell. These two shells are set in relative motion due to rotation of the two symmetrical omniwheels. It is shown that the ball can be moved to any point on the plane along a straight or (in the case of the initial degeneration) polygonal line. Moreover, any prescribed curvilinear trajectory of the ball center can be followed by an appropriate control strategy as far as the diameter connecting both wheels is nonvertical.

On the regularized fermionic projector of the vacuum

NASA Astrophysics Data System (ADS)

Finster, Felix

2008-03-01

We construct families of fermionic projectors with spherically symmetric regularization, which satisfy the condition of a distributional MP-product. The method is to analyze regularization tails with a power law or logarithmic scaling in composite expressions in the fermionic projector. The resulting regularizations break the Lorentz symmetry and give rise to a multilayer structure of the fermionic projector near the light cone. Furthermore, we construct regularizations which go beyond the distributional MP-product in that they yield additional distributional contributions supported at the origin. The remaining freedom for the regularization parameters and the consequences for the normalization of the fermionic states are discussed.

Ab initio method for calculating total cross sections

NASA Technical Reports Server (NTRS)

Bhatia, A. K.; Schneider, B. I.; Temkin, A.

1993-01-01

A method for calculating total cross sections without formally including nonelastic channels is presented. The idea is to use a one channel T-matrix variational principle with a complex correlation function. The derived T matrix is therefore not unitary. Elastic scattering is calculated from T-parallel-squared, but total scattering is derived from the imaginary part of T using the optical theorem. The method is applied to the spherically symmetric model of electron-hydrogen scattering. No spurious structure arises; results for sigma(el) and sigma(total) are in excellent agreement with calculations of Callaway and Oza (1984). The method has wide potential applicability.

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

Gillioz, M.; von Manteuffel, A.; Schwaller, P.

We study skyrmions in the littlest Higgs model and discuss their possible role as dark matter candidates. Stable massive skyrmions can exist in the littlest Higgs model also in absence of an exact parity symmetry, since they carry a conserved topological charge due to the non-trivial third homotopy group of the SU(5)/SO(5) coset. We find a spherically symmetric skyrmion solution in this coset. The effects of gauge fields on the skyrmion solutions are analyzed and found to lead to an upper bound on the skyrmion mass. The relic abundance is in agreement with the observed dark matter density for reasonablemore » parameter choices.« less

Time-dependent corona models - Scaling laws

NASA Technical Reports Server (NTRS)

Korevaar, P.; Martens, P. C. H.

1989-01-01

Scaling laws are derived for the one-dimensional time-dependent Euler equations that describe the evolution of a spherically symmetric stellar atmosphere. With these scaling laws the results of the time-dependent calculations by Korevaar (1989) obtained for one star are applicable over the whole Hertzsprung-Russell diagram and even to elliptic galaxies. The scaling is exact for stars with the same M/R-ratio and a good approximation for stars with a different M/R-ratio. The global relaxation oscillation found by Korevaar (1989) is scaled to main sequence stars, a solar coronal hole, cool giants and elliptic galaxies.

Noether's stars in f (R) gravity

NASA Astrophysics Data System (ADS)

De Laurentis, Mariafelicia

2018-05-01

The Noether Symmetry Approach can be used to construct spherically symmetric solutions in f (R) gravity. Specifically, the Noether conserved quantity is related to the gravitational mass and a gravitational radius that reduces to the Schwarzschild radius in the limit f (R) → R. We show that it is possible to construct the M- R relation for neutron stars depending on the Noether conserved quantity and the associated gravitational radius. This approach enables the recovery of extreme massive stars that could not be stable in the standard Tolman-Oppenheimer-Volkoff based on General Relativity. Examples are given for some power law f (R) gravity models.

Symmetric and antisymmetric forms of the Pauli master equation.

