HARM A Numerical Scheme for General Relativistic Magnetohydrodynamics
Gammie, C F; Tóth, G; Gammie, Charles F.; Kinney, Jonathan C. Mc
2003-01-01
We describe a conservative, shock-capturing scheme for evolving the equations of general relativistic magnetohydrodynamics. The fluxes are calculated using the Harten, Lax, and van Leer scheme. A variant of constrained transport, proposed earlier by T\\'oth, is used to maintain a divergence free magnetic field. Only the covariant form of the metric in a coordinate basis is required to specify the geometry. We describe code performance on a full suite of test problems in both special and general relativity. On smooth flows we show that it converges at second order. We conclude by showing some results from the evolution of a magnetized torus near a rotating black hole.
WhiskyMHD: Numerical Code for General Relativistic Magnetohydrodynamics
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.
WHAM: A WENO-based general relativistic numerical scheme I: Hydrodynamics
Tchekhovskoy, Alexander; Narayan, Ramesh
2007-01-01
Active galactic nuclei, x-ray binaries, pulsars, and gamma-ray bursts are all believed to be powered by compact objects surrounded by relativistic plasma flows driving phenomena such as accretion, winds, and jets. These flows are often accurately modelled by the relativistic magnetohydrodynamics (MHD) approximation. Time-dependent numerical MHD simulations have proven to be especially insightful, but one regime that remains difficult to simulate is when the energy scales (kinetic, thermal, magnetic) within the plasma become disparate. We develop a numerical scheme that significantly improves the accuracy and robustness of the solution in this regime. We use a modified form of the WENO method to construct a finite-volume general relativistic hydrodynamics code called WHAM that converges at fifth order. We avoid (1) field-by-field decomposition by adaptively reducing down to 2-point stencils near discontinuities for a more accurate treatment of shocks, and (2) excessive reduction to low order stencils, as in th...
Numerical solutions of general-relativistic field equations for rapidly rotating neutron stars
Institute of Scientific and Technical Information of China (English)
吴雪君; 须重明
1997-01-01
Stationary axial symmetric equilibrium configurations rapidly rotating with uniform angular velocity in the framework of genera! relativity are considered. Sequences of models are numerically computed by means of a computer code that solves the full Einstein equations exactly. This code employs Neugebauer’s minimal surface formalism, where the field equations are equivalent to two-dimensional minimal surface equations for 4 metric potentials. The calculations are based upon 10 different equations of state. Results of various structures of neutron stars and the rotational effects on stellar structures and properties are reported. Finally some limits to equations of state of neutron stars and the stability for rapidly rotating relativistic neutron stars are discussed.
Numerical Relativistic Quantum Optics
2013-11-08
µm and a = 1. The condition for an atomic spectrum to be non-relativistic is Z α−1 ≈ 137, as follows from elementary Dirac theory. One concludes that...peculiar result that B0 = 1 TG is a weak field. At present, such fields are observed only in connection with astrophysical phenomena [14]. The highest...pulsars. The Astrophysical Journal, 541:367–373, Sep 2000. [15] M. Tatarakis, I. Watts, F.N. Beg, E.L. Clark, A.E. Dangor, A. Gopal, M.G. Haines, P.A
Numerical modeling of a Global Navigation Satellite System in a general relativistic framework
Delva, P; Cadez, A
2010-01-01
In this article we model a Global Navigation Satellite System (GNSS) in a Schwarzschild space-time, as a first approximation of the relativistic geometry around the Earth. The closed time-like and scattering light-like geodesics are obtained analytically, describing respectively trajectories of satellites and electromagnetic signals. We implement an algorithm to calculate Schwarzschild coordinates of a GNSS user who receives proper times sent by four satellites, knowing their orbital parameters; the inverse procedure is implemented to check for consistency. The constellation of satellites therefore realizes a geocentric inertial reference system with no \\emph{a priori} realization of a terrestrial reference frame. We show that the calculation is very fast and could be implemented in a real GNSS, as an alternative to usual post-Newtonian corrections. Effects of non-gravitational perturbations on positioning errors are assessed, and methods to reduce them are sketched. In particular, inter-links between satelli...
Stochastic oscillations of general relativistic disks
Harko, Tiberiu
2012-01-01
We analyze the general relativistic oscillations of thin accretion disks around compact astrophysical objects interacting with the surrounding medium through non-gravitational forces. The interaction with the external medium (a thermal bath) is modeled via a friction force, and a random force, respectively. The general equations describing the stochastically perturbed disks are derived by considering the perturbations of trajectories of the test particles in equatorial orbits, assumed to move along the geodesic lines. By taking into account the presence of a viscous dissipation and of a stochastic force we show that the dynamics of the stochastically perturbed disks can be formulated in terms of a general relativistic Langevin equation. The stochastic energy transport equation is also obtained. The vertical oscillations of the disks in the Schwarzschild and Kerr geometries are considered in detail, and they are analyzed by numerically integrating the corresponding Langevin equations. The vertical displacement...
General relativity and relativistic astrophysics
Mukhopadhyay, Banibrata
2016-01-01
Einstein established the theory of general relativity and the corresponding field equation in 1915 and its vacuum solutions were obtained by Schwarzschild and Kerr for, respectively, static and rotating black holes, in 1916 and 1963, respectively. They are, however, still playing an indispensable role, even after 100 years of their original discovery, to explain high energy astrophysical phenomena. Application of the solutions of Einstein's equation to resolve astrophysical phenomena has formed an important branch, namely relativistic astrophysics. I devote this article to enlightening some of the current astrophysical problems based on general relativity. However, there seem to be some issues with regard to explaining certain astrophysical phenomena based on Einstein's theory alone. I show that Einstein's theory and its modified form, both are necessary to explain modern astrophysical processes, in particular, those related to compact objects.
Physical and Relativistic Numerical Cosmology
Directory of Open Access Journals (Sweden)
Peter Anninos
1998-01-01
Full Text Available In order to account for the observable Universe, any comprehensive theory or model of cosmology must draw from many disciplines of physics, including gauge theories of strong and weak interactions, the hydrodynamics and microphysics of baryonic matter, electromagnetic fields, and spacetime curvature, for example. Although it is difficult to incorporate all these physical elements into a single complete model of our Universe, advances in computing methods and technologies have contributed significantly towards our understanding of cosmological models, the Universe, and astrophysical processes within them. A sample of numerical calculations addressing specific issues in cosmology are reviewed in this article: from the Big Bang singularity dynamics to the fundamental interactions of gravitational waves; from the quark--hadron phase transition to the large scale structure of the Universe. The emphasis, although not exclusively, is on those calculations designed to test different models of cosmology against the observed Universe.
Relativistic Positioning Systems: Numerical Simulations
Puchades, Neus
2014-01-01
The motion of satellite constellations similar to GPS and Galileo is numerically simulated and, then, the region where bifurcation (double positioning) occurs is appropriately represented. In the cases of double positioning, the true location may be found using additional information (angles or times). The zone where the Jacobian, J, of the transformation from inertial to emission coordinates vanishes is also represented and interpreted. It is shown that the uncertainties in the satellite world lines produce positioning errors, which depend on the value of |J|. The smaller this quantity the greater the expected positioning errors. Among all the available 4-tuples of satellites, the most appropriate one -for a given location- should minimize positioning errors (large enough |J| values) avoiding bifurcation. Our study is particularly important to locate objects which are far away from Earth, e.g., satellites.
General relativistic Boltzmann equation, I: Covariant treatment
Debbasch, F.; van Leeuwen, W.A.
2009-01-01
This series of two articles aims at dissipating the rather dense haze existing in the present literature around the General Relativistic Boltzmann equation. In this first article, the general relativistic one-particle distribution function in phase space is defined as an average of delta functions.
A new three-dimensional general-relativistic hydrodynamics code
Baiotti, L.; Hawke, I.; Montero, P. J.; Rezzolla, L.
We present a new three-dimensional general relativistic hydrodynamics code, the Whisky code. This code incorporates the expertise developed over the past years in the numerical solution of Einstein equations and of the hydrodynamics equations in a curved spacetime, and is the result of a collaboration of several European Institutes. We here discuss the ability of the code to carry out long-term accurate evolutions of the linear and nonlinear dynamics of isolated relativistic stars.
A new three-dimensional general-relativistic hydrodynamics code
Baiotti, Luca; Montero, Pedro J; Rezzolla, Luciano
2010-01-01
We present a new three-dimensional general relativistic hydrodynamics code, the Whisky code. This code incorporates the expertise developed over the past years in the numerical solution of Einstein equations and of the hydrodynamics equations in a curved spacetime, and is the result of a collaboration of several European Institutes. We here discuss the ability of the code to carry out long-term accurate evolutions of the linear and nonlinear dynamics of isolated relativistic stars.
General relativistic spectra of accretion disks around rotating neutron stars
Bhattacharya, S; Thampan, A V
2000-01-01
General relativistic spectra from accretion disks around rotating neutron stars in the appropriate space-time geometry for several different equation of state, spin rates and mass of the compact object have been computed. The analysis involves the computation of the relativistically corrected radial temperature profiles and the effect of Doppler and gravitational red-shifts on the spectra. Light bending effects have been omitted for simplicity. The relativistic spectrum is compared with the Newtonian one and it is shown that the difference between the two is primarily due to the different radial temperature profile for the relativistic and Newtonian disk solutions. To facilitate direct comparison with observations, a simple empirical function has been presented which describes the numerically computed relativistic spectra well. This empirical function (which has three parameters including normalization) also describes the Newtonian spectrum adequately. Thus the function can in principle be used to distinguish...
General relativistic corrections and non-Gaussianity
Villa, Eleonora; Matarrese, Sabino
2014-01-01
General relativistic cosmology cannot be reduced to linear relativistic perturbations superposed on an isotropic and homogeneous (Friedmann-Robertson-Walker) background, even though such a simple scheme has been successfully applied to analyse a large variety of phenomena (such as Cosmic Microwave Background primary anisotropies, matter clustering on large scales, weak gravitational lensing, etc.). The general idea of going beyond this simple paradigm is what characterises most of the efforts made in recent years: the study of second and higher-order cosmological perturbations including all general relativistic contributions -- also in connection with primordial non-Gaussianities -- the idea of defining large-scale structure observables directly from a general relativistic perspective, the various attempts to go beyond the Newtonian approximation in the study of non-linear gravitational dynamics, by using e.g., Post-Newtonian treatments, are all examples of this general trend. Here we summarise some of these ...
General Relativistic Mean Field Theory for rotating nuclei
Energy Technology Data Exchange (ETDEWEB)
Madokoro, Hideki [Kyushu Univ., Fukuoka (Japan). Dept. of Physics; Matsuzaki, Masayuki
1998-03-01
The {sigma}-{omega} model Lagrangian is generalized to an accelerated frame by using the technique of general relativity which is known as tetrad formalism. We apply this model to the description of rotating nuclei within the mean field approximation, which we call General Relativistic Mean Field Theory (GRMFT) for rotating nuclei. The resulting equations of motion coincide with those of Munich group whose formulation was not based on the general relativistic transformation property of the spinor fields. Some numerical results are shown for the yrast states of the Mg isotopes and the superdeformed rotational bands in the A {approx} 60 mass region. (author)
General relativistic neutron stars with twisted magnetosphere
Pili, A G; Del Zanna, L
2014-01-01
Soft Gamma-Ray Repeaters and Anomalous X-Ray Pulsars are extreme manifestations of the most magnetized neutron stars: magnetars. The phenomenology of their emission and spectral properties strongly support the idea that the magnetospheres of these astrophysical objects are tightly twisted in the vicinity of the star. Previous studies on equilibrium configurations have so far focused on either the internal or the external magnetic field configuration, without considering a real coupling between the two fields. Here we investigate numerical equilibrium models of magnetized neutron stars endowed with a confined twisted magnetosphere, solving the general relativistic Grad-Shafranov equation both in the interior and in the exterior of the compact object. A comprehensive study of the parameters space is provided to investigate the effects of different current distributions on the overall magnetic field structure.
Numerical Hydrodynamics in General Relativity
Directory of Open Access Journals (Sweden)
Font José A.
2003-01-01
Full Text Available The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. With respect to an earlier version of the article, the present update provides additional information on numerical schemes, and extends the discussion of astrophysical simulations in general relativistic hydrodynamics. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A large sample of available numerical schemes is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of astrophysical simulations in strong gravitational fields is presented. These include gravitational collapse, accretion onto black holes, and hydrodynamical evolutions of neutron stars. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances on the formulation of the gravitational field and hydrodynamic equations and the numerical methodology designed to solve them.
Generalized magnetofluid connections in relativistic magnetohydrodynamics.
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.
Slowly Rotating General Relativistic Superfluid Neutron Stars
Andersson, N
2001-01-01
We present a general formalism to treat slowly rotating general relativistic superfluid neutron stars. As a first approximation, their matter content can be described in terms of a two-fluid model, where one fluid is the neutron superfluid, which is believed to exist in the core and inner crust of mature neutron stars, and the other fluid represents a conglomerate of all other constituents (crust nuclei, protons, electrons, etc.). We obtain a system of equations, good to second-order in the rotational velocities, that determines the metric and the matter variables, irrespective of the equation of state for the two fluids. In particular, allowance is made for the so-called entrainment effect, whereby the momentum of one constituent (e.g. the neutrons) carries along part of the mass of the other constituent. As an illustration of the developed framework, we consider a simplified equation of state for which the two fluids are described by different polytropes. We determine numerically the effects of the two flui...
General relativistic observables of the GRAIL mission
Turyshev, Slava G; Sazhin, Mikhail V
2012-01-01
We present a realization of astronomical relativistic reference frames in the solar system and its application to the GRAIL mission. We model the necessary spacetime coordinate transformations for light-trip time computations and address some practical aspects of the implementation of the resulting model. We develop all the relevant relativistic coordinate transformations that are needed to describe the motion of the GRAIL spacecraft and to compute all observable quantities. We take into account major relativistic effects contributing to the dual one-way range observable, which is derived from one-way signal travel times between the two GRAIL spacecraft. We develop a general relativistic model for this fundamental observable of GRAIL, accurate to 1 $\\mu$m. We develop and present a relativistic model for another key observable of this experiment, the dual one-way range-rate, accurate to 1 $\\mu$m/s. The presented formulation justifies the basic assumptions behind the design of the GRAIL mission. It may also be ...
General Relativistic Effects in Atom Interferometry
Energy Technology Data Exchange (ETDEWEB)
Dimopoulos, Savas; /Stanford U., Phys. Dept.; Graham, Peter W.; /SLAC /Stanford U., Phys. Dept.; 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.
A new spherically symmetric general relativistic hydrodynamical code
Romero, J V; Martí, J M; Miralles, J A; Romero, Jose V; Ibanez, Jose M; Marti, Jose M; Miralles, Juan A
1995-01-01
In this paper we present a full general relativistic one-dimensional hydro-code which incorporates a modern high-resolution shock-capturing algorithm, with an approximate Riemann solver, for the correct modelling of formation and propagation of strong shocks. The efficiency of this code in treating strong shocks is demonstrated by some numerical experiments. The interest of this technique in several astrophysical scenarios is discussed.
Newtonian view of general relativistic stars
Energy Technology Data Exchange (ETDEWEB)
Oliveira, A.M. [Instituto Federal do Espirito Santo (IFES), Grupo de Ciencias Ambientais e Recursos Naturais, Guarapari (Brazil); Velten, H.E.S.; Fabris, J.C. [Universidade Federal do Espirito Santo (UFES), Departamento de Fisica, Vitoria (Brazil); Salako, I.G. [Institut de Mathematiques et de Sciences Physiques (IMSP), Porto-Novo (Benin)
2014-11-15
Although general relativistic cosmological solutions, even in the presence of pressure, can be mimicked by using neo-Newtonian hydrodynamics, it is not clear whether there exists the same Newtonian correspondence for spherical static configurations. General relativity solutions for stars are known as the Tolman-Oppenheimer-Volkoff (TOV) equations. On the other hand, the Newtonian description does not take into account the total pressure effects and therefore cannot be used in strong field regimes. We discuss how to incorporate pressure in the stellar equilibrium equations within the neo-Newtonian framework. We compare the Newtonian, neo-Newtonian, and the full relativistic theory by solving the equilibrium equations for both three approaches and calculating the mass-radius diagrams for some simple neutron stars' equations of state. (orig.)
General relativistic neutrino transport using spectral methods
Peres, Bruno; Penner, Andrew Jason; Novak, Jérôme; Bonazzola, Silvano
2014-02-01
We present a new code, Lorene's Ghost (for Lorene's gravitational handling of spectral transport) developed to treat the problem of neutrino transport in supernovae with the use of spectral methods. First, we derive the expression for the nonrelativistic Liouville operator in doubly spherical coordinates (r, θ, ϕ, ɛ, Θ, Φ), and further its general relativistic counterpart. We use the 3 + 1 formalism with the conformally flat approximation for the spatial metric, to express the Liouville operator in the Eulerian frame. Our formulation does not use any approximations when dealing with the angular arguments (θ, ϕ, Θ, Φ), and is fully energy-dependent. This approach is implemented in a spherical shell, using either Chebyshev polynomials or Fourier series as decomposition bases. It is here restricted to simplified collision terms (isoenergetic scattering) and to the case of a static fluid. We finish this paper by presenting test results using basic configurations, including general relativistic ones in the Schwarzschild metric, in order to demonstrate the convergence properties, the conservation of particle number and correct treatment of some general relativistic effects of our code. The use of spectral methods enables to run our test cases in a six-dimensional setting on a single processor.
