Science.gov

Sample records for axisymmetric general relativistic

  1. Axisymmetric toroidal modes of general relativistic magnetized neutron star models

    SciTech Connect

    Asai, Hidetaka; Lee, Umin E-mail: lee@astr.tohoku.ac.jp

    2014-07-20

    We calculate axisymmetric toroidal modes of magnetized neutron stars with a solid crust in the general relativistic Cowling approximation. We assume that the interior of the star is threaded by a poloidal magnetic field, which is continuous at the surface with an outside dipole field. We examine the cases of the field strength B{sub S} ∼ 10{sup 16} G at the surface. Since separation of variables is not possible for the oscillations of magnetized stars, we employ finite series expansions for the perturbations using spherical harmonic functions. We find discrete normal toroidal modes of odd parity, but no toroidal modes of even parity are found. The frequencies of the toroidal modes form distinct mode sequences and the frequency in a given mode sequence gradually decreases as the number of radial nodes of the eigenfunction increases. From the frequency spectra computed for neutron stars of different masses, we find that the frequency is almost exactly proportional to B{sub S} and is well represented by a linear function of R/M for a given B{sub S}, where M and R are the mass and radius of the star. The toroidal mode frequencies for B{sub S} ∼ 10{sup 15} G are in the frequency range of the quasi-periodic oscillations (QPOs) detected in the soft-gamma-ray repeaters, but we find that the toroidal normal modes cannot explain all the detected QPO frequencies.

  2. Axisymmetric general relativistic simulations of the accretion-induced collapse of white dwarfs

    SciTech Connect

    Abdikamalov, E. B.; Ott, C. D.; Rezzolla, L.; Dessart, L.; Dimmelmeier, H.; Marek, A.; Janka, H.-T.

    2010-02-15

    The accretion-induced collapse (AIC) of a white dwarf may lead to the formation of a protoneutron star and a collapse-driven supernova explosion. This process represents a path alternative to thermonuclear disruption of accreting white dwarfs in type Ia supernovae. In the AIC scenario, the supernova explosion energy is expected to be small and the resulting transient short-lived, making it hard to detect by electromagnetic means alone. Neutrino and gravitational-wave (GW) observations may provide crucial information necessary to reveal a potential AIC. Motivated by the need for systematic predictions of the GW signature of AIC, we present results from an extensive set of general-relativistic AIC simulations using a microphysical finite-temperature equation of state and an approximate treatment of deleptonization during collapse. Investigating a set of 114 progenitor models in axisymmetric rotational equilibrium, with a wide range of rotational configurations, temperatures and central densities, and resulting white dwarf masses, we extend previous Newtonian studies and find that the GW signal has a generic shape akin to what is known as a 'type III' signal in the literature. Despite this reduction to a single type of waveform, we show that the emitted GWs carry information that can be used to constrain the progenitor and the postbounce rotation. We discuss the detectability of the emitted GWs, showing that the signal-to-noise ratio for current or next-generation interferometer detectors could be high enough to detect such events in our Galaxy. Furthermore, we contrast the GW signals of AIC and rotating massive star iron core collapse and find that they can be distinguished, but only if the distance to the source is known and a detailed reconstruction of the GW time series from detector data is possible. Some of our AIC models form massive quasi-Keplerian accretion disks after bounce. The disk mass is very sensitive to progenitor mass and angular momentum

  3. A variational principle for the axisymmetric stability of rotating relativistic stars

    NASA Astrophysics Data System (ADS)

    Prabhu, Kartik; Schiffrin, Joshua S.; Wald, Robert M.

    2016-09-01

    It is well known that all rotating perfect fluid stars in general relativity are unstable to certain non-axisymmetric perturbations via the Chandrasekhar–Friedman–Schutz (CFS) instability. However, the mechanism of the CFS instability requires, in an essential way, the loss of angular momentum by gravitational radiation and, in many instances, it acts on too long a timescale to be physically/astrophysically relevant. It is therefore of interest to examine the stability of rotating, relativistic stars to axisymmetric perturbations, where the CFS instability does not occur. In this paper, we provide a Rayleigh–Ritz-type variational principle for testing the stability of perfect fluid stars to axisymmetric perturbations, which generalizes to axisymmetric perturbations of rotating stars a variational principle given by Chandrasekhar for spherical perturbations of static, spherical stars. Our variational principle provides a lower bound to the rate of exponential growth in the case of instability. The derivation closely parallels the derivation of a recently obtained variational principle for analyzing the axisymmetric stability of black holes.

  4. Exploring Stability of General Relativistic Accretion Disks

    NASA Astrophysics Data System (ADS)

    Korobkin, Oleg; Abdikamalov, Ernazar; Schnetter, Erik; Stergioulas, Nikolaos; Zink, Burkhard

    2011-04-01

    Self-gravitating relativistic disks around black holes can form as transient structures in a number of astrophysical scenarios, involving core collapse of massive stars and mergers of compact ob jects. I will present results on our recent study of the stability of such disks against runaway and non-axisymmetric instabilities, which we explore using three-dimensional hydrodynamics simulations in full general relativity. All of our models develop unstable non-axisymmetric modes on a dynamical timescale. We observe two distinct types of instabilities: the Papaloizou-Pringle and the so-called intermediate type instabilities. The development of the non-axisymmetric mode with azimuthal number m=1 is accompanied by an outspiraling motion of the black hole, which significantly amplifies the growth rate of the m=1 mode in some cases. We will discuss the types, growth rates and pattern speeds of the unstable modes, as well as the detectability of the gravitational waves from such objects.

  5. General Relativistic and Newtonian White Dwarfs

    NASA Astrophysics Data System (ADS)

    Boshkayev, K.; Rueda, J. A.; Ruffini, R.; Siutsou, I.

    2015-01-01

    The properties of uniformly rotating white dwarfs (RWDs) are analyzed within the framework of Newton's gravity and general relativity. In both cases Hartle's formalism is applied to construct the internal and external solutions to the field equations. The white dwarf (WD) matter is described by the Chandrasekhar equation of state. The region of stability of RWDs is constructed taking into account the mass-shedding limit, inverse β-decay instability, and the boundary established by the turning points of constant angular momentum J sequences which separates stable from secularly unstable configurations. We found the minimum rotation period ˜ 0.28 s in both cases and maximum rotating masses ˜ 1.534M⊙ and ˜ 1.516M⊙ for the Newtonian and general relativistic WDs, respectively. By using the turning point method we show that general relativistic WDs can indeed be axisymmetrically unstable whereas the Newtonian WDs are stable.

  6. Axisymmetric rotating relativistic bodies: A new numerical approach for 'exact' solutions

    NASA Astrophysics Data System (ADS)

    Bonazzola, S.; Gourgoulhon, E.; Salgado, M.; Marck, J. A.

    1993-11-01

    A new set of equations and a new numerical method for computing stationary axisymmetric rapidly rotating star models within general relativity is presented. The source term of the gravitational field is not restricted to a perfect fluid one but represents the most general one, including anisotropic stresses, permitted under the assumptions of stationarity, axisymmetry and absence of meridional currents. This allows us to derive the equations governing the equilibrium of rotating neutron stars with strong magnetic fields in a self-consistent and fully relativistic way. As regards to the numerics, the improvement lies in the exact computation of the metric in the whole space outside the star, thanks to a numerial grid which extends to infinity (due to a suitable compactification of the space external to the star). The numerical integration is performed by means of an iterative procedure based on a spectral method, which provides results far more precise than previous methods, with 'evanescent' numerical errors. The code efficiency is demonstrated by considering a simple polytropic equation of state, this paper being not intended to present new astrophysical results but the equations governing more general objects than previously considered (for instance magnetized neutron stars) and the numerical method to integrate them. In that spirit, a particular emphasis is given to the evaluation of the numerical errors. A certain integral quantity is shown to be a very good indicator of the discrepancy between the numerical solution and the exact one.

  7. On General Relativistic Uniformly Rotating White Dwarfs

    NASA Astrophysics Data System (ADS)

    Boshkayev, Kuantay; Rueda, Jorge A.; Ruffini, Remo; Siutsou, Ivan

    2013-01-01

    The properties of uniformly rotating white dwarfs (RWDs) are analyzed within the framework of general relativity. Hartle's formalism is applied to construct the internal and external solutions to the Einstein equations. The white dwarf (WD) matter is described by the relativistic Feynman-Metropolis-Teller equation of state which generalizes that of Salpeter by taking into account the finite size of the nuclei, and the Coulomb interactions as well as electroweak equilibrium in a self-consistent relativistic fashion. The mass M, radius R, angular momentum J, eccentricity epsilon, and quadrupole moment Q of RWDs are calculated as a function of the central density ρ c and rotation angular velocity Ω. We construct the region of stability of RWDs (J-M plane) taking into account the mass-shedding limit, inverse β-decay instability, and the boundary established by the turning points of constant J sequences which separates stable from secularly unstable configurations. We found the minimum rotation periods ~0.3, 0.5, 0.7, and 2.2 s and maximum masses ~1.500, 1.474, 1.467, 1.202 M ⊙ for 4He, 12C, 16O, and 56Fe WDs, respectively. By using the turning-point method, we found that RWDs can indeed be axisymmetrically unstable and we give the range of WD parameters where this occurs. We also construct constant rest-mass evolution tracks of RWDs at fixed chemical composition and show that, by losing angular momentum, sub-Chandrasekhar RWDs (mass smaller than maximum static one) can experience both spin-up and spin-down epochs depending on their initial mass and rotation period, while super-Chandrasekhar RWDs (mass larger than maximum static one) only spin up.

  8. ON GENERAL RELATIVISTIC UNIFORMLY ROTATING WHITE DWARFS

    SciTech Connect

    Boshkayev, Kuantay; Rueda, Jorge A.; Ruffini, Remo; Siutsou, Ivan E-mail: jorge.rueda@icra.it E-mail: siutsou@icranet.org

    2013-01-10

    The properties of uniformly rotating white dwarfs (RWDs) are analyzed within the framework of general relativity. Hartle's formalism is applied to construct the internal and external solutions to the Einstein equations. The white dwarf (WD) matter is described by the relativistic Feynman-Metropolis-Teller equation of state which generalizes that of Salpeter by taking into account the finite size of the nuclei, and the Coulomb interactions as well as electroweak equilibrium in a self-consistent relativistic fashion. The mass M, radius R, angular momentum J, eccentricity {epsilon}, and quadrupole moment Q of RWDs are calculated as a function of the central density {rho} {sub c} and rotation angular velocity {Omega}. We construct the region of stability of RWDs (J-M plane) taking into account the mass-shedding limit, inverse {beta}-decay instability, and the boundary established by the turning points of constant J sequences which separates stable from secularly unstable configurations. We found the minimum rotation periods {approx}0.3, 0.5, 0.7, and 2.2 s and maximum masses {approx}1.500, 1.474, 1.467, 1.202 M {sub Sun} for {sup 4}He, {sup 12}C, {sup 16}O, and {sup 56}Fe WDs, respectively. By using the turning-point method, we found that RWDs can indeed be axisymmetrically unstable and we give the range of WD parameters where this occurs. We also construct constant rest-mass evolution tracks of RWDs at fixed chemical composition and show that, by losing angular momentum, sub-Chandrasekhar RWDs (mass smaller than maximum static one) can experience both spin-up and spin-down epochs depending on their initial mass and rotation period, while super-Chandrasekhar RWDs (mass larger than maximum static one) only spin up.

  9. Stability of general-relativistic accretion disks

    NASA Astrophysics Data System (ADS)

    Korobkin, Oleg; Abdikamalov, Ernazar B.; Schnetter, Erik; Stergioulas, Nikolaos; Zink, Burkhard

    2011-02-01

    Self-gravitating relativistic disks around black holes can form as transient structures in a number of astrophysical scenarios such as binary neutron star and black hole-neutron star coalescences, as well as the core collapse of massive stars. We explore the stability of such disks against runaway and nonaxisymmetric instabilities using three-dimensional hydrodynamics simulations in full general relativity using the Thor code. We model the disk matter using the ideal fluid approximation with a Γ-law equation of state with Γ=4/3. We explore three disk models around nonrotating black holes with disk-to-black hole mass ratios of 0.24, 0.17, and 0.11. Because of metric blending in our initial data, all of our initial models contain an initial axisymmetric perturbation which induces radial disk oscillations. Despite these oscillations, our models do not develop the runaway instability during the first several orbital periods. Instead, all of the models develop unstable nonaxisymmetric modes on a dynamical time scale. We observe two distinct types of instabilities: the Papaloizou-Pringle and the so-called intermediate type instabilities. The development of the nonaxisymmetric mode with azimuthal number m=1 is accompanied by an outspiraling motion of the black hole, which significantly amplifies the growth rate of the m=1 mode in some cases. Overall, our simulations show that the properties of the unstable nonaxisymmetric modes in our disk models are qualitatively similar to those in the Newtonian theory.

  10. Stability of general-relativistic accretion disks

    SciTech Connect

    Korobkin, Oleg; Abdikamalov, Ernazar B.; Schnetter, Erik; Stergioulas, Nikolaos; Zink, Burkhard

    2011-02-15

    Self-gravitating relativistic disks around black holes can form as transient structures in a number of astrophysical scenarios such as binary neutron star and black hole-neutron star coalescences, as well as the core collapse of massive stars. We explore the stability of such disks against runaway and nonaxisymmetric instabilities using three-dimensional hydrodynamics simulations in full general relativity using the Thor code. We model the disk matter using the ideal fluid approximation with a {Gamma}-law equation of state with {Gamma}=4/3. We explore three disk models around nonrotating black holes with disk-to-black hole mass ratios of 0.24, 0.17, and 0.11. Because of metric blending in our initial data, all of our initial models contain an initial axisymmetric perturbation which induces radial disk oscillations. Despite these oscillations, our models do not develop the runaway instability during the first several orbital periods. Instead, all of the models develop unstable nonaxisymmetric modes on a dynamical time scale. We observe two distinct types of instabilities: the Papaloizou-Pringle and the so-called intermediate type instabilities. The development of the nonaxisymmetric mode with azimuthal number m=1 is accompanied by an outspiraling motion of the black hole, which significantly amplifies the growth rate of the m=1 mode in some cases. Overall, our simulations show that the properties of the unstable nonaxisymmetric modes in our disk models are qualitatively similar to those in the Newtonian theory.

  11. Generalized energy principle for flute perturbations in axisymmetric mirror machines

    SciTech Connect

    Lansky, I.M.; Ryutov, D.D.

    1993-01-20

    Axial symmetry is a very desirable property of the mirror devices both for fusion and neutron source applications. The main obstacle to be circumvented in the development of such systems, is the flute instability of axisymmetric mirrors. In recent years there appeared a number of proposals, devoted to the stabilization of the flute perturbations in the framework of axisymmetric magnetic configurations, which are based on the combining of the MHD unstable central cell with various types of end-cell stabilizers. In the present paper we concentrate ourselves just on this scheme, including long solenoid with a uniform field, conjugated with the end stabilizing anchor, intended to provide MHD stability of the system as a whole. The attractive feature of such a configuration is that it allows to exploit finite larmor radius (FLR) effects for the stabilization of the flute perturbations. As is well known, FLR effects, being strong, stabilize all flute modes, except the one with azimuthal number m = 1, corresponding to the ``rigid`` displacement of the plasma column (the ``global`` mode). Consequently, in the conditions when FLR effects dominate, the anchor has to stabilize the ``global` mode only. Bearing in mind a favorable influence of FLR effects we, however, don`t restrict our paper by discussion of only ``global`` mode stability and consider a general case of an arbitrary azimuthal mode.

  12. CoCoNuT: General relativistic hydrodynamics code with dynamical space-time evolution

    NASA Astrophysics Data System (ADS)

    Dimmelmeier, Harald; Novak, Jérôme; Cerdá-Durán, Pablo

    2012-02-01

    CoCoNuT is a general relativistic hydrodynamics code with dynamical space-time evolution. The main aim of this numerical code is the study of several astrophysical scenarios in which general relativity can play an important role, namely the collapse of rapidly rotating stellar cores and the evolution of isolated neutron stars. The code has two flavors: CoCoA, the axisymmetric (2D) magnetized version, and CoCoNuT, the 3D non-magnetized version.

  13. Generalized magnetofluid connections in relativistic magnetohydrodynamics.

    PubMed

    Asenjo, Felipe A; Comisso, Luca

    2015-03-20

    The concept of magnetic connections is extended to nonideal relativistic magnetohydrodynamical plasmas. Adopting a general set of equations for relativistic magnetohydrodynamics including thermal-inertial, thermal electromotive, Hall, and current-inertia effects, we derive a new covariant connection equation showing the existence of generalized magnetofluid connections that are preserved during the dissipationless plasma dynamics. These connections are intimately linked to a general antisymmetric tensor that unifies the electromagnetic and fluid fields, allowing the extension of the magnetic connection notion to a much broader concept. PMID:25839284

  14. Newtonian hydrodynamics with general relativistic pressure

    SciTech Connect

    Hwang, Jai-chan; Noh, Hyerim E-mail: hr@kasi.re.kr

    2013-10-01

    We present the general relativistic pressure correction terms in Newtonian hydrodynamic equations to the nonlinear order: these are equations (1.1)–(1.3). The derivation is made in the zero-shear gauge based on the fully nonlinear formulation of cosmological perturbation in Einstein's gravity. The correction terms differ from many of the previously suggested forms in the literature based on hand-waving manners. We confirm our results by comparing with (i) the nonlinear perturbation theory, (ii) the first order post-Newtonian approximation, and (iii) the special relativistic limit, and by checking (iv) the consistency with full Einstein's equation.

  15. General relativistic effects in atom interferometry

    SciTech Connect

    Dimopoulos, Savas; Hogan, Jason M.; Kasevich, Mark A.; Graham, Peter W.

    2008-08-15

    Atom interferometry is now reaching sufficient precision to motivate laboratory tests of general relativity. We begin by explaining the nonrelativistic calculation of the phase shift in an atom interferometer and deriving its range of validity. From this, we develop a method for calculating the phase shift in general relativity. Both the atoms and the light are treated relativistically and all coordinate dependencies are removed, thus revealing novel terms, cancellations, and new origins for previously calculated terms. This formalism is then used to find the relativistic effects in an atom interferometer in a weak gravitational field for application to laboratory tests of general relativity. The potentially testable relativistic effects include the nonlinear three-graviton coupling, the gravity of kinetic energy, and the falling of light. We propose specific experiments, one currently under construction, to measure each of these effects. These experiments could provide a test of the principle of equivalence to 1 part in 10{sup 15} (300 times better than the present limit), and general relativity at the 10% level, with many potential future improvements. We also consider applications to other metrics including the Lense-Thirring effect, the expansion of the Universe, and preferred frame and location effects.

  16. General Relativistic Effects in Atom Interferometry

    SciTech Connect

    Dimopoulos, Savas; Graham, Peter W.; Hogan, Jason M.; Kasevich, Mark A.; /Stanford U., Phys. Dept.

    2008-03-17

    Atom interferometry is now reaching sufficient precision to motivate laboratory tests of general relativity. We begin by explaining the non-relativistic calculation of the phase shift in an atom interferometer and deriving its range of validity. From this we develop a method for calculating the phase shift in general relativity. This formalism is then used to find the relativistic effects in an atom interferometer in a weak gravitational field for application to laboratory tests of general relativity. The potentially testable relativistic effects include the non-linear three-graviton coupling, the gravity of kinetic energy, and the falling of light. We propose experiments, one currently under construction, that could provide a test of the principle of equivalence to 1 part in 10{sup 15} (300 times better than the present limit), and general relativity at the 10% level, with many potential future improvements. We also consider applications to other metrics including the Lense-Thirring effect, the expansion of the universe, and preferred frame and location effects.

  17. Spectral Methods in General Relativistic MHD Simulations

    NASA Astrophysics Data System (ADS)

    Garrison, David

    2012-03-01

    In this talk I discuss the use of spectral methods in improving the accuracy of a General Relativistic Magnetohydrodynamic (GRMHD) computer code. I introduce SpecCosmo, a GRMHD code developed as a Cactus arrangement at UHCL, and show simulation results using both Fourier spectral methods and finite differencing. This work demonstrates the use of spectral methods with the FFTW 3.3 Fast Fourier Transform package integrated with the Cactus Framework to perform spectral differencing using MPI.

  18. Diffusion processes in general relativistic radiating spheres

    SciTech Connect

    Barreto, W.; Herrera, L.; Santos, N.O.; Universidad Central de Venezuela, Caracas; Observatorio Nacional do Brasil, Rio de Janeiro )

    1989-09-01

    The influence of diffusion processes on the dynamics of general relativistic radiating spheres is systematically studied by means of two examples. Differences between the streaming-out limit and the diffusion limit are exhibited, for both models, through the evolution curves of dynamical variables. In particular it is shown the Bondi mass decreases, for both models, in the diffusion limit as compared with its value at the streaming-out regime. 15 refs.

  19. Multipatch methods in general relativistic astrophysics: Hydrodynamical flows on fixed backgrounds

    SciTech Connect

    Zink, Burkhard; Schnetter, Erik; Tiglio, Manuel

    2008-05-15

    Many systems of interest in general relativistic astrophysics, including neutron stars, accreting compact objects in x-ray binaries and active galactic nuclei, core collapse, and collapsars, are assumed to be approximately spherically symmetric or axisymmetric. In Newtonian or fixed-background relativistic approximations it is common practice to use spherical polar coordinates for computational grids; however, these coordinates have singularities and are difficult to use in fully relativistic models. We present, in this series of papers, a numerical technique which is able to use effectively spherical grids by employing multiple patches. We provide detailed instructions on how to implement such a scheme, and present a number of code tests for the fixed-background case, including an accretion torus around a black hole.

  20. General-relativistic astrophysics. [gravitational wave astronomy

    NASA Technical Reports Server (NTRS)

    Thorne, K. S.

    1978-01-01

    The overall relevance of general relativity to astrophysics is considered, and some of the knowledge about the ways in which general relativity should influence astrophysical systems is reviewed. Attention is focused primarily on finite-sized astrophysical systems, such as stars, globular clusters, galactic nuclei, and primordial black holes. Stages in the evolution of such systems and tools for studying the effects of relativistic gravity in these systems are examined. Gravitational-wave astronomy is discussed in detail, with emphasis placed on estimates of the strongest gravitational waves that bathe earth, present obstacles and future prospects for detection of the predicted waves, the theory of small perturbations of relativistic stars and black holes, and the gravitational waves such objects generate. Characteristics of waves produced by black-hole events in general, pregalactic black-hole events, black-hole events in galactic nuclei and quasars, black-hole events in globular clusters, the collapse of normal stars to form black holes or neutron stars, and corequakes in neutron stars are analyzed. The state of the art in gravitational-wave detection and characteristics of various types of detector are described.

  1. A General Relativistic Magnetohydrodynamic Simulation of Jet Formation

    NASA Astrophysics Data System (ADS)

    Nishikawa, K.-I.; Richardson, G.; Koide, S.; Shibata, K.; Kudoh, T.; Hardee, P.; Fishman, G. J.

    2005-05-01

    We have performed a fully three-dimensional general relativistic magnetohydrodynamic (GRMHD) simulation of jet formation from a thin accretion disk around a Schwarzschild black hole with a free-falling corona. The initial simulation results show that a bipolar jet (velocity ~0.3c) is created, as shown by previous two-dimensional axisymmetric simulations with mirror symmetry at the equator. The three-dimensional simulation ran over 100 light crossing time units (τS=rS/c, where rS≡2GM/c2), which is considerably longer than the previous simulations. We show that the jet is initially formed as predicted owing in part to magnetic pressure from the twisting of the initially uniform magnetic field and from gas pressure associated with shock formation in the region around r=3rS. At later times, the accretion disk becomes thick and the jet fades resulting in a wind that is ejected from the surface of the thickened (torus-like) disk. It should be noted that no streaming matter from a donor is included at the outer boundary in the simulation (an isolated black hole not binary black hole). The wind flows outward with a wider angle than the initial jet. The widening of the jet is consistent with the outward-moving torsional Alfvén waves. This evolution of disk-jet coupling suggests that the jet fades with a thickened accretion disk because of the lack of streaming material from an accompanying star.

  2. A general relativistic model for free-fall absolute gravimeters

    NASA Astrophysics Data System (ADS)

    Tan, Yu-Jie; Shao, Cheng-Gang; Li, Jia; Hu, Zhong-Kun

    2016-04-01

    Although the relativistic manifestations of gravitational fields in gravimetry were first studied 40 years ago, the relativistic effects combined with free-fall absolute gravimeters have rarely been considered. In light of this, we present a general relativistic model for free-fall absolute gravimeters in a local-Fermi coordinates system, where we focus on effects related to the measuring devices: relativistic transverse Doppler effects, gravitational redshift effects and Earth’s rotation effects. Based on this model, a general relativistic expression of the measured gravity acceleration is obtained.

  3. The Exact Solution for Linear Thermoelastic Axisymmetric Deformations of Generally Laminated Circular Cylindrical Shells

    NASA Technical Reports Server (NTRS)

    Nemeth, Michael P.; Schultz, Marc R.

    2012-01-01

    A detailed exact solution is presented for laminated-composite circular cylinders with general wall construction and that undergo axisymmetric deformations. The overall solution is formulated in a general, systematic way and is based on the solution of a single fourth-order, nonhomogeneous ordinary differential equation with constant coefficients in which the radial displacement is the dependent variable. Moreover, the effects of general anisotropy are included and positive-definiteness of the strain energy is used to define uniquely the form of the basis functions spanning the solution space of the ordinary differential equation. Loading conditions are considered that include axisymmetric edge loads, surface tractions, and temperature fields. Likewise, all possible axisymmetric boundary conditions are considered. Results are presented for five examples that demonstrate a wide range of behavior for specially orthotropic and fully anisotropic cylinders.

  4. Improving general relativistic astrophysics workflows with ADIOS

    NASA Astrophysics Data System (ADS)

    Bode, Tanja; Slawinska, Magdalena; Logan, Jeremy; Clark, Michael; Kinsey, Matthew; Wolf, Matthew; Klasky, Scott; Laguna, Pablo

    2013-04-01

    There are many challenges in analyzing and visualizing data from current cutting-edge general relativistic astrophysics simulations. Many of the associated tasks are time-consuming, with large performance degradation due to the magnitude and complexity of the data. The Adaptable IO System (ADIOS) is a componentization of the IO layer that has demonstrated remarkable IO performance improvements on applications running on leadership class machines while also offering new in-memory ``staging'' operations for transforming data in situ. We have incorporated ADIOS staging technologies into our Maya numerical relativity code based on Cactus infrastructure and Carpet mesh refinement. We present results that demonstrate how ADIOS yields significant gains on IO performance while utilizing leveraged investments in ADIOS plugins for visualization tools such as VisIt.

  5. General Relativistic Magnetohydrodynamic Simulations of Collapsars

    NASA Technical Reports Server (NTRS)

    Mizuno, Yosuke; Yamada, S.; Koider, S.; Shipata, K.

    2005-01-01

    We have performed 2.5-dimensional general relativistic magnetohydrodynamic (MHD) simulations of collapsars including a rotating black hole. Initially, we assume that the core collapse has failed in this star. A rotating black hole of a few solar masses is inserted by hand into the calculation. The simulation results show the formation of a disklike structure and the generation of a jetlike outflow near the central black hole. The jetlike outflow propagates and accelerated mainly by the magnetic field. The total jet velocity is approximately 0.3c. When the rotation of the black hole is faster, the magnetic field is twisted strongly owing to the frame-dragging effect. The magnetic energy stored by the twisting magnetic field is directly converted to kinetic energy of the jet rather than propagating as an Alfven wave. Thus, as the rotation of the black hole becomes faster, the poloidal velocity of the jet becomes faster.

  6. User's manual for Axisymmetric Diffuser Duct (ADD) code. Volume 1: General ADD code description

    NASA Technical Reports Server (NTRS)

    Anderson, O. L.; Hankins, G. B., Jr.; Edwards, D. E.

    1982-01-01

    This User's Manual contains a complete description of the computer codes known as the AXISYMMETRIC DIFFUSER DUCT code or ADD code. It includes a list of references which describe the formulation of the ADD code and comparisons of calculation with experimental flows. The input/output and general use of the code is described in the first volume. The second volume contains a detailed description of the code including the global structure of the code, list of FORTRAN variables, and descriptions of the subroutines. The third volume contains a detailed description of the CODUCT code which generates coordinate systems for arbitrary axisymmetric ducts.

  7. Oscillations of general relativistic superfluid neutron stars

    NASA Astrophysics Data System (ADS)

    Andersson, N.; Comer, G. L.; Langlois, D.

    2002-11-01

    We develop a general formalism to treat, in general relativity, the nonradial oscillations of a superfluid neutron star about static (non-rotating) configurations. The matter content of these stars can, as a first approximation, be described by a two-fluid model: one fluid is the neutron superfluid, which is believed to exist in the core and inner crust of mature neutron stars; the other fluid is a conglomerate of all charged constituents (crust nuclei, protons, electrons, etc.). We use a system of equations that governs the perturbations both of the metric and of the matter variables, whatever the equation of state for the two fluids. The entrainment effect is explicitly included. We also take the first step towards allowing for the superfluid to be confined to a part of the star by allowing for an outer envelope composed of ordinary fluid. We derive and implement the junction conditions for the metric and matter variables at the core-envelope interface, and briefly discuss the nature of the involved phase transition. We then determine the frequencies and gravitational-wave damping times for a simple model equation of state, incorporating entrainment through an approximation scheme which extends present Newtonian results to the general relativistic regime. We investigate how the quasinormal modes of a superfluid star are affected by changes in the entrainment parameter, and unveil a series of avoided crossings between the various modes. We provide a proof that, unless the equation of state is very special, all modes of a two-fluid star must radiate gravitationally. We also discuss the future detectability of pulsations in a superfluid star and argue that it may be possible (given advances in the relevant technology) to use gravitational-wave data to constrain the parameters of superfluid neutron stars.

  8. A generalized twistor dynamics of relativistic particles and strings

    SciTech Connect

    Soroka, V.A.; Sorokin, D.P.; Tkach, V.I.; Volkov, D.V. )

    1992-09-30

    In this paper, a generalization of relativistic particle and sting dynamics based on a notion of twistor shift and containing a fundamental length constant is considered, which results in a modification of particle (or string) interactions with background fields.

  9. Fully relativistic multiple scattering calculations for general potentials

    NASA Astrophysics Data System (ADS)

    Ebert, H.; Braun, J.; Ködderitzsch, D.; Mankovsky, S.

    2016-02-01

    The formal basis for fully relativistic Korringa-Kohn-Rostoker (KKR) or multiple scattering calculations for the electronic Green function in case of a general potential is discussed. Simple criteria are given to identify situations that require to distinguish between right- and left-hand-side solutions to the Dirac equation when setting up the electronic Green function. In addition, various technical aspects of an implementation of the relativistic KKR for general local and nonlocal potentials will be discussed.

  10. Non-axisymmetric relativistic wind accretion with velocity gradients on to a rotating black hole

    NASA Astrophysics Data System (ADS)

    Cruz-Osorio, A.; Lora-Clavijo, F. D.

    2016-08-01

    We model, for the first time, the Bondi-Hoyle accretion of a fluid with velocity gradients on to a Kerr black hole, by numerically solving the fully relativistic hydrodynamics equations. Specifically, we consider a supersonic ideal gas, which has velocity gradients perpendicular to the relative motion. We measure the mass and specific angular accretion rates to illustrate whether the fluid presents unstable patterns or not. The initial parameters, we consider in this work, are the velocity gradient ɛv, the black hole spin a, the asymptotic Mach number M_{∞} and adiabatic index Γ. We show that the flow accretion reaches a fairly stationary regime, unlike in the Newtonian case, where significant fluctuations of the mass and angular momentum accretion rates are found. On the other hand, we consider a special case where both density and velocity gradients of the fluid are taken into account. The spin of the black hole and the asymptotic Newtonian Mach number, for this case, are a = 0.98 and M_{∞}=1, respectively. A kind of flip-flop behaviour is found at the early times; nevertheless, the system also reaches a steady state.

  11. Non-axisymmetric relativistic wind accretion with velocity gradients on to a rotating black hole

    NASA Astrophysics Data System (ADS)

    Cruz-Osorio, A.; Lora-Clavijo, F. D.

    2016-08-01

    We model, for the first time, the Bondi-Hoyle accretion of a fluid with velocity gradients onto a Kerr black hole, by numerically solving the fully relativistic hydrodynamics equations. Specifically, we consider a supersonic ideal gas, which has velocity gradients perpendicular to the relative motion. We measure the mass and specific angular accretion rates to illustrate whether the fluid presents unstable patterns or not. The initial parameters, we consider in this work, are the velocity gradient $\\epsilon_{v}$, the black hole spin $a$, the asymptotic Mach number ${\\cal M}_{\\infty}$ and adiabatic index $\\Gamma$. We show that the flow accretion reaches a fairly stationary regime, unlike in the Newtonian case, where significant fluctuations of the mass and angular momentum accretion rates are found. On the other hand, we consider a special case where both density and velocity gradients of the fluid are taken into account. The spin of the black hole and the asymptotic Newtonian Mach number, for this case, are $a=0.98$ and ${\\cal M}_{\\infty}=1$, respectively. A kind of flip-flop behavior is found at the early times; nevertheless, the system also reaches a steady state.

  12. General relativistic observables for the ACES experiment

    NASA Astrophysics Data System (ADS)

    Turyshev, Slava G.; Yu, Nan; Toth, Viktor T.

    2016-02-01

    We develop a high-precision model for relativistic observables of the Atomic Clock Ensemble in Space (ACES) experiment on the International Space Station (ISS). We develop all relativistic coordinate transformations that are needed to describe the motion of ACES in Earth orbit and to compute observable quantities. We analyze the accuracy of the required model as it applies to the proper-to-coordinate time transformations, light-time equation, and spacecraft equations of motion. We consider various sources of nongravitational noise and their effects on ACES. We estimate the accuracy of orbit reconstruction that is needed to satisfy the ACES science objectives. Based on our analysis, we derive models for the relativistic observables of ACES, which also account for the contribution of atmospheric drag on the clock rate. We include the Earth's oblateness coefficient J2 and the effects of major nongravitational forces on the orbit of the ISS. We demonstrate that the ACES reference frame is pseudoinertial at the level of accuracy required by the experiment. We construct a Doppler-canceled science observable representing the gravitational redshift. We derive accuracy requirements for ISS navigation. The improved model is accurate up to <1 ps and ˜4 ×1 0-17 for time and frequency transfers, correspondingly. These limits are determined by the higher-order harmonics in Earth's gravitational potential.

  13. Cosmological measurements with general relativistic galaxy correlations

    NASA Astrophysics Data System (ADS)

    Raccanelli, Alvise; Montanari, Francesco; Bertacca, Daniele; Doré, Olivier; Durrer, Ruth

    2016-05-01

    We investigate the cosmological dependence and the constraining power of large-scale galaxy correlations, including all redshift-distortions, wide-angle, lensing and gravitational potential effects on linear scales. We analyze the cosmological information present in the lensing convergence and in the gravitational potential terms describing the so-called ``relativistic effects'', and we find that, while smaller than the information contained in intrinsic galaxy clustering, it is not negligible. We investigate how neglecting them does bias cosmological measurements performed by future spectroscopic and photometric large-scale surveys such as SKA and Euclid. We perform a Fisher analysis using the CLASS code, modified to include scale-dependent galaxy bias and redshift-dependent magnification and evolution bias. Our results show that neglecting relativistic terms, especially lensing convergence, introduces an error in the forecasted precision in measuring cosmological parameters of the order of a few tens of percent, in particular when measuring the matter content of the Universe and primordial non-Gaussianity parameters. The analysis suggests a possible substantial systematic error in cosmological parameter constraints. Therefore, we argue that radial correlations and integrated relativistic terms need to be taken into account when forecasting the constraining power of future large-scale number counts of galaxy surveys.

  14. A generalized orthogonal coordinate system for describing families of axisymmetric and two-dimensional bodies

    NASA Technical Reports Server (NTRS)

    Gnoffo, P. A.

    1977-01-01

    A generalized curvilinear orthogonal coordinate system is presented which can be used for approximating various axisymmetric and two-dimensional body shapes of interest to aerodynamicists. Such body shapes include spheres, ellipses, spherically capped cones, flat-faced cylinders with rounded corners, circular disks, and planetary probe vehicles. A set of transformation equations is also developed whereby a uniform velocity field approaching a body at any angle of attack can be resolved in the transformed coordinate system. The Navier-Stokes equations are written in terms of a generalized orthogonal coordinate system to show the resultant complexity of the governing equations.

  15. An axisymmetric charged dust distribution with NUT rotation in general relativity

    NASA Astrophysics Data System (ADS)

    Vargas-Rodriguez, H.; Gonzalez-Silva, R. A.; Lopez Benitez, L. I.

    2010-07-01

    An exact solution of the Einstein-Maxwell's field equations is presented. This solution describes an axisymmetric charged dust distribution, with NUT rotation, in the presence of an electromagnetic field of the pure magnetic type. In the comoving reference frame, there is magnetic field only, the dust's electric charges do not interact with themselves, this is due to the vanishing of the Lorentz force. A naked singularity with magnetic charge is present. The solution is of the Petrov type D and possesses four Killing vectors. This is a generalization of the Lukács solution to the case when dust is charged.

  16. General-relativistic rotation laws in rotating fluid bodies

    NASA Astrophysics Data System (ADS)

    Mach, Patryk; Malec, Edward

    2015-06-01

    We formulate new general-relativistic extensions of Newtonian rotation laws for self-gravitating stationary fluids. They have been used to rederive, in the first post-Newtonian approximation, the well-known geometric dragging of frames. We derive two other general-relativistic weak-field effects within rotating tori: the recently discovered dynamic antidragging and a new effect that measures the deviation from the Keplerian motion and/or the contribution of the fluids self-gravity. One can use the rotation laws to study the uniqueness and the convergence of the post-Newtonian approximations as well as the existence of the post-Newtonian limits.

  17. Computational cosmology: A general relativistic approach

    NASA Astrophysics Data System (ADS)

    Matarrese, Sabino

    2016-04-01

    The quality and quantity of current and forthcoming cosmological datasets call for both analytical and numerical modelling of the dynamics of nonlinear gravitational matter based on general relativity.

  18. General Relativistic Radiative Transfer and GeneralRelativistic MHD Simulations of Accretion and Outflows of Black Holes

    SciTech Connect

    Fuerst, Steven V.; Mizuno, Yosuke; Nishikawa, Ken-Ichi; Wu, Kinwah; /Mullard Space Sci. Lab.

    2007-01-05

    We calculate the emission from relativistic flows in black hole systems using a fully general relativistic radiative transfer formulation, with flow structures obtained by general relativistic magneto-hydrodynamic simulations. We consider thermal free-free emission and thermal synchrotron emission. Bright filament-like features protrude (visually) from the accretion disk surface, which are enhancements of synchrotron emission where the magnetic field roughly aligns with the line-of-sight in the co-moving frame. The features move back and forth as the accretion flow evolves, but their visibility and morphology are robust. We propose that variations and drifts of the features produce certain X-ray quasi-periodic oscillations (QPOs) observed in black-hole X-ray binaries.

  19. General relativistic magneto-hydrodynamics with the Einstein Toolkit

    NASA Astrophysics Data System (ADS)

    Moesta, Philipp; Mundim, Bruno; Faber, Joshua; Noble, Scott; Bode, Tanja; Haas, Roland; Loeffler, Frank; Ott, Christian; Reisswig, Christian; Schnetter, Erik

    2013-04-01

    The Einstein Toolkit Consortium is developing and supporting open software for relativistic astrophysics. Its aim is to provide the core computational tools that can enable new science, broaden our community, facilitate interdisciplinary research and take advantage of petascale computers and advanced cyberinfrastructure. The Einstein Toolkit currently consists of an open set of over 100 modules for the Cactus framework, primarily for computational relativity along with associated tools for simulation management and visualization. The toolkit includes solvers for vacuum spacetimes as well as relativistic magneto-hydrodynamics. This talk will present the current capabilities of the Einstein Toolkit with a particular focus on recent improvements made to the general relativistic magneto-hydrodynamics modeling and will point to information how to leverage it for future research.

  20. Causal structure of general relativistic spacetimes

    SciTech Connect

    Howard, Ecaterina

    2010-06-15

    We present some of the recent results and open questions on the causality problem in General Relativity. The concept of singularity is intimately connected with future trapped surface and inner event horizon formation. We offer a brief overview of the Hawking-Penrose singularity theorems and discuss a few open problems concerning the future Cauchy development (domain of dependence), break-down criteria and energy conditions for the horizon stability. A key question is whether causality violating regions, generating a Cauchy horizon are allowed.We raise several questions concerning the invisibility and stability of closed trapped surfaces from future null infinity and derive the imprisonment conditions. We provide an up-to-date perspective of the causal boundaries and spacelike conformal boundary extensions for time oriented Lorentzian manifolds and more exotic settings.

  1. Neoclassical transport coefficients for general axisymmetric equilibria in the banana regime

    NASA Astrophysics Data System (ADS)

    Angioni, C.; Sauter, O.

    2000-04-01

    Using the standard approach of neoclassical theory, a set of relatively simple kinetic equations has been obtained, suited for an implementation in a numerical code to compute a related set of distribution functions. The transport coefficients are then expressed by simple integrals of these functions and they can be easily computed numerically. The code CQL3D [R. W. Harvey and M. G. McCoy, in Proceedings of IAEA Technical Committee Meeting on Advances in Simulation and Modeling of Thermonuclear Plasmas, Montreal, 1992 (International Atomic Energy Agency, Vienna, 1993), pp. 489-526], which uses the full collision operator and considers the realistic axisymmetric configuration of the magnetic surfaces, has been modified to solve the bounce-averaged version of these equations. The coefficients have then been computed for a wide variety of equilibrium parameters, high-lighting interesting features of the influence of geometry at small aspect ratio. Differences with the most recent formulas for the ion neoclassical heat conductivity are pointed out. A set of formulas, which fit the code results, is obtained to easily evaluate all the neoclassical transport coefficients in the banana regime, at all aspect ratios, in general axisymmetric equilibria. This work extends to all the other transport coefficients, at least in the banana regime, the work of Sauter et al. [O. Sauter, C. Angioni, and Y. R. Lin-Liu, Phys. Plasmas 6, 2834 (1999)] which evaluates the neoclassical conductivity and all the bootstrap current coefficients. Formulas for arbitrary collisionality regime are proposed, obtained combining our results for the banana regime with the results of Hinton and Hazeltine [F. L. Hinton and R. D. Hazeltine, Rev. Mod. Phys. 48, 239 (1976)], adapted for small aspect ratio.

  2. General Relativistic Radiative Transfer: Applications to Black-Hole Systems

    NASA Technical Reports Server (NTRS)

    Wu, Kinwah; Fuerst, Steven V.; Mizuno, Yosuke; Nishikawa, Ken-Ichi; Branduardi-Raymont, Graziella; Lee, Khee-Gan

    2007-01-01

    We present general relativistic radiation transfer formulations which include opacity effects due to absorption, emission and scattering explicitly. We consider a moment expansions for the transfer in the presence of scattering. The formulation is applied to calculation emissions from accretion and outflows in black-hole systems. Cases with thin accretion disks and accretion tori are considered. Effects, such as emission anisotropy, non-stationary flows and geometrical self-occultation are investigated. Polarisation transfer in curved space-time is discussed qualitatively.

  3. Relativistic mean field model for entrainment in general relativistic superfluid neutron stars

    NASA Astrophysics Data System (ADS)

    Comer, G. L.; Joynt, R.

    2003-07-01

    General relativistic superfluid neutron stars have a significantly more intricate dynamics than their ordinary fluid counterparts. Superfluidity allows different superfluid (and superconducting) species of particles to have independent fluid flows, a consequence of which is that the fluid equations of motion contain as many fluid element velocities as superfluid species. Whenever the particles of one superfluid interact with those of another, the momentum of each superfluid will be a linear combination of both superfluid velocities. This leads to the so-called entrainment effect whereby the motion of one superfluid will induce a momentum in the other superfluid. We have constructed a fully relativistic model for entrainment between superfluid neutrons and superconducting protons using a relativistic σ-ω mean field model for the nucleons and their interactions. In this context there are two notions of “relativistic”: relativistic motion of the individual nucleons with respect to a local region of the star (i.e. a fluid element containing, say, an Avogadro’s number of particles), and the motion of fluid elements with respect to the rest of the star. While it is the case that the fluid elements will typically maintain average speeds at a fraction of that of light, the supranuclear densities in the core of a neutron star can make the nucleons themselves have quite high average speeds within each fluid element. The formalism is applied to the problem of slowly rotating superfluid neutron star configurations, a distinguishing characteristic being that the neutrons can rotate at a rate different from that of the protons.

  4. General relativistic models of binary neutron stars in quasiequilibrium

    NASA Astrophysics Data System (ADS)

    Baumgarte, T. W.; Cook, G. B.; Scheel, M. A.; Shapiro, S. L.; Teukolsky, S. A.

    1998-06-01

    We perform fully relativistic calculations of binary neutron stars in corotating, circular orbit. While Newtonian gravity allows for a strict equilibrium, a relativistic binary system emits gravitational radiation, causing the system to lose energy and slowly spiral inwards. However, since inspiral occurs on a time scale much longer than the orbital period, we can treat the binary to be in quasiequilibrium. In this approximation, we integrate a subset of the Einstein equations coupled to the relativistic equation of hydrostatic equilibrium to solve the initial value problem for binaries of arbitrary separation. We adopt a polytropic equation of state to determine the structure and maximum mass of neutron stars in close binaries for polytropic indices n=1, 1.5 and 2. We construct sequences of constant rest-mass and locate turning points along energy equilibrium curves to identify the onset of orbital instability. In particular, we locate the innermost stable circular orbit and its angular velocity. We construct the first contact binary systems in full general relativity. These arise whenever the equation of state is sufficiently soft (n>~1.5). A radial stability analysis reveals no tendency for neutron stars in close binaries to collapse to black holes prior to merger.

  5. General relativistic magnetohydrodynamic simulations of accretion on to Sgr A*: how important are radiative losses?

    NASA Astrophysics Data System (ADS)

    Dibi, S.; Drappeau, S.; Fragile, P. C.; Markoff, S.; Dexter, J.

    2012-11-01

    We present general relativistic magnetohydrodynamic numerical simulations of the accretion flow around the supermassive black hole in the Galactic Centre, Sagittarius A* (Sgr A*). The simulations include for the first time radiative cooling processes (synchrotron, bremsstrahlung and inverse Compton) self-consistently in the dynamics, allowing us to test the common simplification of ignoring all cooling losses in the modelling of Sgr A*. We confirm that for Sgr A*, neglecting the cooling losses is a reasonable approximation if the Galactic Centre is accreting below ˜10-8 M⊙ yr-1, i.e. M⊙<10-7M⊙ Edd . However, above this limit, we show that radiative losses should be taken into account as significant differences appear in the dynamics and the resulting spectra when comparing simulations with and without cooling. This limit implies that most nearby low-luminosity active galactic nuclei are in the regime where cooling should be taken into account. We further make a parameter study of axisymmetric gas accretion around the supermassive black hole at the Galactic Centre. This approach allows us to investigate the physics of gas accretion in general, while confronting our results with the well-studied and observed source, Sgr A*, as a test case. We confirm that the nature of the accretion flow and outflow is strongly dependent on the initial geometry of the magnetic field. For example, we find it difficult, even with very high spins, to generate powerful outflows from discs threaded with multiple, separate poloidal field loops.

  6. A generally relativistic gauge classification of the Dirac fields

    NASA Astrophysics Data System (ADS)

    Fabbri, Luca

    2016-04-01

    We consider generally relativistic gauge transformations for the spinorial fields finding two mutually exclusive but together exhaustive classes in which fermions are placed adding supplementary information to the results obtained by Lounesto, and identifying quantities analogous to the momentum vector and the Pauli-Lubanski axial vector. We discuss how our results are similar to those obtained by Wigner by taking into account the system of Dirac field equations. We will investigate the consequences for the dynamics and in particular we shall address the problem of getting the nonrelativistic approximation in a consistent way. We are going to comment on extensions.

  7. Weak-field general relativistic dynamics and the Newtonian limit

    NASA Astrophysics Data System (ADS)

    Cooperstock, F. I.

    2016-01-01

    We show that the generally held view that the gravity of weak-field nonrelativistic-velocity sources being invariably almost equivalent to Newtonian gravity (NG) (the “Newtonian limit” approach) is in some instances misleading and in other cases incorrect. A particularly transparent example is provided by comparing the Newtonian and general relativistic analyses of a simple variant of van Stockum’s infinite rotating dust cylinder. We show that some very recent criticisms of our work that had been motivated by the Newtonian limit approach were incorrect and note that no specific errors in our work were found in the critique. In the process, we underline some problems that arise from inappropriate coordinate transformations. As further support for our methodology, we note that our weak-field general relativistic treatment of a model galaxy was vindicated recently by the observations of Xu et al. regarding our prediction that the Milky Way was 19-21 kpc in radius as opposed to the commonly held view that the radius was 15 kpc.

  8. Axisymmetric electrostatic magnetohydrodynamic oscillations in tokamaks with general cross-sections and toroidal flow

    NASA Astrophysics Data System (ADS)

    Chu, M. S.; Guo, Wenfeng

    2016-06-01

    The frequency spectrum and mode structure of axisymmetric electrostatic oscillations [the zonal flow (ZF), sound waves (SW), geodesic acoustic modes (GAM), and electrostatic mean flows (EMF)] in tokamaks with general cross-sections and toroidal flows are studied analytically using the electrostatic approximation for magnetohydrodynamic modes. These modes constitute the "electrostatic continua." Starting from the energy principle for a tokamak plasma with toroidal rotation, we showed that these modes are completely stable. The ZF, the SW, and the EMF could all be viewed as special cases of the general GAM. The Euler equations for the general GAM are obtained and are solved analytically for both the low and high range of Mach numbers. The solution consists of the usual countable infinite set of eigen-modes with discrete eigen-frequencies, and two modes with lower frequencies. The countable infinite set is identified with the regular GAM. The lower frequency mode, which is also divergence free as the plasma rotation tends to zero, is identified as the ZF. The other lower (zero) frequency mode is a pure geodesic E×B flow and not divergence free is identified as the EMF. The frequency of the EMF is shown to be exactly 0 independent of plasma cross-section or its flow Mach number. We also show that in general, sound waves with no geodesic components are (almost) completely lost in tokamaks with a general cross-sectional shape. The exception is the special case of strict up-down symmetry. In this case, half of the GAMs would have no geodesic displacements. They are identified as the SW. Present day tokamaks, although not strictly up-down symmetric, usually are only slightly up-down asymmetric. They are expected to share the property with the up-down symmetric tokamak in that half of the GAMs would be more sound wave-like, i.e., have much weaker coupling to the geodesic components than the other half of non-sound-wave-like modes with stronger coupling to the geodesic

  9. General-relativistic celestial mechanics. II. Translational equations of motion

    SciTech Connect

    Damour, T. Departement d'Astrophysique Relativiste et de Cosmologie, Observatoire de Paris, Centre National de la Recherche Scientifique, 92195 Meudon CEDEX ); Soffel, M.; Xu, C. )

    1992-02-15

    The translational laws of motion for gravitationally interacting systems of {ital N} arbitrarily composed and shaped, weakly self-gravitating, rotating, deformable bodies are obtained at the first post-Newtonian approximation of general relativity. The derivation uses our recently introduced multi-reference-system method and obtains the translational laws of motion by writing that, in the local center-of-mass frame of each body, relativistic inertial effects combine with post-Newtonian self- and externally generated gravitational forces to produce a global equilibrium (relativistic generalization of d'Alembert's principle). Within the first post-Newtonian approximation (i.e., neglecting terms of order ({ital v}/{ital c}){sup 4} in the equations of motion), our work is the first to obtain complete and explicit results, in the form of infinite series, for the laws of motion of arbitrarily composed and shaped bodies. We first obtain the laws of motion of each body as an infinite series exhibiting the coupling of all the (Blanchet-Damour) post-Newtonian multipole moments of this body to the post-Newtonian tidal moments (recently defined by us) felt by this body. We then give the explicit expression of these tidal moments in terms of post-Newtonian multipole moments of the other bodies.

  10. General relativistic celestial mechanics. 2. Translational equations of motion

    SciTech Connect

    Damour, T.; Soffel, M.; Xu, C.

    1991-10-01

    The translational laws of motion for gravitationally interacting systems of N, arbitrarily composed and shaped, weakly self-gravitating, rotating, deformable bodies are obtained at the first post-Newtonian approximation of general relativity. The derivation uses the authors' recently introduced multi-reference-system method and obtains the translational laws of motion by writing that, in the local center-of-mass frame of each body, relativistic inertial effects combine with post-Newtonian self- and externally generated gravitational forces to produce global equilibrium (relativistic generalization of d'Alembert's principle). Within the post-Newtonian approximation i.e. neglecting terms of order v/c to the 4th power in the equations of motion, the authors' work is the first to obtain complete and explicit results, in the form of infinite series, for the laws of motion of arbitrarily composed and shaped bodies. The authors first obtain the laws of motion of each body as an infinite series exhibiting the coupling of all the (Blanchet-Damour) post-Newtonian multipole moments of the body to the post-Newtonian tidal moments (recently defined by them) felt by the body. They then give the explicit expression of these tidal moments in terms of the post-Newtonian multiple moments of the other bodies.

  11. General relativistic simulations of slowly rotating, magnetized stars: A perturbative metric approach

    NASA Astrophysics Data System (ADS)

    Etienne, Zachariah; Liu, Y. T.; Shapiro, S.

    2007-04-01

    Understanding the role general relativistic magnetohydrodynamic (GRMHD) effects play in the evolution of nascent neutron stars is a problem at the forefront of theoretical astrophysics. To this end, we performed long-term (˜10^4 M) axisymmetric simulations of differentially rotating magnetized neutron stars in the slow-rotation, weak magnetic field limit using a dynamically updated perturbative metric evolution technique. Although the perturbative metric approach yields results comparable to those obtained via a nonperturbative (BSSN) metric evolution technique, simulations performed with the perturbative metric solver require about 1/4 the computational resources at a given resolution. This computational efficiency enabled us to observe and analyze the effects of magnetic braking and the magnetorotational instability (MRI) at very high resolution. Our GRMHD simulations demonstrate that (1) MRI is not observed unless the estimated fastest-growing mode wavelength is resolved by >˜ 10 gridpoints; (2) as resolution is improved, the MRI growth rate converges, but due to the small-scale nature of MRI-induced turbulence, the maximum growth amplitude increases, but does not exhibit convergence, even at the highest resolution; and (3) independent of resolution, magnetic braking drives the star toward uniform rotation as energy is sapped from differential rotation by winding magnetic fields.

  12. A General Relativistic Magnetohydrodynamics Simulation of Jet Formation with a State Transition

    NASA Technical Reports Server (NTRS)

    Nishikawa, K. I.; Richardson, G.; Koide, S.; Shibata, K.; Kudoh, T.; Hardee, P.; Fushman, G. J.

    2004-01-01

    We have performed the first fully three-dimensional general relativistic magnetohydrodynamic (GRMHD) simulation of jet formation from a thin accretion disk around a Schwarzschild black hole with a free-falling corona. The initial simulation results show that a bipolar jet (velocity sim 0.3c) is created as shown by previous two-dimensional axisymmetric simulations with mirror symmetry at the equator. The 3-D simulation ran over one hundred light-crossing time units which is considerably longer than the previous simulations. We show that the jet is initially formed as predicted due in part to magnetic pressure from the twisting the initially uniform magnetic field and from gas pressure associated with shock formation. At later times, the accretion disk becomes thick and the jet fades resulting in a wind that is ejected from the surface of the thickened (torus-like) disk. It should be noted that no streaming matter from a donor is included at the outer boundary in the simulation (an isolated black hole not binary black hole). The wind flows outwards with a wider angle than the initial jet. The widening of the jet is consistent with the outward moving shock wave. This evolution of jet-disk coupling suggests that the low/hard state of the jet system may switch to the high/soft state with a wind, as the accretion rate diminishes.

  13. Generalized charge-screening in relativistic Thomas-Fermi model

    NASA Astrophysics Data System (ADS)

    Akbari-Moghanjoughi, M.

    2014-10-01

    In this paper, we study the charge shielding within the relativistic Thomas-Fermi model for a wide range of electron number-densities and the atomic-number of screened ions. A generalized energy-density relation is obtained using the force-balance equation and taking into account the Chandrasekhar's relativistic electron degeneracy pressure. By numerically solving a second-order nonlinear differential equation, the Thomas-Fermi screening length is investigated, and the results are compared for three distinct regimes of the solid-density, warm-dense-matter, and white-dwarfs (WDs). It is revealed that our nonlinear screening theory is compatible with the exponentially decaying Thomas-Fermi-type shielding predicted by the linear response theory. Moreover, the variation of relative Thomas-Fermi screening length shows that extremely dense quantum electron fluids are relatively poor charge shielders. Calculation of the total number of screening electrons around a nucleus shows that there is a position of maximum number of screening localized electrons around the screened nucleus, which moves closer to the point-like nucleus by increase in the plasma number density but is unaffected due to increase in the atomic-number value. It is discovered that the total number of screening electrons, ( N s ∝ r T F 3 / r d 3 where rTF and rd are the Thomas-Fermi and interparticle distance, respectively) has a distinct limit for extremely dense plasmas such as WD-cores and neutron star crusts, which is unique for all given values of the atomic-number. This is equal to saying that in an ultrarelativistic degeneracy limit of electron-ion plasma, the screening length couples with the system dimensionality and the plasma becomes spherically self-similar. Current analysis can provide useful information on the effects of relativistic correction to the charge screening for a wide range of plasma density, such as the inertial-confined plasmas and compact stellar objects.

  14. Cherenkov radiation from short relativistic bunches: general approach.

    PubMed

    Baturin, S S; Kanareykin, A D

    2014-11-21

    In recent years new interest in Cherenkov radiation has arisen based on progress in its new applications like biomedical imaging, photonic structures, metamaterials, and beam physics. These new applications require Cherenkov radiation theory of short bunches to be extended to rather more complicated media and structures than considered originally. We present a new general approach to the analysis of Cherenkov fields and loss factors for relativistic short bunches in arbitrary slow wave guiding systems. This new formalism is obtained by considering a general integral relation that allows calculation of the fields in the vicinity of the charge. The proposed approach dramatically simplifies simulations using analytical fields near the moving source of Cherenkov radiation. PMID:25479498

  15. GENERALIZED GENERAL RELATIVISTIC MAGNETOHYDRODYNAMIC EQUATIONS AND DISTINCTIVE PLASMA DYNAMICS AROUND ROTATING BLACK HOLES

    SciTech Connect

    Koide, Shinji

    2010-01-10

    To study phenomena of plasmas around rotating black holes, we have derived a set of 3+1 formalism of generalized general relativistic magnetohydrodynamic (GRMHD) equations. In particular, we investigated general relativistic phenomena with respect to the Ohm's law. We confirmed the electromotive force due to the gravitation, centrifugal force, and frame-dragging effect in plasmas near the black holes. These effects are significant only in the local small-scale phenomena compared to the scale of astrophysical objects. We discuss the possibility of magnetic reconnection, which is triggered by one of these effects in a small-scale region and influences the plasmas globally. We clarify the conditions of applicability of the generalized GRMHD, standard resistive GRMHD, and ideal GRMHD for plasmas in black hole magnetospheres.

  16. WhiskyMHD: Numerical Code for General Relativistic Magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

    Baiotti, Luca; Giacomazzo, Bruno; Hawke, Ian; et al.

    2010-10-01

    Whisky is a code to evolve the equations of general relativistic hydrodynamics (GRHD) and magnetohydrodynamics (GRMHD) in 3D Cartesian coordinates on a curved dynamical background. It was originally developed by and for members of the EU Network on Sources of Gravitational Radiation and is based on the Cactus Computational Toolkit. Whisky can also implement adaptive mesh refinement (AMR) if compiled together with Carpet. Whisky has grown from earlier codes such as GR3D and GRAstro_Hydro, but has been rewritten to take advantage of some of the latest research performed here in the EU. The motivation behind Whisky is to compute gravitational radiation waveforms for systems that involve matter. Examples would include the merger of a binary system containing a neutron star, which are expected to be reasonably common in the universe and expected to produce substantial amounts of radiation. Other possible sources are given in the projects list.

  17. General Relativistic Magnetohydrodynamic Simulations of Magnetically Choked Accretion Flows around Black Holes

    SciTech Connect

    McKinney, Jonathan C.; Tchekhovskoy, Alexander; Blandford, Roger D.

    2012-04-26

    Black hole (BH) accretion flows and jets are qualitatively affected by the presence of ordered magnetic fields. We study fully three-dimensional global general relativistic magnetohydrodynamic (MHD) simulations of radially extended and thick (height H to cylindrical radius R ratio of |H/R| {approx} 0.2-1) accretion flows around BHs with various dimensionless spins (a/M, with BH mass M) and with initially toroidally-dominated ({phi}-directed) and poloidally-dominated (R-z directed) magnetic fields. Firstly, for toroidal field models and BHs with high enough |a/M|, coherent large-scale (i.e. >> H) dipolar poloidal magnetic flux patches emerge, thread the BH, and generate transient relativistic jets. Secondly, for poloidal field models, poloidal magnetic flux readily accretes through the disk from large radii and builds-up to a natural saturation point near the BH. While models with |H/R| {approx} 1 and |a/M| {le} 0.5 do not launch jets due to quenching by mass infall, for sufficiently high |a/M| or low |H/R| the polar magnetic field compresses the inflow into a geometrically thin highly non-axisymmetric 'magnetically choked accretion flow' (MCAF) within which the standard linear magneto-rotational instability is suppressed. The condition of a highly-magnetized state over most of the horizon is optimal for the Blandford-Znajek mechanism that generates persistent relativistic jets with and 100% efficiency for |a/M| {approx}> 0.9. A magnetic Rayleigh-Taylor and Kelvin-Helmholtz unstable magnetospheric interface forms between the compressed inflow and bulging jet magnetosphere, which drives a new jet-disk oscillation (JDO) type of quasi-periodic oscillation (QPO) mechanism. The high-frequency QPO has spherical harmonic |m| = 1 mode period of {tau} {approx} 70GM/c{sup 3} for a/M {approx} 0.9 with coherence quality factors Q {approx}> 10. Overall, our models are qualitatively distinct from most prior MHD simulations (typically, |H/R| << 1 and poloidal flux is limited by

  18. Generalized charge-screening in relativistic Thomas–Fermi model

    SciTech Connect

    Akbari-Moghanjoughi, M.

    2014-10-15

    In this paper, we study the charge shielding within the relativistic Thomas-Fermi model for a wide range of electron number-densities and the atomic-number of screened ions. A generalized energy-density relation is obtained using the force-balance equation and taking into account the Chandrasekhar's relativistic electron degeneracy pressure. By numerically solving a second-order nonlinear differential equation, the Thomas-Fermi screening length is investigated, and the results are compared for three distinct regimes of the solid-density, warm-dense-matter, and white-dwarfs (WDs). It is revealed that our nonlinear screening theory is compatible with the exponentially decaying Thomas-Fermi-type shielding predicted by the linear response theory. Moreover, the variation of relative Thomas-Fermi screening length shows that extremely dense quantum electron fluids are relatively poor charge shielders. Calculation of the total number of screening electrons around a nucleus shows that there is a position of maximum number of screening localized electrons around the screened nucleus, which moves closer to the point-like nucleus by increase in the plasma number density but is unaffected due to increase in the atomic-number value. It is discovered that the total number of screening electrons, (N{sub s}∝r{sub TF}{sup 3}/r{sub d}{sup 3} where r{sub TF} and r{sub d} are the Thomas-Fermi and interparticle distance, respectively) has a distinct limit for extremely dense plasmas such as WD-cores and neutron star crusts, which is unique for all given values of the atomic-number. This is equal to saying that in an ultrarelativistic degeneracy limit of electron-ion plasma, the screening length couples with the system dimensionality and the plasma becomes spherically self-similar. Current analysis can provide useful information on the effects of relativistic correction to the charge screening for a wide range of plasma density, such as the inertial-confined plasmas and compact stellar

  19. General parametrization of axisymmetric black holes in metric theories of gravity

    NASA Astrophysics Data System (ADS)

    Konoplya, Roman; Rezzolla, Luciano; Zhidenko, Alexander

    2016-03-01

    Following previous work of ours in spherical symmetry, we here propose a new parametric framework to describe the spacetime of axisymmetric black holes in generic metric theories of gravity. In this case, the metric components are functions of both the radial and the polar angular coordinates, forcing a double expansion to obtain a generic axisymmetric metric expression. In particular, we use a continued-fraction expansion in terms of a compactified radial coordinate to express the radial dependence, while we exploit a Taylor expansion in terms of the cosine of the polar angle for the polar dependence. These choices lead to a superior convergence in the radial direction and to an exact limit on the equatorial plane. As a validation of our approach, we build parametrized representations of Kerr, rotating dilaton, and Einstein-dilaton-Gauss-Bonnet black holes. The match is already very good at lowest order in the expansion and improves as new orders are added. We expect a similar behavior for any stationary and axisymmetric black-hole metric.