PubMed

Klimenko, A Y

2016-07-21

When applied to matter and antimatter states, the Pauli master equation (PME) may have two forms: time-symmetric, which is conventional, and time-antisymmetric, which is suggested in the present work. The symmetric and antisymmetric forms correspond to symmetric and antisymmetric extensions of thermodynamics from matter to antimatter - this is demonstrated by proving the corresponding H-theorem. The two forms are based on the thermodynamic similarity of matter and antimatter and differ only in the directions of thermodynamic time for matter and antimatter (the same in the time-symmetric case and the opposite in the time-antisymmetric case). We demonstrate that, while the symmetric form of PME predicts an equibalance between matter and antimatter, the antisymmetric form of PME favours full conversion of antimatter into matter. At this stage, it is impossible to make an experimentally justified choice in favour of the symmetric or antisymmetric versions of thermodynamics since we have no experience of thermodynamic properties of macroscopic objects made of antimatter, but experiments of this kind may become possible in the future.

Pre-Big-Bang bubbles from the gravitational instability of generic string vacua

NASA Astrophysics Data System (ADS)

Buonanno, A.; Damour, T.; Veneziano, G.

1999-03-01

We formulate the basic postulate of pre-Big-Bang cosmology as one of ``asymptotic past triviality", by which we mean that the initial state is a generic perturbative solution of the tree-level low-energy effective action. Such a past-trivial ``string vacuum'' is made of an arbitrary ensemble of incoming gravitational and dilatonic waves, and is generically prone to gravitational instability, leading to the possible formation of many black holes hiding singular space-like hypersurfaces. Each such singular space-like hypersurface of gravitational collapse becomes, in the string-frame metric, the usual Big-Bang t=0 hypersurface, i.e. the place of birth of a baby Friedmann universe after a period of dilaton-driven inflation. Specializing to the spherically symmetric case, we review and reinterpret previous work on the subject, and propose a simple, scale-invariant criterion for collapse/inflation in terms of asymptotic data at past null infinity. Those data should determine whether, when, and where collapse/inflation occurs, and, when it does, fix its characteristics, including anisotropies on the Big-Bang hypersurface whose imprint could have survived till now. Using Bayesian probability concepts, we finally attempt to answer some fine-tuning objections recently moved to the pre-Big-Bang scenario.

Anchoring Polar Magnetic Field in a Stationary Thick Accretion Disk

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

Samadi, Maryam; Abbassi, Shahram, E-mail: samadimojarad@um.ac.ir

We investigate the properties of a hot accretion flow bathed in a poloidal magnetic field. We consider an axisymmetric viscous-resistive flow in the steady-state configuration. We assume that the dominant mechanism of energy dissipation is due to turbulence viscosity and magnetic diffusivity. A certain fraction of that energy can be advected toward the central compact object. We employ the self-similar method in the radial direction to find a system of ODEs with just one varible, θ in the spherical coordinates. For the existence and maintenance of a purely poloidal magnetic field in a rotating thick disk, we find that themore » necessary condition is a constant value of angular velocity along a magnetic field line. We obtain an analytical solution for the poloidal magnetic flux. We explore possible changes in the vertical structure of the disk under the influences of symmetric and asymmetric magnetic fields. Our results reveal that a polar magnetic field with even symmetry about the equatorial plane makes the disk vertically thin. Moreover, the accretion rate decreases when we consider a strong magnetic field. Finally, we notice that hot magnetized accretion flows can be fully advected even in a slim shape.« less

Preparation of Geophysical Fluid Flow Experiments With The Rotating Spherical Gap Flow Model In Space

NASA Astrophysics Data System (ADS)

Egbers, C.