Generalized One-Dimensional Point Interaction in Relativistic and Non-relativistic Quantum Mechanics
Shigehara, T; Mishima, T; Cheon, T; Cheon, Taksu
1999-01-01
We first give the solution for the local approximation of a four parameter family of generalized one-dimensional point interactions within the framework of non-relativistic model with three neighboring $\\delta$ functions. We also discuss the problem within relativistic (Dirac) framework and give the solution for a three parameter family. It gives a physical interpretation for so-called high energy substantially differ between non-relativistic and relativistic cases.
Leibnizian relationalism for general relativistic physics
Vassallo, Antonio
2016-01-01
An ontology of Leibnizian relationalism, consisting in distance relations among sparse matter points and their change only, is well recognized as a serious option in the context of classical mechanics. In this paper, we investigate how this ontology fares when it comes to general relativistic physics. Using a Humean strategy, we regard the gravitational field as a means to represent the overall change in the distance relations among point particles in a way that achieves the best combination of being simple and being informative.
Numerical Simulations of Driven Supersonic Relativistic MHD Turbulence
Zrake, Jonathan; 10.1063/1.3621748
2011-01-01
Models for GRB outflows invoke turbulence in relativistically hot magnetized fluids. In order to investigate these conditions we have performed high-resolution three-dimensional numerical simulations of relativistic magneto-hydrodynamical (RMHD) turbulence. We find that magnetic energy is amplified to several percent of the total energy density by turbulent twisting and folding of magnetic field lines. Values of epsilon_B near 1% are thus naturally expected. We study the dependence of saturated magnetic field energy fraction as a function of Mach number and relativistic temperature. We then present power spectra of the turbulent kinetic and magnetic energies. We also present solenoidal (curl-like) and dilatational (divergence-like) power spectra of kinetic energy. We propose that relativistic effects introduce novel couplings between these spectral components. The case we explore in most detail is for equal amounts of thermal and rest mass energy, corresponding to conditions after collisions of shells with re...
A time-implicit numerical method and benchmarks for the relativistic Vlasov–Ampere equations
Energy Technology Data Exchange (ETDEWEB)
Carrié, Michael, E-mail: mcarrie2@unl.edu; Shadwick, B. A., E-mail: shadwick@mailaps.org [Department of Physics and Astronomy, University of Nebraska-Lincoln, Lincoln, Nebraska 68588 (United States)
2016-01-15
We present a time-implicit numerical method to solve the relativistic Vlasov–Ampere system of equations on a two dimensional phase space grid. The time-splitting algorithm we use allows the generalization of the work presented here to higher dimensions keeping the linear aspect of the resulting discrete set of equations. The implicit method is benchmarked against linear theory results for the relativistic Landau damping for which analytical expressions using the Maxwell-Jüttner distribution function are derived. We note that, independently from the shape of the distribution function, the relativistic treatment features collective behaviours that do not exist in the nonrelativistic case. The numerical study of the relativistic two-stream instability completes the set of benchmarking tests.
On general relativistic uniformly rotating white dwarfs
Boshkayev, Kuantay; Ruffini, Remo; Siutsou, Ivan
2012-01-01
Uniformly rotating white dwarfs (RWDs) are analyzed within the framework of general relativity. The Hartle's formalism is applied to construct self-consistently the internal and external solutions to the Einstein equations. The relativistic Feynman-Metropolis-Teller EoS that generalizes the Salpeter's one taking fully into account the finite size of nuclei, the Coulomb interactions as well as electroweak equilibrium in a self-consistent relativistic fashion is used to describe the WD matter. The mass, radius, angular momentum, eccentricity and quadrupole moment of RWDs are calculated as a function of the central density and rotation angular velocity. We construct the region of stability of RWDs taking into account the mass-shedding limit, inverse beta-decay instability, and the boundary established by the turning points of constant angular momentum sequences that separates stable from secularly unstable configurations. We found the minimum rotation periods 0.3, 0.5, 0.7 and 2.2 seconds and maximum masses 1.50...
General Relativistic Smoothed Particle Hydrodynamics code developments: A progress report
Faber, Joshua; Silberman, Zachary; Rizzo, Monica
2017-01-01
We report on our progress in developing a new general relativistic Smoothed Particle Hydrodynamics (SPH) code, which will be appropriate for studying the properties of accretion disks around black holes as well as compact object binary mergers and their ejecta. We will discuss in turn the relativistic formalisms being used to handle the evolution, our techniques for dealing with conservative and primitive variables, as well as those used to ensure proper conservation of various physical quantities. Code tests and performance metrics will be discussed, as will the prospects for including smoothed particle hydrodynamics codes within other numerical relativity codebases, particularly the publicly available Einstein Toolkit. We acknowledge support from NSF award ACI-1550436 and an internal RIT D-RIG grant.
Donmez, O
2004-01-01
In this paper, the general procedure to solve the General Relativistic Hydrodynamical(GRH) equations with Adaptive-Mesh Refinement (AMR) is presented. In order to achieve, the GRH equations are written in the conservation form to exploit their hyperbolic character. The numerical solutions of general relativistic hydrodynamic equations are done by High Resolution Shock Capturing schemes (HRSC), specifically designed to solve non-linear hyperbolic systems of conservation laws. These schemes depend on the characteristic information of the system. The Marquina fluxes with MUSCL left and right states are used to solve GRH equations. First, different test problems with uniform and AMR grids on the special relativistic hydrodynamics equations are carried out to verify the second order convergence of the code in 1D, 2D and 3D. Results from uniform and AMR grid are compared. It is found that adaptive grid does a better job when the number of resolution is increased. Second, the general relativistic hydrodynamical equa...
General relativistic neutrino transport using spectral methods
Peres, Bruno; Novak, Jerome; Bonazzola, Silvano
2014-01-01
We present a new code, Lorene's Ghost (for Lorene's gravitational handling of spectral transport) developed to treat the problem of neutrino transport in supernovae with the use of spectral methods. First, we derive the expression for the nonrelativistic Liouville operator in doubly spherical coordinates (r, theta, phi, epsilon, Theta, Phi)$, and further its general relativistic counterpart. We use the 3 + 1 formalism with the conformally flat approximation for the spatial metric, to express the Liouville operator in the Eulerian frame. Our formulation does not use any approximations when dealing with the angular arguments (theta, phi, Theta, Phi), and is fully energy-dependent. This approach is implemented in a spherical shell, using either Chebyshev polynomials or Fourier series as decomposition bases. It is here restricted to simplified collision terms (isoenergetic scattering) and to the case of a static fluid. We finish this paper by presenting test results using basic configurations, including general r...
Bruce, Adam L
2015-01-01
We show the traditional rocket problem, where the ejecta velocity is assumed constant, can be reduced to an integral quadrature of which the completely non-relativistic equation of Tsiolkovsky, as well as the fully relativistic equation derived by Ackeret, are limiting cases. By expanding this quadrature in series, it is shown explicitly how relativistic corrections to the mass ratio equation as the rocket transitions from the Newtonian to the relativistic regime can be represented as products of exponential functions of the rocket velocity, ejecta velocity, and the speed of light. We find that even low order correction products approximate the traditional relativistic equation to a high accuracy in flight regimes up to $0.5c$ while retaining a clear distinction between the non-relativistic base-case and relativistic corrections. We furthermore use the results developed to consider the case where the rocket is not moving relativistically but the ejecta stream is, and where the ejecta stream is massless.
Review of numerical special relativistic hydrodynamics
Odyck, D.E.A. van
2002-01-01
This paper gives an overview of numerical methods for special relativistichydrodynamics (SRHD). First, a short summary of special relativity is given. Next, the SRHD equations are introduced. The exact solution for the SRHD Riemann problem is described. This solution is used in a Godunov scheme to c
Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity
Directory of Open Access Journals (Sweden)
Font José A.
2008-09-01
Full Text Available This article presents a comprehensive overview of numerical hydrodynamics and magnetohydrodynamics (MHD in general relativity. Some significant additions have been incorporated with respect to the previous two versions of this review (2000, 2003, most notably the coverage of general-relativistic MHD, a field in which remarkable activity and progress has occurred in the last few years. Correspondingly, the discussion of astrophysical simulations in general-relativistic hydrodynamics is enlarged to account for recent relevant advances, while those dealing with general-relativistic MHD are amply covered in this review for the first time. The basic outline of this article is nevertheless similar to its earlier versions, save for the addition of MHD-related issues throughout. Hence, different formulations of both the hydrodynamics and MHD equations are presented, with special mention of conservative and hyperbolic formulations well adapted to advanced numerical methods. A large sample of numerical approaches for solving such hyperbolic systems of equations is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. As previously stated, a comprehensive summary of astrophysical simulations in strong gravitational fields is also presented. These are detailed in three basic sections, namely gravitational collapse, black-hole accretion, and neutron-star evolutions; despite the boundaries, these sections may (and in fact do overlap throughout the discussion. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances in the formulation of the gravitational field, hydrodynamics and MHD equations and the numerical methodology designed to solve them. To keep the length of this article reasonable
General Relativistic Simulations of the Collapsar Scenario
DeBrye, N; Aloy, M A; Font, J A
2013-01-01
We are exploring the viability of the collapsar model for long-soft gamma-ray bursts. For this we perform state-of-the-art general relativistic hydrodynamic simulations in a dynamically evolving space-time with the CoCoNuT code. We start from massive low metallicity stellar models evolved up to core gravitational instability, and then follow the subsequent evolution until the system collapses forming a compact remnant. A preliminary study of the collapse outcome is performed by varying the typical parameters of the scenario, such as the initial stellar mass, metallicity, and rotational profile of the stellar progenitor. 1D models (without rotation) have been used to test our newly developed neutrino leakage scheme. This is a fundamental piece of our approach as it allows the central remnant (in all cases considered, a metastable high-mass neutron star) to cool down, eventually collapsing to a black hole. In two dimensions, we show that sufficiently fast rotating cores lead to the formation of Kerr black holes...
Generalized quantum similarity in atomic systems: A quantifier of relativistic effects
Martín, A. L.; Angulo, J. C.; Antolín, J.; López-Rosa, S.
2017-02-01
Quantum similarity between Hartree-Fock and Dirac-Fock electron densities reveals the depth of relativistic effects on the core and valence regions in atomic systems. The results emphasize the relevance of differences in the outermost subshells, as pointed out in recent studies by means of Shannon-like functionals. In this work, a generalized similarity functional allows us to go far beyond the Shannon-based analyses. The numerical results for systems throughout the Periodic Table show that discrepancies between the relativistic and non-relativistic descriptions are patently governed by shell-filling patterns.
General relativistic observables for the ACES experiment
Turyshev, Slava G; Toth, Viktor T
2015-01-01
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 $J_2$ and the effects of major nongravitational forces on the orbit of the ISS. We demonstrate that the ACES reference frame is pseudo-inertial at th...
General relativistic tidal heating for Moller pseudotensor
So, Lau Loi
2015-01-01
Thorne elucidated that the relativistic tidal heating is the same as the Newtonian theory. Moreover, Thorne also claimed that the tidal heating is independent of how one localizes gravitational energy and is unambiguously given by a certain formula. Purdue and Favata calculated the tidal heating for different classical pseudotensors including Moller and obtained the results all matched with the Newtonian perspective. After re-examined this Moller pseudotensor, we find that there does not exist any tidal heating value. Thus we claim that the relativistic tidal heating is pseudotensor independent under the condition that if the peusdotensor is a Freud typed superpotential.
Relativistic Radiation Magnetohydrodynamics in Dynamical Spacetimes: Numerical Methods and Tests
2008-01-01
Many systems of current interest in relativistic astrophysics require a knowledge of radiative transfer in a magnetized gas flowing in a strongly-curved, dynamical spacetime. Such systems include coalescing compact binaries containing neutron stars or white dwarfs, disks around merging black holes, core collapse supernovae, collapsars, and gamma-ray burst sources. To model these phenomena, all of which involve general relativity, radiation (photon and/or neutrino), and magnetohydrodynamics, w...
General relativistic aspects of ferromagneto-fluid
Energy Technology Data Exchange (ETDEWEB)
Asgekar, G.G.; Patwardhan, C.G.
1988-03-01
The implications of Bianchi identities pertaining to the spacetime of relativistic ferrofluid with infinite conductivity and variable magnetic permeability are investigated. Some kinematical and dynamical corollaries emerging out of a preferred geometrical symmetry called an isometry with respect to the flow vector and the magnetic field vector are developed.
General relativistic aspects of ferromagneto-fluid.
Asgekar, G. G.; Patwardhan, C. G.
1988-03-01
The implications of Bianchi identities pertaining to the spacetime of relativistic ferrofluid with infinite conductivity and variable magnetic permeability are investigated. Some kinematical and dynamical corollaries emerging out of a preferred geometrical symmetry called an isometry with respect to the flow vector and the magnetic field vector are developed.
General-Relativistic Resistive Magnetohydrodynamics in three dimensions: formulation and tests
Dionysopoulou, Kyriaki; Palenzuela, Carlos; Rezzolla, Luciano; Giacomazzo, Bruno
2013-01-01
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 small 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 physical setups in all ranges 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 testbed for general-relativistic codes with dynamical electromagnetic fields, we study the collapse of a nonrotating star to a black hole. We show that als...
Cosmological Measurements with General Relativistic Galaxy Correlations
Raccanelli, Alvise; Bertacca, Daniele; Doré, Olivier; Durrer, Ruth
2015-01-01
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 introduces an error in the forecasted precision in measuring cosmological parameters of the order of a few tens of percent, in particular when measuring ...
Newtonian and General Relativistic Models of Spherical Shells
Vogt, D
2009-01-01
A family of spherical shells with varying thickness is derived by using a simple Newtonian potential-density pair. Then, a particular isotropic form of a metric in spherical coordinates is used to construct a General Relativistic version of the Newtonian family of shells. The matter of these relativistic shells presents equal azimuthal and polar pressures, while the radial pressure is a constant times the tangential pressure. We also make a first study of stability of both the Newtonian and relativistic families of shells.
A general relativistic signature in the galaxy bispectrum
Umeh, Obinna; Maartens, Roy; Clarkson, Chris
2016-01-01
Next-generation galaxy surveys will increasingly rely on the galaxy bispectrum to improve cosmological constraints, especially on primordial non-Gaussianity. A key theoretical requirement that remains to be developed is the analysis of general relativistic effects on the bispectrum, which arise from observing galaxies on the past lightcone. Here we compute for the first time all the local relativistic corrections to the bispectrum, from Doppler, gravitational potential and higher-order effects. For the galaxy bispectrum, the problem is much more complex than for the power spectrum, since we need the lightcone corrections at second order. Mode-coupling contributions at second order mean that relativistic corrections can be non-negligible at smaller scales than in the case of the power spectrum. In a primordial Gaussian universe, we show that the relativistic bispectrum for a moderately squeezed shape can differ from the Newtonian prediction by $\\sim 30\\%$ when the short modes are at the equality scale. For the...
Numerical magneto-hydrodynamics for relativistic nuclear collisions
Inghirami, Gabriele; Beraudo, Andrea; Moghaddam, Mohsen Haddadi; Becattini, Francesco; Bleicher, Marcus
2016-01-01
We present an improved version of the ECHO-QGP numerical code, which self-consistently includes for the first time the effects of electromagnetic fields within the framework of relativistic magnetohydrodynamics (RMHD). We discuss results of its application in relativistic heavy-ion collisions in the limit of infinite electrical conductivity of the plasma. After reviewing the relevant covariant $3\\!+\\!1$ formalisms, we illustrate the implementation of the evolution equations in the code and show the results of several tests aimed at assessing the accuracy and robustness of the implementation. After providing some estimates of the magnetic fields arising in non-central high-energy nuclear collisions, we perform full RMHD simulations of the evolution of the Quark-Gluon Plasma in the presence of electromagnetic fields and discuss the results. In our ideal RMHD setup we find that the magnetic field developing in non-central collisions does not significantly modify the elliptic-flow of the final hadrons. However, s...