  20. Magnetohydrodynamics in stationary and axisymmetric spacetimes: A fully covariant approach

    NASA Astrophysics Data System (ADS)

    Gourgoulhon, Eric; Markakis, Charalampos; Uryū, Kōji; Eriguchi, Yoshiharu

    2011-05-01

    A fully geometrical treatment of general relativistic magnetohydrodynamics is developed under the hypotheses of perfect conductivity, stationarity, and axisymmetry. The spacetime is not assumed to be circular, which allows for greater generality than the Kerr-type spacetimes usually considered in general relativistic magnetohydrodynamics. Expressing the electromagnetic field tensor solely in terms of three scalar fields related to the spacetime symmetries, we generalize previously obtained results in various directions. In particular, we present the first relativistic version of the Soloviev transfield equation, subcases of which lead to fully covariant versions of the Grad-Shafranov equation and of the Stokes equation in the hydrodynamical limit. We have also derived, as another subcase of the relativistic Soloviev equation, the equation governing magnetohydrodynamical equilibria with purely toroidal magnetic fields in stationary and axisymmetric spacetimes.

  1. Multiple-event probability in general-relativistic quantum mechanics

    SciTech Connect

    Hellmann, Frank; Mondragon, Mauricio; Perez, Alejandro; Rovelli, Carlo

    2007-04-15

    We discuss the definition of quantum probability in the context of 'timeless' general-relativistic quantum mechanics. In particular, we study the probability of sequences of events, or multievent probability. In conventional quantum mechanics this can be obtained by means of the 'wave function collapse' algorithm. We first point out certain difficulties of some natural definitions of multievent probability, including the conditional probability widely considered in the literature. We then observe that multievent probability can be reduced to single-event probability, by taking into account the quantum nature of the measuring apparatus. In fact, by exploiting the von-Neumann freedom of moving the quantum/classical boundary, one can always trade a sequence of noncommuting quantum measurements at different times, with an ensemble of simultaneous commuting measurements on the joint system+apparatus system. This observation permits a formulation of quantum theory based only on single-event probability, where the results of the wave function collapse algorithm can nevertheless be recovered. The discussion also bears on the nature of the quantum collapse.

  2. Relativistic Generalization of the Inertial and Gravitational Masses Equivalence Principle

    NASA Astrophysics Data System (ADS)

    Mitskievich, Nikolai V.

    2008-09-01

    The Newtonian approximation in the gravitational field description not necessarily involves admission of non-relativistic properties of the source terms in Einstein's equations: it is sufficient to merely consider the weak-field condition for gravitational field. When, e.g., a source has electromagnetic nature, one simply cannot ignore its intrinsically relativistic properties, since there cannot be invented any non-relativistic approximation which would adequately describe electromagnetic stress-energy tensor even at large distances where the fields become naturally weak. But the test particle on which gravitational field is acting, should be treated as non-relativistic (this premise is required for introduction of the Newtonian potential ΦN from the geodesic equation).

  3. General-relativistic force-free pulsar magnetospheres

    NASA Astrophysics Data System (ADS)

    Pétri, J.

    2016-02-01

    Pulsar magnetospheres are shaped by ultrarelativistic electron/positron plasmas flowing in a strong magnetic field and subject to strong gravitational fields. The former induces magnetospheric currents and space charges responsible for the distortion of the electromagnetic field based on pure electrodynamics. The latter induces other perturbations in these fields based on space-time curvature. The force-free approximation describes the response of this magnetosphere to the presence of currents and charges and has been investigated by many authors. In this context, general relativity has been less discussed to quantify its influence on the neutron star electrodynamics. It is the purpose of this paper to compute general-relativistic force-free pulsar magnetospheres for realistic magnetic field configurations such as the inclined dipole. We performed time-dependent simulations of Maxwell equations in the 3+1 formalism of a stationary background metric in the slow-rotation approximation. We computed the resulting Poynting flux depending on the ratio R/rL and on frame-dragging through the spin parameter as, R is the neutron star radius and rL the light-cylinder radius. Both effects act together to increase the total Poynting flux seen by a distant observer by a factor up to 2 depending on the rotation rate. Moreover we retrieve the sin 2χ dependence of this luminosity, χ being the obliquity of the pulsar, as well as a braking index close to n = 3. We also show that the angular dependence of the Poynting flux scales like sin 2ϑ for the aligned rotator but like sin 4ϑ for the orthogonal rotator, ϑ being the colatitude.

  4. A General Relativistic Magnetohydrodynamic Simulation of Jet Formation

    NASA Technical Reports Server (NTRS)

    Nishikawa, K.-I.; Richardson, G.; Koide, S.; Shibata, K.; Kudoh, T.; Hardee, P.; Fishman, G. J.

    2005-01-01

    We have performed a fully three-dimensional general relativistic magnetohydrodynamic (GRMHD) simulation ofjet formation from a thin accretion disk around a Schwarzschild black hole with a free-falling corona. The initial simulation results show that a bipolar jet (velocity approx.0.3c) is created, as shown by previous two-dimensional axi- symmetric simulations with mirror symmetry at the equator. The three-dimensional simulation ran over 100 light crossing time units (T(sub s) = r(sub s)/c, where r(sub s = 2GM/c(sup 2), which is considerably longer than the previous simulations. We show that the jet is initially formed as predicted owing in part to magnetic pressure from the twisting of the initially uniform magnetic field and from gas pressure associated with shock formation in the region around r = 3r(sub s). At later times, the accretion disk becomes thick and the jet fades resulting in a wind that is ejected from the surface ofthe thickened (torus-like) disk. It should be noted that no streaming matter from a donor is included at the outer boundary in the simulation (an isolated black hole not binary black hole). The wind flows outward with a wider angle than the initial jet. The widening of the jet is consistent with the outward-moving torsional Alfven waves. This evolution of disk-jet coupling suggests that the jet fades with a thickened accretion disk because of the iack of streaming materiai from an accompanying star.

  5. Axisymmetric, Nonstationary Black Hole Magnetospheres: Revisited

    NASA Astrophysics Data System (ADS)

    Song, Yoo Geun; Park, Seok Jae

    2015-10-01

    An axisymmetric, stationary, general-relativistic, electrodynamic engine model of an active galactic nucleus was formulated by Macdonald and Thorne that consisted of a supermassive black hole surrounded by a plasma magnetosphere and a magnetized accretion disk. Based on this initial formulation, a nonstationary, force-free version of their model was constructed by Park & Vishniac (PV), with the simplifying assumption that the poloidal component of the magnetic field line velocity be confined along the radial direction in cylindrical polar coordinates. In this paper, we derive the new, nonstationary “Transfield Equation,” which was not specified in PV. If we can solve this “Transfield Equation” numerically, then we will understand the axisymmetric, nonstationary black hole magnetosphere in more rigorous ways.

  6. A First Approach to Hydrodynamics in General Relativistic Systems Using SPH

    NASA Astrophysics Data System (ADS)

    Cruz-Pérez, J. P.; González, J. A.; Montoya, E.

    2010-07-01

    In this work we present the Lagrangian formulation of the general relativistic ideal fluid equations. With the help of the standard Smoothed Particle Hydrodynamics (SPH) method we obtain a discretization of the motion equations. Having in mind that several of the most interesting astrophysical systems that we observe in the universe have been shaped by fluid dynamical processes, we want to use this method to study them. We present the first steps to implement such general relativistic SPH codes.

  7. Axi-symmetric generalized thermoelastic diffusion problem with two-temperature and initial stress under fractional order heat conduction

    NASA Astrophysics Data System (ADS)

    Deswal, Sunita; Kalkal, Kapil Kumar; Sheoran, Sandeep Singh

    2016-09-01

    A mathematical model of fractional order two-temperature generalized thermoelasticity with diffusion and initial stress is proposed to analyze the transient wave phenomenon in an infinite thermoelastic half-space. The governing equations are derived in cylindrical coordinates for a two dimensional axi-symmetric problem. The analytical solution is procured by employing the Laplace and Hankel transforms for time and space variables respectively. The solutions are investigated in detail for a time dependent heat source. By using numerical inversion method of integral transforms, we obtain the solutions for displacement, stress, temperature and diffusion fields in physical domain. Computations are carried out for copper material and displayed graphically. The effect of fractional order parameter, two-temperature parameter, diffusion, initial stress and time on the different thermoelastic and diffusion fields is analyzed on the basis of analytical and numerical results. Some special cases have also been deduced from the present investigation.

  8. Waves in general relativistic two-fluid plasma around a Schwarzschild black hole

    NASA Astrophysics Data System (ADS)

    Rahman, M. Atiqur

    2012-10-01

    Waves propagating in the relativistic electron-positron or ions plasma are investigated in a frame of two-fluid equations using the 3+1 formalism of general relativity developed by Thorne, Price and Macdonald (TPM). The plasma is assumed to be freefalling in the radial direction toward the event horizon due to the strong gravitational field of a Schwarzschild black hole. The local dispersion relations for transverse and longitudinal waves have been derived, in analogy with the special relativistic formulation as explained in an earlier paper, to take account of relativistic effects due to the event horizon using WKB approximation.

  9. General Relativistic MHD Models of Sgr A* and M87

    NASA Astrophysics Data System (ADS)

    Dexter, Jason

    2011-01-01

    Ongoing high resolution observations of the Galactic center black hole provide a direct probe of the structure of its accretion flow (Sgr A*) on event-horizon scales. Due to its low luminosity, this source is uniquely suitable for modeling with relativistic MHD simulations. We perform time-dependent, relativistic radiative transfer on 3D simulation data to compute images and light curves of Sgr A* at millimeter wavelengths. Fitting the images to observations allows us to constrain the parameters of the accretion flow and black hole. Simulations with misaligned angular momentum and black hole spin axes ("tilted") are also considered. Due to the precession of these accretion flows, the inferred best fit parameters should appear to change on week timescales if Sgr A* is tilted. Light curves from all simulations exhibit flaring behavior consistent with the observations. The black hole shadow, a signature of the event horizon, is visible in all best fit models and may be detected in the next 5-10 years. Preliminary results from similar models of M87 are also discussed.

  10. Polar Cap Pair Production for an Axisymmetric Pulsar Requires General Relativity

    NASA Astrophysics Data System (ADS)

    Belyaev, Mikhail

    2016-04-01

    Using an analytical approach coupled to a condition for pair production derived from particle in cell simulations, we show that pair production by curvature photons on magnetic field lines at the polar cap is inactive if general relativity is ignored. In particular, general relativisitic frame-dragging lowers the value of the Goldreich-Julian density at the polar cap compared to its value for a flat spacetime. This leads to a region of space-like current near the surface of the neutron star where pair production is possible.However, even when general relativity is included, we show analytically that pair production on magnetic field lines is suppressed near the outer edge of the polar cap. This leads to the possibility of a ``vacuum" region of unscreened parallel electric field on open field lines near the last open field line. Such a vacuum region has indeed been observed in particle in cell simulations of the pulsar magnetosphere.Because of the generality of our analytical approach (which does not assume a dipolar surface field), our conclusions are true independent of the detailed structure of the magnetic field at the surface of the neutron star. We confirm our analytical results by comparing them to force-free simulations of a pulsar with a dipolar surface field.

  11. Predictions of axisymmetric free turbulent shear flows using a generalized eddy-viscosity approach

    NASA Technical Reports Server (NTRS)

    Morgenthaler, J. H.

    1973-01-01

    The generalized eddy viscosity approach is described and results are presented of test cases which show that predictions obtained by this approach are adequate for most engineering applications. Because of the importance of starting computations from the injection station where experimentally determined mean and turbulence parameters are rarely available, a very simple core model applicable to simple step-type (slug) profiles was developed. Agreement between predicted and experimental mean profiles was generally almost as good for calculations made by using this model throughout the core region and the transition model for all subsequent regions as predictions made by starting from experimental profiles in the transition region. The generalized eddy-viscosity model, which was developed in part through correlation of turbulence parameters, successfully predicted turbulent shear stress, turbulent intensity, and mean velocity profiles for a 0.040-inch-diameter microjet. Therefore, successful scaling by the model was demonstrated since data used in its development was for jet areas up to 90,000 times as large as the microjet and velocities only 1/20th as high.

  12. General relativistic magnetohydrodynamical simulations of the jet in M 87

    NASA Astrophysics Data System (ADS)

    Mościbrodzka, Monika; Falcke, Heino; Shiokawa, Hotaka

    2016-02-01

    Context. The connection between black hole, accretion disk, and radio jet can be constrained best by fitting models to observations of nearby low-luminosity galactic nuclei, in particular the well-studied sources Sgr A* and M 87. There has been considerable progress in modeling the central engine of active galactic nuclei by an accreting supermassive black hole coupled to a relativistic plasma jet. However, can a single model be applied to a range of black hole masses and accretion rates? Aims: Here we want to compare the latest three-dimensional numerical model, originally developed for Sgr A* in the center of the Milky Way, to radio observations of the much more powerful and more massive black hole in M 87. Methods: We postprocess three-dimensional GRMHD models of a jet-producing radiatively inefficient accretion flow around a spinning black hole using relativistic radiative transfer and ray-tracing to produce model spectra and images. As a key new ingredient in these models, we allow the proton-electron coupling in these simulations depend on the magnetic properties of the plasma. Results: We find that the radio emission in M 87 is described well by a combination of a two-temperature accretion flow and a hot single-temperature jet. Most of the radio emission in our simulations comes from the jet sheath. The model fits the basic observed characteristics of the M 87 radio core: it is "edge-brightened", starts subluminally, has a flat spectrum, and increases in size with wavelength. The best fit model has a mass-accretion rate of Ṁ ~ 9 × 10-3M⊙ yr-1 and a total jet power of Pj ~ 1043 erg s-1. Emission at λ = 1.3 mm is produced by the counter-jet close to the event horizon. Its characteristic crescent shape surrounding the black hole shadow could be resolved by future millimeter-wave VLBI experiments. Conclusions: The model was successfully derived from one for the supermassive black hole in the center of the Milky Way by appropriately scaling mass and

  13. Search for general relativistic effects in table-top displacement metrology

    NASA Technical Reports Server (NTRS)

    Halverson, Peter G.; Diaz, Rosemary T.; Macdonald, Daniel R.

    2004-01-01

    As displacement metrology accuracy improves, general relativistic effects will become noticeable. Metrology gauges developed for the Space Interferometry Mission, were used to search for locally anisotropic space-time, with a null result at the 10 to the negative 10th power level.

  14. Search for general relativistic effects in table-top displacement metrology

    NASA Technical Reports Server (NTRS)

    Halverson, Peter G.; Macdonald, Daniel R.; Diaz, Rosemary T.

    2004-01-01

    As displacement metrology accuracy improves, general relativistic effects will become noticeable. Metrology gauges developed for the Space Interferometry Mission were used to search for locally anisotropic space-time, with a null result at the 10 to the negative tenth power level.

  15. The generalized Coulomb interactions for relativistic scalar bosons

    NASA Astrophysics Data System (ADS)

    Zarrinkamar, S.; Panahi, H.; Rezaei, M.

    2016-07-01

    Approximate analytical solutions of Duffin-Kemmer-Petiau (DKP) equation are obtained for the truncated Coulomb, generalized Cornell, Richardson and Song-Lin potentials via the quasi-exact analytical ansatz approach.

  16. Axisymmetric collapse simulations of rotating massive stellar cores in full general relativity: Numerical study for prompt black hole formation

    SciTech Connect

    Sekiguchi, Yu-ichirou; Shibata, Masaru

    2005-04-15

    We perform axisymmetric simulations for gravitational collapse of a massive iron core to a black hole in full general relativity. The iron cores are modeled by {gamma}=4/3 equilibrium polytrope for simplicity. The hydrodynamic equations are solved using a high-resolution shock-capturing scheme with a parametric equation of state. The Cartoon method is adopted for solving the Einstein equations. Simulations are performed for a wide variety of initial conditions changing the mass ({approx_equal}2.0-3.0M{sub {center_dot}}), the angular momentum, the rotational velocity profile of the core, and the parameters of the equations of state which are chosen so that the maximum mass of the cold spherical polytrope is {approx_equal}1.6M{sub {center_dot}}. Then, the criterion for the prompt black hole formation is clarified in terms of the mass and the angular momentum for several rotational velocity profile of the core and equations of state. It is found that (i) with the increase of the thermal energy generated by shocks, the threshold mass for the prompt black hole formation is increased by 20-40%, (ii) the rotational centrifugal force increases the threshold mass by < or approx. 25%, (iii) with the increase of the degree of differential rotation, the threshold mass is also increased, and (iv) the amplification factors shown in the results (i)-(iii) depend sensitively on the equation of state. We also find that the collapse dynamics and the structure of the shock formed at the bounce depend strongly on the stiffness of the adopted equation of state. In particular, as a new feature, a strong bipolar explosion is observed for the collapse of rapidly rotating iron cores with an equation of state which is stiff in subnuclear density and soft in supranuclear density. Gravitational waves are computed in terms of a quadrupole formula. It is also found that the waveform depends sensitively on the equations of state.

  17. A fully general relativistic numerical simulation code for spherically symmetric matter

    NASA Astrophysics Data System (ADS)

    Park, Dong-Ho; Cho, Inyong; Kang, Gungwon; Lee, Hyung Mok

    2013-02-01

    We present a fully general relativistic open-source code that can be used for simulating a system of spherically symmetric perfect fluid matter. It is based on the Arnowitt-Deser-Misner 3+1 formalism with maximal slicing and isotropic spatial coordinates. For hydrodynamic matter High Resolution Shock Capturing (HRSC) schemes with a monotonized central-difference limiter and approximated Riemann solvers are used in the Eulerian viewpoint. The accuracy and the convergence of our numerical code are verified by performing several test problems. These include a relativistic blast wave, relativistic spherical accretion of matter into a black hole, Tolman-Oppenheimer-Volkoff (TOV) stars and Oppenheimer-Snyder (OS) dust collapses. In particular, a dynamical code test is done for the OS collapse by explicitly performing numerical coordinate transformations between our coordinate 8system and the one used for the analytic solution. Finally, some TOV star solutions are presented for the Eddington-inspired Born-Infeld gravity theory.

  18. General Relativistic Theory of the VLBI Time Delay in the Gravitational Field of Moving Bodies

    NASA Technical Reports Server (NTRS)

    Kopeikin, Sergei

    2003-01-01

    The general relativistic theory of the gravitational VLBI experiment conducted on September 8, 2002 by Fomalont and Kopeikin is explained. Equations of radio waves (light) propagating from the quasar to the observer are integrated in the time-dependent gravitational field of the solar system by making use of either retarded or advanced solutions of the Einstein field equations. This mathematical technique separates explicitly the effects associated with the propagation of gravity from those associated with light in the integral expression for the relativistic VLBI time delay of light. We prove that the relativistic correction to the Shapiro time delay, discovered by Kopeikin (ApJ, 556, L1, 2001), changes sign if one retains direction of the light propagation but replaces the retarded for the advanced solution of the Einstein equations. Hence, this correction is associated with the propagation of gravity. The VLBI observation measured its speed, and that the retarded solution is the correct one.

  19. Heavy meson mass-spectra by general relativistic methods (*)

    SciTech Connect

    Italiano, A.; Lattuada, M.; Maccarrone, G.D.; Recami, E.; Riggi, F.; Vinciguerra, D.

    1984-11-01

    By applying the classical methods of general relativity to elementary particles, one can get-in a natural way-the observed confinement of their constituents, avoiding any recourse to phenomenological models such as the bag model and allowing the deduction of the heavy meson (i.e., charmonium (J/psi) and bottomonium (..gamma..)) mass-spectra.

  20. Gravity: Newtonian, Post-Newtonian, and General Relativistic

    NASA Astrophysics Data System (ADS)

    Will, Clifford M.

    We present a pedagogical introduction to gravitational theory, with the main focus on weak gravitational fields. We begin with a thorough survey of Newtonian gravitational theory. After a brief introduction to general relativity, we develop the post-Minkowskian formulation of the field equations, which is ideally suited to studying weak-field gravity. We then discuss applications of this formulation, including post-Newtonian theory, the parametrized post-Newtonian framework, and gravitational radiation.

  1. General relativistic effects in quantum interference of “clocks”

    NASA Astrophysics Data System (ADS)

    Zych, M.; Pikovski, I.; Costa, F.; Brukner, Č.

    2016-06-01

    Quantum mechanics and general relativity have been each successfully tested in numerous experiments. However, the regime where both theories are jointly required to explain physical phenomena remains untested by laboratory experiments, and is also not fully understood by theory. This contribution reviews recent ideas for a new type of experiments: quantum interference of “clocks”, which aim to test novel quantum effects that arise from time dilation. “Clock” interference experiments could be realised with atoms or photons in near future laboratory experiments.

  2. RAISHIN: A High-Resolution Three-Dimensional General Relativistic Magnetohydrodynamics Code

    NASA Technical Reports Server (NTRS)

    Mizuno, Yosuke; Nishikawa, Ken-Ichi; Koide, Shinji; Hardee, Philip; Fishman, Gerald J.

    2006-01-01

    We have developed a new three-dimensional general relativistic magnetohydrodynamic (GRMHD) code, RAISHIN, using a conservative, high resolution shock-capturing scheme. The numerical fluxes are calculated using the Harten, Lax, & van Leer (HLL) approximate Riemann solver scheme. The flux-interpolated, constrained transport scheme is used to maintain a divergence-free magnetic field. In order to examine the numerical accuracy and the numerical efficiency, the code uses four different reconstruction methods: piecewise linear methods with Minmod and MC slope-limiter function, convex essentially non-oscillatory (CENO) method, and piecewise parabolic method (PPM) using multistep TVD Runge-Kutta time advance methods with second and third-order time accuracy. We describe code performance on an extensive set of test problems in both special and general relativity. Our new GRMHD code has proven to be accurate in second order and has successfully passed with all tests performed, including highly relativistic and magnetized cases in both special and general relativity.

  3. General relativistic delays in current and future VLBI

    NASA Astrophysics Data System (ADS)

    Soja, B.; Plank, L.; Schuh, H.

    2012-12-01

    The effect of gravitational time delay due to general relativity is clearly visible in VLBI measurements. While the Sun and the Earth cause gravitational delays up to some nanoseconds respectively picoseconds in geodetic VLBI observables, standard delay models also recommend the inclusion of Jupiter, the Earth's Moon and some of the other planets on the modeling side. Using the IERS Conventions model, we have calculated the gravitational time delay of standard VLBI observation constellations of the past years. The influences due to the Sun, the Earth, the Moon, Jupiter, Saturn and Venus were large enough to justify their consideration in routine VLBI data analysis (based on the accuracy of the upcoming VLBI2010 system). For VLBI data before 2002, the higher order term of the Sun should also be taken into account. Additionally, the relation between the gravitational delay of the Earth and the estimated tropospheric parameters (e.g. zenith wet delays) was investigated.

  4. Critical rotation of general-relativistic polytropic models revisited

    NASA Astrophysics Data System (ADS)

    Geroyannis, V.; Karageorgopoulos, V.

    2013-09-01

    We develop a perturbation method for computing the critical rotational parameter as a function of the equatorial radius of a rigidly rotating polytropic model in the "post-Newtonia approximation" (PNA). We treat our models as "initial value problems" (IVP) of ordinary differential equations in the complex plane. The computations are carried out by the code dcrkf54.f95 (Geroyannis and Valvi 2012 [P1]; modified Runge-Kutta-Fehlberg code of fourth and fifth order for solving initial value problems in the complex plane). Such a complex-plane treatment removes the syndromes appearing in this particular family of IVPs (see e.g. P1, Sec. 3) and allows continuation of the numerical integrations beyond the surface of the star. Thus all the required values of the Lane-Emden function(s) in the post-Newtonian approximation are calculated by interpolation (so avoiding any extrapolation). An interesting point is that, in our computations, we take into account the complete correction due to the gravitational term, and this issue is a remarkable difference compared to the classical PNA. We solve the generalized density as a function of the equatorial radius and find the critical rotational parameter. Our computations are extended to certain other physical characteristics (like mass, angular momentum, rotational kinetic energy, etc). We find that our method yields results comparable with those of other reliable methods. REFERENCE: V.S. Geroyannis and F.N. Valvi 2012, International Journal of Modern Physics C, 23, No 5, 1250038:1-15.

  5. Relativistic model of anisotropic charged fluid sphere in general relativity

    NASA Astrophysics Data System (ADS)

    Pant, Neeraj; Pradhan, N.; Bansal, Rajeev K.

    2016-01-01

    In this present paper, we present a class of static, spherically symmetric charged anisotropic fluid models of super dense stars in isotropic coordinates by considering a particular type of metric potential, a specific choice of electric field intensity E and pressure anisotropy factor Δ which involve parameters K (charge) and α (anisotropy) respectively. The solutions so obtained are utilized to construct the models for super-dense stars like neutron stars and strange quark stars. Our solutions are well behaved within the following ranges of different constant parameters. In the absence of pressure anisotropy and charge present model reduces to the isotropic model Pant et al. (Astrophys. Space Sci. 330:353-359, 2010). Our solution is well behaved in all respects for all values of X lying in the range 0< X ≤ 0.18, α lying in the range 0 ≤ α ≤6.6, K lying in the range 0< K ≤ 6.6 and Schwarzschild compactness parameter "u" lying in the range 0< u ≤ 0.38. Since our solution is well behaved for a wide ranges of the parameters, we can model many different types of ultra-cold compact stars like quark stars and neutron stars. We have shown that corresponding to X=0.088, α=0.6 and K=4.3 for which u=0.2054 and by assuming surface density ρb = 4.6888 × 10^{14} g/cm3 the mass and radius are found to be 1.51 M_{\\varTheta} and 10.90 km respectively. Assuming surface density ρb = 2 × 10^{14} g/cm3 the mass and radius for a neutron star candidate are found to be 2.313 M_{\\varTheta} and 16.690 km respectively. Hence we obtain masses and radii that fall in the range of what is generally expected for quark stars and neutron stars.

  6. Confinement and hadron-hadron interactions by general relativistic methods

    NASA Astrophysics Data System (ADS)

    Recami, Erasmo

    By postulating covariance of physical laws under global dilations, one can describe gravitational and strong interactions in a unified way. Namely, in terms of the new discrete dilational degree of freedom, our cosmos and hadrons can be regarded as finite, similar systems. And a discrete hierarchy of finite ``universes'' may be defined, which are governed by fields with strengths inversally proportional to their radii; in each universe an Equivalence Principle holds, so that the relevant field can be there geometrized. Scaled-down Einstein equations -with cosmological term- are assumed to hold inside hadrons (= strong micro-cosmoses); and they yield in a natural way classical confinement, as well as ``asymptotic freedom'', of the hadron constituents. In other words, the association of strong micro-universes of Friedmann type with hadrons (i.e., applying the methods of General Relativity to subnuclear particle physics) allows avoiding recourse to phenomenological models such as the Bag Model. Inside hadrons we have to deal with a tensorial field (= strong gravity), and hadron constituents are supposed to exchange spin-2 ``gluons''. Our approach allows us also to write down a tensorial, bi-scale field theory of hadron-hadron interactions, based on modified Einstein-type equations here proposed for strong interactions in our space. We obtain in particular: (i) the correct Yukawa behaviour of the strong scalar potential at the static limit and for r>~l fm; (ii) the value of hadron radii. As a byproduct, we derive a whole ``numerology'', connecting our gravitational cosmos with the strong micro-cosmoses (hadrons), such that it does imply no variation of G with the epoch. Finally, since a structute of the ``micro-universe'' type seems to be characteristic even of leptons, a hope for the future is including also weak interactions in our classical unification of the fundamental forces.

  7. Quantum interferometric visibility as a witness of general relativistic proper time.

    PubMed

    Zych, Magdalena; Costa, Fabio; Pikovski, Igor; Brukner, Časlav

    2011-01-01

    Current attempts to probe general relativistic effects in quantum mechanics focus on precision measurements of phase shifts in matter-wave interferometry. Yet, phase shifts can always be explained as arising because of an Aharonov-Bohm effect, where a particle in a flat space-time is subject to an effective potential. Here we propose a quantum effect that cannot be explained without the general relativistic notion of proper time. We consider interference of a 'clock'-a particle with evolving internal degrees of freedom-that will not only display a phase shift, but also reduce the visibility of the interference pattern. According to general relativity, proper time flows at different rates in different regions of space-time. Therefore, because of quantum complementarity, the visibility will drop to the extent to which the path information becomes available from reading out the proper time from the 'clock'. Such a gravitationally induced decoherence would provide the first test of the genuine general relativistic notion of proper time in quantum mechanics. PMID:22009037

  8. Dark-matter distributions around massive black holes: A general relativistic analysis

    NASA Astrophysics Data System (ADS)

    Sadeghian, Laleh; Ferrer, Francesc; Will, Clifford M.

    2013-09-01

    The cold dark matter at the center of a galaxy will be redistributed by the presence of a massive black hole. The redistribution may be determined using an approach pioneered by Gondolo and Silk: begin with a model distribution function for the dark matter, and “grow” the black hole adiabatically, holding the adiabatic invariants of the motion constant. Unlike the approach of Gondolo and Silk, which adopted Newtonian theory together with ad hoc correction factors to mimic general relativistic effects, we carry out the calculation fully relativistically, using the exact Schwarzschild geometry of the black hole. We find that the density of dark matter generically vanishes at r=2RS, not 4RS as found by Gondolo and Silk, where RS is the Schwarzschild radius, and that the spike very close to the black hole reaches significantly higher densities. We apply the relativistic adiabatic growth framework to obtain the final dark-matter density for both cored and cusped initial distributions. Besides the implications of these results for indirect detection estimates, we show that the gravitational effects of such a dark-matter spike are significantly smaller than the relativistic effects of the black hole, including frame dragging and quadrupolar effects, for stars orbiting close to the black hole that might be candidates for testing the black-hole no-hair theorems.

  9. Near-critical spherical accretion by neutron stars - General relativistic treatment

    NASA Technical Reports Server (NTRS)

    Park, Myeong-Gu; Miller, Guy S.

    1991-01-01

    Time-independent spherical accretion by a neutron star is studied using general relativistic radiation hydrodynamics. Numerical integrations of the flow equations are presented. These show that when the luminosity is sufficiently close to (but below) the Eddington limit, the flow velocity increases with decreasing radius far from the neutron star, reaches a maximum at an intermediate radius, and decreases at small radii. A large fraction of the binding energy of the flow is transferred to the radiation through scattering before the flow strikes the surface of the neutron star. Following Miller's treatment of accretion at luminosites near the Eddington limit (which neglected general relativistic effects), analytic approximations for the decelerating phase of the flow's velocity profile are derived. The dependence of the solutions on the variable Eddington factor prescription chosen to close the radiation moment equations is also examined.

  10. General relativistic polarized radiative transfer: building a dynamics-observations interface

    NASA Astrophysics Data System (ADS)

    Shcherbakov, Roman V.; Huang, Lei

    2011-01-01

    The rising number of polarized observations of relativistic sources necessitates a correct theory for proper model fitting. The equations for general relativistic (GR) polarized radiative transfer are derived starting from the Boltzmann equation and basic ideas of general relativity. The derivation is aimed at providing a practical guide to reproducing the synchrotron part of radio and submillimetre emission from low-luminosity active galactic nuclei (LLAGNs), in particular Sgr A*, and jets. A recipe for the fast exact calculation of cyclo-synchrotron emissivities, absorptivities, Faraday rotation and conversion coefficients is given for isotropic particle distributions. The multitude of physical effects influencing simulated spectra is discussed. The application of the prescribed technique is necessary to determine the black hole spin in LLAGNs. The observations of total flux, linear and circular polarization fractions, and electric vector position angle as functions of the observed frequency could substantially constrain the absolute value and orientation of spin.

  11. Relativistic Feynman-Metropolis-Teller theory for white dwarfs in general relativity

    SciTech Connect

    Rotondo, Michael; Rueda, Jorge A.; Ruffini, Remo; Xue Shesheng

    2011-10-15

    The recent formulation of the relativistic Thomas-Fermi model within the Feynman-Metropolis-Teller theory for compressed atoms is applied to the study of general relativistic white dwarf equilibrium configurations. The equation of state, which takes into account the {beta}-equilibrium, the nuclear and the Coulomb interactions between the nuclei and the surrounding electrons, is obtained as a function of the compression by considering each atom constrained in a Wigner-Seitz cell. The contribution of quantum statistics, weak, nuclear, and electromagnetic interactions is obtained by the determination of the chemical potential of the Wigner-Seitz cell. The further contribution of the general relativistic equilibrium of white dwarf matter is expressed by the simple formula {radical}(g{sub 00}){mu}{sub ws}=constant, which links the chemical potential of the Wigner-Seitz cell {mu}{sub ws} with the general relativistic gravitational potential g{sub 00} at each point of the configuration. The configuration outside each Wigner-Seitz cell is strictly neutral and therefore no global electric field is necessary to warranty the equilibrium of the white dwarf. These equations modify the ones used by Chandrasekhar by taking into due account the Coulomb interaction between the nuclei and the electrons as well as inverse {beta} decay. They also generalize the work of Salpeter by considering a unified self-consistent approach to the Coulomb interaction in each Wigner-Seitz cell. The consequences on the numerical value of the Chandrasekhar-Landau mass limit as well as on the mass-radius relation of {sup 4}He, {sup 12}C, {sup 16}O and {sup 56}Fe white dwarfs are presented. All these effects should be taken into account in processes requiring a precision knowledge of the white dwarf parameters.

  12. Generalized Ohm's law for a background plasma in the presence of relativistic charged particles.

    PubMed

    Sherlock, M

    2010-05-21

    A generalized Ohm's law is derived for a system composed of a background magnetohydrodynamic plasma and a lower density relativistic charged-particle distribution. The interpretation of Ohmic electric fields occurring due to force balance breaks down for such a system and instead an approach based on Maxwell's equations along with the particle flux equations is necessary. Three additional terms arise in Ohm's law and each is verified numerically. PMID:20867035

  13. Generalized Ohm's Law for a Background Plasma in the Presence of Relativistic Charged Particles

    SciTech Connect

    Sherlock, M.

    2010-05-21

    A generalized Ohm's law is derived for a system composed of a background magnetohydrodynamic plasma and a lower density relativistic charged-particle distribution. The interpretation of Ohmic electric fields occurring due to force balance breaks down for such a system and instead an approach based on Maxwell's equations along with the particle flux equations is necessary. Three additional terms arise in Ohm's law and each is verified numerically.

  14. General relativistic monopole magnetosphere of neutron stars: a pseudo-spectral discontinuous Galerkin approach

    NASA Astrophysics Data System (ADS)

    Pétri, J.

    2015-03-01

    The close vicinity of neutron stars remains poorly constrained by observations. Although plenty of data are available for the peculiar class of pulsars we are still unable to deduce the underlying plasma distribution in their magnetosphere. In the present paper, we try to unravel the magnetospheric structure starting from basic physics principles and reasonable assumptions about the magnetosphere. Beginning with the monopole force-free case, we compute accurate general relativistic solutions for the electromagnetic field around a slowly rotating magnetized neutron star. Moreover, here we address this problem by including the important effect of plasma screening. This is achieved by solving the time-dependent Maxwell equations in a curved space-time following the 3+1 formalism. We improved our previous numerical code based on pseudo-spectral methods in order to allow for possible discontinuities in the solution. Our algorithm based on a multidomain decomposition of the simulation box belongs to the discontinuous Galerkin finite element methods. We performed several sets of simulations to look for the general relativistic force-free monopole and split monopole solutions. Results show that our code is extremely powerful in handling extended domains of hundredth of light cylinder radii rL. The code has been validated against known exact analytical monopole solutions in flat space-time. We also present semi-analytical calculations for the general relativistic vacuum monopole.

  15. General-relativistic resistive magnetohydrodynamics in three dimensions: Formulation and tests

    NASA Astrophysics Data System (ADS)

    Dionysopoulou, Kyriaki; Alic, Daniela; Palenzuela, Carlos; Rezzolla, Luciano; Giacomazzo, Bruno

    2013-08-01

    We present a new numerical implementation of the general-relativistic resistive magnetohydrodynamics (MHD) equations within the Whisky code. The numerical method adopted exploits the properties of implicit-explicit Runge-Kutta numerical schemes to treat the stiff terms that appear in the equations for large electrical conductivities. Using tests in one, two, and three dimensions, we show that our implementation is robust and recovers the ideal-MHD limit in regimes of very high conductivity. Moreover, the results illustrate that the code is capable of describing scenarios in a very wide range of conductivities. In addition to tests in flat spacetime, we report simulations of magnetized nonrotating relativistic stars, both in the Cowling approximation and in dynamical spacetimes. Finally, because of its astrophysical relevance and because it provides a severe tested for general-relativistic codes with dynamical electromagnetic fields, we study the collapse of a nonrotating star to a black hole. We show that also in this case our results on the quasinormal mode frequencies of the excited electromagnetic fields in the Schwarzschild background agree with the perturbative studies within 0.7% and 5.6% for the real and the imaginary part of the ℓ=1 mode eigenfrequency, respectively. Finally we provide an estimate of the electromagnetic efficiency of this process.

  16. Exact relativistic expressions for wave refraction in a generally moving fluid.

    PubMed

    Cavalleri, G; Tonni, E; Barbero, F

    2013-04-01

    The law for the refraction of a wave when the two fluids and the interface are moving with relativistic velocities is given in an exact form, at the same time correcting a first order error in a previous paper [Cavalleri and Tonni, Phys. Rev. E 57, 3478 (1998)]. The treatment is then extended to a generally moving fluid with variable refractive index, ready to be applied to the refraction of acoustic, electromagnetic, or magnetohydrodynamic waves in the atmosphere of rapidly rotating stars. In the particular case of a gas cloud receding because of the universe expansion, our result can be applied to predict observable micro- and mesolensings. The first order approximation of our exact result for the deviation due to refraction of the light coming from a further quasar has a relativistic dependence equal to the one obtained by Einsteins' linearized theory of gravitation. PMID:23679540

  17. Stochastic Oscillations of General Relativistic Disks Described by a Fractional Langevin Equation with Fractional Gaussian Noise

    NASA Astrophysics Data System (ADS)

    Zhi-Yun, Wang; Pei-Jie, Chen

    2016-06-01

    A generalized Langevin equation driven by fractional Brownian motion is used to describe the vertical oscillations of general relativistic disks. By means of numerical calculation method, the displacements, velocities and luminosities of oscillating disks are explicitly obtained for different Hurst exponent H. The results show that as H increases, the energies and luminosities of oscillating disk are enhanced, and the spectral slope at high frequencies of the power spectrum density of disk luminosity is also increased. This could explain the observational features related to the Intra Day Variability of the BL Lac objects.

  18. The Relativistic Quantized Force: Newton's Second Law, Inertial and Gravitational; Generalization of Schwarzschild Metric for Strong and Weak Gravitational Field

    NASA Astrophysics Data System (ADS)

    Almosallami, Azzam

    2011-03-01

    In this paper we derived the relativistic Quantized force, where the force given as a function of frequency [1]. Where, in this paper we defined the relativistic momentum as a function of frequency equivalent to the energy held by a body, and time, and then the quantized force is given as the first derivative of the momentum with respect to time. Subsequently we introduce in section one Newton's second law as it is relativistic quantized, and in section two we introduce the relativistic quantized inertial force, and then the relativistic quantized gravitational force, and the quantized gravitational time dilation. At the end we shall generalize the Schwartzschild metric to describe the weak and strong gravitational field.

  19. Relativistic Jet Formation from Black Hole Magnetized Accretion Disks: Method, Tests, and Applications of a General RelativisticMagnetohydrodynamic Numerical Code

    NASA Astrophysics Data System (ADS)

    Koide, Shinji; Shibata, Kazunari; Kudoh, Takahiro

    1999-09-01

    Relativistic jets are observed in both active galactic nuclei (AGNs) and ``microquasars'' in our Galaxy. It is believed that these relativistic jets are ejected from the vicinity of black holes. To investigate the formation mechanism of these jets, we have developed a new general relativistic magnetohydrodynamic (GRMHD) code. We report on the basic methods and test calculations to check whether the code reproduces some analytical solutions, such as a standing shock and a Keplerian disk with a steady state infalling corona or with a corona in hydrostatic equilibrium. We then apply the code to the formation of relativistic MHD jets, investigating the dynamics of an accretion disk initially threaded by a uniform poloidal magnetic field in a nonrotating corona (either in a steady state infall or in hydrostatic equilibrium) around a nonrotating black hole. The numerical results show the following: as time goes on, the disk loses angular momentum as a result of magnetic braking and falls into the black hole. The infalling motion of the disk, which is faster than in the nonrelativistic case because of general relativistic effects below 3rS (rS is the Schwarzschild radius), is strongly decelerated around r=2rS by centrifugal force to form a shock inside the disk. The magnetic field is tightly twisted by the differential rotation, and plasma in the shocked region of the disk is accelerated by the JXB force to form bipolar relativistic jets. In addition, and interior to, this magnetically driven jet, we also found a gas-pressure-driven jet ejected from the shocked region by the gas-pressure force. This two-layered jet structure is formed not only in the hydrostatic corona case but also in the steady state falling corona case.

  20. HERO - A 3D general relativistic radiative post-processor for accretion discs around black holes

    NASA Astrophysics Data System (ADS)

    Zhu, Yucong; Narayan, Ramesh; Sadowski, Aleksander; Psaltis, Dimitrios

    2015-08-01

    HERO (Hybrid Evaluator for Radiative Objects) is a 3D general relativistic radiative transfer code which has been tailored to the problem of analysing radiation from simulations of relativistic accretion discs around black holes. HERO is designed to be used as a post-processor. Given some fixed fluid structure for the disc (i.e. density and velocity as a function of position from a hydrodynamic or magnetohydrodynamic simulation), the code obtains a self-consistent solution for the radiation field and for the gas temperatures using the condition of radiative equilibrium. The novel aspect of HERO is that it combines two techniques: (1) a short-characteristics (SC) solver that quickly converges to a self-consistent disc temperature and radiation field, with (2) a long-characteristics (LC) solver that provides a more accurate solution for the radiation near the photosphere and in the optically thin regions. By combining these two techniques, we gain both the computational speed of SC and the high accuracy of LC. We present tests of HERO on a range of 1D, 2D, and 3D problems in flat space and show that the results agree well with both analytical and benchmark solutions. We also test the ability of the code to handle relativistic problems in curved space. Finally, we discuss the important topic of ray defects, a major limitation of the SC method, and describe our strategy for minimizing the induced error.

  1. HEROIC: 3D general relativistic radiative post-processor with comptonization for black hole accretion discs

    NASA Astrophysics Data System (ADS)

    Narayan, Ramesh; Zhu, Yucong; Psaltis, Dimitrios; Saḑowski, Aleksander

    2016-03-01

    We describe Hybrid Evaluator for Radiative Objects Including Comptonization (HEROIC), an upgraded version of the relativistic radiative post-processor code HERO described in a previous paper, but which now Includes Comptonization. HEROIC models Comptonization via the Kompaneets equation, using a quadratic approximation for the source function in a short characteristics radiation solver. It employs a simple form of accelerated lambda iteration to handle regions of high scattering opacity. In addition to solving for the radiation field, HEROIC also solves for the gas temperature by applying the condition of radiative equilibrium. We present benchmarks and tests of the Comptonization module in HEROIC with simple 1D and 3D scattering problems. We also test the ability of the code to handle various relativistic effects using model atmospheres and accretion flows in a black hole space-time. We present two applications of HEROIC to general relativistic magnetohydrodynamics simulations of accretion discs. One application is to a thin accretion disc around a black hole. We find that the gas below the photosphere in the multidimensional HEROIC solution is nearly isothermal, quite different from previous solutions based on 1D plane parallel atmospheres. The second application is to a geometrically thick radiation-dominated accretion disc accreting at 11 times the Eddington rate. Here, the multidimensional HEROIC solution shows that, for observers who are on axis and look down the polar funnel, the isotropic equivalent luminosity could be more than 10 times the Eddington limit, even though the spectrum might still look thermal and show no signs of relativistic beaming.

  2. General-relativistic simulations of binary black hole-neutron stars: Precursor electromagnetic signals

    NASA Astrophysics Data System (ADS)

    Paschalidis, Vasileios; Etienne, Zachariah B.; Shapiro, Stuart L.

    2013-07-01

    We perform the first general relativistic force-free simulations of neutron star magnetospheres in orbit about spinning and nonspinning black holes. We find promising precursor electromagnetic emission: typical Poynting luminosities at, e.g., an orbital separation of r=6.6RNS are LEM˜6×1042(BNS,p/1013G)2(MNS/1.4M⊙)2erg/s. The Poynting flux peaks within a broad beam of ˜40° in the azimuthal direction and within ˜60° from the orbital plane, establishing a possible lighthouse effect. Our calculations, though preliminary, preview more detailed simulations of these systems that we plan to perform in the future.

  3. Numerical treatment of the spherically symmetric general-relativistic Boltzmann equation for massless and massive particles

    SciTech Connect

    Harleston, H. Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Distrito Federal ); Vishniac, E.T. )

    1992-06-15

    The Arnowitt-Deser-Misner formalism is used to write the Einstein-Boltzmann coupled system of equations. The sources of gravitational field are represented by ordinary matter described by a perfect-fluid approximation together with a particle gas described by a phase-space distribution function obeying the general-relativistic Boltzmann transport equation. Through the use of the Liouville operator in phase space, we obtain a form of the Boltzmann equation that makes it very amenable for numerical treatment. The resulting system of equations can be used for the numerical study of either massless or massive particles interacting with ordinary matter.

  4. An investigation of the general relativistic (1PN) hydrodynamics in DSX scheme.

    NASA Astrophysics Data System (ADS)

    Dai, Yurong; Wu, Xuejun; Xu, Chongming

    1999-11-01

    In this paper the general relativistic (1PN) hydrodynamics is established by means of DSX scheme in both local and global coordinates. The stress-energy tensor Tμν of ordinary fluids is calculated in terms of the software Maple, then the energy equation and Euler equation are got in DSX scheme after being reduced and trimmed. All these are done in local coordinates, and the result in global coordinates can be found through the transformation law. Finally, the energy equation and Euler equation in local coordinates in the case of perfect fluids are discussed. The result in global coordinates can be found in the same way.

  5. NEUTRINO SPECTRA FROM ACCRETION DISKS: NEUTRINO GENERAL RELATIVISTIC EFFECTS AND THE CONSEQUENCES FOR NUCLEOSYNTHESIS

    SciTech Connect

    Caballero, O. L.; McLaughlin, G. C.; Surman, R. E-mail: olcaball@ncsu.edu E-mail: surmanr@union.edu

    2012-02-01

    Black hole (BH) accretion disks have been proposed as good candidates for a range of interesting nucleosynthesis, including the r-process. The presence of the BH influences the neutrino fluxes and affects the nucleosynthesis resulting from the interaction of the emitted neutrinos and hot outflowing material ejected from the disk. We study the impact of general relativistic effects on the neutrinos emitted from BH accretion disks. We present abundances obtained by considering null geodesics and energy shifts for two different disk models. We find that both the bending of the neutrino trajectories and the energy shifts have important consequences for the nucleosynthetic outcome.

  6. General relativistic x ray (UV) polarization rotations as a quantitative test for black holes

    NASA Technical Reports Server (NTRS)

    Stark, Richard F.

    1989-01-01

    It is now 11 years since a potentially easily observable and quantitative test for black holes using general relativistic polarization rotations was proposed (Stark and Connors 1977, and Connors and Stark 1977). General relativistic rotations of the x ray polarization plane of 10 to 100 degrees with x ray energy (between 1 and 100 keV) are predicted for black hole x ray binaries. (Classically, by symmetry, there is no rotation.) Unfortunately, x ray polarimetry has not been taken sufficiently seriously during this period, and this test has not yet been performed. A similar (though probably less clean) effect is expected in the UV for supermassive black holes in some quasars active galactic nuclei. Summarizing: (1) a quantitative test (proposed in 1977) for black holes exists; (2) x ray polarimetry of galactic x ray binaries sensitive to at least 1/2 percent between 1 keV and 100 keV is needed (polarimetry in the UV of quasars and AGN will also be of interest); and (3) proportional counters using timerise discrimination were shown in laboratory experiments able to perform x ray polarimetry and this and other methods need to be developed.

  7. THE GENERAL RELATIVISTIC EQUATIONS OF RADIATION HYDRODYNAMICS IN THE VISCOUS LIMIT

    SciTech Connect

    Coughlin, Eric R.; Begelman, Mitchell C. E-mail: mitch@jila.colorado.edu

    2014-12-20

    We present an analysis of the general relativistic Boltzmann equation for radiation, appropriate to the case where particles and photons interact through Thomson scattering, and derive the radiation energy-momentum tensor in the diffusion limit with viscous terms included. Contrary to relativistic generalizations of the viscous stress tensor that appear in the literature, we find that the stress tensor should contain a correction to the comoving energy density proportional to the divergence of the four-velocity, as well as a finite bulk viscosity. These modifications are consistent with the framework of radiation hydrodynamics in the limit of large optical depth, and do not depend on thermodynamic arguments such as the assignment of a temperature to the zeroth-order photon distribution. We perform a perturbation analysis on our equations and demonstrate that as long as the wave numbers do not probe scales smaller than the mean free path of the radiation, the viscosity contributes only decaying, i.e., stable, corrections to the dispersion relations. The astrophysical applications of our equations, including jets launched from super-Eddington tidal disruption events and those from collapsars, are discussed and will be considered further in future papers.

  8. The General Relativistic Equations of Radiation Hydrodynamics in the Viscous Limit

    NASA Astrophysics Data System (ADS)

    Coughlin, Eric R.; Begelman, Mitchell C.

    2014-12-01

    We present an analysis of the general relativistic Boltzmann equation for radiation, appropriate to the case where particles and photons interact through Thomson scattering, and derive the radiation energy-momentum tensor in the diffusion limit with viscous terms included. Contrary to relativistic generalizations of the viscous stress tensor that appear in the literature, we find that the stress tensor should contain a correction to the comoving energy density proportional to the divergence of the four-velocity, as well as a finite bulk viscosity. These modifications are consistent with the framework of radiation hydrodynamics in the limit of large optical depth, and do not depend on thermodynamic arguments such as the assignment of a temperature to the zeroth-order photon distribution. We perform a perturbation analysis on our equations and demonstrate that as long as the wave numbers do not probe scales smaller than the mean free path of the radiation, the viscosity contributes only decaying, i.e., stable, corrections to the dispersion relations. The astrophysical applications of our equations, including jets launched from super-Eddington tidal disruption events and those from collapsars, are discussed and will be considered further in future papers.

  9. General method of the relativistic Foldy-Wouthuysen transformation and proof of validity of the Foldy-Wouthuysen Hamiltonian

    NASA Astrophysics Data System (ADS)

    Silenko, Alexander J.

    2015-02-01

    A general method of the Foldy-Wouthuysen transformation is developed. This method is applicable to relativistic particles with any spin in arbitrarily strong external fields. It can be used when the de Broglie wavelength is much smaller than the characteristic distance. Contrary to previously developed relativistic methods, the present method satisfies the condition of the exact Foldy-Wouthuysen transformation and is well substantiated. The derived relativistic Foldy-Wouthuysen Hamiltonian is expanded in powers of the Planck constant. In this expansion, terms proportional to the zero and first powers are determined exactly in accordance with the above condition, and terms proportional to higher powers are not specified. The obtained result agrees with the corresponding formula for the Foldy-Wouthuysen Hamiltonian previously deduced by an iterative relativistic method and proves the validity of results obtained with this formula.

  10. Dissipative collapse of axially symmetric, general relativistic sources: A general framework and some applications

    NASA Astrophysics Data System (ADS)

    Herrera, L.; Di Prisco, A.; Ibáñez, J.; Ospino, J.

    2014-04-01

    We carry out a general study on the collapse of axially (and reflection-)symmetric sources in the context of general relativity. All basic equations and concepts required to perform such a general study are deployed. These equations are written down for a general anisotropic dissipative fluid. The proposed approach allows for analytical studies as well as for numerical applications. A causal transport equation derived from the Israel-Stewart theory is applied, to discuss some thermodynamic aspects of the problem. A set of scalar functions (the structure scalars) derived from the orthogonal splitting of the Riemann tensor are calculated and their role in the dynamics of the source is clearly exhibited. The characterization of the gravitational radiation emitted by the source is discussed.

  11. General-relativistic celestial mechanics. I. Method and definition of reference systems

    SciTech Connect

    Damour, T. Departement d'Astrophysique Relativiste et de Cosmologie, Observatoire de Paris, Centre National de la Recherche Scientifique, 92195 Meudon CEDEX, France ); Soffel, M.; Xu, C. )

    1991-05-15

    We present a new formalism for treating the general-relativistic celestial mechanics of systems of {ital N} arbitrarily composed and shaped, weakly self-gravitating, rotating, deformable bodies. This formalism is aimed at yielding a complete description, at the first post-Newtonian approximation level, of (i) the global dynamics of such {ital N}-body systems ( external problem''), (ii) the local gravitational structure of each body ( internal problem''), and, (iii) the way the external and the internal problems fit together ( theory of reference systems''). This formalism uses in a complementary manner {ital N}+1 coordinate charts (or reference systems''): one global'' chart for describing the overall dynamics of the {ital N} bodies, and {ital N} local'' charts adapted to the separate description of the structure and environment of each body. The main tool which allows us to develop, in an elegant manner, a constructive theory of these {ital N}+1 reference systems is a systematic use of a particular exponential'' parametrization of the metric tensor which has the effect of linearizing both the field equations, and the transformation laws under a change of reference system. This linearity allows a treatment of the first post-Newtonian relativistic celestial mechanics which is, from a structural point of view, nearly as simple and transparent as its Newtonian analogue.

  12. General relativistic N-body simulations in the weak field limit

    NASA Astrophysics Data System (ADS)

    Adamek, Julian; Daverio, David; Durrer, Ruth; Kunz, Martin

    2013-11-01

    We develop a formalism for general relativistic N-body simulations in the weak field regime, suitable for cosmological applications. The problem is kept tractable by retaining the metric perturbations to first order, the first derivatives to second order, and second derivatives to all orders, thus taking into account the most important nonlinear effects of Einstein gravity. It is also expected that any significant “backreaction” should appear at this order. We show that the simulation scheme is feasible in practice by implementing it for a plane-symmetric situation and running two test cases, one with only cold dark matter, and one which also includes a cosmological constant. For these plane-symmetric situations, the deviations from the usual Newtonian N-body simulations remain small and, apart from a nontrivial correction to the background, can be accurately estimated within the Newtonian framework. The correction to the background scale factor, which is a genuine backreaction effect, can be robustly obtained with our algorithm. Our numerical approach is also naturally suited for the inclusion of extra relativistic fields and thus for dark energy or modified gravity simulations.

  13. ECHO: a Eulerian conservative high-order scheme for general relativistic magnetohydrodynamics and magnetodynamics

    NASA Astrophysics Data System (ADS)

    Del Zanna, L.; Zanotti, O.; Bucciantini, N.; Londrillo, P.

    2007-10-01

    Aims:We present a new numerical code, ECHO, based on a Eulerian conservative high-order scheme for time dependent three-dimensional general relativistic magnetohydrodynamics (GRMHD) and magnetodynamics (GRMD). ECHO is aimed at providing a shock-capturing conservative method able to work at an arbitrary level of formal accuracy (for smooth flows), where the other existing GRMHD and GRMD schemes yield an overall second order at most. Moreover, our goal is to present a general framework based on the 3+1 Eulerian formalism, allowing for different sets of equations and different algorithms and working in a generic space-time metric, so that ECHO may be easily coupled to any solver for Einstein's equations. Methods: Our finite-difference conservative scheme previously developed for special relativistic hydrodynamics and MHD is extended here to the general relativistic case. Various high-order reconstruction methods are implemented and a two-wave approximate Riemann solver is used. The induction equation is treated by adopting the upwind constrained transport (UCT) procedures, appropriate to preserving the divergence-free condition of the magnetic field in shock-capturing methods. The limiting case of magnetodynamics (also known as force-free degenerate electrodynamics) is implemented by simply replacing the fluid velocity with the electromagnetic drift velocity and by neglecting the contribution of matter to the stress tensor. Results: ECHO is particularly accurate, efficient, versatile, and robust. It has been tested against several astrophysical applications, like magnetized accretion onto black holes and constant angular momentum thick disks threaded by toroidal fields. A novel test of the propagation of large-amplitude, circularly polarized Alfvén waves is proposed, and this allows us to prove the spatial and temporal high-order properties of ECHO very accurately. In particular, we show that reconstruction based on a monotonicity-preserving (MP) filter applied to a

  14. General relativistic corrections in the gamma-ray emission from pulsars

    NASA Technical Reports Server (NTRS)

    Gonthier, P. L.; Harding, A. K.

    1994-01-01

    We examine the importance of general relativistic corrections to the production of gamma rays near the surface of a neutron star. Due to the change in the magnetic dipole field in curved spacetime, the polar cap angle decreases by 30% compared to flat spacetime. However, the curved photon trajectories compensate for the decrease in the polar cap angle, and, as a result, the pulse profile of the photons emitted parallel to the field is expected to be very similar in curved spacetime and in flat spacetime. We find that the curved spacetime metric significantly increases the magnitude of the magnetic field and, therefore, the attenuation coefficients of curvature radiation gamma rays for pair production in a magnetic field can be increased by factors as large as 100. As a resutl the survival distance of 1 GeV photons for pair production is decreased by a factor of 2 for B is approximately 10(exp 12) G.

  15. General Relativistic Magnetohydrodynamics Simulations of Tilted Black Hole Accretion Flows and Their Radiative Properties

    NASA Astrophysics Data System (ADS)

    Shiokawa, Hotaka; Gammie, C. F.; Dolence, J.; Noble, S. C.

    2013-01-01

    We perform global General Relativistic Magnetohydrodynamics (GRMHD) simulations of non-radiative, magnetized disks that are initially tilted with respect to the black hole's spin axis. We run the simulations with different size and tilt angle of the tori for 2 different resolutions. We also perform radiative transfer using Monte Carlo based code that includes synchrotron emission, absorption and Compton scattering to obtain spectral energy distribution and light curves. Similar work was done by Fragile et al. (2007) and Dexter & Fragile (2012) to model the super massive black hole SgrA* with tilted accretion disks. We compare our results of fully conservative hydrodynamic code and spectra that include X-ray, with their results.

  16. General Relativistic Ray Tracing for X-ray Reverberation and Polarimetry Studies of Black Holes

    NASA Astrophysics Data System (ADS)

    Hoormann, Janie; Krawczynski, Henric

    2015-01-01

    We present the results of General Relativistic (GR) ray tracing calculations of the X-ray emission from mass accreting stellar mass and supermassive black holes. Our study aims at exploring the X-ray reverberation and X-ray polarimetry signatures of different accretion flow geometries and different spacetime backgrounds (GR and non-GR backgrounds). We present first results derived for the well-known lamp-post model, where a point source of continuum emission illuminates an accretion disk with high energy photons which are tracked by parallel transporting the photon wave and polarization vectors. The simulation code models the reprocessing and reflection by of photons impinging on the accretion disk. We study the degeneracy of astrophysical parameters (parametrizing the geometry of the accretion disk and the location and properties of the lamppost photon source) and the parameters describing the underlying metrics. We emphasize furthermore the difference of the observational signatures for stellar mass and supermassive black holes.

  17. General Relativistic Mini-Disk Dynamics during Black Hole Binary Inspiral

    NASA Astrophysics Data System (ADS)

    Bowen, Dennis

    2016-01-01

    During galaxy mergers, as a result of dynamical friction (stars, gas, etc.) and gravitational slingshot, the supermassive black holes (SMBHs) from each galaxy will become gravitationally bound and eventually merge due to gravitational radiation. It is expected that gas will form a circumbinary accretion disk around the SMBH binary that will persistently feed individual "mini-disks" via dense streams out to their tidal truncation radii. However, these radii are not well known during the late stages of inspiral and merger. We present general relativistic hydrodynamic simulations aimed at resolving this uncertainty and producing templates of unique electromagnetic (EM) signatures for such systems to assist in direct observational detection with currently available observatories. We place particular emphasis on the dynamics of the individual "mini-disks" where violent shocks via disk-disk and disk-stream interactions will likely produce intense EM emission.

  18. Non-Relativistic Phase Shifts for Scattering on Generalized Radial Yukawa Potentials

    NASA Astrophysics Data System (ADS)

    O. J., Oluwadare; K. E., Thylwe; K. J., Oyewumi

    2016-04-01

    Non-relativistic phase shifts for a generalized Yukawa potential V(r) = ‑ V0(e‑αr/r) ‑ V1(e‑2αr/r2) are studied by the amplitude-phase method and by a frequently used analytic method based on a Pekeris-type approximation of power-law potential terms. Small variations of V1 seem to have marginal effects on the effective potential and on exact phase shifts. However, as pointed out in this study, a Pekeris-type approximation in scattering applications often implies serious distortions of both effective potentials and phase shifts. The Pekeris-type based analytic approximation in this study seems to give low-quality scattering results for this model potential at low energies.

  19. General-relativistic Simulations of Three-dimensional Core-collapse Supernovae

    NASA Astrophysics Data System (ADS)

    Ott, Christian D.; Abdikamalov, Ernazar; Mösta, Philipp; Haas, Roland; Drasco, Steve; O'Connor, Evan P.; Reisswig, Christian; Meakin, Casey A.; Schnetter, Erik

    2013-05-01

    We study the three-dimensional (3D) hydrodynamics of the post-core-bounce phase of the collapse of a 27 M ⊙ star and pay special attention to the development of the standing accretion shock instability (SASI) and neutrino-driven convection. To this end, we perform 3D general-relativistic simulations with a three-species neutrino leakage scheme. The leakage scheme captures the essential aspects of neutrino cooling, heating, and lepton number exchange as predicted by radiation-hydrodynamics simulations. The 27 M ⊙ progenitor was studied in 2D by Müller et al., who observed strong growth of the SASI while neutrino-driven convection was suppressed. In our 3D simulations, neutrino-driven convection grows from numerical perturbations imposed by our Cartesian grid. It becomes the dominant instability and leads to large-scale non-oscillatory deformations of the shock front. These will result in strongly aspherical explosions without the need for large-scale SASI shock oscillations. Low-l-mode SASI oscillations are present in our models, but saturate at small amplitudes that decrease with increasing neutrino heating and vigor of convection. Our results, in agreement with simpler 3D Newtonian simulations, suggest that once neutrino-driven convection is started, it is likely to become the dominant instability in 3D. Whether it is the primary instability after bounce will ultimately depend on the physical seed perturbations present in the cores of massive stars. The gravitational wave signal, which we extract and analyze for the first time from 3D general-relativistic models, will serve as an observational probe of the postbounce dynamics and, in combination with neutrinos, may allow us to determine the primary hydrodynamic instability.

  20. GENERAL-RELATIVISTIC SIMULATIONS OF THREE-DIMENSIONAL CORE-COLLAPSE SUPERNOVAE

    SciTech Connect

    Ott, Christian D.; Abdikamalov, Ernazar; Moesta, Philipp; Haas, Roland; Drasco, Steve; O'Connor, Evan P.; Reisswig, Christian; Meakin, Casey A.; Schnetter, Erik

    2013-05-10

    We study the three-dimensional (3D) hydrodynamics of the post-core-bounce phase of the collapse of a 27 M{sub Sun} star and pay special attention to the development of the standing accretion shock instability (SASI) and neutrino-driven convection. To this end, we perform 3D general-relativistic simulations with a three-species neutrino leakage scheme. The leakage scheme captures the essential aspects of neutrino cooling, heating, and lepton number exchange as predicted by radiation-hydrodynamics simulations. The 27 M{sub Sun} progenitor was studied in 2D by Mueller et al., who observed strong growth of the SASI while neutrino-driven convection was suppressed. In our 3D simulations, neutrino-driven convection grows from numerical perturbations imposed by our Cartesian grid. It becomes the dominant instability and leads to large-scale non-oscillatory deformations of the shock front. These will result in strongly aspherical explosions without the need for large-scale SASI shock oscillations. Low-l-mode SASI oscillations are present in our models, but saturate at small amplitudes that decrease with increasing neutrino heating and vigor of convection. Our results, in agreement with simpler 3D Newtonian simulations, suggest that once neutrino-driven convection is started, it is likely to become the dominant instability in 3D. Whether it is the primary instability after bounce will ultimately depend on the physical seed perturbations present in the cores of massive stars. The gravitational wave signal, which we extract and analyze for the first time from 3D general-relativistic models, will serve as an observational probe of the postbounce dynamics and, in combination with neutrinos, may allow us to determine the primary hydrodynamic instability.