The'GeoFlow' is an ESA experiment planned for the Fluid Science Laboratory on ISS under the scientific coordination (PI) of the Department of Aerodynamics and Fluid Mechanics (LAS) at the Brandenburg Technical University (BTU) of Cottbus, Germany. The objective of the experiment is to study thermal convection in the gap between two concentric rotating (full) spheres. A central symmetric force field simi- lar to the gravity field acting on planets can be produced by applying a high voltage between inner and outer sphere using the dielectrophoretic effect (rotating capacitor). To counter the unidirectional gravity under terrestrial conditions, this experiment re- quires a microgravity environment. The parameters of the experiment are chosen in analogy to the thermal convective motions in the outer core of the Earth. In analogy to geophysical motions in the Earth`s liquid core the experiment can rotate as solid body as well as differential (inner to outer). Thermal convection is produced by heat- ing the inner sphere and cooling the outer ones. Furtheron, the variation of radius ratio between inner and outer sphere is foreseen as a parameter variation. The flows to be investigated will strongly depend on the gap width and on the Prandtl number.

Semiclassical gravitational effects on the gravitational lensing in the spacetime of topological defects

NASA Astrophysics Data System (ADS)

Jusufi, Kimet; Rahaman, Farook; Banerjee, Ayan

2018-02-01

The theory of gravitational lensing has revealed many generic and fundamental properties of compact objects like black holes and wormholes. In this article, we utilize a recent formulation to compute the quantum effects on the deflection angle of a light ray, namely, the Gauss-Bonnet theorem (GBT) to explore the semiclassical gravitational effects in the spacetime of a point-like global monopole and a cosmic string. Previously, the Gauss-Bonnet theorem (Gibbons and Werner, 2008) was proposed as an alternative way to compute the deflection angle of light in a static, spherically symmetric and asymptotically flat spacetime. In the present article we have used the celebrated GBT that applied to the optical metric as well as the geodesic method in computing the deflection angle. Interestingly one can observe that we have found an exact result between GBT and the standard approach up to the third-order contributions terms by modifying the domain of integration for cosmic string and global monopole deflection angles. Finally we have considered the time delay in the cosmic string/global monopole spacetime and found that the delay in time is proportional to the linear mass density of the cosmic string and global monopole parameter, respectively.

The influence of object shape and center of mass on grasp and gaze

PubMed Central

Desanghere, Loni; Marotta, Jonathan J.

2015-01-01

Recent experiments examining where participants look when grasping an object found that fixations favor the eventual index finger landing position on the object. Even though the act of picking up an object must involve complex high-level computations such as the visual analysis of object contours, surface properties, knowledge of an object’s function and center of mass (COM) location, these investigations have generally used simple symmetrical objects – where COM and horizontal midline overlap. Less research has been aimed at looking at how variations in object properties, such as differences in curvature and changes in COM location, affect visual and motor control. The purpose of this study was to examine grasp and fixation locations when grasping objects whose COM was positioned to the left or right of the objects horizontal midline (Experiment 1) and objects whose COM was moved progressively further from the midline of the objects based on the alteration of the object’s shape (Experiment 2). Results from Experiment 1 showed that object COM position influenced fixation locations and grasp locations differently, with fixations not as tightly linked to index finger grasp locations as was previously reported with symmetrical objects. Fixation positions were also found to be more central on the non-symmetrical objects. This difference in gaze position may provide a more holistic view, which would allow both index finger and thumb positions to be monitored while grasping. Finally, manipulations of COM distance (Experiment 2) exerted marked effects on the visual analysis of the objects when compared to its influence on grasp locations, with fixation locations more sensitive to these manipulations. Together, these findings demonstrate how object features differentially influence gaze vs. grasp positions during object interaction. PMID:26528207

A self-similar magnetohydrodynamic model for ball lightnings

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

Tsui, K. H.