Numerical magneto-hydrodynamics for relativistic nuclear collisions
Inghirami, Gabriele; Del Zanna, Luca; Beraudo, Andrea; Moghaddam, Mohsen Haddadi; Becattini, Francesco; Bleicher, Marcus
2016-12-01
We present an improved version of the ECHO-QGP numerical code, which self-consistently includes for the first time the effects of electromagnetic fields within the framework of relativistic magneto-hydrodynamics (RMHD). We discuss results of its application in relativistic heavy-ion collisions in the limit of infinite electrical conductivity of the plasma. After reviewing the relevant covariant 3+1 formalisms, we illustrate the implementation of the evolution equations in the code and show the results of several tests aimed at assessing the accuracy and robustness of the implementation. After providing some estimates of the magnetic fields arising in non-central high-energy nuclear collisions, we perform full RMHD simulations of the evolution of the quark-gluon plasma in the presence of electromagnetic fields and discuss the results. In our ideal RMHD setup we find that the magnetic field developing in non-central collisions does not significantly modify the elliptic flow of the final hadrons. However, since there are uncertainties in the description of the pre-equilibrium phase and also in the properties of the medium, a more extensive survey of the possible initial conditions as well as the inclusion of dissipative effects are indeed necessary to validate this preliminary result.
Numerical magneto-hydrodynamics for relativistic nuclear collisions
Energy Technology Data Exchange (ETDEWEB)
Inghirami, Gabriele [Frankfurt Institute for Advanced Studies, Frankfurt am Main (Germany); Goethe-Universitaet, Institute for Theoretical Physics, Frankfurt am Main (Germany); GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Darmstadt (Germany); Forschungszentrum Juelich, John von Neumann Institute for Computing, Juelich (Germany); Del Zanna, Luca [Universita di Firenze, Dipartimento di Fisica e Astronomia, Firenze (Italy); INAF - Osservatorio Astrofisico di Arcetri, Firenze (Italy); INFN - Sezione di Firenze, Firenze (Italy); Beraudo, Andrea [INFN - Sezione di Torino, Torino (Italy); Moghaddam, Mohsen Haddadi [INFN - Sezione di Torino, Torino (Italy); Hakim Sabzevari University, Department of Physics, P. O. Box 397, Sabzevar (Iran, Islamic Republic of); Becattini, Francesco [Universita di Firenze, Dipartimento di Fisica e Astronomia, Firenze (Italy); INFN - Sezione di Firenze, Firenze (Italy); Bleicher, Marcus [Frankfurt Institute for Advanced Studies, Frankfurt am Main (Germany); Goethe-Universitaet, Institute for Theoretical Physics, Frankfurt am Main (Germany); GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Darmstadt (Germany); Forschungszentrum Juelich, John von Neumann Institute for Computing, Juelich (Germany)
2016-12-15
We present an improved version of the ECHO-QGP numerical code, which self-consistently includes for the first time the effects of electromagnetic fields within the framework of relativistic magneto-hydrodynamics (RMHD). We discuss results of its application in relativistic heavy-ion collisions in the limit of infinite electrical conductivity of the plasma. After reviewing the relevant covariant 3 + 1 formalisms, we illustrate the implementation of the evolution equations in the code and show the results of several tests aimed at assessing the accuracy and robustness of the implementation. After providing some estimates of the magnetic fields arising in non-central high-energy nuclear collisions, we perform full RMHD simulations of the evolution of the quark-gluon plasma in the presence of electromagnetic fields and discuss the results. In our ideal RMHD setup we find that the magnetic field developing in non-central collisions does not significantly modify the elliptic flow of the final hadrons. However, since there are uncertainties in the description of the pre-equilibrium phase and also in the properties of the medium, a more extensive survey of the possible initial conditions as well as the inclusion of dissipative effects are indeed necessary to validate this preliminary result. (orig.)
Generalized Relativistic Chapman-Enskog Solution of the Boltzmann Equation
García-Perciante, A L; García-Colin, L S
2007-01-01
The Chapman-Enskog method of solution of the relativistic Boltzmann equation is generalized in order to admit a time-derivative term associated to the thermodynamic force in its first order solution. Both existence and uniqueness of such a solution are proved based on the standard theory of integral equations. The mathematical implications of the generalization here introduced are briefly explored.
RAISHIN: A High-Resolution Three-Dimensional General Relativistic Magnetohydrodynamics Code
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.
GRHydro: A new open source general-relativistic magnetohydrodynamics code for the Einstein Toolkit
Moesta, Philipp; Faber, Joshua A; Haas, Roland; Noble, Scott C; Bode, Tanja; Loeffler, Frank; Ott, Christian D; Reisswig, Christian; Schnetter, Erik
2013-01-01
We present the new general-relativistic magnetohydrodynamics (GRMHD) capabilities of the Einstein Toolkit, an open-source community-driven numerical relativity and computational relativistic astrophysics code. The GRMHD extension of the Toolkit builds upon previous releases and implements the evolution of relativistic magnetised fluids in the ideal MHD limit in fully dynamical spacetimes using the same shock-capturing techniques previously applied to hydrodynamical evolution. In order to maintain the divergence-free character of the magnetic field, the code implements both hyperbolic divergence cleaning and constrained transport schemes. We present test results for a number of MHD tests in Minkowski and curved spacetimes. Minkowski tests include aligned and oblique planar shocks, cylindrical explosions, magnetic rotors, Alfv\\'en waves and advected loops, as well as a set of tests designed to study the response of the divergence cleaning scheme to numerically generated monopoles. We study the code's performanc...
A generally-relativistic gauge classification of the Dirac fields
Fabbri, Luca
2016-01-01
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 most general Dirac equations we will investigate the consequences for the dynamics: and in particular we shall address the problem of getting the non-relativistic approximation in a consistent way. We are going to comment on extensions.
RAISHIN: A High-Resolution Three-Dimensional General Relativistic Magnetohydrodynamics Code
Mizuno, Y; Koide, S; Hardee, P; Fishman, G J; 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 mag...
General relativistic Boltzmann equation, II: Manifestly covariant treatment
Debbasch, F.; van Leeuwen, W.A.
2009-01-01
In a preceding article we presented a general relativistic treatment of the derivation of the Boltzmann equation. The four-momenta occurring in this formalism were all on-shell four-momenta, verifying the mass-shell restriction p(2) = m(2)c(2). Due to this restriction, the resulting Boltzmann equati
General relativistic Boltzmann equation, II: Manifestly covariant treatment
Debbasch, F.; van Leeuwen, W.A.
2009-01-01
In a preceding article we presented a general relativistic treatment of the derivation of the Boltzmann equation. The four-momenta occurring in this formalism were all on-shell four-momenta, verifying the mass-shell restriction p(2) = m(2)c(2). Due to this restriction, the resulting Boltzmann
Energy Technology Data Exchange (ETDEWEB)
Fuerst, Steven V.; /KIPAC, Menlo Park; Mizuno, Yosuke; /USRA, Huntsville; Nishikawa, Ken-Ichi; /USRA, Huntsville /Alabama U., Huntsville; Wu, Kinwah; /Mullard Space Sci.
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.
Cherenkov loss factor of short relativistic bunches:general approach
Baturin, S S
2013-01-01
The interaction of short relativistic charged particle bunches with waveguides and other accelerator system components is a critical issue for the development of X-ray FELs (free electron lasers) and linear collider projects. Wakefield Cherenkov losses of short bunches have been studied previously for resistive wall, disk-loaded, corrugated and dielectric loaded waveguides. It was noted in various publications [1] that if the slowdown layer is thin, the Cherenkov loss factor of a short bunch does not depend on the guiding system material and is a constant for any given transverse cross section dimensions of the waveguides. In this paper, we consider a new approach to the analysis of loss factors for relativistic short bunches and formulate a general integral relation that allows calculation of the loss factor for a short relativistic bunch passing an arbitrary waveguide system. The loss factors calculated by this new method for various types of waveguides with arbitrary thickness slowdown layers, including in...
Causal Stability Conditions for General Relativistic Spacetimes
Howard, E M
2016-01-01
A brief overview of some open questions in general relativity with important consequences for causality theory is presented, aiming to a better understanding of the causal structure of the spacetime. Special attention is accorded to the problem of fundamental causal stability conditions. Several questions are raised and some of the potential consequences of recent results regarding the causality problem in general relativity are presented. A key question is whether causality violating regions are locally allowed. The new concept of almost stable causality is introduced; meanwhile, related conditions and criteria for the stability and almost stability of the causal structure are discussed.
Whistler-Mode Waves Growth by a Generalized Relativistic Kappa-Type Distribution
Institute of Scientific and Technical Information of China (English)
ZHOU Qing-Hua; JIANG Bin; SHI Xiang-Hua; LI Jun-Qiu
2009-01-01
The instability of field-aligned Whistler-mode waves in space plasmas is studied by using a recently developed generalized relativistic kappa-type (KT) distribution. Numerical calculations are performed for a direct compar-ison between the new KT distribution and the current kappa distribution. We show that the wave growth for the KT distribution tends to occur in the lower wave frequency (e.g., ω 0.1Ωe) due to a larger fractional num-ber of the resonant electrons ηrel (which controls the wave growth), while primarily locating in the higher wave frequency for the kappa distribution. Moreover, the relativistic anisotropy Arel by the KT distribution is found to be smaller than that by the kappa distribution, leading to a smaller peak of wave growth. The results present a further understanding of plasma wave instability particularly in those plasmas where relativistic electrons are present.
TOPICAL REVIEW: General relativistic boson stars
Schunck, Franz E
2008-01-01
There is accumulating evidence that (fundamental) scalar fields may exist in Nature. The gravitational collapse of such a boson cloud would lead to a boson star (BS) as a new type of a compact object. Similarly as for white dwarfs and neutron stars, there exists a limiting mass, below which a BS is stable against complete gravitational collapse to a black hole. According to the form of the self-interaction of the basic constituents and the spacetime symmetry, we can distinguish mini-, axidilaton, soliton, charged, oscillating and rotating BSs. Their compactness prevents a Newtonian approximation, however, modifications of general relativity, as in the case of Jordan-Brans-Dicke theory as a low energy limit of strings, would provide them with gravitational memory. In general, a BS is a compact, completely regular configuration with structured layers due to the anisotropy of scalar matter, an exponentially decreasing 'halo', a critical mass inversely proportional to constituent mass, an effective radius, and a ...
Donmez, Orhan
We present a general procedure to solve the General Relativistic Hydrodynamical (GRH) equations with Adaptive-Mesh Refinement (AMR) and model of an accretion disk around a black hole. To do this, the GRH equations are written in a conservative form to exploit their hyperbolic character. The numerical solutions of the general relativistic hydrodynamic equations is done by High Resolution Shock Capturing schemes (HRSC), specifically designed to solve non-linear hyperbolic systems of conservation laws. These schemes depend on the characteristic information of the system. We use Marquina fluxes with MUSCL left and right states to solve GRH equations. First, we carry out different test problems with uniform and AMR grids on the special relativistic hydrodynamics equations to verify the second order convergence of the code in 1D, 2 D and 3D. Second, we solve the GRH equations and use the general relativistic test problems to compare the numerical solutions with analytic ones. In order to this, we couple the flux part of general relativistic hydrodynamic equation with a source part using Strang splitting. The coupling of the GRH equations is carried out in a treatment which gives second order accurate solutions in space and time. The test problems examined include shock tubes, geodesic flows, and circular motion of particle around the black hole. Finally, we apply this code to the accretion disk problems around the black hole using the Schwarzschild metric at the background of the computational domain. We find spiral shocks on the accretion disk. They are observationally expected results. We also examine the star-disk interaction near a massive black hole. We find that when stars are grounded down or a hole is punched on the accretion disk, they create shock waves which destroy the accretion disk.
General relativistic treatment of LISA optical links
Dhurandhar, S V; Nayak, K Rajesh
2008-01-01
LISA is a joint space mission of the NASA and the ESA for detecting low frequency gravitational waves in the band $10^{-5} - 1$ Hz. In order to attain the requisite sensitivity for LISA, the laser frequency noise must be suppressed below the other secondary noises such as the optical path noise, acceleration noise etc. This is achieved by combining time-delayed data for which precise knowledge of time-delays is required. The gravitational field, mainly that of the Sun and the motion of LISA affect the time-delays and the optical links. Further, the effect of the gravitational field of the Earth on the orbits of spacecraft is included. This leads to additional flexing over and above that of the Sun. We have written a numerical code which computes the optical links, that is, the time-delays with great accuracy $\\sim 10^{-2}$ metres - more than what is required for time delay interferometry (TDI) - for most of the orbit and with sufficient accuracy within $\\sim 10$ metres for an integrated time window of about s...
TOPICAL REVIEW: General relativistic boson stars
Schunck, Franz E.; Mielke, Eckehard W.
2003-10-01
There is accumulating evidence that (fundamental) scalar fields may exist in nature. The gravitational collapse of such a boson cloud would lead to a boson star (BS) as a new type of a compact object. As with white dwarfs and neutron stars, a limiting mass exists similarly, below which a BS is stable against complete gravitational collapse to a black hole. According to the form of the self-interaction of the basic constituents and spacetime symmetry, we can distinguish mini-, axidilaton, soliton, charged, oscillating and rotating BSs. Their compactness prevents a Newtonian approximation; however, modifications of general relativity, as in the case of Jordan Brans Dicke theory as a low-energy limit of strings, would provide them with gravitational memory. In general, a BS is a compact, completely regular configuration with structured layers due to the anisotropy of scalar matter, an exponentially decreasing 'halo', a critical mass inversely proportional to the constituent mass, an effective radius and a large particle number. Due to the Heisenberg principle, a completely stable branch exists, and as a coherent state, it allows for rotating solutions with quantized angular momentum. In this review, we concentrate on the fascinating possibilities of detecting the various subtypes of (excited) BSs: possible signals include gravitational redshift and (micro-)lensing, emission of gravitational waves, or, in the case of a giant BS, its dark matter contribution to the rotation curves of galactic halos.
General Relativistic White Dwarfs and Their Astrophysical Implications
Boshkayev, Kuantay; Ruffini, Remo; Siutsou, Ivan
2014-01-01
We consider applications of general relativistic uniformly-rotating white dwarfs to several astrophysical phenomena related to the spin-up and the spin-down epochs and to delayed type Ia supernova explosions of super-Chandrasekhar white dwarfs, where we estimate the "spinning down" lifetime due to magnetic-dipole braking. In addition, we describe the physical properties of Soft Gamma Repeaters and Anomalous X-Ray Pulsars as massive rapidly-rotating highly-magnetized white dwarfs. Particularly we consider one of the so-called low-magnetic-field magnetars SGR 0418+5729 as a massive rapidly-rotating highly-magnetized white dwarf and give bounds for the mass, radius, moment of inertia, and magnetic field by requiring the general relativistic uniformly-rotating configurations to be stable.
General relativistic white dwarfs and their astrophysical implications
Energy Technology Data Exchange (ETDEWEB)
Boshkayev, Kuantay [Al-Farabi Kazakh National University, Almaty (Kazakhstan); Rueda, Jorge A.; Ruffini, Remo [Sapienza University of Rome, Rome (Italy); Siutsou, Ivan [ICRANet, Square of Republic, Pescara (Italy)
2014-09-15
We consider applications of general relativistic uniformly-rotating white dwarfs to several astrophysical phenomena related to the spin-up and the spin-down epochs and to delayed type Ia supernova explosions of super-Chandrasekhar white dwarfs, where we estimate the 'spinning down' lifetime due to magnetic-dipole braking. In addition, we describe the physical properties of Soft Gamma Repeaters and Anomalous X-Ray Pulsars as massive rapidly-rotating highly-magnetized white dwarfs. Particularly we consider one of the so-called low-magnetic-field magnetars SGR 0418+5729 as a massive rapidly-rotating highly- magnetized white dwarf and give bounds for the mass, radius, moment of inertia, and magnetic field by requiring the general relativistic uniformly rotating configurations to be stable.
General Relativistic Transfer Equation on a Kerr Black Hole
Zannias, T.
1998-12-01
The general relativistic transfer equation describing the interaction of a massless gas with a hot plasma is analyzed on the background of a Kerr black hole. On physical grounds we single out two natural orthonormal frames relative to which the radiative transfer equation takes its simplest form. First the field of the local rest frame defined by the plasma and secondly the local rest frame associated with Bardeens-ZAMOS observers. Applications of the formalism to accretion problems will also briefly discussed.
General factorization scheme with application to relativistic Hermite polynomials
Rosu, H C; Obregón, O; Reyes, Marco A; Obregon, Octavio
1995-01-01
We present a sufficiently general factorization scheme of second-order linear differential equations having discrete (polynomial) indeces both in the coefficient of the first-derivative term and of the derivative-free one. We apply it to the relativistic Hermite equation in order to perform the factorization with respect to the polynomial degree confirming the factorization of Aldaya, Bisquert and Navarro-Salas, but also obtaining another slightly modified factorization, and to the Gegenbauer equation for the factorization with respect to the order. Moreover, by making use of Nagel's relation between Gegenbauer and relativistic Hermite polynomials we write down ladder-like operations with respect to the order for the latter ones, which are another interesting result of the paper.