  1. Evolution of Central Moments for a General-Relativistic Boltzmann Equation

    NASA Astrophysics Data System (ADS)

    Banach, Zbigniew; Larecki, Wieslaw

    Beginning from the relativistic Boltzmann equation in a curved space-time, and assuming that there exists a fiducial congruence of timelike world lines with four-velocity vector field u, it is the aim of this paper to present a systematic derivation of a hierarchy of closed systems of moment equations. These systems are found by using the closure by entropy maximization. Our concepts are primarily applied to the formalism of central moments because if an alternative and more familiar theory of covariant moments is taken into account, then the method of maximum entropy is ill-defined in a neighborhood of equilibrium states. The central moments are not covariant in the following sense: two observers looking at the same relativistic gas will, in general, extract two different sets of central moments, not related to each other by a tensorial linear transformation. After a brief review of the formalism of trace-free symmetric spacelike tensors, the differential equations for irreducible central moments are obtained and compared with those of Ellis et al. [Ann. Phys. (NY) 150 (1983) 455]. We derive some auxiliary algebraic identities which involve the set of central moments and the corresponding set of Lagrange multipliers; these identities enable us to show that there is an additional balance law interpreted as the equation of balance of entropy. The above results are valid for an arbitrary choice of the Lorentzian metric g and the four-velocity vector field u. Later, the definition of u as in the well-known theory of Arnowitt, Deser, and Misner is proposed in order to construct a hierarchy of symmetric hyperbolic systems of field equations. Also, the Eckart and Landau-Lifshitz definitions of u are discussed. Specifically, it is demonstrated that they lead, in general, to the systems of nonconservative equations.

  2. General Relativistic Continuum Mechanics and the Post-Newtonian Equations of Motion

    NASA Astrophysics Data System (ADS)

    Morrill, Thomas H.

    This dissertation examines aspects of general relativistic continuum mechanics. It deals with, but does not restrict itself to, perfectly elastic materials. It also emphasizes the derivation of their equations of motion, in the post-Newtonian approximation. As a basis for this study, I present a reformulation, based on the tetrad formalism, of Carter and Quintana's theory of general relativistic elastic continua. I derive a field Lagrangian describing perfect material media; show that the usual covariant conservations law (vanishing of the covariant divergence of the energy -momentum tensor) for perfectly elastic media is fully equivalent to the Euler-Lagrange equations describing these same media; and further show that the equations of motion for such materials follow directly from Einsteins's field equations. In addition, I introduce a version of Mach's principle that is completely independent of metric. My version of this principle shows that the local mass density in curved space -time partially depends on the amount and distribution of mass energy in the entire universe and is related to the mass density that would occur if space-time were flat. I also expand the total Lagrangian (field plus gravitational) in an EIH (Einstein, Infeld, Hoffmann) series to obtain a total post-Newtonian Lagrangian. This Lagrangian fails to reproduce even the Newtonian gravitational potential unless it incorporates the post-Newtonian form of my version of Mach's principle. I derive the metric coefficients required to obtain the post-Newtonian equations of motion, as well as the post-Newtonian equations of motion for perfect continua, from the Post-Newtonian Lagrangian incorporating my version of Mach's principle. These results agree with those found by solving Einstein's equations for the metric coefficients and by deriving the post-Newtonian equations of motion from the covariant conservation law.

  3. Cosmology and stellar equilibrium using Newtonian hydrodynamics with general relativistic pressure

    NASA Astrophysics Data System (ADS)

    Baqui, P. O.; Fabris, J. C.; Piattella, O. F.

    2016-04-01

    We revisit the analysis made by Hwang and Noh [JCAP 1310 (2013)] aiming the construction of a Newtonian set of equations incorporating pressure effects typical of the General Relativity theory. We explicitly derive the Hwang-Noh equations, comparing them with similar computations found in the literature. Then, we investigate i) the cosmological expansion, ii) linear cosmological perturbations theory and iii) stellar equilibrium by using the new set of equations and comparing the results with those coming from the usual Newtonian theory, from the Neo-Newtonian theory and from the General Relativity theory. We show that the predictions for the background evolution of the Universe are deeply changed with respect to the General Relativity theory: the acceleration of the Universe is achieved with positive pressure. On the other hand, the behaviour of small cosmological perturbations reproduces the one found in the relativistic context, even if only at small scales. We argue that this last result may open new possibilities for numerical simulations for structure formation in the Universe. Finally, the properties of neutron stars are qualitatively reproduced by Hwang-Noh equations, but the upper mass limit is at least one order of magnitude higher than the one obtained in General Relativity.

  4. Non-axisymmetric annular curtain stability

    NASA Astrophysics Data System (ADS)

    Ahmed, Zahir U.; Khayat, Roger E.; Maissa, Philippe; Mathis, Christian

    2013-08-01

    A stability analysis of non-axisymmetric annular curtain is carried out for an axially moving viscous jet subject in surrounding viscous gas media. The effect of inertia, surface tension, gas-to-liquid density ratio, inner-to-outer radius ratio, and gas-to-liquid viscosity ratio on the stability of the jet is studied. In general, the axisymmetric disturbance is found to be the dominant mode. However, for small wavenumber, the non-axisymmetric mode is the most unstable mode and the one likely observed in reality. Inertia and the viscosity ratio for non-axisymmetric disturbances show a similar stability influence as observed for axisymmetric disturbances. The maximum growth rate in non-axisymmetric flow, interestingly, appears at very small wavenumber for all inertia levels. The dominant wavenumber increases (decreases) with inertia for non-axisymmetric (axisymmetric) flow. Gas-to-liquid density ratio, curvature effect, and surface tension, however, exhibit an opposite influence on growth rate compared to axisymmetric disturbances. Surface tension tends to stabilize the flow with reductions of the unstable wavenumber range and the maximum growth rate as well as the dominant wavenumber. The dominant wavenumber remains independent of viscosity ratio indicating the viscosity ratio increases the breakup length of the sheet with very little influence on the size of the drops. The range of unstable wavenumbers is affected only by curvature in axisymmetric flow, whereas all the stability parameters control the range of unstable wavenumbers in non-axisymmetric flow. Inertia and gas density increase the unstable wavenumber range, whereas the radius ratio, surface tension, and the viscosity ratio decrease the unstable wavenumber range. Neutral curves are plotted to separate the stable and unstable domains. Critical radius ratio decreases linearly and nonlinearly with the wavenumber for axisymmetric and non-axisymmetric disturbances, respectively. At smaller Weber numbers, a

  5. Resonant behavior of stochastic oscillations of general relativistic disks driven by a memory-damped friction

    NASA Astrophysics Data System (ADS)

    Wang, Zhi-Yun; Chen, Pei-Jie; Zhang, Liang-Ying

    2015-05-01

    By using a generalized Langevin equation to describe the vertical oscillations of a general relativistic disk subjected to a memory-damped friction and a stochastic force, we derive the power spectrum density (PSD) of accretion disk oscillating luminosity by the method of Laplace transform, and discuss the influence of the system parameters on the resonant behavior in PSD curves. The results show that as the damping strength α and memory time τ of the friction increase, the variation of PSD with spectrum frequency f from monotonous decreasing to occurring maximums, and the phenomenon of a general stochastic resonance (SR) with a single peak and multi-peaks can be found in PSD curves. The radial distance parameter n, the mass M, and spin parameter a* of the black hole determine the inherent frequency of vertical oscillations in the disk, and they have significant influences on the SR phenomena in a system of black hole binaries. Project supported by the National Natural Science Foundation of China (Grant No. 11045004) and the Key Program of the Scientific Research Foundation of the Education Bureau of Hubei Province, China (Grant No. D20132603).

  6. Towards Observational Astronomy of Jets in Active Galaxies from General Relativistic Magnetohydrodynamic Simulations

    NASA Astrophysics Data System (ADS)

    Anantua, Richard; Roger Blandford, Jonathan McKinney and Alexander Tchekhovskoy

    2016-01-01

    We carry out the process of "observing" simulations of active galactic nuclei (AGN) with relativistic jets (hereafter called jet/accretion disk/black hole (JAB) systems) from ray tracing between image plane and source to convolving the resulting images with a point spread function. Images are generated at arbitrary observer angle relative to the black hole spin axis by implementing spatial and temporal interpolation of conserved magnetohydrodynamic flow quantities from a time series of output datablocks from fully general relativistic 3D simulations. We also describe the evolution of simulations of JAB systems' dynamical and kinematic variables, e.g., velocity shear and momentum density, respectively, and the variation of these variables with respect to observer polar and azimuthal angles. We produce, at frequencies from radio to optical, fixed observer time intensity and polarization maps using various plasma physics motivated prescriptions for the emissivity function of physical quantities from the simulation output, and analyze the corresponding light curves. Our hypothesis is that this approach reproduces observed features of JAB systems such as superluminal bulk flow projections and quasi-periodic oscillations in the light curves more closely than extant stylized analytical models, e.g., cannonball bulk flows. Moreover, our development of user-friendly, versatile C++ routines for processing images of state-of-the-art simulations of JAB systems may afford greater flexibility for observing a wide range of sources from high power BL-Lacs to low power quasars (possibly with the same simulation) without requiring years of observation using multiple telescopes. Advantages of observing simulations instead of observing astrophysical sources directly include: the absence of a diffraction limit, panoramic views of the same object and the ability to freely track features. Light travel time effects become significant for high Lorentz factor and small angles between

  7. A GENERAL RELATIVISTIC MODEL OF ACCRETION DISKS WITH CORONAE SURROUNDING KERR BLACK HOLES

    SciTech Connect

    You Bei; Cao Xinwu; Yuan Yefei E-mail: cxw@shao.ac.cn

    2012-12-20

    We calculate the structure of a standard accretion disk with a corona surrounding a massive Kerr black hole in the general relativistic frame, in which the corona is assumed to be heated by the reconnection of the strongly buoyant magnetic fields generated in the cold accretion disk. The emergent spectra of accretion disk-corona systems are calculated by using the relativistic ray-tracing method. We propose a new method to calculate the emergent Comptonized spectra from the coronae. The spectra of disk-corona systems with a modified {alpha}-magnetic stress show that both the hard X-ray spectral index and the hard X-ray bolometric correction factor L{sub bol}/L{sub X,2-10keV} increase with the dimensionless mass accretion rate, which is qualitatively consistent with the observations of active galactic nuclei. The fraction of the power dissipated in the corona decreases with increasing black hole spin parameter a, which leads to lower electron temperatures of the coronae for rapidly spinning black holes. The X-ray emission from the coronae surrounding rapidly spinning black holes becomes weak and soft. The ratio of the X-ray luminosity to the optical/UV luminosity increases with the viewing angle, while the spectral shape in the X-ray band is insensitive to the viewing angle. We find that the spectral index in the infrared waveband depends on the mass accretion rate and the black hole spin a, which deviates from the f{sub {nu}}{proportional_to}{nu}{sup 1/3} relation expected by the standard thin disk model.

  8. General-relativistic magnetohydrodynamics simulations of black hole accretion disks: Dynamics and radiative properties

    NASA Astrophysics Data System (ADS)

    Shiokawa, Hotaka

    The goal of the series of studies in this thesis is to understand the black hole accretion process and predict its observational properties. The highly non-linear process involves a turbulent magnetized plasma in a general relativistic regime, thus making it hard to study analytically. We use numerical simulations, specifically general relativistic magnetohydrodynamics (GRMHD), to construct a realistic dynamical and radiation model of accretion disks. Our simulations are for black holes in low luminous regimes that probably possesses a hot and thick accretion disk. Flows in this regime are called radiatively inefficient accretion flows (RIAF). The most plausible mechanism for transporting angular momentum is turbulence induced by magnetorotational instability (MRI). The RIAF model has been used to model the supermassive black hole at the center of our Milky Way galaxy, Sagittarius A* (Sgr A*). Owing to its proximity, rich observational data of Sgr A* is available to compare with the simulation results. We focus mainly on four topics. First, we analyse numerical convergence of 3D GRMHD global disk simulations. Convergence is one of the essential factors in deciding quantitative outcomes of the simulations. We analyzed dimensionless shell-averaged quantities such as plasma beta, the azimuthal correlation length (angle) of fluid variables, and spectra of the source for four different resolutions. We found that all the variables converged with the highest resolution (384x384x256 in radial, poloidal, and azimuthal directions) except the magnetic field correlation length. It probably requires another factor of 2 in resolution to achieve convergence. Second, we studied the effect of equation of state on dynamics of GRMHD simulation and radiative transfer. Temperature of RIAF gas is high, and all the electrons are relativistic, but not the ions. In addition, the dynamical time scale of the accretion disk is shorter than the collisional time scale of electrons and ions

  9. Quasi-Radial Modes of Pulsating Neutron Stars: Numerical Results for General-Relativistic Rigidly Rotating Polytropic Models

    NASA Astrophysics Data System (ADS)

    Geroyannis, Vassilis; Tzelati, Eleftheria

    In this paper we compute general-relativistic polytropic models simulating rigidly rotating, pulsating neutron stars. These relativistic compact objects, with a radius of $\\sim 10 \\, \\mathrm{km}$ and mass between $\\sim 1.4$ and $3.2$ solar masses, are closely related to pulsars. We emphasize on computing the change in the pulsation eigenfrequencies owing to a rigid rotation, which, in turn, is a decisive issue for studying stability of such objects. In our computations, we keep rotational perturbation terms of up to second order in the angular velocity.

  10. Simple solutions for relativistic generalizations of the Child-Langmuir law and the Langmuir-Blodgett law

    SciTech Connect

    Zhang Yongpeng; Liu Guozhi; Yang Zhanfeng; Shao Hao; Xiao Renzhen; Xing Qingzi; Zhong Huaqiang; Lin Yuzheng

    2009-04-15

    In this paper, the Child-Langmuir law and Langmuir-Blodgett law are generalized to the relativistic regime by a simple method. Two classical laws suitable for the nonrelativistic regime are modified to simple approximate expressions applicable for calculating the space-charge-limited currents of one-dimensional steady-state planar diodes and coaxial diodes under the relativistic regime. The simple approximate expressions, extending the Child-Langmuir law and Langmuir-Blodgett law to fit the full range of voltage, have small relative errors less than 1% for one-dimensional planar diodes and less than 5% for coaxial diodes.

  11. Generalized Lagrangian-Path Representation of Non-Relativistic Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Tessarotto, Massimo; Cremaschini, Claudio

    2016-08-01

    In this paper a new trajectory-based representation to non-relativistic quantum mechanics is formulated. This is ahieved by generalizing the notion of Lagrangian path (LP) which lies at the heart of the deBroglie-Bohm " pilot-wave" interpretation. In particular, it is shown that each LP can be replaced with a statistical ensemble formed by an infinite family of stochastic curves, referred to as generalized Lagrangian paths (GLP). This permits the introduction of a new parametric representation of the Schrödinger equation, denoted as GLP-parametrization, and of the associated quantum hydrodynamic equations. The remarkable aspect of the GLP approach presented here is that it realizes at the same time also a new solution method for the N-body Schrödinger equation. As an application, Gaussian-like particular solutions for the quantum probability density function (PDF) are considered, which are proved to be dynamically consistent. For them, the Schrödinger equation is reduced to a single Hamilton-Jacobi evolution equation. Particular solutions of this type are explicitly constructed, which include the case of free particles occurring in 1- or N-body quantum systems as well as the dynamics in the presence of suitable potential forces. In all these cases the initial Gaussian PDFs are shown to be free of the spreading behavior usually ascribed to quantum wave-packets, in that they exhibit the characteristic feature of remaining at all times spatially-localized.

  12. Newtonian analogue of static general relativistic spacetimes: An extension to naked singularities

    NASA Astrophysics Data System (ADS)

    Ghosh, Shubhrangshu; Sarkar, Tamal; Bhadra, Arunava

    2015-10-01

    We formulate a generic Newtonian-like analogous potential for static spherically symmetric general relativistic (GR) spacetime and subsequently derived proper Newtonian-like analogous potential corresponding to Janis-Newman-Winicour (JNW) and Reissner-Nordström (RN) spacetimes, both exhibiting naked singularities. The derived potentials were found to reproduce the entire GR features including the orbital dynamics of the test particle motion and the orbital trajectories, with precise accuracy. The nature of the particle orbital dynamics including their trajectory profiles in JNW and RN geometries show altogether different behaviors with distinctive traits as compared to the nature of particle dynamics in Schwarzschild geometry. Exploiting the Newtonian-like analogous potentials, we found that the radiative efficiency of a geometrically thin and optically thick Keplerian accretion disk around naked singularities corresponding to both JNW and RN geometries, in general, is always higher than that for Schwarzschild geometry. The derived potentials would thus be useful to study astrophysical processes, especially to investigate more complex accretion phenomena in active galactic nuclei (AGNs) or in x-ray binaries (XRBs) in the presence of naked singularities and thereby to explore any noticeable differences in their observational features from those in the presence of black holes (BHs) to ascertain outstanding debatable issues relating to gravity—whether the end state of gravitational collapse in our physical Universe renders BH or naked singularity.

  13. General relativistic, nonstandard model for the dark sector of the Universe

    NASA Astrophysics Data System (ADS)

    Stichel, P. C.; Zakrzewski, W. J.

    2015-01-01

    We present a general relativistic version of the self-gravitating fluid model for the dark sector of the Universe (darkon fluid) introduced in Stichel and Zakrzewski (Phys Rev D 80:083513, 2009) and extended and reviewed in Stichel and Zakrzewski (Entropy 15:559, 2013). This model contains no free parameters in its Lagrangian. The resulting energy-momentum tensor is dustlike with a nontrivial energy flow. In an approximation valid at sub-Hubble scales we find that the present-day cosmic acceleration is not attributed to any kind of negative pressure but it is due to a dynamically determined negative energy density. This property turns out to be equivalent to a time-dependent spatial curvature. The obtained cosmological equations, at sub-Hubble scales, agree with those of the nonrelativistic model but they are given a new physical interpretation. Furthermore, we have derived the self-consistent equation to be satisfied by the nonrelativistic gravitational potential produced by a galactic halo in our model from a weak-field limit of a generalized Tolman-Oppenheimer-Volkoff equation.

  14. Generalized Lagrangian-Path Representation of Non-Relativistic Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Tessarotto, Massimo; Cremaschini, Claudio

    2016-02-01

    In this paper a new trajectory-based representation to non-relativistic quantum mechanics is formulated. This is ahieved by generalizing the notion of Lagrangian path (LP) which lies at the heart of the deBroglie-Bohm " pilot-wave" interpretation. In particular, it is shown that each LP can be replaced with a statistical ensemble formed by an infinite family of stochastic curves, referred to as generalized Lagrangian paths (GLP). This permits the introduction of a new parametric representation of the Schrödinger equation, denoted as GLP-parametrization, and of the associated quantum hydrodynamic equations. The remarkable aspect of the GLP approach presented here is that it realizes at the same time also a new solution method for the N-body Schrödinger equation. As an application, Gaussian-like particular solutions for the quantum probability density function (PDF) are considered, which are proved to be dynamically consistent. For them, the Schrödinger equation is reduced to a single Hamilton-Jacobi evolution equation. Particular solutions of this type are explicitly constructed, which include the case of free particles occurring in 1- or N-body quantum systems as well as the dynamics in the presence of suitable potential forces. In all these cases the initial Gaussian PDFs are shown to be free of the spreading behavior usually ascribed to quantum wave-packets, in that they exhibit the characteristic feature of remaining at all times spatially-localized.

  15. Hybrid guiding-centre/full-orbit simulations in non-axisymmetric magnetic geometry exploiting general criterion for guiding-centre accuracy

    NASA Astrophysics Data System (ADS)

    Pfefferlé, D.; Graves, J. P.; Cooper, W. A.

    2015-05-01

    To identify under what conditions guiding-centre or full-orbit tracing should be used, an estimation of the spatial variation of the magnetic field is proposed, not only taking into account gradient and curvature terms but also parallel currents and the local shearing of field-lines. The criterion is derived for general three-dimensional magnetic equilibria including stellarator plasmas. Details are provided on how to implement it in cylindrical coordinates and in flux coordinates that rely on the geometric toroidal angle. A means of switching between guiding-centre and full-orbit equations at first order in Larmor radius with minimal discrepancy is shown. Techniques are applied to a MAST (mega amp spherical tokamak) helical core equilibrium in which the inner kinked flux-surfaces are tightly compressed against the outer axisymmetric mantle and where the parallel current peaks at the nearly rational surface. This is put in relation with the simpler situation B(x, y, z) = B0[sin(kx)ey + cos(kx)ez], for which full orbits and lowest order drifts are obtained analytically. In the kinked equilibrium, the full orbits of NBI fast ions are solved numerically and shown to follow helical drift surfaces. This result partially explains the off-axis redistribution of neutral beam injection fast particles in the presence of MAST long-lived modes (LLM).

  16. A New Multi-dimensional General Relativistic Neutrino Hydrodynamics Code for Core-collapse Supernovae. II. Relativistic Explosion Models of Core-collapse Supernovae

    NASA Astrophysics Data System (ADS)

    Müller, Bernhard; Janka, Hans-Thomas; Marek, Andreas

    2012-09-01

    We present the first two-dimensional general relativistic (GR) simulations of stellar core collapse and explosion with the COCONUT hydrodynamics code in combination with the VERTEX solver for energy-dependent, three-flavor neutrino transport, using the extended conformal flatness condition for approximating the space-time metric and a ray-by-ray-plus ansatz to tackle the multi-dimensionality of the transport. For both of the investigated 11.2 and 15 M ⊙ progenitors we obtain successful, though seemingly marginal, neutrino-driven supernova explosions. This outcome and the time evolution of the models basically agree with results previously obtained with the PROMETHEUS hydro solver including an approximative treatment of relativistic effects by a modified Newtonian potential. However, GR models exhibit subtle differences in the neutrinospheric conditions compared with Newtonian and pseudo-Newtonian simulations. These differences lead to significantly higher luminosities and mean energies of the radiated electron neutrinos and antineutrinos and therefore to larger energy-deposition rates and heating efficiencies in the gain layer with favorable consequences for strong nonradial mass motions and ultimately for an explosion. Moreover, energy transfer to the stellar medium around the neutrinospheres through nucleon recoil in scattering reactions of heavy-lepton neutrinos also enhances the mentioned effects. Together with previous pseudo-Newtonian models, the presented relativistic calculations suggest that the treatment of gravity and energy-exchanging neutrino interactions can make differences of even 50%-100% in some quantities and is likely to contribute to a finally successful explosion mechanism on no minor level than hydrodynamical differences between different dimensions.

  17. A NEW MULTI-DIMENSIONAL GENERAL RELATIVISTIC NEUTRINO HYDRODYNAMICS CODE FOR CORE-COLLAPSE SUPERNOVAE. II. RELATIVISTIC EXPLOSION MODELS OF CORE-COLLAPSE SUPERNOVAE

    SciTech Connect

    Mueller, Bernhard; Janka, Hans-Thomas; Marek, Andreas E-mail: thj@mpa-garching.mpg.de

    2012-09-01

    We present the first two-dimensional general relativistic (GR) simulations of stellar core collapse and explosion with the COCONUT hydrodynamics code in combination with the VERTEX solver for energy-dependent, three-flavor neutrino transport, using the extended conformal flatness condition for approximating the space-time metric and a ray-by-ray-plus ansatz to tackle the multi-dimensionality of the transport. For both of the investigated 11.2 and 15 M{sub Sun} progenitors we obtain successful, though seemingly marginal, neutrino-driven supernova explosions. This outcome and the time evolution of the models basically agree with results previously obtained with the PROMETHEUS hydro solver including an approximative treatment of relativistic effects by a modified Newtonian potential. However, GR models exhibit subtle differences in the neutrinospheric conditions compared with Newtonian and pseudo-Newtonian simulations. These differences lead to significantly higher luminosities and mean energies of the radiated electron neutrinos and antineutrinos and therefore to larger energy-deposition rates and heating efficiencies in the gain layer with favorable consequences for strong nonradial mass motions and ultimately for an explosion. Moreover, energy transfer to the stellar medium around the neutrinospheres through nucleon recoil in scattering reactions of heavy-lepton neutrinos also enhances the mentioned effects. Together with previous pseudo-Newtonian models, the presented relativistic calculations suggest that the treatment of gravity and energy-exchanging neutrino interactions can make differences of even 50%-100% in some quantities and is likely to contribute to a finally successful explosion mechanism on no minor level than hydrodynamical differences between different dimensions.

  18. High-order fully general-relativistic hydrodynamics: new approaches and tests

    NASA Astrophysics Data System (ADS)

    Radice, David; Rezzolla, Luciano; Galeazzi, Filippo

    2014-04-01

    We present a new approach for achieving high-order convergence in fully general-relativistic hydrodynamic simulations. The approach is implemented in WhiskyTHC, a new code that makes use of state-of-the-art numerical schemes and was key in achieving, for the first time, higher than second-order convergence in the calculation of the gravitational radiation from inspiraling binary neutron stars (Radice et al 2014 Mon. Not. R. Astron. Soc. 437 L46-L50). Here, we give a detailed description of the algorithms employed and present results obtained for a series of classical tests involving isolated neutron stars. In addition, using the gravitational-wave emission from the late-inspiral and merger of binary neutron stars, we make a detailed comparison between the results obtained with the new code and those obtained when using standard second-order schemes commonly employed for matter simulations in numerical relativity. We find that even at moderate resolutions and for binaries with large compactness, the phase accuracy is improved by a factor 50 or more.

  19. The general relativistic instability supernova of a supermassive population III star

    SciTech Connect

    Chen, Ke-Jung; Woosley, Stan; Heger, Alexander; Almgren, Ann; Whalen, Daniel J.; Johnson, Jarrett L.

    2014-08-01

    The formation of supermassive Population III stars with masses ≳10,000 M{sub ☉} in primeval galaxies in strong ultraviolet backgrounds at z ∼ 15 may be the most viable pathway to the formation of supermassive black holes by z ∼ 7. Most of these stars are expected to live for short times and then directly collapse to black holes, with little or no mass loss over their lives. However, we have now discovered that non-rotating primordial stars with masses close to 55,000 M{sub ☉} can instead die as highly energetic thermonuclear supernovae powered by explosive helium burning, releasing up to 10{sup 55} erg, or about 10,000 times the energy of a Type Ia supernova. The explosion is triggered by the general relativistic contribution of thermal photons to gravity in the core of the star, which causes the core to contract and explosively burn. The energy release completely unbinds the star, leaving no compact remnant, and about half of the mass of the star is ejected into the early cosmos in the form of heavy elements. The explosion would be visible in the near infrared at z ≲ 20 to Euclid and the Wide-Field Infrared Survey Telescope, perhaps signaling the birth of supermassive black hole seeds and the first quasars.

  20. Odyssey: A Public GPU-based Code for General Relativistic Radiative Transfer in Kerr Spacetime

    NASA Astrophysics Data System (ADS)

    Pu, Hung-Yi; Yun, Kiyun; Younsi, Ziri; Yoon, Suk-Jin

    2016-04-01

    General relativistic radiative transfer calculations coupled with the calculation of geodesics in the Kerr spacetime are an essential tool for determining the images, spectra, and light curves from matter in the vicinity of black holes. Such studies are especially important for ongoing and upcoming millimeter/submillimeter very long baseline interferometry observations of the supermassive black holes at the centers of Sgr A* and M87. To this end we introduce Odyssey, a graphics processing unit (GPU) based code for ray tracing and radiative transfer in the Kerr spacetime. On a single GPU, the performance of Odyssey can exceed 1 ns per photon, per Runge-Kutta integration step. Odyssey is publicly available, fast, accurate, and flexible enough to be modified to suit the specific needs of new users. Along with a Graphical User Interface powered by a video-accelerated display architecture, we also present an educational software tool, Odyssey_Edu, for showing in real time how null geodesics around a Kerr black hole vary as a function of black hole spin and angle of incidence onto the black hole.

  1. Investigations of -gravity counterparts of the general relativistic shear-free conjecture by illustrative examples

    NASA Astrophysics Data System (ADS)

    Sofuoğlu, Değer; Mutuş, Haşim

    2014-12-01

    By adopting a metric based approach and making use of -gravity extended tetrad equations, we have considered three spatially homogeneous metrics in order to investigate the existence of simultaneously rotating and expanding solutions of the -gravity field equations with shear-free perfect fluids as sources. We have shown that the Gödel type expanding universe, as well as a rotating Bianchi-type II spacetime allow no such solutions of the field equations of this modified gravity. On the other hand, we have found that there exist two types of models in which a shear-free Bianchi-type IX universe can expand and rotate at the same time. The matter content of this universe is described by a perfect fluid having positive or negative pressure, depending on the type of model and on the cosmological constant; in the particular case of a vanishing cosmological constant we have found that the universe is filled with a pure radiation. Whatsoever the cases, the universe exhibits always coasting anisotropic expansions along three spatial directions evolving like a flat Milne universe, and has a vorticity inversely proportional to cosmic time. A further result is that, due to the nonvanishing of the gravito-magnetic part of the Weyl tensor, this model allows for gravitational waves. Our solution constitutes one more example giving support to that in -gravity there is no counterpart of the general relativistic shear-free conjecture.

  2. Pinpointing the base of the AGN jets through general relativistic X-ray reverberation studies

    NASA Astrophysics Data System (ADS)

    Emmanoulopoulos, D.

    2015-03-01

    Many theoretical models of Active Galactic Nuclei (AGN) predict that the X-ray corona, lying above the black hole, constitutes the base of the X-ray jet. Thus, by studying the exact geometry of the close black hole environment, we can pinpoint the launching site of the jet. Detection of negative X-ray reverberation time delays (i.e. soft band X-ray variations lagging behind the corresponding hard band X-ray variations) can yield significant information about the geometrical properties of the AGN, such as the location of the X-ray source, as well as the physical properties of the the black hole, such as its mass and spin. In the frame-work of the lamp-post geometry, I present the first systematic X-ray time-lag modelling results of an ensemble of 12 AGN, using a fully general relativistic (GR) ray tracing approach for the estimation of the systems' response functions. By combing these state-of-the art GR response models with statistically innovative fitting routines, I derive the geometrical layout of the close BH environment for each source, unveiling the position of the AGN jet-base.

  3. The General Relativistic Instability Supernova of a Supermassive Population III Star

    NASA Astrophysics Data System (ADS)

    Chen, Ke-Jung; Heger, Alexander; Woosley, Stan; Almgren, Ann; Whalen, Daniel J.; Johnson, Jarrett L.

    2014-08-01

    The formation of supermassive Population III stars with masses gsim10,000 M ⊙ in primeval galaxies in strong ultraviolet backgrounds at z ~ 15 may be the most viable pathway to the formation of supermassive black holes by z ~ 7. Most of these stars are expected to live for short times and then directly collapse to black holes, with little or no mass loss over their lives. However, we have now discovered that non-rotating primordial stars with masses close to 55,000 M ⊙ can instead die as highly energetic thermonuclear supernovae powered by explosive helium burning, releasing up to 1055 erg, or about 10,000 times the energy of a Type Ia supernova. The explosion is triggered by the general relativistic contribution of thermal photons to gravity in the core of the star, which causes the core to contract and explosively burn. The energy release completely unbinds the star, leaving no compact remnant, and about half of the mass of the star is ejected into the early cosmos in the form of heavy elements. The explosion would be visible in the near infrared at z <~ 20 to Euclid and the Wide-Field Infrared Survey Telescope, perhaps signaling the birth of supermassive black hole seeds and the first quasars.

  4. General relativistic magnetohydrodynamic simulations of binary neutron star mergers with the APR4 equation of state

    NASA Astrophysics Data System (ADS)

    Endrizzi, A.; Ciolfi, R.; Giacomazzo, B.; Kastaun, W.; Kawamura, T.

    2016-08-01

    We present new results of fully general relativistic magnetohydrodynamic simulations of binary neutron star (BNS) mergers performed with the Whisky code. All the models use a piecewise polytropic approximation of the APR4 equation of state for cold matter, together with a ‘hybrid’ part to incorporate thermal effects during the evolution. We consider both equal and unequal-mass models, with total masses such that either a supramassive NS or a black hole is formed after merger. Each model is evolved with and without a magnetic field initially confined to the stellar interior. We present the different gravitational wave (GW) signals as well as a detailed description of the matter dynamics (magnetic field evolution, ejected mass, post-merger remnant/disk properties). Our simulations provide new insights into BNS mergers, the associated GW emission and the possible connection with the engine of short gamma-ray bursts (both in the ‘standard’ and in the ‘time-reversal’ scenarios) and other electromagnetic counterparts.

  5. General-relativistic approach to the nonlinear evolution of collisionless matter

    SciTech Connect

    Matarrese, S.; Pantano, O. ); Saez, D. )

    1993-02-15

    A new general-relativistic algorithm is developed to study the nonlinear evolution of scalar (density) perturbations of an irrotational collisionless fluid up to shell crossing, under the approximation of neglecting the interaction with tensor (gravitational-wave) perturbations. The dynamics of each fluid element is separately followed in its own inertial rest frame by a system of twelve coupled first-order ordinary differential equations, which can be further reduced to six under very general conditions. Initial conditions are obtained in a cosmological framework, from linear theory, in terms of a single gauge-invariant potential. Physical observables, which are expressed in the Lagrangian form at different times, can be traced back to the Eulerian picture by solving supplementary first-order differential equations for the relative position vectors of neighboring fluid elements. Similarly to the Zel'dovich approximation, in our approach the evolution of each fluid element is completely determined by the local initial conditions and can be independently followed up to the time when it enters a multistream region. Unlike the Zel'dovich approximation, however, our approach is correct also in three dimensions (except for the possible role of gravitational waves). The accuracy of our numerical procedure is tested by integrating the nonlinear evolution of a spherical perturbation in an otherwise spatially flat Friedmann-Robertson-Walker universe and comparing the results with the exact Tolman-Bondi solution for the same initial profile. An exact solution for the planar symmetric case is also given, which turns out to be locally identical to the Zel'dovich solution.

  6. A method for numerical relativity: Simulation of axisymmetric gravitational collapse and gravitational radiation generation

    NASA Astrophysics Data System (ADS)

    Evans, C. R., II

    A method is presented which allows fully self-consistent numerical simulation of asymptotically flat axisymmetric nonrotating general relativistic systems. These techniques have been developed to model and understand resulting relativistic effects in gravitational core collapse and gravitational radiation generation. Both vacuum (Brill) spacetimes and matter-filled configurations can be treated. The (3 + 1) decomposition of Arnowitt, Deser and Misner is used to write general relativity in a dynamical form. The conformal approach, including the transverse-traceless decomposition of extrinsic curvature due to York, is used to solve the initial value problem. In addition, these techniques are extended to provide a fully constrained evolution scheme. Several new boundary conditions, applied at large but finite radius, are derived for the elliptic constraint equations. This method uses a simplifying three-gauge, placing the metric in quasi-isotropic form.

  7. Relativistic perturbations of planetary orbits in the three-parameter generalized Schwarzschild metric - The case of Mercury

    NASA Astrophysics Data System (ADS)

    Lestrade, J.-F.

    1981-07-01

    Analytical formulas are presented for relativistic perturbations of planetary orbits in the generalized three-parameter Schwarzschild metric, and a semianalytic Newtonian solution combined with the present relativistic corrections for the orbital motion of Mercury is compared with results of numerical integrations. The Lagrangian corresponding to the generalized three-parameter Schwarzschild metric in the first post-Newtonian approximation is used to construct a first-order analytical solution for the post-Newtonian corrections to the Newtonian solutions for the orbital motions of the planets in terms of the osculating orbital elements. Comparisons of the Newtonian semianalytical solution of Bretagnon (1980) corrected by the present formulas with the numerical solutions of Oesterwinter and Cohen (1972) and the DE 102 solution of Newhall (1980) are then used to propose new integration constants for the orbit of Mercury fit to the respective numerical orbits.

  8. Relativistic fluid dynamics. Proceedings.

    NASA Astrophysics Data System (ADS)

    Anile, A. M.; Choquet-Bruhat, Y.

    Contents: 1. Covariant theory of conductivity in ideal fluid or solid media (B. Carter). 2. Hamiltonian techniques for relativistic fluid dynamics and stability theory (D. D. Holm). 3. Covariant fluid mechanics and thermodynamics: an introduction (W. Israel). 4. Relativistic plasmas (H. Weitzner). 5. An improved relativistic warm plasma model (A. M. Anile, S. Pennisi). 6. Relativistic extended thermodynamics II (I. Müller). 7. Relativistic extended thermodynamics: general assumptions and mathematical procedure (T. Ruggeri). 8. Relativistic hydrodynamics and heavy ion reactions (D. Strottman). 9. Some problems in relativistic hydrodynamics (C. G. van Weert).

  9. General relativistic radiation hydrodynamics of accretion flows - II. Treating stiff source terms and exploring physical limitations

    NASA Astrophysics Data System (ADS)

    Roedig, C.; Zanotti, O.; Alic, D.

    2012-10-01

    We present the implementation of an implicit-explicit (IMEX) Runge-Kutta numerical scheme for general relativistic (GR) hydrodynamics coupled to an optically thick radiation field in two existing GR-(magneto)hydrodynamics codes. We argue that the necessity of such an improvement arises naturally in most astrophysically relevant regimes where the optical thickness is high as the equations become stiff. By performing several simple 1D tests, we verify the codes' new ability to deal with this stiffness and show consistency. Then, still in one spatial dimension, we compute a luminosity versus accretion rate diagram for the set-up of spherical accretion on to a Schwarzschild black hole and find good agreement with previous work which included more radiation processes than we currently have available. Lastly, we revisit the supersonic Bondi-Hoyle-Lyttleton (BHL) accretion in two dimensions where we can now present simulations of realistic temperatures, down to T ˜ 106 K or less. Here we find that radiation pressure plays an important role, but also that these highly dynamical set-ups push our approximate treatment towards the limit of physical applicability. The main features of radiation hydrodynamics BHL flows manifest as (i) an effective adiabatic index approaching γeff ˜ 4/3; (ii) accretion rates two orders of magnitude lower than without radiation pressure, but still super-Eddington; (iii) luminosity estimates around the Eddington limit, hence with an overall radiative efficiency as small as ηBHL˜10-2; (iv) strong departures from thermal equilibrium in shocked regions; (v) no appearance of the flip-flop instability. We conclude that the current optically thick approximation to the radiation transfer does give physically substantial improvements over the pure hydro also in set-ups departing from equilibrium, and, once accompanied by an optically thin treatment, is likely to provide a fundamental tool for investigating accretion flows in a large variety of

  10. Finite axisymmetric charged dust disks in conformastatic spacetimes

    SciTech Connect

    Gonzalez, Guillermo A.; Gutierrez-Pineres, Antonio C.; Ospina, Paolo A.

    2008-09-15

    An infinite family of axisymmetric charged dust disks of finite extension is presented. The disks are obtained by solving the vacuum Einstein-Maxwell equations for conformastatic spacetimes, which are characterized by only one metric function. In order to obtain the solutions, a functional relationship between the metric function and the electric potential is assumed. It is also assumed that the metric function is functionally dependent on another auxiliary function, which is taken as a solution of the Laplace equation. The solutions for the auxiliary function are then taken as given by the infinite family of generalized Kalnajs disks recently obtained by Gonzalez and Reina [G. A. Gonzalez and J. I. Reina, Mon. Not. R. Astron. Soc. 371, 1873 (2006).], expressed in terms of the oblate spheroidal coordinates and corresponding to a family of well-behaved Newtonian axisymmetric thin disks of finite radius. The obtained relativistic thin disks have a charge density that is equal, except maybe by a sign, to their mass density, in such a way that the electric and gravitational forces are in exact balance. The energy density of the disks is everywhere positive and well behaved, vanishing at the edge. Accordingly, as the disks are made of dust, their energy-momentum tensor agrees with all the energy conditions.

  11. Finite axisymmetric charged dust disks in conformastatic spacetimes

    NASA Astrophysics Data System (ADS)

    González, Guillermo A.; Gutiérrez-Piñeres, Antonio C.; Ospina, Paolo A.

    2008-09-01

    An infinite family of axisymmetric charged dust disks of finite extension is presented. The disks are obtained by solving the vacuum Einstein-Maxwell equations for conformastatic spacetimes, which are characterized by only one metric function. In order to obtain the solutions, a functional relationship between the metric function and the electric potential is assumed. It is also assumed that the metric function is functionally dependent on another auxiliary function, which is taken as a solution of the Laplace equation. The solutions for the auxiliary function are then taken as given by the infinite family of generalized Kalnajs disks recently obtained by González and Reina [G. A. González and J. I. Reina, Mon. Not. R. Astron. Soc. 371, 1873 (2006).MNRAA40035-871110.1111/j.1365-2966.2006.10819.x], expressed in terms of the oblate spheroidal coordinates and corresponding to a family of well-behaved Newtonian axisymmetric thin disks of finite radius. The obtained relativistic thin disks have a charge density that is equal, except maybe by a sign, to their mass density, in such a way that the electric and gravitational forces are in exact balance. The energy density of the disks is everywhere positive and well behaved, vanishing at the edge. Accordingly, as the disks are made of dust, their energy-momentum tensor agrees with all the energy conditions.

  12. Stability of axisymmetric liquid bridges

    NASA Astrophysics Data System (ADS)

    Fel, Leonid G.; Rubinstein, Boris Y.

    2015-12-01

    Based on the Weierstrass representation of second variation, we develop a non-spectral theory of stability for isoperimetric problem with minimized and constrained two-dimensional functionals of general type and free endpoints allowed to move along two given planar curves. We establish the stability criterion and apply this theory to the axisymmetric liquid bridge between two axisymmetric solid bodies without gravity to determine the stability of menisci with free contact lines. For catenoid and cylinder menisci and different solid shapes, we determine the stability domain. The other menisci (unduloid, nodoid and sphere) are considered in a simple setup between two plates. We find the existence conditions of stable unduloid menisci with and without inflection points.

  13. Discretizations of axisymmetric systems

    NASA Astrophysics Data System (ADS)

    Frauendiener, Jörg

    2002-11-01

    In this paper we discuss stability properties of various discretizations for axisymmetric systems including the so-called cartoon method which was proposed by Alcubierre et al. for the simulation of such systems on Cartesian grids. We show that within the context of the method of lines such discretizations tend to be unstable unless one takes care in the way individual singular terms are treated. Examples are given for the linear axisymmetric wave equation in flat space.

  14. GPU-based four-dimensional general-relativistic ray tracing

    NASA Astrophysics Data System (ADS)

    Kuchelmeister, Daniel; Müller, Thomas; Ament, Marco; Wunner, Günter; Weiskopf, Daniel

    2012-10-01

    This paper presents a new general-relativistic ray tracer that enables image synthesis on an interactive basis by exploiting the performance of graphics processing units (GPUs). The application is capable of visualizing the distortion of the stellar background as well as trajectories of moving astronomical objects orbiting a compact mass. Its source code includes metric definitions for the Schwarzschild and Kerr spacetimes that can be easily extended to other metric definitions, relying on its object-oriented design. The basic functionality features a scene description interface based on the scripting language Lua, real-time image output, and the ability to edit almost every parameter at runtime. The ray tracing code itself is implemented for parallel execution on the GPU using NVidia's Compute Unified Device Architecture (CUDA), which leads to performance improvement of an order of magnitude compared to a single CPU and makes the application competitive with small CPU cluster architectures. Program summary Program title: GpuRay4D Catalog identifier: AEMV_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEMV_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 73649 No. of bytes in distributed program, including test data, etc.: 1334251 Distribution format: tar.gz Programming language: C++, CUDA. Computer: Linux platforms with a NVidia CUDA enabled GPU (Compute Capability 1.3 or higher), C++ compiler, NVCC (The CUDA Compiler Driver). Operating system: Linux. RAM: 2 GB Classification: 1.5. External routines: OpenGL Utility Toolkit development files, NVidia CUDA Toolkit 3.2, Lua5.2 Nature of problem: Ray tracing in four-dimensional Lorentzian spacetimes. Solution method: Numerical integration of light rays, GPU-based parallel programming using CUDA, 3D

  15. Relativistic and non-relativistic magnetohydrodynamic flows around compact stars

    NASA Astrophysics Data System (ADS)

    Mobarry, Clark Matthew

    A set of theoretical tools are developed for studying the magnetized accretion disks and astrophysical jets in active galaxies. A general theory is developed for the steady axisymmetric flow of an ideal general-relativistic fluid around a Schwarzschild black hole. The theory leads to a second-order partial differential equation, a Grad-Shafranov equation, for the magnetic flux function psi(R, theta). The magnetic surface functions of the Grad-Shafranov method are shown to be the Lagrange multipliers of an energy principle. Thus, the magnetic surface functions are not arbitrary functions, but must be chosen consistent with physically stable equilibria. From the energy principle, a numerical artificial friction method is developed to solve the general relativistic Grad-Shafranov equation with fluid flow. This method is suited for the internal boundaries between elliptic and hyperbolic behavior present in magnetospheres with fluid flow. The friction method is shown to be compatible with a theory for the slow dissipative evolution of a nearly ideal MagnetoHydroDynamic (MHD) fluid. A virial theorem is derived from the basic equations of general relativistic MHD. It is used to obtain an upper bound on the total energy in the electromagnetic field in terms of the total gravitational binding energy between the black hole and the matter (and energy) outside it. An analysis is made of the motion of a charged test particle in the electromagnetic field of a magnetized accretion disk surrounding a black hole. The results are consistent with stable orbits close to the event horizon. A semi-analytical model is developed for the evolution and dissipation of narrow magnetized jets from an active galaxy. This model exhibits the acceleration and expansion of the jets with increasing axial distance from the central object.

  16. A New Multi-dimensional General Relativistic Neutrino Hydrodynamics Code for Core-collapse Supernovae. IV. The Neutrino Signal

    NASA Astrophysics Data System (ADS)

    Müller, Bernhard; Janka, Hans-Thomas

    2014-06-01

    Considering six general relativistic, two-dimensional (2D) supernova (SN) explosion models of progenitor stars between 8.1 and 27 M ⊙, we systematically analyze the properties of the neutrino emission from core collapse and bounce to the post-explosion phase. The models were computed with the VERTEX-COCONUT code, using three-flavor, energy-dependent neutrino transport in the ray-by-ray-plus approximation. Our results confirm the close similarity of the mean energies, langErang, of \\bar{\

  17. Galaxies, Axisymmetric Systems and Relativity

    NASA Astrophysics Data System (ADS)

    MacCallum, M. A. H.

    2011-06-01

    List of contributors; Preface; Prof. W. B. Bonnor: a biological sketch; Part I. Galaxies and Cosmology: 1. The origin of large scale cosmic structure B. J. T. Jones and P. L. Palmer; 2. The problem of origin of the primordial pertubations and the modern cosmology V. N. Lukash and I. D. Novikov; 3. The automorphism group and field equations for Bianchi universes W. L. Rogue and G. F. R. Ellis; 4. New perspectives on galaxy formation J. Silk; Part II. Axisymmetric Systems: 5. On exact radiative solutions representing finite sources J. Bicak; 6. Proof of a generalized Geroch conjecture I. Hauser and F. J. Ernst; 7. Limits of the double Kerr solution C. Hoenselaers; 8. Non-inheritance of static symmetry by Maxwell fields M. A. H. MacCallum and N. Van den Bergh; 9. Stationary axisymmetric electrovacuum fields in general relativity G. Neugebauer and D. Kramer; 10. An almost conformal approach to axial symmetry Z. Perjes; 11. Conformally stationary axisymmetric space-times J. Winicour; Part III. Relativity: 12. A family of conformally flat space-times having the same curvature tensor in a given co-ordinate frame C. D. Collinson; 13. On the Bell-Szekeres solution for colliding electromagnetic waves J. B. Griffiths; 14. A remark on the Hauser metric A. Held; 15. Numerical relativity by power series R. Penrose; 16. Projective relativity and the equation of motion E. Schmutzer; 17. On generalized equations of goedesic deviation B. F. Schutz; 18. Lobatchevski plane gravitational waves S. T. C. Siklos; 19. Perfect fluid and vacuum solutions of Einstein's field equations with flat 3-dimensional slices H. Stephani and Th. Wolf; 20. Self-similar solutions of Einstein's equations J. Wainwright.

  18. General Relativistic Hydrodynamic Simulation of Accretion Flow from a Stellar Tidal Disruption

    NASA Astrophysics Data System (ADS)

    Shiokawa, Hotaka; Krolik, Julian H.; Cheng, Roseanne M.; Piran, Tsvi; Noble, Scott C.

    2015-05-01

    We study how the matter dispersed when a supermassive black hole tidally disrupts a star joins an accretion flow. Combining a relativistic hydrodynamic simulation of the stellar disruption with a relativistic hydrodynamics simulation of the subsequent debris motion, we track the evolution of such a system until ≃ 80% of the stellar mass bound to the black hole has settled into an accretion flow. Shocks near the stellar pericenter and also near the apocenter of the most tightly bound debris dissipate orbital energy, but only enough to make its characteristic radius comparable to the semimajor axis of the most bound material, not the tidal radius as previously envisioned. The outer shocks are caused by post-Newtonian relativistic effects, both on the stellar orbit during its disruption and on the tidal forces. Accumulation of mass into the accretion flow is both non-monotonic and slow, requiring several to 10 times the orbital period of the most tightly bound tidal streams, while the inflow time for most of the mass may be comparable to or longer than the mass accumulation time. Deflection by shocks does, however, cause some mass to lose both angular momentum and energy, permitting it to move inward even before most of the mass is accumulated into the accretion flow. Although the accretion rate still rises sharply and then decays roughly as a power law, its maximum is ≃ 0.1× the previous expectation, and the timescale of the peak is ≃ 5× longer than previously predicted. The geometric mean of the black hole mass and stellar mass inferred from a measured event timescale is therefore ≃ 0.2× the value given by classical theory.

  19. Two- and four-component relativistic generalized-active-space coupled cluster method: implementation and application to BiH.

    PubMed

    Sørensen, Lasse K; Olsen, Jeppe; Fleig, Timo

    2011-06-01

    A string-based coupled-cluster method of general excitation rank and with optimal scaling which accounts for special relativity within the four-component framework is presented. The method opens the way for the treatment of multi-reference problems through an active-space inspired single-reference based state-selective expansion of the model space. The evaluation of the coupled-cluster vector function is implemented by considering contractions of elementary second-quantized operators without setting up the amplitude equations explicitly. The capabilities of the new method are demonstrated in application to the electronic ground state of the bismuth monohydride molecule. In these calculations simulated multi-reference expansions with both doubles and triples excitations into the external space as well as the regular coupled-cluster hierarchy up to full quadruples excitations are compared. The importance of atomic outer core-correlation for obtaining accurate results is shown. Comparison to the non-relativistic framework is performed throughout to illustrate the additional work of the transition to the four-component relativistic framework both in implementation and application. Furthermore, an evaluation of the highest order scaling for general-order expansions is presented. PMID:21663339

  20. Understanding the Relativistic Generalization of Density Functional Theory (DFT) and Completing it in Practice

    NASA Astrophysics Data System (ADS)

    Bagayoko, Diola

    In 2014, 50 years following the introduction of density functional theory (DFT), a rigorous understanding of it was published [AIP Advances, 4, 127104 (2014)]. This understanding included necessary steps ab initio electronic structure calculations have to take if their results are to possess the full physical content of DFT. These steps guarantee the fulfillment of conditions of validity of DFT; not surprisingly, they have led to accurate descriptions of several dozens of semiconductors, from first principle, without invoking derivative discontinuity or self-interaction correction. This presentation shows the mathematically and physically rigorous understanding of the relativistic extension of DFT by Rajagopal and Callaway {Phys. Rev. B 7, 1912 (1973)]. As in the non-relativistic case, the attainment of the absolute minima of the occupied energies is a necessary condition for the corresponding current density to be that of the ground state of the system and for computational results to agree with corresponding, experimental ones. Acknowledgments:This work was funded in part by the US National Science Foundation [NSF, Award Nos. EPS-1003897, NSF (2010-2015)-RII-SUBR, and HRD-1002541], the US Department of Energy, National Nuclear Security Administration (NNSA, Award No. DE-NA0002630), LaSPACE, and LONI-SUBR.

  1. A general relativistic approach to the Navarro Frenk White galactic halos

    NASA Astrophysics Data System (ADS)

    Matos, Tonatiuh; Núñez, Darío; Sussman, Roberto A.

    2004-11-01

    Although galactic dark matter halos are basically Newtonian structures, the study of their interplay with large-scale cosmic evolution and with relativistic effects, such as gravitational lenses, quintessence sources or gravitational waves, makes it necessary to obtain adequate relativistic descriptions for these self-gravitating systems. With this purpose in mind, we construct a post-Newtonian fluid framework for the 'Navarro Frenk White' (NFW) models of galactic halos that follow from N-body numerical simulations. Since these simulations are unable to resolve regions very near the halo centre, the extrapolation of the fitting formula leads to a spherically averaged 'universal' density profile that diverges at the origin. We remove this inconvenient feature by replacing a small central region of the NFW halo with an interior Schwarzschild solution with constant density, continuously matched to the remaining NFW spacetime. A model of a single halo, as an isolated object with finite mass, follows by smoothly matching the NFW spacetime to a Schwarzschild vacuum exterior along the virial radius, the physical 'cut-off' customarily imposed, as the mass associated with NFW profiles diverges asymptotically. Numerical simulations assume weakly interacting collisionless particles, hence we suggest that NFW halos approximately satisfy an 'ideal gas' type of equation of state, where mass-density is the dominant rest-mass contribution to matter-energy, with the internal energy contribution associated with an anisotropic kinetic pressure. We show that, outside the central core, this pressure and the mass density roughly satisfy a polytropic relation. Since stellar polytropes are the equilibrium configurations in Tsallis' non-extensive formalism of statistical mechanics, we argue that NFW halos might provide a rough empirical estimate of the free parameter q of Tsallis' formalism.

  2. Exact two-component relativistic theory for NMR parameters: General formulation and pilot application

    NASA Astrophysics Data System (ADS)

    Sun, Qiming; Xiao, Yunlong; Liu, Wenjian

    2012-11-01

    The previously proposed exact two-component (X2C) relativistic theory of nuclear magnetic resonance (NMR) parameters [Q. Sun, W. Liu, Y. Xiao, and L. Cheng, J. Chem. Phys. 131, 081101 (2009), 10.1063/1.3216471] is reformulated to accommodate two schemes for kinetic balance, five schemes for magnetic balance, and three schemes for decoupling in a unified manner, at both matrix and operator levels. In addition, three definitions of spin magnetization are considered in the coupled-perturbed Kohn-Sham equation. Apart from its simplicity, the most salient feature of X2C-NMR lies in that its diamagnetic and paramagnetic terms agree individually with the corresponding four-component counterparts for any finite basis. For practical applications, five approximate schemes for the first order coupling matrix X10 and four approximate schemes for the treatment of two-electron integrals are introduced, which render the computations of X2C-NMR very much the same as those of approximate two-component approaches.

  3. General Relativistic Magnetohydrodynamic Simulations of Jet Formation with a Thin Keplerian Disk

    NASA Technical Reports Server (NTRS)

    Mizuno, Yosuke; Nishikawa, Ken-Ichi; Koide, Shinji; Hardee, Philip; Gerald, J. Fishman

    2006-01-01

    We have performed several simulations of black hole systems (non-rotating, black hole spin parameter a = 0.0 and rapidly rotating, a = 0.95) with a geometrically thin Keplerian disk using the newly developed RAISHIN code. The simulation results show the formation of jets driven by the Lorentz force and the gas pressure gradient. The jets have mildly relativistic speed (greater than or equal to 0.4 c). The matter is continuously supplied from the accretion disk and the jet propagates outward until each applicable terminal simulation time (non-rotating: t/tau S = 275 and rotating: t/tau S = 200, tau s equivalent to r(sub s/c). It appears that a rotating black hole creates an additional, faster, and more collimated inner outflow (greater than or equal to 0.5 c) formed and accelerated by the twisted magnetic field resulting from frame-dragging in the black hole ergosphere. This new result indicates that jet kinematic structure depends on black hole rotation.

  4. General relativistic considerations of the field shedding model of fast radio bursts

    NASA Astrophysics Data System (ADS)

    Punsly, Brian; Bini, Donato

    2016-06-01

    Popular models of fast radio bursts (FRBs) involve the gravitational collapse of neutron star progenitors to black holes. It has been proposed that the shedding of the strong neutron star magnetic field (B) during the collapse is the power source for the radio emission. Previously, these models have utilized the simplicity of the Schwarzschild metric which has the restriction that the magnetic flux is magnetic `hair' that must be shed before final collapse. But neutron stars have angular momentum and charge and a fully relativistic Kerr-Newman solution exists in which B has its source inside of the event horizon. In this Letter, we consider the magnetic flux to be shed as a consequence of the electric discharge of a metastable collapsed state of a Kerr-Newman black hole. It has also been argued that the shedding model will not operate due to pair creation. By considering the pulsar death line, we find that for a neutron star with B = 1011-1013 G and a long rotation period, >1s this is not a concern. We also discuss the observational evidence supporting the plausibility of magnetic flux shedding models of FRBs that are spawned from rapidly rotating progenitors.

  5. General properties of the radiation spectra from relativistic electrons moving in Langmuir turbulence

    SciTech Connect

    Teraki, Yuto; Takahara, Fumio

    2014-05-20

    Using a numerical method, we examine the radiation spectra from relativistic electrons moving in Langmuir turbulence, which are expected to exist in high energy astrophysical objects. The spectral shape is characterized by the spatial scale λ, field strength σ, and frequency of the Langmuir waves, and in terms of frequency they are represented by ω{sub 0} = 2πc/λ, ω{sub st} = eσ/mc, and ω{sub p}, respectively. We normalize ω{sub st} and ω {sub p} by ω{sub 0} as a ≡ ω{sub st}/ω{sub 0} and b ≡ ω{sub p}/ω{sub 0}, and examine the spectral shape in the a–b plane. An earlier study based on the diffusive radiation in Langmuir turbulence (DRL) theory by Fleishman and Toptygin showed that the typical frequency is γ{sup 2}ω{sub p} and that the low frequency spectrum behaves as F {sub ω}∝ω{sup 1} for b > 1 irrespective of a. Here, we adopt the first principle numerical approach to obtain the radiation spectra in more detail. We generate Langmuir turbulence by superposing Fourier modes, injecting monoenergetic electrons, solving the equation of motion, and calculating the radiation spectra using a Lienard-Wiechert potential. We find different features from the DRL theory for a > b > 1. The peak frequency turns out to be γ{sup 2}ω{sub st}, which is higher than the γ{sup 2}ω{sub p} predicted by the DRL theory, and the spectral index of the low frequency region is not 1 but 1/3. This is because the typical deflection angle of electrons is larger than the angle of the beaming cone ∼1/γ. We call the radiation for this case 'wiggler radiation in Langmuir turbulence'.

  6. Exact power series solutions of the structure equations of the general relativistic isotropic fluid stars with linear barotropic and polytropic equations of state

    NASA Astrophysics Data System (ADS)

    Harko, T.; Mak, M. K.

    2016-09-01

    Obtaining exact solutions of the spherically symmetric general relativistic gravitational field equations describing the interior structure of an isotropic fluid sphere is a long standing problem in theoretical and mathematical physics. The usual approach to this problem consists mainly in the numerical investigation of the Tolman-Oppenheimer-Volkoff and of the mass continuity equations, which describes the hydrostatic stability of the dense stars. In the present paper we introduce an alternative approach for the study of the relativistic fluid sphere, based on the relativistic mass equation, obtained by eliminating the energy density in the Tolman-Oppenheimer-Volkoff equation. Despite its apparent complexity, the relativistic mass equation can be solved exactly by using a power series representation for the mass, and the Cauchy convolution for infinite power series. We obtain exact series solutions for general relativistic dense astrophysical objects described by the linear barotropic and the polytropic equations of state, respectively. For the polytropic case we obtain the exact power series solution corresponding to arbitrary values of the polytropic index n. The explicit form of the solution is presented for the polytropic index n=1, and for the indexes n=1/2 and n=1/5, respectively. The case of n=3 is also considered. In each case the exact power series solution is compared with the exact numerical solutions, which are reproduced by the power series solutions truncated to seven terms only. The power series representations of the geometric and physical properties of the linear barotropic and polytropic stars are also obtained.

  7. General Relativistic Radiation Pressure Supported Stars as Quasar Central Engines in an Universe Which is Recycling Matter

    NASA Astrophysics Data System (ADS)

    Mitra, Abhas

    2011-11-01

    Hoyle & Folwler (1963a,b) suggested that quasars may contain Radiation Pressure Supported Stars (RPSS), which are quasi-Newtonian (surface redshitf z ≪ 1) and supermassive. This proposal however did not work and one of the reasons was that such quasi-Newtonian PRSSs are unstable to gravitational contraction to become extremely general relativistic RPSSs. And since trapped surfaces are not allowed, (Mitra 2009a) these relativistic RPSSs are bound to hover around their instantaneous "Schwarzschild Radius" Rs = 2GM/c2. In view of the fact that they have z ≫ 1, they appear as "Black Holes" (BH) to distant observers. However since, they are always radiating, in a strict sense, they are always contracting. During such extreme compatification, RPSSs are likely to acquire extremely large magnetic field due to magnetic flux freezing, and hence they have strong magnetosphere around them by which they may arrest the accretion disk surrounding them at "Alfven Radius", Ra ≫ Rs. In contrast, for an accreting Schwarzschild black hole, one expects the inner edge of the accretion disk to be at Ri = 3Rs. Consequently, such ultramagnetized RPSSs have been nick named as Magnetospheric Eternally Collapsing Objects" (MECOs). Microlensing studies of several quasar structures have shown that indeed Ri ˜ 35Rs rather that R1 = 3Rs, and which confirms that quasars harbor MECOs rather than true black holes (Schild et al. 2006, 2008, Lovegrove et al. 2011). Further the recent proof that the true BHs have M = 0 confirms that the BH candidates are not true BHs (Mitra 2004a,b; 2009b). Here we highlight the facts (i) outflows from quasars and (ii) their ability to recycle cosmic matter for having new stars and galaxies are best understood by realizing that they contain MECOs rather than true BHs.

  8. Axisymmetric multiwormholes revisited

    NASA Astrophysics Data System (ADS)

    Clément, Gérard

    2016-06-01

    The construction of stationary axisymmetric multiwormhole solutions to gravitating field theories admitting toroidal reductions to three-dimensional gravitating sigma models is reviewed. We show that, as in the multi-black hole case, strut singularities always appear in this construction, except for very special configurations with an odd number of centers. We also review the analytical continuation of the multicenter solution across the n cuts associated with the wormhole mouths. The resulting Riemann manifold has 2^n sheets interconnected by 2^{n-1}n wormholes. We find that the maximally extended multicenter solution can never be asymptotically locally flat in all the Riemann sheets.

  9. Magneto-hydrodynamically stable axisymmetric mirrorsa)

    NASA Astrophysics Data System (ADS)

    Ryutov, D. D.; Berk, H. L.; Cohen, B. I.; Molvik, A. W.; Simonen, T. C.

    2011-09-01

    Making axisymmetric mirrors magnetohydrodynamically (MHD) stable opens up exciting opportunities for using mirror devices as neutron sources, fusion-fission hybrids, and pure-fusion reactors. This is also of interest from a general physics standpoint (as it seemingly contradicts well-established criteria of curvature-driven instabilities). The axial symmetry allows for much simpler and more reliable designs of mirror-based fusion facilities than the well-known quadrupole mirror configurations. In this tutorial, after a summary of classical results, several techniques for achieving MHD stabilization of the axisymmetric mirrors are considered, in particular: (1) employing the favorable field-line curvature in the end tanks; (2) using the line-tying effect; (3) controlling the radial potential distribution; (4) imposing a divertor configuration on the solenoidal magnetic field; and (5) affecting the plasma dynamics by the ponderomotive force. Some illuminative theoretical approaches for understanding axisymmetric mirror stability are described. The applicability of the various stabilization techniques to axisymmetric mirrors as neutron sources, hybrids, and pure-fusion reactors are discussed; and the constraints on the plasma parameters are formulated.

  10. A confirmation of the general relativistic prediction of the Lense-Thirring effect.

    PubMed

    Ciufolini, I; Pavlis, E C

    2004-10-21

    An important early prediction of Einstein's general relativity was the advance of the perihelion of Mercury's orbit, whose measurement provided one of the classical tests of Einstein's theory. The advance of the orbital point-of-closest-approach also applies to a binary pulsar system and to an Earth-orbiting satellite. General relativity also predicts that the rotation of a body like Earth will drag the local inertial frames of reference around it, which will affect the orbit of a satellite. This Lense-Thirring effect has hitherto not been detected with high accuracy, but its detection with an error of about 1 per cent is the main goal of Gravity Probe B--an ongoing space mission using orbiting gyroscopes. Here we report a measurement of the Lense-Thirring effect on two Earth satellites: it is 99 +/- 5 per cent of the value predicted by general relativity; the uncertainty of this measurement includes all known random and systematic errors, but we allow for a total +/- 10 per cent uncertainty to include underestimated and unknown sources of error. PMID:15496915

  11. The field lines of an axisymmetric magnetic field

    NASA Technical Reports Server (NTRS)

    Backus, George E.

    1988-01-01

    The equations of Willis and Young (1987) for the field lines of an arbitrary axisymmetric multipole are generalized to an arbitrary linear combination of multipoles, i.e., to an arbitrary axisymmetric magnetic field B outside a sphere of radius a, S(a), centered on the origin, and containing all the sources of B. For this field, axisymmetric Stokes stream function is expressed in terms of the Gauss coefficients. It is shown that if only one Gauss coefficient is nonzero, the field line equations are identical to those obtained by Willis and Young.