2006-07-15

Ball lightning is modeled by magnetohydrodynamic (MHD) equations in two-dimensional spherical geometry with azimuthal symmetry. Dynamic evolutions in the radial direction are described by the self-similar evolution function y(t). The plasma pressure, mass density, and magnetic fields are solved in terms of the radial label {eta}. This model gives spherical MHD plasmoids with axisymmetric force-free magnetic field, and spherically symmetric plasma pressure and mass density, which self-consistently determine the polytropic index {gamma}. The spatially oscillating nature of the radial and meridional field structures indicate embedded regions of closed field lines. These regions are named secondary plasmoids, whereas the overall self-similarmore » spherical structure is named the primary plasmoid. According to this model, the time evolution function allows the primary plasmoid expand outward in two modes. The corresponding ejection of the embedded secondary plasmoids results in ball lightning offering an answer as how they come into being. The first is an accelerated expanding mode. This mode appears to fit plasmoids ejected from thundercloud tops with acceleration to ionosphere seen in high altitude atmospheric observations of sprites and blue jets. It also appears to account for midair high-speed ball lightning overtaking airplanes, and ground level high-speed energetic ball lightning. The second is a decelerated expanding mode, and it appears to be compatible to slowly moving ball lightning seen near ground level. The inverse of this second mode corresponds to an accelerated inward collapse, which could bring ball lightning to an end sometimes with a cracking sound.« less

View-tolerant face recognition and Hebbian learning imply mirror-symmetric neural tuning to head orientation

PubMed Central

Leibo, Joel Z.; Liao, Qianli; Freiwald, Winrich A.; Anselmi, Fabio; Poggio, Tomaso

2017-01-01

SUMMARY The primate brain contains a hierarchy of visual areas, dubbed the ventral stream, which rapidly computes object representations that are both specific for object identity and robust against identity-preserving transformations like depth-rotations [1, 2]. Current computational models of object recognition, including recent deep learning networks, generate these properties through a hierarchy of alternating selectivity-increasing filtering and tolerance-increasing pooling operations, similar to simple-complex cells operations [3, 4, 5, 6]. Here we prove that a class of hierarchical architectures and a broad set of biologically plausible learning rules generate approximate invariance to identity-preserving transformations at the top level of the processing hierarchy. However, all past models tested failed to reproduce the most salient property of an intermediate representation of a three-level face-processing hierarchy in the brain: mirror-symmetric tuning to head orientation [7]. Here we demonstrate that one specific biologically-plausible Hebb-type learning rule generates mirror-symmetric tuning to bilaterally symmetric stimuli like faces at intermediate levels of the architecture and show why it does so. Thus the tuning properties of individual cells inside the visual stream appear to result from group properties of the stimuli they encode and to reflect the learning rules that sculpted the information-processing system within which they reside. PMID:27916522

Haptic discrimination of bilateral symmetry in 2-dimensional and 3-dimensional unfamiliar displays.

PubMed

Ballesteros, S; Manga, D; Reales, J M

1997-01-01

In five experiments, we tested the accuracy and sensitivity of the haptic system in detecting bilateral symmetry of raised-line shapes (Experiments 1 and 2) and unfamiliar 3-D objects (Experiments 3-5) under different time constraints and different modes of exploration. Touch was moderately accurate for detecting this property in raised displays. Experiment 1 showed that asymmetric judgments were systematically more accurate than were symmetric judgements with scanning by one finger. Experiments 2 confirmed the results of Experiment 1 but also showed that bimanual exploration facilitated processing of symmetric shapes without improving asymmetric detections. Bimanual exploration of 3-D objects was very accurate and significantly facilitated processing of symmetric objects under different time constraints (Experiment 3). Unimanual exploration did not differ from bimanual exploration (Experiment 4), but restricting hand movements to one enclosure reduced performance significantly (Experiment 5). Spatial reference information, signal detection measures, and hand movements in processing bilateral symmetry by touch are discussed.

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.