Equation of State in a Generalized Relativistic Density Functional Approach
Typel, Stefan
2015-01-01
The basic concepts of a generalized relativistic density functional approach to the equation of state of dense matter are presented. The model is an extension of relativistic mean-field models with density-dependent couplings. It includes explicit cluster degrees of freedom. The formation and dissolution of nuclei is described with the help of mass shifts. The model can be adapted to the description of finite nuclei in order to study the effect of $\\alpha$-particle correlations at the nuclear surface on the neutron skin thickness of heavy nuclei. Further extensions of the model to include quark degrees of freedom or an energy dependence of the nucleon self-energies are outlined.
General-relativistic resistive magnetohydrodynamics in three dimensions: Formulation and tests
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.
General relativistic polytropes with a repulsive cosmological constant
Stuchlík, Zdeněk; Hledík, Stanislav; Novotný, Jan
2016-11-01
Spherically symmetric equilibrium configurations of perfect fluid obeying a polytropic equation of state are studied in spacetimes with a repulsive cosmological constant. The configurations are specified in terms of three parameters—the polytropic index n , the ratio of central pressure and central energy density of matter σ , and the ratio of energy density of vacuum and central density of matter λ . The static equilibrium configurations are determined by two coupled first-order nonlinear differential equations that are solved by numerical methods with the exception of polytropes with n =0 corresponding to the configurations with a uniform distribution of energy density, when the solution is given in terms of elementary functions. The geometry of the polytropes is conveniently represented by embedding diagrams of both the ordinary space geometry and the optical reference geometry reflecting some dynamical properties of the geodesic motion. The polytropes are represented by radial profiles of energy density, pressure, mass, and metric coefficients. For all tested values of n >0 , the static equilibrium configurations with fixed parameters n , σ , are allowed only up to a critical value of the cosmological parameter λc=λc(n ,σ ). In the case of n >3 , the critical value λc tends to zero for special values of σ . The gravitational potential energy and the binding energy of the polytropes are determined and studied by numerical methods. We discuss in detail the polytropes with an extension comparable to those of the dark matter halos related to galaxies, i.e., with extension ℓ>100 kpc and mass M >1 012 M⊙ . For such largely extended polytropes, the cosmological parameter relating the vacuum energy to the central density has to be larger than λ =ρvac/ρc˜10-9. We demonstrate that the extension of the static general relativistic polytropic configurations cannot exceed the so-called static radius related to their external spacetime, supporting the idea
Results from Numerical General Relativity
Baker, John G.
2011-01-01
For several years numerical simulations have been revealing the details of general relativity's predictions for the dynamical interactions of merging black holes. I will review what has been learned of the rich phenomenology of these mergers and the resulting gravitational wave signatures. These wave forms provide a potentially observable record of the powerful astronomical events, a central target of gravitational wave astronomy. Asymmetric radiation can produce a thrust on the system which may accelerate the single black hole resulting from the merger to high relative velocity.
On numerical relativistic hydrodynamics and barotropic equations of state
Ibáñez, José María; Miralles, Juan Antornio
2012-01-01
The characteristic formulation of the relativistic hydrodynamic equations (Donat et al 1998 J. Comput. Phys. 146 58), which has been implemented in many relativistic hydro-codes that make use of Godunov-type methods, has to be slightly modified in the case of evolving barotropic flows. For a barotropic equation of state, a removable singularity appears in one of the eigenvectors. The singularity can be avoided by means of a simple renormalization which makes the system of eigenvectors well defined and complete. An alternative strategy for the particular case of barotropic flows is discussed.
Indian Academy of Sciences (India)
Wang Zhi-Yun; Chen Pei-Jie
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.
Numerical simulations of dynamics and emission from relativistic astrophysical jets
Mimica, Petar; Rueda-Becerril, Jesus Misrayim; Tabik, Siham; Aloy, Carmen
2012-01-01
Broadband emission from relativistic outflows (jets) of active galactic nuclei (AGN) and gamma-ray bursts (GRBs) contains valuable information about the nature of the jet itself, and about the central engine which launches it. Using special relativistic hydrodynamics and magnetohydronamics simulations we study the dynamics of the jet and its interaction with the surrounding medium. The observational signature of the simulated jets is computed using a radiative transfer code developed specifically for the purpose of computing multi-wavelength, time-dependent, non-thermal emission from astrophysical plasmas. We present results of a series of long-term projects devoted to understanding the dynamics and emission of jets in parsec-scale AGN jets, blazars and the afterglow phase of the GRBs.
A New Formulation for General Relativistic Force-Free Electrodynamics and Its Applications
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
We formulate the general relativistic force-free electrodynamics in a new 3+1 language. In this formulation, when we have properly defined electric and magnetic fields, the covariant Maxwell equations could be cast in the traditional form with new vacuum con stitutive constraint equations. The fundamental equation governing a stationary, axisymmet ric force-free black hole magnetosphere is derived using this formulation which recasts the Grad-Shafranov equation in a simpler way. Compared to the classic 3+1 system of Thorne and MacDonald, the new system of 3+1 equations is more suitable for numerical use for it keeps the hyperbolic structure of the electrodynamics and avoids the singularity at the event horizon. This formulation could be readily extended to non-relativistic limit and find applications in flat spacetime. We investigate its application to disk wind, black hole magnetosphere and solar physics in both flat and curved spacetime.
General Relativistic Radiative Transfer Code in Rotating Black Hole Spacetime: {ARTIST}
Takahashi, Rohta; Umemura, Masayuki
2016-10-01
We present a general relativistic radiative transfer code, {ARTIST} (Authentic Radiative Transfer In Space-Time), which is a perfectly causal scheme to pursue the propagation of radiation with absorption and scattering around a Kerr black hole. The code explicitly solves the invariant radiation intensity along null geodesics in the Kerr-Schild coordinates, and therefore properly includes light bending, Doppler boosting, frame dragging, and gravitational redshifts. The notable aspect of {ARTIST} is that it conserves the radiative energy with high accuracy, and is not subject to the numerical diffusion, since the transfer is solved on long characteristics along null geodesics. We first solve the wavefront propagation around a Kerr black hole, which was originally explored by Hanni (1977). This demonstrates repeated wavefront collisions, light bending, and causal propagation of radiation with the speed of light. We show that the decay rate of the total energy of wavefronts near a black hole is determined solely by the black hole spin in late phases, in agreement with analytic expectations. As a result, the {ARTIST} turns out to correctly solve the general relativistic radiation fields until late phases as t ˜ 90M. We also explore the effects of absorption and scattering, and apply this code for a photon wall problem and an orbiting hot spot problem. All the simulations in the present study are performed in the equatorial plane around a Kerr black hole. The {ARTIST} is the first step to realize the general relativistic radiation hydrodynamics.
General relativistic radiative transfer code in rotating black hole space-time: ARTIST
Takahashi, Rohta; Umemura, Masayuki
2017-02-01
We present a general relativistic radiative transfer code, ARTIST (Authentic Radiative Transfer In Space-Time), that is a perfectly causal scheme to pursue the propagation of radiation with absorption and scattering around a Kerr black hole. The code explicitly solves the invariant radiation intensity along null geodesics in the Kerr-Schild coordinates, and therefore properly includes light bending, Doppler boosting, frame dragging, and gravitational redshifts. The notable aspect of ARTIST is that it conserves the radiative energy with high accuracy, and is not subject to the numerical diffusion, since the transfer is solved on long characteristics along null geodesics. We first solve the wavefront propagation around a Kerr black hole that was originally explored by Hanni. This demonstrates repeated wavefront collisions, light bending, and causal propagation of radiation with the speed of light. We show that the decay rate of the total energy of wavefronts near a black hole is determined solely by the black hole spin in late phases, in agreement with analytic expectations. As a result, the ARTIST turns out to correctly solve the general relativistic radiation fields until late phases as t ˜ 90 M. We also explore the effects of absorption and scattering, and apply this code for a photon wall problem and an orbiting hotspot problem. All the simulations in this study are performed in the equatorial plane around a Kerr black hole. The ARTIST is the first step to realize the general relativistic radiation hydrodynamics.
Observability of the General Relativistic Precession of Periastra in Exoplanets
Jordan, Andres
2008-01-01
The general relativistic precession rate of periastra in close-in exoplanets can be orders of magnitude larger than the magnitude of the same effect for Mercury. The realization that some of the close-in exoplanets have significant eccentricities raises the possibility that this precession might be detectable. We explore in this work the observability of the periastra precession using radial velocity and transit light curve observations. Our analysis is independent of the source of precession, which can also have significant contributions due to additional planets and tidal deformations. We find that precession of the periastra of the magnitude expected from general relativity can be detectable in timescales of <~ 10 years with current observational capabilities by measuring the change in the primary transit duration or in the time difference between primary and secondary transits. Radial velocity curves alone would be able to detect this precession for super-massive, close-in exoplanets orbiting inactive ...
Dönmez, Orhan
2004-09-01
In this paper, the general procedure to solve the general relativistic hydrodynamical (GRH) equations with adaptive-mesh refinement (AMR) is presented. In order to achieve, the GRH equations are written in the conservation form to exploit their hyperbolic character. The numerical solutions of GRH equations are obtained by high resolution shock Capturing schemes (HRSC), specifically designed to solve nonlinear hyperbolic systems of conservation laws. These schemes depend on the characteristic information of the system. The Marquina fluxes with MUSCL left and right states are used to solve GRH equations. First, different test problems with uniform and AMR grids on the special relativistic hydrodynamics equations are carried out to verify the second-order convergence of the code in one, two and three dimensions. Results from uniform and AMR grid are compared. It is found that adaptive grid does a better job when the number of resolution is increased. Second, the GRH equations are tested using two different test problems which are Geodesic flow and Circular motion of particle In order to do this, the flux part of GRH equations is coupled with source part using Strang splitting. The coupling of the GRH equations is carried out in a treatment which gives second order accurate solutions in space and time.
English, W.; Hardcastle, M. J.; Krause, M. G. H.
2016-09-01
We present results from two suites of simulations of powerful radio galaxies in poor cluster environments, with a focus on the formation and evolution of the radio lobes. One suite of models uses relativistic hydrodynamics and the other relativistic magnetohydrodynamics; both are set up to cover a range of jet powers and velocities. The dynamics of the lobes are shown to be in good agreement with analytical models and with previous numerical models, confirming in the relativistic regime that the observed widths of radio lobes may be explained if they are driven by very light jets. The ratio of energy stored in the radio lobes to that put into the intracluster gas is seen to be the same regardless of jet power, jet velocity or simulation type, suggesting that we have a robust understanding of the work done on the ambient gas by this type of radio source. For the most powerful jets, we at times find magnetic field amplification by up to a factor of 2 in energy, but mostly the magnetic energy in the lobes is consistent with the magnetic energy injected. We confirm our earlier result that for jets with a toroidally injected magnetic field, the field in the lobes is predominantly aligned with the jet axis once the lobes are well developed, and that this leads to radio flux anisotropies of up to a factor of about two for mature sources. We reproduce the relationship between 151 MHz luminosity and jet power determined analytically in the literature.
Modelling general relativistic perfect fluids in field theoretic language
Mitskievich, N V
1999-01-01
Skew-symmetric massless fields, their potentials being $r$-forms, are close analogues of Maxwell's field (though the non-linear cases also should be considered). We observe that only two of them ($r=$2 and 3) automatically yield stress-energy tensors characteristic to normal perfect fluids. It is shown that they naturally describe both non-rotating ($r=2$) and rotating (then a combination of $r=2$ and $r=3$ fields is indispensable) general relativistic perfect fluids possessing every type of equations of state. Meanwile, a free $r=3$ field is completely equivalent to appearance of the cosmological term in Einstein's equations. Sound waves represent perturbations propagating on the background of the $r=2$ field. Some exotic properties of these two fields are outlined.
General Relativistic Simulations of Magnetized Binary Neutron Stars
Giacomazzo, Bruno
2011-04-01
Binary neutron stars are among the most important sources of gravitational waves which are expected to be detected by the current or next generation of gravitational wave detectors, such as LIGO and Virgo, and they are also thought to be at the origin of very important astrophysical phenomena, such as short gamma-ray bursts. I will report on some recent results obtained using the fully general relativistic magnetohydrodynamic code Whisky in simulating equal-mass binary neutron star systems during the last phases of inspiral, merger and collapse to black hole surrounded by a torus. I will in particular describe how magnetic fields can affect the gravitational wave signal emitted by these sources and their possible role in powering short gamma-ray bursts.
General Relativistic Simulations of Binary Neutron Star Mergers
Giacomazzo, Bruno; Rezzolla, Luciano; Baiotti, Luca; Link, David; Font, José A.
2011-08-01
Binary neutron star mergers are one of the possible candidates for the central engine of short gamma-ray bursts (GRBs) and they are also powerful sources of gravitational waves. We have used our fully general relativistic hydrodynamical code Whisky to investigate the merger of binary neutron star systems and we have in particular studied the properties of the tori that can be formed by these systems, their possible connection with the engine of short GRBs and the gravitational wave signals that detectors such as advanced LIGO will be able to detect. We have also shown how the mass of the torus varies as a function of the total mass of the neutron stars composing the binary and of their mass ratio and we have found that tori sufficiently massive to power short GRBs can indeed be formed.
General Relativistic Effects in the Core Collapse Supernova Mechanism
Bruenn, S W; Mezzacappa, A
2001-01-01
We apply our recently developed code for spherically symmetric, fully general relativistic (GR) Lagrangian hydrodynamics and multigroup flux-limited diffusion neutrino transport to examine the effects of GR on the hydrodynamics and transport during collapse, bounce, and the critical shock reheating phase of core collapse supernovae. Comparisons of models computed with GR versus Newtonian hydrodynamics show that collapse to bounce takes slightly less time in the GR limit, and that the shock propagates slightly farther out in radius before receding. After a secondary quasistatic rise in the shock radius, the shock radius declines considerably more rapidly in the GR simulations than in the corresponding Newtonian simulations. During the shock reheating phase, core collapse computed with GR hydrodynamics results in a substantially more compact structure from the center out to the stagnated shock. The inflow speed of material behind the shock is also increased. Comparisons also show that the luminosity and rms ene...
Sdowski, Aleksander; Tchekhovskoy, Alexander; Zhu, Yucong
2012-01-01
A numerical scheme is described for including radiation in multi-dimensional general-relativistic conservative fluid dynamics codes. In this method, a covariant form of the M1 closure scheme is used to close the radiation moments, and the radiative source terms are treated semi-implicitly in order to handle both optically thin and optically thick regimes. The scheme has been implemented in a conservative general relativistic radiation hydrodynamics code KORAL. The robustness of the code is demonstrated on a number of test problems, including radiative relativistic shock tubes, static radiation pressure supported atmosphere, shadows, beams of light in curved spacetime, and radiative Bondi accretion. The advantages of M1 closure relative to other approaches such as Eddington closure and flux-limited diffusion are discussed, and its limitations are also highlighted.
Gallo, Emanuel
2016-01-01
We present a general approach for the formulation of equations of motion for compact objects in general relativistic theories. The particle is assumed to be moving in a geometric background which in turn is asymptotically flat. By construction, the model incorporates the back reaction due to gravitational radiation generated by the motion of the particle. Our approach differs from other constructions tackling the same kind of problem.
Geroyannis, Vassilis S
2014-01-01
We develop a "hybrid approximative scheme" in the framework of the post-Newtonian approximation for computing general-relativistic polytropic models simulating neutron stars in critical rigid rotation. We treat the differential equations governing such a model as a "complex initial value problem", and we solve it by using the so-called "complex-plane strategy". We incorporate into the computations the complete solution for the relativistic effects, this issue representing a significant improvement with regard to the classical post-Newtonian approximation, as verified by extended comparisons of the numerical results.
Harko, T
2016-01-01
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 equa...
Numerical Stability of Generalized Entropies
Steinbrecher, György
2016-01-01
In many applications, the probability density function is subject to experimental errors. In this work the continuos dependence of a class of generalized entropies on the experimental errors is studied. This class includes the C. Shannon, C. Tsallis, A. R\\'enyi and generalized R\\'enyi entropies. By using the connection between R\\'enyi or Tsallis entropies, and the "distance" in a family of metric functional spaces, family that includes the Lebesgue normed vector spaces, we introduce a further extensive generalizations of the R\\'enyi entropy. In this work we suppose that the experimental error is measured by some $L^{p}$ norm. In line with the methodology normally used for treating the so called "ill-posed problems", auxiliary stabilizing conditions are determined, such that small - in the sense of $L^{p}$ metric - experimental errors provoke small variations of the classical and generalized entropies. These stabilizing conditions are formulated in terms of $L^{p}$ metric in a class of generalized $L^{p}$ spac...
Amano, Takanobu
2016-01-01
A new multidimensional simulation code for relativistic two-fluid electrodynamics (RTFED) is described. The basic equations consist of the full set of Maxwell's equations coupled with relativistic hydrodynamic equations for separate two charged fluids, representing the dynamics of either an electron-positron or an electron-proton plasma. It can be recognized as an extension of conventional relativistic magnetohydrodynamics (RMHD). Finite resistivity may be introduced as a friction between the two species, which reduces to resistive RMHD in the long wavelength limit without suffering from a singularity at infinite conductivity. A numerical scheme based on HLL (Harten-Lax-Van Leer) Riemann solver is proposed that exactly preserves the two divergence constraints for Maxwell's equations simultaneously. Several benchmark problems demonstrate that it is capable of describing RMHD shocks/discontinuities at long wavelength limit, as well as dispersive characteristics due to the two-fluid effect appearing at small sca...