  12. The Effective-One-Body Approach to the General Relativistic Two Body Problem

    NASA Astrophysics Data System (ADS)

    Damour, Thibault; Nagar, Alessandro

    The two-body problem in General Relativity has been the subject of many analytical investigations. After reviewing some of the methods used to tackle this problem (and, more generally, the N-body problem), we focus on a new, recently introduced approach to the motion and radiation of (comparable mass) binary systems: the Effective One Body (EOB) formalism. We review the basic elements of this formalism, and discuss some of its recent developments. Several recent comparisons between EOB predictions and Numerical Relativity (NR) simulations have shown the aptitude of the EOB formalism to provide accurate descriptions of the dynamics and radiation of various binary systems (comprising black holes or neutron stars) in regimes that are inaccessible to other analytical approaches (such as the last orbits and the merger of comparable mass black holes). In synergy with NR simulations, post-Newtonian (PN) theory and Gravitational Self-Force (GSF) computations, the EOB formalism is likely to provide an efficient way of computing the very many accurate template waveforms that are needed for Gravitational Wave (GW) data analysis purposes.

  13. Global Classical Solutions of the Relativistic Vlasov-Darwin System with Small Cauchy Data: The Generalized Variables Approach

    NASA Astrophysics Data System (ADS)

    Sospedra-Alfonso, Reinel; Agueh, Martial; Illner, Reinhard

    2012-09-01

    We show that a smooth, small enough Cauchy datum launches a unique classical solution of the relativistic Vlasov-Darwin (RVD) system globally in time. A similar result is claimed in Seehafer (Commun Math Sci 6:749-769, 2008) following the work in Pallard (Int Mat Res Not 57191:1-31, 2006). Our proof does not require estimates derived from the conservation of the total energy, nor those previously given on the transversal component of the electric field. These estimates are crucial in the references cited above. Instead, we exploit the formulation of the RVD system in terms of the generalized space and momentum variables. By doing so, we produce a simple a priori estimate on the transversal component of the electric field. We widen the functional space required for the Cauchy datum to extend the solution globally in time, and we improve decay estimates given in Seehafer (2008) on the electromagnetic field and its space derivatives. Our method extends the constructive proof presented in Rein (Handbook of differential equations: evolutionary equations, vol 3. Elsevier, Amsterdam, 2007) to solve the Cauchy problem for the Vlasov-Poisson system with a small initial datum.

  14. Theoretical investigations in nonlinear quantum optics, theory of measurement, and pulsations of general relativistic models of neutron stars

    SciTech Connect

    Schumaker, B.L.

    1985-01-01

    This thesis is a collection of six papers. The first four constitute the heart of the thesis; they are concerned with quantum-mechanical properties of certain harmonic-oscillator states. The first paper is a discourse on single-mode and two-mode Gaussian pure states (GPS), states produced when harmonic oscillators in their ground states are exposed to potentials that are linear or quadratic in oscillator position and momentum variables (creation and annihilation operators). The second and third papers develop a formalism for analyzing two photon devices (e.g., parametric amplifiers and phase-conjugate mirrors), in which photons in the output modes arise from two-proton transitions, i.e., are created or destroyed two at a time. The fourth paper is an analysis of the noise in homodyne detection, a phase-sensitive detection scheme in which the special properties of (single-mode) squeezed states are revealed. The fifth paper considers the validity of the standard quantum limit (SQL) for measurements that monitor the position of a free mass. The sixth paper develops the mathematical theory of torsional (toroidal) oscillations in fully general relativistic, nonrotating, spherical stellar models and of the gravitational waves they emit.

  15. LAGEOS II pericenter general relativistic precession (1993-2005): Error budget and constraints in gravitational physics

    NASA Astrophysics Data System (ADS)

    Lucchesi, David M.; Peron, Roberto

    2014-04-01

    The aim of this paper is to extend, clarify, and deepen the results of our previous work [D. M. Lucchesi and R. Peron, Phys. Rev. Lett. 105, 231103 (2010)], related to the precise measurement of LAGEOS (LAser GEOdynamics Satellite) II pericenter shift. A 13-year time span of LAGEOS satellites' laser tracking data has been considered, obtaining a very precise orbit and correspondingly residuals time series from which to extract the relevant signals. A thorough description is provided of the data analysis strategy and the dynamical models employed, along with a detailed discussion of the known sources of error in the experiment, both statistical and systematic. From this analysis, a confirmation of the predictions of Einstein's general relativity, as well as strong bounds on alternative theories of gravitation, clearly emerge. In particular, taking conservatively into account the stricter error bound due to systematic effects, general relativity has been confirmed in the Earth's field at the 98% level (meaning the measurement of a suitable combination of β and γ PPN parameters in weak-field conditions). This bound has been used to constrain possible deviations from the inverse-square law parameterized by a Yukawa-like new long range interaction with strength |α|≲1×10-10 at a characteristic range λ ≃1 Earth radius, a possible nonsymmetric gravitation theory with the interaction parameter C⊕LAGEOS II≲(9 × 10-2 km)4, and a possible spacetime torsion with a characteristic parameter combination |2t2+t3|≲7×10-2. Conversely, if we consider the results obtained from our best fit of the LAGEOS II orbit, the constraints in fundamental physics improve by at least 2 orders of magnitude.

  16. Light propagation in the field of a moving axisymmetric body: Theory and applications to the Juno mission

    NASA Astrophysics Data System (ADS)

    Hees, A.; Bertone, S.; Le Poncin-Lafitte, C.

    2014-10-01

    Given the extreme accuracy of modern space science, a precise relativistic modeling of observations is required. We use the time transfer function formalism to study light propagation in the field of uniformly moving axisymmetric bodies, which extends the field of application of previous works. We first present a space-time metric adapted to describe the geometry of an ensemble of uniformly moving bodies. Then, we show that the expression of the time transfer functions in the field of a uniformly moving body can be easily derived from its well-known expression in a stationary field by using a change of variables. We also give a general expression of the time transfer function in the case of an ensemble of arbitrarily moving point masses. This result is given in the form of an integral that is easily computable numerically. We also provide the derivatives of the time transfer function in this case, which are mandatory to compute Doppler and astrometric observables. We particularize our results in the case of moving axisymmetric bodies. Finally, we apply our results to study the different relativistic contributions to the range and Doppler tracking for the Juno mission in the Jovian system.

  17. Does Pressure Accentuate General Relativistic Gravitational Collapse and Formation of Trapped Surfaces?

    NASA Astrophysics Data System (ADS)

    Mitra, Abhas

    2013-04-01

    It is widely believed that though pressure resists gravitational collapse in Newtonian gravity, it aids the same in general relativity (GR) so that GR collapse should eventually be similar to the monotonous free fall case. But we show that, even in the context of radiationless adiabatic collapse of a perfect fluid, pressure tends to resist GR collapse in a manner which is more pronounced than the corresponding Newtonian case and formation of trapped surfaces is inhibited. In fact there are many works which show such collapse to rebound or become oscillatory implying a tug of war between attractive gravity and repulsive pressure gradient. Furthermore, for an imperfect fluid, the resistive effect of pressure could be significant due to likely dramatic increase of tangential pressure beyond the "photon sphere." Indeed, with inclusion of tangential pressure, in principle, there can be static objects with surface gravitational redshift z → ∞. Therefore, pressure can certainly oppose gravitational contraction in GR in a significant manner in contradiction to the idea of Roger Penrose that GR continued collapse must be unstoppable.

  18. The motion of axisymmetric satellite with drag and radiation pressure

    NASA Astrophysics Data System (ADS)

    Elshaboury, S. M.; Mostafa, A.

    2014-08-01

    The axisymmetric satellite problem including radiation pressure and drag is treated. The equations of motion of the satellite are derived. The energy-like and Laplace-like invariants of motion have been derived for a general drag force function of the polar angle, and the Laplace-like invariant is used to find the orbit equation in the case of a spherical satellite. Then using the small parameter, the orbit of the satellite is determined for an axisymmetric satellite.

  19. A General Relativistic Null Hypothesis Test with Event Horizon Telescope Observations of the Black Hole Shadow in Sgr A*

    NASA Astrophysics Data System (ADS)

    Psaltis, Dimitrios; Özel, Feryal; Chan, Chi-Kwan; Marrone, Daniel P.

    2015-12-01

    The half opening angle of a Kerr black hole shadow is always equal to (5 ± 0.2)GM/Dc2, where M is the mass of the black hole and D is its distance from the Earth. Therefore, measuring the size of a shadow and verifying whether it is within this 4% range constitutes a null hypothesis test of general relativity. We show that the black hole in the center of the Milky Way, Sgr A*, is the optimal target for performing this test with upcoming observations using the Event Horizon Telescope (EHT). We use the results of optical/IR monitoring of stellar orbits to show that the mass-to-distance ratio for Sgr A* is already known to an accuracy of ∼4%. We investigate our prior knowledge of the properties of the scattering screen between Sgr A* and the Earth, the effects of which will need to be corrected for in order for the black hole shadow to appear sharp against the background emission. Finally, we explore an edge detection scheme for interferometric data and a pattern matching algorithm based on the Hough/Radon transform and demonstrate that the shadow of the black hole at 1.3 mm can be localized, in principle, to within ∼9%. All these results suggest that our prior knowledge of the properties of the black hole, of scattering broadening, and of the accretion flow can only limit this general relativistic null hypothesis test with EHT observations of Sgr A* to ≲10%.

  20. General Relativistic Magnetohydrodynamic Simulations of Jets from Black Hole Accretions Disks: Two-Component Jets Driven by Nonsteady Accretion of Magnetized Disks

    NASA Astrophysics Data System (ADS)

    Koide, Shinji; Shibata, Kazunari; Kudoh, Takahiro

    1998-03-01

    The radio observations have revealed the compelling evidence of the existence of relativistic jets not only from active galactic nuclei but also from ``microquasars'' in our Galaxy. In the cores of these objects, it is believed that a black hole exists and that violent phenomena occur in the black hole magnetosphere, forming the relativistic jets. To simulate the jet formation in the magnetosphere, we have newly developed the general relativistic magnetohydrodynamic code. Using the code, we present a model of these relativistic jets, in which magnetic fields penetrating the accretion disk around a black hole play a fundamental role of inducing nonsteady accretion and ejection of plasmas. According to our simulations, a jet is ejected from a close vicinity to a black hole (inside 3rS, where rS is the Schwarzschild radius) at a maximum speed of ~90% of the light velocity (i.e., a Lorentz factor of ~2). The jet has a two-layered shell structure consisting of a fast gas pressure-driven jet in the inner part and a slow magnetically driven jet in the outer part, both of which are collimated by the global poloidal magnetic field penetrating the disk. The former jet is a result of a strong pressure increase due to shock formation in the disk through fast accretion flow (``advection-dominated disk'') inside 3rS, which has never been seen in the nonrelativistic calculations.

  1. Attitude stability criteria of axisymmetric solar sail

    NASA Astrophysics Data System (ADS)

    Hu, Xiaosai; Gong, Shengping; Li, Junfeng

    2014-07-01

    Passive attitude stability criteria of a solar sail whose membrane surface is axisymmetric are studied in this paper under a general SRP model. This paper proves that arbitrary attitude equilibrium position can be designed through adjusting the deviation between the pressure center and the mass center of the sail. The linearized method is applied to inspect analytically the stability of the equilibrium point from two different points of views. The results show that the attitude stability depends on the membrane surface shape and area. The results of simulation with full dynamic equations confirm that the two stability criteria are effective in judging the attitude stability for axisymmetric solar sail. Several possible applications of the study are also mentioned.

  2. General relativistic ray-tracing algorithm for the determination of the electron-positron energy deposition rate from neutrino pair annihilation around rotating neutron and quark stars

    NASA Astrophysics Data System (ADS)

    Kovács, Z.; Harko, T.

    2011-11-01

    We present a full general relativistic numerical code for estimating the energy-momentum deposition rate (EMDR) from neutrino pair annihilation (?). The source of the neutrinos is assumed to be a neutrino-cooled accretion disc around neutron and quark stars. We calculate the neutrino trajectories by using a ray-tracing algorithm with the general relativistic Hamilton's equations for neutrinos and derive the spatial distribution of the EMDR due to the annihilations of neutrinos and antineutrinos around rotating neutron and quark stars. We obtain the EMDR for several classes of rotating neutron stars, described by different equations of state of the neutron matter, and for quark stars, described by the Massachusetts Institute of Technology (MIT) bag model equation of state and in the colour-flavour-locked (CFL) phase. The distribution of the total annihilation rate of the neutrino-antineutrino pairs around rotating neutron and quark stars is studied for isothermal discs and accretion discs in thermodynamical equilibrium. We demonstrate both the differences in the equations of state for neutron and quark matter and rotation with the general relativistic effects significantly modify the EMDR of the electrons and positrons generated by the neutrino-antineutrino pair annihilation around compact stellar objects, as measured at infinity.

  3. A General Relativistic Ray-tracing Method for Estimating the Energy and Momentum Deposition by Neutrino Pair Annihilation in Collapsars

    NASA Astrophysics Data System (ADS)

    Harikae, Seiji; Kotake, Kei; Takiwaki, Tomoya; Sekiguchi, Yu-ichiro

    2010-09-01

    Bearing in mind the application to the collapsar models of gamma-ray bursts (GRBs), we develop a numerical scheme and code for estimating the deposition of energy and momentum due to the neutrino pair annihilation (ν + {\\bar{ν}} → e^{-} + e^{+}) in the vicinity of an accretion tori around a Kerr black hole. Our code is designed to solve the general relativistic (GR) neutrino transfer by a ray-tracing method. To solve the collisional Boltzmann equation in curved spacetime, we numerically integrate the so-called rendering equation along the null geodesics. We employ the Fehlberg (4,5) adaptive integrator in the Runge-Kutta method to perform the numerical integration accurately. For the neutrino opacity, the charged-current β-processes, which are dominant in the vicinity of the accretion tori, are taken into account. The numerical accuracy of the developed code is certified by several tests in which we show comparisons with the corresponding analytical solutions. In order to solve the energy-dependent ray-tracing transport, we propose that an adaptive-mesh-refinement approach, which we take for the two radiation angles (θ, phi) and the neutrino energy, is useful in reducing the computational cost significantly. Based on the hydrodynamical data in our collapsar simulation, we estimate the annihilation rates in a post-processing manner. Increasing the Kerr parameter from 0 to 1, it is found that the GR effect can increase the local energy deposition rate by about one order of magnitude, and the net energy deposition rate by several tens of percent. After the accretion disk settles into a stationary state (typically later than ~9 s from the onset of gravitational collapse), we point out that the neutrino-heating timescale in the vicinity of the polar funnel region can be shorter than the dynamical timescale. Our results suggest that the neutrino pair annihilation is potentially as important as the conventional magnetohydrodynamic mechanism for igniting the GRB

  4. A new multi-dimensional general relativistic neutrino hydrodynamics code for core-collapse supernovae. IV. The neutrino signal

    SciTech Connect

    Müller, Bernhard; Janka, Hans-Thomas E-mail: bjmuellr@mpa-garching.mpg.de

    2014-06-10

    Considering six general relativistic, two-dimensional (2D) supernova (SN) explosion models of progenitor stars between 8.1 and 27 M {sub ☉}, we systematically analyze the properties of the neutrino emission from core collapse and bounce to the post-explosion phase. The models were computed with the VERTEX-COCONUT code, using three-flavor, energy-dependent neutrino transport in the ray-by-ray-plus approximation. Our results confirm the close similarity of the mean energies, (E), of ν-bar {sub e} and heavy-lepton neutrinos and even their crossing during the accretion phase for stars with M ≳ 10 M {sub ☉} as observed in previous 1D and 2D simulations with state-of-the-art neutrino transport. We establish a roughly linear scaling of 〈E{sub ν-bar{sub e}}〉 with the proto-neutron star (PNS) mass, which holds in time as well as for different progenitors. Convection inside the PNS affects the neutrino emission on the 10%-20% level, and accretion continuing beyond the onset of the explosion prevents the abrupt drop of the neutrino luminosities seen in artificially exploded 1D models. We demonstrate that a wavelet-based time-frequency analysis of SN neutrino signals in IceCube will offer sensitive diagnostics for the SN core dynamics up to at least ∼10 kpc distance. Strong, narrow-band signal modulations indicate quasi-periodic shock sloshing motions due to the standing accretion shock instability (SASI), and the frequency evolution of such 'SASI neutrino chirps' reveals shock expansion or contraction. The onset of the explosion is accompanied by a shift of the modulation frequency below 40-50 Hz, and post-explosion, episodic accretion downflows will be signaled by activity intervals stretching over an extended frequency range in the wavelet spectrogram.

  5. Formation of Overheated Regions and Truncated Disks around Black Holes: Three-dimensional General Relativistic Radiation-magnetohydrodynamics Simulations

    NASA Astrophysics Data System (ADS)

    Takahashi, Hiroyuki R.; Ohsuga, Ken; Kawashima, Tomohisa; Sekiguchi, Yuichiro

    2016-07-01

    Using three-dimensional general relativistic radiation-magnetohydrodynamics simulations of accretion flows around stellar mass black holes, we report that the relatively cold disk (≳ {10}7 {{K}}) is truncated near the black hole. Hot and less dense regions, of which the gas temperature is ≳ {10}9 {{K}} and more than 10 times higher than the radiation temperature (overheated regions), appear within the truncation radius. The overheated regions also appear above as well as below the disk, sandwiching the cold disk, leading to the effective Compton upscattering. The truncation radius is ∼ 30{r}{{g}} for \\dot{M}∼ {L}{{Edd}}/{c}2, where {r}{{g}},\\dot{M},{L}{Edd},c are the gravitational radius, mass accretion rate, Eddington luminosity, and light speed, respectively. Our results are consistent with observations of a very high state, whereby the truncated disk is thought to be embedded in the hot rarefied regions. The truncation radius shifts inward to ∼ 10{r}{{g}} with increasing mass accretion rate \\dot{M}∼ 100{L}{{Edd}}/{c}2, which is very close to an innermost stable circular orbit. This model corresponds to the slim disk state observed in ultraluminous X-ray sources. Although the overheated regions shrink if the Compton cooling effectively reduces the gas temperature, the sandwich structure does not disappear at the range of \\dot{M}≲ 100{L}{{Edd}}/{c}2. Our simulations also reveal that the gas temperature in the overheated regions depends on black hole spin, which would be due to efficient energy transport from black hole to disks through the Poynting flux, resulting in gas heating.

  6. Formation of Overheated Regions and Truncated Disks around Black Holes: Three-dimensional General Relativistic Radiation-magnetohydrodynamics Simulations

    NASA Astrophysics Data System (ADS)

    Takahashi, Hiroyuki R.; Ohsuga, Ken; Kawashima, Tomohisa; Sekiguchi, Yuichiro

    2016-07-01

    Using three-dimensional general relativistic radiation-magnetohydrodynamics simulations of accretion flows around stellar mass black holes, we report that the relatively cold disk (≳ {10}7 {{K}}) is truncated near the black hole. Hot and less dense regions, of which the gas temperature is ≳ {10}9 {{K}} and more than 10 times higher than the radiation temperature (overheated regions), appear within the truncation radius. The overheated regions also appear above as well as below the disk, sandwiching the cold disk, leading to the effective Compton upscattering. The truncation radius is ˜ 30{r}{{g}} for \\dot{M}˜ {L}{{Edd}}/{c}2, where {r}{{g}},\\dot{M},{L}{Edd},c are the gravitational radius, mass accretion rate, Eddington luminosity, and light speed, respectively. Our results are consistent with observations of a very high state, whereby the truncated disk is thought to be embedded in the hot rarefied regions. The truncation radius shifts inward to ˜ 10{r}{{g}} with increasing mass accretion rate \\dot{M}˜ 100{L}{{Edd}}/{c}2, which is very close to an innermost stable circular orbit. This model corresponds to the slim disk state observed in ultraluminous X-ray sources. Although the overheated regions shrink if the Compton cooling effectively reduces the gas temperature, the sandwich structure does not disappear at the range of \\dot{M}≲ 100{L}{{Edd}}/{c}2. Our simulations also reveal that the gas temperature in the overheated regions depends on black hole spin, which would be due to efficient energy transport from black hole to disks through the Poynting flux, resulting in gas heating.

  7. Method for numerical relativity: simulation of axisymmetric gravitational collapse and gravitational radiation generation

    SciTech Connect

    Evans, C.R. II

    1984-01-01

    A method is presented that allows fully self-consistent numerical simulation of asymptotically flat axisymmetric nonrotating general relativistic systems. These techniques were developed to model and understand resulting relativistic effects in gravitational core collapse and gravitational radiation generation. Both vacuum (Brill) spacetimes and matter-filled configurations can be treated. The author uses the (3 + 1) composition of Arnowitt, Deser, and Misner to write general relativity in a dynamical form. The conformal approach, including the transverse-traceless decomposition of extrinsic curvature due to York, is used to solve the initial-value problem. In addition, these techniques are extended to provide a fully constrained evolution scheme. Several new boundary conditions, applied at large but finite radius, are derived for the elliptic constraint equations. The method uses a simplifying three-gauge, placing the metric in quasi-isotropic form. The resulting three-metric contains only two components that must be solved. One, the conformal factor, is fixed by the Hamiltonian constraint. The second has nice radiative features and is related in the weak-field limit to the usual transverse-traceless gravitational wave amplitude. The time slicing is determined by implementation of the maximal slicing condition.

  8. Axisymmetric magnetic gauges

    SciTech Connect

    Wright, B.L.; Alrick, K.R.; Fritz, J.N.

    1994-05-01

    Axisymmetric magnetic (ASM) gauges are useful diagnostic tools in the study of the conversion of energy from underground explosions to distant seismic signals. Requiring no external power, they measure the strength (particle velocity) of the emerging shock wave under conditions that would destroy most instrumentation. Shock pins are included with each gauge to determine the angle of the shock front. For the Non-Proliferation Experiment, two ASM gauges were installed in the ANFO mixture to monitor the detonation wave and 10 were grouted into boreholes at various ranges in the surrounding rock (10 to 64 m from the center of explosion). These gauges were of a standard 3.8-inch-diameter design. In addition, two unique Jumbo ASM gauges (3-ft by 3-ft in cross section) were grouted to the wall of a drift at a range of 65 m. We discuss issues encountered in data analysis, present the results of our measurements, and compare these results with those of model simulations of the experiment.

  9. Stationary axisymmetric configuration of the resistive thick accretion tori around a Schwarzschild black hole

    NASA Astrophysics Data System (ADS)

    Shaghaghian, M.

    2016-02-01

    We examine a thick accretion disc in the presence of external gravity and intrinsic dipolar magnetic field due to a non-rotating central object. In this paper, we generalize the Newtonian theory of stationary axisymmetric resistive tori of Tripathy, Prasanna & Das by including the fully general relativistic features. If we are to obtain the steady state configuration, we have to take into account the finite resistivity for the magnetofluid in order to avoid the piling up of the field lines anywhere in the accretion discs. The efficient value of conductivity must be much smaller than the classical conductivity to be astrophysically interesting. The accreting plasma in the presence of an external dipole magnetic field gives rise to a current in the azimuthal direction. The azimuthal current produced due to the motion of the magnetofluid modifies the magnetic field structure inside the disc and generates a poloidal magnetic field for the disc. The solutions we have found show that the radial inflow, pressure and density distributions are strongly modified by the electrical conductivity both in relativistic and Newtonian regimes. However, the range of conductivity coefficient is different for both regimes, as well as that of the angular momentum parameter and the radius of the innermost stable circular orbit. Furthermore, it is shown that the azimuthal velocity of the disc which is not dependent on conductivity is sub-Keplerian in all radial distances for both regimes. Owing to the presence of pressure gradient and magnetic forces. This work may also be important for the general relativistic computational magnetohydrodynamics that suffers from the lack of exact analytic solutions that are needed to test computer codes.

  10. Axisymmetric Coanda-assisted vectoring

    NASA Astrophysics Data System (ADS)

    Allen, Dustin; Smith, Barton L.

    2009-01-01

    An experimental demonstration of a jet vectoring technique used in our novel spray method called Coanda-assisted Spray Manipulation (CSM) is presented. CSM makes use of the Coanda effect on axisymmetric geometries through the interaction of two jets: a primary jet and a control jet. The primary jet has larger volume flow rate but generally a smaller momentum flux than the control jet. The primary jet flows through the center of a rounded collar. The control jet is parallel to the primary and is adjacent to the convex collar. The Reynolds number range for the primary jet at the exit plane was between 20,000 and 80,000. The flow was in the incompressible Mach number range (Mach < 0.3). The control jet attaches to the convex wall and vectors according to known Coanda effect principles, entraining and vectoring the primary jet, resulting in controllable r - θ directional spraying. Several annular control slots and collar radii were tested over a range of momentum flux ratios to determine the effects of these variables on the vectored jet angle and spreading. Two and Three-component Particle Image Velocimetry systems were used to determine the vectoring angle and the profile of the combined jet in each experiment. The experiments show that the control slot and expansion radius, along with the momentum ratios of the two jets predominantly affected the vectoring angle and profile of the combined jets.

  11. Generally Contracted Valence-Core/Valence Basis Sets for Use with Relativistic Effective Core Potentials and Spin-Orbit Coupling Operators

    SciTech Connect

    Ermler, Walter V.; Tilson, Jeffrey L.

    2012-12-15

    A procedure for structuring generally contracted valence-core/valence basis sets of Gaussian-type functions for use with relativistic effective core potentials (gcv-c/v-RECP basis sets) is presented. Large valence basis sets are enhanced using a compact basis set derived for outer core electrons in the presence of small-core RECPs. When core electrons are represented by relativistic effective core potentials (RECPs), and appropriate levels of theory, these basis sets are shown to provide accurate representations of atomic and molecular valence and outer-core electrons. Core/valence polarization and correlation effects can be calculated using these basis sets through standard methods for treating electron correlation. Calculations of energies and spectra for Ru, Os, Ir, In and Cs are reported. Spectroscopic constants for RuO2+, OsO2+, Cs2 and InH are calculated and compared with experiment.

  12. Magneto-hydrodynamically stable axisymmetric mirrors

    NASA Astrophysics Data System (ADS)

    Ryutov, Dmitri

    2010-11-01

    The achievement of high beta (60%) plasma with near classical confinement in a linear axisymmetric magnetic configuration has sparked interest in the Gas Dynamic Trap concept. The significance of these results is that they can be projected directly to a neutron source for materials testing. The possibility of axisymmetric mirrors (AM) being magneto-hydrodynamically (MHD) stable is also of interest from a general physics standpoint (as it seemingly contradicts to well-established criteria of curvature-driven instabilities). The axial symmetry allows for much simpler and more reliable designs of mirror-based fusion facilities than the well-known quadrupole mirror configurations. In this tutorial, after a brief summary of classical results (in particular of the Rosenbluth-Longmire theory and of the energy principle as applied to AM) several approaches towards achieving MHD stabilization of the AM will be considered: 1) Employing the favorable field-line curvature in the end tanks; 2) Using the line-tying effect; 3) Setting the plasma in a slow or fast differential rotation; 4) Imposing a divertor configuration on the solenoidal magnetic field; 5) Controlling the plasma dynamics by the ponderomotive force; 6) Other techniques. Several of these approaches go beyond pure MHD and require accounting for finite Larmor radius effects and trapped particle modes. Some illuminative theoretical approaches for understanding axisymmetric mirror stability will be described. Wherever possible comparison of theoretical and experimental results on AM will be provided. The applicability of the various stabilization techniques to axisymmetric mirrors as neutron sources, hybrids, and pure-fusion reactors will be discussed and the constraints on the plasma parameters will be formulated. Prepared by LLNL under Contract DE-AC52-07NA27344.

  13. Axisymmetric annular curtain stability

    NASA Astrophysics Data System (ADS)

    Ahmed, Zahir U.; Khayat, Roger E.; Maissa, Philippe; Mathis, Christian

    2012-06-01

    A temporal stability analysis was carried out to investigate the stability of an axially moving viscous annular liquid jet subject to axisymmetric disturbances in surrounding co-flowing viscous gas media. We investigated in this study the effects of inertia, surface tension, the gas-to-liquid density ratio, the inner-to-outer radius ratio and the gas-to-liquid viscosity ratio on the stability of the jet. With an increase in inertia, the growth rate of the unstable disturbances is found to increase. The dominant (or most unstable) wavenumber decreases with increasing Reynolds number for larger values of the gas-to-liquid viscosity ratio. However, an opposite tendency for the most unstable wavenumber is predicted for small viscosity ratio in the same inertia range. The surrounding gas density, in the presence of viscosity, always reduces the growth rate, hence stabilizing the flow. There exists a critical value of the density ratio above which the flow becomes stable for very small viscosity ratio, whereas for large viscosity ratio, no stable flow appears in the same range of the density ratio. The curvature has a significant destabilizing effect on the thin annular jet, whereas for a relatively thick jet, the maximum growth rate decreases as the inner radius increases, irrespective of the surrounding gas viscosity. The degree of instability increases with Weber number for a relatively large viscosity ratio. In contrast, for small viscosity ratio, the growth rate exhibits a dramatic dependence on the surface tension. There is a small Weber number range, which depends on the viscosity ratio, where the flow is stable. The viscosity ratio always stabilizes the flow. However, the dominant wavenumber increases with increasing viscosity ratio. The range of unstable wavenumbers is affected only by the curvature effect.

  14. Relativistic causality

    NASA Astrophysics Data System (ADS)

    Valente, Giovanni; Owen Weatherall, James

    2014-11-01

    Relativity theory is often taken to include, or to imply, a prohibition on superluminal propagation of causal processes. Yet, what exactly the prohibition on superluminal propagation amounts to and how one should deal with its possible violation have remained open philosophical problems, both in the context of the metaphysics of causation and the foundations of physics. In particular, recent work in philosophy of physics has focused on the causal structure of spacetime in relativity theory and on how this causal structure manifests itself in our most fundamental theories of matter. These topics were the subject of a workshop on "Relativistic Causality in Quantum Field Theory and General Relativity" that we organized (along with John Earman) at the Center for Philosophy of Science in Pittsburgh on April 5-7, 2013. The present Special Issue comprises contributions by speakers in that workshop as well as several other experts exploring different aspects of relativistic causality. We are grateful to the journal for hosting this Special Issue, to the journal's managing editor, Femke Kuiling, for her help and support in putting the issue together, and to the authors and the referees for their excellent work.

  15. A New Multi-dimensional General Relativistic Neutrino Hydrodynamic Code for Core-collapse Supernovae. I. Method and Code Tests in Spherical Symmetry

    NASA Astrophysics Data System (ADS)

    Müller, Bernhard; Janka, Hans-Thomas; Dimmelmeier, Harald

    2010-07-01

    We present a new general relativistic code for hydrodynamical supernova simulations with neutrino transport in spherical and azimuthal symmetry (one dimension and two dimensions, respectively). The code is a combination of the COCONUT hydro module, which is a Riemann-solver-based, high-resolution shock-capturing method, and the three-flavor, fully energy-dependent VERTEX scheme for the transport of massless neutrinos. VERTEX integrates the coupled neutrino energy and momentum equations with a variable Eddington factor closure computed from a model Boltzmann equation and uses the "ray-by-ray plus" approximation in two dimensions, assuming the neutrino distribution to be axially symmetric around the radial direction at every point in space, and thus the neutrino flux to be radial. Our spacetime treatment employs the Arnowitt-Deser-Misner 3+1 formalism with the conformal flatness condition for the spatial three metric. This approach is exact for the one-dimensional case and has previously been shown to yield very accurate results for spherical and rotational stellar core collapse. We introduce new formulations of the energy equation to improve total energy conservation in relativistic and Newtonian hydro simulations with grid-based Eulerian finite-volume codes. Moreover, a modified version of the VERTEX scheme is developed that simultaneously conserves energy and lepton number in the neutrino transport with better accuracy and higher numerical stability in the high-energy tail of the spectrum. To verify our code, we conduct a series of tests in spherical symmetry, including a detailed comparison with published results of the collapse, shock formation, shock breakout, and accretion phases. Long-time simulations of proto-neutron star cooling until several seconds after core bounce both demonstrate the robustness of the new COCONUT-VERTEX code and show the approximate treatment of relativistic effects by means of an effective relativistic gravitational potential as in

  16. A NEW MULTI-DIMENSIONAL GENERAL RELATIVISTIC NEUTRINO HYDRODYNAMIC CODE FOR CORE-COLLAPSE SUPERNOVAE. I. METHOD AND CODE TESTS IN SPHERICAL SYMMETRY

    SciTech Connect

    Mueller, Bernhard; Janka, Hans-Thomas; Dimmelmeier, Harald E-mail: thj@mpa-garching.mpg.d

    2010-07-15

    We present a new general relativistic code for hydrodynamical supernova simulations with neutrino transport in spherical and azimuthal symmetry (one dimension and two dimensions, respectively). The code is a combination of the COCONUT hydro module, which is a Riemann-solver-based, high-resolution shock-capturing method, and the three-flavor, fully energy-dependent VERTEX scheme for the transport of massless neutrinos. VERTEX integrates the coupled neutrino energy and momentum equations with a variable Eddington factor closure computed from a model Boltzmann equation and uses the 'ray-by-ray plus' approximation in two dimensions, assuming the neutrino distribution to be axially symmetric around the radial direction at every point in space, and thus the neutrino flux to be radial. Our spacetime treatment employs the Arnowitt-Deser-Misner 3+1 formalism with the conformal flatness condition for the spatial three metric. This approach is exact for the one-dimensional case and has previously been shown to yield very accurate results for spherical and rotational stellar core collapse. We introduce new formulations of the energy equation to improve total energy conservation in relativistic and Newtonian hydro simulations with grid-based Eulerian finite-volume codes. Moreover, a modified version of the VERTEX scheme is developed that simultaneously conserves energy and lepton number in the neutrino transport with better accuracy and higher numerical stability in the high-energy tail of the spectrum. To verify our code, we conduct a series of tests in spherical symmetry, including a detailed comparison with published results of the collapse, shock formation, shock breakout, and accretion phases. Long-time simulations of proto-neutron star cooling until several seconds after core bounce both demonstrate the robustness of the new COCONUT-VERTEX code and show the approximate treatment of relativistic effects by means of an effective relativistic gravitational potential as in

  17. A SCILAB Program for Computing General-Relativistic Models of Rotating Neutron Stars by Implementing Hartle's Perturbation Method

    NASA Astrophysics Data System (ADS)

    Papasotiriou, P. J.; Geroyannis, V. S.

    We implement Hartle's perturbation method to the computation of relativistic rigidly rotating neutron star models. The program has been written in SCILAB (© INRIA ENPC), a matrix-oriented high-level programming language. The numerical method is described in very detail and is applied to many models in slow or fast rotation. We show that, although the method is perturbative, it gives accurate results for all practical purposes and it should prove an efficient tool for computing rapidly rotating pulsars.

  18. Generalization of the Bennett equilibrium condition for a relativistic electron beam propagating in the Ohmic plasma channel and ion focusing regime along an external magnetic field

    NASA Astrophysics Data System (ADS)

    Kolesnikov, E. K.; Manuilov, A. S.

    2016-04-01

    The problem of formulating the generalization of the Bennett equilibrium condition is considered for a relativistic electron beam propagating in the Ohmic plasma channel, as well as in the ion focusing regime in the presence of an external longitudinal uniform magnetic field. We assume that the electron component of the background plasma is not completely removed from the region occupied by the beam. This equilibrium condition is derived using the mass and momentum transport equations obtained for a paraxial monoenergetic beam from the Fokker-Planck kinetic equation.

  19. Relativistic viscoelastic fluid mechanics

    SciTech Connect

    Fukuma, Masafumi; Sakatani, Yuho

    2011-08-15

    A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.

  20. REVIEW ARTICLE: Control of non-axisymmetric toroidal plasmas

    NASA Astrophysics Data System (ADS)

    Boozer, Allen H.

    2010-10-01

    The control of non-axisymmetric toroidal plasmas, stellarators, has a different character than the control of tokamaks for two reasons. Non-axisymmetric magnetic fields (1) can provide an arbitrarily large fraction of the poloidal magnetic field and (2) can strongly center the plasma in the chamber making it impossible to lose position control. The focus of stellarator design is on plasmas that are stable without feedback, need little or no change in the external magnetic field as the plasma evolves, and require no external power to maintain the desired magnetic configuration. The physics of non-axisymmetric fields is the same whether in a tokamak or a stellarator and whether introduced intentionally or accidentally. Fundamental physics indicates that plasma shape, which is controlled by the distribution of the external magnetic field that is normal to the plasma surface, is the primary control for fusion plasmas. The importance of non-axisymmetric control is set by the importance of toroidal plasma physics. Informed decisions on the development strategy of tokamaks, as well as magnetic fusion in general, require an understanding of the capabilities and difficulties of plasma control at various levels of non-axisymmetric shaping.

  1. Stationary axisymmetric fields in a teleparallel theory of gravitation

    NASA Astrophysics Data System (ADS)

    Saez, D.

    1984-12-01

    The stationary axisymmetric field in the tetrad theory of gravitation of Moller (1978) and hence (as shown by Meyre, 1982) in the teleparallel limit of the gauge theory of Hehl et al. (1978) is investigated analytically. A set of tetrads satisfying the Moller equations and giving a Kerr metric is defined, and its existence is proved. It is suggested that the introduction of suitable conditions could reduce the number of tetrads in the Kerr case to one or a small number, and that the present analytical techniques could be applied to other stationary axisymmetric metrics of general relativity.

  2. Magnetic-field-induced electric quadrupole moments for relativistic hydrogenlike atoms: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function

    NASA Astrophysics Data System (ADS)

    Stefańska, Patrycja

    2016-02-01

    We consider a Dirac one-electron atom placed in a weak, static, uniform magnetic field. We show that, to the first order in the strength B of the external field, the only electric multipole moments, which are induced by the perturbation in the atom, are those of an even order. Using the Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30, 825 (1997), 10.1088/0953-4075/30/4/007; J. Phys. B 30, 2747 (1997), 10.1088/0953-4075/30/11/023], We derive a closed-form expression for the electric quadrupole moment induced in the atom in an arbitrary discrete energy eigenstate. The result, which has the form of a double finite sum involving the generalized hypergeometric functions 3F2 of the unit argument, agrees with the earlier relativistic formula for that quantity, obtained by us for the ground state of the atom.

  3. Axisymmetric Vortices with Swirl

    NASA Astrophysics Data System (ADS)

    Elcrat, A.

    2007-11-01

    This talk is concerned with finding solutions of the Euler equations by solving elliptic boundary value problems for the Bragg-Hawthorne equation L u= -urr -(1/r)ur - = r^2f (u) + h(u). Theoretical results have been given for previously (Elcrat and Miller, Differential and Integral Equations 16(4) 2003, 949-968) for problems with swirl and general classes of profile functions f, h by iterating Lu(n+1)= rf(u)n)) + h(u(n)), and showing u(n) converges montonically to a solution. The solutions obtained depend on the initial guess, which can be thought of as prescribing level sets of the vortex. When a computational program was attempted these monotone iterations turned out to be numerically unstable, and a stable computation was acheived by fixing the moment of the cross section of a vortex in the merideanal plane. (This generalizes previous computational results in Elcrat, Fornberg and Miller, JFM 433 2001, (315-328) We obtain famillies of vortices related to vortex rings with swirl, Moffatt's generalization of Hill's vortex and tubes of vorticity with swirl wrapped around the symmetry axis. The vortices are embedded in either an irrotational flow or a flow with shear, and we deal with the transition form no swirl in the vortex to flow with only swirl, a Beltrami flow.

  4. The Formation of Relativistic Jets from Kerr Black Holes

    NASA Technical Reports Server (NTRS)

    Nishikawa, K.-I.; Richardson, G.; Preece, R.; Hardee, P.; Koide, S.; Shibata, K.; Kudoh, T.; Sol, H.; Fishman, G. J.

    2003-01-01

    We have performed the first fully three-dimensional general relativistic magnetohydrodynamics (GRMHD) simulation for Schwarzschild and Kerr black holes with a free falling corona and thin accretion disk. The initial simulation results with a Schwarzschild metric show that a jet is created as in the previous axisymmetric simulations with mirror symmetry at the equator. However, the time to form the jet is slightly longer than in the 2-D axisymmetric simulation. We expect that the dynamics of jet formation are modified due to the additional freedom in the azimuth dimension without axisymmetry with respect to the Z axis and reflection symmetry respect to the equatorial plane. The jet which is initially formed due to the twisted magnetic fields and shocks becomes a wind at the later time. The wind flows out with a much wider angle than the initial jet. The twisted magnetic fields at the earlier time were untwisted and less pinched. The accretion disk became thicker than the initial condition. Further simulations with initial perturbations will provide insights for accretion dynamics with instabilities such as magneto-rotational instability (MRI) and accretion-eject instability (AEI). These instabilities may contribute to variabilities observed in microquasars and AGN jets.

  5. Rotating and binary relativistic stars with magnetic field

    NASA Astrophysics Data System (ADS)

    Markakis, Charalampos

    We develop a geometrical treatment of general relativistic magnetohydrodynamics for perfectly conducting fluids in Einstein--Maxwell--Euler spacetimes. The theory is applied to describe a neutron star that is rotating or is orbiting a black hole or another neutron star. Under the hypotheses of stationarity and axisymmetry, we obtain the equations governing magnetohydrodynamic equilibria of rotating neutron stars with poloidal, toroidal or mixed magnetic fields. Under the hypothesis of an approximate helical symmetry, we obtain the first law of thermodynamics governing magnetized equilibria of double neutron star or black hole - neutron star systems in close circular orbits. The first law is written as a relation between the change in the asymptotic Noether charge deltaQ and the changes in the area and electric charge of black holes, and in the vorticity, baryon rest mass, entropy, charge and magnetic flux of the magnetofluid. In an attempt to provide a better theoretical understanding of the methods used to construct models of isolated rotating stars and corotating or irrotational binaries and their unexplained convergence properties, we analytically examine the behavior of different iterative schemes near a static solution. We find the spectrum of the linearized iteration operator and show for self-consistent field methods that iterative instability corresponds to unstable modes of this operator. On the other hand, we show that the success of iteratively stable methods is due to (quasi-)nilpotency of this operator. Finally, we examine the integrability of motion of test particles in a stationary axisymmetric gravitational field. We use a direct approach to seek nontrivial constants of motion polynomial in the momenta---in addition to energy and angular momentum about the symmetry axis. We establish the existence and uniqueness of quadratic constants and the nonexistence of quartic constants for stationary axisymmetric Newtonian potentials with equatorial symmetry

  6. Experiments in axisymmetric supersonic jets

    NASA Astrophysics Data System (ADS)

    Moore, Cyrille Dennis

    An experimental study of the effects of exit Mach number and density ratio on the development of axisymmetric jets is described in this thesis. Jet exit Mach numbers of 1.41, 2.0, and 3.0, were studied for jets of helium, argon, and nitrogen. The jets exit into a gas at rest (velocity ratio = 0), in order to better isolate the effects of compressibility and density ratio. Density ratios vary from 0.23 to 5.5.In order to generate shock free-jets, unique nozzles were designed and constructed for each gas and Mach number combination. A plating method for the construction of the nozzles was developed to ensure high-accuracy and a good surface finish at a cost significantly less than direct-machining techniques.The spreading rate of the jet for several downstream locations is measured with a pitot probe. Centerline data are used to characterise the length of the potential core of the jet, which correlates well with the relative spreading rates. Limited frequency data is obtained through the use of piezo-resistive pressure probes. This method is promising for flows that are not conducive to hot-wire probes.Spark shadography is used to visualize both the mean and instantaneous flow, with the minimum spark time being 20 nanoseconds. The convection velocity of large-scale disturbances is estimated from the visible Mach-type acoustic waves emanating from the jet.For a wide range of jet Mach and Reynolds numbers, the convection velocity of the large scale disturbances in the potential core region of the jet is approximately 0.8 times the jet velocity, the approximate velocity of the first helical instability mode of the jet.The main objectives of the present work were to investigate the effects of compressibility and density on the initial development of the axisymmetric jet. Although the data are not sufficient to determine if the convective Mach number concept used in 2-d shear layer research will work in the case of an axisymmetric jet, it is clear that the axisymmetric

  7. Relativistic general-order coupled-cluster method for high-precision calculations: Application to the Al{sup +} atomic clock

    SciTech Connect

    Kallay, Mihaly; Nataraj, H. S.; Sahoo, B. K.; Das, B. P.; Visscher, Lucas

    2011-03-15

    We report the implementation of a general-order relativistic coupled-cluster method for performing high-precision calculations of atomic and molecular properties. As a first application, the black-body radiation shift of the Al{sup +} clock has been estimated precisely. The computed shift relative to the frequency of the 3s{sup 2} {sup 1}S{sub 0}{sup e}{yields}3s3p {sup 3}P{sub 0}{sup o} clock transition given by (-3.66{+-}0.60)x10{sup -18} calls for an improvement over the recent measurement with a reported result of (-9{+-}3)x10{sup -18}[Phys. Rev. Lett. 104, 070802 (2010)].

  8. A GENERAL RELATIVISTIC MAGNETOHYDRODYNAMIC MODEL OF HIGH FREQUENCY QUASI-PERIODIC OSCILLATIONS IN BLACK HOLE LOW-MASS X-RAY BINARIES

    SciTech Connect

    Shi Changsheng; Li Xiangdong E-mail: lixd@nju.edu.c

    2010-05-10

    We suggest a possible explanation for the high frequency quasi-periodic oscillations (QPOs) in black hole (BH) low-mass X-ray binaries. By solving the perturbation general relativistic magnetohydrodynamic equations, we find two stable modes of the Alfven wave in the accretion disks with toroidal magnetic fields. We suggest that these two modes may lead to the double high frequency QPOs if they are produced in the transition region between the inner advection-dominated accretion flow and the outer thin disk. This model naturally accounts for the 3:2 relation for the upper and lower frequencies of the QPOs, and the relation between the BH mass and QPO frequency.

  9. Binary neutron-star mergers with Whisky and SACRA: First quantitative comparison of results from independent general-relativistic hydrodynamics codes

    NASA Astrophysics Data System (ADS)

    Baiotti, Luca; Shibata, Masaru; Yamamoto, Tetsuro

    2010-09-01

    We present the first quantitative comparison of two independent general-relativistic hydrodynamics codes, the whisky code and the sacra code. We compare the output of simulations starting from the same initial data and carried out with the configuration (numerical methods, grid setup, resolution, gauges) which for each code has been found to give consistent and sufficiently accurate results, in particular, in terms of cleanness of gravitational waveforms. We focus on the quantities that should be conserved during the evolution (rest mass, total mass energy, and total angular momentum) and on the gravitational-wave amplitude and frequency. We find that the results produced by the two codes agree at a reasonable level, with variations in the different quantities but always at better than about 10%.

  10. Axisymmetric supersonic flow in rotating impellers

    NASA Technical Reports Server (NTRS)

    Goldstein, Arthur W

    1952-01-01

    General equations are developed for isentropic, frictionless, axisymmetric flow in rotating impellers with blade thickness taken into account and with blade forces eliminated in favor of the blade-surface function. It is shown that the total energy of the gas relative to the rotating coordinate system is dependent on the stream function only, and that if the flow upstream of the impeller is vortex-free, a velocity potential exists which is a function of only the radial and axial distances in the impeller. The characteristic equations for supersonic flow are developed and used to investigate flows in several configurations in order to ascertain the effect of variations of the boundary conditions on the internal flow and the work input. Conditions varied are prerotation of the gas, blade turning rate, gas velocity at the blade tips, blade thickness, and sweep of the leading edge.

  11. A dynamo model for axisymmetric and non-axisymmetric solar magnetic fields

    NASA Astrophysics Data System (ADS)

    Jiang, J.; Wang, J. X.

    2007-05-01

    More and more observations are showing a relatively weak, but persistent, non-axisymmetric magnetic field co-existing with the dominant axisymmetric field on the Sun. Its existence indicates that the non-axisymmetric magnetic field plays an important role in the origin of solar activity. A linear non-axisymmetric α2-Ω dynamo model is derived to explore the characteristics of the axisymmetric (m = 0) and the first non-axisymmetric (m = 1) modes and to provide a theoretical basis with which to explain the `active longitude', `flip-flop' and other non-axisymmetric phenomena. The model consists of an updated solar internal differential rotation, a turbulent diffusivity varying with depth, and an α-effect working at the tachocline in a rotating spherical system. The difference between the α2-Ω and the α-Ω models and the conditions that favour the non-axisymmetric modes under solar-like parameters are also presented.

  12. ACCELERATION AND COLLIMATION OF RELATIVISTIC MAGNETOHYDRODYNAMIC DISK WINDS

    SciTech Connect

    Porth, Oliver; Fendt, Christian E-mail: fendt@mpia.d

    2010-02-01

    We perform axisymmetric relativistic magnetohydrodynamic simulations to investigate the acceleration and collimation of jets and outflows from disks around compact objects. Newtonian gravity is added to the relativistic treatment in order to establish the physical boundary condition of an underlying accretion disk in centrifugal and pressure equilibrium. The fiducial disk surface (respectively a slow disk wind) is prescribed as boundary condition for the outflow. We apply this technique for the first time in the context of relativistic jets. The strength of this approach is that it allows us to run a parameter study in order to investigate how the accretion disk conditions govern the outflow formation. Substantial effort has been made to implement a current-free, numerical outflow boundary condition in order to avoid artificial collimation present in the standard outflow conditions. Our simulations using the PLUTO code run for 500 inner disk rotations and on a physical grid size of 100 x 200 inner disk radii. The simulations evolve from an initial state in hydrostatic equilibrium and an initially force-free magnetic field configuration. Two options for the initial field geometries are applied-an hourglass-shaped potential magnetic field and a split monopole field. Most of our parameter runs evolve into a steady state solution which can be further analyzed concerning the physical mechanism at work. In general, we obtain collimated beams of mildly relativistic speed with Lorentz factors up to 6 and mass-weighted half-opening angles of 3-7 deg. The split-monopole initial setup usually results in less collimated outflows. The light surface of the outflow magnetosphere tends to align vertically-implying three relativistically distinct regimes in the flow-an inner subrelativistic domain close to the jet axis, a (rather narrow) relativistic jet and a surrounding subrelativistic outflow launched from the outer disk surface-similar to the spine-sheath structure currently

  13. Local stability of axisymmetric plumes

    NASA Astrophysics Data System (ADS)

    R. v. K., Chakravarthy; Lesshafft, Lutz; Huerre, Patrick

    2014-11-01

    A linear stability analysis of a forced plume with non-zero momentum at the inlet is performed for Pr = 1 , Re = 100 and Ri near 1. The steady base flow is obtained as a laminar solution of the steady Navier Stokes equations. The base flow asymptotes to a self-similar solution as it evolves downstream. In the non-self-similar regime close to the inlet, both axisymmetric mode (m = 0) and the helical mode (m = 1) are convectively unstable at sufficiently low Richardson number. In the self-similar regime, only the helical mode is absolutely unstable and the axisymmetric mode is stable. Higher helical modes (m >= 2) are seen to be convectively unstable very close to the inlet and become stable as the flow evolves downstream. The transition from convective to absolute instability makes the flow a good candidate for observing steep nonlinear global modes associated with buoyancy. This work is supported by a PhD scholarship from Ecole polytechnique.

  14. Transition from gas to plasma kinetic equilibria in gravitating axisymmetric structures

    SciTech Connect

    Cremaschini, Claudio; Stuchlík, Zdeněk

    2014-04-15

    The problem of the transition from gas to plasma in gravitating axisymmetric structures is addressed under the assumption of having initial and final states realized by kinetic Maxwellian-like equilibria. In astrophysics, the theory applies to accretion-disc scenarios around compact objects. A formulation based on non-relativistic kinetic theory for collisionless systems is adopted. Equilibrium solutions for the kinetic distribution functions describing the initial neutral matter and the resulting plasma state are constructed in terms of single-particle invariants and expressed by generalized Maxwellian distributions. The final plasma configuration is related to the initial gas distribution by the introduction of appropriate functional constraints. Qualitative aspects of the solution are investigated and physical properties of the system are pointed out. In particular, the admitted functional dependences of the fluid fields carried by the corresponding equilibrium distributions are determined. Then, the plasma is proved to violate the condition of quasi-neutrality, implying a net charge separation between ions and electrons. This result is shown to be independent of the precise realization of the plasma distribution function, while a physical mechanism able to support a non-neutral equilibrium state is proposed.

  15. The relativistic equations of stellar structure and evolution

    NASA Technical Reports Server (NTRS)

    Thorne, K. S.

    1977-01-01

    The general-relativistic equations of stellar structure and evolution are reformulated in a notation which makes easy contact with Newtonian theory. Also, a general-relativistic version of the mixing-length formalism for convection is presented.

  16. Simulations of Relativistic Extragalactic Jets

    NASA Astrophysics Data System (ADS)

    Hughes, P. A.; Duncan, G. C.

    1994-05-01

    We present results for 2-D, axisymmetric simulations of flows with Lorentz factors ~ 5 -- 10, typical of values inferred for superluminal BL Lacs and QSOs. The simulations were performed with a numerical hydrodynamic code that admits relativistic flow speed. We exploit the property that the relativistic Euler equations for mass, momentum and total energy densities in the laboratory frame have the same form as the nonrelativistic equations, to solve for laboratory frame variables using a conventional Godunov-type scheme with approximate Riemann solver: the HLLE method. The relativistic nature of the flow is incorporated by performing a Lorentz transformation at every step, at each cell center or cell boundary where pressure, sound speed or velocity are required. Determination of the velocity in this manner is a robust algebraic procedure within which we can ensure that vrelativistic flows exhibit a less pronounced pattern of incident and reflection shocks on axis. For flows which have propagated to a fixed number of jet radii, the Kelvin-Helmholtz instability at the contact surface is much less evident in the high Lorentz factor cases, supporting the contention that relativistic flows are less prone to such instability. We describe how the morphology of the cocoon and shocked ambient gas change with increasing Lorentz factor. This work was supported by NSF grant AST 9120224 and by the Ohio Supercomputer Center from a Cray Research Software Development Grant.

  17. Relativistic diffusion

    NASA Astrophysics Data System (ADS)

    Haba, Z.

    2009-02-01

    We discuss relativistic diffusion in proper time in the approach of Schay (Ph.D. thesis, Princeton University, Princeton, NJ, 1961) and Dudley [Ark. Mat. 6, 241 (1965)]. We derive (Langevin) stochastic differential equations in various coordinates. We show that in some coordinates the stochastic differential equations become linear. We obtain momentum probability distribution in an explicit form. We discuss a relativistic particle diffusing in an external electromagnetic field. We solve the Langevin equations in the case of parallel electric and magnetic fields. We derive a kinetic equation for the evolution of the probability distribution. We discuss drag terms leading to an equilibrium distribution. The relativistic analog of the Ornstein-Uhlenbeck process is not unique. We show that if the drag comes from a diffusion approximation to the master equation then its form is strongly restricted. The drag leading to the Tsallis equilibrium distribution satisfies this restriction whereas the one of the Jüttner distribution does not. We show that any function of the relativistic energy can be the equilibrium distribution for a particle in a static electric field. A preliminary study of the time evolution with friction is presented. It is shown that the problem is equivalent to quantum mechanics of a particle moving on a hyperboloid with a potential determined by the drag. A relation to diffusions appearing in heavy ion collisions is briefly discussed.

  18. Relativistic diffusion.

    PubMed

    Haba, Z

    2009-02-01

    We discuss relativistic diffusion in proper time in the approach of Schay (Ph.D. thesis, Princeton University, Princeton, NJ, 1961) and Dudley [Ark. Mat. 6, 241 (1965)]. We derive (Langevin) stochastic differential equations in various coordinates. We show that in some coordinates the stochastic differential equations become linear. We obtain momentum probability distribution in an explicit form. We discuss a relativistic particle diffusing in an external electromagnetic field. We solve the Langevin equations in the case of parallel electric and magnetic fields. We derive a kinetic equation for the evolution of the probability distribution. We discuss drag terms leading to an equilibrium distribution. The relativistic analog of the Ornstein-Uhlenbeck process is not unique. We show that if the drag comes from a diffusion approximation to the master equation then its form is strongly restricted. The drag leading to the Tsallis equilibrium distribution satisfies this restriction whereas the one of the Jüttner distribution does not. We show that any function of the relativistic energy can be the equilibrium distribution for a particle in a static electric field. A preliminary study of the time evolution with friction is presented. It is shown that the problem is equivalent to quantum mechanics of a particle moving on a hyperboloid with a potential determined by the drag. A relation to diffusions appearing in heavy ion collisions is briefly discussed. PMID:19391727

  19. The r-process in black hole-neutron star mergers based on a fully general-relativistic simulation

    NASA Astrophysics Data System (ADS)

    Nishimura, N.; Wanajo, S.; Sekiguchi, Y.; Kiuchi, K.; Kyutoku, K.; Shibata, M.

    2016-01-01

    We investigate the black hole-neutron star binary merger in the contest of the r-process nucleosynthesis. Employing a hydrodynamical model simulated in the framework of full general relativity, we perform nuclear reaction network calculations. The extremely neutron-rich matter with the total mass 0.01 M⊙ is ejected, in which a strong r-process with fission cycling proceeds due to the high neutron number density. We discuss relevant astrophysical issues such as the origin of r-process elements as well as the r-process powered electromagnetic transients.

  20. Post-Newtonian reference ellipsoid for relativistic geodesy

    NASA Astrophysics Data System (ADS)

    Kopeikin, Sergei; Han, Wenbiao; Mazurova, Elena

    2016-02-01

    We apply general relativity to construct the post-Newtonian background manifold that serves as a reference spacetime in relativistic geodesy for conducting a relativistic calculation of the geoid's undulation and the deflection of the plumb line from the vertical. We chose an axisymmetric ellipsoidal body made up of a perfect homogeneous fluid uniformly rotating around a fixed axis, as a source generating the reference geometry of the background manifold through Einstein's equations. We then reformulate and extend hydrodynamic calculations of rotating fluids done by a number of previous researchers for astrophysical applications to the realm of relativistic geodesy to set up algebraic equations defining the shape of the post-Newtonian reference ellipsoid. To complete this task, we explicitly perform all integrals characterizing gravitational field potentials inside the fluid body and represent them in terms of the elementary functions depending on the eccentricity of the ellipsoid. We fully explore the coordinate (gauge) freedom of the equations describing the post-Newtonian ellipsoid and demonstrate that the fractional deviation of the post-Newtonian level surface from the Maclaurin ellipsoid can be made much smaller than the previously anticipated estimate based on the astrophysical application of the coordinate gauge advocated by Bardeen and Chandrasekhar. We also derive the gauge-invariant relations of the post-Newtonian mass and the constant angular velocity of the rotating fluid with the parameters characterizing the shape of the post-Newtonian ellipsoid including its eccentricity, a semiminor axis, and a semimajor axis. We formulate the post-Newtonian theorems of Pizzetti and Clairaut that are used in geodesy to connect the geometric parameters of the reference ellipsoid to the physically measurable force of gravity at the pole and equator of the ellipsoid. Finally, we expand the post-Newtonian geodetic equations describing the post-Newtonian ellipsoid to

  1. 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

  2. Relativistic radiation transport in dispersive media

    SciTech Connect

    Kichenassamy, S.; Krikorian, R.A.

    1985-10-15

    A general-relativistic radiative transfer equation in an isotropic, weakly absorbing, nonmagnetized dispersive medium is derived using the kinetic-theoretical approach and the relativistic Hamiltonian theory of geometrical optics in those media. It yields the generally accepted classical equation in the special-relativistic approximation and in stationary conditions. The influence of the gravitational field and of space-time variations of the refractive index n on the radiation distribution is made explicit in the case of spherical symmetry.

  3. The Case for General Relativistic Effects in the Fe K(alpha) Profile of an Active Galaxy

    NASA Technical Reports Server (NTRS)

    Turner, T. J.; Mushotzky, R.; Yaqoob, T.; George, I. M.; Snowden, S. L.; Netzer, H.; Kraemer, S. B.; Nandra, K.; Chelouche, D.; White, Nicholas E. (Technical Monitor)

    2002-01-01

    We present results from a simultaneous Chandra HETG (High Energy Transmission Grating) and XMM (X-ray Multi-mirror Mission)-Newton observation of NGC 3516. We find evidence for several narrow components of Fe K(alpha) along with a broad line. We consider the possibility that the lines arise in a blob of material ejected from the nucleus with velocity of approximately 0.25c. We also consider an origin in a neutral accretion disk, suffering enhanced illumination at 35 and 175 R(sub g), perhaps due to magnetic reconnection. The presence of these narrow features indicates there is no Comptonizing region along the line-of-sight to the nucleus. This in turn is compelling support for the hypothesis that broad Fe K(alpha) components are, in general, produced by strong gravity.

  4. Characteristics of transonic spherical symmetric accretion flow in Schwarzschild-de Sitter and Schwarzschild anti-de Sitter backgrounds, in pseudo-general relativistic paradigm

    NASA Astrophysics Data System (ADS)

    Ghosh, Shubhrangshu; Banik, Prabir

    2015-07-01

    In this paper, we present a complete work on steady state spherically symmetric Bondi type accretion flow in the presence of cosmological constant (Λ) in both Schwarzschild-de Sitter (SDS) and Schwarzschild anti-de Sitter (SADS) backgrounds considering an isolated supermassive black hole (SMBH), with the inclusion of a simple radiative transfer scheme, in the pseudo-general relativistic paradigm. We do an extensive analysis on the transonic behavior of the Bondi type accretion flow onto the cosmological BHs including a complete analysis of the global parameter space and the stability of flow, and do a complete study of the global family of solutions for a generic polytropic flow. Bondi type accretion flow in SADS background renders multiplicity in its transonic behavior with inner "saddle" type and outer "center" type sonic points, with the transonic solutions forming closed loops or contours. There is always a limiting value for ∣Λ∣ up to which we obtain valid stationary transonic solutions, which correspond to both SDS and SADS geometries; this limiting value moderately increases with the increasing radiative efficiency of the flow, especially correspond to Bondi type accretion flow in SADS background. Repulsive Λ suppresses the Bondi accretion rate by an order of magnitude for relativistic Bondi type accretion flow for a certain range in temperature, and with a marginal increase in the Bondi accretion rate if the corresponding accretion flow occurs in SADS background. However, for a strongly radiative Bondi type accretion flow with high mass accretion rate, the presence of cosmological constant do not much influence the corresponding Bondi accretion rate of the flow. Our analysis show that the relic cosmological constant has a substantial effect on Bondi type accretion flow onto isolated SMBHs and their transonic solutions beyond length-scale of kiloparsecs, especially if the Bondi type accretion occurs onto the host supergiant ellipticals or central

  5. Relativistic geodesy

    NASA Astrophysics Data System (ADS)

    Flury, J.

    2016-06-01

    Quantum metrology enables new applications in geodesy, including relativistic geodesy. The recent progress in optical atomic clocks and in long-distance frequency transfer by optical fiber together pave the way for using measurements of the gravitational frequency redshift for geodesy. The remote comparison of frequencies generated by calibrated clocks will allow for a purely relativistic determination of differences in gravitational potential and height between stations on Earth surface (chronometric leveling). The long-term perspective is to tie potential and height differences to atomic standards in order to overcome the weaknesses and inhomogeneity of height systems determined by classical spirit leveling. Complementarily, gravity measurements with atom interferometric setups, and satellite gravimetry with space borne laser interferometers allow for new sensitivities in the measurement of the Earth's gravity field.

  6. Relativistic klystrons

    SciTech Connect

    Allen, M.A.; Azuma, O.; Callin, R.S.; Deruyter, H.; Eppley, K.R.; Fant, K.S.; Fowkes, W.R.; Herrmannsfeldt, W.B.; Hoag, H.A.; Koontz, R.F.

    1989-03-01

    Experimental work is underway by a SLAC-LLNL-LBL collaboration to investigate the feasibility of using relativistic klystrons as a power source for future high gradient accelerators. Two different relativistic klystron configurations have been built and tested to date: a high grain multicavity klystron at 11.4 GHz and a low gain two cavity subharmonic buncher driven at 5.7 GHz. In both configurations power is extracted at 11.4 GHz. In order to understand the basic physics issues involved in extracting RF from a high power beam, we have used both a single resonant cavity and a multi-cell traveling wave structure for energy extraction. We have learned how to overcome our previously reported problem of high power RF pulse shortening, and have achieved peak RF power levels of 170 MW with the RF pulse of the same duration as the beam current pulse. 6 refs., 3 figs., 3 tabs.

  7. Relativistic Astrophysics

    NASA Astrophysics Data System (ADS)

    Jones, Bernard J. T.; Markovic, Dragoljub

    1997-06-01

    Preface; Prologue: Conference overview Bernard Carr; Part I. The Universe At Large and Very Large Redshifts: 2. The size and age of the Universe Gustav A. Tammann; 3. Active galaxies at large redshifts Malcolm S. Longair; 4. Observational cosmology with the cosmic microwave background George F. Smoot; 5. Future prospects in measuring the CMB power spectrum Philip M. Lubin; 6. Inflationary cosmology Michael S. Turner; 7. The signature of the Universe Bernard J. T. Jones; 8. Theory of large-scale structure Sergei F. Shandarin; 9. The origin of matter in the universe Lev A. Kofman; 10. New guises for cold-dark matter suspects Edward W. Kolb; Part II. Physics and Astrophysics Of Relativistic Compact Objects: 11. On the unification of gravitational and inertial forces Donald Lynden-Bell; 12. Internal structure of astrophysical black holes Werner Israel; 13. Black hole entropy: external facade and internal reality Valery Frolov; 14. Accretion disks around black holes Marek A. Abramowicz; 15. Black hole X-ray transients J. Craig Wheeler; 16. X-rays and gamma rays from active galactic nuclei Roland Svensson; 17. Gamma-ray bursts: a challenge to relativistic astrophysics Martin Rees; 18. Probing black holes and other exotic objects with gravitational waves Kip Thorne; Epilogue: the past and future of relativistic astrophysics Igor D. Novikov; I. D. Novikov's scientific papers and books.