On electromagnetic and quantum invisibility

NASA Astrophysics Data System (ADS)

Mundru, Pattabhiraju Chowdary

The principle objective of this dissertation is to investigate the fundamental properties of electromagnetic wave interactions with artificially fabricated materials i.e., metamaterials for application in advanced stealth technology called electromagnetic cloaking. The main goal is to theoretically design a metamaterial shell around an object that completely eliminates the dipolar and higher order multipolar scattering, thus making the object invisible. In this context, we developed a quasi-effective medium theory that determines the optical properties of multi-layered-composites beyond the quasi-static limit. The proposed theory exactly reproduces the far-field scattering/extinction cross sections through an iterative process in which mode-dependent quasi-effective impedances of the composite system are introduced. In the large wavelength limit, our theory is consistent with Maxwell-Garnett formalism. Possible applications in determining the hybridization particle resonances of multi-shell structures and electromagnetic cloaking are identified. This dissertation proposes a multi-shell generic cloaking system. A transparency condition independent of the object's optical and geometrical properties is proposed in the quasi-static regime of operation. The suppression of dipolar scattering is demonstrated in both cylindrically and spherically symmetric systems. A realistic tunable low-loss shell design is proposed based on the composite metal-dielectric shell. The effects due to dissipation and dispersion on the overall scattering cross-section are thoroughly evaluated. It is shown that a strong reduction of scattering by a factor of up to 103 can be achieved across the entire optical spectrum. Full wave numerical simulations for complex shaped particle are performed to validate the analytical theory. The proposed design does not require optical magnetism and is generic in the sense that it is independent of the object's material and geometrical properties. A generic quantum cloak analogous to the optical cloak is also proposed. The transparency conditions required for the shells to cloak an object impinged by a low energy beam of particles are derived. A realistic cloaking system with semiconductor material shells is studied.

Rapid Optimal SPH Particle Distributions in Spherical Geometries For Creating Astrophysical Initial Conditions

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

Raskin, Cody; Owen, J. Michael

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

Rapid Optimal SPH Particle Distributions in Spherical Geometries For Creating Astrophysical Initial Conditions

DOE PAGES

Raskin, Cody; Owen, J. Michael

2016-03-24

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

RAPID OPTIMAL SPH PARTICLE DISTRIBUTIONS IN SPHERICAL GEOMETRIES FOR CREATING ASTROPHYSICAL INITIAL CONDITIONS

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

Raskin, Cody; Owen, J. Michael

2016-04-01

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

Rough surfaces: Is the dark stuff just shadow?. ;Who knows what evil lurks in the hearts of men? The shadow knows!;☆

NASA Astrophysics Data System (ADS)

Cuzzi, Jeffrey N.; Chambers, Lindsey B.; Hendrix, Amanda R.

2017-06-01

Remote observations of the surfaces of airless planetary objects are fundamental to inferring the physical structure and compositional makeup of the surface material. A number of forward models have been developed to reproduce the photometric behavior of these surfaces, based on specific, assumed structural properties such as macroscopic roughness and associated shadowing. Most work of this type is applied to geometric albedos, which are affected by complicated effects near zero phase angle that represent only a tiny fraction of the net energy reflected by the object. Other applications include parameter fits to resolved portions of some planetary surface as viewed over a range of geometries. The spherical albedo of the entire object (when it can be determined) captures the net energy balance of the particle more robustly than the geometric albedo. In most treatments involving spherical albedos, spherical albedos and particle phase functions are often treated as if they are independent, neglecting the effects of roughness. In this paper we take a different approach. We note that whatever function captures the phase angle dependence of the brightness of a realistic rough, shadowed, flat surface element relative to that of a smooth granular surface of the same material, it is manifested directly in both the integral phase function and the spherical albedo of the object. We suggest that, where broad phase angle coverage is possible, spherical albedos may be easily corrected for the effects of shadowing using observed (or assumed) phase functions, and then modeled more robustly using smooth-surface regolith radiative transfer models without further imposed (forward-modeled) shadowing corrections. Our approach attributes observed "powerlaw" phase functions of various slope (and "linear" ranges of magnitude-vs.-phase angle) to shadowing, as have others, and goes in to suggest that regolith-model-based inferences of composition based on shadow-uncorrected spherical albedos overestimate the amount of absorbing material contained in the regolith.