Leung, Chun Sing; Harko, Tiberiu
2013-01-01
We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects based on the generalized Langevin equation, which accounts for the general retarded effects of the frictional force, and on the fluctuation-dissipation theorems. The vertical displacements, velocities and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and the Kerr cases. The Power Spectral Distribution of the luminosity it is also obtained, and it is shown that it has non-standard values. The theoretical predictions of the model are compared with the observational data for the luminosity time variation of the BL Lac S5 0716+714 object.
Generalized Langevin Equation Description of Stochastic Oscillations of General Relativistic Disks
Indian Academy of Sciences (India)
Chun Sing Leung; Gabriela Mocanu; Tiberiu Harko
2014-09-01
We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects based on the generalized Langevin equation, which accounts for the general retarded effects of the frictional force, and on the fluctuation–dissipation theorems. The vertical displacements, velocities and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and Kerr cases. The power spectral distribution of the luminosity is also obtained, and it is shown that it has non-standard values. The theoretical predictions of the model are compared with the observational data for the luminosity time variation of the BL Lac S5 0716+714 object.
General relativistic simulations of magnetized binary neutron star mergers
Liu, Yuk Tung; Etienne, Zachariah B; Taniguchi, Keisuke
2008-01-01
Binary neutron stars (NSNS) are expected to be among the leading sources of gravitational waves observable by ground-based laser interferometers and may be the progenitors of short-hard gamma ray bursts. We present a series of general relativistic NSNS coalescence simulations both for unmagnetized and magnetized stars. We adopt quasiequilibrium initial data for circular, irrotational binaries constructed in the conformal thin-sandwich (CTS) framework. We adopt the BSSN formulation for evolving the metric and a high-resolution shock-capturing scheme to handle the magnetohydrodynamics. Our simulations of unmagnetized binaries confirm the results of Shibata, Taniguchi and Uryu (2003). In cases in which the mergers result in a prompt collapse to a black hole, we are able to use puncture gauge conditions to extend the evolution and determine the mass of the material that forms a disk. We find that the disk mass is less than 2% of the total mass in all cases studied. We then add a small poloidal magnetic field to t...
Relativistic Configuration Interaction Treatment of Generalized Oscillator Strength for Krypton
Institute of Scientific and Technical Information of China (English)
WANG Huang-Chun; QU Yi-Zhi; LIU Chun-Hua
2007-01-01
A fully relativistic configuration interaction method is developed to investigate the transition energies and general oscillator strengths of the lower lying states of krypton, for both optically allowed and optically forbidden transitions. The calculated results are in agreement with the recent experimental measurements. The calculated transition energies for the 5s and 5s' transitions are 9.970 and 10.717eV, which agree with the experimental data of 10.033 and 10.643 eV. The calculated oscillator strengths are 0.211 and 0.170, comparable with the experimental results 0.214(±0.012) and 0.194 (±0.012), respectively. The momentum transfer positions ( K2 in a.u.) of the minimum and maximum GOSs in the 4s24p6 → 4s24p5 (5s + 5s') transitions are 1.105 and 2.225, comparable with the measurements results 1.24 and 2.97 [Phys. Rev. A 67 (2003) 062708].
General relativistic magnetohydrodynamic simulations of collapsars: Rotating black hole cases
Energy Technology Data Exchange (ETDEWEB)
Mizuno, Y. [Kyoto Univ., Kyoto (Japan). Department of Astronomy; Yamada, S. [Waseda Univ., Tokyo (Japan). Science and Engineering; Koide, S. [Toyama Univ., Toyama (Japan). Department of Engineering; Shibata, K. [Kyoto Univ., Kyoto (Japan). Kwasan and Hida Observatory
2005-06-01
We have performed 2.5-dimensional general relativistic magnetohydrodynamic (MHD) simulations of coIIapsars including a rotating black hole. InitiaIIy, we assume that the care 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 diskIike structure and the generation of a jetIike outflow near the central black hole. The jetIike outflow propagates and accelerated mainly by the magnetic field. The total jet velocity is {approx} 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.
Numerical instability due to relativistic plasma drift in EM-PIC simulations
Xu, Xinlu; Martins, Samual F; Tsung, Frank S; Decyk, Viktor K; Fonseca, Ricardo A; Lu, Wei; Silva, Luis O; Mori, Warren B
2012-01-01
The numerical instability observed in the Electromagnetic-Particle-in-cell (EM-PIC) simulations with a plasma drifting with relativistic velocities is studied using both theory and computer simulations. We derive the numerical dispersion relation for a cold plasma drifting with a relativistic velocity and find an instability attributed to the coupling between the beam modes of the drifting plasma and the electromagnetic modes in the system. The characteristic pattern of the instability in Fourier space for various simulation setups and Maxwell Equation solvers are explored by solving the corresponding numerical dispersion relations. Furthermore, based upon these characteristic patterns we derive an asymptotic expression for the instability growth rate. The results are compared against simulation results and good agreement is found. The results are used as a guide to develop possible approaches to mitigate the instability. We examine the use of a spectral solver and show that such a solver when combined with a...
Godfrey, Brendan B
2013-01-01
Rapidly growing numerical instabilities routinely occur in multidimensional particle-in-cell computer simulations of plasma-based particle accelerators, astrophysical phenomena, and relativistic charged particle beams. Reducing instability growth to acceptable levels has necessitated higher resolution grids, high-order field solvers, current filtering, etc. except for certain ratios of the time step to the axial cell size, for which numerical growth rates and saturation levels are reduced substantially. This paper derives and solves the cold beam dispersion relation for numerical instabilities in multidimensional, relativistic, electromagnetic particle-in-cell programs employing either the standard or the Cole-Karkkainnen finite difference field solver on a staggered mesh and the common Esirkepov current-gathering algorithm. Good overall agreement is achieved with previously reported results of the WARP code. In particular, the existence of select time steps for which instabilities are minimized is explained....
Numerical Construction of Magnetosphere with Relativistic Two-fluid Plasma Flows
Kojima, Yasufumi
2009-01-01
We present a numerical model in which a cold pair plasma is ejected with relativistic speed through a polar cap region and flows almost radially outside the light cylinder. Stationary axisymmetric structures of electromagnetic fields and plasma flows are self-consistently calculated. In our model, motions of positively and negatively charged particles are assumed to be determined by electromagnetic forces and inertial terms, without pair creation and annihilation or radiation loss. The global electromagnetic fields are calculated by the Maxwell's equations for the plasma density and velocity, without using ideal MHD condition. Numerical result demonstrates the acceleration and deceleration of plasma due to parallel component of the electric fields. Numerical model is successfully constructed for weak magnetic fields or highly relativistic fluid velocity, i.e, kinetic energy dominated outflow. It is found that appropriate choices of boundary conditions and plasma injection model at the polar cap should be expl...
Numerical study of ultra-relativistic electromagnetic filamentation in boosted frames
Martins, S. F.; Fonseca, R. A.; Mori, W. B.; Silva, L. O.
2007-11-01
We address the simulation of relativistic shocks in astrophysics, namely the numerical implications of ultra-relativistic particles and the large time/space scales associated with these systems. It was recently shown [1] that performing simulations in optimized Lorentz frames can decrease simulation run times by orders of magnitude, completely changing computational resources required. The Lorentz transformation for a boosted frame was implemented in osiris 2.0 [2] and encompassed several difficulties that will be discussed. For instance, transformation of quantities back to the laboratory frame may require massive data handling and complex diagnostic/visualization, and can cancel the potential gains from the time scale reduction due to the boost. The possibility of using a boosted frame to suppress numerical noise (e.g. due to numerical Cerenkov radiation) will also be explored. [1] J.-L. Vay, PRL 98, 130405 (2007) [2] R. A. Fonseca et al, Lecture Notes in Computer Science 2329, III-342 (Springer-Verlag, 2002)
General relativistic effects in quantum interference of "clocks"
Zych, Magdalena; Costa, Fabio; Brukner, Časlav
2016-01-01
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.
Pétri, J
2014-01-01
Pulsars are believed to loose their rotational kinetic energy primarily by a large amplitude low frequency electromagnetic wave which is eventually converted into particle creation, acceleration and followed by a broad band radiation spectrum. To date, there exist no detailed calculation of the exact spin-down luminosity with respect to the neutron star magnetic moment and spin frequency, including general-relativistic effects. Estimates are usually given according to the flat spacetime magnetodipole formula. The present paper pursue our effort to look for accurate solutions of the general-relativistic electromagnetic field around a slowly rotating magnetized neutron star. In a previous work, we already found approximate stationary solutions to this problem. Here we address again this problem but using a more general approach. We indeed solve the full set of time-dependent Maxwell equations in a curved vacuum space-time following the 3+1 formalism. The numerical code is based on our pseudo-spectral method exp...
Matsas, G E A
2003-01-01
We investigate and solve in the context of General Relativity the apparent paradox which appears when bodies floating in a background fluid are set in relativistic motion. Suppose some macroscopic body, say, a submarine designed to lie just in equilibrium when it rests (totally) immersed in a certain background fluid. The puzzle arises when different observers are asked to describe what is expected to happen when the submarine is given some high velocity parallel to the direction of the fluid surface. On the one hand, according to observers at rest with the fluid, the submarine would contract and, thus, sink as a consequence of the density increase. On the other hand, mariners at rest with the submarine using an analogous reasoning for the fluid elements would reach the opposite conclusion. The general relativistic extension of the Arquimedes law for moving bodies shows that the submarine sinks.
Godfrey, Brendan B.; Vay, Jean-Luc
2013-09-01
Rapidly growing numerical instabilities routinely occur in multidimensional particle-in-cell computer simulations of plasma-based particle accelerators, astrophysical phenomena, and relativistic charged particle beams. Reducing instability growth to acceptable levels has necessitated higher resolution grids, high-order field solvers, current filtering, etc. except for certain ratios of the time step to the axial cell size, for which numerical growth rates and saturation levels are reduced substantially. This paper derives and solves the cold beam dispersion relation for numerical instabilities in multidimensional, relativistic, electromagnetic particle-in-cell programs employing either the standard or the Cole-Karkkainnen finite difference field solver on a staggered mesh and the common Esirkepov current-gathering algorithm. Good overall agreement is achieved with previously reported results of the WARP code. In particular, the existence of select time steps for which instabilities are minimized is explained. Additionally, an alternative field interpolation algorithm is proposed for which instabilities are almost completely eliminated for a particular time step in ultra-relativistic simulations.
General relativistic effects in quantum interference of “clocks”
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.
Pétri, J
2014-01-01
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 multi-domain decomposition of the simulation box belongs to the discontinu...
Fragile, P Chris
2008-01-01
(Abridged) We present one of the first physically-motivated two-dimensional general relativistic magnetohydrodynamic (GRMHD) numerical simulations of a radiatively-cooled black-hole accretion disk. The fiducial simulation combines a total-energy-conserving formulation with a radiative cooling function, which includes bremsstrahlung, synchrotron, and Compton effects. By comparison with other simulations we show that in optically thin advection-dominated accretion flows, radiative cooling can significantly affect the structure, without necessarily leading to an optically thick, geometrically thin accretion disk. We further compare the results of our radiatively-cooled simulation to the predictions of a previously developed analytic model for such flows. For the very low stress parameter and accretion rate found in our simulated disk, we closely match a state called the "transition" solution between an outer advection-dominated accretion flow and what would be a magnetically-dominated accretion flow (MDAF) in th...
General relativistic radiative transfer in hot astrophysical plasmas a characteristic approach
Zane, S; Nobili, L; Erna, M; Zane, Silvia; Turolla, Roberto; Nobili, Luciano; Erna, Myris
1996-01-01
In this paper we present a characteristic method for solving the transfer equation in differentially moving media in a curved spacetime. The method is completely general, but its capabilities are exploited at best in presence of symmetries, when the existence of conserved quantities allows to derive analytical expressions for the photon trajectories in phase space. In spherically--symmetric, stationary configurations the solution of the transfer problem is reduced to the integration of a single ordinary differential equation along the bi--parametric family of characteristic rays. Accurate expressions for the radiative processes relevant to continuum transfer in a hot astrophysical plasma have been used in evaluating the source term, including relativistic e--p, e--e bremsstrahlung and Compton scattering. A numerical code for the solution of the transfer problem in moving media in a Schwarzschild spacetime has been developed and tested. Some applications, concerning ``hot'' and ``cold'' accretion onto non--rot...
Probing the Internal Structure of Magnetized, Relativistic Jets with Numerical Simulations
Directory of Open Access Journals (Sweden)
José-María Martí
2016-10-01
Full Text Available From an observational point of view, unveiling the physical processes behind the nature of the jets emanating from radio-loud AGN demands the resolution of the structure across the jet with the highest angular resolutions. Relying on a magneto-fluid dynamical description, numerical simulations can help to characterize the internal structure of jets (transversal structure, magnetic field structure, internal shocks, etc.. In the first part of the paper, we shall discuss equilibrium models of magnetized, relativistic, infinite, axisymmetric jets with rotation propagating through a homogeneous, static, unmagnetized ambient medium. Then, these transversal equilibrium profiles will be used to build steady models of overpressured, superfast-magnetosonic, relativistic jets, with the aim of characterizing their internal structure in connection with their dominant type of energy (internal energy: hot jets; rest-mass energy: kinetically-dominated jets; magnetic energy: Poynting-flux-dominated jets.
Waves in General Relativistic Two-fluid Plasma around a Schwarzschild Black Hole
Rahman, M Atiqur
2010-01-01
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
General Relativistic Precession in Small Solar System Bodies
Sekhar, Aswin; Werner, Stephanie; Hoffmann, Volker; Asher, David; Vaubaillon, Jeremie; Hajdukova, Maria; Li, Gongjie
2016-10-01
Introduction: One of the greatest successes of the Einstein's General Theory of Relativity (GR) was the correct prediction of the precession of perihelion of Mercury. The closed form expression to compute this precession tells us that substantial GR precession would occur only if the bodies have a combination of both moderately small perihelion distance and semi-major axis. Minimum Orbit Intersection Distance (MOID) is a quantity which helps us to understand the closest proximity of two orbits in space. Hence evaluating MOID is crucial to understand close encounters and collision scenarios better. In this work, we look at the possible scenarios where a small GR precession in argument of pericentre (ω) can create substantial changes in MOID for small bodies ranging from meteoroids to comets and asteroids.Analytical Approach and Numerical Integrations: Previous works have looked into neat analytical techniques to understand different collision scenarios and we use those standard expressions to compute MOID analytically. We find the nature of this mathematical function is such that a relatively small GR precession can lead to drastic changes in MOID values depending on the initial value of ω. Numerical integrations were done with package MERCURY incorporating the GR code to test the same effects. Numerical approach showed the same interesting relationship (as shown by analytical theory) between values of ω and the peaks/dips in MOID values. Previous works have shown that GR precession suppresses Kozai oscillations and this aspect was verified using our integrations. There is an overall agreement between both analytical and numerical methods.Summary and Discussion: We find that GR precession could play an important role in the calculations pertaining to MOID and close encounter scenarios in the case of certain small solar system bodies (depending on their initial orbital elements). Previous works have looked into impact probabilities and collision scenarios on
Choreographic solution to the general-relativistic three-body problem.
Imai, Tatsunori; Chiba, Takamasa; Asada, Hideki
2007-05-18
We reexamine the three-body problem in the framework of general relativity. The Newtonian N-body problem admits choreographic solutions, where a solution is called choreographic if every massive particle moves periodically in a single closed orbit. One is a stable figure-eight orbit for a three-body system, which was found first by Moore (1993) and rediscovered with its existence proof by Chenciner and Montgomery (2000). In general relativity, however, the periastron shift prohibits a binary system from orbiting in a single closed curve. Therefore, it is unclear whether general-relativistic effects admit choreography such as the figure eight. We examine general-relativistic corrections to initial conditions so that an orbit for a three-body system can be choreographic and a figure eight. This illustration suggests that the general-relativistic N-body problem also may admit a certain class of choreographic solutions.
Horak, Jiri
2013-01-01
We study the dynamics of spiral waves and oscillation modes in relativistic rotating discs around black holes. Generalizing the Newtonian theory, we show that wave absorption can take place at the corotation resonance, where the pattern frequency of the wave matches the background disc rotation rate. We derive the general relativistic expression for the disc vortensity (vorticity divided by surface density), which governs the behaviour of density perturbation near corotation. Depending on the gradient of the generalized disc vortensity, corotational wave absorption can lead to the amplification or damping of the spiral wave. We apply our general theory of relativistic wave dynamics to calculate the non-axisymmetric inertial-acoustic modes (also called p-modes) trapped in the inner-most region of a black hole accretion disc. Because general relativity changes the profiles of the radial epicyclic frequency and disc vortensity near the inner disc edge close to the black hole, these p-modes can become overstable ...