  8. Non-axisymmetric viscous lower-branch modes in axisymmetric supersonic flows

    NASA Technical Reports Server (NTRS)

    Duck, Peter W.; Hall, Philip

    1990-01-01

    A previous paper by Duck and Hall (1989) considered the weakly nonlinear interaction of a pair of axisymmetric lower-branch Tollmien-Schlichting instabilities in cylindrical supersonic flows. Here, the possibility that nonaxisymmetric modes might also exist is investigated. In fact, it is found that such modes do exist and, on the basis of linear theory, it appears that these modes are the most important. The nonaxisymmetric modes are found to exist for flows around cylinders with nondimensional radius a less than some critical value a(c). This critical value a(c) is found to increase monotonically with the azimuthal wavenumber n of the disturbance, and it is found that unstable modes always occur in pairs. It is shown that, in general, instability in the form of lower-branch Tollmien-Schlichting waves will occur first for nonaxisymmetric modes and that, in the unstable regime, the largest growth rates correspond to the latter modes.

  9. MAGNETIC ENERGY BUILDUP FOR RELATIVISTIC MAGNETAR GIANT FLARES

    SciTech Connect

    Yu Cong

    2011-09-01

    Motivated by coronal mass ejection studies, we construct general relativistic models of a magnetar magnetosphere endowed with strong magnetic fields. The equilibrium states of the stationary, axisymmetric magnetic fields in the magnetar magnetosphere are obtained as solutions of the Grad-Shafranov equation in a Schwarzschild spacetime. To understand the magnetic energy buildup in the magnetar magnetosphere, a generalized magnetic virial theorem in the Schwarzschild metric is newly derived. We carefully address the question whether the magnetar magnetospheric magnetic field can build up sufficient magnetic energy to account for the work required to open up the magnetic field during magnetar giant flares. We point out the importance of the Aly-Sturrock constraint, which has been widely studied in solar corona mass ejections, as a reference state in understanding magnetar energy storage processes. We examine how the magnetic field can possess enough energy to overcome the Aly-Sturrock energy constraint and open up. In particular, general relativistic (GR) effects on the Aly-Sturrock energy constraint in the Schwarzschild spacetime are carefully investigated. It is found that, for magnetar outbursts, the Aly-Sturrock constraint is more stringent, i.e., the Aly-Sturrock energy threshold is enhanced due to the GR effects. In addition, neutron stars with greater mass have a higher Aly-Sturrock energy threshold and are more difficult to erupt. This indicates that magnetars are probably not neutron stars with extreme mass. For a typical neutron star with mass of 1-2 M{sub sun}, we further explore the cross-field current effects, caused by the mass loading, on the possibility of stored magnetic field energy exceeding the Aly-Sturrock threshold.

  10. Radiation from Axisymmetric Waveguide Fed Horns

    NASA Technical Reports Server (NTRS)

    Chinn, G. C.; Hoppe, D. J.; Epp, L. W.

    1995-01-01

    Return losses and radiation patterns for axisymmetric waveguide fed horns are calculated with the finite element method (FEM) in conjunction with the method of moments (MoM) and the mode matching technique (MM).

  11. Relativistic Bernstein waves in a degenerate plasma

    SciTech Connect

    Ali, Muddasir; Hussain, Azhar; Murtaza, G.

    2011-09-15

    Bernstein mode for a relativistic degenerate electron plasma is investigated. Using relativistic Vlasov-Maxwell equations, a general expression for the conductivity tensor is derived and then employing Fermi-Dirac distribution function a generalized dispersion relation for the Bernstein mode is obtained. Two limiting cases, i.e., non-relativistic and ultra-relativistic are discussed. The dispersion relations obtained are also graphically presented for some specific values of the parameters depicting how the propagation characteristics of Bernstein waves as well as the Upper Hybrid oscillations are modified with the increase in plasma number density.

  12. New code for equilibriums and quasiequilibrium initial data of compact objects. III. Axisymmetric and triaxial rotating stars

    NASA Astrophysics Data System (ADS)

    Uryū, Kōji; Tsokaros, Antonios; Galeazzi, Filippo; Hotta, Hideya; Sugimura, Misa; Taniguchi, Keisuke; Yoshida, Shin'ichirou

    2016-02-01

    We introduce new code for stationary and axisymmetric equilibriums, as well as for triaxial quasiequilibrium initial data, of single rotating relativistic stars. The new code is developed as a part of our versatile initial data code for compact objects, Compact Object CALculator (cocal). In computing strong gravitational fields, the waveless formulation is incorporated into the cocal code on top of the previously developed Isenberg-Wilson-Mathews formulation (conformally flat thin-sandwich formulation). Also introduced is a new differential rotation law that contains two parameters to control an angular velocity profile and a transition from uniform to differential rotation. We present convergence tests and solution sequences for both uniformly and differentially rotating equilibriums of stationary axisymmetric compact stars, as well as for quasiequilibrium initial data of uniformly rotating triaxial (nonaxisymmetric) compact stars. We also show comparisons of uniformly rotating axisymmetric solutions computed with three different codes: cocal, lorene, and the RNS code.

  13. Four motional invariants in axisymmetric tori equilibria

    SciTech Connect

    A ring gren, O.; Moiseenko, V.E.

    2006-05-15

    In addition to the standard set ({epsilon},{mu},p{sub {phi}}) of three invariants in axisymmetric tori, there exists a fourth independent radial drift invariant I{sub r}. For confined particles, the net radial drift has to be zero, whereby the drift orbit average I{sub r}= of the gyro center radial Clebsch coordinate is constant. To lowest order in the banana width, the radial invariant is the gyro center radial coordinate r{sub 0}(x,v), and to this order the gyro center moves on a magnetic flux surface. The gyro center orbit projected on the (r,z) plane determines the radial invariant and first order banana width corrections to I{sub r} are calculated. The radial drift invariant exists for trapped as well as passing particles. The new invariant is applied to construct Vlasov equilibria, where the magnetic field satisfies a generalized Grad-Shafranov equation with a poloidal plasma current and a bridge to ideal magnetohydrodynamic equilibria is found. For equilibria with sufficiently small banana widths and radial drift excursions, the approximation I{sub r}{approx_equal}r{sub 0}(x,v) can be used for the equilibrium state.

  14. The inviscid stability of supersonic flow past axisymmetric bodies

    NASA Technical Reports Server (NTRS)

    Duck, Peter W.

    1990-01-01

    The supersonic flow past a sharp cone is studied. The associated boundary layer flow (i.e., the velocity and temperature field) is computed. The inviscid linear temporal stability of axisymmetric boundary layers in general is considered, and in particular, a so-called 'triply generalized' inflection condition for 'subsonic' nonaxisymmetric neutral modes is presented. Preliminary numerical results for the stability of the cone boundary layer are presented for a freestream Mach number of 3.8. In particular, a new inviscid mode of instability is seen to occur in certain regimes, and this is shown to be related to a viscous mode found by Duck and Hall (1988).

  15. Transition and mixing in axisymmetric jets and vortex rings

    NASA Technical Reports Server (NTRS)

    Allen, G. A., Jr.; Cantwell, B. J.

    1986-01-01

    A class of impulsively started, axisymmetric, laminar jets produced by a time dependent joint source of momentum are considered. These jets are different flows, each initially at rest in an unbounded fluid. The study is conducted at three levels of detail. First, a generalized set of analytic creeping flow solutions are derived with a method of flow classification. Second, from this set, three specific creeping flow solutions are studied in detail: the vortex ring, the round jet, and the ramp jet. This study involves derivation of vorticity, stream function, entrainment diagrams, and evolution of time lines through computer animation. From entrainment diagrams, critical points are derived and analyzed. The flow geometry is dictated by the properties and location of critical points which undergo bifurcation and topological transformation (a form of transition) with changing Reynolds number. Transition Reynolds numbers were calculated. A state space trajectory was derived describing the topological behavior of these critical points. This state space derivation yielded three states of motion which are universal for all axisymmetric jets. Third, the axisymmetric round jet is solved numerically using the unsteady laminar Navier Stokes equations. These equations were shown to be self similar for the round jet. Numerical calculations were performed up to a Reynolds number of 30 for a 60x60 point mesh. Animations generated from numerical solution showed each of the three states of motion for the round jet, including the Re = 30 case.

  16. Axisymmetric MHD Instabilities in Solar/Stellar Tachoclines

    NASA Astrophysics Data System (ADS)

    Dikpati, Mausumi; Gilman, Peter A.; Cally, Paul S.; Miesch, Mark S.

    2009-02-01

    Extensive studies over the past decade showed that HD and MHD nonaxisymmetric instabilities exist in the solar tachocline for a wide range of toroidal field profiles, amplitudes, and latitude locations. Axisymmetric instabilities (m = 0) do not exist in two dimensions, and are excited in quasi-three-dimensional shallow-water systems only for very high field strengths (2 mG). We investigate here MHD axisymmetric instabilities in a three-dimensional thin-shell model of the solar/stellar tachocline, employing a hydrostatic, non-Boussinesq system of equations. We deduce a number of general properties of the instability by use of an integral theorem, as well as finding detailed numerical solutions for unstable modes. Toroidal bands become unstable to axisymmetric perturbations for solar-like field strengths (100 kG). The e-folding time can be months down to a few hours if the field strength is 1 mG or higher, which might occur in the solar core, white dwarfs, or neutron stars. These instabilities exist without rotation, with rotation, and with differential rotation, although both rotation and differential rotation have stabilizing effects. Broad toroidal fields are stable. The instability for modes with m = 0 is driven from the poleward shoulder of banded profiles by a perturbation magnetic curvature stress that overcomes the stabilizing Coriolis force. The nonaxisymmetric instability tips or deforms a band; with axisymmetric instability, the fluid can roll in latitude and radius, and can convert bands into tubes stacked in radius. The velocity produced by this instability in the case of low-latitude bands crosses the equator, and hence can provide a mechanism for interhemispheric coupling.

  17. KINETIC THEORY OF EQUILIBRIUM AXISYMMETRIC COLLISIONLESS PLASMAS IN OFF-EQUATORIAL TORI AROUND COMPACT OBJECTS

    SciTech Connect

    Cremaschini, Claudio; Kovář, Jiří; Slaný, Petr; Stuchlík, Zdeněk; Karas, Vladimír

    2013-11-01

    The possible occurrence of equilibrium off-equatorial tori in the gravitational and electromagnetic fields of astrophysical compact objects has been recently proved based on non-ideal magnetohydrodynamic theory. These stationary structures can represent plausible candidates for the modeling of coronal plasmas expected to arise in association with accretion disks. However, accretion disk coronae are formed by a highly diluted environment, and so the fluid description may be inappropriate. The question is posed of whether similar off-equatorial solutions can also be determined in the case of collisionless plasmas for which treatment based on kinetic theory, rather than a fluid one, is demanded. In this paper the issue is addressed in the framework of the Vlasov-Maxwell description for non-relativistic, multi-species axisymmetric plasmas subject to an external dominant spherical gravitational and dipolar magnetic field. Equilibrium configurations are investigated and explicit solutions for the species kinetic distribution function are constructed, which are expressed in terms of generalized Maxwellian functions characterized by isotropic temperature and non-uniform fluid fields. The conditions for the existence of off-equatorial tori are investigated. It is proved that these levitating systems are admitted under general conditions when both gravitational and magnetic fields contribute to shaping the spatial profiles of equilibrium plasma fluid fields. Then, specifically, kinetic effects carried by the equilibrium solution are explicitly provided and identified here with diamagnetic energy-correction and electrostatic contributions. It is shown that these kinetic terms characterize the plasma equation of state by introducing non-vanishing deviations from the assumption of thermal pressure.

  18. Oscillations of rapidly rotating relativistic stars

    SciTech Connect

    Gaertig, Erich; Kokkotas, Kostas D.

    2008-09-15

    Nonaxisymmetric oscillations of rapidly rotating relativistic stars are studied using the Cowling approximation. The oscillation spectra have been estimated by Fourier transforming the evolution equations describing the perturbations. This is the first study of its kind and provides information on the effect of fast rotation on the oscillation spectra while it offers the possibility of studying the complete problem by including space-time perturbations. Our study includes both axisymmetric and nonaxisymmetric perturbations and provides limits for the onset of the secular bar mode rotational instability. We also present approximate formulas for the dependence of the oscillation spectrum from rotation. The results suggest that it is possible to extract the relativistic star's parameters from the observed gravitational wave spectrum.

  19. On the equilibrium structures of self-gravitating masses of gas containing axisymmetric magnetic fields

    NASA Technical Reports Server (NTRS)

    Lerche, I.; Low, B. C.

    1980-01-01

    The general equations describing the equilibrium shapes of self-gravitating gas clouds containing axisymmetric magnetic fields are presented. The general equations admit of a large class of solutions. It is shown that if one additional (ad hoc) asumption is made that the mass be spherically symmetrically distributed, then the gas pressure and the boundary conditions are sufficiently constraining that the general topological structure of the solution is effectively determined. The further assumption of isothermal conditions for this case demands that all solutions possess force-free axisymmetric magnetic fields. It is also shown how the construction of aspherical (but axisymmetric) configurations can be achieved in some special cases, and it is demonstrated that the detailed form of the possible equilibrium shapes depends upon the arbitrary choice of the functional form of the variation of the gas pressure along the field lines.

  20. Relativistic magnetohydrodynamics in one dimension.

    PubMed

    Lyutikov, Maxim; Hadden, Samuel

    2012-02-01

    We derive a number of solutions for one-dimensional dynamics of relativistic magnetized plasma that can be used as benchmark estimates in relativistic hydrodynamic and magnetohydrodynamic numerical codes. First, we analyze the properties of simple waves of fast modes propagating orthogonally to the magnetic field in relativistically hot plasma. The magnetic and kinetic pressures obey different equations of state, so that the system behaves as a mixture of gases with different polytropic indices. We find the self-similar solutions for the expansion of hot strongly magnetized plasma into vacuum. Second, we derive linear hodograph and Darboux equations for the relativistic Khalatnikov potential, which describe arbitrary one-dimensional isentropic relativistic motion of cold magnetized plasma and find their general and particular solutions. The obtained hodograph and Darboux equations are very powerful: A system of highly nonlinear, relativistic, time-dependent equations describing arbitrary (not necessarily self-similar) dynamics of highly magnetized plasma reduces to a single linear differential equation. PMID:22463331

  1. Dissipation in Relativistic Pair-Plasma Reconnection

    NASA Technical Reports Server (NTRS)

    Hesse, Michael; Zenitani, Seiji

    2007-01-01

    We present an investigation of the relativistic dissipation in magnetic reconnection. The investigated system consists of an electron-positron plasma. A relativistic generalization of Ohm's law is derived. We analyze a set of numerical simulations, composed of runs with and without guide magnetic field, and of runs with different species temperatures. The calculations indicate that the thermal inertia-based dissipation process survives in relativistic plasmas. For anti-parallel reconnection, it is found that the pressure tensor divergence remains the sole contributor to the reconnection electric field, whereas relativistic guide field reconnection exhibits a similarly important role of the bulk inertia terms.

  2. Dissipation in relativistic pair-plasma reconnection

    SciTech Connect

    Hesse, Michael; Zenitani, Seiji

    2007-11-15

    An investigation into the relativistic dissipation in magnetic reconnection is presented. The investigated system consists of an electron-positron plasma. A relativistic generalization of Ohm's law is derived. A set of numerical simulations is analyzed, composed of runs with and without guide magnetic field, and of runs with different species temperatures. The calculations indicate that the thermal inertia-based dissipation process survives in relativistic plasmas. For antiparallel reconnection, it is found that the pressure tensor divergence remains the sole contributor to the reconnection electric field, whereas relativistic guide field reconnection exhibits a similarly important role of the bulk inertia terms.

  3. Relativistic electrons associated with solar flares.

    NASA Technical Reports Server (NTRS)

    Sakurai, K.

    1972-01-01

    Solar flares which produce relativistic electrons generally occur within sunspot groups which are active in the emission of meter type I noise storms. It is suggested that relativistic electrons in solar flares are accelerated from the keV-energy electrons responsible for the type I noise storms. The relationship between flare developments and the ejection of keV-electrons is briefly considered.

  4. Constants of motion in stationary axisymmetric gravitational fields

    NASA Astrophysics Data System (ADS)

    Markakis, C.

    2014-07-01

    The motion of test particles in stationary axisymmetric gravitational fields is generally non-integrable unless a non-trivial constant of motion, in addition to energy and angular momentum along the symmetry axis, exists. The Carter constant in Kerr-de Sitter space-time is the only example known to date. Proposed astrophysical tests of the black hole no-hair theorem have often involved integrable gravitational fields more general than the Kerr family, but the existence of such fields has been a matter of debate. To elucidate this problem, we treat its Newtonian analogue by systematically searching for non-trivial constants of motion polynomial in the momenta and obtain two theorems. First, solving a set of quadratic integrability conditions, we establish the existence and uniqueness of the family of stationary axisymmetric potentials admitting a quadratic constant. As in Kerr-de Sitter space-time, the mass moments of this class satisfy a `no-hair' recursion relation M2l +2 = a2M2l, and the constant is Noether related to a second-order Killing-Stäckel tensor. Second, solving a new set of quartic integrability conditions, we establish non-existence of quartic constants. Remarkably, a subset of these conditions is satisfied when the mass moments obey a generalized `no-hair' recursion relation M2l +4 = (a2 + b2)M2l +2 - a2b2M2l. The full set of quartic integrability conditions, however, cannot be satisfied non-trivially by any stationary axisymmetric vacuum potential.

  5. Supersonic quasi-axisymmetric vortex breakdown

    NASA Technical Reports Server (NTRS)

    Kandil, Osama A.; Kandil, Hamdy A.; Liu, C. H.

    1991-01-01

    An extensive computational study of supersonic quasi-axisymmetric vortex breakdown in a configured circular duct is presented. The unsteady, compressible, full Navier-Stokes (NS) equations are used. The NS equations are solved for the quasi-axisymmetric flows using an implicit, upwind, flux difference splitting, finite volume scheme. The quasi-axisymmetric solutions are time accurate and are obtained by forcing the components of the flowfield vector to be equal on two axial planes, which are in close proximity of each other. The effect of Reynolds number, for laminar flows, on the evolution and persistence of vortex breakdown, is studied. Finally, the effect of swirl ration at the duct inlet is investigated.

  6. Marginally stable circular orbits in stationary axisymmetric spacetimes

    NASA Astrophysics Data System (ADS)

    Beheshti, Shabnam; Gasperín, Edgar

    2016-07-01

    We derive necessary and sufficient conditions for the existence of marginally stable circular orbits (MSCOs) of test particles in a stationary axisymmetric (SAS) spacetime which possesses a reflection symmetry with respect to the equatorial plane; photon orbits and marginally bound orbits (MBOs) are also addressed. Energy and angular momentum are shown to decouple from metric quantities, rendering a purely geometric characterization of circular orbits for this general class of metrics. The subsequent system is analyzed using resultants, providing an algorithmic approach for finding MSCO conditions. MSCOs, photon orbits and MBOs are explicitly calculated for concrete examples of physical interest.

  7. Quasi-static axisymmetric eversion hemispherical domes made of elastomers

    NASA Astrophysics Data System (ADS)

    Kabrits, Sergey A.; Kolpak, Eugeny P.

    2016-06-01

    The paper considers numerical solution for the problem of quasi-static axisymmetric eversion of a spherical shell (hemisphere) under action of external pressure. Results based on the general nonlinear theory of shells made of elastomers, proposed by K. F. Chernykh. It is used two models of shells based on the hypotheses of the Kirchhoff and Timoshenko, modified K.F. Chernykh for the case of hyperelastic rubber-like material. The article presents diagrams of equilibrium states of eversion hemispheres for both models as well as the shape of the shell at different points in the diagram.

  8. Kinetic theory of quasi-stationary collisionless axisymmetric plasmas in the presence of strong rotation phenomena

    SciTech Connect

    Cremaschini, Claudio; Stuchlík, Zdeněk; Tessarotto, Massimo

    2013-05-15

    The problem of formulating a kinetic treatment for quasi-stationary collisionless plasmas in axisymmetric systems subject to the possibly independent presence of local strong velocity-shear and supersonic rotation velocities is posed. The theory is developed in the framework of the Vlasov-Maxwell description for multi-species non-relativistic plasmas. Applications to astrophysical accretion discs arising around compact objects and to plasmas in laboratory devices are considered. Explicit solutions for the equilibrium kinetic distribution function (KDF) are constructed based on the identification of the relevant particle adiabatic invariants. These are shown to be expressed in terms of generalized non-isotropic Gaussian distributions. A suitable perturbative theory is then developed which allows for the treatment of non-uniform strong velocity-shear/supersonic plasmas. This yields a series representation for the equilibrium KDF in which the leading-order term depends on both a finite set of fluid fields as well as on the gradients of an appropriate rotational frequency. Constitutive equations for the fluid number density, flow velocity, and pressure tensor are explicitly calculated. As a notable outcome, the discovery of a new mechanism for generating temperature and pressure anisotropies is pointed out, which represents a characteristic feature of plasmas considered here. This is shown to arise as a consequence of the canonical momentum conservation and to contribute to the occurrence of temperature anisotropy in combination with the adiabatic conservation of the particle magnetic moment. The physical relevance of the result and the implications of the kinetic solution for the self-generation of quasi-stationary electrostatic and magnetic fields through a kinetic dynamo are discussed.

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

    NASA Astrophysics Data System (ADS)

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

    2015-05-01

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

  10. The relativistic Doppler broadening of the line absorption profile

    NASA Astrophysics Data System (ADS)

    Kichenassamy, S.; Krikorian, R.; Nikogosian, A.

    1982-06-01

    The classical results of Doppler broadening of the line absorption profile are generalized to a relativistic gas in thermal equilibrium by taking into account the relativistic variance of the volume absorption coefficients of the gas, as derived by L. H. Thomas. This variance produces a small correction, even in the non-relativistic approximation.

  11. Republication of: Relativistic cosmology

    NASA Astrophysics Data System (ADS)

    Robertson, H. P.

    2012-08-01

    This is a reprinting of the paper by Howard Percy Robertson, first published in 1933 in Rev. Mod. Phys., that is a very authoritative summary of relativistic cosmology at the stage at which it was up to 1933. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by George Ellis, and by Robertson's biography, compiled by Andrzej Krasinski from printed sources.

  12. Axisymmetric and non-axisymmetric exhaust jet induced effects on a V/STOL vehicle design. Part 3: Experimental technique

    NASA Technical Reports Server (NTRS)

    Schnell, W. C.

    1982-01-01

    The jet induced effects of several exhaust nozzle configurations (axisymmetric, and vectoring/modulating varients) on the aeropropulsive performance of a twin engine V/STOL fighter design was determined. A 1/8 scale model was tested in an 11 ft transonic tunnel at static conditions and over a range of Mach Numbers from 0.4 to 1.4. The experimental aspects of the static and wind-on programs are discussed. Jet effects test techniques in general, fow through balance calibrations and tare force corrections, ASME nozzle thrust and mass flow calibrations, test problems and solutions are emphasized.

  13. Particle trajectory computer program for icing analysis of axisymmetric bodies

    NASA Technical Reports Server (NTRS)

    Frost, Walter; Chang, Ho-Pen; Kimble, Kenneth R.

    1982-01-01

    General aviation aircraft and helicopters exposed to an icing environment can accumulate ice resulting in a sharp increase in drag and reduction of maximum lift causing hazardous flight conditions. NASA Lewis Research Center (LeRC) is conducting a program to examine, with the aid of high-speed computer facilities, how the trajectories of particles contribute to the ice accumulation on airfoils and engine inlets. This study, as part of the NASA/LeRC research program, develops a computer program for the calculation of icing particle trajectories and impingement limits relative to axisymmetric bodies in the leeward-windward symmetry plane. The methodology employed in the current particle trajectory calculation is to integrate the governing equations of particle motion in a flow field computed by the Douglas axisymmetric potential flow program. The three-degrees-of-freedom (horizontal, vertical, and pitch) motion of the particle is considered. The particle is assumed to be acted upon by aerodynamic lift and drag forces, gravitational forces, and for nonspherical particles, aerodynamic moments. The particle momentum equation is integrated to determine the particle trajectory. Derivation of the governing equations and the method of their solution are described in Section 2.0. General features, as well as input/output instructions for the particle trajectory computer program, are described in Section 3.0. The details of the computer program are described in Section 4.0. Examples of the calculation of particle trajectories demonstrating application of the trajectory program to given axisymmetric inlet test cases are presented in Section 5.0. For the examples presented, the particles are treated as spherical water droplets. In Section 6.0, limitations of the program relative to excessive computer time and recommendations in this regard are discussed.

  14. Stability of perturbed geodesics in nD axisymmetric spacetimes

    NASA Astrophysics Data System (ADS)

    Coimbra-Araújo, C. H.; Anjos, R. C.

    2016-09-01

    The effect of self-gravity of a disk matter is evaluated by the simplest modes of oscillation frequencies for perturbed circular geodesics. We plotted the radial profiles of free oscillations of an equatorial circular geodesic perturbed within the orbital plane or in the vertical direction. The calculation is carried out to geodesics of an axisymmetric n-dimensional spacetime. The profiles are computed by examples of disks embeded in five-dimensional or six-dimensional spacetime, where we studied the motion of free test particles for three axisymmetric cases: (i) the Newtonian limit of a general proposed 5D and 6D axisymmetric spacetime; (ii) a simple Randall–Sundrum (RS) 5D spacetime; (iii) general 5D and 6D RS spacetime. The equation of motion of such particles is derived and the stability study is computed for both horizontal and vertical directions, to see how extra dimensions could affect the system. In particular, we investigate a disk constructed from Miyamoto–Nagai and Chazy–Curzon with a cut parameter to generate a disk potential. Those solutions have a simple extension for extra dimensions in case (i), and by solving vacuum Einstein field equations for a kind of RS–Weyl metric in cases (ii) and (iii). We find that it is possible to compute a range of possible solutions where such perturbed geodesics are stable. Basically, the stable solutions appear, for the radial direction, in special cases when the system has 5D and in all cases when the system has 6D and, for the axial direction, in all cases when the system has both 5D or 6D.

  15. Computer Aided Process Planning for Non-Axisymmetric Deep Drawing Products

    NASA Astrophysics Data System (ADS)

    Park, Dong Hwan; Yarlagadda, Prasad K. D. V.

    2004-06-01

    In general, deep drawing products have various cross-section shapes such as cylindrical, rectangular and non-axisymmetric shapes. The application of the surface area calculation to non-axisymmetric deep drawing process has not been published yet. In this research, a surface area calculation for non-axisymmetric deep drawing products with elliptical shape was constructed for a design of blank shape of deep drawing products by using an AutoLISP function of AutoCAD software. A computer-aided process planning (CAPP) system for rotationally symmetric deep drawing products has been developed. However, the application of the system to non-axisymmetric components has not been reported yet. Thus, the CAPP system for non-axisymmetric deep drawing products with elliptical shape was constructed by using process sequence design. The system developed in this work consists of four modules. The first is recognition of shape module to recognize non-axisymmetric products. The second is a three-dimensional (3-D) modeling module to calculate the surface area for non-axisymmetric products. The third is a blank design module to create an oval-shaped blank with the identical surface area. The forth is a process planning module based on the production rules that play the best important role in an expert system for manufacturing. The production rules are generated and upgraded by interviewing field engineers. Especially, the drawing coefficient, the punch and die radii for elliptical shape products are considered as main design parameters. The suitability of this system was verified by applying to a real deep drawing product. This CAPP system constructed would be very useful to reduce lead-time for manufacturing and improve an accuracy of products.

  16. Fabrication of Submillimeter Axisymmetric Optical Components

    NASA Technical Reports Server (NTRS)

    Grudinin, Ivan; Savchenkov, Anatoliy; Strekalov, Dmitry

    2007-01-01

    It is now possible to fashion transparent crystalline materials into axisymmetric optical components having diameters ranging from hundreds down to tens of micrometers, whereas previously, the smallest attainable diameter was 500 m. A major step in the fabrication process that makes this possible can be characterized as diamond turning or computer numerically controlled machining on an ultrahigh-precision lathe.

  17. Axisymmetric ideal MHD stellar wind flow

    NASA Technical Reports Server (NTRS)

    Heinemann, M.; Olbert, S.

    1978-01-01

    The ideal MHD equations are reduced to a single equation under the assumption of axisymmetric flow. A variational principle from which the equation is derivable is given. The characteristics of the equation are briefly discussed. The equation is used to rederive the theorem of Gussenhoven and Carovillano.

  18. Formation of Relativistic Jets : Magnetohydrodynamics and Synchrotron Radiation

    NASA Astrophysics Data System (ADS)

    Porth, Oliver J. G.

    2011-11-01

    force, such that we obtain an increased stability of relativistic flows. Accordingly, the non-axisymmetric modes applied to the field-line foot-points saturate quickly, with no signs of enhanced dissipation or disruption near the jet launching site.

  19. Theory of the relativistic gyrotwistron

    NASA Astrophysics Data System (ADS)

    Nusinovich, G. S.; Li, H.

    1992-04-01

    A generalized theory of the relativistic gyrotwistron, the device combining the elements of the gyroklystron and the gyro-traveling wave tube, is presented. A modulation of electrons in the input cavity is considered with the account of modulation in an electron axial momentum that is important for relativistic particles passing through a short cavity. A comprehensive study of large-signal operation of the output waveguide section in the cases of gyroresonance at the fundamental and second cyclotron harmonics has demonstrated a wide variety of electron bunching phenomena and the possibility of achieving high electron efficiency in a wide range of gyrotwistron parameters.

  20. Fluctuations in relativistic causal hydrodynamics

    NASA Astrophysics Data System (ADS)

    Kumar, Avdhesh; Bhatt, Jitesh R.; Mishra, Ananta P.

    2014-05-01

    Formalism to calculate the hydrodynamic fluctuations by applying the Onsager theory to the relativistic Navier-Stokes equation is already known. In this work, we calculate hydrodynamic fluctuations within the framework of the second order hydrodynamics of Müller, Israel and Stewart and its generalization to the third order. We have also calculated the fluctuations for several other causal hydrodynamical equations. We show that the form for the Onsager-coefficients and form of the correlation functions remain the same as those obtained by the relativistic Navier-Stokes equation and do not depend on any specific model of hydrodynamics. Further we numerically investigate evolution of the correlation function using the one dimensional boost-invariant (Bjorken) flow. We compare the correlation functions obtained using the causal hydrodynamics with the correlation function for the relativistic Navier-Stokes equation. We find that the qualitative behavior of the correlation functions remains the same for all the models of the causal hydrodynamics.

  1. Non-Relativistic Superstring Theories

    SciTech Connect

    Kim, Bom Soo

    2007-12-14

    We construct a supersymmetric version of the 'critical' non-relativistic bosonic string theory [1] with its manifest global symmetry. We introduce the anticommuting bc CFT which is the super partner of the {beta}{gamma} CFT. The conformal weights of the b and c fields are both 1/2. The action of the fermionic sector can be transformed into that of the relativistic superstring theory. We explicitly quantize the theory with manifest SO(8) symmetry and find that the spectrum is similar to that of Type IIB superstring theory. There is one notable difference: the fermions are non-chiral. We further consider 'noncritical' generalizations of the supersymmetric theory using the superspace formulation. There is an infinite range of possible string theories similar to the supercritical string theories. We comment on the connection between the critical non-relativistic string theory and the lightlike Linear Dilaton theory.

  2. User's manual for Axisymmetric Diffuser Duct (ADD) code. Volume 3: ADD code coordinate generator

    NASA Technical Reports Server (NTRS)

    Anderson, O. L.; Hankins, G. B., Jr.; Edwards, D. E.

    1982-01-01

    This User's Manual contains a complete description of the computer codes known as the Axisymmetric Diffuser Duct (ADD) code. It includes a list of references which describe the formulation of the ADD code and comparisons of calculation with experimental flows. The input/output and general use of the code is described in the first volume. The second volume contains a detailed description of the code including the global structure of the code, list of FORTRAN variables, and descriptions of the subroutines. The third volume contains a detailed description of the CODUCT code which generates coordinate systems for arbitrary axisymmetric ducts.

  3. The direct numerical simulations of the turbulent wakes of axisymmetric bodies

    NASA Technical Reports Server (NTRS)

    Riley, J. J.; Metcalfe, R. W.

    1978-01-01

    Results of direct numerical simulations of turbulence are compared with both laboratory data and self-similarity theory for the case of the turbulent wakes of towed, axisymmetric bodies. In general, the agreement of the simulation results with both the laboratory data and the self-similarity theory is good, although the comparisons are hampered by inadequate procedures for initializing the numerical simulations.

  4. Relativistic electron beam generator

    DOEpatents

    Mooney, L.J.; Hyatt, H.M.

    1975-11-11

    A relativistic electron beam generator for laser media excitation is described. The device employs a diode type relativistic electron beam source having a cathode shape which provides a rectangular output beam with uniform current density.

  5. Relativistic electron and ion dust charging currents

    SciTech Connect

    Tribeche, Mouloud; Boukhalfa, Soufiane

    2009-09-15

    A first theoretical attempt is made to present a relativistic generalization of the well-known orbit-limited motion theory. The appropriate relativistic (electron and ion) dust charging currents are derived. The nonlinear electrostatic potential is then expressed in terms of the variable dust charge and we take advantage of this new transcendental relation to investigate briefly the effects of relativistic charge carriers. As the relativistic character of the plasma increases, it becomes evident that certain negative values of the dust charge can never be achieved as increasingly larger values of the nonlinear potential are involved. The obtained formulas bring a possibility to build theories of nonlinear collective process in relativistic dusty plasmas.

  6. The relativistic equations of stellar structure and evolution

    NASA Technical Reports Server (NTRS)

    Thorne, K. S.

    1975-01-01

    The general relativistic equations of stellar structure and evolution are reformulated in a notation which makes easy contact with Newtonian theory. A general relativistic version of the mixing-length formalism for convection is presented. It is argued that in work on spherical systems, general relativity theorists have identified the wrong quantity as total mass-energy inside radius r.

  7. Seismic wave propagation in fully anisotropic axisymmetric media

    NASA Astrophysics Data System (ADS)

    van Driel, Martin; Nissen-Meyer, Tarje

    2014-11-01

    We present a numerical method to compute 3-D elastic waves in fully anisotropic axisymmetric media. This method is based on a decomposition of the wave equation into a series of uncoupled 2-D equations for which the dependence of the wavefield on the azimuth can be solved analytically. Four independent equations up to quadrupole order appear as solutions for moment-tensor sources located on the symmetry axis while single forces can be accommodated by two separate solutions up to dipole order. This decomposition gives rise to an efficient solution of the 3-D wave equation in a 2-D axisymmetric medium. First, we prove the validity of the decomposition of the wavefield in the presence of general anisotropy. Then we use it to derive the reduced 2-D equations of motions and discretize them using the spectral element method. Finally, we benchmark the numerical implementation for global wave propagation at 1 Hz and consider inner core anisotropy as an application for high-frequency wave propagation in anisotropic media at frequencies up to 2 Hz.

  8. Buckling of a thin, viscous film in an axisymmetric geometry

    NASA Astrophysics Data System (ADS)

    Bhattacharya, S.; Craster, R. V.; Flynn, M. R.

    2013-04-01

    By adapting the Föppl-von Kàrmàn equation, which describes the deformation of a thin elastic membrane, we present an analysis of the buckling pattern of a thin, very viscous fluid layer subject to shear in an axisymmetric geometry. A linear stability analysis yields a differential eigenvalue problem, whose solution, obtained using spectral techniques, yields the most unstable azimuthal wave-number, m⋆. Contrary to the discussion of Slim et al. [J. Fluid Mech. 694, 5-28 (2012)], 10.1017/jfm.2011.437, it is argued that the axisymmetric problem shares the same degeneracy as its rectilinear counterpart, i.e., at the onset of instability, m⋆ is indefinitely large. Away from this point, however, a comparison with analogue experimental results is both possible and generally favorable. In this vein, we describe the laboratory apparatus used to make new measurements of m⋆, the phase speed and the wave amplitude; note that no prediction concerning the latter two quantities can be made using the present theory. Experiments reveal a limited range of angular velocities wherein waves of either small or large amplitude may be excited. Transition from one to the other regime does not appear to be associated with a notable change in m⋆.

  9. Two-integral distribution functions for axisymmetric galaxies

    NASA Technical Reports Server (NTRS)

    Hunter, C.; Qian, Edward

    1993-01-01

    The new method presented for finding distribution functions, which depend only on the classical integrals of energy and angular momentum for stellar systems with known axisymmetric densities, is the analog for the axisymmetric case of Eddington's classical solution for the isotropic distribution function, depending only on energy, of a known spherical density. It is required that density be expressed as a function of the potential and of a radial coordinate. Our solution is also an integral which is derived directly from the density, and hence can be used with complicated densities. A numerical quadrature is generally required to evaluate this solution, but contour integrals can be computed accurately by numerical quadrature; this is preferable to an explicit evaluation if the latter is an infinite series, such as is obtained using Fricke's method. We give several examples, including some for which our distribution functions are new. Our method can be extended simply to the related problems of finding anisotropic distribution functions for spherical or disk systems.

  10. Axisymmetric nonlinear waves and structures in Hall plasmas

    SciTech Connect

    Islam, Tanim

    2012-06-15

    In this paper, a general equation for the evolution of an axisymmetric magnetic field in a Hall plasma is derived, with an integral similar to the Grad-Shafranov equation. Special solutions arising from curvature-whistler drift modes that propagate along the electron drift as a Burger's shock and nonlinear periodic and soliton-like solutions to the generalized Grad-Shafranov integral-are analyzed. We derive analytical and numerical solutions in a classical electron-ion Hall plasma, in which electrons and ions are the only species in the plasmas. Results may then be applied to the following low-ionized astrophysical plasmas: in protostellar disks, in which the ions may be coupled to the motion of gases; and in molecular clouds and protostellar jets, in which the much heavier charged dust in a dusty Hall plasma may be collisionally coupled to the gas.

  11. Newtonian and relativistic cosmologies

    NASA Astrophysics Data System (ADS)

    Green, Stephen R.; Wald, Robert M.

    2012-03-01

    Cosmological N-body simulations are now being performed using Newtonian gravity on scales larger than the Hubble radius. It is well known that a uniformly expanding, homogeneous ball of dust in Newtonian gravity satisfies the same equations as arise in relativistic Friedmann-Lemaître-Robinson-Walker cosmology, and it also is known that a correspondence between Newtonian and relativistic dust cosmologies continues to hold in linearized perturbation theory in the marginally bound/spatially flat case. Nevertheless, it is far from obvious that Newtonian gravity can provide a good global description of an inhomogeneous cosmology when there is significant nonlinear dynamical behavior at small scales. We investigate this issue in the light of a perturbative framework that we have recently developed [S. R. Green and R. M. Wald, Phys. Rev. DPRVDAQ1550-7998 83, 084020 (2011).10.1103/PhysRevD.83.084020], which allows for such nonlinearity at small scales. We propose a relatively straightforward dictionary—which is exact at the linearized level—that maps Newtonian dust cosmologies into general relativistic dust cosmologies, and we use our “ordering scheme” to determine the degree to which the resulting metric and matter distribution solve Einstein’s equation. We find that, within our ordering scheme, Einstein’s equation fails to hold at “order 1” at small scales and at “order ɛ” at large scales. We then find the additional corrections to the metric and matter distribution needed to satisfy Einstein’s equation to these orders. While these corrections are of some interest in their own right, our main purpose in calculating them is that their smallness should provide a criterion for the validity of the original dictionary (as well as simplified versions of this dictionary). We expect that, in realistic Newtonian cosmologies, these additional corrections will be very small; if so, this should provide strong justification for the use of Newtonian simulations

  12. Axisymmetric single shear element combustion instability experiment

    NASA Astrophysics Data System (ADS)

    Breisacher, Kevin J.

    1993-06-01

    The combustion stability characteristics of a combustor consisting of a single shear element and a cylindrical chamber utilizing LOX and gaseous hydrogen as propellants are presented. The combustor geometry and the resulting longitudinal mode instability are axisymmetric. Hydrogen injection temperature and pyrotechnic pulsing were used to determine stability boundaries. Mixture ratio, fuel annulus gap, and LOX post configuration were varied. Performance and stability data are presented for chamber pressures of 300 and 1000 psia.

  13. Nonlinear axisymmetric flexural vibration of spherical shells

    NASA Technical Reports Server (NTRS)

    Kunieda, H.

    1972-01-01

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

  14. Axisymmetric single shear element combustion instability experiment

    NASA Technical Reports Server (NTRS)

    Breisacher, Kevin J.

    1993-01-01

    The combustion stability characteristics of a combustor consisting of a single shear element and a cylindrical chamber utilizing LOX and gaseous hydrogen as propellants are presented. The combustor geometry and the resulting longitudinal mode instability are axisymmetric. Hydrogen injection temperature and pyrotechnic pulsing were used to determine stability boundaries. Mixture ratio, fuel annulus gap, and LOX post configuration were varied. Performance and stability data are presented for chamber pressures of 300 and 1000 psia.

  15. Axisymmetric single shear element combustion instability experiment

    NASA Technical Reports Server (NTRS)

    Breisacher, Kevin J.

    1993-01-01

    The combustion stability characteristics of a combustor consisting of a single shear element and a cylindrical chamber utilizing LOX and gaseous hydrogen as propellants are presented. The combustor geometry and the resulting longitudinal mode instability are axisymmetric. Hydrogen injection temperature and pyrotechnic pulsing were used to determine stability boundaries. Mixture ratio, fuel annulus gap, and LOX post configuration were varied. Performance and stability data were obtained for chamber pressures of 300 and 1000 psia.

  16. A NEW MULTI-DIMENSIONAL GENERAL RELATIVISTIC NEUTRINO HYDRODYNAMICS CODE OF CORE-COLLAPSE SUPERNOVAE. III. GRAVITATIONAL WAVE SIGNALS FROM SUPERNOVA EXPLOSION MODELS

    SciTech Connect

    Mueller, Bernhard; Janka, Hans-Thomas; Marek, Andreas E-mail: thj@mpa-garching.mpg.de

    2013-03-20

    We present a detailed theoretical analysis of the gravitational wave (GW) signal of the post-bounce evolution of core-collapse supernovae (SNe), employing for the first time relativistic, two-dimensional explosion models with multi-group, three-flavor neutrino transport based on the ray-by-ray-plus approximation. The waveforms reflect the accelerated mass motions associated with the characteristic evolutionary stages that were also identified in previous works: a quasi-periodic modulation by prompt post-shock convection is followed by a phase of relative quiescence before growing amplitudes signal violent hydrodynamical activity due to convection and the standing accretion shock instability during the accretion period of the stalled shock. Finally, a high-frequency, low-amplitude variation from proto-neutron star (PNS) convection below the neutrinosphere appears superimposed on the low-frequency trend associated with the aspherical expansion of the SN shock after the onset of the explosion. Relativistic effects in combination with detailed neutrino transport are shown to be essential for quantitative predictions of the GW frequency evolution and energy spectrum, because they determine the structure of the PNS surface layer and its characteristic g-mode frequency. Burst-like high-frequency activity phases, correlated with sudden luminosity increase and spectral hardening of electron (anti-)neutrino emission for some 10 ms, are discovered as new features after the onset of the explosion. They correspond to intermittent episodes of anisotropic accretion by the PNS in the case of fallback SNe. We find stronger signals for more massive progenitors with large accretion rates. The typical frequencies are higher for massive PNSs, though the time-integrated spectrum also strongly depends on the model dynamics.

  17. Relativistic astronomy

    NASA Astrophysics Data System (ADS)

    Klimishin, I. A.

    The ideas of special and general relativity are discussed in relation to astronomy, in particular, problems concerning blackholes and models of the universe. Such problems as the redshift in the spectra of galaxies, the nature of quasars, and the possible relationships between the microcosm and the macrocosm are also treated. Special attention is given to problems of topology and the three-dimensionality of the universe.

  18. Relativistic stars in bigravity theory

    NASA Astrophysics Data System (ADS)

    Aoki, Katsuki; Maeda, Kei-ichi; Tanabe, Makoto

    2016-03-01

    Assuming static and spherically symmetric spacetimes in the ghost-free bigravity theory, we find a relativistic star solution, which is very close to that in general relativity. The coupling constants are classified into two classes: Class [I] and Class [II]. Although the Vainshtein screening mechanism is found in the weak gravitational field for both classes, we find that there is no regular solution beyond the critical value of the compactness in Class [I]. This implies that the maximum mass of a neutron star in Class [I] becomes much smaller than that in general relativity (GR). On the other hand, for the solution in Class [II], the Vainshtein screening mechanism works well even in a relativistic star and the result in GR is recovered.

  19. Induced stresses due to fluid extraction from axisymmetric reservoirs

    USGS Publications Warehouse

    Segall, P.

    1992-01-01

    Earthquakes can be induced by fluid extraction, as well as by fluid injection. Segall (1989) proposed that poroelastic stresses are responsible for inducing earthquakes associated with fluid extraction. Here, I present methods for computing poroelastic stress changes due to fluid extraction for general axisymmetric reservoir geometries. The results of Geertsma (1973) for a thin disk reservoir with uniform pressure drop are recovered as a special case. Predicted surface subsidence agrees very well with measured leveling changes over the deep Lacq gas field in southwestern France. The induced stresses are finite if the reservoir pressure changes are continuous. Computed stress changes are on the order of several bars, suggesting that the preexisting stress states in regions of extraction induced seismicity are very close to frictional instability prior to production. ?? 1992 Birkha??user Verlag.

  20. Nonaxisymmetric viscous lower branch modes in axisymmetric supersonic flows

    NASA Technical Reports Server (NTRS)

    Duck, Peter W.; Hall, Philip

    1988-01-01

    In a previous paper, the weakly nonlinear interaction of a pair of axisymmetric lower branch Tollmien-Schlichting instabilities in cylindrical supersonic flows was considered. Here the possibility that nonaxisymmetric modes might also exist is investigated. In fact, it is found that such modes do exist and, on the basis of linear theory, it appears that these modes are the most important. The nonaxisymmetric modes are found to exist for flows around cylinders with nondimensional radius alpha less than some critical value alpha sub c. This critical value alpha sub c is found to increase monotonically with the azimuthal wavenumber nu of the disturbance and it is found that unstable modes always occur in pairs. It is also shown that, in general, instability in the form of lower branch Tollmien-Schlichting waves will occur first for nonaxisymmetric modes and that in the unstable regime the largest growth rates correspond to the latter modes.

  1. Time and 'angular' dependent backgrounds from stationary axisymmetric solutions

    SciTech Connect

    Obregon, Octavio; Quevedo, Hernando; Ryan, Michael P.

    2004-09-15

    Backgrounds depending on time and on angular variable, namely, polarized and unpolarized S{sup 1}xS{sup 2} Gowdy models, are generated as the sector inside the horizons of the manifold corresponding to axisymmetric solutions. As is known, an analytical continuation of ordinary D-branes, iD-branes allow one to find S-brane solutions. Simple models have been constructed by means of analytic continuation of the Schwarzschild and the Kerr metrics. The possibility of studying the i-Gowdy models obtained here is outlined with an eye toward seeing if they could represent some kind of generalized S-branes depending not only on time but also on an angular variable.

  2. Nonlinear electromagnetic gyrokinetic equations for rotating axisymmetric plasmas

    SciTech Connect

    Artun, M.; Tang, W.M.

    1994-03-01

    The influence of sheared equilibrium flows on the confinement properties of tokamak plasmas is a topic of much current interest. A proper theoretical foundation for the systematic kinetic analysis of this important problem has been provided here by presented the derivation of a set of nonlinear electromagnetic gyrokinetic equations applicable to low frequency microinstabilities in a rotating axisymmetric plasma. The subsonic rotation velocity considered is in the direction of symmetry with the angular rotation frequency being a function of the equilibrium magnetic flux surface. In accordance with experimental observations, the rotation profile is chosen to scale with the ion temperature. The results obtained represent the shear flow generalization of the earlier analysis by Frieman and Chen where such flows were not taken into account. In order to make it readily applicable to gyrokinetic particle simulations, this set of equations is cast in a phase-space-conserving continuity equation form.

  3. On the existence of certain axisymmetric interior metrics

    SciTech Connect

    Angulo Santacruz, C.; Batic, D.; Nowakowski, M.

    2010-08-15

    One of the effects of noncommutative coordinate operators is that the delta function connected to the quantum mechanical amplitude between states sharp to the position operator gets smeared by a Gaussian distribution. Although this is not the full account of the effects of noncommutativity, this effect is, in particular, important as it removes the point singularities of Schwarzschild and Reissner-Nordstroem solutions. In this context, it seems to be of some importance to probe also into ringlike singularities which appear in the Kerr case. In particular, starting with an anisotropic energy-momentum tensor and a general axisymmetric ansatz of the metric together with an arbitrary mass distribution (e.g., Gaussian), we derive the full set of Einstein equations that the noncommutative geometry inspired Kerr solution should satisfy. Using these equations we prove two theorems regarding the existence of certain Kerr metrics inspired by noncommutative geometry.

  4. Steady axisymmetric vortex flows with swirl and shear

    NASA Astrophysics Data System (ADS)

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

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

  5. Numerical simulation of axisymmetric turbulent flow in combustors and diffusers

    NASA Technical Reports Server (NTRS)

    Yung, Chain-Nan; Keith, Theo G., Jr.; De Witt, Kenneth J.

    1989-01-01

    Numerical studies of turbulent flow in an axisymmetric 45-deg-expansion combustor and bifurcated diffuser are presented. The Navier-Stokes equations incorporating a k-epsilon model were solved in a nonorthogonal curvilinear coordinate system. A zonal-grid method, where the flow field was divided into several subsections, was developed. This approach permitted different computational schemes to be used in the various zones. In addition, grid generation was made a more simple task. Boundary overlap and interpolating techniques were used, and an adjustment of the flow variables was required to assure conservation of mass flux. Three finite-differencing methods (hybrid, quadratic upwind, and skew upwind) were used to represent the convection terms. Results were compared with existing experimental data. In general, good agreement between predicted and measured values was obtained.

  6. Asymptotic structure of hydromagnetically driven relativistic winds

    NASA Technical Reports Server (NTRS)

    Chiueh, Tzihong; Li, Zhi-Yun; Begelman, Mitchell C.

    1991-01-01

    A fully relativistic analysis has been performed of the asymptotic structure of stationary axisymmetric hydromagnetic winds. If a flow fills the region containing the rotation axis, then the flux surfaces in the flow must collimate to a set of current-carrying cylindrical surface extending to infinite transverse radius, collimate to a set of cylindrical surfaces extending to a finite radius, or collimate to a current-free paraboloidal field configuration which fills up the entire space. If an asymptotically cylindrical flow carries a finite current at radii well beyond the light cylinder, then the Lorentz factor of the terminal flow speed on a given flux surface is proportional to the total current enclosed within this flux surface. If a flow is of type II paraboloidal, then its asymptotic energy flux is carried entirely by the gas motion rather than the electromagnetic fields.

  7. Relativistic HD and MHD modelling for AGN jets

    NASA Astrophysics Data System (ADS)

    Keppens, R.; Porth, O.; Monceau-Baroux, R.; Walg, S.

    2013-12-01

    Relativistic hydro and magnetohydrodynamics (MHD) provide a continuum fluid description for plasma dynamics characterized by shock-dominated flows approaching the speed of light. Significant progress in its numerical modelling emerged in the last two decades; we highlight selected examples of modern grid-adaptive, massively parallel simulations realized by our open-source software MPI-AMRVAC (Keppens et al 2012 J. Comput. Phys. 231 718). Hydrodynamical models quantify how energy transfer from active galactic nuclei (AGN) jets to their surrounding interstellar/intergalactic medium (ISM/IGM) gets mediated through shocks and various fluid instability mechanisms (Monceau-Baroux et al 2012 Astron. Astrophys. 545 A62). With jet parameters representative for Fanaroff-Riley type-II jets with finite opening angles, we can quantify the ISM volumes affected by jet injection and distinguish the roles of mixing versus shock-heating in cocoon regions. This provides insight in energy feedback by AGN jets, usually incorporated parametrically in cosmological evolution scenarios. We discuss recent axisymmetric studies up to full 3D simulations for precessing relativistic jets, where synthetic radio maps can confront observations. While relativistic hydrodynamic models allow one to better constrain dynamical parameters like the Lorentz factor and density contrast between jets and their surroundings, the role of magnetic fields in AGN jet dynamics and propagation characteristics needs full relativistic MHD treatments. Then, we can demonstrate the collimating properties of an overal helical magnetic field backbone and study differences between poloidal versus toroidal field dominated scenarios (Keppens et al 2008 Astron. Astrophys. 486 663). Full 3D simulations allow one to consider the fate of non-axisymmetric perturbations on relativistic jet propagation from rotating magnetospheres (Porth 2013 Mon. Not. R. Astron. Soc. 429 2482). Self-stabilization mechanisms related to the detailed

  8. Implementation of Analytical Energy Gradient of Spin-Dependent General Hartree-Fock Method Based on the Infinite-Order Douglas-Kroll-Hess Relativistic Hamiltonian with Local Unitary Transformation.

    PubMed

    Nakajima, Yuya; Seino, Junji; Nakai, Hiromi

    2016-05-10

    An analytical energy gradient for the spin-dependent general Hartree-Fock method based on the infinite-order Douglas-Kroll-Hess (IODKH) method was developed. To treat realistic systems, the local unitary transformation (LUT) scheme was employed both in energy and energy gradient calculations. The present energy gradient method was numerically assessed to investigate the accuracy in several diatomic molecules containing fifth- and sixth-period elements and to examine the efficiency in one-, two-, and three-dimensional silver clusters. To arrive at a practical calculation, we also determined the geometrical parameters of fac-tris(2-phenylpyridine)iridium and investigated the efficiency. The numerical results confirmed that the present method describes a highly accurate relativistic effect with high efficiency. The present method can be a powerful scheme for determining geometries of large molecules, including heavy-element atoms. PMID:27045757

  9. Relativistic Collapse of Rotating Supermassive Stars to Supermassive Black Holes

    NASA Astrophysics Data System (ADS)

    Shapiro, Stuart L.

    2003-10-01

    There is compelling evidence that supermassive black holes (SMBHs) exist. Yet the origin of these objects, or their seeds, is still unknown. We are performing general relativistic simulations of gravitational collapse to black holes in different scenarios to help reveal how SMBH seeds might arise in the universe. SMBHs with ~ 109 Msolar must have formed by z > 6, or within 109 yrs after the Big Bang, to power quasars. It may be difficult for gas accretion to build up such a SMBH by this time unless the initial seed black hole already has a substantial mass. One plausible progenitor of a massive seed black hole is a supermassive star (SMS). We have followed the collapse of a SMS to a SMBH by means of 3D hydrodynamic simulations in post-Newtonian gravity and axisymmetric simulations in full general relativity. The initial SMS of arbitrary mass M in these simulations rotates uniformly at the mass-shedding limit and is marginally unstable to radial collapse. The final black hole mass and spin are determined to be Mh/M ~ 0.9 and Jh/Mh2 ~ 0.75. The remaining mass goes into a disk of mass Mdisk/M ~ 0.1. This disk arises even though the total spin of the progenitor star, J/M2 = 0.97, is safely below the Kerr limit. The collapse generates a mild burst gravitational radiation. Nonaxisymmetric bars or one-armed spirals may arise during the quasi-stationary evolution of a SMS, during its collapse, or in the ambient disk about the hole, and are potential sources of quasi-periodic waves, detectable by LISA.

  10. Non-axisymmetric ultrasonic guided waves for tubing inspection

    NASA Astrophysics Data System (ADS)

    Shin, Hyeon Jae

    1997-11-01

    The purpose of this study is to understand the physical phenomena of wave propagation in hollow cylinders and also to investigate the utility of ultrasonic guided waves in hollow cylinders for nondestructive evaluation purposes. In this document, a theoretical and experimental study of axisymmetric and non-axisymmetric ultrasonic guided wave modes is carried out. Guided wave modes in hollow cylinders are calculated and are represented in phase and group velocity dispersion diagrams based on wave mechanics and the theory of elasticity. Guided wave propagation characteristics and proper mode selection concepts are discussed by analyzing the acoustic fields. Excellent inspection results of using axisymmetric modes for programmed flaws are given. Designs of a bore probe and specifications of a high power tone burst system are given for practical implementation. The work also focuses on an experimental study on the utilization of non-axisymmetric guided waves generated by a non-axisymmetric oblique incident partial loading transducer setup. For complete coverage in tubing inspection with non-axisymmetric guided waves, three dimensional tuning concepts are developed. An experimental study on the relationship between the circumferential loading angle and the generated guided waves was carried out. It is found that a 180 degree partial loading comb transducer set up could generate strong axisymmetric modes. The expected non-axisymmetric guided wave fields are studied by normal mode expansion. The non-axisymmetric source design parameters are discussed for partial uniform pressure loading on the outer boundary of a sample tube.

  11. Preferential axisymmetric field growth in kinematic geodynamo models

    NASA Astrophysics Data System (ADS)

    Livermore, Philip W.; Jackson, Andrew

    2004-11-01

    Earth's magnetic field, generated by fluid motion and inductive processes in Earth's core, has a predominantly axisymmetric dipolar component. Yet indefinite self-excitation of purely axisymmetric fields through any dynamo mechanism is specifically disallowed, begging the question of why the geodynamo sustains this dominant axisymmetric component. By considering a number of different fluid flow models modified from existing studies, we show that axisymmetric fields are consistently the most easily regenerated magnetic fields on short timescales, despite the fact that on long timescales they must die away. We argue that this transient field generation may play an important role in generating Earth's magnetic field, especially in the recovery after reversals.

  12. Axisymmetric instability in a thinning electrified jet

    NASA Astrophysics Data System (ADS)

    Dharmansh; Chokshi, Paresh

    2016-04-01

    The axisymmetric stability of an electrified jet is analyzed under electrospinning conditions using the linear stability theory. The fluid is considered Newtonian with a finite electrical conductivity, modeled as a leaky dielectric medium. While the previous studies impose axisymmetric disturbances on a cylindrical jet of uniform radius, referred to as the base state, in the present study the actual thinning jet profile, obtained as the steady-state solution of the one-dimensional slender filament model, is treated as the base state. The analysis takes into account the role of variation in the jet variables like radius, velocity, electric field, and surface charge density along the thinning jet in the stability behavior. The eigenspectrum of the axisymmetric disturbance growth rate is constructed from the linearized disturbance equations discretized using the Chebyshev collocation method. The most unstable growth rate for the thinning jet is significantly different from that for the uniform radius jet. For the same electrospinning conditions, while the uniform radius jet is predicted to be highly unstable, the thinning jet profile is found to be unstable but with a relatively very low growth rate. The stabilizing role of the thinning jet is attributed to the variation in the surface charge density as well as the extensional deformation rate in the fluid ignored in the uniform radius jet analysis. The dominant mode for the thinning jet is an oscillatory conducting mode driven by the field-charge coupling. The disturbance energy balance finds the electric force to be the dominant force responsible for the disturbance growth, potentially leading to bead formation along the fiber. The role of various material and process parameters in the stability behavior is also investigated.

  13. The breaking of axisymmetric slender liquid bridges

    NASA Astrophysics Data System (ADS)

    Meseguer, J.

    1983-05-01

    Liquids held by surface tension forces can bridge the gap between two solid bodies placed not too far apart from each other. The equilibrium conditions and stability criteria for static, cylindrical liquid bridges are well known. However, the behaviour of an unstable liquid bridge, regarding both its transition toward breaking and the resulting configuration, is a matter for discussion. The dynamical problem of axisymmetric rupture of a long liquid bridge anchored at two equal coaxial disks is treated in this paper through the adoption of one-dimensional theories which are widely used in capillary jet problems.

  14. Lagrangian aspects of the axisymmetric Euler equation

    NASA Astrophysics Data System (ADS)

    Preston, Stephen C.; Sarria, Alejandro

    2016-03-01

    In this paper we are interested in geometric aspects of blowup in the axisymmetric three-dimensional (3D) Euler equations with swirl on a cylinder. Writing the equations in Lagrangian form for the flow derivative along either the axis or the boundary and imposing oddness on the vertical component of the flow, we extend some blowup criteria due to Chae, Constantin and Wu related to assumptions on the sign of the pressure Hessian. In addition. we give a geometric interpretation of the results, both in terms of the local geometry along trajectories and in terms of the Riemannian geometry of the volume-preserving diffeomorphism group.

  15. Isodynamic axisymmetric equilibrium near the magnetic axis

    SciTech Connect

    Arsenin, V. V.

    2013-08-15

    Plasma equilibrium near the magnetic axis of an axisymmetric toroidal magnetic confinement system is described in orthogonal flux coordinates. For the case of a constant current density in the vicinity of the axis and magnetic surfaces with nearly circular cross sections, expressions for the poloidal and toroidal magnetic field components are obtained in these coordinates by using expansion in the reciprocal of the aspect ratio. These expressions allow one to easily derive relationships between quantities in an isodynamic equilibrium, in which the absolute value of the magnetic field is constant along the magnetic surface (Palumbo’s configuration)

  16. Isodynamic axisymmetric equilibrium near the magnetic axis

    NASA Astrophysics Data System (ADS)

    Arsenin, V. V.

    2013-08-01

    Plasma equilibrium near the magnetic axis of an axisymmetric toroidal magnetic confinement system is described in orthogonal flux coordinates. For the case of a constant current density in the vicinity of the axis and magnetic surfaces with nearly circular cross sections, expressions for the poloidal and toroidal magnetic field components are obtained in these coordinates by using expansion in the reciprocal of the aspect ratio. These expressions allow one to easily derive relationships between quantities in an isodynamic equilibrium, in which the absolute value of the magnetic field is constant along the magnetic surface (Palumbo's configuration).

  17. Mach disk from underexpanded axisymmetric nozzle flow

    NASA Technical Reports Server (NTRS)

    Chang, I.-S.; Chow, W. L.

    1974-01-01

    The flowfield associated with the underexpanded axisymmetric nozzle freejet flow including the appearance of a Mach disk has been studied. It is shown that the location and size of the Mach disk are governed by the appearance of a triple-point shock configuration and the condition that the central core flow will reach a state of 'choking at a throat'. It is recognized that coalescence of waves requires special attention and the reflected wave, as well as the vorticity generated from these wave interactions, have to be taken accurately into account. The theoretical results obtained agreed well with the experimental data.

  18. Calculation of rf fields in axisymmetric cavities

    SciTech Connect

    Iwashita, Y.

    1985-01-01

    A new code, PISCES, has been developed for calculating a complete set of rf electromagnetic modes in an axisymmetric cavity. The finite-element method is used with up to third-order shape functions. Although two components are enough to express these modes, three components are used as unknown variables to take advantage of the symmetry of the element matrix. The unknowns are taken to be either the electric field components or the magnetic field components. The zero-divergence condition will be satisfied by the shape function within each element.

  19. Axisymmetric scrape-off plasma transport

    SciTech Connect

    Singer, C.E.; Langer, W.D.

    1983-05-01

    The two-dimensional flow of a collision dominated hydrogen scrape-off plasma in an axisymmetric tokamak is examined. This flow is described by a set of equations which contain the dominant terms in a maximal ordering appropriate to high density experimental divertors and reactor scrape-off plasmas. Comparison of the theory to estimates of scrape-off parameters in the Doublet III expanded boundary plasmas suggests that analysis of classical and neoclassical processes alone may be sufficient to predict plasma transport in high density scrape-off plasmas of practical importance.

  20. Minimal energy damping in an axisymmetric flow

    NASA Astrophysics Data System (ADS)

    Sachs, Alexander

    2008-05-01

    The method of Lagrange's undetermined multipliers is used to find the velocity field which minimizes the energy damping for a viscous incompressible fluid described by the Navier- Stoke equation. The vorticity of this velocity field obeys a Helmholtz equation with an undetermined parameter. This Helmholtz equation is used to determine the axisymmetric velocity field in a cylinder. This velocity field is slightly different from the Poiseuille velocity field. The rate of energy damping per unit energy is calculated as a function of the parameter. It is a minimum when the parameter is equal to the root of a Bessel function.

  1. Relativistic Guiding Center Equations

    SciTech Connect

    White, R. B.; Gobbin, M.

    2014-10-01

    In toroidal fusion devices it is relatively easy that electrons achieve relativistic velocities, so to simulate runaway electrons and other high energy phenomena a nonrelativistic guiding center formalism is not sufficient. Relativistic guiding center equations including flute mode time dependent field perturbations are derived. The same variables as used in a previous nonrelativistic guiding center code are adopted, so that a straightforward modifications of those equations can produce a relativistic version.

  2. Relativistic Linear Restoring Force

    ERIC Educational Resources Information Center

    Clark, D.; Franklin, J.; Mann, N.