Amano, Takanobu
2016-11-01
A new multidimensional simulation code for relativistic two-fluid electrodynamics (RTFED) is described. The basic equations consist of the full set of Maxwell’s equations coupled with relativistic hydrodynamic equations for separate two charged fluids, representing the dynamics of either an electron-positron or an electron-proton plasma. It can be recognized as an extension of conventional relativistic magnetohydrodynamics (RMHD). Finite resistivity may be introduced as a friction between the two species, which reduces to resistive RMHD in the long wavelength limit without suffering from a singularity at infinite conductivity. A numerical scheme based on HLL (Harten-Lax-Van Leer) Riemann solver is proposed that exactly preserves the two divergence constraints for Maxwell’s equations simultaneously. Several benchmark problems demonstrate that it is capable of describing RMHD shocks/discontinuities at long wavelength limit, as well as dispersive characteristics due to the two-fluid effect appearing at small scales. This shows that the RTFED model is a promising tool for high energy astrophysics application.
Generalized Relativistic Wave Equations with Intrinsic Maximum Momentum
Ching, Chee Leong
2013-01-01
We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wavefunctions of one-dimensional Klein-Gordon and Dirac equation with linear confining potentials, and the Dirac oscillator. Bound state solutions are only possible when the strength of scalar potential are stronger than vector potential. The energy spectrum of the systems studied are bounded from above, whereby classical characteristics are observed in the uncertainties of position and momentum operators. Also, there is a truncation in the maximum number of bound states that is allowed. Some of these quantum-gravitational features may have future applications.
Generalized relativistic wave equations with intrinsic maximum momentum
Ching, Chee Leong; Ng, Wei Khim
2014-05-01
We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wave functions of one-dimensional Klein-Gordon and Dirac equation with linear confining potentials, and the Dirac oscillator. Bound state solutions are only possible when the strength of scalar potential is stronger than vector potential. The energy spectrum of the systems studied is bounded from above, whereby classical characteristics are observed in the uncertainties of position and momentum operators. Also, there is a truncation in the maximum number of bound states that is allowed. Some of these quantum-gravitational features may have future applications.
Bancelin, D; Thuillot, W
2016-01-01
The integration of the equations of motion in gravitational dynamical systems -- either in our Solar System or for extra-solar planetary system -- being non integrable in the global case, is usually performed by means of numerical integration. Among the different numerical techniques available for solving ordinary differential equations, the numerical integration using Lie series has shown some advantages. In its original form (Hanslmeier 1984), it was limited to the N-body problem where only gravitational interactions are taken into account. We present in this paper a generalisation of the method by deriving an expression of the Lie-terms when other major forces are considered. As a matter of fact, previous studies had been made but only for objects moving under gravitational attraction. If other perturbations are added, the Lie integrator has to be re-built. In the present work we consider two cases involving position and position-velocity dependent perturbations: relativistic acceleration in the framework ...
High order numerical simulations of the Richtmyer Meshkov instability in a relativistic fluid
Zanotti, Olindo
2014-01-01
We study the Richtmyer--Meshkov (RM) instability of a relativistic perfect fluid by means of high order numerical simulations with adaptive mesh refinement (AMR). The numerical scheme adopts a finite volume Weighted Essentially Non-Oscillatory (WENO) reconstruction to increase accuracy in space, a local space-time discontinuous Galerkin predictor method to obtain high order of accuracy in time and a high order one-step time update scheme together with a "cell-by-cell" space-time AMR strategy with time-accurate local time stepping. In this way, third order accurate (both in space and in time) numerical simulations of the RM instability are performed, spanning a wide parameter space. We present results both for the case in which a light fluid penetrates into a higher density one (Atwood number $A>0$), and for the case in which a heavy fluid penetrates into a lower density one (Atwood number $A<0$). We find that, for large Lorentz factors \\gamma_s of the incident shock wave, the relativistic RM instability is...
Numerical studies of relativistic corrections to Fermion dynamics and the Aharonov-Casher effect
Energy Technology Data Exchange (ETDEWEB)
Ferreira Filho, L.G. [Universidade do Estado, Resende, RJ (Brazil). Faculdade de Tecnologia]. E-mail: gonzaga@fat.uerj.br; Helayel-Neto, J.A.; Murga, J.L.C. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]|[Grupo de Fisica Teorica Jose Leite Lopes, Petropolis, RJ (Brazil); E-mail: helayel@cbpf.br
2004-05-01
Dirac equation with minimal electromagnetic coupling yields, in the weakly relativistic regime, the Pauli equation for two-component minimally-interacting electron endowed with magnetic moment coupling and the right value of the Lande g-factor, g=2. On the other hand, another remarkable feature associated with spinning particles is the coupling of the magnetic dipole moment to an electric field, which gives rise to the so-called Aharonov-Casher phase for the wave function of the test particle. This phase shift shows up even though there is no force acting on the particle, just as in the familiar case of the Aharonov-Bohm effect. The most accurate experimental measurements of the spin-electric field interaction are carried out with atomic systems. This work sets out to investigate how the Aharonov-Casher effect may be related to the relativistic regime: in practical terms, how it may appear by means of relativistic corrections to the Schroedinger equation, once an external electromagnetic field is switched on. One should understand at which order of velocities the Aharonov-Casher shift arises, either by adding up higher-order gradient terms to the Schroedinger equation or by carrying out the non-relativistic limit of Dirac equation with higher-derivative terms. The latter has very interesting consequences whenever adjoined to the Dirac equation, leading to a rich excitation spectrum and inducing interesting couplings in the low-energy regime. In view of the calculational complexity inherent to the task of finding solutions to these higher-derivatives partial differential equations, wave-function solutions and phase shifts have to be searched for with the help of numerical methods and computer-algebra software. (author)
Relativistic corrections to the central force problem in a generalized potential approach
Singh, Ashmeet
2014-01-01
We present a novel technique to obtain the relativistic corrections to the central force problem in the Lagrangian formulation, using a generalized potential energy. Throughout the paper, we focus on the attractive inverse square law central force. The generalised potential can be made a part of the regular classical lagrangian which can reproduce the relativistic force equation upto second order in $|\\vec{v}|/c$. We then go on to derive the relativistically corrected Hamiltonian from the Lagrangian and estimate the corrections to the total energy of the system. We employ our methodology to calculate the relativistic correction to the circular orbit in attractive gravitational force. We also estimate to the first order energy correction in the ground state of the hydrogen atom in the semi-classical approach. Our predictions in both problems give the reasonable agreement with the known results. Thus we feel that this work has pedagogical value and can be used by undergraduate students to better understand the ...
Critical rotation of general-relativistic polytropic models revisited
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.
High-Order Fully General-Relativistic Hydrodynamics: new Approaches and Tests
Radice, David; Galeazzi, Filippo
2013-01-01
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. (2013). 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 mo...
De Rijcke, Sven; Boelens, Thomas
2014-01-01
We show that the general relativistic theory of the dynamics of isotropic stellar clusters can be developed essentially along the same lines as the Newtonian theory. We prove that the distribution function can be derived from any isotropic momentum moment and that every higher-order moment of the distribution can be written as an integral over a zeroth-order moment. We propose a mathematically simple expression for the distribution function of a family of isotropic general relativistic cluster models and investigate their dynamical properties. In the Newtonian limit, these models obtain a distribution function of the form F(E) ~ (E-E_0)^alpha, with E binding energy and E_0 a constant that determines the model's outer radius. The slope alpha sets the steepness of the distribution function and the corresponding radial density and pressure profiles. We show that the field equations only yield solutions with finite mass for alpha3.5, only Newtonian models exist. In other words: within the context of this family o...
Novak, Jerome; Dimmelmeier, Harrald; Font-Roda, Jose A.
2004-12-01
We present a new three-dimensional general relativistic hydrodynamics code which can be applied to study stellar core collapses and the resulting gravitational radiation. This code uses two different numerical techniques to solve partial differential equations arising in the model: high-resolution shock capturing (HRSC) schemes for the evolution of hydrodynamic quantities and spectral methods for the solution of Einstein equations. The equations are written and solved using spherical polar coordinates, best suited to stellar topology. Einstein equations are formulated within the 3+1 formalism and conformal flat condition (CFC) for the 3-metric and gravitational radiation is extracted using Newtonian quadrupole formulation.
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.
Numerical instability due to relativistic plasma drift in EM-PIC simulations
Xu, Xinlu; Yu, Peicheng; Martins, Samual F.; Tsung, Frank S.; Decyk, Viktor K.; Vieira, Jorge; Fonseca, Ricardo A.; Lu, Wei; Silva, Luis O.; Mori, Warren B.
2013-11-01
The numerical instability observed in electromagnetic particle-in-cell (EM-PIC) simulations with a plasma drifting with relativistic velocities is studied using both theory and computer simulations. We derive the numerical dispersion relation for a cold plasma drifting with a relativistic velocity, and find an instability attributed to the intersection between beam resonances and the electromagnetic modes in the drifting plasma. The intersection can occur in the fundamental Brillouin zones when EM waves with phase velocities less than the speed of light exist, and from aliasing beam resonances and aliasing EM modes. The unstable modes are neither purely transverse nor longitudinal. The characteristic patterns of the instability in Fourier space for various simulation setups and Maxwell equation solvers are explored by solving the corresponding numerical dispersion relations. Furthermore, based upon these characteristic patterns, we derive an asymptotic expression for the instability growth rate. The asymptotic expression greatly speeds up the calculation of the instability growth rate and makes the parameter scans for minimal growth rate feasible even for full three dimensions. The results are compared against simulation results, and good agreements are found. These results can be used as a guide to develop possible approaches to mitigate the instability. We examine the use of a spectral solver and show that such a solver when combined with a low pass filter with a cutoff value of |k→| essentially eliminates the instability while not modifying modes of physical interest. The use of a spectral solver also provides minimal errors to electromagnetic modes in the lowest Brillouin zones.
Institute of Scientific and Technical Information of China (English)
WANG Yu-Sheng; ZHANG Xiao-Ni; YUAN Bao-He; FANG Jian-Hui; YANG Guo-Hong; LIN Peng; PANG Ting
2008-01-01
Based on the concept of higher-order adiabatic invariants of mechanical system with action of a small perturbation, the perturbation to Lie symmetry and generalized Hojman adiabatic invariants for the relativistic Hamilton system are studied. Perturbation to Lie symmetry is discussed under general infinitesimal transformation of groups in which time is variable. The form and the criterion of generalized Hojman adiabatic invariants for this system are obtained. Finally, an example is given to illustrate the results.
Post-relativistic gravity a hidden variable theory for general relativity
Schmelzer, I
1996-01-01
Post-relativistic gravity is a hidden variable theory for general relativity. It introduces the pre-relativistic notions absolute space, absolute time, and ether as hidden variables into general relativity. Evolution is defined by the equations of general relativity and the harmonic coordinate condition interpreted as a physical equation. There are minor differences in predictions compared with general relativity (i.e. trivial topology of the universe is predicted). The unobservable absolute time is designed to solve the problem of time in quantization of general relativity. Background space and time define a Newtonian frame for the quantization of the gravitational field. By the way, a lot of other conceptual problems of quantization will be solved (i.e. no constraints, no topological foam, no black hole and bib bang singularities, natural vacuum definition for quantum fields on classical background).
Numerical simulations of the internal shock model in magnetized relativistic jets of blazars
Rueda-Becerril, Jesus M; Aloy, Miguel A
2015-01-01
The internal shocks scenario in relativistic jets is used to explain the variability of the blazar emission. Recent studies have shown that the magnetic field significantly alters the shell collision dynamics, producing a variety of spectral energy distributions and light-curves patterns. However, the role played by magnetization in such emission processes is still not entirely understood. In this work we numerically solve the magnetohydodynamic evolution of the magnetized shells collision, and determine the influence of the magnetization on the observed radiation. Our procedure consists in systematically varying the shell Lorentz factor, relative velocity, and viewing angle. The calculations needed to produce the whole broadband spectral energy distributions and light-curves are computationally expensive, and are achieved using a high-performance parallel code.
Takahashi, Hiroyuki R
2013-01-01
We develop a numerical scheme for solving a fully special relativistic resistive radiation magnetohydrodynamics. Our code guarantees conservations of total mass, momentum and energy. Radiation energy density and radiation flux are consistently updated using the M-1 closure method, which can resolve an anisotropic radiation fields in contrast to the Eddington approximation as well as the flux-limited diffusion approximation. For the resistive part, we adopt a simple form of the Ohm's law. The advection terms are explicitly solved with an approximate Riemann solver, mainly HLL scheme, and HLLC and HLLD schemes for some tests. The source terms, which describe the gas-radiation interaction and the magnetic energy dissipation, are implicitly integrated, relaxing the Courant-Friedrichs-Lewy condition even in optically thick regime or a large magnetic Reynolds number regime. Although we need to invert $4\\times 4$ (for gas-radiation interaction) and $3\\times 3$ (for magnetic energy dissipation) matrices at each grid ...
Roedig, Constanze; Alic, Daniela
2012-01-01
We present the implementation of an implicit-explicit (IMEX) Runge-Kutta numerical scheme for general relativistic hydrodynamics coupled to an optically thick radiation field in two existing GR-hydrodynamics codes. We argue that the necessity of such an improvement arises naturally in astrophysically relevant regimes where the optical thickness is high as the equations become stiff. By performing several 1D tests we verify the codes' new ability to deal with this stiffness and show consistency. Then, still in 1D, we compute a luminosity versus accretion rate diagram for the setup of spherical accretion onto a Schwarzschild black hole and find good agreement with previous work. Lastly, we revisit the supersonic Bondi Hoyle Lyttleton (BHL) accretion in 2D where we can now present simulations of realistic temperatures, down to T~10^6 K. 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 applicabil...
General-Relativistic Simulations of Three-Dimensional Core-Collapse Supernovae
Ott, C D; Moesta, P; Haas, R; Drasco, S; O'Connor, E; Reisswig, C; Meakin, C; Schnetter, E
2012-01-01
We study the three-dimensional (3D) hydrodynamics of the post-core-bounce phase of the collapse of a 27 solar-mass 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 3-species neutrino leakage scheme with neutrino heating. Unlike "light-bulb" heating/cooling schemes, the leakage scheme captures the essential aspects of neutrino cooling, heating, and lepton number exchange as predicted by radiation-hydrodynamics simulations. The 27 solar-mass progenitor was studied in 2D by B. Mueller et al. (2012; arXiv:1205.7078), 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...
Narayan, Ramesh; Psaltis, Dimitrios; Sadowski, Aleksander
2015-01-01
We describe 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 the 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 MHD simulations of accretion discs. One application is to a thin accretion disc around a black hole. We find that the gas below ...
The generalized Coulomb interactions for relativistic scalar bosons
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.
Herrera, L; Ibañez, J; Ospino, J
2014-01-01
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.
General relativistic polytropes with a repulsive cosmological constant
Stuchlík, Zdeněk; Novotný, Jan
2016-01-01
Spherically symmetric equilibrium configurations of perfect fluid obeying a polytropic equation of state are studied in spacetimes with a repulsive cosmological constant. The configurations are specified in terms of three parameters---the polytropic index $n$, the ratio of central pressure and central energy density of matter $\\sigma$, and the ratio of energy density of vacuum and central density of matter $\\lambda$. The static equilibrium configurations are determined by two coupled first-order nonlinear differential equations that are solved by numerical methods with the exception of polytropes with $n=0$ corresponding to the configurations with a uniform distribution of energy density, when the solution is given in terms of elementary functions. The geometry of the polytropes is conveniently represented by embedding diagrams of both the ordinary space geometry and the optical reference geometry reflecting some dynamical properties of the geodesic motion. The polytropes are represented by radial profiles of...
Lou, Yu-Qing; Xia, Yu-Kai
2017-05-01
We study magnetohydrodynamic (MHD) self-similar collapses and void evolution, with or without shocks, of a general polytropic quasi-spherical magnetofluid permeated by random transverse magnetic fields under the Paczynski-Wiita gravity that captures essential general relativistic effects of a Schwarzschild black hole (BH) with a growing mass. Based on the derived set of non-linear MHD ordinary differential equations, we obtain various asymptotic MHD solutions, the geometric and analytical properties of the magnetosonic critical curve (MSCC) and MHD shock jump conditions. Novel asymptotic MHD solution behaviours near the rim of central expanding voids are derived analytically. By exploring numerical global MHD solutions, we identify allowable boundary conditions at large radii that accommodate a smooth solution and show that a reasonable amount of magnetization significantly increases the mass accretion rate in the expansion-wave-collapse solution scenario. We also construct the counterparts of envelope-expansion-core-collapse solutions that cross the MSCC twice, which are found to be closely paired with a sequence of global smooth solutions satisfying a novel type of central MHD behaviours. MHD shocks with static outer and various inner flow profiles are also examined. Astrophysical applications include dynamic core collapses of magnetized massive stars and compact objects as well as formation of supermassive, hypermassive, dark matter and mixed matter BHs in the Universe, including the early Universe. Such gigantic BHs can be detected in X-ray/gamma-ray sources, quasars, ultraluminous infrared galaxies or extremely luminous infrared galaxies and dark matter overwhelmingly dominated elliptical galaxies as well as massive dark matter halos, etc. Gravitational waves and electromagnetic wave emissions in broad band (including e.g., gamma-ray bursts and fast radio bursts) can result from this type of dynamic collapses of forming BHs involving magnetized media.
General relativistic simulations of binary neutron star mergers
Energy Technology Data Exchange (ETDEWEB)
Giacomazzo, Bruno [Trento Univ. (Italy)
2016-11-01
Currently, we are running additional simulations to investigate additional models for the properties of dense matter. Furthermore, we are using remote visualization resources provided by LRZ to produce movies showing 3D visualizations of our simulations, which will be available soon on the web page of our group. One of the main challenges for our simulations is the fact that some important effects leading to magnetic field amplification happen on small length scales. This makes it very difficult to resolve them numerically. In order to further improve the accuracy, we proposed a follow- up study in which we will evolve one or more models with very high resolution and then use the results to calibrate a so-called sub-grid model, which is designed to capture the field amplification on scales not resolved with the lower, more affordable resolutions. Once calibrated, the sub-grid approach will allow to investigate a large number of models without the need for very high resolutions.
A choreographic solution to the general relativistic three-body problem
Imai, T; Chiba, T; Asada, Hideki; Chiba, Takamasa; Imai, Tatsunori
2007-01-01
We revisit the three-body problem in the framework of general relativity. The Newtonian N-body problem admits choreographic solutions, where a solution is called choreographic if every massive particles move periodically in a single closed orbit. One is a stable figure-eight orbit of a three-body system, which was found first by Moore (1993) and re-discovered with its existence proof by Chenciner and Montgomery (2000), In general relativity, however, the periastron shift prohibits a binary system from orbiting in a closed curve. Therefore, it is unclear whether general relativistic effects admit a choreographic solution such as the figure-eight. We carefully examine general relativistic corrections to initial conditions so that an orbit to a three-body system can be closed in a figure-eight. This solution is still choreographic without causing periastron shift. This illustration suggests that the general relativistic N-body problem also may admit a certain class of choreographic solutions.
General Relativistic Non-radial Oscillations of Compact Stars
Hall, Zack, II; Jaikumar, Prashanth
2017-01-01
Currently, we lack a means of identifying the type of matter at the core of compact stars, but in the future, we may be able to use gravitational wave signals produced by fluid oscillations inside compact stars to discover new phases of dense matter. To this end, we study the fluid perturbations inside compact stars such as Neutron Stars and Strange Quark Stars, focusing on modes that couple to gravitational waves. Using a modern equation of state for quark matter that incorporates interactions at moderately high densities, we implement an efficient computational scheme to solve the oscillation equations in the framework of General Relativity, and determine the complex eigenfrequencies that describe the oscillation and damping of the non-radial fluid modes. We discuss the significance of our results for future detection of these modes through gravitational waves. This work is supported in part by the CSULB Graduate Research Fellowship and by the National Science Foundation NSF PHY-1608959.
Quantum interferometric visibility as a witness of general relativistic proper time.
Zych, Magdalena; Costa, Fabio; Pikovski, Igor; Brukner, Časlav
2011-10-18
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.
General Relativistic Simulations of Magnetized Plasmas around Merging Supermassive Black Holes
Giacomazzo, Bruno; Miller, M Coleman; Reynolds, Christopher S; van Meter, James R
2012-01-01
Coalescing supermassive black hole binaries are produced by the mergers of galaxies and are the most powerful sources of gravitational waves accessible to space-based gravitational observatories. Some such mergers may occur in the presence of matter and magnetic fields and hence generate an electromagnetic counterpart. In this paper we present the first general relativistic simulations of magnetized plasma around merging supermassive black holes using the general relativistic magnetohydrodynamic code Whisky. By considering different magnetic field strengths, going from non-magnetically dominated to magnetically dominated regimes, we explore how magnetic fields affect the dynamics of the plasma and the possible emission of electromagnetic signals. In particular we observe a total amplification of the magnetic field of ~2 orders of magnitude which is driven by the accretion onto the binary and that leads to much stronger electromagnetic signals, more than a factor of 10^4 larger than comparable calculations don...
General Relativistic Simulations of Magnetized Plasmas around Merging Supermassive Black Holes
Giacomazzo, Bruno; Baker, John G.; Miller, M. Coleman; Reynolds, Christopher S.; van Meter, James R.
2012-06-01
Coalescing supermassive black hole binaries are produced by the mergers of galaxies and are the most powerful sources of gravitational waves accessible to space-based gravitational observatories. Some such mergers may occur in the presence of matter and magnetic fields and hence generate an electromagnetic counterpart. In this Letter, we present the first general relativistic simulations of magnetized plasma around merging supermassive black holes using the general relativistic magnetohydrodynamic code Whisky. By considering different magnetic field strengths, going from non-magnetically dominated to magnetically dominated regimes, we explore how magnetic fields affect the dynamics of the plasma and the possible emission of electromagnetic signals. In particular, we observe a total amplification of the magnetic field of ~2 orders of magnitude, which is driven by the accretion onto the binary and that leads to much stronger electromagnetic signals, more than a factor of 104 larger than comparable calculations done in the force-free regime where such amplifications are not possible.
Cosmology and stellar equilibrium using Newtonian hydrodynamics with general relativistic pressure
Baqui, P O; Piattella, O F
2015-01-01
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 General Relativity theory. We perform in an explicit way the deduction of the Hwang-Noh equations, comparing it with similar computations found in the literature. Later, we investigate stellar equilibrium and cosmology, at background and perturbative levels, using the new set of equations. It is shown that, in this context, the predictions for the background evolution of the universe are deeply changed with respect to the full relativistic theory: the acceleration of the universe is achieved with positive pressure. The properties of neutron stars are reproduced qualitatively, but the upper mass is at least one order of magnitude higher than that obtained in General Relativity. However, the perturbed cosmological equations at small scales reproduce those found in the relativistic context. We argue that this last result may open new possibilities for ...
Institute of Scientific and Technical Information of China (English)
Luo Shao-Kai
2007-01-01
For a relativistic holonomic nonconservative system, by using the Noether symmetry, a new non-Noether conserved quantity is given under general infinitesimal transformations of groups. On the basis of the theory of invariance of differential equations of motion under general infinitesimal transformations, we construct the relativistic Noether symmetry, Lie symmetry and the condition under which the Noether symmetry is a Lie symmetry under general infinitesimal transformations. By using the Noether symmetry, a new relativistic non-Noether conserved quantity is given which only depends on the variables t, qs and (q)s. An example is given to illustrate the application of the results.
A generalized Jaynes-Cummings model: The relativistic parametric amplifier and a single trapped ion
Energy Technology Data Exchange (ETDEWEB)
Ojeda-Guillén, D., E-mail: dojedag@ipn.mx [Escuela Superior de Cómputo, Instituto Politécnico Nacional, Av. Juan de Dios Bátiz esq. Av. Miguel Othón de Mendizábal, Col. Lindavista, Delegación Gustavo A. Madero, C.P. 07738 Ciudad de México (Mexico); Mota, R. D. [Escuela Superior de Ingeniería Mecánica y Eléctrica, Unidad Culhuacán, Instituto Politécnico Nacional, Av. Santa Ana No. 1000, Col. San Francisco Culhuacán, Delegación Coyoacán, C.P. 04430 Ciudad de México (Mexico); Granados, V. D. [Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Ed. 9, Unidad Profesional Adolfo López Mateos, Delegación Gustavo A. Madero, C.P. 07738 Ciudad de México (Mexico)
2016-06-15
We introduce a generalization of the Jaynes-Cummings model and study some of its properties. We obtain the energy spectrum and eigenfunctions of this model by using the tilting transformation and the squeezed number states of the one-dimensional harmonic oscillator. As physical applications, we connect this new model to two important and novelty problems: the relativistic parametric amplifier and the quantum simulation of a single trapped ion.
Relativistic magnetohydrodynamics in one dimension.
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.
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
Sekhar, Aswin; Asher, David; Morbidelli, Alessandro; Werner, Stephanie; Vaubaillon, Jeremie; Li, Gongjie
2017-06-01
Two well known phenomena in orbital dynamics associated with low perihelion distance bodies are general relativistic (GR) precession and Lidov-Kozai (LK) oscillations.In this work, we are interested to identify bodies evolving in the near future (i.e. thousands of years in this case) into rapid sungrazing and sun colliding phases and undergoing inclination flips, due to LK like oscillations and being GR active at the same time. We find that LK mechanism leads to secular lowering of perihelion distance which in turn leads to a huge increase in GR precession of the argument of pericentre depending on the initial orbital elements. This in turn gives feedback to the LK mechanism as the eccentricity, inclination and argument of pericentre in Kozai cycles are closely correlated. In this work, we find real examples of solar system bodies which show rapid enhancement in GR precession rates due to LK like oscillations and there are cases where GR precession rate peaks to about 60 times that of the GR precession of Mercury thus showing the strength and complementary nature between these two dynamical phenomena.An analytical treatment is done on few bodies to understand the difference in their orbital evolution in the context of LK mechanism with and without GR precession term by incorporating suitable Hamiltonian dynamics. This result is subsequently matched using numerical integrations to find direct correlations. Real solar system bodies showing both GR precession and LK like oscillations are identified using compiled observational records from IAU-Minor Planet Center, Cometary Catalogue, IAU-Meteor Data Center and performing analytical plus numerical tests on them. This intermediate state (where GR and LK effects are comparable and co-exist) brings up the interesting possibility of drastic changes in GR precession rates during orbital evolution due to sungrazing and sun colliding phases induced by the LK like mechanism, thus combining both these important effects in a
Gonthier, P L; Baring, M G; Costello, R M; Mercer, C L; Gonthier, Peter L.; Harding, Alice K.; Baring, Matthew G.; Costello, Rachel M.; Mercer, Cassandra L.
2000-01-01
This paper explores the effects of strong magnetic fields on the Compton scattering of relativistic electrons. Recent studies of upscattering and energy loss by relativistic electrons that have used the non-relativistic, magnetic Thomson cross section for resonant scattering or the Klein-Nishina cross section for non-resonant scattering do not account for the relativistic quantum effects of strong fields ($ > 4 \\times 10^{12}$ G). We have derived a simplified expression for the exact QED scattering cross section for the broadly-applicable case where relativistic electrons move along the magnetic field. To facilitate applications to astrophysical models, we have also developed compact approximate expressions for both the differential and total polarization-dependent cross sections, with the latter representing well the exact total QED cross section even at the high fields believed to be present in environments near the stellar surfaces of Soft Gamma-Ray Repeaters and Anomalous X-Ray Pulsars. We find that stron...
Yoo, Jaiyul; Seljak, Uros; Zaldarriaga, Matias
2012-01-01
Kaiser redshift-space distortion formula describes well the clustering of galaxies in redshift surveys on small scales, but there are numerous additional terms that arise on large scales. Some of these terms can be described using Newtonian dynamics and have been discussed in the literature, while the others require proper general relativistic description that was only recently developed. Accounting for these terms in galaxy clustering is the first step toward tests of general relativity on horizon scales. The effects can be classified as two terms that represent the velocity and the gravitational potential contributions. Their amplitude is determined by effects such as the volume and luminosity distance fluctuation effects and the time evolution of galaxy number density and Hubble parameter. We compare the Newtonian approximation often used in the redshift-space distortion literature to the fully general relativistic equation, and show that Newtonian approximation accounts for most of the terms contributing ...
Analytical Solution of Relativistic Few-Body Bound Systems with a Generalized Yukawa Potential
Aslanzadeh, M.; Rajabi, A. A.
2016-03-01
We have investigated in this paper the few-body bound systems in a simple semi-relativistic scheme. For this aim, we introduced a spin independent relativistic description for a few-identical body system by presenting the analytical solution of few-particle Klein-Gordon equation. Performing calculations in D-dimensional configuration on the basis of the hypercentral approach, we reduced the few-body Klein-Gordon equation to a Schrödinger-like form. This equation is solved by using the Nikiforov-Uvarov method, through which the energy equations and eigenfunctions for a few-body bound system are obtained. We used the spin- and isospin-independent generalized Yukawa potential in our calculations, and the dependence of the few-body binding energies on the potential parameters has been investigated.
On the General Solution to Einstein's Vacuum Field and Its Implications for Relativistic Degeneracy
Directory of Open Access Journals (Sweden)
Crothers S. J.
2005-04-01
Full Text Available The general solution to Einstein’s vacuum field equations for the point-mass in all its configurations must be determined in such a way as to provide a means by which an infinite sequence of particular solutions can be readily constructed. It is from such a solution that the underlying geometry of Einstein’s universe can be rightly explored. I report here on the determination of the general solution and its consequences for the theoretical basis of relativistic degeneracy, i.e. gravitational collapse and the black hole.
Nagataki, S
2009-01-01
In order to investigate formation of relativistic jets at the center of a progenitor of a long gamma-ray burst (GRB), we develop a two-dimensional general relativistic magnetohydrodynamic (GRMHD) code. We show the code passes many, well-known test calculations, by which the reliability of the code is confirmed. Then we perform a numerical simulation of a collapsar using a realistic progenitor model. It is shown that a jet is launched from the center of the progenitor. We also find that the mass accretion rate after the launch of the jet shows rapid time variability that resembles to a typical time profile of a GRB. The structure of the jet is similar to the previous study: a poynting flux jet is surrounded by a funnel-wall jet. Even at the final stage of the simulation, bulk Lorentz factor of the jet is still low, and total energy of the jet is still as small as 10^48 erg. However, we find that the energy flux per unit rest-mass flux is as high as 10^2 at the bottom of the jet. Thus we conclude that the bulk ...
Wu, Kailiang; Tang, Huazhong
2017-01-01
The ideal gas equation of state (EOS) with a constant adiabatic index is a poor approximation for most relativistic astrophysical flows, although it is commonly used in relativistic hydrodynamics (RHD). This paper develops high-order accurate, physical-constraints-preserving (PCP), central, discontinuous Galerkin (DG) methods for the one- and two-dimensional special RHD equations with a general EOS. It is built on our theoretical analysis of the admissible states for RHD and the PCP limiting procedure that enforce the admissibility of central DG solutions. The convexity, scaling invariance, orthogonal invariance, and Lax–Friedrichs splitting property of the admissible state set are first proved with the aid of its equivalent form. Then, the high-order central DG methods with the PCP limiting procedure and strong stability-preserving time discretization are proved, to preserve the positivity of the density, pressure, specific internal energy, and the bound of the fluid velocity, maintain high-order accuracy, and be L1-stable. The accuracy, robustness, and effectiveness of the proposed methods are demonstrated by several 1D and 2D numerical examples involving large Lorentz factor, strong discontinuities, or low density/pressure, etc.
Improved Numerical Cherenkov Instability Suppression in the Generalized PSTD PIC Algorithm
Godfrey, Brendan B
2015-01-01
The family of generalized Pseudo-Spectral Time Domain (including the Pseudo-Spectral Analytical Time Domain) Particle-in-Cell algorithms offers substantial versatility for simulating particle beams and plasmas, and well written codes using these algorithms run reasonably fast. When simulating relativistic beams and streaming plasmas in multiple dimensions, they are, however, subject to the numerical Cherenkov instability. Previous studies have shown that instability growth rates can be reduced substantially by modifying slightly the transverse fields as seen by the streaming particles . Here, we offer an approach which completely eliminates the fundamental mode of the numerical Cherenkov instability while minimizing the transverse field corrections. The procedure, numerically computed residual growth rates (from weaker, higher order instability aliases), and comparisons with WARP simulations are presented. In some instances, there are no numerical instabilities whatsoever, at least in the linear regime.
HERO - A 3D general relativistic radiative post-processor for accretion discs around black holes
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.
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.
Demianski, Marek
2013-01-01
Relativistic Astrophysics brings together important astronomical discoveries and the significant achievements, as well as the difficulties in the field of relativistic astrophysics. This book is divided into 10 chapters that tackle some aspects of the field, including the gravitational field, stellar equilibrium, black holes, and cosmology. The opening chapters introduce the theories to delineate gravitational field and the elements of relativistic thermodynamics and hydrodynamics. The succeeding chapters deal with the gravitational fields in matter; stellar equilibrium and general relativity
The 2D surfaces that generate Newtonian and general relativistic orbits with small eccentricities
Middleton, Chad A
2015-01-01
Embedding diagrams prove to be quite useful when learning general relativity as they offer a way of visualizing spacetime curvature through warped two dimensional (2D) surfaces. In this manuscript we present a different 2D construct that also serves as a useful conceptual tool for gaining insight into gravitation, in particular, orbital dynamics - namely the cylindrically symmetric surfaces that generate Newtonian and general relativistic orbits with small eccentricities. Although we first show that no such surface exists that can exactly reproduce the arbitrary bound orbits of Newtonian gravitation or of general relativity (or, more generally, of any spherically symmetric potential), surfaces do exist that closely approximate the resulting orbital motion for small eccentricities; exactly the regime that describes the motion of the solar system planets. These surfaces help to illustrate the similarities, as well as the differences, between the two theories of gravitation (i.e. stationary elliptical orbits in ...