    2012-01-01

    We consider two different forms for a relativistic version of a linear restoring force. The pair comes from taking Hooke's law to be the force appearing on the right-hand side of the relativistic expressions: d"p"/d"t" or d"p"/d["tau"]. Either formulation recovers Hooke's law in the non-relativistic limit. In addition to these two forces, we…

  3. Exact Relativistic Newtonian Representation of Gravitational static Spacetime Geometries

    NASA Astrophysics Data System (ADS)

    Ghosh, Shubhrangshu; Sarkar, Tamal; Bhadra, Arunava

    2016-09-01

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

  4. Turbulent dynamo action in axisymmetric linear machine

    NASA Astrophysics Data System (ADS)

    Kabantsev, A. A.; Reva, V. B.; Sokolov, V. G.

    1997-11-01

    Generation of large-scale magnetic fields by turbulent motion of an electrically conducting fluids plays an important role not only for astrophysical applications, but also for magnetic fusion confinement phenomena. The well-studied turbulent dynamo α-effect comes from helical properties of turbulent motion. Under this dynamo the mean electric current is produced in the direction parallel or antiparallel to the mean magnetic field. In particular, the α-effect leads to the generation of plasma current along the magnetic field in reversed field pinches. We have shown that the α-effect takes place also in axisymmetric linear machines. In axisymmetric mirror traps AMBAL-M and MAL (BINP) the electrostatic turbulence, having mean helicity h≈ 6\\cdot 10^6 m/s^2, caused as a result of unstable differential rotation of plasma column in crossed E×B fields. By manipulating the trap's magnetic and plasma conditions, we can obtain both the parallel and the antiparallel B electric current to the order of 100 A/cm^2 (total current up to 6 kA) in the plasma. The measured mean electromotive force F_em= has linear growth with turbulent diffusion coefficient DT and reaches up to 50 V/m.

  5. Classification of Stellar Orbits in Axisymmetric Galaxies

    NASA Astrophysics Data System (ADS)

    Li, Baile; Holley-Bockelmann, Kelly; Khan, Fazeel Mahmood

    2015-09-01

    It is known that two supermassive black holes (SMBHs) cannot merge in a spherical galaxy within a Hubble time; an emerging picture is that galaxy geometry, rotation, and large potential perturbations may usher the SMBH binary through the critical three-body scattering phase and ultimately drive the SMBH to coalesce. We explore the orbital content within an N-body model of a mildly flattened, non-rotating, SMBH-embedded elliptical galaxy. When used as the foundation for a study on the SMBH binary coalescence, the black holes bypassed the binary stalling often seen within spherical galaxies and merged on gigayear timescales. Using both frequency-mapping and angular momentum criteria, we identify a wealth of resonant orbits in the axisymmetric model, including saucers, that are absent from an otherwise identical spherical system and that can potentially interact with the binary. We quantified the set of orbits that could be scattered by the SMBH binary, and found that the axisymmetric model contained nearly six times the number of these potential loss cone orbits compared to our equivalent spherical model. In this flattened model, the mass of these orbits is more than three times that of the SMBH, which is consistent with what the SMBH binary needs to scatter to transition into the gravitational wave regime.

  6. Vortexons in axisymmetric Poiseuille pipe flows

    NASA Astrophysics Data System (ADS)

    Fedele, F.; Dutykh, D.

    2013-02-01

    We present a study on the nonlinear dynamics of small long-wave disturbances to the laminar state in non-rotating axisymmetric Poiseuille pipe flows. At high Reynolds numbers, the associated Navier-Stokes equations can be reduced to a set of coupled Korteweg-de Vries-type (KdV) equations that support inviscid and smooth travelling waves numerically computed using the Petviashvili method. In physical space they correspond to localized toroidal vortices concentrated near the pipe boundaries (wall vortexons) or that wrap around the pipe axis (centre vortexons), in agreement with the analytical soliton solutions derived by Fedele (Fluid Dyn. Res., 44 (2012) 45509). The KdV dynamics of a perturbation is also investigated by means of a high accurate Fourier-based numerical scheme. We observe that an initial vortical patch splits into a centre vortexon radiating patches of vorticity near the wall. These can undergo further splitting leading to a proliferation of centre vortexons that eventually decay due to viscous effects. The splitting process originates from a radial flux of azimuthal vorticity from the wall to the pipe axis in agreement with the inverse cascade of cross-stream vorticity identified in channel flows by Eyink (Plysica D, 237 (2008) 1956). The inviscid vortexon most likely is unstable to non-axisymmetric disturbances and may be a precursor to puffs and slug flow formation.

  7. Linear lateral vibration of axisymmetric liquid briges

    NASA Astrophysics Data System (ADS)

    Ferrera, C.; Montanero, J. M.; Cabezas, M. G.

    A liquid bridge is a mass of liquid sustained by the action of the surface tension force between two parallel supporting disks Apart from their basic scientific interest a liquid bridge can be considered as the simplest idealization of the configuration appearing in the floating zone technique used for crystal growth and purification of high melting point materials footnote Messeguer et al emph Crystal Growth Res bf 5 27 1999 This has conferred considerable interest on the study of liquid bridges not only in fluid mechanics but also in the field of material engineering The axisymmetric dynamics of an isothermal liquid bridge has been frequently analysed over the past years The studies have considered different phenomena such as free oscillations footnote Montanero emph E J Mech B Fluids bf 22 169 2003 footnote Acero and Montanero emph Phys Fluids bf 17 078105 2005 forced vibrations footnote Perales and Messeguer emph Phys Fluids A bf 4 1110 1992 g-jitter effects footnote Messeguer and Perales emph Phys Fluids A bf 3 2332 1991 extensional deformation footnote Zhang et al emph J Fluid Mech bf 329 207 1996 and breakup process footnote Espino et al emph Phys Fluids bf 14 3710 2002 among others Works considering the nonaxisymmetric dynamical behaviour of a liquid bridge has been far less common footnote Sanz and Diez emph J Fluid Mech bf 205 503 1989 In the present study the linear vibration of an axisymmetric liquid

  8. Coherent states for the relativistic harmonic oscillator

    NASA Technical Reports Server (NTRS)

    Aldaya, Victor; Guerrero, J.

    1995-01-01

    Recently we have obtained, on the basis of a group approach to quantization, a Bargmann-Fock-like realization of the Relativistic Harmonic Oscillator as well as a generalized Bargmann transform relating fock wave functions and a set of relativistic Hermite polynomials. Nevertheless, the relativistic creation and annihilation operators satisfy typical relativistic commutation relations of the Lie product (vector-z, vector-z(sup dagger)) approximately equals Energy (an SL(2,R) algebra). Here we find higher-order polarization operators on the SL(2,R) group, providing canonical creation and annihilation operators satisfying the Lie product (vector-a, vector-a(sup dagger)) = identity vector 1, the eigenstates of which are 'true' coherent states.

  9. The Development of Explosions in Axisymmetric Ab Initio Core-collapse Supernova Simulations of 12-25 M Stars

    NASA Astrophysics Data System (ADS)

    Bruenn, Stephen W.; Lentz, Eric J.; Hix, W. Raphael; Mezzacappa, Anthony; Harris, J. Austin; Messer, O. E. Bronson; Endeve, Eirik; Blondin, John M.; Chertkow, Merek Austin; Lingerfelt, Eric J.; Marronetti, Pedro; Yakunin, Konstantin N.

    2016-02-01

    We present four ab initio axisymmetric core-collapse supernova simulations initiated from 12, 15, 20, and 25 {M}⊙ zero-age main sequence progenitors. All of the simulations yield explosions and have been evolved for at least 1.2 s after core bounce and 1 s after material first becomes unbound. These simulations were computed with our Chimera code employing RbR spectral neutrino transport, special and general relativistic transport effects, and state-of-the-art neutrino interactions. Continuing the evolution beyond 1 s after core bounce allows the explosions to develop more fully and the processes involved in powering the explosions to become more clearly evident. We compute explosion energy estimates, including the negative gravitational binding energy of the stellar envelope outside the expanding shock, of 0.34, 0.88, 0.38, and 0.70 Bethe (B ≡ {10}51 erg) and increasing at 0.03, 0.15, 0.19, and 0.52 {\\text{B s}}-1, respectively, for the 12, 15, 20, and 25 {M}⊙ models at the endpoint of this report. We examine the growth of the explosion energy in our models through detailed analyses of the energy sources and flows. We discuss how the explosion energies may be subject to stochastic variations as exemplfied by the effect of the explosion geometry of the 20 {M}⊙ model in reducing its explosion energy. We compute the proto-neutron star masses and kick velocities. We compare our results for the explosion energies and ejected {}56{Ni} masses against some observational standards despite the large error bars in both models and observations.

  10. The development of explosions in axisymmetric ab initio core-collapse supernova simulations of 12–25 M⊙ stars

    DOE PAGESBeta

    Bruenn, Stephen W.; Lentz, Eric J.; Hix, William Raphael; Mezzacappa, Anthony; Harris, James Austin; Messer, O. E. Bronson; Endeve, Eirik; Blondin, John M.; Chertkow, Merek Austin; Lingerfelt, Eric J.; et al

    2016-02-16

    We present four ab initio axisymmetric core-collapse supernova simulations initiated from 12, 15, 20, and 25 M⊙ zero-age main sequence progenitors. All of the simulations yield explosions and have been evolved for at least 1.2 s after core bounce and 1 s after material first becomes unbound. These simulations were computed with our Chimera code employing RbR spectral neutrino transport, special and general relativistic transport effects, and state-of-the-art neutrino interactions. Continuing the evolution beyond 1 s after core bounce allows the explosions to develop more fully and the processes involved in powering the explosions to become more clearly evident. Wemore » compute explosion energy estimates, including the negative gravitational binding energy of the stellar envelope outside the expanding shock, of 0.34, 0.88, 0.38, and 0.70 Bethe (B ≡ 1051 erg) and increasing at 0.03, 0.15, 0.19, and 0.52 BS–1, respectively, for the 12, 15, 20, and 25 M⊙ models at the endpoint of this report. We examine the growth of the explosion energy in our models through detailed analyses of the energy sources and flows. We discuss how the explosion energies may be subject to stochastic variations as exemplfied by the effect of the explosion geometry of the 20 M⊙ model in reducing its explosion energy. We compute the proto-neutron star masses and kick velocities. In conclusion, we compare our results for the explosion energies and ejected 56Ni masses against some observational standards despite the large error bars in both models and observations.« less

  11. Extension of the flow-rate-of-strain tensor formulation of plasma rotation theory to non-axisymmetric tokamaks

    NASA Astrophysics Data System (ADS)

    Stacey, W. M.; Bae, C.

    2015-06-01

    A systematic formalism for the calculation of rotation in non-axisymmetric tokamaks with 3D magnetic fields is described. The Braginskii Ω τ -ordered viscous stress tensor formalism, generalized to accommodate non-axisymmetric 3D magnetic fields in general toroidal flux surface geometry, and the resulting fluid moment equations provide a systematic formalism for the calculation of toroidal and poloidal rotation and radial ion flow in tokamaks in the presence of various non-axisymmetric "neoclassical toroidal viscosity" mechanisms. The relation among rotation velocities, radial ion particle flux, ion orbit loss, and radial electric field is discussed, and the possibility of controlling these quantities by producing externally controllable toroidal and/or poloidal currents in the edge plasma for this purpose is suggested for future investigation.

  12. Extension of the flow-rate-of-strain tensor formulation of plasma rotation theory to non-axisymmetric tokamaks

    SciTech Connect

    Stacey, W. M.; Bae, C.

    2015-06-15

    A systematic formalism for the calculation of rotation in non-axisymmetric tokamaks with 3D magnetic fields is described. The Braginskii Ωτ-ordered viscous stress tensor formalism, generalized to accommodate non-axisymmetric 3D magnetic fields in general toroidal flux surface geometry, and the resulting fluid moment equations provide a systematic formalism for the calculation of toroidal and poloidal rotation and radial ion flow in tokamaks in the presence of various non-axisymmetric “neoclassical toroidal viscosity” mechanisms. The relation among rotation velocities, radial ion particle flux, ion orbit loss, and radial electric field is discussed, and the possibility of controlling these quantities by producing externally controllable toroidal and/or poloidal currents in the edge plasma for this purpose is suggested for future investigation.

  13. Impingement of supersonic jets on an axisymmetric deflector

    NASA Astrophysics Data System (ADS)

    Prasad, J. K.; Mehta, R. C.; Sreekanth, A. K.

    1994-07-01

    Experimental and numerical studies are carried out to investigate impingement flowfield produced on a typical axisymmetric jet deflector. The experiments consisted of schlieren flow visualization and measurements of pressure. The present study will be useful for the design of a typical axisymmetric jet deflector during the liftoff phase of a rocket.

  14. Relativistic generation of vortex and magnetic field

    SciTech Connect

    Mahajan, S. M.; Yoshida, Z.

    2011-05-15

    The implications of the recently demonstrated relativistic mechanism for generating generalized vorticity in purely ideal dynamics [Mahajan and Yoshida, Phys. Rev. Lett. 105, 095005 (2010)] are worked out. The said mechanism has its origin in the space-time distortion caused by the demands of special relativity; these distortions break the topological constraint (conservation of generalized helicity) forbidding the emergence of magnetic field (a generalized vorticity) in an ideal nonrelativistic dynamics. After delineating the steps in the ''evolution'' of vortex dynamics, as the physical system goes from a nonrelativistic to a relativistically fast and hot plasma, a simple theory is developed to disentangle the two distinct components comprising the generalized vorticity--the magnetic field and the thermal-kinetic vorticity. The ''strength'' of the new universal mechanism is, then, estimated for a few representative cases; in particular, the level of seed fields, created in the cosmic setting of the early hot universe filled with relativistic particle-antiparticle pairs (up to the end of the electron-positron era), are computed. Possible applications of the mechanism in intense laser produced plasmas are also explored. It is suggested that highly relativistic laser plasma could provide a laboratory for testing the essence of the relativistic drive.

  15. Einstein Toolkit for Relativistic Astrophysics

    NASA Astrophysics Data System (ADS)

    Collaborative Effort

    2011-02-01

    The Einstein Toolkit is a collection of software components and tools for simulating and analyzing general relativistic astrophysical systems. Such systems include gravitational wave space-times, collisions of compact objects such as black holes or neutron stars, accretion onto compact objects, core collapse supernovae and Gamma-Ray Bursts. The Einstein Toolkit builds on numerous software efforts in the numerical relativity community including CactusEinstein, Whisky, and Carpet. The Einstein Toolkit currently uses the Cactus Framework as the underlying computational infrastructure that provides large-scale parallelization, general computational components, and a model for collaborative, portable code development.

  16. Spin Stability Criteria for Axisymmetric Spinning Body with Large Flexible Membrane

    NASA Astrophysics Data System (ADS)

    Tsuda, Yuichi

    Stability of the dynamics of spinning spacecraft equipped with a large flexible membrane is discussed. The spin stability of an object having a flexible structure is deteriorated from that of a rigid object with the same shape in general, which makes a significant impact on the design of such spacecraft systems. This paper provides a fully analytical solution for the stability criteria of axisymmetric spinner spacecraft equipped with a large flexible membrane. Distinct from past studies, this paper does not impose restrictions on axial offset of the membrane attachment, and provides a stability condition using energy-angular momentum analysis when the membrane is subject only to an outer-plane first-order mode deformation. These criteria can be applied to the design of such missions as spinner solar sail spacecraft, large solar power satellite and other general spacecraft with large axisymmetric structures.

  17. A simple model of axisymmetric turbulent boundary layers along long thin circular cylinders

    NASA Astrophysics Data System (ADS)

    Jordan, Stephen A.

    2014-08-01

    Useful empirical and semi-empirical models of the turbulent boundary layer (TBL) and skin friction evolution along planar geometries are not applicable for axisymmetric thin cylinder flows. Their dissimilarity is readily detectable once the TBL thickness exceeds the cylinder radius (a). Although several recent empirically based axisymmetric models recognize this fact, their acceptable fidelity is either restrictive or deficient for general applicability. Herein, we correct this deficit by building a simple model for the specific canonical class of axisymmetric turbulent flows along long thin cylinders with a zero streamwise pressure gradient. Streamwise growth of the TBL thickness (δ/a), integral scales [displacement (δ*/a) and momentum thicknesses (θ/a)] and skin friction coefficient (Cf) can be estimated along the cylinder length via the respective axial mean velocity profile in wall units. This profile is given by Spalding's formula with algebraic expressions for the two input parameters (κ, κβ) that cover all turbulent Reynolds numbers. The necessary database for empirically tuning Spalding's parameters entails both experimental measurements and new numerical computations. Our present-day understanding of the axisymmetric TBL is replicated by the simple model where δ/a, δ*/a, and θ/a grow slower than the planar-type flow with Cf comparatively elevating once δ/a > O(1). These differences manifest themselves in the radial impact imposed by the thin cylinder transverse curvature. Interestingly, the axial-based Reynolds numbers Rea ≈ 7500 and a+ ≈ 350 at δ/a ≈ 21 mark earliest signs of a homogeneous streamwise state (constant Cf) near the cylinder wall. Owning a simple model of axisymmetric turbulent flows along thin cylinders eliminates expensive and timely experiments and/or computations. Its practicality targets both the Naval and oceanographic communities.

  18. Non-relativistic leptogenesis

    NASA Astrophysics Data System (ADS)

    Bödeker, Dietrich; Wörmann, Mirco

    2014-02-01

    In many phenomenologically interesting models of thermal leptogenesis the heavy neutrinos are non-relativistic when they decay and produce the baryon asymmetry of the Universe. We propose a non-relativistic approximation for the corresponding rate equations in the non-resonant case, and a systematic way for computing relativistic corrections. We determine the leading order coefficients in these equations, and the first relativistic corrections. The non-relativistic approximation works remarkably well. It appears to be consistent with results obtained using a Boltzmann equation taking into account the momentum distribution of the heavy neutrinos, while being much simpler. We also compute radiative corrections to some of the coefficients in the rate equations. Their effect is of order 1% in the regime favored by neutrino oscillation data. We obtain the correct leading order lepton number washout rate in this regime, which leads to large ( ~ 20%) effects compared to previous computations.

  19. 3D Hydrodynamic Simulations of Relativistic Jets

    NASA Astrophysics Data System (ADS)

    Hughes, P. A.; Miller, M. A.; Duncan, G. C.; Swift, C. M.

    1998-12-01

    We present the results of validation runs and the first extragalactic jet simulations performed with a 3D relativistic numerical hydrodynamic code employing a solver of the RHLLE type and using adaptive mesh refinement (AMR; Duncan & Hughes, 1994, Ap. J., 436, L119). Test problems include the shock tube, blast wave and spherical shock reflection (implosion). Trials with the code show that as a consequence of AMR it is viable to perform exploratory runs on workstation class machines (with no more than 128Mb of memory) prior to production runs. In the former case we achieve a resolution not much less than that normally regarded as the minimum needed to capture the essential physics of a problem, which means that such runs can provide valuable guidance allowing the optimum use of supercomputer resources. We present initial results from a program to explore the 3D stability properties of flows previously studied using a 2D axisymmetric code, and our first attempt to explore the structure and morphology of a relativistic jet encountering an ambient density gradient that mimics an ambient inhomogeneity or cloud.

  20. Emission of sound from axisymmetric turbulence convected by a mean flow with application to jet noise

    NASA Technical Reports Server (NTRS)

    Goldstein, M. E.; Rosenbaum, B. M.

    1972-01-01

    A model, based on Lighthill's theory, for predicting aerodynamic noise from a turbulent shear flow is developed. This model is a generalization of the one developed by Ribner. Unlike Ribner's model, it does not require that the turbulent correlations factor into space and time-dependent parts. It replaces his assumption of isotropic. turbulence by the more realistic one of axisymmetric turbulence. The implications of the model for jet noise are discussed.

  1. Compact neutron imaging system using axisymmetric mirrors

    SciTech Connect

    Khaykovich, Boris; Moncton, David E; Gubarev, Mikhail V; Ramsey, Brian D; Engelhaupt, Darell E

    2014-05-27

    A dispersed release of neutrons is generated from a source. A portion of this dispersed neutron release is reflected by surfaces of a plurality of nested, axisymmetric mirrors in at least an inner mirror layer and an outer mirror layer, wherein the neutrons reflected by the inner mirror layer are incident on at least one mirror surface of the inner mirror layer N times, wherein N is an integer, and wherein neutrons reflected by the outer mirror are incident on a plurality of mirror surfaces of the outer layer N+i times, where i is a positive integer, to redirect the neutrons toward a target. The mirrors can be formed by a periodically reversed pulsed-plating process.

  2. A Compact Quasi-axisymmetric Stellarator Reactor

    SciTech Connect

    L.P. Ku; the ARIES-CS Team

    2003-10-20

    We report the progress made in assessing the potential of compact, quasi-axisymmetric stellarators as power-producing reactors. Using an aspect ratio A=4.5 configuration derived from NCSX and optimized with respect to the quasi-axisymmetry and MHD stability in the linear regime as an example, we show that a reactor of 1 GW(e) maybe realizable with a major radius *8 m. This is significantly smaller than the designs of stellarator reactors attempted before. We further show the design of modular coils and discuss the optimization of coil aspect ratios in order to accommodate the blanket for tritium breeding and radiation shielding for coil protection. In addition, we discuss the effects of coil aspect ratio on the peak magnetic field in the coils.

  3. Ideal ballooning modes in axisymmetric mirror machines

    SciTech Connect

    Baldwin, D.E.; McNamara, B.; Willmann, P.

    1980-12-15

    A simple code is described that finds marginally stable (..omega../sup 2/ = 0) ballooning-type MHD modes, localized about a field line in an axisymmetric, open-ended, plasma confinement device. The equations are based on a lower bound for the perturbed energy delta W, derived by W. Newcomb from the ideal MHD energy principle, and are cast in the form of a Ricatti equation for the first derivative of the eigenfunction, with the open boundary conditions that this derivative vanish at the plasma boundary down each field line. The input to the code is the two-dimensional shape of a field line, the field strength B(s), and parameters to define pressure profiles throughout the system. The objective is to find the highest plasma pressures for which the given line is MHD-stable.

  4. Relativistic Navigation: A Theoretical Foundation

    NASA Technical Reports Server (NTRS)

    Turyshev, Slava G.

    1996-01-01

    We present a theoretical foundation for relativistic astronomical measurements in curved space-time. In particular, we discuss a new iterative approach for describing the dynamics of an isolated astronomical N-body system in metric theories of gravity. To do this, we generalize the Fock-Chandrasekhar method of the weak-field and slow-motion approximation (WFSMA) and develop a theory of relativistic reference frames (RF's) for a gravitationally bounded many-extended-body problem. In any proper RF constructed in the immediate vicinity of an arbitrary body, the N-body solutions of the gravitational field equations are formally presented as a sum of the Riemann-flat inertial space-time, the gravitational field generated by the body itself, the unperturbed solutions for each body in the system transformed to the coordinates of this proper RF, and the gravitational interaction term. We develop the basic concept of a general WFSMA theory of the celestial RF's applicable to a wide class of metric theories of gravity and an arbitrary model of matter distribution. We apply the proposed method to general relativity. Celestial bodies are described using a perfect fluid model; as such, they possess any number of internal mass and current multipole moments that explicitly characterize their internal structures. The obtained relativistic corrections to the geodetic equations of motion arise because of a coupling of the bodies' multiple moments to the surrounding gravitational field. The resulting relativistic transformations between the different RF's extend the Poincare group to the motion of deformable self-gravitating bodies. Within the present accuracy of astronomical measurements we discuss the properties of the Fermi-normal-like proper RF that is defined in the immediate vicinity of the extended compact bodies. We further generalize the proposed approximation method and include two Eddington parameters (gamma, Beta). This generalized approach was used to derive the

  5. Relativistic MHD simulations of extragalactic jets

    NASA Astrophysics Data System (ADS)

    Leismann, T.; Antón, L.; Aloy, M. A.; Müller, E.; Martí, J. M.; Miralles, J. A.; Ibáñez, J. M.

    2005-06-01

    We have performed a comprehensive parameter study of the morphology and dynamics of axisymmetric, magnetized, relativistic jets by means of numerical simulations. The simulations have been performed with an upgraded version of the GENESIS code which is based on a second-order accurate finite volume method involving an approximate Riemann solver suitable for relativistic ideal magnetohydrodynamic flows, and a method of lines. Starting from pure hydrodynamic models we consider the effect of a magnetic field of increasing strength (up to β ≡ |b|2/2p ≈ 3.3 times the equipartition value) and different topology (purely toroidal or poloidal). We computed several series of models investigating the dependence of the dynamics on the magnetic field in jets of different beam Lorentz factor and adiabatic index. We find that the inclusion of the magnetic field leads to diverse effects which contrary to Newtonian magnetohydrodynamics models do not always scale linearly with the (relative) strength of the magnetic field. The relativistic models show, however, some clear trends. Axisymmetric jets with toroidal magnetic fields produce a cavity which consists of two parts: an inner one surrounding the beam which is compressed by magnetic forces, and an adjacent outer part which is inflated due to the action of the magnetic field. The outer border of the outer part of the cavity is given by the bow-shock where its interaction with the external medium takes place. Toroidal magnetic fields well below equipartition (β = 0.05) combined with a value of the adiabatic index of 4/3 yield extremely smooth jet cavities and stable beams. Prominent nose cones form when jets are confined by toroidal fields and carry a high Poynting flux (σ≡ |b|2/ρ>0.01 and β≥ 1). In contrast, none of our models possessing a poloidal field develops such a nose cone. The size of the nose cone is correlated with the propagation speed of the Mach disc (the smaller the speed the larger is the size). If two

  6. The evolution of swirling axisymmetric vortex rings

    NASA Astrophysics Data System (ADS)

    Gargan-Shingles, C.; Rudman, M.; Ryan, K.

    2015-08-01

    Swirling vortex rings form in any turbulent flow where a swirling component is present, such as in combustion chambers or the downwash of helicopter blades. Instabilities on initially non-swirling vortex rings result in a localized swirl velocity being generated within the core. The presence of a swirl component of velocity in a vortex ring modifies the relaxation and evolution of numerical Gaussian cores in a manner that is currently unknown. The evolution of Gaussian axisymmetric vortex rings of size 0.2 < Λ < 0.5, with Gaussian swirls of magnitude 0.0 < W < 0.5, is analyzed with reference to the governing equations. A relaxation time, at which the initial Gaussian approximation has minimal influence on the subsequent evolution, has been estimated for each case. An axial vortex forms along the axis of the ring and is responsible for the growth of a shear layer that is found to form at the leading edge. The circulation based Reynolds number is set at 10 000 to encourage the growth of shear layer instabilities from within this region. Secondary vortex rings are subsequently shown to evolve from the Kelvin-Helmholtz instability for shear layers of sufficient strength and are convected around the original ring and shed from the system. It is shown that complete settling of the strain rate within the core does not occur until all sheddings have ceased. Increasing the swirl magnitude past that considered in this paper is expected to result in the original ring losing its structure before the instability can occur. The evolution is found to be qualitatively similar to that of a piston generated axisymmetric vortex ring with swirl, with both cases eventually reaching a similar quasi-steady state.

  7. Relativistic blast waves in two dimensions. I - The adiabatic case

    NASA Technical Reports Server (NTRS)

    Shapiro, P. R.

    1979-01-01

    Approximate solutions are presented for the dynamical evolution of strong adiabatic relativistic blast waves which result from a point explosion in an ambient gas in which the density varies both with distance from the explosion center and with polar angle in axisymmetry. Solutions are analytical or quasi-analytical for the extreme relativistic case and numerical for the arbitrarily relativistic case. Some general properties of nonplanar relativistic shocks are also discussed, including the incoherence of spherical ultrarelativistic blast-wave fronts on angular scales greater than the reciprocal of the shock Lorentz factor, as well as the conditions for producing blast-wave acceleration.

  8. Weakly nonlinear kink-type solitary waves in a fully relativistic plasma

    SciTech Connect

    Tribeche, Mouloud; Boukhalfa, Soufiane; Zerguini, Taha Houssine

    2010-08-15

    A fully and coherent relativistic fluid model derived from the covariant formulation of relativistic fluid equations is used to study small but finite amplitude solitary waves. This approach has the characteristic to be consistent with the relativistic principle and consequently leads to a more general set of equations valid for fully relativistic plasmas with arbitrary Lorentz relativistic factor. A kink-solitary wave solution is outlined. Due to electron relativistic effect, the localized structure may experience either a spreading or a compression. This latter phenomenon (compression) becomes less effective and less noticeable as the relativistic character of the ions becomes important. Our results may be relevant to cosmic relativistic double-layers and relativistic plasma structures that involve energetic plasma flows.

  9. Axisymmetric Plume Simulations with NASA's DSMC Analysis Code

    NASA Technical Reports Server (NTRS)

    Stewart, B. D.; Lumpkin, F. E., III

    2012-01-01

    A comparison of axisymmetric Direct Simulation Monte Carlo (DSMC) Analysis Code (DAC) results to analytic and Computational Fluid Dynamics (CFD) solutions in the near continuum regime and to 3D DAC solutions in the rarefied regime for expansion plumes into a vacuum is performed to investigate the validity of the newest DAC axisymmetric implementation. This new implementation, based on the standard DSMC axisymmetric approach where the representative molecules are allowed to move in all three dimensions but are rotated back to the plane of symmetry by the end of the move step, has been fully integrated into the 3D-based DAC code and therefore retains all of DAC s features, such as being able to compute flow over complex geometries and to model chemistry. Axisymmetric DAC results for a spherically symmetric isentropic expansion are in very good agreement with a source flow analytic solution in the continuum regime and show departure from equilibrium downstream of the estimated breakdown location. Axisymmetric density contours also compare favorably against CFD results for the R1E thruster while temperature contours depart from equilibrium very rapidly away from the estimated breakdown surface. Finally, axisymmetric and 3D DAC results are in very good agreement over the entire plume region and, as expected, this new axisymmetric implementation shows a significant reduction in computer resources required to achieve accurate simulations for this problem over the 3D simulations.

  10. Relativistic spin precession in the double pulsar.

    PubMed

    Breton, Rene P; Kaspi, Victoria M; Kramer, Michael; McLaughlin, Maura A; Lyutikov, Maxim; Ransom, Scott M; Stairs, Ingrid H; Ferdman, Robert D; Camilo, Fernando; Possenti, Andrea

    2008-07-01

    The double pulsar PSR J0737-3039A/B consists of two neutron stars in a highly relativistic orbit that displays a roughly 30-second eclipse when pulsar A passes behind pulsar B. Describing this eclipse of pulsar A as due to absorption occurring in the magnetosphere of pulsar B, we successfully used a simple geometric model to characterize the observed changing eclipse morphology and to measure the relativistic precession of pulsar B's spin axis around the total orbital angular momentum. This provides a test of general relativity and alternative theories of gravity in the strong-field regime. Our measured relativistic spin precession rate of 4.77 degrees (-0 degrees .65)(+0 degrees .66) per year (68% confidence level) is consistent with that predicted by general relativity within an uncertainty of 13%. PMID:18599782

  11. Relativistic transport theory for cosmic-rays

    NASA Technical Reports Server (NTRS)

    Webb, G. M.

    1985-01-01

    Various aspects of the transport of cosmic-rays in a relativistically moving magnetized plasma supporting a spectrum of hydromagnetic waves that scatter the cosmic-rays are presented. A local Lorentz frame moving with the waves or turbulence scattering the cosmic-rays is used to specify the individual particle momentum. The comoving frame is in general a noninertial frame in which the observer's volume element is expanding and shearing, geometric energy change terms appear in the cosmic-ray transport equation which consist of the relativistic generalization of the adiabatic deceleration term and a further term involving the acceleration vector of the scatterers. A relativistic version of the pitch angle evolution equation, including the effects of adiabatic focussing, pitch angle scattering, and energy changes is presented.

  12. SYNCHROTRON RADIATION OF SELF-COLLIMATING RELATIVISTIC MAGNETOHYDRODYNAMIC JETS

    SciTech Connect

    Porth, Oliver; Fendt, Christian; Vaidya, Bhargav; Meliani, Zakaria E-mail: fendt@mpia.de

    2011-08-10

    The goal of this paper is to derive signatures of synchrotron radiation from state-of-the-art simulation models of collimating relativistic magnetohydrodynamic (MHD) jets featuring a large-scale helical magnetic field. We perform axisymmetric special relativistic MHD simulations of the jet acceleration region using the PLUTO code. The computational domain extends from the slow-magnetosonic launching surface of the disk up to 6000{sup 2} Schwarzschild radii allowing jets to reach highly relativistic Lorentz factors. The Poynting-dominated disk wind develops into a jet with Lorentz factors of {Gamma} {approx_equal} 8 and is collimated to 1{sup 0}. In addition to the disk jet, we evolve a thermally driven spine jet emanating from a hypothetical black hole corona. Solving the linearly polarized synchrotron radiation transport within the jet, we derive very long baseline interferometry radio and (sub-) millimeter diagnostics such as core shift, polarization structure, intensity maps, spectra, and Faraday rotation measure (RM) directly from the Stokes parameters. We also investigate depolarization and the detectability of a {lambda}{sup 2}-law RM depending on beam resolution and observing frequency. We find non-monotonic intrinsic RM profiles that could be detected at a resolution of 100 Schwarzschild radii. In our collimating jet geometry, the strict bimodality in the polarization direction (as predicted by Pariev et al.) can be circumvented. Due to relativistic aberration, asymmetries in the polarization vectors across the jet can hint at the spin direction of the central engine.

  13. Non-Axisymmetric Wave Focusing in Pipe Inspection

    NASA Astrophysics Data System (ADS)

    Sun, Zongqi; Rose, Joseph L.; Song, Won-Joon; Hayashi, Takahiro

    2003-03-01

    Non-axisymmetric guided waves have been applied to pipe inspection recently. Due to the non-axisymmetric characteristics of the waves, the circumferential displacement distribution is non-axisymmetric. It shows a natural focusing phenomenon. With the aid of a circumferential transducer array, we developed an algorithm to focus wave energy at arbitrary locations. The algorithm is based on applying different amplitude and time delay to each of the excitation elements. A series of experiments were carried out to show the focusing effect.

  14. An axisymmetric and fully 3D poroelastic model for the evolution of hydrocephalus.

    PubMed

    Wirth, Benedikt; Sobey, Ian

    2006-12-01

    We formulate in general terms the equations for axisymmetric and fully 3D models of a hydrocephalic brain. The model is developed using small strain poroelasticity that includes non-linear permeability. The axisymmetric model is solved for four ventricle shapes, an ellipsoid, a 'peanut' shape, a 'cross' shape and a 'bone' shape. The distribution of fluid pressure, velocity and content in the deformed parenchyma for a blocked aqueduct provides new qualitative insight into hydrocepahlus. Some observations are offered for two forms of cerebrospinal fluid flow abnormality, normal pressure hydrocephalus and idiopathic intracranial hypertension. The model is extended to include a gravitational term in the governing equations and the effect of hydrostatic pressure variation is considered. Results of a fully 3D simulations are described for two horn-like lateral ventricles and one case with two lateral ventricles and a third ventricle. PMID:16740629

  15. Marginal Stability Boundaries for Infinite-n Ballooning Modes in a Quasi-axisymmetric Stellarator

    SciTech Connect

    S.R. Hudson; C.C. Hegna

    2003-09-15

    A method for computing the ideal-MHD stability boundaries in three-dimensional equilibria is employed. Following Hegna and Nakajima [Phys. Plasmas 5 (May 1998) 1336], a two-dimensional family of equilibria are constructed by perturbing the pressure and rotational-transform profiles in the vicinity of a flux surface for a given stellarator equilibrium. The perturbations are constrained to preserve the magnetohydrodynamic equilibrium condition. For each perturbed equilibrium, the infinite-n ballooning stability is calculated. Marginal stability diagrams are thus constructed that are analogous to (s; a) diagrams for axisymmetric configurations. A quasi-axisymmetric stellarator is considered. Calculations of stability boundaries generally show regions of instability can occur for either sign of the average magnetic shear. Additionally, regions of second-stability are present.

  16. Different Paths to Some Fundamental Physical Laws: Relativistic Polarization of a Moving Magnetic Dipole

    ERIC Educational Resources Information Center

    Kholmetskii, Alexander L.; Yarman, T.

    2010-01-01

    In this paper we consider the relativistic polarization of a moving magnetic dipole and show that this effect can be understood via the relativistic generalization of Kirchhoff's first law to a moving closed circuit with a steady current. This approach allows us to better understand the law of relativistic transformation of four-current density…

  17. Accurate Measurement in the Field of the Earth of the General-Relativistic Precession of the LAGEOS II Pericenter and New Constraints on Non-Newtonian Gravity

    NASA Astrophysics Data System (ADS)

    Lucchesi, David M.; Peron, Roberto

    2010-12-01

    The pericenter shift of a binary system represents a suitable observable to test for possible deviations from the Newtonian inverse-square law in favor of new weak interactions between macroscopic objects. We analyzed 13 years of tracking data of the LAGEOS satellites with GEODYN II software but with no models for general relativity. From the fit of LAGEOS II pericenter residuals we have been able to obtain a 99.8% agreement with the predictions of Einstein’s theory. This result may be considered as a 99.8% measurement in the field of the Earth of the combination of the γ and β parameters of general relativity, and it may be used to constrain possible deviations from the inverse-square law in favor of new weak interactions parametrized by a Yukawa-like potential with strength α and range λ. We obtained |α|≲1×10-11, a huge improvement at a range of about 1 Earth radius.

  18. Accurate measurement in the field of the earth of the general-relativistic precession of the LAGEOS II pericenter and new constraints on non-newtonian gravity.

    PubMed

    Lucchesi, David M; Peron, Roberto

    2010-12-01

    The pericenter shift of a binary system represents a suitable observable to test for possible deviations from the newtonian inverse-square law in favor of new weak interactions between macroscopic objects. We analyzed 13 years of tracking data of the LAGEOS satellites with GEODYN II software but with no models for general relativity. From the fit of LAGEOS II pericenter residuals we have been able to obtain a 99.8% agreement with the predictions of Einstein's theory. This result may be considered as a 99.8% measurement in the field of the Earth of the combination of the γ and β parameters of general relativity, and it may be used to constrain possible deviations from the inverse-square law in favor of new weak interactions parametrized by a Yukawa-like potential with strength α and range λ. We obtained |α| ≲ 1 × 10(-11), a huge improvement at a range of about 1 Earth radius. PMID:21231446

  19. Weakly relativistic plasma expansion

    SciTech Connect

    Fermous, Rachid Djebli, Mourad

    2015-04-15

    Plasma expansion is an important physical process that takes place in laser interactions with solid targets. Within a self-similar model for the hydrodynamical multi-fluid equations, we investigated the expansion of both dense and under-dense plasmas. The weakly relativistic electrons are produced by ultra-intense laser pulses, while ions are supposed to be in a non-relativistic regime. Numerical investigations have shown that relativistic effects are important for under-dense plasma and are characterized by a finite ion front velocity. Dense plasma expansion is found to be governed mainly by quantum contributions in the fluid equations that originate from the degenerate pressure in addition to the nonlinear contributions from exchange and correlation potentials. The quantum degeneracy parameter profile provides clues to set the limit between under-dense and dense relativistic plasma expansions at a given density and temperature.

  20. Relativistic Hall effect.

    PubMed

    Bliokh, Konstantin Y; Nori, Franco

    2012-03-23

    We consider the relativistic deformation of quantum waves and mechanical bodies carrying intrinsic angular momentum (AM). When observed in a moving reference frame, the centroid of the object undergoes an AM-dependent transverse shift. This is the relativistic analogue of the spin-Hall effect, which occurs in free space without any external fields. Remarkably, the shifts of the geometric and energy centroids differ by a factor of 2, and both centroids are crucial for the Lorentz transformations of the AM tensor. We examine manifestations of the relativistic Hall effect in quantum vortices and mechanical flywheels and also discuss various fundamental aspects of this phenomenon. The perfect agreement of quantum and relativistic approaches allows applications at strikingly different scales, from elementary spinning particles, through classical light, to rotating black holes. PMID:22540559

  1. Relativistic heavy ion facilities: worldwide

    SciTech Connect

    Schroeder, L.S.

    1986-05-01

    A review of relativistic heavy ion facilities which exist, are in a construction phase, or are on the drawing boards as proposals is presented. These facilities span the energy range from fixed target machines in the 1 to 2 GeV/nucleon regime, up to heavy ion colliders of 100 GeV/nucleon on 100 GeV/nucleon. In addition to specifying the general features of such machines, an outline of the central physics themes to be carried out at these facilities is given, along with a sampling of the detectors which will be used to extract the physics. 22 refs., 17 figs., 3 tabs.

  2. Exact Relativistic `Antigravity' Propulsion

    NASA Astrophysics Data System (ADS)

    Felber, Franklin S.

    2006-01-01

    The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3-1/2 times the speed of light, even a small mass gravitationally repels a payload. At relativistic speeds, a suitable mass can quickly propel a heavy payload from rest nearly to the speed of light with negligible stresses on the payload.

  3. Relativistic Quantum Scars

    SciTech Connect

    Huang, Liang; Lai Yingcheng; Ferry, David K.; Goodnick, Stephen M.; Akis, Richard

    2009-07-31

    The concentrations of wave functions about classical periodic orbits, or quantum scars, are a fundamental phenomenon in physics. An open question is whether scarring can occur in relativistic quantum systems. To address this question, we investigate confinements made of graphene whose classical dynamics are chaotic and find unequivocal evidence of relativistic quantum scars. The scarred states can lead to strong conductance fluctuations in the corresponding open quantum dots via the mechanism of resonant transmission.

  4. Static electric multipole susceptibilities of the relativistic hydrogenlike atom in the ground state: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function

    NASA Astrophysics Data System (ADS)

    Szmytkowski, Radosław; Łukasik, Grzegorz

    2016-06-01

    The ground state of the Dirac one-electron atom, placed in a weak, static electric field of definite 2L polarity, is studied within the framework of the first-order perturbation theory. The Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B: At. Mol. Opt. Phys. 30, 825 (1997), 10.1088/0953-4075/30/4/007; erratum R. Szmytkowski, J. Phys. B: At. Mol. Opt. Phys. 30, 2747 (1997), 10.1088/0953-4075/30/11/023] is used to derive closed-form analytical expressions for various far-field and near-nucleus static electric multipole susceptibilities of the atom. The far-field multipole susceptibilities—the polarizabilities αL, the electric-to-magnetic cross susceptibilities αE L →M (L ∓1 ), and the electric-to-toroidal-magnetic cross susceptibilities αE L →T L —are found to be expressible in terms of one or two nonterminating generalized hypergeometric functions F2 with the unit argument. Counterpart formulas for the near-nucleus multipole susceptibilities—the electric nuclear shielding constants σEL→E L, the near-nucleus electric-to-magnetic cross susceptibilities σE L →M (L ∓1 ), and the near-nucleus electric-to-toroidal-magnetic cross susceptibilities σE L →T L —involve one or two terminating F2(1 ) series and for each L may be rewritten in terms of elementary functions. Numerical values of the far-field dipole, quadrupole, octupole, and hexadecapole susceptibilities are provided for selected hydrogenic ions. The effect of a declared uncertainty in the CODATA 2014 recommended value of the fine-structure constant α on the accuracy of numerical results is investigated. Analytical quasirelativistic approximations, valid to the second order in α Z , where Z is the nuclear charge number, are also derived for all types of the far-field and near-nucleus susceptibilities considered in the paper.

  5. Numerical simulations of rotating axisymmetric sunspots

    NASA Astrophysics Data System (ADS)

    Botha, G. J. J.; Busse, F. H.; Hurlburt, N. E.; Rucklidge, A. M.

    2008-07-01

    A numerical model of axisymmetric convection in the presence of a vertical magnetic flux bundle and rotation about the axis is presented. The model contains a compressible plasma described by the non-linear MHD equations, with density and temperature gradients simulating the upper layer of the Sun's convection zone. The solutions exhibit a central magnetic flux tube in a cylindrical numerical domain, with convection cells forming collar flows around the tube. When the numerical domain is rotated with a constant angular velocity, the plasma forms a Rankine vortex, with the plasma rotating as a rigid body where the magnetic field is strong, as in the flux tube, while experiencing sheared azimuthal flow in the surrounding convection cells, forming a free vortex. As a result, the azimuthal velocity component has its maximum value close to the outer edge of the flux tube. The azimuthal flow inside the magnetic flux tube and the vortex flow is prograde relative to the rotating cylindrical reference frame. A retrograde flow appears at the outer wall. The most significant convection cell outside the flux tube is the location for the maximum value of the azimuthal magnetic field component. The azimuthal flow and magnetic structure are not generated spontaneously, but decay exponentially in the absence of any imposed rotation of the cylindrical domain.

  6. Axisymmetric inlet minimum weight design method

    NASA Technical Reports Server (NTRS)

    Nadell, Shari-Beth

    1995-01-01

    An analytical method for determining the minimum weight design of an axisymmetric supersonic inlet has been developed. The goal of this method development project was to improve the ability to predict the weight of high-speed inlets in conceptual and preliminary design. The initial model was developed using information that was available from inlet conceptual design tools (e.g., the inlet internal and external geometries and pressure distributions). Stiffened shell construction was assumed. Mass properties were computed by analyzing a parametric cubic curve representation of the inlet geometry. Design loads and stresses were developed at analysis stations along the length of the inlet. The equivalent minimum structural thicknesses for both shell and frame structures required to support the maximum loads produced by various load conditions were then determined. Preliminary results indicated that inlet hammershock pressures produced the critical design load condition for a significant portion of the inlet. By improving the accuracy of inlet weight predictions, the method will improve the fidelity of propulsion and vehicle design studies and increase the accuracy of weight versus cost studies.

  7. Axisymmetric, Ventilated Supercavitation in Unsteady, Horizontal Flow

    NASA Astrophysics Data System (ADS)

    Kawakami, Ellison; Lee, Seung-Jae; Arndt, Roger

    2012-11-01

    Drag reduction and/or speed augmentation of marine vehicles by means of supercavitation is a topic of great interest. During the initial launch of a supercavitating vehicle, an artificial supercavity is required until the vehicle can reach conditions at which a natural supercavity can be sustained. Previous studies at Saint Anthony Falls Laboratory (SAFL) focused on the behavior of ventilated supercavities in steady horizontal flows. In open waters, vehicles can encounter unsteady flows, especially when traveling under waves. A study has been carried out at SAFL to investigate the effects of unsteady flow on axisymmetric supercavities. An attempt is made to duplicate sea states seen in open waters. In an effort to track cavity dimensions throughout a wave cycle, an automated cavity tracking script has been developed. Using a high speed camera and the proper software, it is possible to synchronize cavity dimensions with pressure measurements taken inside the cavity. Results regarding supercavity shape, ventilation demand, cavitation parameters and closure methods are presented. It was found that flow unsteadiness caused a decrease in the overall length of the supercavity while having only a minimal effect on the maximum diameter. The supercavity volume varied with cavitation number and a possible relationship between the two is being explored. (Supported by ONR)

  8. Transient, hypervelocity flow in an axisymmetric nozzle

    NASA Technical Reports Server (NTRS)

    Jacobs, P. A.

    1991-01-01

    The performance of an axisymmetric nozzle was examined which was designed to produce uniform, parallel flow with a nominal Mach number of 8. A free-piston driven shock tube was used to supply the nozzle with high-temperature, high-pressure test gas. Performance was assessed by measuring Pitot pressures across the exit plane of the nozzle and, over the range of operating conditions examined, the nozzle produced satisfactory test flows. However, there were flow disturbances that persisted for significant times after flow initiation. The detailed starting process of the nozzle was also investigated by performing numerical simulations at several nominal test conditions. The classical description of the starting process, based on a quasi-one-dimensional model, provided a reasonable approximation and was used to demonstrate that the starting process could consume a significant fraction of the otherwise usable test gas. This was especially important at high operating enthalpies where nozzle supply conditions were maintained for shorter times. Multidimensional simulations illustrated a mechanism by which the starting process in the actual nozzle could take longer than that predicted by the quasi-one-dimensional analysis. However, the cause of the persistent disturbances observed in the experimental calibration was not identified.

  9. Design of swirled axisymmetric turbulent jets

    NASA Astrophysics Data System (ADS)

    Zhumayev, Z. S.; Abramov, A. A.; Fayziyev, R. A.

    1984-10-01

    The problem of swirling a jet for such applications as turbulization of the flame from burners in industrial furnaces or combustion chambers is treated on the basis of steady state turbulent straight axisymmetric flow of an incompressible fluid with the addition of a tangential velocity component. In the corresponding system of four partial differential equations there appears an exchange coefficient proportional to the mixing half width squared. After reduction to dimensionless form, this system of nonlinear equations is solved for the appropriate boundary conditions with constant momentum flow and constant moment of momentum. Radial profiles of both axial and tangential velocity components at various distances from the nozzle throat have been calculated numerically by the method of finite differences with an implicit scheme. The maxima of both velocity components are found to decrease and to shift toward the jet axis with increasing distance from the nozzle. A sharp swirl can give rise to a positive pressure gradient sufficiently large to produce a backcurrent. The results agree qualitatively with experimental data.

  10. EXACT VECTORIAL LAW FOR AXISYMMETRIC MAGNETOHYDRODYNAMICS TURBULENCE

    SciTech Connect

    Galtier, S.

    2009-10-20

    Three-dimensional incompressible magnetohydrodynamics turbulence is investigated under the assumptions of homogeneity and axisymmetry. We demonstrate that previous works of Chandrasekhar may be improved significantly by using a different formalism for the representation of two-point correlation tensors. From this axisymmetric kinematics, the equations a la von Karman-Howarth are derived from which an exact relation is found in terms of measurable correlations. The relation is then analyzed in the particular case of a medium permeated by an imposed magnetic field B{sub 0} . We make the ansatz that the development of anisotropy implies an algebraic relation between the axial and the radial components of the separation vector r and we derive an exact vectorial law which is parameterized by the intensity of anisotropy. The critical balance proposed by Goldreich and Sridhar is used to fix this parameter and to obtain a unique exact expression; the particular limits of correlations transverse and parallel to B{sub 0} are given for which simple expressions are found. Predictions for the energy spectra are also proposed by a straightforward dimensional analysis of the exact law; it gives a stronger theoretical background to the heuristic spectra previously proposed in the context of the critical balance. We also discuss the wave turbulence limit of an asymptotically large external magnetic field which appears as a natural limit of the vectorial relation. A new interpretation of the anisotropic solar wind observations is eventually discussed.

  11. Magnetic surfaces in an axisymmetric torus

    SciTech Connect

    Skovoroda, A. A.

    2013-04-15

    A method is developed for specifying the boundary equilibrium magnetic surface in an axially symmetric torus by using the absolute values of the magnetic field B = B{sub s}({theta}) and the gradient of the poloidal flux vertical bar vertical bar {nabla}{Psi} vertical bar = vertical bar {nabla}{Psi} vertical bar {sub s}({theta}) in a special flux coordinate system. By setting two surface constants (e.g., the safety factor q and dp/d{Psi}) and matching the absolute values of the magnetic field and the flux gradient on a closed magnetic surface, it is possible to find all equilibrium magnetic functions (including n {center_dot} {nabla} ln B and the local shear s) and all constants (including the toroidal current J and the shear d{mu}/d{Psi}) on this surface. Such a non-traditional formulation of the boundary conditions in solving the stability problem in an axisymmetric torus allows one to impose intentional conditions on plasma confinement and MHD stability at the periphery of the system.

  12. Relativistic equations with fractional and pseudodifferential operators

    SciTech Connect

    Babusci, D.; Dattoli, G.; Quattromini, M.

    2011-06-15

    In this paper we use different techniques from the fractional and pseudo-operators calculus to solve partial differential equations involving operators with noninteger exponents. We apply the method to equations resembling generalizations of the heat equations and discuss the possibility of extending the procedure to the relativistic Schroedinger and Dirac equations.

  13. Multiscale structures in relativistic pair plasmas

    SciTech Connect

    Iqbal, M.; Berezhiani, V. I.; Yoshida, Z.

    2008-03-15

    The steady-state solution of a pair plasma with relativistic thermal velocity of the constituent particles (electrons and positrons) is investigated. The relaxed state can be written as a superposition of three Beltrami fields. Generally, the associated scale parameters could be a complex conjugate pair and a real one. It is shown that at higher thermal energies, all the scale parameters become real. It is also observed that one component gets a large scale (system size) while the other two components appear with small scale of the order of the skin depth at relativistic temperature.

  14. Axisymmetric curvature-driven instability in a model divertor geometry

    SciTech Connect

    Farmer, W. A.; Lawrence Livermore National Laboratory, 7000 East Ave., Livermore, California 94550 ; Ryutov, D. D.

    2013-09-15

    A model problem is presented which qualitatively describes a pressure-driven instability which can occur near the null-point in the divertor region of a tokamak where the poloidal field becomes small. The model problem is described by a horizontal slot with a vertical magnetic field which plays the role of the poloidal field. Line-tying boundary conditions are applied at the planes defining the slot. A toroidal field lying parallel to the planes is assumed to be very strong, thereby constraining the possible structure of the perturbations. Axisymmetric perturbations which leave the toroidal field unperturbed are analyzed. Ideal magnetohydrodynamics is used, and the instability threshold is determined by the energy principle. Because of the boundary conditions, the Euler equation is, in general, non-separable except at marginal stability. This problem may be useful in understanding the source of heat transport into the private flux region in a snowflake divertor which possesses a large region of small poloidal field, and for code benchmarking as it yields simple analytic results in an interesting geometry.

  15. Rapid Numerical Simulation of Viscous Axisymmetric Flow Fields

    NASA Technical Reports Server (NTRS)

    Tweedt, Daniel L.; Chima, Rodrick V.

    1995-01-01

    A two-dimensional Navier-Stokes code has been developed for rapid numerical simulation of axisymmetric flow fields, including flow fields with an azimuthal velocity component. The azimuthal-invariant Navier-Stokes equations in a cylindrical coordinate system are mapped to a general body-fitted coordinate system, with the streamwise viscous terms then neglected by applying the thin-layer approximation. Turbulence effects are modeled using an algebraic model, typically the Baldwin-Lomax turbulence model, although a modified Cebeci-Smith model can also be used. The equations are discretized using central finite differences and solved using a multistage Runge-Kutta algorithm with a spatially varying time step and implicit residual smoothing. Results are presented for calculations of supersonic flow over a waisted body-of-revolution, transonic flow through a normal shock wave in a straight circular duct of constant cross sectional area, swirling supersonic (inviscid) flow through a strong shock in a straight radial duct, and swirling subsonic flow in an annular-to-circular diffuser duct. Comparisons between computed and experimental results are in fair to good agreement, demonstrating that the viscous code can be a useful tool for practical engineering design and analysis work.

  16. Refraction and Shielding of Noise in Non-Axisymmetric Jets

    NASA Technical Reports Server (NTRS)

    Khavaran, Abbas

    1996-01-01

    This paper examines the shielding effect of the mean flow and refraction of sound in non-axisymmetric jets. A general three-dimensional ray-acoustic approach is applied. The methodology is independent of the exit geometry and may account for jet spreading and transverse as well as streamwise flow gradients. We assume that noise is dominated by small-scale turbulence. The source correlation terms, as described by the acoustic analogy approach, are simplified and a model is proposed that relates the source strength to 7/2 power of turbulence kinetic energy. Local characteristics of the source such as its strength, time- or length-scale, convection velocity and characteristic frequency are inferred from the mean flow considerations. Compressible Navier Stokes equations are solved with a k-e turbulence model. Numerical predictions are presented for a Mach 1.5, aspect ratio 2:1 elliptic jet. The predicted sound pressure level directivity demonstrates favorable agreement with reported data, indicating a relative quiet zone on the side of the major axis of the elliptic jet.

  17. Computing Axisymmetric Jet Screech Tones Using Unstructured Grids

    NASA Technical Reports Server (NTRS)

    Jorgenson, Philip C. E.; Loh, Ching Y.

    2002-01-01

    The space-time conservation element and solution element (CE/SE) method is used to solve the conservation law form of the compressible axisymmetric Navier-Stokes equations. The equations are time marched to predict the unsteady flow and the near-field screech tone noise issuing from an underexpanded circular jet. The CE/SE method uses an unstructured grid based data structure. The unstructured grids for these calculations are generated based on the method of Delaunay triangulation. The purpose of this paper is to show that an acoustics solution with a feedback loop can be obtained using truly unstructured grid technology. Numerical results are presented for two different nozzle geometries. The first is considered to have a thin nozzle lip and the second has a thick nozzle lip. Comparisons with available experimental data are shown for flows corresponding to several different jet Mach numbers. Generally good agreement is obtained in terms of flow physics, screech tone frequency, and sound pressure level.

  18. Computing Axisymmetric Jet Screech Tones using Unstructured Grids

    NASA Technical Reports Server (NTRS)

    Jorgenson, Philip C. E.; Loh, Ching Y.

    2003-01-01

    The purpose of this paper is to show that computations with an aeroacoustic feedback loop, the jet screech noise, can be obtained using truly unstructured grid technology. Numerical results are presented for a nozzle with two different lip thicknesses which will be referred to in this paper as a thin and a thick lip nozzle respectively. The space-time conservation element and solution element (CE/SE) method is used to solve the conservation laws of the compressible axisymmetric Navier-Stokes equations. The equations are time marched to predict the unsteady flow and the near-field screech tone noise issuing from an underexpanded circular jet. The CE/SE method uses an unstructured grid based data structure. The unstructured grids for these calculations are generated based on the method of Delaunay triangulation. Comparisons of numerical results with available experimental data are shown for flows corresponding to several different jet Mach numbers. Generally good agreement is obtained in terms of flow physics, screech tone frequency, and sound pressure level.

  19. Kinetic axisymmetric gravitational equilibria in collisionless accretion disk plasmas

    SciTech Connect

    Cremaschini, Claudio; Miller, John C.; Tessarotto, Massimo

    2010-07-15

    A theoretical treatment is presented of kinetic equilibria in accretion disks (AD) around compact objects, for cases where the plasma can be considered as collisionless. The plasma is assumed to be axisymmetric and to be acted on by gravitational and electromagnetic fields; in this paper, the particular case is considered where the magnetic field admits a family of toroidal magnetic surfaces, which are locally mutually nested and closed. It is pointed out that there exist asymptotic kinetic equilibria represented by generalized bi-Maxwellian distribution functions and characterized by primarily toroidal differential rotation and temperature anisotropy. It is conjectured that kinetic equilibria of this type can exist which are able to sustain both toroidal and poloidal electric current densities, the latter being produced via finite Larmor-radius effects associated with the temperature anisotropy. This leads to the possibility of existence of a new kinetic effect - referred to here as a 'kinetic dynamo effect - resulting in the self-generation of toroidal magnetic field even by a stationary plasma, without any net radial accretion flow being required. The conditions for these equilibria to occur, their basic theoretical features, and their physical properties are all discussed in detail.

  20. The development of an axisymmetric curved turbulent wall jet

    NASA Astrophysics Data System (ADS)

    Gregory-Smith, D. G.; Hawkins, M. J.

    1991-12-01

    An experimental study has been carried out of the low speed Coanda wall jet with both streamwise and axisymmetric curvature. A single component laser Doppler technique was used, and by taking several orientations at a given point, values of the three mean velocities and five of the six Reynolds stresses were obtained. The lateral divergence and convex streamwise curvature both enhanced the turbulence in the outer part of the jet compared with a plane two-dimensional wall jet. The inner layer exhibited a large separation of the positions of maximum velocity and zero shear stress. It was found that the streamwise mean velocity profile became established very rapidly downstream of the slot exit. The profile appeared fairly similar at later downstream positions, but the mean radial velocity and turbulence parameters showed the expected nonself preservation of the flow. Removal of the streamwise curvature resulted in a general return of the jet conditions toward those expected of a plane wall jet. The range and accuracy of the data may be used for developing turbulence models and computational techniques for this type of flow.

  1. Transonic analysis and design of axisymmetric bodies in nonuniform flow

    NASA Technical Reports Server (NTRS)

    Chang, Jen-Fu; Lan, C. Edward

    1987-01-01

    An inviscid nonuniform axisymmetric transonic code was developed for applications in analysis and design. Propfan slipstream effect on pressure distribution for a body with and without sting was investigated. Results show that nonuniformity causes pressure coefficient to be more negative and shock strength to be stronger and more rearward. Sting attached to a body reduced the pressure peak and moves the rear shock forward. Extent and Mach profile shapes of the nonuniformity region appeared to have little effect on the pressure distribution. Increasing nonuniformity magnitude made pressure coefficient more negative and moved the shock rearward. Design study was conducted with the CONMIN optimizer for an ellipsoid and a body with the NACA-0012 counter. For the ellipsoid, the general trend showed that to reduce the pressure drag, the front portion of the body should be thinner and the contour of the rear portion should be flatter than the ellipsoid. For the design of a body with a sharp trailing edge in transonic flow with an initial shape given by the NACA-0012 contour, the pressure drag was reduced by decreasing the nose radius and increasing the thickness in the aft portion. Drag reduction percentages are given.

  2. Optimal geometry of an axisymmetric wave energy converter

    NASA Astrophysics Data System (ADS)

    Edwards, Emma; Yue, Dick K. P.; Vortical Flow Research Laboratory Team

    2015-11-01

    There have been a number of theoretical, experimental and pilot-scale studies on wave energy converters with varying shapes and designs, but due to the complex nature of wave-body hydrodynamics, as yet there is not one single three-dimensional shape that is agreed-upon to be optimal for wave power extraction. Our objective is to determine the optimal geometry to maximize power uptake over a spectrum of incident waves. As an initial investigation, we consider an axisymmetric floating wave power extraction device operating in heave. We assume linear wave conditions. The body geometry is described by smooth polynomial basis functions and is allowed to be completely general, subject to simple constraints. We consider a linear power uptake with a fixed damping coefficient (which could be optimized). For each frequency in the spectrum, hydrodynamic coefficients are calculated using a linear frequency-domain panel method. Then, for a specific incident wave spectrum, maximal extractable power is integrated over the entire spectrum. We will discuss the optimal geometry and associated maximum power for different geometrical constraints and wave conditions.

  3. Thermally relativistic flows induced by gravitational-force-free particle motion in curved spacetime

    SciTech Connect

    Yano, Ryosuke; Suzuki, Kojiro; Kuroda, Hisayasu

    2009-12-15

    Thermally relativistic flows in the early Universe can be characterized by the emergence of flows induced by gravitational-force-free particle motion in curved spacetime as well as induced by the gravitational force. In this paper, thermally relativistic flows induced by gravitational-force-free particle motion in curved spacetime are discussed on the basis of the general relativistic Boltzmann equation. As an object of analysis, we consider the flow from the static state inside the Schwarzschild radius of a thermally relativistic stuffed black hole induced by such motion. Analytical results obtained using the collisionless, nongravitational general relativistic Boltzmann equation reveal that the initial cluster is induced by gravitational-force-free particle motion. Numerical results obtained using the nongravitational general relativistic Anderson-Witting model confirm the presence of an initial cluster inside the thermally relativistic stuffed black hole, which is induced by gravitational-force-free particle motion.

  4. Corrugation of Relativistic Magnetized Shock Waves

    NASA Astrophysics Data System (ADS)

    Lemoine, Martin; Ramos, Oscar; Gremillet, Laurent

    2016-08-01

    As a shock front interacts with turbulence it develops corrugation, which induces outgoing wave modes in the downstream plasma. For a fast shock wave, the incoming wave modes can either be fast magnetosonic waves originating downstream, outrunning the shock, or eigenmodes of the upstream plasma drifting through the shock. Using linear perturbation theory in relativistic MHD, this paper provides a general analysis of the corrugation of relativistic magnetized fast shock waves resulting from their interaction with small amplitude disturbances. Transfer functions characterizing the linear response for each of the outgoing modes are calculated as a function of the magnetization of the upstream medium and as a function of the nature of the incoming wave. Interestingly, if the latter is an eigenmode of the upstream plasma, we find that there exists a resonance at which the (linear) response of the shock becomes large or even diverges. This result may have profound consequences on the phenomenology of astrophysical relativistic magnetized shock waves.

  5. Ion-acoustic solitary waves in a fully relativistic ion-electron-positron plasma

    NASA Astrophysics Data System (ADS)

    Tribeche, Mouloud; Boukhalfa, Soufiane

    2011-04-01

    A fully and coherent relativistic fluid model derived from the covariant formulation of relativistic fluid equations is used to study ion-acoustic solitary waves in a fully relativistic ion-electron-positron plasma. This approach has the characteristic to be consistent with the relativistic principle and consequently leads to a more general set of equations valid for fully relativistic plasmas with arbitrary Lorentz relativistic factor. Our results may be relevant to cosmic relativistic double- layers and relativistic plasma structures involving energetic plasma flows that may occur in space plasmas. Furthermore, they may complement and provide new insights into recently published results (G. Lu et al. in Astrophys. Space Sci., doi: 10.1007/s10509-010-0363-5, 2010).

  6. Relativistic modeling capabilities in PERSEUS extended MHD simulation code for HED plasmas

    SciTech Connect

    Hamlin, Nathaniel D.; Seyler, Charles E.

    2014-12-15

    We discuss the incorporation of relativistic modeling capabilities into the PERSEUS extended MHD simulation code for high-energy-density (HED) plasmas, and present the latest hybrid X-pinch simulation results. The use of fully relativistic equations enables the model to remain self-consistent in simulations of such relativistic phenomena as X-pinches and laser-plasma interactions. By suitable formulation of the relativistic generalized Ohm’s law as an evolution equation, we have reduced the recovery of primitive variables, a major technical challenge in relativistic codes, to a straightforward algebraic computation. Our code recovers expected results in the non-relativistic limit, and reveals new physics in the modeling of electron beam acceleration following an X-pinch. Through the use of a relaxation scheme, relativistic PERSEUS is able to handle nine orders of magnitude in density variation, making it the first fluid code, to our knowledge, that can simulate relativistic HED plasmas.

  7. The axisymmetric stellar wind of AG Carinae

    NASA Technical Reports Server (NTRS)

    Schulte-Ladbeck, Regina E.; Clayton, Geoffrey C.; Hillier, D. John; Harries, Tim J.; Howarth, Ian D.

    1994-01-01

    We present optical linear spectropolarimetry of the Luminous Blue Variable AG Carinae obtained after a recent visual brightness increase. The absence of He II lambda 4686 emission, together with the weakening of the He I spectrum and the appearance of Fe lines in the region around 5300 A, confirm that AG Car has started a new excursion across the HR diagram. The H alpha line profile exhibits very extended line wings that are polarized differently in both amount and position angle from either the continuum or the line core. The polarization changes across H alpha, together with variable continuum polarization, indicate the presence of intrinsic polarization. Coexistence of the line-wing polarization with extended flux-line wings evidences that both are formed by electron scattering in a dense wind. The position angle rotates across the line profiles, in a way that presently available models suggest is due to rotation and expansion of the scattering material. AG Car displays very large variations of its linear polarization with time, Delta P approximately 1.2%, indicating significant variations in envelope opacity. We find that the polarization varies along a preferred position angle of approximately 145 deg (with a scatter of +/- 10 deg) which we interpret as a symmetry axis of the stellar wind (with an ambiguity of 90 deg). This position angle is co-aligned with the major axis of the AG Car ring nebula and perpendicular to the AG Car jet. Our observations thus suggest that the axisymmetric geometry seen in the resolved circumstellar environment at various distances already exists within a few stellar radii of AG Car. From the H alpha polarization profile we deduce an interstellar polarization of Q = 0.31%, U = -1.15% at H alpha. The inferred interstellar polarization implies that the intrinsic polarization is not always of the same sign. This indicates either significant temporal changes in the envelope geometry, or it may arise from effects of multiple scattering

  8. Axisymmetric Control in Alcator C-Mod

    NASA Astrophysics Data System (ADS)

    Tinios, Gerasimos

    1995-01-01

    This thesis investigates the degree to which linear axisymmetric modeling of the response of a tokamak plasma can reproduce observed experimental behavior. The emphasis is on the vertical instability. The motivation for this work lies in the fact that, once dependable models have been developed, modern control theory methods can be used to design feedback laws for more effective and efficient tokamak control. The models are tested against experimental data from the Alcator C-Mod tokamak. A linear model for each subsystem of the closed-loop system constituting an Alcator C-Mod discharge under feedback control has been constructed. A non-rigid, approximately flux-conserving, perturbed equilibrium plasma response model is used in the comparison to experiment. A detailed toroidally symmetric model of the vacuum vessel and the supporting superstructure is used. Modeling of the power supplies feeding the active coils has been included. Experiments have been conducted with vertically unstable plasmas where the feedback was turned off and the plasma response was observed in an open -loop configuration. The closed-loop behavior has been examined by injecting step perturbations into the desired vertical position of the plasma. The agreement between theory and experiment in the open-loop configuration was very satisfactory, proving that the perturbed equilibrium plasma response model and a toroidally symmetric electromagnetic model of the vacuum vessel and the structure can be trusted for the purpose of calculations for control law design. When the power supplies and the feedback computer hardware are added to the system, however, as they are in the closed-loop configuration, they introduce nonlinearities that make it difficult to explain observed behavior with linear theory. Nonlinear simulation of the time evolution of the closed-loop experiments was able to account for the discrepancies between linear theory and experiment. (Copies available exclusively from MIT Libraries

  9. Relativistic Weierstrass random walks.

    PubMed

    Saa, Alberto; Venegeroles, Roberto

    2010-08-01

    The Weierstrass random walk is a paradigmatic Markov chain giving rise to a Lévy-type superdiffusive behavior. It is well known that special relativity prevents the arbitrarily high velocities necessary to establish a superdiffusive behavior in any process occurring in Minkowski spacetime, implying, in particular, that any relativistic Markov chain describing spacetime phenomena must be essentially Gaussian. Here, we introduce a simple relativistic extension of the Weierstrass random walk and show that there must exist a transition time t{c} delimiting two qualitative distinct dynamical regimes: the (nonrelativistic) superdiffusive Lévy flights, for trelativistic) Gaussian diffusion, for t>t{c} . Implications of this crossover between different diffusion regimes are discussed for some explicit examples. The study of such an explicit and simple Markov chain can shed some light on several results obtained in much more involved contexts. PMID:20866862

  10. SAMPEX Relativistic Microbursts Observation

    NASA Astrophysics Data System (ADS)

    Liang, X.; Comess, M.; Smith, D. M.; Selesnick, R. S.; Sample, J. G.; Millan, R. M.

    2012-12-01

    Relativistic (>1 MeV) electron microburst precipitation is thought to account for significant relativistic electron loss. We present the statistical and spectral analysis of relativistic microbursts observed by the Proton/Electron Telescope (PET) on board the Solar Anomalous Magnetospheric Particle Explorer(SAMPEX) satellite from 1992 to 2004. Spectrally we find that microbursts are well fit by an exponential energy distribution in the 0.5-4 MeV range with a spectral e-folding energy of E0 < 375 keV. We also discuss the comparison of morning microbursts with events at midnight, which were first identified as microbursts by O'Brien et al. (2004). Finally, we compare the loss-rates due to microbursts and non-microburst precipitation during storm times and averaged over all times.

  11. Magnetogenesis through Relativistic Velocity Shear

    NASA Astrophysics Data System (ADS)

    Miller, Evan

    Magnetic fields at all scales are prevalent in our universe. However, current cosmological models predict that initially the universe was bereft of large-scale fields. Standard magnetohydrodynamics (MHD) does not permit magnetogenesis; in the MHD Faraday's law, the change in magnetic field B depends on B itself. Thus if B is initially zero, it will remain zero for all time. A more accurate physical model is needed to explain the origins of the galactic-scale magnetic fields observed today. In this thesis, I explore two velocity-driven mechanisms for magnetogenesis in 2-fluid plasma. The first is a novel kinematic 'battery' arising from convection of vorticity. A coupling between thermal and plasma oscillations, this non-relativistic mechanism can operate in flows that are incompressible, quasi-neutral and barotropic. The second mechanism results from inclusion of thermal effects in relativistic shear flow instabilities. In such flows, parallel perturbations are ubiquitously unstable at small scales, with growth rates of order with the plasma frequency over a defined range of parameter-space. Of these two processes, instabilities seem far more likely to account for galactic magnetic fields. Stable kinematic effects will, at best, be comparable to an ideal Biermann battery, which is suspected to be orders of magnitude too weak to produce the observed galactic fields. On the other hand, instabilities grow until saturation is reached, a topic that has yet to be explored in detail on cosmological scales. In addition to investigating these magnetogenesis sources, I derive a general dispersion relation for three dimensional, warm, two species plasma with discontinuous shear flow. The mathematics of relativistic plasma, sheared-flow instability and the Biermann battery are also discussed.

  12. Electromagnetic wave equations for relativistically degenerate quantum magnetoplasmas.

    PubMed

    Masood, Waqas; Eliasson, Bengt; Shukla, Padma K

    2010-06-01

    A generalized set of nonlinear electromagnetic quantum hydrodynamic (QHD) equations is derived for a magnetized quantum plasma, including collisional, electron spin- 1/2, and relativistically degenerate electron pressure effects that are relevant for dense astrophysical systems, such as white dwarfs. For illustrative purposes, linear dispersion relations are derived for one-dimensional magnetoacoustic waves for a collisionless nonrelativistic degenerate gas in the presence of the electron spin- 1/2 contribution and for magnetoacoustic waves in a plasma containing relativistically degenerate electrons. It is found that both the spin and relativistic degeneracy at high densities tend to slow down the magnetoacoustic wave due to the Pauli paramagnetic effect and relativistic electron mass increase. The present study outlines the theoretical framework for the investigation of linear and nonlinear behaviors of electromagnetic waves in dense astrophysical systems. The results are applied to calculate the magnetoacoustic speeds for both the nonrelativistic and relativistic electron degeneracy cases typical for white dwarf stars. PMID:20866534

  13. Relativistic nuclear dynamics

    SciTech Connect

    Coester, F.

    1985-01-01

    A review is presented of three distinct approaches to the construction of relativistic dynamical models: (1) Relativistic canonical quantum mechanics. (The Hilbert space of states is independent of the interactions, which are introduced by modifying the energy operator.) (2) Hilbert spaces of manifestly covariant wave functions. (The interactions modify the metric of the Hilbert space.) (3) Covariant Green functions. In each of the three approaches the focus is on the formulation of the two-body dynamics, and problems in the construction of the corresponding many-body dynamics are discussed briefly. 21 refs.

  14. Perspective: relativistic effects.

    PubMed

    Autschbach, Jochen

    2012-04-21

    This perspective article discusses some broadly-known and some less broadly-known consequences of Einstein's special relativity in quantum chemistry, and provides a brief outline of the theoretical methods currently in use, along with a discussion of recent developments and selected applications. The treatment of the electron correlation problem in relativistic quantum chemistry methods, and expanding the reach of the available relativistic methods to calculate all kinds of energy derivative properties, in particular spectroscopic and magnetic properties, requires on-going efforts. PMID:22519307

  15. Cracking of general relativistic anisotropic polytropes

    NASA Astrophysics Data System (ADS)

    Herrera, L.; Fuenmayor, E.; León, P.

    2016-01-01

    We discuss the effect that small fluctuations of the local anisotropy of pressure and of the energy density may have on the occurrence of cracking in spherical compact objects, satisfying a polytropic equation of state. Two different kinds of polytropes are considered. For both, it is shown that departures from equilibrium may lead to the appearance of cracking, for a wide range of values of the parameters defining the polytrope. Prospective applications of the obtained results to some astrophysical scenarios are pointed out.

  16. Fast optimization of static axisymmetric shell structures

    NASA Astrophysics Data System (ADS)

    Jacoby, Jeffrey

    An axisymmetric shell optimization procedure is developed which is a fast, user-friendly and practical tool for design use in disciplines including aerospace, mechanical and civil engineering. The shape and thickness of a shell can be optimized to minimize shell mass, mass/volume ratio or stress with constraints imposed on von Mises stress and local buckling. The procedure was created with the aid of the GENOPT optimization development system (Dr. D. Bushnell, Lockheed Missiles and Space Co) and uses the FAST1 shell analysis program (Prof. C. R. Steele, Stanford University) to perform the constraint analysis. The optimization method used is the modified method of feasible directions. The procedure is fast because exact analysis methods allow complex shells to be modelled with only a few large shell elements and still retain a sufficiently accurate solution. This is of particular advantage near shell boundaries and intersections which can have small regions of very detailed variation in the solution. Finite element methods would require many small elements to capture accurately this detail with a resulting increase in computation time and model complexity. Reducing the complexity of the model also reduces the size of the required input and contributes to the simplicity of the procedure. Optimization design variables are the radial and axial coordinates of nodes and the shape parameters and thicknesses of the elements. Thickness distribution within an element can be optimized by specifying the thickness at evenly spaced control points. Spline interpolation is used to provide a smooth thickness variation between the control points. An effective method is developed for reducing the number of required stress constraint equations. Various shells have been optimized and include models for comparison with published results. Shape, thickness and shape/thickness optimization has been performed on examples including a simple aerobrake, sphere-nozzle intersections, ring

  17. Axisymmetric Tandem Mirrors: Stabilization and Confinement Studies

    SciTech Connect

    Post, R F; Fowler, T K; Bulmer, R; Byers, J; Hua, D; Tung, L

    2004-07-15

    The 'Kinetic Stabilizer' has been proposed as a means of MHD stabilizing an axisymmetric tandem mirror system. The K-S concept is based on theoretical studies by Ryutov, confirmed experimentally in the Gas Dynamic Trap experiment in Novosibirsk. In the K-S beams of ions are directed into the end of an 'expander' region outside the outer mirror of a tandem mirror. These ions, slowed, stagnated, and reflected as they move up the magnetic gradient, produce a low-density stabilizing plasma. At the Lawrence Livermore National Laboratory we have been conducting theoretical and computational studies of the K-S Tandem Mirror. These studies have employed a low-beta code written especially to analyze the beam injection/stabilization process, and a new code SYMTRAN (by Hua and Fowler) that solves the coupled radial and axial particle and energy transport in a K-S TM. Also, a 'legacy' MHD stability code, FLORA, has been upgraded and employed to benchmark the injection/stabilization code and to extend its results to high beta values. The FLORA code studies so far have confirmed the effectiveness of the K-S in stabilizing high-beta (40%) plasmas with stabilizer plasmas the peak pressures of which are several orders of magnitude smaller than those of the confined plasma. Also the SYMTRAN code has shown D-T plasma ignition from alpha particle energy deposition in T-M regimes with strong end plugging. Our studies have confirmed the viability of the K-S-T-M concept with respect to MHD stability and radial and axial confinement. We are continuing these studies in order to optimize the parameters and to examine means for the stabilization of possible residual instability modes, such as drift modes and 'trapped-particle' modes. These modes may in principle be controlled by tailoring the stabilizer plasma distribution and/or the radial potential distribution. In the paper the results to date of our studies are summarized and projected to scope out possible fusion-power versions of the K

  18. Axisymmetric Tandem Mirrors: Stabilization and Confinement Studies

    SciTech Connect

    Post, R.F.; Fowler, T.K.; Bulmer, R.; Byers, J.; Hua, D.; Tung, L.

    2005-01-15

    The 'Kinetic Stabilizer' has been proposed as a means of MHD stabilizing an axisymmetric tandem mirror system. The K-S concept is based on theoretical studies by Ryutov, confirmed experimentally in the Gas Dynamic Trap experiment in Novosibirsk. In the K-S beams of ions are directed into the end of an 'expander' region outside the outer mirror of a tandem mirror. These ions, slowed, stagnated, and reflected as they move up the magnetic gradient, produce a low-density stabilizing plasma.At the Lawrence Livermore National Laboratory we have been conducting theoretical and computational studies of the K-S Tandem Mirror. These studies have employed a low-beta code written especially to analyze the beam injection/stabilization process,and a new code SYMTRAN (by Hua and Fowler)that solves the coupled radial and axial particle and energy transport in a K-S T-M. Also, a 'legacy' MHD stability code, FLORA, has been upgraded and employed to benchmark the injection/stabilization code and to extend its results to high beta values.The FLORA code studies so far have confirmed the effectiveness of the K-S in stabilizing high-beta (40%) plasmas with stabilizer plasmas the peak pressures of which are several orders of magnitude smaller than those of the confined plasma.Also the SYMTRAN code has shown D-T plasma ignition from alpha particle energy deposition in T-M regimes with strong end plugging.Our studies have confirmed the viability of the K-S T-M concept with respect to MHD stability and radial and axial confinement. We are continuing these studies in order to optimize the parameters and to examine means for the stabilization of possible residual instability modes, such as drift modes and 'trapped-particle' modes. These modes may in principle be controlled by tailoring the stabilizer plasma distribution and/or the radial potential distribution.In the paper the results to date of our studies are summarized and projected to scope out possible fusion-power versions of the K-S T-M.

  19. Relativistic virial relation for cosmological structures

    NASA Astrophysics Data System (ADS)

    Javadinezhad, Reza; Firouzjaee, Javad T.; Mansouri, Reza

    2016-01-01

    Starting with the relativistic Boltzmann equation for a system of particles defined by a distribution function, we have derived the virial relation for a spherical structure within an expanding background in the context of general relativity. This generalized form of the virial relation is then applied to the static case of a spherically symmetric structure to see the difference in the simplest case to the Newtonian relation. A relativistic mass-temperature relation for this simple case is also derived which can be applied to compact objects in astrophysics. Our general virial relation is then applied to the nonstatic case of a structure within an expanding universe where an extra term, usually missed in studies of structures in the presence of the dark energy, appears.

  20. Relativistic impulse dynamics.

    PubMed

    Swanson, Stanley M

    2011-08-01

    Classical electrodynamics has some annoying rough edges. The self-energy of charges is infinite without a cutoff. The calculation of relativistic trajectories is difficult because of retardation and an average radiation reaction term. By reconceptuallizing electrodynamics in terms of exchanges of impulses rather than describing it by forces and potentials, we eliminate these problems. A fully relativistic theory using photonlike null impulses is developed. Numerical calculations for a two-body, one-impulse-in-transit model are discussed. A simple relationship between center-of-mass scattering angle and angular momentum was found. It reproduces the Rutherford cross section at low velocities and agrees with the leading term of relativistic distinguishable-particle quantum cross sections (Møller, Mott) when the distance of closest approach is larger than the Compton wavelength of the particle. Magnetism emerges as a consequence of viewing retarded and advanced interactions from the vantage point of an instantaneous radius vector. Radiation reaction becomes the local conservation of energy-momentum between the radiating particle and the emitted impulse. A net action is defined that could be used in developing quantum dynamics without potentials. A reinterpretation of Newton's laws extends them to relativistic motion. PMID:21929132

  1. Radiation from Relativistic Jets

    NASA Technical Reports Server (NTRS)

    Nishikawa, K.-I.; Mizuno, Y.; Hardee, P.; Sol, H.; Medvedev, M.; Zhang, B.; Nordlund, A.; Frederiksen, J. T.; Fishman, G. J.; Preece, R.

    2008-01-01

    Nonthermal radiation observed from astrophysical systems containing relativistic jets and shocks, e.g., gamma-ray bursts (GRBs), active galactic nuclei (AGNs), and Galactic microquasar systems usually have power-law emission spectra. Recent PIC simulations of relativistic electron-ion (electron-positron) jets injected into a stationary medium show that particle acceleration occurs within the downstream jet. In the presence of relativistic jets, instabilities such as the Buneman instability, other two-streaming instability, and the Weibel (filamentation) instability create collisionless shocks, which are responsible for particle (electron, positron, and ion) acceleration. The simulation results show that the Weibel instability is responsible for generating and amplifying highly nonuniform, small-scale magnetic fields. These magnetic fields contribute to the electron's transverse deflection behind the jet head. The 'jitter' radiation from deflected electrons in small-scale magnetic fields has different properties than synchrotron radiation which is calculated in a uniform magnetic field. This jitter radiation, a case of diffusive synchrotron radiation, may be important to understand the complex time evolution and/or spectral structure in gamma-ray bursts, relativistic jets, and supernova remnants.

  2. A relativistic spherical vortex

    PubMed Central

    Pekeris, C. L.

    1976-01-01

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

  3. The Relativistic Rocket

    ERIC Educational Resources Information Center

    Antippa, Adel F.

    2009-01-01

    We solve the problem of the relativistic rocket by making use of the relation between Lorentzian and Galilean velocities, as well as the laws of superposition of successive collinear Lorentz boosts in the limit of infinitesimal boosts. The solution is conceptually simple, and technically straightforward, and provides an example of a powerful…

  4. Relativistic effects on plasma expansion

    SciTech Connect

    Benkhelifa, El-Amine; Djebli, Mourad

    2014-07-15

    The expansion of electron-ion plasma is studied through a fully relativistic multi-fluids plasma model which includes thermal pressure, ambipolar electrostatic potential, and internal energy conversion. Numerical investigation, based on quasi-neutral assumption, is performed for three different regimes: nonrelativistic, weakly relativistic, and relativistic. Ions' front in weakly relativistic regime exhibits spiky structure associated with a break-down of quasi-neutrality at the expanding front. In the relativistic regime, ion velocity is found to reach a saturation limit which occurs at earlier stages of the expansion. This limit is enhanced by higher electron velocity.

  5. Dynamics of relativistic jets

    NASA Astrophysics Data System (ADS)

    Nishikawa, K.-I.; Frank, J.; Christodoulou, D. M.; Koide, S.; Sakai, J.-I.; Sol, Hélène; Mutel, Robert L.

    1998-12-01

    We discuss the structure and relativistic kinematics that develop in three spatial dimensions when a moderately hot, supersonic jet propagates into a denser background medium and encounters resistance from an oblique magnetic field. Our simulations incorporate relativistic MHD in a four-dimensional spacetime and clearly show that (a) relatively weak, oblique fields (at 1/16 of the equipartition value) have only a negligible influence on the propagating jet and they are passively pushed away by the relativistically moving head; (b) oblique fields in equipartition with the ambient plasma provide more resistance and cause bending at the jet head, but the magnitude of this deflection and the associated backflow are small compared to those identified by previous studies. The new results are understood as follows: Relativistic simulations have consistently shown that these jets are effectively heavy and so they do not suffer substantial momentum losses and are not decelerated as efficiently as their nonrelativistic counterparts. In addition, the ambient magnetic field, however strong, can be pushed aside with relative ease by the beam, provided that the degrees of freedom associated with all three spatial dimensions are followed self-consistently during the simulations. The effect is analogous to pushing Japanese "noren" or vertical Venetian blinds out of the way while the slats are allowed to bend and twist in 3-D space. Applied to relativistic extragalactic jets from blazars, the new results are encouraging since superluminal outflows exhibit bending near their sources and their environments are profoundly magnetized - but observations do not provide support for irregular kinematics such as large-scale vortical motions and pronounced reverse flows near the points of origin.

  6. DYNAMICS OF STRONGLY TWISTED RELATIVISTIC MAGNETOSPHERES

    SciTech Connect

    Parfrey, Kyle; Beloborodov, Andrei M.; Hui, Lam

    2013-09-10

    Magnetar magnetospheres are believed to be strongly twisted due to shearing of the stellar crust by internal magnetic stresses. We present time-dependent axisymmetric simulations showing in detail the evolution of relativistic force-free magnetospheres subjected to slow twisting through large angles. When the twist amplitude is small, the magnetosphere moves quasi-statically through a sequence of equilibria of increasing free energy. At some twist amplitude the magnetosphere becomes tearing-mode unstable to forming a resistive current sheet, initiating large-scale magnetic reconnection in which a significant fraction of the magnetic free energy can be dissipated. This ''critical'' twist angle is insensitive to the resistive length scale. Rapid shearing temporarily stabilizes the magnetosphere beyond the critical angle, allowing the magnetosphere of a rapidly differentially rotating star to store and dissipate more free energy. In addition to these effects, shearing the surface of a rotating star increases the spindown torque applied to the star. If shearing is much slower than rotation, the resulting spikes in spindown rate can occur on timescales anywhere from the long twisting timescale to the stellar spin period or shorter, depending both on the stellar shear distribution and the existing distribution of magnetospheric twists. A model in which energy is stored in the magnetosphere and released by a magnetospheric instability therefore predicts large changes in the measured spindown rate before soft gamma repeater giant flares.

  7. Efficient acceleration of relativistic magnetohydrodynamic jets

    NASA Astrophysics Data System (ADS)

    Toma, Kenji; Takahara, Fumio

    2013-08-01

    Relativistic jets in active galactic nuclei, galactic microquasars, and gamma-ray bursts are widely considered to be magnetohydrodynamically driven by black hole accretion systems, although the conversion mechanism from the Poynting into the particle kinetic energy flux is still open. Recent detailed numerical and analytical studies of global structures of steady, axisymmetric magnetohydrodynamic (MHD) flows with specific boundary conditions have not reproduced as rapid an energy conversion as required by observations. In order to find more suitable boundary conditions, we focus on the flow along a poloidal magnetic field line just inside the external boundary, without treating the transfield force balance in detail. We find some examples of the poloidal field structure and corresponding external pressure profile for an efficient and rapid energy conversion as required by observations, and that the rapid acceleration requires a rapid decrease of the external pressure above the accretion disk. We also clarify the differences between the fast magnetosonic point of the MHD flow and the sonic point of the de Laval nozzle.

  8. 2-D/Axisymmetric Formulation of Multi-dimensional Upwind Scheme

    NASA Technical Reports Server (NTRS)

    Wood, William A.; Kleb, William L.

    2001-01-01

    A multi-dimensional upwind discretization of the two-dimensional/axisymmetric Navier-Stokes equations is detailed for unstructured meshes. The algorithm is an extension of the fluctuation splitting scheme of Sidilkover. Boundary conditions are implemented weakly so that all nodes are updated using the base scheme, and eigen-value limiting is incorporated to suppress expansion shocks. Test cases for Mach numbers ranging from 0.1-17 are considered, with results compared against an unstructured upwind finite volume scheme. The fluctuation splitting inviscid distribution requires fewer operations than the finite volume routine, and is seen to produce less artificial dissipation, leading to generally improved solution accuracy.

  9. The axisymmetric problem with electrostatic fields and some spherically symmetric black holes in EMD theory

    NASA Astrophysics Data System (ADS)

    Huan Wei, Yi

    2004-02-01

    The fundamental axisymmetric field equations of Einstein Maxwell dilation (EMD) theory with electric fields are simplified to Ernst-like and Laplace equations; all the solutions in the low-energy limit of string theory are generalized to the current case. On the basis of the work of Wei et al (2002 Class. Quantum Grav. 19 6469), the TS-like class of solutions and the class of solutions given in terms of two harmonics are further analysed and discussed, particularly the spherically symmetric solutions.

  10. On the flow of non-axisymmetric perturbations of cylinders via surface diffusion

    NASA Astrophysics Data System (ADS)

    LeCrone, Jeremy; Simonett, Gieri

    2016-03-01

    We study the surface diffusion flow acting on a class of general (non-axisymmetric) perturbations of cylinders Cr in IR3. Using tools from parabolic theory on uniformly regular manifolds, and maximal regularity, we establish existence and uniqueness of solutions to surface diffusion flow starting from (spatially-unbounded) surfaces defined over Cr via scalar height functions which are uniformly bounded away from the central cylindrical axis. Additionally, we show that Cr is normally stable with respect to 2π-axially-periodic perturbations if the radius r > 1, and unstable if 0 < r < 1. Stability is also shown to hold in settings with axial Neumann boundary conditions.

  11. Ion temperature gradient turbulence in helical and axisymmetric RFP plasmas

    SciTech Connect

    Predebon, I.; Xanthopoulos, P.

    2015-05-15

    Turbulence induced by the ion temperature gradient (ITG) is investigated in the helical and axisymmetric plasma states of a reversed field pinch device by means of gyrokinetic calculations. The two magnetic configurations are systematically compared, both linearly and nonlinearly, in order to evaluate the impact of the geometry on the instability and its ensuing transport, as well as on the production of zonal flows. Despite its enhanced confinement, the high-current helical state demonstrates a lower ITG stability threshold compared to the axisymmetric state, and ITG turbulence is expected to become an important contributor to the total heat transport.

  12. Ion temperature gradient turbulence in helical and axisymmetric RFP plasmas

    NASA Astrophysics Data System (ADS)

    Predebon, I.; Xanthopoulos, P.

    2015-05-01

    Turbulence induced by the ion temperature gradient (ITG) is investigated in the helical and axisymmetric plasma states of a reversed field pinch device by means of gyrokinetic calculations. The two magnetic configurations are systematically compared, both linearly and nonlinearly, in order to evaluate the impact of the geometry on the instability and its ensuing transport, as well as on the production of zonal flows. Despite its enhanced confinement, the high-current helical state demonstrates a lower ITG stability threshold compared to the axisymmetric state, and ITG turbulence is expected to become an important contributor to the total heat transport.

  13. Potential flow past axisymmetric bodies at angle of attack

    NASA Technical Reports Server (NTRS)

    Kuhlman, J. M.; Shu, J.-Y.

    1984-01-01

    The Karamcheti (1966) suggestion concerning the use of higher order singularity techniques has been developed for the calculation of incompressible flow past an axisymmetric body at angle of attack. Attention is given to the results of a convergence study using this axial singularity method, where solution accuracy has been investigated for ellipsoids of slenderness ratio in the 1-10 range for both axial and inclined flow. Effects of singularity type, element number and size distribution, and singularity line inset distance, are noted, and a paneling scheme is developed which yields accurate results for the class of axisymmetric bodies having continuous body slopes with discontinuous curvature jumps.

  14. Study of axisymmetric flow problems by Hele-Shaw models

    NASA Astrophysics Data System (ADS)

    Rao, P. V.; Sachan, J. S.

    1980-05-01

    Hele-Shaw models have been applied for solving two-dimensional, irrotational flow problems such as flow past bodies or radial seepage flow. The gap between the two plates is varied as a cubic parabola in the radial direction. Results are presented for seven axisymmetric models, including a cylindrical body with 60-deg conical head forms, an axisymmetric sluice entrance with a compound elliptical transition and radial flow to a well with a free surface. Pressure distributions were computed and compared with water-tunnel data, wind-tunnel data, finite-differential solutions and exact solutions.

  15. Impingement of supersonic jets on an axisymmetric deflector

    NASA Astrophysics Data System (ADS)

    Prasad, J. K.; Mehta, R. C.; Sreekanth, A. K.

    1994-07-01

    The phenomenon of supersonic jets and their interaction with solid surfaces is found in many engineering applications such as impingement of exhaust from launch vehicles during the liftoff phase, during stage separation of multistage rockets, and VTOL/STOL operation of aircraft, etc. In this paper, experimental and numerical studies are carried out to investigate impingement flowfield produced on a typical axisymmetric jet deflector. The experiments consisted of schlieren flow visualization and measurements of pressure. The present study will be useful for the design of a typical axisymmetric jet deflector during the liftoff phase of a rocket.

  16. Time-dependent closure relations for relativistic collisionless fluid equations.

    PubMed

    Bendib-Kalache, K; Bendib, A; El Hadj, K Mohammed

    2010-11-01

    Linear fluid equations for relativistic and collisionless plasmas are derived. Closure relations for the fluid equations are analytically computed from the relativistic Vlasov equation in the Fourier space (ω,k), where ω and k are the conjugate variables of time t and space x variables, respectively. The mathematical method used is based on the projection operator techniques and the continued fraction mathematical tools. The generalized heat flux and stress tensor are calculated for arbitrary parameter ω/kc where c is the speed of light, and for arbitrary relativistic parameter z=mc²/T , where m is the particle rest mass and T, the plasma temperature in energy units. PMID:21230596

  17. Multiple scattering calculations of relativistic electron energy loss spectra

    NASA Astrophysics Data System (ADS)

    Jorissen, K.; Rehr, J. J.; Verbeeck, J.

    2010-04-01

    A generalization of the real-space Green’s-function approach is presented for ab initio calculations of relativistic electron energy loss spectra (EELS) which are particularly important in anisotropic materials. The approach incorporates relativistic effects in terms of the transition tensor within the dipole-selection rule. In particular, the method accounts for relativistic corrections to the magic angle in orientation resolved EELS experiments. The approach is validated by a study of the graphite CK edge, for which we present an accurate magic angle measurement consistent with the predicted value.

  18. Time-dependent closure relations for relativistic collisionless fluid equations

    SciTech Connect

    Bendib-Kalache, K.; Bendib, A.; El Hadj, K. Mohammed

    2010-11-15

    Linear fluid equations for relativistic and collisionless plasmas are derived. Closure relations for the fluid equations are analytically computed from the relativistic Vlasov equation in the Fourier space ({omega},k), where {omega} and k are the conjugate variables of time t and space x variables, respectively. The mathematical method used is based on the projection operator techniques and the continued fraction mathematical tools. The generalized heat flux and stress tensor are calculated for arbitrary parameter {omega}/kc where c is the speed of light, and for arbitrary relativistic parameter z=mc{sup 2}/T, where m is the particle rest mass and T, the plasma temperature in energy units.

  19. Relativistic Transverse Gravitational Redshift

    NASA Astrophysics Data System (ADS)

    Mayer, A. F.

    2012-12-01

    symmetric energy potential exists between the frames that is quantified by the instantaneous Δ {v} = v\\cdot{d}φ between them; in order for either frame to become indistinguishable from the other, such that their respective velocity and acceleration vectors are parallel, a change in velocity is required. While the qualitative features of general relativity imply this phenomenon (i.e., a symmetric potential difference between two points on a Newtonian `equipotential surface' that is similar to a friction effect), it is not predicted by the field equations due to a modeling error concerning time. This is an error of omission; time has fundamental geometric properties implied by the principles of relativity that are not reflected in the field equations. Where b is the radius and g is the gravitational acceleration characterizing a spherical geoid S of an ideal point-source gravitational field, an elegant derivation that rests on first principles shows that for two points at rest on S separated by a distance d << b, a symmetric relativistic redshift exists between these points of magnitude z = gd2/bc^2, which over 1 km at Earth sea level yields z ˜{10-17}. It can be tested with a variety of methods, in particular laser interferometry. A more sophisticated derivation yields a considerably more complex predictive formula for any two points in a gravitational field.

  20. Sound speed and viscosity of semi-relativistic relic neutrinos

    NASA Astrophysics Data System (ADS)

    Krauss, Lawrence; Long, Andrew J.

    2016-07-01

    Generalized fluid equations, using sound speed ceff2 and viscosity cvis2 as effective parameters, provide a convenient phenomenological formalism for testing the relic neutrino "null hypothesis," i.e. that that neutrinos are relativistic and free-streaming prior to recombination. In this work, we relax the relativistic assumption and ask "to what extent can the generalized fluid equations accommodate finite neutrino mass?" We consider both the mass of active neutrinos, which are largely still relativistic at recombination m2 / T2 ~ 0.2, and the effect of a semi-relativistic sterile component. While there is no one-to-one mapping between mass/mixing parameters and ceff2 and cvis2, we demonstrate that the existence of a neutrino mass could induce a bias to measurements of ceff2 and cvis2 at the level of 0.01 m2 / T2 ~ 10‑3.

  1. Invisibility cloaks in relativistic motion

    NASA Astrophysics Data System (ADS)

    Halimeh, Jad C.; Thompson, Robert T.; Wegener, Martin

    2016-01-01

    We consider an ideal invisibility cloak which is illuminated by monochromatic light and which moves in vacuum at constant relativistic velocity with respect to the common inertial frame of light source and observer. We show that, in general, the moving cloak becomes detectable by image distortions and by generating a broad frequency spectrum of the scattered light. However, for many special combinations of incident light frequency, wave vector of light, and cloak velocity, ideal cloaking remains possible. It becomes nonreciprocal though. This means that light rays emitted by the light source arrive at the observer as though they have traveled through vacuum, but they take completely different paths after being retroreflected at the observer position.

  2. Solitary solutions to a relativistic two-body problem

    NASA Astrophysics Data System (ADS)

    Marcinkevicius, R.; Navickas, Z.; Ragulskis, M.; Telksnys, T.

    2016-06-01

    Necessary and sufficient conditions for the existence of solitary solutions to a generalized model of a two-body problem perturbed by small post-Newtonian relativistic term are derived in this paper. It is demonstrated that kink, bright and dark solitary solutions exist in the model, when the relativistic effects are treated as higher order perturbations. Numerical experiments are used to verify theoretical results.

  3. Superoscillations underlying remote state preparation for relativistic fields

    NASA Astrophysics Data System (ADS)

    Ber, Ran; Kenneth, Oded; Reznik, Benni

    2015-05-01

    We present a physical (gedanken) implementation of a generalized remote state preparation of relativistic quantum field states for an arbitrary set of observers. The prepared states are created in regions that are outside the future light cone of the generating region. The mechanism, which is based on utilizing the vacuum state of a relativistic quantum field as a resource, sheds light on the well known Reeh-Schlieder theorem, indicating its strong connection with the mathematical phenomenon of superoscillations.

  4. Relativistic radiative transfer and relativistic plane-parallel flows

    NASA Astrophysics Data System (ADS)

    Fukue, Jun

    2015-04-01

    Relativistic radiative transfer and relativistic plane-parallel flows accelerated from their base like accretion disk winds are numerically examined under the special relativistic treatment. We first solve the relativistic transfer equation iteratively, using a given velocity field, and obtain specific intensities as well as moment quantities. Using the obtained flux, we then solve the hydrodynamical equation, and obtain the new velocity field and the mass-loss rate as an eigen value. We repeat these double-iteration processes until both the intensity and velocity profiles converge. Under this double iteration, we solve the relativistic radiative transfer equation and relativistic flows in the vertical direction, simultaneously. The flows are gradually accelerated, as the optical depth decreases towards the surface. The mass-loss rate dot{J} is roughly expressed in terms of the optical depth τb and terminal speed βs of the flow as dot{J} ˜ 10 τ_b β _s^{-3/4}.

  5. Non-axisymmetric equilibrium reconstruction for stellarators, reversed field pinches and tokamaks

    NASA Astrophysics Data System (ADS)

    Hanson, J. D.; Anderson, D. T.; Cianciosa, M.; Franz, P.; Harris, J. H.; Hartwell, G. H.; Hirshman, S. P.; Knowlton, S. F.; Lao, L. L.; Lazarus, E. A.; Marrelli, L.; Maurer, D. A.; Schmitt, J. C.; Sontag, A. C.; Stevenson, B. A.; Terranova, D.

    2013-08-01

    Axisymmetric equilibrium reconstruction using magnetohydrodynamic equilibrium solutions to the Grad-Shafranov equation has long been an important tool for interpreting tokamak experiments. This paper describes recent results in non-axisymmetric (three-dimensional) equilibrium reconstruction of nominally axisymmetric plasmas (tokamaks and reversed field pinches (RFPs)), and fully non-axisymmetric plasmas (stellarators). Results from applying the V3FIT code to CTH and HSX stellarator plasmas, RFX-mod RFP plasmas and the DIII-D tokamak are presented.

  6. Local relativistic exact decoupling.

    PubMed

    Peng, Daoling; Reiher, Markus

    2012-06-28

    We present a systematic hierarchy of approximations for local exact decoupling of four-component quantum chemical Hamiltonians based on the Dirac equation. Our ansatz reaches beyond the trivial local approximation that is based on a unitary transformation of only the atomic block-diagonal part of the Hamiltonian. Systematically, off-diagonal Hamiltonian matrix blocks can be subjected to a unitary transformation to yield relativistically corrected matrix elements. The full hierarchy is investigated with respect to the accuracy reached for the electronic energy and for selected molecular properties on a balanced test molecule set that comprises molecules with heavy elements in different bonding situations. Our atomic (local) assembly of the unitary exact-decoupling transformation--called local approximation to the unitary decoupling transformation (DLU)--provides an excellent local approximation for any relativistic exact-decoupling approach. Its order-N(2) scaling can be further reduced to linear scaling by employing a neighboring-atomic-blocks approximation. Therefore, DLU is an efficient relativistic method well suited for relativistic calculations on large molecules. If a large molecule contains many light atoms (typically hydrogen atoms), the computational costs can be further reduced by employing a well-defined nonrelativistic approximation for these light atoms without significant loss of accuracy. We also demonstrate that the standard and straightforward transformation of only the atomic block-diagonal entries in the Hamiltonian--denoted diagonal local approximation to the Hamiltonian (DLH) in this paper--introduces an error that is on the order of the error of second-order Douglas-Kroll-Hess (i.e., DKH2) when compared with exact-decoupling results. Hence, the local DLH approximation would be pointless in an exact-decoupling framework, but can be efficiently employed in combination with the fast to evaluate DKH2 Hamiltonian in order to speed up calculations

  7. Relativistic tidal disruption events

    NASA Astrophysics Data System (ADS)

    Levan, A.

    2012-12-01

    In March 2011 Swift detected an extremely luminous and long-lived outburst from the nucleus of an otherwise quiescent, low luminosity (LMC-like) galaxy. Named Swift J1644+57, its combination of high-energy luminosity (1048 ergs s-1 at peak), rapid X-ray variability (factors of >100 on timescales of 100 seconds) and luminous, rising radio emission suggested that we were witnessing the birth of a moderately relativistic jet (Γ ˜ 2 - 5), created when a star is tidally disrupted by the supermassive black hole in the centre of the galaxy. A second event, Swift J2058+0516, detected two months later, with broadly similar properties lends further weight to this interpretation. Taken together this suggests that a fraction of tidal disruption events do indeed create relativistic outflows, demonstrates their detectability, and also implies that low mass galaxies can host massive black holes. Here, I briefly outline the observational properties of these relativistic tidal flares observed last year, and their evolution over the first year since their discovery.

  8. MHD-stable plasma confinement in an axisymmetric mirror system

    SciTech Connect

    Stupakov, G.V.

    1988-02-01

    If the magnetic field of a nonparaxial mirror system is chosen appropriately, it is possible to maintain a sharp plasma boundary in an open axisymmetric confinement system in a manner which is stable against flute modes (both global and small-scale). Stability prevails in the ideal MHD approximation without finite-ion-Larmor radius effects.

  9. Non-Axisymmetric Shaping of Tokamaks Preserving Quasi-Axisymmetry

    SciTech Connect

    Long-Poe Ku and Allen H. Boozer

    2009-06-05

    If quasi-axisymmetry is preserved, non-axisymmetric shaping can be used to design tokamaks that do not require current drive, are resilient to disruptions, and have robust plasma stability without feedback. Suggestions for addressing the critical issues of tokamaks can only be validated when presented with sufficient specificity that validating experiments can be designed. The purpose of this paper is provide that specificity for non-axisymmetric shaping. To our knowledge, no other suggestions for the solution of a number of tokamak issues, such as disruptions, have reached this level of specificity. Sequences of three-field-period quasi-axisymmetric plasmas are studied. These sequences address the questions: (1) What can be achieved at various levels of non-axisymmetric shaping? (2) What simplifications to the coils can be achieved by going to a larger aspect ratio? (3) What range of shaping can be achieved in a single experimental facility? The sequences of plasmas found in this study provide a set of interesting and potentially important configurations.

  10. Stability of a compound sessile drop at the axisymmetric configuration.

    PubMed

    Zhang, Ying; Chatain, Dominique; Anna, Shelley L; Garoff, Stephen

    2016-01-15

    The equilibrium configuration of compound sessile drops has been calculated previously in the absence of gravity. Using the Laplace equations, we establish seven dimensionless parameters describing the axisymmetric configuration in the presence of gravity. The equilibrium axisymmetric configuration can be either stable or unstable depending on the fluid properties. A stability criterion is established by calculating forces on a perturbed Laplacian shape. In the zero Bond number limit, the stability criterion depends on the density ratio, two ratios of interfacial tensions, the volume ratio of the two drops, and the contact angle. We use Surface Evolver to examine the stability of compound sessile drops at small and large Bond numbers and compare with the zero Bond number approximation. Experimentally, we realize a stable axisymmetric compound sessile drop in air, where the buoyancy force exerted by the air is negligible. Finally, using a pair of fluids in which the density ratio can be tuned nearly independently of the interfacial tensions, the stability transition is verified for the axisymmetric configuration. Even though the perturbations are different for the theory, simulations and experiments, both simulations and experiments agree closely with the zero Bond number approximation, exhibiting a small discrepancy at large Bond number. PMID:26433481

  11. Consistent lattice Boltzmann methods for incompressible axisymmetric flows.

    PubMed

    Zhang, Liangqi; Yang, Shiliang; Zeng, Zhong; Yin, Linmao; Zhao, Ya; Chew, Jia Wei

    2016-08-01

    In this work, consistent lattice Boltzmann (LB) methods for incompressible axisymmetric flows are developed based on two efficient axisymmetric LB models available in the literature. In accord with their respective original models, the proposed axisymmetric models evolve within the framework of the standard LB method and the source terms contain no gradient calculations. Moreover, the incompressibility conditions are realized with the Hermite expansion, thus the compressibility errors arising in the existing models are expected to be reduced by the proposed incompressible models. In addition, an extra relaxation parameter is added to the Bhatnagar-Gross-Krook collision operator to suppress the effect of the ghost variable and thus the numerical stability of the present models is significantly improved. Theoretical analyses, based on the Chapman-Enskog expansion and the equivalent moment system, are performed to derive the macroscopic equations from the LB models and the resulting truncation terms (i.e., the compressibility errors) are investigated. In addition, numerical validations are carried out based on four well-acknowledged benchmark tests and the accuracy and applicability of the proposed incompressible axisymmetric LB models are verified. PMID:27627407

  12. Non-axisymmetric flow characteristics in centrifugal compressor

    NASA Astrophysics Data System (ADS)

    Wang, Leilei; Lao, Dazhong; Liu, Yixiong; Yang, Ce

    2015-06-01

    The flow field distribution in centrifugal compressor is significantly affected by the non-axisymmetric geometry structure of the volute. The experimental and numerical simulation methods were adopted in this work to study the compressor flow field distribution with different flow conditions. The results show that the pressure distributionin volute is characterized by the circumferential non-uniform phenomenon and the pressure fluctuation on the high static pressure zone propagates reversely to upstream, which results in the non-axisymmetric flow inside the compressor. The non-uniform level of pressure distribution in large flow condition is higher than that in small flow condition, its effect on the upstream flow field is also stronger. Additionally, the non-uniform circumferential pressure distribution in volute brings the non-axisymmetric flow at impeller outlet. In different flow conditions,the circumferential variation of the absolute flow angle at impeller outlet is also different. Meanwhile, the non-axisymmetric flow characteristics in internal impeller can be also reflected by the distribution of the mass flow. The high static pressure region of the volute corresponds to the decrease of mass flow in upstream blade channel, while the low static pressure zone of the volute corresponds to the increase of the mass flow. In small flow condition, the mass flow difference in the blade channel is bigger than that in the large flow condition.

  13. Non-Linear Lessons from Axisymmetric Vortex Rings

    NASA Technical Reports Server (NTRS)

    Shariff, Karim; Mansour, Nagi (Technical Monitor)

    2001-01-01

    For presentation at Northwestern University, May 14-28, 2001, the talk will present two types of phenomena, both recognizable to students of nonlinearity, that are exhibited by axisymmetric vortex rings in numerical and laboratory experiments. (1) The first type of phenomenon is reminiscent of inelastic solitons.

  14. Consistent lattice Boltzmann methods for incompressible axisymmetric flows

    NASA Astrophysics Data System (ADS)

    Zhang, Liangqi; Yang, Shiliang; Zeng, Zhong; Yin, Linmao; Zhao, Ya; Chew, Jia Wei

    2016-08-01

    In this work, consistent lattice Boltzmann (LB) methods for incompressible axisymmetric flows are developed based on two efficient axisymmetric LB models available in the literature. In accord with their respective original models, the proposed axisymmetric models evolve within the framework of the standard LB method and the source terms contain no gradient calculations. Moreover, the incompressibility conditions are realized with the Hermite expansion, thus the compressibility errors arising in the existing models are expected to be reduced by the proposed incompressible models. In addition, an extra relaxation parameter is added to the Bhatnagar-Gross-Krook collision operator to suppress the effect of the ghost variable and thus the numerical stability of the present models is significantly improved. Theoretical analyses, based on the Chapman-Enskog expansion and the equivalent moment system, are performed to derive the macroscopic equations from the LB models and the resulting truncation terms (i.e., the compressibility errors) are investigated. In addition, numerical validations are carried out based on four well-acknowledged benchmark tests and the accuracy and applicability of the proposed incompressible axisymmetric LB models are verified.

  15. Distortion of homogeneous turbulence by axisymmetric strain and dilatation

    NASA Technical Reports Server (NTRS)

    Lee, Moon Joo

    1989-01-01

    Rapid distortion theory is applied to study distortion of homogeneous turbulence subject to two different axisymmetric strain modes: the axisymmetric contraction (AC, nozzle-type flow), and the axisymmetric expansion (AE, diffuser-type flow). The paper explores the differences in effects of the two axisymmetric strain modes on the anisotropy of correlations and structures of turbulence; examines the effect of dilatation on the distortion of turbulence; and provides a theoretical background for turbulence model development. It is found that velocity and vorticity fluctuations are enhanced more efficiently by contraction than by expansion; contraction produces much higher anisotropy in velocity and vorticity than expansion; root-mean-square pressure is slightly reduced during contraction, whereas it increases rapidly during expansion; and vortical structures of rodlike shape develop in a contraction flow, while disklike structures develop in an expansion flow. A simple model that reflects the dependence of turbulence evolution on structural parameters such as the Reynolds-stress anisotropy and total strain is proposed, and is shown to outperform all other models for all cases examined, regardless of the mean strain rate.

  16. Non-axisymmetric instabilities in discs with imposed zonal flows

    NASA Astrophysics Data System (ADS)

    Vanon, R.; Ogilvie, G. I.

    2016-09-01

    We conduct a linear stability calculation of an ideal Keplerian flow on which a sinusoidal zonal flow is imposed. The analysis uses the shearing sheet model and is carried out both in isothermal and adiabatic conditions, with and without self-gravity (SG). In the non-SG regime a structure in the potential vorticity (PV) leads to a non-axisymmetric Kelvin-Helmholtz (KH) instability; in the short-wavelength limit its growth rate agrees with the incompressible calculation by Lithwick (2007), which only considers perturbations elongated in the streamwise direction. The instability's strength is analysed as a function of the structure's properties, and zonal flows are found to be stable if their wavelength is ≳ 8H, where H is the disc's scale height, regardless of the value of the adiabatic index γ. The non-axisymmetric KH instability can operate in Rayleigh-stable conditions, and it therefore represents the limiting factor to the structure's properties. Introducing SG triggers a second non-axisymmetric instability, which is found to be located around a PV maximum, while the KH instability is linked to a PV minimum, as expected. In the adiabatic regime, the same gravitational instability is detected even when the structure is present only in the entropy (not in the PV) and the instability spreads to weaker SG conditions as the entropy structure's amplitude is increased. This eventually yields a non-axisymmetric instability in the non-SG regime, albeit of weak strength, localised around an entropy maximum.

  17. Relativistic diffusive motion in thermal electromagnetic fields

    NASA Astrophysics Data System (ADS)

    Haba, Z.

    2013-04-01

    We discuss relativistic dynamics in a random electromagnetic field which can be considered as a high temperature limit of the quantum electromagnetic field in a heat bath (cavity) moving with a uniform velocity w. We derive a diffusion approximation for the particle’s dynamics generalizing the diffusion of Schay and Dudley. It is shown that the Jüttner distribution is the equilibrium state of the diffusion.

  18. Generation and Properties of Large-Scale Non-axisymmetric Magnetic Fields by Solar Dynamo

    NASA Astrophysics Data System (ADS)

    Pipin, Valery; Kosovichev, Alexander

    2015-08-01

    Large-scale non-axisymmetric magnetic fields generated by the solar dynamo, and presumably responsible for the phenomenon of "active longitudes", play an important role in the distribution of solar activity and flares. By calculating 3D mean-field dynamo models, we show that nonlinear coupling between axisymmetric and non-axisymmetric modes, e.g. due to the magnetic feedback on the alpha-effect (see, e.g., [1]), can maintain a large-scale non-axisymmetric dynamo process. Non-axisymmetric random fluctuations of dynamo parameters can be another source for the non-axisymmetric magnetic fields on the Sun. Such fluctuations can provide a mechanism of the magnetic energy transfer from the global field to the non-axisymmetric modes. It is shown that the rotational periods of the non-axisymmetric field correspond to the dynamo process operating in the subsurface shear layer which is located in the range of depths 0.85-0.95R. We find that the magnetic helicity conservation quenches generation of the non-axisymmetric dynamo modes as well as it does for the axisymmetric dynamo. It is concluded that the 3D mean-field non-axisymmetric dynamo models can potentially explain the observed distribution of the solar magnetic activity.1. Moss, D.,Non-axisymmetric solar magnetic fields, 1999, MNRAS, 306, 300On 3/18/2015 2:29 PM, Valery Pipin wrote:

  19. Point form relativistic quantum mechanics and relativistic SU(6)

    NASA Technical Reports Server (NTRS)

    Klink, W. H.

    1993-01-01

    The point form is used as a framework for formulating a relativistic quantum mechanics, with the mass operator carrying the interactions of underlying constituents. A symplectic Lie algebra of mass operators is introduced from which a relativistic harmonic oscillator mass operator is formed. Mass splittings within the degenerate harmonic oscillator levels arise from relativistically invariant spin-spin, spin-orbit, and tensor mass operators. Internal flavor (and color) symmetries are introduced which make it possible to formulate a relativistic SU(6) model of baryons (and mesons). Careful attention is paid to the permutation symmetry properties of the hadronic wave functions, which are written as polynomials in Bargmann spaces.

  20. Collisionless kinetic regimes for quasi-stationary axisymmetric accretion disc plasmas

    SciTech Connect

    Cremaschini, C.; Tessarotto, M.

    2012-08-15

    This paper is concerned with the kinetic treatment of quasi-stationary axisymmetric collisionless accretion disc plasmas. The conditions of validity of the kinetic description for non-relativistic magnetized and gravitationally bound plasmas of this type are discussed. A classification of the possible collisionless plasma regimes which can arise in these systems is proposed, which can apply to accretion discs around both stellar-mass compact objects and galactic-center black holes. Two different classifications are determined, which are referred to, respectively, as energy-based and magnetic field-based classifications. Different regimes are pointed out for each plasma species, depending both on the relative magnitudes of kinetic and potential energies and the magnitude of the magnetic field. It is shown that in all cases, there can be quasi-stationary Maxwellian-like solutions of the Vlasov equation. The perturbative approach outlined here permits unique analytical determination of the functional form for the distribution function consistent, in each kinetic regime, with the explicit inclusion of finite Larmor radius-diamagnetic and/or energy-correction effects.

  1. Relativistic kinetic theory of magnetoplasmas

    SciTech Connect

    Beklemishev, Alexei; Nicolini, Piero; Tessarotto, Massimo

    2005-05-16

    Recently, an increasing interest in astrophysical as well as laboratory plasmas has been manifested in reference to the existence of relativistic flows, related in turn to the production of intense electric fields in magnetized systems. Such phenomena require their description in the framework of a consistent relativistic kinetic theory, rather than on relativistic MHD equations, subject to specific closure conditions. The purpose of this work is to apply the relativistic single-particle guiding-center theory developed by Beklemishev and Tessarotto, including the nonlinear treatment of small-wavelength EM perturbations which may naturally arise in such systems. As a result, a closed set of relativistic gyrokinetic equations, consisting of the collisionless relativistic kinetic equation, expressed in hybrid gyrokinetic variables, and the averaged Maxwell's equations, is derived for an arbitrary four-dimensional coordinate system.

  2. Relativistic electron beam acceleration by Compton scattering of extraordinary waves

    SciTech Connect

    Sugaya, R.

    2006-05-15

    Relativistic transport equations, which demonstrate that relativistic and nonrelativistic particle acceleration along and across a magnetic field and the generation of an electric field transverse to the magnetic field, are induced by nonlinear wave-particle scattering (nonlinear Landau and cyclotron damping) of almost perpendicularly propagating electromagnetic waves in a relativistic magnetized plasma were derived from the relativistic Vlasov-Maxwell equations. The relativistic transport equations show that electromagnetic waves can accelerate particles in the k{sup ''} direction (k{sup ''}=k-k{sup '}). Simultaneously, an intense cross-field electric field, E{sub 0}=B{sub 0}xv{sub d}/c, is generated via the dynamo effect owing to perpendicular particle drift to satisfy the generalized Ohm's law, which means that this cross-field particle drift is identical to the ExB drift. On the basis of these equations, acceleration and heating of a relativistic electron beam due to nonlinear wave-particle scattering of electromagnetic waves in a magnetized plasma were investigated theoretically and numerically. Two electromagnetic waves interact nonlinearly with the relativistic electron beam, satisfying the resonance condition of {omega}{sub k}-{omega}{sub k{sup '}}-(k{sub perpendicular}-k{sub perpendicula=} r{sup '})v{sub d}-(k{sub parallel}-k{sub parallel}{sup '})v{sub b}{approx_equal}m{omega}{sub ce}, where v{sub b} and v{sub d} are the parallel and perpendicular velocities of the relativistic electron beam, respectively, and {omega}{sub ce} is the relativistic electron cyclotron frequency. The relativistic transport equations using the relativistic drifted Maxwellian momentum distribution function of the relativistic electron beam were derived and analyzed. It was verified numerically that extraordinary waves can accelerate the highly relativistic electron beam efficiently with {beta}m{sub e}c{sup 2} < or approx. 1 GeV, where {beta}=(1-v{sub b}{sup 2}/c{sup 2}){sup -1/2}.

  3. Series solution for a cylindrical composite shell subject to axisymmetric loadings

    NASA Astrophysics Data System (ADS)

    Lindstrom, D. W.

    1990-07-01

    Elasticity equations were solved to an arbitrary degree of precision for a thick-walled orthotropic cylinder subject to axisymmetric loading. The theory is directly applicable to a layered composite material where each layer is orthotropic in character. The solution proceeds by representing the deformations of the cylinder wall as a power series in a nondimensional radial parameter. By introducing a generalized stress resultant and a generalized stiffness for the material, a series of coupled second order differential equations in the coefficients of the deformation series results. These were solved using a generalized eigenvalue technique for an infinitely long cylinder, a simply held cylinder, and a rigidly clamped cylinder. The solution was shown to reduce to standard shell solutions for thin cylinders. A thick-walled filament wound test specimen is also described that when fabricated and pressurized would experimentally verify the refined theory developed.

  4. Diagnosed Three-Dimensional Axisymmetric Structure of the Mulhall Tornado on 3 May 1999.

    NASA Astrophysics Data System (ADS)

    Lee, Wen-Chau; Wurman, Joshua

    2005-07-01

    On 3 May 1999, an unusually large tornado that caused F4-level damage and killed several people was intercepted by the Doppler on Wheels (DOW) mobile radar near Mulhall, Oklahoma, from a range of 4 to 9 km, resulting in high-resolution volumetric data every 55 s up to 1.5-km altitude over a period of 14 min. For the first time, the evolution and three-dimensional structure of a tornado were deduced using the ground-based velocity track display (GBVTD) technique. After the circulation center was determined, the tangential wind and radial wind were derived from the GBVTD technique at each radius and height. In addition, the axisymmetric vertical velocity, angular momentum, vorticity, and perturbation pressure were deduced from the tangential and radial wind fields. This study focuses on the axisymmetric aspects of this tornado.The primary circulation of the Mulhall tornado consisted of an 84 ms-1 peak axisymmetric tangential wind with the radius of maximum wind (RMW) ranging from 500 to 1000 m. The secondary circulation exhibited a two-cell structure characterized by a central downdraft surrounded by an annular updraft near the RMW. The calculated maximum pressure deficit from a 3-km radius to the tornado center at 50-m altitude was -80 hPa. The maximum vorticity during the first 8 min of observation was located inside the RMW away from the tornado center. This vorticity profile satisfied the necessary condition of barotropic instability. As the tornado weakened afterward, the vorticity monotonically increased toward the center. The computed swirl ratios were between 2 and 6, consistent with the observed multiple vortex radar signatures and the vorticity pattern. Swirl ratios were generally smaller during the weakening phase.

  5. Relativistic klystron afterburner simulation techniques

    SciTech Connect

    Ryne, R.D.; Jong, R.A.; Westenskow, G.A.; Yu, S.S.

    1990-01-24

    We are developing computer codes for the numerical simulations of relativistic klystrons and relativistic klystron afterburners''. The purpose of this note is to discuss the main features of our numerical model. A relativistic klystron afterburner'' is a scheme to extract power from a spent FEL electron beam. Power is extracted from the beam by passing it through klystron output cavities. To study the feasibility of this concept, we are developing computer codes for the numerical simulation of relativistic klystrons and afterburners. The purpose of this note is to discuss the main features of our numerical model.

  6. Relativistic interactions and realistic applications

    SciTech Connect

    Hoch, T.; Madland, D.; Manakos, P.; Mannel, T.; Nikolaus, B.A.; Strottman, D. |

    1992-12-31

    A four-fermion-coupling Lagrangian (relativistic Skyrme-type) interaction has been proposed for relativistic nuclear structure calculations. This interaction, which has the merit of simplicity, is from the outset tailored as an effective interaction for relativistic Hartree-Fock calculations. Various extensions of such a model are discussed and compared with Walecka`s meson-nucleon mean field approach. We also present results of the calculation of nuclear ground state properties with an extended (density dependent) version of the four fermion interaction in a relativistic Hartree-Fock approximation.

  7. Relativistic differential-difference momentum operators and noncommutative differential calculus

    SciTech Connect

    Mir-Kasimov, R. M.

    2013-09-15

    The relativistic kinetic momentum operators are introduced in the framework of the Quantum Mechanics (QM) in the Relativistic Configuration Space (RCS). These operators correspond to the half of the non-Euclidean distance in the Lobachevsky momentum space. In terms of kinetic momentum operators the relativistic kinetic energy is separated as the independent term of the total Hamiltonian. This relativistic kinetic energy term is not distinguishing in form from its nonrelativistic counterpart. The role of the plane wave (wave function of the motion with definite value of momentum and energy) plays the generating function for the matrix elements of the unitary irreps of Lorentz group (generalized Jacobi polynomials). The kinetic momentum operators are the interior derivatives in the framework of the noncommutative differential calculus over the commutative algebra generated by the coordinate functions over the RCS.

  8. On the asymptotic balance between electric and magnetic energies for hydromagnetic relativistic flows

    SciTech Connect

    Núñez, Manuel

    2013-06-15

    In the equations of classical magnetohydrodynamics, the displacement current is considered vanishingly small due to low plasma velocities. For velocities comparable to the speed of light, the full relativistic electromagnetic equations must be used. In the absence of gravitational forcings and with an isotropic Ohm's law, it is proved that for poloidal magnetic field and velocity and toroidal electric field, the electric and magnetic energies tend to be equivalent in average for large times. This represents a partial extension of Cowling's theorem for axisymmetric fields.

  9. Accuracy of the non-relativistic approximation to relativistic probability densities for a low-speed weak-gravity system

    NASA Astrophysics Data System (ADS)

    Liang, Shiuan-Ni; Lan, Boon Leong

    2015-11-01

    The Newtonian and general-relativistic position and velocity probability densities, which are calculated from the same initial Gaussian ensemble of trajectories using the same system parameters, are compared for a low-speed weak-gravity bouncing ball system. The Newtonian approximation to the general-relativistic probability densities does not always break down rapidly if the trajectories in the ensembles are chaotic -- the rapid breakdown occurs only if the initial position and velocity standard deviations are sufficiently small. This result is in contrast to the previously studied single-trajectory case where the Newtonian approximation to a general-relativistic trajectory will always break down rapidly if the two trajectories are chaotic. Similar rapid breakdown of the Newtonian approximation to the general-relativistic probability densities should also occur for other low-speed weak-gravity chaotic systems since it is due to sensitivity to the small difference between the two dynamical theories at low speed and weak gravity. For the bouncing ball system, the breakdown of the Newtonian approximation is transient because the Newtonian and general-relativistic probability densities eventually converge to invariant densities which are close in agreement.

  10. Extension to an analysis of turbulent swirling compressible flow for application to axisymmetric small gas turbine ducts

    NASA Technical Reports Server (NTRS)

    Anderson, O. L.; Hankins, G. B.; Edwards, D. E.

    1981-01-01

    An existing computer program, the Axisymmetric Diffuser Duct Code (ADD code), which calculates compressible turbulent swirling flow through axisymmetric ducts was modified to permit calculation of flows through small gas turbine ducts with struts, guide vanes and large degrees of turning. The improvements include a coordinate generator, an end-wall loss model, and a generalized geometry capability to describe struts and guide vanes in ducts which turn more than 90 degrees. An improved output format was developed to provide the solution on any arbitrary plane in the duct and an extensive literature survey of calculation procedures used in gas turbine technology was completed which suggests improvements in the computer code. Calculations are presented for the flow through the AGT101 small gas turbine inlet duct and turbine exhaust diffuser which demonstrate the ADD code modifications implemented in the investigation. The computed results compare favorably with experimental results.

  11. Relativistic Quantum Communication

    NASA Astrophysics Data System (ADS)

    Hosler, Dominic

    In this Ph.D. thesis, I investigate the communication abilities of non-inertial observers and the precision to which they can measure parametrized states. I introduce relativistic quantum field theory with field quantisation, and the definition and transformations of mode functions in Minkowski, Schwarzschild and Rindler spaces. I introduce information theory by discussing the nature of information, defining the entropic information measures, and highlighting the differences between classical and quantum information. I review the field of relativistic quantum information. We investigate the communication abilities of an inertial observer to a relativistic observer hovering above a Schwarzschild black hole, using the Rindler approximation. We compare both classical communication and quantum entanglement generation of the state merging protocol, for both the single and dual rail encodings. We find that while classical communication remains finite right up to the horizon, the quantum entanglement generation tends to zero. We investigate the observers' abilities to precisely measure the parameter of a state that is communicated between Alice and Rob. This parameter was encoded to either the amplitudes of a single excitation state or the phase of a NOON state. With NOON states the dual rail encoding provided greater precision, which is different to the results for the other situations. The precision was maximum for a particular number of excitations in the NOON state. We calculated the bipartite communication for Alice-Rob and Alice-AntiRob beyond the single mode approximation. Rob and AntiRob are causally disconnected counter-accelerating observers. We found that Alice must choose in advance with whom, Rob or AntiRob she wants to create entanglement using a particular setup. She could communicate classically to both.

  12. A covariant Fokker-Planck equation for a simple gas from relativistic kinetic theory

    SciTech Connect

    Chacon-Acosta, Guillermo; Dagdug, Leonardo; Morales-Tecotl, Hugo A.

    2010-12-14

    A manifestly covariant Fokker-Planck differential equation is derived for the case of a relativistic simple gas by taking a small momentum transfer approximation within the collision integral of the relativistic Boltzmann equation. We follow closely previous work, with the main difference that we keep manifest covariance at every stage of the analysis. In addition, we use the covariant Juettner distribution function to find a relativistic generalization of the Einstein's fluctuation-dissipation relation.

  13. Frequency agile relativistic magnetrons

    SciTech Connect

    Levine, J.S.; Harteneck, B.D.; Price, H.D.

    1995-11-01

    The authors are developing a family of frequency agile relativistic magnetrons to continuously cover the bands from 1 to 3 GHz. They have achieved tuning ranges of > 33%. The magnetrons have been operated repetitively in burst mode at rates up to 100 pps for 10 sec. Power is extracted from two resonators, and is in the range of 400--600 MW, fairly flat across the tuning bandwidth. They are using a network of phase shifters and 3-dB hybrids to combine the power into a single arm and to provide a continuously adjustable attenuator.

  14. Relativistic nuclear collisions: theory

    SciTech Connect

    Gyulassy, M.

    1980-07-01

    Some of the recent theoretical developments in relativistic (0.5 to 2.0-GeV/nucleon) nuclear collisions are reviewed. The statistical model, hydrodynamic model, classical equation of motion calculations, billiard ball dynamics, and intranuclear cascade models are discussed in detail. Inclusive proton and pion spectra are analyzed for a variety of reactions. Particular attention is focused on how the complex interplay of the basic reaction mechanism hinders attempts to deduce the nuclear matter equation of state from data. 102 references, 19 figures.

  15. Ultrabaric relativistic superfluids

    NASA Astrophysics Data System (ADS)

    Papini, G.; Weiss, M.

    1985-09-01

    Ultrabaric superfluid solutions are obtained for Einstein's equations to examine the possibility of the existence of superluminal sound speeds. The discussion is restricted only by requiring the energy-momentum tensor and the equation of state of matter to be represented by full relativistic equations. Only a few universes are known to satisfy the conditions, and those exhibit tension and are inflationary. Superluminal sound velocities are shown, therefore, to be possible for the interior Schwarzchild metric, which has been used to explain the red shift of quasars, and the Stephiani solution (1967). The latter indicates repeated transitions between superluminal and subliminal sound velocities in the hyperbaric superfluid of the early universe.

  16. Modeling relativistic nuclear collisions.

    SciTech Connect

    Anderlik, C.; Magas, V.; Strottman, D.; Csernai, L. P.

    2001-01-01

    Modeling Ultra-Relativistic Heavy Ion Collisioiis at RHIC and LHC energies using a Multi Module Model is presented. The first Module is the Effective String Rope Model for the calculation of the initial stages of the reaction; the output of this module is used as the initial state for the subsequent one-fluid hydrodynainical calculation module. It is shown that such an initial state leads to the creation of the third flow component. The hydrodynamical evolution of the energy density distribution is presented for RHIC energies. The final module describing the Freeze Out; and Hadronization is also discussed.

  17. Relativistic apsidal motion in eccentric eclipsing binaries

    NASA Astrophysics Data System (ADS)

    Wolf, M.; Claret, A.; Kotková, L.; Kučáková, H.; Kocián, R.; Brát, L.; Svoboda, P.; Šmelcer, L.

    2010-01-01

    Context. The study of apsidal motion in detached eclipsing binary systems is known to be an important source of information about stellar internal structure as well as the possibility of verifying of General Relativity outside the Solar System. Aims: As part of the long-term Ondřejov and Ostrava observational projects, we aim to measure precise times of minima for eccentric eclipsing binaries, needed for the accurate determination of apsidal motion, providing a suitable test of the effects of General Relativity. Methods: About seventy new times of minimum light recorded with photoelectric or CCD photometers were obtained for ten eccentric-orbit eclipsing binaries with significant relativistic apsidal motion. Their O-C diagrams were analysed using all reliable timings found in the literature, and new or improved elements of apsidal motion were obtained. Results: We confirm very long periods of apsidal motion for all systems. For BF Dra and V1094 Tau, we present the first apsidal-motion solution. The relativistic effects are dominant, representing up to 100% of the total observable apsidal-motion rate in several systems. The theoretical and observed values of the internal structure constant k 2 were compared for systems with lower relativistic contribution. Using the light-time effect solution, we predict a faint third component for V1094 Tau orbiting with a short period of about 8 years. Partly based on photoelectric observations secured at the Hvar Observatory, Faculty of Geodesy, Zagreb, Croatia, in October 2008.

  18. Texas Symposium on Relativistic Astrophysics, 11th, Austin, TX, December 12-17, 1982, Proceedings

    NASA Technical Reports Server (NTRS)

    Evans, D. S. (Editor)

    1984-01-01

    Various papers on relativistic astrophysics are presented. The general subjects addressed include: particle physics and astrophysics, general relativity, large-scale structure, big bang cosmology, new-generation telescopes, pulsars, supernovae, high-energy astrophysics, and active galaxies.

  19. Adaptive Mesh Refinement Simulations of Relativistic Binaries

    NASA Astrophysics Data System (ADS)

    Motl, Patrick M.; Anderson, M.; Lehner, L.; Olabarrieta, I.; Tohline, J. E.; Liebling, S. L.; Rahman, T.; Hirschman, E.; Neilsen, D.

    2006-09-01

    We present recent results from our efforts to evolve relativistic binaries composed of compact objects. We simultaneously solve the general relativistic hydrodynamics equations to evolve the material components of the binary and Einstein's equations to evolve the space-time. These two codes are coupled through an adaptive mesh refinement driver (had). One of the ultimate goals of this project is to address the merger of a neutron star and black hole and assess the possible observational signature of such systems as gamma ray bursts. This work has been supported in part by NSF grants AST 04-07070 and PHY 03-26311 and in part through NASA's ATP program grant NAG5-13430. The computations were performed primarily at NCSA through grant MCA98N043 and at LSU's Center for Computation & Technology.

  20. Multidimensional numerical scheme for resistive relativistic magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

    Komissarov, Serguei S.

    2007-12-01

    The paper describes a new upwind conservative numerical scheme for special relativistic resistive magnetohydrodynamics with scalar resistivity. The magnetic field is kept approximately divergence free and the divergence of the electric field is kept consistent with the electric charge distribution via the method of Generalized Lagrange Multiplier. The hyperbolic fluxes are computed using the Harten-Lax-van Leer (HLL) prescription and the source terms are accounted via the time-splitting technique. The results of test simulations show that the scheme can handle equally well both resistive current sheets and shock waves, and thus can be a useful tool for studying phenomena of relativistic astrophysics that involve both colliding supersonic flows and magnetic reconnection.

  1. Fluid dynamical description of relativistic nuclear collisions

    NASA Technical Reports Server (NTRS)

    Nix, J. R.; Strottman, D.

    1982-01-01

    On the basis of both a conventional relativistic nuclear fluid dynamic model and a two fluid generalization that takes into account the interpenetration of the target and projectile upon contact, collisions between heavy nuclei moving at relativistic speeds are calculated. This is done by solving the relevant equations of motion numerically in three spatial dimensions by use of particle in cell finite difference computing techniques. The effect of incorporating a density isomer, or quasistable state, in the nuclear equation of state at three times normal nuclear density, and the effect of doubling the nuclear compressibility coefficient are studied. For the reaction 20Ne + 238U at a laboratory bombarding energy per nucleon of 393 MeV, the calculated distributions in energy and angle of outgoing charged particles are compared with recent experimental data both integrated over all impact parameters and for nearly central collisions.

  2. Graphical evaluation of relativistic matrix elements

    NASA Technical Reports Server (NTRS)

    Huang, K. N.

    1978-01-01

    A graphical representation of angular momentum was used to evaluate relativistic matrix elements between antisymmetrized states of many particle configurations having any number of open shells. The antisymmetrized matrix element was expanded as a sum of semisymmetrized matrix elements. The diagram representing a semisymmetrized matrix element was composed of four diagram blocks; the bra block, the ket block, the spectator block, and the interaction block. The first three blocks indicate the couplings of the two interacting configurations while the last depends on the interaction and is the replaceable component. Interaction blocks for relativistic operators and commonly used potentials were summarized in ready to use forms. A simple step by step procedure was prescribed generally for calculating antisymmetrized matrix elements of one and two particle operators.

  3. On the vibration of axisymmetric shells

    NASA Astrophysics Data System (ADS)

    Heppler, G. R.; Wahl, L.

    1989-05-01

    The application of nonconventional basis functions to the linear vibration problem is explored. By employing shell coordinates the elements allow the exact geometrical modelling of shells of revolution with arbitrary meridians and the elements are able to reproduce strain free states under an arbitrary rigid body motion due to the use of these special basis functions. A generalization of the Reissner Mindlin plate theories is used because they have a broader range of applicability than the usual thin/shallow shell theories and also the trial functions need only be of class C(sup 0). The geometry treated is a hyperbola of revolution, in two configurations.

  4. Relativistic generation of vortex and magnetic field a)

    NASA Astrophysics Data System (ADS)

    Mahajan, S. M.; Yoshida, Z.

    2011-05-01

    The implications of the recently demonstrated relativistic mechanism for generating generalized vorticity in purely ideal dynamics [Mahajan and Yoshida, Phys. Rev. Lett. 105, 095005 (2010)] are worked out. The said mechanism has its origin in the space-time distortion caused by the demands of special relativity; these distortions break the topological constraint (conservation of generalized helicity) forbidding the emergence of magnetic field (a generalized vorticity) in an ideal nonrelativistic dynamics. After delineating the steps in the "evolution" of vortex dynamics, as the physical system goes from a nonrelativistic to a relativistically fast and hot plasma, a simple theory is developed to disentangle the two distinct components comprising the generalized vorticity—the magnetic field and the thermal-kinetic vorticity. The "strength" of the new universal mechanism is, then, estimated for a few representative cases; in particular, the level of seed fields, created in the cosmic setting of the early hot universe filled with relativistic particle-antiparticle pairs (up to the end of the electron-positron era), are computed. Possible applications of the mechanism in intense laser produced plasmas are also explored. It is suggested that highly relativistic laser plasma could provide a laboratory for testing the essence of the relativistic drive.

  5. Space-based Tests of Relativistic Gravitation

    NASA Astrophysics Data System (ADS)

    Turyshev, Vyacheslav G.

    Since its initial publication, Einstein's general theory of relativity had been tested to a very high precision and presently is considered to be the standard theory of gravitation, especially when the phenomena in astrophysics, cosmology, and fundamental physics are concerned. As such, this theory has many practically important applications including spacecraft navigation, relativistic geodesy, time transfer, etc. Here we discuss the foundations of general relativity, present its current empirical status, and highlight the need for the new generation of high-accuracy tests. We present some space-based gravitational experiments and discuss anticipated advances in our understanding of the fundamental laws of nature.

  6. A Simple Relativistic Bohr Atom

    ERIC Educational Resources Information Center

    Terzis, Andreas F.

    2008-01-01

    A simple concise relativistic modification of the standard Bohr model for hydrogen-like atoms with circular orbits is presented. As the derivation requires basic knowledge of classical and relativistic mechanics, it can be taught in standard courses in modern physics and introductory quantum mechanics. In addition, it can be shown in a class that…

  7. Nonlinear optics in relativistic plasmas.

    PubMed

    Umstadter, D; Chen, S Y; Wagner, R; Maksimchuk, A; Sarkisov, G

    1998-03-30

    We review our recent work on the various nonlinear optical processes that occur as an intense laser propagates through a relativistic plasma. These include the experimental observations of electron acceleration driven by laser-wakefield generation, relativistic self-focusing, waveguide formation and laser self-channeling. PMID:19377614

  8. relline: Relativistic line profiles calculation

    NASA Astrophysics Data System (ADS)

    Dauser, Thomas

    2015-05-01

    relline calculates relativistic line profiles; it is compatible with the common X-ray data analysis software XSPEC (ascl:9910.005) and ISIS (ascl:1302.002). The two basic forms are an additive line model (RELLINE) and a convolution model to calculate relativistic smearing (RELCONV).

  9. Calculations of the stability of some axisymmetric flows proposed as a model of vortex breakdown

    NASA Technical Reports Server (NTRS)

    Mhuiris, N. M. G.

    1986-01-01

    The term vortex breakdown refers to the abrupt and drastic changes of structure that can sometimes occur in swirling flows. It was conjectured that the bubble type of breakdown can be viewed as an axisymmetric wave traveling upstream in a primarily columnar vortex flow. In this scenario the wave's upstream progress is impeded only when it reaches a critical amplitude and it loses stability to some nonaxisymmetric disturbance. The stability of some axisymmetric wavy flows to three dimensional disturbances, viewing the amplitude of the wave as a bifurcation parameter is examined. The stability of a set of related columnar vortex flows, constructed by taking the two dimensional flow at a single axial location and extending it throughout the domain without variation, is investigated. The method used will be to expand the perturbation velocity in a series of divergence free vectors which ensures that the continuity equation for the incompressible fluid is satisfied exactly by the computed velocity field. Projections of the stability equation onto the space of inviscid vector fields eliminated the pressure term from the equation and reduces the differential eigen problem to a generalized matrix eigen problem. Results are presented both for the one dimensional, columnar vortex flows and also for the wavy bubble flow.

  10. Perturbed particle orbits and kinetic plasma response in non-axisymmetric tokamaks

    NASA Astrophysics Data System (ADS)

    Kim, Kimin; Park, J.-K.; Boozer, A. H.; Logan, N. C.; Wang, Z. R.; Menard, J. E.

    2014-10-01

    Non-axisymmetric magnetic fields interact with the drift trajectories of ions and electrons to create an anisotropic plasma pressure. The force produced by the gradient of this anisotropic pressure produces a torque, the Neoclassical Toroidal Viscosity (NTV), which tends to relax the plasma rotation to a specific offset rotation, and modifies the energy required to perturb the plasma. Complexities, such as resonances of the ExB drift with particle bounce frequencies, finite orbit width, and full collisional effects, require full numerical simulation to determine the NTV and the perturbation energy. The POCA delta-f drift kinetic particle code has been used to: (1) demonstrate the existence of the bounce resonances with the ExB drift and show that they often dominate the magnitude of the NTV, (2) show the NTV of perturbations with different toroidal mode numbers are generally decoupled, and (3) verify a quadratic NTV dependence on the asymmetric magnetic field. Such results imply the pressure anisotropy is linear in the magnetic perturbation and can produce a significant change in the applied non-axisymmetric field. Progress on integrating this pressure anisotropy into a perturbed equilibrium solver to obtain self-consistent solutions is presented. This work was supported by US DOE Contract DE-AC02-09CH11466.

  11. A numerical study of global axisymmetric states and their stability to quasi-geostrophic disturbances

    NASA Technical Reports Server (NTRS)

    Henderson, H. W.; Dutton, J. A.

    1985-01-01

    A steady, axisymmetric model of the general circulation is developed as a basis for climate stability studies. The model includes the effects of heating, rotation, and internal friction, but neglects topography. It is assumed that the axisymmetric flow may be modeled by making the Boussinesq and deep convection approximations. The hydrostatic assumption is not made, thus permitting the advective terms to be included in the vertical equation of motion. The initial set of five primitive equations is reduced to three equations in terms of the zonal velocity, meridional streamfunction, and the potential temperature perturbation. The application of the Boussinesq, deep convection, and quasi-geostrophic assumptions limits the ranges of the heating and rotation rates. For values not too far from typical atmospheric values, the model produces a stability boundary separating Hadley from Rossby flow. The boundary is characterized by a particular value of vertical wind shear, which suggests that baroclinic instability is the primary mechanism for the loss of stability. The initial growth rates are largest for longitudinal waves 4-7, also in agreement with studies of baroclinic instability.

  12. Relativistic jets in astrophysics

    NASA Astrophysics Data System (ADS)

    Derishev, E. V.; Zheleznyakov, V. V.; Koryagin, S. A.; Kocharovsky, Vl. V.

    The properties of the plasma state of matter are determined by the motion and the electromagnetic emission of the non-bound electrically charged particles --- electrons, positrons, protons and ions. It is not easy to create plasma in a laboratory. However this state is typical for the cosmic conditions --- at the stars and in the interstellar space. The properties of the laboratory as well as the space plasma are investigated at the Institute of Applied Physics of the Russian Academy of Sciences. The research is focused on the mechanisms of generation and propagation of the electromagnetic radiation --- from the radio waves to the gamma-rays --- in the planetary and stellar atmospheres and at the other astrophysical objects. The extreme physical conditions for a plasma are realized near the compact objects like black holes, neutron stars and collapsing nuclei of the massive stars. The plasma could be strongly non-equlibrium and can produce strong electromagnetic fields. Its bulk motion as well as the chaotic motion of the constituting particles can be relativistic, i. e. the motion can achieve velocities close to the speed of light. The relativistic plasma is frequently observed in the form of jets.

  13. A relativistic trolley paradox

    NASA Astrophysics Data System (ADS)

    Matvejev, Vadim N.; Matvejev, Oleg V.; Grøn, Ø.

    2016-06-01

    We present an apparent paradox within the special theory of relativity, involving a trolley with relativistic velocity and its rolling wheels. Two solutions are given, both making clear the physical reality of the Lorentz contraction, and that the distance on the rails between each time a specific point on the rim touches the rail is not equal to 2 π R , where R is the radius of the wheel, but 2 π R / √{ 1 - R 2 Ω 2 / c 2 } , where Ω is the angular velocity of the wheels. In one solution, the wheel radius is constant as the velocity of the trolley increases, and in the other the wheels contract in the radial direction. We also explain two surprising facts. First that the shape of a rolling wheel is elliptical in spite of the fact that the upper part of the wheel moves faster than the lower part, and thus is more Lorentz contracted, and second that a Lorentz contracted wheel with relativistic velocity rolls out a larger distance between two successive touches of a point of the wheel on the rails than the length of a circle with the same radius as the wheels.

  14. Relativistic harmonic oscillator revisited

    SciTech Connect

    Bars, Itzhak

    2009-02-15

    The familiar Fock space commonly used to describe the relativistic harmonic oscillator, for example, as part of string theory, is insufficient to describe all the states of the relativistic oscillator. We find that there are three different vacua leading to three disconnected Fock sectors, all constructed with the same creation-annihilation operators. These have different spacetime geometric properties as well as different algebraic symmetry properties or different quantum numbers. Two of these Fock spaces include negative norm ghosts (as in string theory), while the third one is completely free of ghosts. We discuss a gauge symmetry in a worldline theory approach that supplies appropriate constraints to remove all the ghosts from all Fock sectors of the single oscillator. The resulting ghost-free quantum spectrum in d+1 dimensions is then classified in unitary representations of the Lorentz group SO(d,1). Moreover, all states of the single oscillator put together make up a single infinite dimensional unitary representation of a hidden global symmetry SU(d,1), whose Casimir eigenvalues are computed. Possible applications of these new results in string theory and other areas of physics and mathematics are briefly mentioned.

  15. Relativistic Continuum Shell Model

    NASA Astrophysics Data System (ADS)

    Grineviciute, Janina; Halderson, Dean

    2011-04-01

    The R-matrix formalism of Lane and Thomas has been extended to the relativistic case so that the many-coupled channels problem may be solved for systems in which binary breakup channels satisfy a relative Dirac equation. The formalism was previously applied to the relativistic impulse approximation RIA and now we applied it to Quantum Hadrodynamics QHD in the continuum Tamm-Dancoff approximation TDA with the classical meson fields replaced by one-meson exchange potentials. None of the published QHD parameters provide a decent fit to the 15 N + p elastic cross section. The deficiency is also evident in inability of the QHD parameters with the one meson exchange potentials to reproduce the QHD single particle energies. Results with alternate parameters sets are presented. A. M. Lane and R. G. Thomas, R-Matrix Theory of Nuclear Reactions, Reviews of Modern Physics, 30 (1958) 257

  16. Non-axisymmetric instability of core-annular flow

    NASA Astrophysics Data System (ADS)

    Hu, Howard H.; Patankar, Neelesh

    1995-05-01

    Stability of core-annular flow of water and oil in a vertical circular pipe is studied with respect to non-axisymmetric disturbances. Results show that when the oil core is thin, the flow is most unstable to the asymmetric sinuous mode of disturbance, and the core moves in the form of corkscrew waves as observed in experiments. The asymmetric mode of disturbance is the most dangerous mode for quite a wide range of material and flow parameters. This asymmetric mode persists in vertical pipes with upward and downward flows and in horizontal pipes. The analysis also applies to the instability of freely rising axisymmetric cigarette smoke or a thermal plume. The study predicts a unique wavelength for the asymmetric meandering waves.

  17. Modeling the Orion nebula as an axisymmetric blister

    NASA Technical Reports Server (NTRS)

    Rubin, R. H.; Simpson, J. P.; Haas, M. R.; Erickson, E. F.

    1991-01-01

    The ionized gas in the Orion nebula is examined by means of axisymmetric modeling that is based on observational data from the ionized, neutral, and molecular regions. Nonsymmetrical features are omitted, radial dependence from the Trapezium is assumed, and azimuthal symmetry in the plane of the sky is used. Stellar properties and abundances of certain elements are described, and these data are used to compare the present axisymmetric-blister model to a previous spherical model. Strong singly-ionized emission that are visible near the Trapezium are found to originate in the ionization-bounded region in the dense Trapezium zone. The model can be more tightly constrained by adding near-IR data on noncentral zones for (Ar II), (AR III), (Ne II), and (S IV). The quadrant with the 'bar' creates an nonsymmetry that influences the observational data, and the model can therefore be improved with the additional data.

  18. Application of the PTT model to axisymmetric free surface flows

    NASA Astrophysics Data System (ADS)

    Merejolli, R.; Paulo, G. S.; Tomé, M. F.

    2013-10-01

    This work is concerned with numerical simulation of axisymmetric viscoelastic free surface flows using the Phan-Thien-Tanner (PTT) constitutive equation. A finite difference technique for solving the governing equations for unsteady incompressible flows written in Cylindrical coordinates on a staggered grid is described. The fluid is modelled by a Marker-and-Cell type method and an accurate representation of the fluid surface is employed. The full free surface stress conditions are applied. The numerical method is verified by comparing numerical predictions of fully developed flow in a pipe with the corresponding analytic solutions. To demonstrate that the numerical method can simulate axisymmetric free surface flows governed by the PTT model, numerical results of the flow evolution of a drop impacting on a rigid dry plate are presented. In these simulations, the rheological effects of the parameters ɛ and ξ are investigated.

  19. Design optimization of axisymmetric bodies in nonuniform transonic flow

    NASA Technical Reports Server (NTRS)

    Lan, C. Edward

    1989-01-01

    An inviscid transonic code capable of designing an axisymmetric body in a uniform or nonuniform flow was developed. The design was achieved by direct optimiation by coupling an analysis code with an optimizer. Design examples were provided for axisymmetric bodies with fineness ratios of 8.33 and 5 at different Mach numbers. It was shown that by reducing the nose radius and increasing the afterbody thickness of initial shapes obtained from symmetric NACA four-digit airfoil contours, wave drag could be reduced by 29 percent for a body of fineness ratio 8.33 in a nonuniform transonic flow of M = 0.98 to 0.995. The reduction was 41 percent for a body of fineness ratio 5 in a uniform transonic flow of M = 0.925 and 65 percent for the same body but in a nonuniform transonic flow of M = 0.90 to 0.95.

  20. The inviscid axisymmetric stability of the supersonic flow along a circular cylinder

    NASA Technical Reports Server (NTRS)

    Duck, Peter W.

    1990-01-01

    The supersonic flow past a thin straight circular cylinder is investigated. The associated boundary-layer flow (i.e. the velocity and temperature field) is computed; the asymptotic, far downstream solution is obtained, and compared with the full numerical results. The inviscid, linear, axisymmetric (temporal) stability of this boundary layer is also studied. A so-called 'doubly generalized' inflexion condition is derived, which is a condition for the existence of so-called 'subsonic' neutral modes. The eigenvalue problem (for the complex wavespeed) is computed for two free-stream Mach numbers (2.8 and 3.8), and this reveals that curvature has a profound effect on the stability of the flow. The first unstable inviscid mode is seen to disappear rapidly as curvature is introduced, while the second (and generally the most important) mode suffers a substantially reduced amplification rate.

  1. The inviscid axisymmetric stability of the supersonic flow along a circular cylinder

    NASA Technical Reports Server (NTRS)

    Duck, Peter W.

    1989-01-01

    The supersonic flow past a thin straight circular cylinder is investigated. The associated boundary layer flow (i.e., the velocity and temperature field) is computed; the asymptotic, far downstream solution is obtained, and compared with the full numerical results. The inviscid, linear, axisymmetric (temporal) stability of this boundary layer is also studied. A so called doubly generalized inflexion condition is derived, which is a condition for the existence of so called subsonic neutral modes. The eigenvalue problem (for the complex wavespeed) is computed for two freestream Mach numbers (2.8 and 3.8), and this reveals that curvature has a profound effect on the stability of the flow. The first unstable inviscid mode is seen to rapidly disappear as curvature is introduced, while the second (and generally the most important) mode suffers a substantially reduced amplification rate.

  2. Particle acceleration and non-thermal emission in Pulsar Wind Nebulae from relativistic MHD simulations

    NASA Astrophysics Data System (ADS)

    Olmi, B.; Del Zanna, L.; Amato, E.; Bucciantini, N.; Bandiera, R.

    2015-09-01

    Pulsar wind nebulae are among the most powerful particle accelerators in the Galaxy with acceleration efficiencies that reach up to 30% and maximum particle energies in the PeV range. In recent years relativistic axisymmetric MHD models have proven to be excellent tools for describing the physics of such objects, and particularly successful at explaining their high energy morphology, down to very fine details. Nevertheless, some important aspects of the physics of PWNe are still obscure: the mechanism(s) responsible for the acceleration of particles of all energies is (are) still unclear, and the origin of the lowest energy (radio emitting) particles is most mysterious. The correct interpretation of the origin of radio emitting particles is of fundamental importance, as this holds information about the amount of pair production in the pulsar magnetosphere, and hence on the role of pulsars as antimatter factories. On the other hand, the long lifetimes of these particles against synchrotron losses, allows them to travel far from their injection location, making their acceleration site difficult to constrain. As far as the highest energy (X and gamma-ray emitting) particles are concerned, their acceleration is commonly believed to occur at the pulsar wind termination shock. But since the upstream flow is thought to have non-uniform properties along the shock surface, important constraints on the acceleration mechanism(s) could come from exact knowledge of the location and flow properties where particles are being accelerated. We investigate in detail both topics by means of 2D numerical MHD simulations. Different assumptions on the origin of radio particles and more generally on the injection sites of all particles are considered, and the corresponding emission properties are computed. We discuss the physical constraints that can be inferred from comparison of the synthetic emission properties against multiwavelength observations of the PWN class prototype, the Crab

  3. Fractional Relativistic Yamaleev Oscillator Model and Its Dynamical Behaviors

    NASA Astrophysics Data System (ADS)

    Luo, Shao-Kai; He, Jin-Man; Xu, Yan-Li; Zhang, Xiao-Tian

    2016-07-01

    In the paper we construct a new kind of fractional dynamical model, i.e. the fractional relativistic Yamaleev oscillator model, and explore its dynamical behaviors. We will find that the fractional relativistic Yamaleev oscillator model possesses Lie algebraic structure and satisfies generalized Poisson conservation law. We will also give the Poisson conserved quantities of the model. Further, the relation between conserved quantities and integral invariants of the model is studied and it is proved that, by using the Poisson conserved quantities, we can construct integral invariants of the model. Finally, the stability of the manifold of equilibrium states of the fractional relativistic Yamaleev oscillator model is studied. The paper provides a general method, i.e. fractional generalized Hamiltonian method, for constructing a family of fractional dynamical models of an actual dynamical system.

  4. The relativistic equations of stellar structure and evolution. Stars with degenerate neutron cores. 1: Structure of equilibrium models

    NASA Technical Reports Server (NTRS)

    Thorne, K. S.; Zytkow, A. N.

    1976-01-01

    The general relativistic equations of stellar structure and evolution are reformulated in a notation which makes easy contact with Newtonian theory. Also, a general relativistic version of the mixing-length formalism for convection is presented. Finally, it is argued that in previous work on spherical systems general relativity theorists have identified the wrong quantity as "total mass-energy inside radius r."

  5. Toroidal angular momentum transport with non-axisymmetric magnetic fields

    NASA Astrophysics Data System (ADS)

    Seol, J.; Park, B. H.

    2016-05-01

    In this study, we calculate the radial transport of the toroidal angular momentum in the presence of non-axisymmetric magnetic fields. It is shown that the radial transport of the toroidal angular momentum, R 2 ∇ ζ . V , is proportional to the first order of gyro-radius. This implies that the neoclassical toroidal viscosity caused by asymmetric magnetic fields can change the toroidal rotation significantly.

  6. Resonant Absorption of Axisymmetric Modes in Twisted Magnetic Flux Tubes

    NASA Astrophysics Data System (ADS)

    Giagkiozis, I.; Goossens, M.; Verth, G.; Fedun, V.; Van Doorsselaere, T.

    2016-06-01

    It has been shown recently that magnetic twist and axisymmetric MHD modes are ubiquitous in the solar atmosphere, and therefore the study of resonant absorption for these modes has become a pressing issue because it can have important consequences for heating magnetic flux tubes in the solar atmosphere and the observed damping. In this investigation, for the first time, we calculate the damping rate for axisymmetric MHD waves in weakly twisted magnetic flux tubes. Our aim is to investigate the impact of resonant damping of these modes for solar atmospheric conditions. This analytical study is based on an idealized configuration of a straight magnetic flux tube with a weak magnetic twist inside as well as outside the tube. By implementing the conservation laws derived by Sakurai et al. and the analytic solutions for weakly twisted flux tubes obtained recently by Giagkiozis et al. we derive a dispersion relation for resonantly damped axisymmetric modes in the spectrum of the Alfvén continuum. We also obtain an insightful analytical expression for the damping rate in the long wavelength limit. Furthermore, it is shown that both the longitudinal magnetic field and the density, which are allowed to vary continuously in the inhomogeneous layer, have a significant impact on the damping time. Given the conditions in the solar atmosphere, resonantly damped axisymmetric modes are highly likely to be ubiquitous and play an important role in energy dissipation. We also suggest that, given the character of these waves, it is likely that they have already been observed in the guise of Alfvén waves.

  7. Small Engine Technology (SET) - Task 14 Axisymmetric Engine Simulation Environment

    NASA Technical Reports Server (NTRS)

    Miller, Max J.

    1999-01-01

    As part of the NPSS (Numerical Propulsion Simulation System) project, NASA Lewis has a goal of developing an U.S. industry standard for an axisymmetric engine simulation environment. In this program, AlliedSignal Engines (AE) contributed to this goal by evaluating the ENG20 software and developing support tools. ENG20 is a NASA developed axisymmetric engine simulation tool. The project was divided into six subtasks which are summarized below: Evaluate the capabilities of the ENG20 code using an existing test case to see how this procedure can capture the component interactions for a full engine. Link AE's compressor and turbine axisymmetric streamline curvature codes (UD0300M and TAPS) with ENG20, which will provide the necessary boundary conditions for an ENG20 engine simulation. Evaluate GE's Global Data System (GDS), attempt to use GDS to do the linking of codes described in Subtask 2 above. Use a turbofan engine test case to evaluate various aspects of the system, including the linkage of UD0300M and TAPS with ENG20 and the GE data storage system. Also, compare the solution results with cycle deck results, axisymmetric solutions (UD0300M and TAPS), and test data to determine the accuracy of the solution. Evaluate the order of accuracy and the convergence time for the solution. Provide a monthly status report and a final formal report documenting AE's evaluation of ENG20. Provide the developed interfaces that link UD0300M and TAPS with ENG20, to NASA. The interface that links UD0300M with ENG20 will be compatible with the industr,, version of UD0300M.

  8. Axisymmetric Implementation for 3D-Based DSMC Codes

    NASA Technical Reports Server (NTRS)

    Stewart, Benedicte; Lumpkin, F. E.; LeBeau, G. J.

    2011-01-01

    The primary objective in developing NASA s DSMC Analysis Code (DAC) was to provide a high fidelity modeling tool for 3D rarefied flows such as vacuum plume impingement and hypersonic re-entry flows [1]. The initial implementation has been expanded over time to offer other capabilities including a novel axisymmetric implementation. Because of the inherently 3D nature of DAC, this axisymmetric implementation uses a 3D Cartesian domain and 3D surfaces. Molecules are moved in all three dimensions but their movements are limited by physical walls to a small wedge centered on the plane of symmetry (Figure 1). Unfortunately, far from the axis of symmetry, the cell size in the direction perpendicular to the plane of symmetry (the Z-direction) may become large compared to the flow mean free path. This frequently results in inaccuracies in these regions of the domain. A new axisymmetric implementation is presented which aims to solve this issue by using Bird s approach for the molecular movement while preserving the 3D nature of the DAC software [2]. First, the computational domain is similar to that previously used such that a wedge must still be used to define the inflow surface and solid walls within the domain. As before molecules are created inside the inflow wedge triangles but they are now rotated back to the symmetry plane. During the move step, molecules are moved in 3D but instead of interacting with the wedge walls, the molecules are rotated back to the plane of symmetry at the end of the move step. This new implementation was tested for multiple flows over axisymmetric shapes, including a sphere, a cone, a double cone and a hollow cylinder. Comparisons to previous DSMC solutions and experiments, when available, are made.

  9. Holographic measurement of wave propagation in axi-symmetric shells

    NASA Technical Reports Server (NTRS)

    Evensen, D. A.; Aprahamian, R.; Jacoby, J. L.

    1972-01-01

    The report deals with the use of pulsed, double-exposure holographic interferometry to record the propagation of transverse waves in thin-walled axi-symmetric shells. The report is subdivided into sections dealing with: (1) wave propagation in circular cylindrical shells, (2) wave propagation past cut-outs and stiffeners, and (3) wave propagation in conical shells. Several interferograms are presented herein which show the waves reflecting from the shell boundaries, from cut-outs, and from stiffening rings. The initial response of the shell was nearly axi-symmetric in all cases, but nonsymmetric modes soon appeared in the radial response. This result suggests that the axi-symmetric response of the shell may be dynamically unstable, and thus may preferentially excite certain circumferential harmonics through parametric excitation. Attempts were made throughout to correlate the experimental data with analysis. For the most part, good agreement between theory and experiment was obtained. Occasional differences were attributed primarily to simplifying assumptions used in the analysis. From the standpoint of engineering applications, it is clear that pulsed laser holography can be used to obtain quantitative engineering data. Areas of dynamic stress concentration, stress concentration factors, local anomalies, etc., can be readily determined by holography.

  10. Options for axisymmetric operation of MFTF-B

    SciTech Connect

    Fenstermacher, M.E.; Devoto, R.S.; Thomassen, K.I.

    1986-03-30

    The flexibility of MFTF-B for axisymmetric experiments has been investigated. Interhcanging the axicell coils and increasing their separation results in an axisymmetric plug cell with 12:1 and 6:1 inner and outer mirror ratios, respectively. For axisymmetric operation, the sloshing-ion neutral beams, ECRH gyrotrons, and the pumping system would be moved to the axicell. Stabilization by E-rings could be explored in this configuration. With the addition of octopole magnets, off-axis multipole stabilization could also be tested. Operating points for octopole and E-ring-stabilized configurations with properties similar to those of the quadrupole MFTF-B, namely T/sub ic/ = 10 - 15 keV and n/sub c/ approx. = 3 x 10/sup 13/ cm/sup -3/, have been obtained. Because of the negligible radial transport of central-cell ions, the required neutral-beam power in the central cell has been dramatically reduced. In addition, because MHD stabilization is achieved by off-axis hot electrons in both cases, much lower barrier beta is possible, which aids in reducing the barrier ECRH power. Total ECRH power in the end cell is projected to be approx. =1 MW. Possible operating points for both octopole and E-ring configurations are described along with the stability considerations involved.

  11. Three-Dimensional Electromagnetic High Frequency Axisymmetric Cavity Scars.

    SciTech Connect

    Warne, Larry K.; Jorgenson, Roy E.

    2014-10-01

    This report examines the localization of high frequency electromagnetic fi elds in three-dimensional axisymmetric cavities along periodic paths between opposing sides of the cavity. The cases where these orbits lead to unstable localized modes are known as scars. This report treats both the case where the opposing sides, or mirrors, are convex, where there are no interior foci, and the case where they are concave, leading to interior foci. The scalar problem is treated fi rst but the approximations required to treat the vector fi eld components are also examined. Particular att ention is focused on the normalization through the electromagnetic energy theorem. Both projections of the fi eld along the scarred orbit as well as point statistics are examined. Statistical comparisons are m ade with a numerical calculation of the scars run with an axisymmetric simulation. This axisymmetric cas eformstheoppositeextreme(wherethetwomirror radii at each end of the ray orbit are equal) from the two -dimensional solution examined previously (where one mirror radius is vastly di ff erent from the other). The enhancement of the fi eldontheorbitaxiscanbe larger here than in the two-dimensional case. Intentionally Left Blank

  12. Energy and energy flux in axisymmetric slow and fast waves

    NASA Astrophysics Data System (ADS)

    Moreels, M. G.; Van Doorsselaere, T.; Grant, S. D. T.; Jess, D. B.; Goossens, M.

    2015-06-01

    Aims: We aim to calculate the kinetic, magnetic, thermal, and total energy densities and the flux of energy in axisymmetric sausage modes. The resulting equations should contain as few parameters as possible to facilitate applicability for different observations. Methods: The background equilibrium is a one-dimensional cylindrical flux tube model with a piecewise constant radial density profile. This enables us to use linearised magnetohydrodynamic equations to calculate the energy densities and the flux of energy for axisymmetric sausage modes. Results: The equations used to calculate the energy densities and the flux of energy in axisymmetric sausage modes depend on the radius of the flux tube, the equilibrium sound and Alfvén speeds, the density of the plasma, the period and phase speed of the wave, and the radial or longitudinal components of the Lagrangian displacement at the flux tube boundary. Approximate relations for limiting cases of propagating slow and fast sausage modes are also obtained. We also obtained the dispersive first-order correction term to the phase speed for both the fundamental slow body mode under coronal conditions and the slow surface mode under photospheric conditions. Appendix A is available in electronic form at http://www.aanda.org

  13. Two-dimensional axisymmetric Child-Langmuir scaling law

    SciTech Connect

    Ragan-Kelley, Benjamin; Verboncoeur, John; Feng Yang

    2009-10-15

    The classical one-dimensional (1D) Child-Langmuir law was previously extended to two dimensions by numerical calculation in planar geometries. By considering an axisymmetric cylindrical system with axial emission from a circular cathode of radius r, outer drift tube radius R>r, and gap length L, we further examine the space charge limit in two dimensions. Simulations were done with no applied magnetic field as well as with a large (100 T) longitudinal magnetic field to restrict motion of particles to 1D. The ratio of the observed current density limit J{sub CL2} to the theoretical 1D value J{sub CL1} is found to be a monotonically decreasing function of the ratio of emission radius to gap separation r/L. This result is in agreement with the planar results, where the emission area is proportional to the cathode width W. The drift tube in axisymmetric systems is shown to have a small but measurable effect on the space charge limit. Strong beam edge effects are observed with J(r)/J(0) approaching 3.5. Two-dimensional axisymmetric electrostatic particle-in-cell simulations were used to produce these results.

  14. Axisymmetric Simulations of the ITER Vertical Stability Coil

    SciTech Connect

    Titus, Peter H.

    2013-07-09

    The ITER in-vessel coil system includes Vertical Stability (VS) coils and Edge Localized Mode (ELM) coils. There are two large VS ring coils, one upper and one lower. Each has four turns which are independently connected. The VS coils are needed for successful operation of ITER for most all of its operating modes. The VS coils must be highly reliable and fault tolerant. The operating environment includes normal and disruption Lorentz forces. To parametrically address all these design conditions in a tractable analysis requires a simplified model. The VS coils are predominately axisymmetric, and this suggests that an axisymmetric model can be meaningfully used to address the variations in mechanical design, loading, material properties, and time dependency. The axisymmetric finite element analysis described in this paper includes simulations of the bolted frictional connections used for the mounting details. Radiation and elastic-plastic response are modeled particularly for the extreme faulted conditions. Thermal connectivity is varied to study the effects of partial thermal connection of the actively cooled conductor to the remaining structure.

  15. Relativistic environmental effects in (29)Si NMR chemical shifts of halosilanes: light nucleus, heavy environment.

    PubMed

    Fedorov, Sergey V; Rusakov, Yury Yu; Krivdin, Leonid B

    2015-06-01

    Relativistic calculations of (29)Si NMR shielding constants (chemical shifts) in the series of halosilanes SiX(n)H(4-n) (X = F, Cl, Br and I) are performed within a full four-component relativistic Dirac's scheme using relativistic Dyall's basis sets. Three different theoretical levels are tested in the computation of (29)Si NMR chemical shifts in comparison with experiment: namely, four-component relativistic GIAO-DFT, four-component relativistic GIAO-RPA, and a hybrid scheme of a nonrelativistic GIAO-MP2 with taking into account relativistic corrections using the four-component relativistic GIAO-RPA. The DFT results give larger relativistic effects as compared to the RPA data which might be rationalized in terms of the manifestation of correlation effects taken into account at the DFT level and not accounted for at the uncorrelated RPA level. Taking into account solvent effects slightly improves agreement with experiment, however, being not a matter of principle. Generally, relativistic pure nonempirical wave function methods perform much better as compared to relativistic DFT methods when benchmarked to experiment. PMID:25946056

  16. Spontaneous symmetry breaking of rapidly rotating stars in general relativity: influence of the 3D-shift vector

    NASA Astrophysics Data System (ADS)

    Bonazzola, S.; Frieben, J.; Gourgoulhon, E.

    1998-03-01

    An analytical scheme and a numerical method in order to study the effects of general relativity on the viscosity driven secular bar mode instability of rapidly rotating stars are presented. The approach consists in perturbing an axisymmetric and stationary configuration and studying its evolution by constructing a series of triaxial quasi-equilibrium configurations. These are obtained by solution of an approximate set of field equations where only the dominant non-axisymmetric terms are taken into account. The progress with respect to our former investigation consists in a higher relativistic order of the non-axisymmetric terms included into the computation, namely the fully three-dimensional treatment of the vector part of the space-time metric tensor as opposed to the scalar part, solely, in the former case. The scheme is applied to rotating stars built on a polytropic equation of state and compared to our previous results. The 3D-vector part turns out to inhibit the symmetry breaking efficiently. Nevertheless, the bar mode instability is still possible for an astrophysically relevant mass of M_ns=3D1.4M_⊙ when a stiff polytropic equation of state with an adiabatic index of gamma =3D2.5 is employed. Triaxial neutron stars may be efficient emitters of gravitational waves and are thus potentially interesting sources for the forthcoming laser interferometric gravitational wave detectors such as LIGO, VIRGO and GEO600. >From a numerical point of view, the solution of the three-dimensional minimal-distortion shift vector equation in spherical coordinates is an important achievement of our code.

  17. Relativistic hadrons and the origin of relativistic outflows in active galactic nuclei

    NASA Technical Reports Server (NTRS)

    Contopoulos, John; Kazanas, D.

    1995-01-01

    We examine the hydrodynamic origin of relativistic outflows in active galactic nuclei (AGN). Specifically, we propose that the presence of a population of relativistic hadrons in the AGN 'central engine' and the associated neutron production suffices to produce outflows which under rather general conditions could be relativistic. The main such condition is that the size of the neutron production region be larger than the neutron flight path tau(sub n) approximately 3 x 10(exp 13) cm. This condition guarantees that the mean energy per particle in the proton fluid, resulting from the decay of the neutrons outside their production region, be greater than the proton rest mass. The expansion of this fluid can then lead naturally to a relativistic outflow by conversion of its internal energy to directed motion. We follow the development of such flows by solving the mass, energy as well as the kinetic equation for the proton gas in steady state, taking into account the source terms due to compute accurately the adiabatic index of the expanding gas, and in conjunction with Bernoulli's equation the detailed evolution of the bulk Lorentz factor. We further examine the role of large-scale magnetic fields in confining these outflows to produce the jets observed at larger scales.

  18. Transport characteristics of a Glaser magnet for an axisymmetric and non-axisymmetric space charge dominated beam

    SciTech Connect

    Goswami, A.; Sing Babu, P.; Pandit, V. S.

    2012-12-15

    This paper describes the dynamics of space charge dominated beam through a Glaser magnet which is often used to focus charged particle beams in the low energy section of accelerators and in many other devices. Various beam optical properties of the magnet and emittance evolution that results from the coupling between the two transverse planes are studied. We have derived ten independent first order differential equations for the beam sigma matrix elements assuming the linear space-charge force consistent with the assumption of the canonically transformed KV like distribution. In addition, the feasibility of using a Glaser magnet doublet in a low energy beam injection line to match an initial non-axisymmetric high intensity beam with net angular momentum to an axisymmetric system to suppress effective emittance growth after transition back to an uncoupled system, has also been studied.

  19. Transport characteristics of a Glaser magnet for an axisymmetric and non-axisymmetric space charge dominated beam

    NASA Astrophysics Data System (ADS)

    Goswami, A.; Sing Babu, P.; Pandit, V. S.

    2012-12-01

    This paper describes the dynamics of space charge dominated beam through a Glaser magnet which is often used to focus charged particle beams in the low energy section of accelerators and in many other devices. Various beam optical properties of the magnet and emittance evolution that results from the coupling between the two transverse planes are studied. We have derived ten independent first order differential equations for the beam sigma matrix elements assuming the linear space-charge force consistent with the assumption of the canonically transformed KV like distribution. In addition, the feasibility of using a Glaser magnet doublet in a low energy beam injection line to match an initial non-axisymmetric high intensity beam with net angular momentum to an axisymmetric system to suppress effective emittance growth after transition back to an uncoupled system, has also been studied.

  20. Balance equations in semi-relativistic quantum hydrodynamics

    NASA Astrophysics Data System (ADS)

    Ivanov, A. Yu.; Andreev, P. A.; Kuz'menkov, L. S.

    2014-05-01

    Method of the quantum hydrodynamics has been applied in quantum plasmas studies. As the first step in our consideration, derivation of classical semi-relativistic (i.e., described by the Darwin Lagrangian on microscopic level) hydrodynamical equations is given after a brief review of method development. It provides better distinguishing between classic and quantum semi-relativistic effects. Derivation of the classical equations is interesting since it is made by a natural, but not very widespread method. This derivation contains explicit averaging of the microscopic dynamics. Derivation of corresponding quantum hydrodynamic equations is presented further. Equations are obtained in the five-momentum approximation including the continuity equation, Euler and energy balance equations. It is shown that relativistic corrections lead to presence of new quantum terms in expressions for a force field, a work field etc. The semi-relativistic generalization of the quantum Bohm potential is obtained. Quantum part of the energy current, which is an analog of the quantum Bohm potential for the energy evolution equation, is derived. The Langmuir wave dispersion in semi-relativistic quantum plasmas, corresponding to the Darwin Lagrangian, is also considered to demonstrate contribution of semi-relativistic effects on basic plasma phenomenon.

  1. Relativistic astrophysics explorer

    NASA Astrophysics Data System (ADS)

    Kaaret, P.

    2004-01-01

    The great success of the Rossi X-Ray Timing Explorer (RXTE) has shown that X-ray timing is an excellent tool for the study of strong gravitational fields and the measurement of fundamental physical properties of black holes and neutron stars. Here, we describe a next-generation X-ray timing mission, the Relativistic Astrophysics Explorer (RAE), designed to fit within the envelope of a medium-sized mission. The instruments will be a narrow-field X-ray detector array with an area of 6 m 2 equal to 10 times that of RXTE and a wide-field X-ray monitor. We describe the science made possible with this mission, the design of the instruments, and results on prototype large-area X-ray detectors.

  2. The Relativistic Astrophysics Explorer

    NASA Astrophysics Data System (ADS)

    Kaaret, P.

    The great success of the Rossi X-Ray Timing Explorer (RXTE) has shown that X-ray timing is an excellent tool for the study of strong gravitational fields and the measurement of fundamental physical properties of black holes and neutron stars. Here, we describe a next-generation X-ray timing mission, the Relativistic Astrophysics Explorer (RAE), designed to fit within the envelope of a medium-sized mission. The instruments will be a narrow-field X-ray detector array with an area of 60,000 cm2 equal to ten times that of RXTE and a wide-field X-ray monitor. We describe the science made possible with this mission, the design of the instruments, and results on prototype large-area X-ray detectors.

  3. Relativistic Jets in Collapsars

    NASA Astrophysics Data System (ADS)

    Zhang, Weiqun; Woosley, S. E.; MacFadyen, A. I.

    2003-04-01

    We examine the propagation of two-dimensional relativistic jets through the stellar progenitor in the collapsar model for gamma-ray bursts. In agreement with previous studies, we find that the jet is collimated by its passage. Moreover, interaction of the jet with the star causes mixing that sporadically decelerates the jet, leading to a highly variable Lorentz factor. The jet that finally emerges has a moderate Lorentz factor, but a very large internal energy loading. In a second series of calculations we follow the emergence of such enegy-loaded jets from the star. For the initial conditions chosen, conversion of the remaining internal energy gives a terminal Lorentz factor of approximately 150. Implications of our calculations for GRB light curves, the luminosity-variability relation, and the GRB-supernova association are discussed.

  4. Photodetachment of relativistic ions

    SciTech Connect

    Donahue, J.B.; Gram, P.A.M.; Hamm, M.E.; Hamm, R.W.; Bryant, H.C.; Butterfield, K.B.; Clark, D.A.; Frost, C.A.; Smith, W.W.

    1980-01-01

    A series of fundamental laser ion beam experiments has been made feasible by the high-quality, relativistic (..beta.. = 0.842) H/sup -/ ion beam available at the Clinton P. Anderson Meson Physics Facility (LAMPF). The relatavistic Doppler shift of the light from an ordinary ultraviolet laser provides what is, in effect, a continuously tunable vacuum-ultraviolet laser in the rest frame of the moving ions. The Lorentz transformation of a modest laboratory magnetic field provides an electric field of several megavolts/centimeter. The latest results of photo-detachment work with H/sup -/ beams and our spectroscopic work with H/sup 0/ beams are presented. Plans for future work are discussed.

  5. Relativistic quantum cryptography

    NASA Astrophysics Data System (ADS)

    Molotkov, S. N.; Nazin, S. S.

    2003-07-01

    The problem of unconditional security of quantum cryptography (i.e. the security which is guaranteed by the fundamental laws of nature rather than by technical limitations) is one of the central points in quantum information theory. We propose a relativistic quantum cryptosystem and prove its unconditional security against any eavesdropping attempts. Relativistitic causality arguments allow to demonstrate the security of the system in a simple way. Since the proposed protocol does not empoly collective measurements and quantum codes, the cryptosystem can be experimentally realized with the present state-of-art in fiber optics technologies. The proposed cryptosystem employs only the individual measurements and classical codes and, in addition, the key distribution problem allows to postpone the choice of the state encoding scheme until after the states are already received instead of choosing it before sending the states into the communication channel (i.e. to employ a sort of "antedate" coding).

  6. Relativistic Heavy Ion Collider

    SciTech Connect

    Willen, E.H.

    1986-01-01

    The Relativistic Heavy Ion Collider (RHIC) is a proposed research facility at Brookhaven National Laboratory to study the collision of beams of heavy ions, up to gold in mass and at beam energies up to 100 GeV/nucleon. The physics to be explored by this collider is an overlap between the traditional disciplines of nuclear physics and high energy physics and is a continuation of the planned program of light and heavy ion physics at BNL. The machine is to be constructed in the now-empty tunnel built for the former CBA project. Various other facilities to support the collider are either in place or under construction at BNL. The collider itself, including the magnets, is in an advanced state of design, and a construction start is anticipated in the next several years.

  7. Hydrodynamics of Relativistic Fireballs

    NASA Technical Reports Server (NTRS)

    Piran, Tsvi; Shemi, Amotz; Narayan, Ramesh

    1993-01-01

    Many models of gamma-ray bursts involve a fireball, which is an optically thick concentration of radiation energy with a high ratio of energy density to rest mass. We examine analytically and numerically the evolution of a relativistic fireball. We show that, after an early rearrangement phase, most of the matter and energy in the fireball is concentrated within a narrow shell. The shell propagates at nearly the speed of light, with a frozen radial profile, and according to a simple set of scaling laws. The spectrum of the escaping radiation is harder at early times and softer later on. Depending on the initial energy-to-mass ratio, the final outcome of a fireball is either photons with roughly the initial temperature or ultrarelativistic baryons. In the latter case, the energy could be converted back to gamma-rays via interaction with surrounding material.

  8. The JKR-type adhesive contact problems for power-law shaped axisymmetric punches

    NASA Astrophysics Data System (ADS)

    Borodich, Feodor M.; Galanov, Boris A.; Suarez-Alvarez, Maria M.

    2014-08-01

    The JKR (Johnson, Kendall, and Roberts) and Boussinesq-Kendall models describe adhesive frictionless contact between two isotropic elastic spheres, and between a flat-ended axisymmetric punch and an elastic half-space respectively. However, the shapes of contacting solids may be more general than spherical or flat ones. In addition, the derivation of the main formulae of these models is based on the assumption that the material points within the contact region can move along the punch surface without any friction. However, it is more natural to assume that a material point that came to contact with the punch sticks to its surface, i.e. to assume that the non-slipping boundary conditions are valid. It is shown that the frictionless JKR model may be generalized to arbitrary convex, blunt axisymmetric body, in particular to the case of the punch shape being described by monomial (power-law) punches of an arbitrary degree d≥1. The JKR and Boussinesq-Kendall models are particular cases of the problems for monomial punches, when the degree of the punch d is equal to two or it goes to infinity respectively. The generalized problems for monomial punches are studied under both frictionless and non-slipping (or no-slip) boundary conditions. It is shown that regardless of the boundary conditions, the solution to the problems is reduced to the same dimensionless relations among the actual force, displacements and contact radius. The explicit expressions are derived for the values of the pull-off force and for the corresponding critical contact radius. Connections of the results obtained for problems of nanoindentation in the case of the indenter shape near the tip has some deviation from its nominal shape and the shape function can be approximated by a monomial function of radius, are discussed.

  9. Bernoulli theorem generalized to rheologically complex viscous fluid flow

    NASA Astrophysics Data System (ADS)

    Brutyan, M. A.; Krapivskii, P. L.

    1992-08-01

    The Bernoulli theorem is generalized to two-dimensional and axisymmetric micropolar incompressible fluid flows. It is shown that the approach developed is also applicable to magnetohydrodynamic flows of a viscous Newtonian fluid.

  10. Some problems in relativistic thermodynamics

    SciTech Connect

    Veitsman, E. V.

    2007-11-15

    The relativistic equations of state for ideal and real gases, as well as for various interface regions, have been derived. These dependences help to eliminate some controversies in the relativistic thermodynamics based on the special theory of relativity. It is shown, in particular, that the temperature of system whose velocity tends to the velocity of light in vacuum varies in accordance with the Ott law T = T{sub 0}/{radical}1 - v{sup 2}/c{sup 2}. Relativistic dependences for heat and mass transfer, for Ohm's law, and for a viscous flow of a liquid have also been derived.

  11. Relativistic Dipole Matrix Element Zeros

    NASA Astrophysics Data System (ADS)

    Lajohn, L. A.; Pratt, R. H.

    2002-05-01

    There is a special class of relativistic high energy dipole matrix element zeros (RZ), whose positions with respect to photon energy ω , only depend on the bound state l quantum number according to ω^0=mc^2/(l_b+1) (independent of primary quantum number n, nuclear charge Z, central potential V and dipole retardation). These RZ only occur in (n,l_b,j_b)arrow (ɛ , l_b+1,j_b) transitions such as ns_1/2arrow ɛ p_1/2; np_3/2arrow ɛ d_3/2: nd_5/2arrow ɛ f_5/2 etc. The nonrelativistic limit of these matrix elements can be established explicitly in the Coulomb case. Within the general matrix element formalism (such as that in [1]); when |κ | is substituted for γ in analytic expressions for matrix elements, the zeros remain, but ω^0 now becomes dependent on n and Z. When the reduction to nonrelativistic form is completed by application of the low energy approximation ω mc^2 mc^2, the zeros disappear. This nonzero behavior was noted in nonrelativistic dipole Coulomb matrix elements by Fano and Cooper [2] and later proven by Oh and Pratt[3]. (J. H. Scofield, Phys. Rev. A 40), 3054 (1989 (U. Fano and J. W. Cooper, Rev. Mod. Phys. 40), 441 (1968). (D. Oh and R. H. Pratt, Phys. Rev. A 34), 2486 (1986); 37, 1524 (1988); 45, 1583 (1992).

  12. Relativistic positioning systems: Numerical simulations

    NASA Astrophysics Data System (ADS)

    Puchades Colmenero, Neus

    The position of users located on the Earth's surface or near it may be found with the classic positioning systems (CPS). Certain information broadcast by satellites of global navigation systems, as GPS and GALILEO, may be used for positioning. The CPS are based on the Newtonian formalism, although relativistic post-Newtonian corrections are done when they are necessary. This thesis contributes to the development of a different positioning approach, which is fully relativistic from the beginning. In the relativistic positioning systems (RPS), the space-time position of any user (ship, spacecraft, and so on) can be calculated with the help of four satellites, which broadcast their proper times by means of codified electromagnetic signals. In this thesis, we have simulated satellite 4-tuples of the GPS and GALILEO constellations. If a user receives the signals from four satellites simultaneously, the emission proper times read -after decoding- are the user "emission coordinates". In order to find the user "positioning coordinates", in an appropriate almost inertial reference system, there are two possibilities: (a) the explicit relation between positioning and emission coordinates (broadcast by the satellites) is analytically found or (b) numerical codes are designed to calculate the positioning coordinates from the emission ones. Method (a) is only viable in simple ideal cases, whereas (b) allows us to consider realistic situations. In this thesis, we have designed numerical codes with the essential aim of studying two appropriate RPS, which may be generalized. Sometimes, there are two real users placed in different positions, which receive the same proper times from the same satellites; then, we say that there is bifurcation, and additional data are needed to choose the real user position. In this thesis, bifurcation is studied in detail. We have analyzed in depth two RPS models; in both, it is considered that the satellites move in the Schwarzschild's space

  13. Relativistic spin effects in the baryon spectrum

    SciTech Connect

    Garcilazo, Humberto

    2005-04-01

    We study the nonstrange baryon spectrum within a three-body theory that treats relativistically both the space and the spin variables. The relativistic effects of the spin are about one order of magnitude smaller than those due to the use of relativistic momentum variables. The relativistic treatment of the spin breaks the degenerancy that is present in the nonrelativistic model and in the model with only relativistic momentum variables.

  14. A Family of Vortices to Study Axisymmetric Vortex Breakdown and Reconnection

    NASA Technical Reports Server (NTRS)

    Young, Larry A.

    2007-01-01

    A new analytic model describing a family of vortices has been developed to study some of the axisymmetric vortex breakdown and reconnection fluid dynamic processes underlying body-vortex interactions that are frequently manifested in rotorcraft and propeller-driven fixed-wing aircraft wakes. The family of vortices incorporates a wide range of prescribed initial vorticity distributions -- including single or dual-core vorticity distributions. The result is analytical solutions for the vorticity and velocities for each member of the family of vortices. This model is of sufficient generality to further illustrate the dependence of vortex reconnection and breakdown on initial vorticity distribution as was suggested by earlier analytical work. This family of vortices, though laminar in nature, is anticipated to provide valuable insight into the vortical evolution of large-scale rotor and propeller wakes.

  15. The inviscid stability of supersonic flow past heated or cooled axisymmetric bodies

    NASA Technical Reports Server (NTRS)

    Shaw, Stephen J.; Duck, Peter W.

    1992-01-01

    The inviscid, linear, nonaxisymmetric, temporal stability of the boundary layer associated with the supersonic flow past axisymmetric bodies (with particular emphasis on long thin, straight circular cylinders), subject to heated or cooled wall conditions is investigated. The eigenvalue problem is computed in some detail for a particular Mach number or 3.8, revealing that the effect of curvature and the choice of wall conditions both have a significant effect on the stability of the flow. Both the asymptotic, large azimuthal wavenumber solution and the asymptotic, far downstream solution are obtained for the stability analysis and compared with numerical results. Additionally, asymptotic analyses valid for large radii of curvature with cooled/heated wall conditions are presented. In general, important differences were found to exist between the wall temperature conditions imposed and the adiabatic wall conditions considered previously.

  16. The inviscid stability of supersonic flow past heated or cooled axisymmetric bodies

    NASA Technical Reports Server (NTRS)

    Shaw, Stephen J.; Duck, Peter W.

    1990-01-01

    The inviscid, linear, nonaxisymmetric, temporal stability of the boundary layer associated with the supersonic flow past axisymmetric bodies (with particular emphasis on long thin, straight circular cylinders), subject to heated or cooled wall conditions is investigated. The eigenvalue problem is computed in some detail for a particular Mach number or 3.8, revealing that the effect of curvature and the choice of wall conditions both have a significant effect on the stability of the flow. Both the asymptotic, large azimuthal wavenumber solution and the asymptotic, far downstream solution are obtained for the stability analysis and compared with numerical results. Additionally, asymptotic analyses valid for large radii of curvature with cooled/heated wall conditions, are presented. In general, important differences were found to exist between the wall temperature conditions imposed and the adiabatic wall conditions considered previously.

  17. Non Axisymmetric Three-Dimensional Magnetic Bernstein-Greene-Kruskal (BGK) Modes

    NASA Astrophysics Data System (ADS)

    Ng, Chung-Sang

    2013-10-01

    The theory of three-dimensional (3D) magnetic Magnetic Bernstein-Greene-Kruskal (BGK) modes has been generalized to the non axisymmetric case. While the shape of the electrostatic structure is usually elongated along the direction of the strong large-scale magnetic field, a limiting case with the elongated direction along one of the perpendicular direction is also possible. Essentially this makes the solution 2D with the magnetic field on the 2D plane. Note that such 2D BGK modes are very different from those described by another theory, of which the magnetic field is perpendicular to the 2D plane. This theory might explain 2D BGK modes observed in some numerical simulations. This work is supported by a National Science Foundation grant PHY-1004357 and by the National Science Foundation of China NSFC under Grant No. 41128004.

  18. Viscous linear stability of axisymmetric low-density jets: Parameters influencing absolute instability

    NASA Astrophysics Data System (ADS)

    Srinivasan, V.; Hallberg, M. P.; Strykowski, P. J.

    2010-02-01

    Viscous linear stability calculations are presented for model low-density axisymmetric jet flows. Absolute growth transitions for the jet column mode are mapped out in a parametric space including velocity ratio, density ratio, Reynolds number, momentum thickness, and subtle differences between velocity and density profiles. Strictly speaking, the profiles used in most jet stability studies to date are only applicable to unity Prandtl numbers and zero pressure gradient flows—the present work relaxes this requirement. Results reveal how subtle differences between the velocity and density profiles generally used in jet stability theory can dramatically alter the absolute growth rate of the jet column mode in these low-density flows. The results suggest heating/cooling or mass diffusion at the outer nozzle surface can suppress absolute instability and potentially global instability in low-density jets.

  19. Axisymmetric indentation of curved elastic membranes by a convex rigid indenter

    PubMed Central

    Pearce, S.P.; King, J.R.; Holdsworth, M.J.

    2011-01-01

    Motivated by applications to seed germination, we consider the transverse deflection that results from the axisymmetric indentation of an elastic membrane by a rigid body. The elastic membrane is fixed around its boundary, with or without an initial pre-stretch, and may be initially curved prior to indentation. General indenter shapes are considered, and the load–indentation curves that result for a range of spheroidal tips are obtained for both flat and curved membranes. Wrinkling may occur when the membrane is initially curved, and a relaxed strain-energy function is used to calculate the deformed profile in this case. Applications to experiments designed to measure the mechanical properties of seed endosperms are discussed. PMID:22298913

  20. Type D stationary axisymmetric solutions to Einstein-Maxwell equations conformal to Carter spacetimes

    NASA Astrophysics Data System (ADS)

    Garcia-Diaz, Alberto A.; Gutierrez-Cano, Gustavo

    It is established that the conformal type D electrovacuum stationary axisymmetric Carter class of metrics splits into three families of solutions: the Plebański-Demiański family, the Carter-Plebański spacetimes, and the trigonometric-hyperbolic conformal class. This last class, via coordinate transformations, can be brought to the C-P form. These metrics admit an Abelian group of motions G2 with commuting stationary and angular Killing vectors, are of Petrov type D; the null eigenvectors of the general electromagnetic field coincide with the directions of the Debever null vectors of Weyl curvature tensor. These solutions exhibit, for certain ranges of the coordinate variables, a black hole behavior; a "ring" singularity similar to the one of the Kerr metric is present. The limiting transition of these solutions leads to the Kerr-Newman black hole solution as a subbranch.