Change in General Relativistic precession rates due to Lidov-Kozai oscillations in the Solar System
Sekhar, Aswin; Asher, David J.; Werner, Stephanie C.; Vaubaillon, Jeremie; Li, Gongjie
2017-04-01
Introduction: Two well known phenomena associated with low perihelion distance bodies in orbital dynamics are general relativistic (GR) precession and Lidov-Kozai (LK) oscillations. The accurate prediction of the perihelion shift of Mercury in accord with real observations is one of the significant triumphs of the general theory of relativity developed by Einstein. The Lidov-Kozai mechanism was first proposed and derived by Kozai and independently by Lidov explaining the periodic exchange between eccentricities e and inclinations i thereby increasing or decreasing the perihelion distance q secularly in the orbiting body. Co-existence of GR Precession and LK Oscillations: In this work, we were interested to identify bodies evolving in the near future (i.e. thousands of years in this case) into rapid sungrazing and sun colliding phases and undergoing inclination flips, due to LK oscillations and being GR active at the same time. Of all the bodies we checked from the IAU-Minor Planet Center, and Marsden plus Kracht families from the comet catalogue, 96P/Machholz 1 stands out because it shows all these trends in the near future. LK leads to secular lowering of q which in turn leads to a huge increase in GR precession of argument of pericentre. This in turn gives feedback to the LK mechanism as the e,i and argument of pericentre in Kozai cycles are closely correlated. In this work, we find real examples of solar system bodies which show the continuum nature between GR precession domi-nant and LK mechanism dominant regimes. Results and Discussion: We have shown that there are bodies in the solar system in which both GR precession and LK mechanism can co-exist at the same time and for which these effects can be measured and identified using analytical and numerical techniques. Thus there is a continuum of bodies encompassing, firstly GR precession dominant, secondly GR precession plus LK mechanism co-existing and finally LK mechanism dominant states which are all
Magnetic collimation of meridional-self-similar general relativistic MHD flows
Globus, Noemie; Sauty, Christophe; Cayatte, Véronique; Celnikier, Ludwik M.
2014-06-01
We present a model for the spine of relativistic Magnetohydrodynamics outflows in the Kerr geometry. Meridional self-similarity is invoked to derive semianalytical solutions close to the polar axis. The study of the energy conservation along a particular field line gives a simple criterion for the collimation of jets. Such parameter have already been derived in the classical case by Sauty et al. 1999 and also extended to the Schwarzschild metric by Meliani et al. 2006. We generalize the same study to the Kerr metric. We show that the rotation of the black hole increases the magnetic self-confinement.
Magnetic collimation of meridional-self-similar general relativistic MHD flows
Globus, Noemie; Cayatte, Véronique; Celnikier, Ludwik M
2014-01-01
We present a model for the spine of relativistic MHD outflows in the Kerr geometry. Meridional self-similarity is invoked to derive semi-analytical solutions close to the polar axis. The study of the energy conservation along a particular field line gives a simple criterion for the collimation of jets. Such parameter have already been derived in the classical case by Sauty et al. 1999 and also extended to the Schwarzschild metric by Meliani et al. 2006. We generalize the same study to the Kerr metric. We show that the rotation of the black hole increases the magnetic self-confinement.
GPU-based four-dimensional general-relativistic ray tracing
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
The role of currents distribution in general relativistic equilibria of magnetized neutron stars
Bucciantini, N; Del Zanna, L
2014-01-01
Magnetic fields play a critical role in the phenomenology of neutron stars. There is virtually no observable aspect which is not governed by them. Despite this, only recently efforts have been done to model magnetic fields in the correct general relativistic regime, characteristic of these compact objects. In this work we present, for the first time a comprehensive and detailed parameter study, in general relativity, of the role that the current distribution, and the related magnetic field structure, have in determining the precise structure of neutron stars. In particular, we show how the presence of localized currents can modify the field strength at the stellar surface, and we look for general trends, both in terms of energetic properties, and magnetic field configurations. Here we verify that, among other things, for a large class of different current distributions the resulting magnetic configurations are always dominated by the poloidal component of the current.
GENERAL RELATIVISTIC SIMULATIONS OF MAGNETIZED PLASMAS AROUND MERGING SUPERMASSIVE BLACK HOLES
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Giacomazzo, Bruno [JILA, University of Colorado and National Institute of Standards and Technology, 440 UCB, Boulder, CO 80309 (United States); Baker, John G.; Van Meter, James R. [Gravitational Astrophysics Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD 21114 (United States); Coleman Miller, M.; Reynolds, Christopher S. [Department of Astronomy, University of Maryland, College Park, MD 20742 (United States)
2012-06-10
Coalescing supermassive black hole binaries are produced by the mergers of galaxies and are the most powerful sources of gravitational waves accessible to space-based gravitational observatories. Some such mergers may occur in the presence of matter and magnetic fields and hence generate an electromagnetic counterpart. In this Letter, we present the first general relativistic simulations of magnetized plasma around merging supermassive black holes using the general relativistic magnetohydrodynamic code Whisky. By considering different magnetic field strengths, going from non-magnetically dominated to magnetically dominated regimes, we explore how magnetic fields affect the dynamics of the plasma and the possible emission of electromagnetic signals. In particular, we observe a total amplification of the magnetic field of {approx}2 orders of magnitude, which is driven by the accretion onto the binary and that leads to much stronger electromagnetic signals, more than a factor of 10{sup 4} larger than comparable calculations done in the force-free regime where such amplifications are not possible.
Nakano, Masahiko; Seino, Junji; Nakai, Hiromi
2017-05-01
We have derived and implemented a universal formulation of the second-order generalized Møller-Plesset perturbation theory (GMP2) for spin-dependent (SD) two-component relativistic many-electron Hamiltonians, such as the infinite-order Douglas-Kroll-Hess Hamiltonian for many-electron systems, which is denoted as IODKH/IODKH. Numerical assessments for He- and Ne-like atoms and 16 diatomic molecules show that the MP2 correlation energies with IODKH/IODKH agree well with those calculated with the four-component Dirac-Coulomb (DC) Hamiltonian, indicating a systematic improvement on the inclusion of relativistic two-electron terms. The present MP2 scheme for IODKH/IODKH is demonstrated to be computationally more efficient than that for DC.
McKinney, Jonathan C; Sadowski, Aleksander; Narayan, Ramesh
2013-01-01
Black hole (BH) accretion flows and jets are dynamic hot relativistic magnetized plasma flows whose radiative opacity can significantly affect flow structure and behavior. We describe a numerical scheme, tests, and an astrophysically relevant application using the M1 radiation closure within a new three-dimensional (3D) general relativistic (GR) radiation (R) magnetohydrodynamics (MHD) massively parallel code called HARMRAD. Our 3D GRRMHD simulation of super-Eddington accretion (about $20$ times Eddington) onto a rapidly rotating BH (dimensionless spin $j=0.9375$) shows sustained non-axisymmemtric disk turbulence, a persistent electromagnetic jet driven by the Blandford-Znajek effect, and a total radiative output consistently near the Eddington rate. The total accretion efficiency is of order $20\\%$, the large-scale electromagnetic jet efficiency is of order $10\\%$, and the total radiative efficiency that reaches large distances remains low at only order $1\\%$. However, the radiation jet and the electromagnet...
On the relativistic mass function and averaging in cosmology
Ostrowski, Jan J; Roukema, Boudewijn F
2016-01-01
The general relativistic description of cosmological structure formation is an important challenge from both the theoretical and the numerical point of views. In this paper we present a brief prescription for a general relativistic treatment of structure formation and a resulting mass function on galaxy cluster scales in a highly generic scenario. To obtain this we use an exact scalar averaging scheme together with the relativistic generalization of Zel'dovich's approximation (RZA) that serves as a closure condition for the averaged equations.
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.
A general relativistic approach to the Navarro-Frenk-White (NFW) galactic halos
Matos, T; Sussman, R A; Matos, Tonatiuh; Nunez, Dario; Sussman, Roberto A
2004-01-01
In order to study their interplay with large scale cosmic evolution and with relativistic effects, such as gravitational lenses, quintessence sources or gravitational waves, 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 center, 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 asymptotica...
A general relativistic approach to the Navarro Frenk White galactic halos
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.
English, William; Krause, Martin G H
2016-01-01
We present results from two suites of simulations of powerful radio galaxies in poor cluster environments, with a focus on the formation and evolution of the radio lobes. One suite of models uses relativistic hydrodynamics and the other relativistic magnetohydrodynamics; both are set up to cover a range of jet powers and velocities. The dynamics of the lobes are shown to be in good agreement with analytical models and with previous numerical models, confirming in the relativistic regime that the observed widths of radio lobes may be explained if they are driven by very light jets. The ratio of energy stored in the radio lobes to that put into the intracluster gas is seen to be the same regardless of jet power, jet velocity or simulation type, suggesting that we have a robust understanding of the work done on the ambient gas by this type of radio source. For the most powerful jets we at times find magnetic field amplification by up to a factor of two in energy, but mostly the magnetic energy in the lobes is co...
Newtonian analogue of static general relativistic spacetimes: An extension to naked singularities
Ghosh, Shubhrangshu; Bhadra, Arunava
2015-01-01
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-Nordstr\\"{o}m (RN) spacetimes, both exhibiting naked singularities. The derived potentials 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 behavior 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...
Mueller, B; Marek, A
2012-01-01
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 spacetime 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 solar mass 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 to Newtonian and pseudo-Newtonian simulations. These differences lead to significantly higher luminosities and mean energies of the radiated ele...
Fully General Relativistic Simulations of Black Hole-Neutron Star Mergers
Etienne, Zachariah B; Liu, Yuk Tung; Shapiro, Stuart L; Taniguchi, Keisuke; Baumgarte, Thomas W
2007-01-01
Black hole-neutron star (BHNS) binaries are expected to be among the leading sources of gravitational waves observable by ground-based detectors, and may be the progenitors of short-hard gamma ray bursts (SGRBs) as well. Here, we discuss our new fully general relativistic calculations of merging BHNS binaries, which use high-accuracy, low-eccentricity, conformal thin-sandwich configurations as initial data. Our evolutions are performed using the moving puncture method and include a fully relativistic, high-resolution shock-capturing hydrodynamics treatment. Focusing on systems in which the neutron star is irrotational and the black hole is nonspinning with a 3:1 mass ratio, we investigate the inspiral, merger, and disk formation in the system. We find that the vast majority of material is promptly accreted and no more than 3% of the neutron star's rest mass is ejected into a tenuous, gravitationally bound disk. We find similar results for mass ratios of 2:1 and 1:1, even when we reduce the NS compaction in th...
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Shiokawa, Hotaka; Dolence, Joshua C.; Gammie, Charles F. [Department of Astronomy, University of Illinois at Urbana-Champaign, 1002 West Green Street, Urbana, IL 61801 (United States); Noble, Scott C. [Center for Computational Relativity and Gravitation, School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623 (United States)
2012-01-10
Global, general relativistic magnetohydrodynamic (GRMHD) simulations of non-radiative, magnetized disks are widely used to model accreting black holes. We have performed a convergence study of GRMHD models computed with HARM3D. The models span a factor of four in linear resolution, from 96 Multiplication-Sign 96 Multiplication-Sign 64 to 384 Multiplication-Sign 384 Multiplication-Sign 256. We consider three diagnostics of convergence: (1) dimensionless shell-averaged quantities such as plasma {beta}; (2) the azimuthal correlation length of fluid variables; and (3) synthetic spectra of the source including synchrotron emission, absorption, and Compton scattering. Shell-averaged temperature is, except for the lowest resolution run, nearly independent of resolution; shell-averaged plasma {beta} decreases steadily with resolution but shows signs of convergence. The azimuthal correlation lengths of density, internal energy, and temperature decrease steadily with resolution but show signs of convergence. In contrast, the azimuthal correlation length of magnetic field decreases nearly linearly with grid size. We argue by analogy with local models, however, that convergence should be achieved with another factor of two in resolution. Synthetic spectra are, except for the lowest resolution run, nearly independent of resolution. The convergence behavior is consistent with that of higher physical resolution local model ({sup s}hearing box{sup )} calculations and with the recent non-relativistic global convergence studies of Hawley et al.
HERO: A 3D General Relativistic Radiative Postprocessor for Accretion Discs around Black Holes
Zhu, Yucong; Sadowski, Aleksander; Psaltis, Dimitrios
2015-01-01
HERO (Hybrid Evaluator for Radiative Objects) is a 3D general relativistic radiative transfer code which has been tailored to the problem of analyzing radiation from simulations of relativistic accretion discs around black holes. HERO is designed to be used as a postprocessor. Given some fixed fluid structure for the disc (i.e. density and velocity as a function of position from a hydrodynamics or magnetohydrodynamics 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. W...
Multipath diffusion: A general numerical model
Lee, J. K. W.; Aldama, A. A.
1992-06-01
The effect of high-diffusivity pathways on bulk diffusion of a solute in a material has been modeled previously for simple geometries such as those in tracer diffusion experiments, but not for the geometries and boundary conditions appropriate for experiments involving bulk exchange. Using a coupled system of equations for simultaneous diffusion of a solute through two families of diffusion pathways with differing diffusivities, a general 1-D finite difference model written in FORTRAN has been developed which can be used to examine the effect of high-diffusivity paths on partial and total concentration profiles within a homogeneous isotropic sphere, infinite cylinder, and infinite slab. The partial differential equations are discretized using the θ-method/central-difference scheme, and an iterative procedure analogous to the Gauss-Seidel method is employed to solve the two systems of coupled equations. Using Fourier convergence analysis, the procedure is shown to be unconditionally convergent. Computer simulations demonstrate that a multipath diffusion mechanism can enhance significantly the bulk diffusivity of a diffusing solute species through a material. The amount of solute escaping from a material is dependent strongly on the exchange coefficients, which govern the transfer of solute from the crystal lattice to the high-diffusivity paths and vice versa. In addition, the exchange coefficients ( ϰ1, and ϰ2) seem to control not only the amount of solute that is lost, but also the shape of the concentration profile. If | K1| < | K2|, concentration profiles generally are non-Fickian in shape, typically having shallow concentration gradients near the center (radius r = 0) and steep gradients towards the outer boundary of the material ( r = R). When | K1| ⩾ | K2| a concentration profile is generated which resembles a Fickian (volume) diffusion profile with an apparent bulk diffusivity between that of the crystal lattice and that of the high-diffusivity pathways
Broderick, Avery E
2010-01-01
For the first time it has become possible to compare global 3D general relativistic magnetohydrodynamic (GRMHD) jet formation simulations directly to very-long baseline interferometric multi-frequency polarization observations of the pc-scale structure of active galactic nucleus (AGN) jets. Unlike the jet emission, which requires post hoc modeling of the non-thermal electrons, the Faraday rotation measures (RMs) depend primarily upon simulated quantities and thus provide a robust way in which to confront simulations with observations. We compute RM distributions of 3D global GRMHD jet formation simulations, with which we explore the dependence upon model and observational parameters, emphasizing the signatures of structures generic to the theory of MHD jets. With typical parameters, we find that it is possible to reproduce the observed magnitudes and many of the structures found in AGN jet RMs, including the presence of transverse RM gradients. In our simulations the RMs are generated within a smooth extensio...
Teraki, Yuto
2014-01-01
We examine the radiation spectra from relativistic electrons moving in a Langmuir turbulence expected to exist in high energy astrophysical objects by using numerical method. The spectral shape is characterized by the spatial scale {\\lambda}, field strength {\\sigma}, and frequency of the Langmuir waves, and in term of frequency they are represented by {\\omega}_0 = 2{\\pi}c/{\\lambda}, {\\omega}_st = e{\\sigma}/mc, and {\\omega}_p, respectively. We normalize {\\omega}_st and {\\omega}_p by {\\omega}_0 as \\a \\equiv {\\omega}_st/{\\omega}_0 and \\b \\equiv{\\omega}_p/{\\omega}_0, and examine the spectral shape in the a-b plane. An earlier study based on Diffusive Radiation in Langmuir turbulence (DRL) theory by Fleishman and Toptygin showed that the typical frequency is {\\gamma}^2{\\omega}_p and that the low frequency spectrum behaves as F_{\\omega} pronto {\\omega}^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 ...
Rueda-Becerril, Jesus M; Aloy, Miguel A; Aloy, Carmen
2013-01-01
The internal-shocks scenario in relativistic jets has been used to explain the variability of blazars' outflow emission. Recent simulations have shown that the magnetic field alters the dynamics of these shocks producing a whole zoo of spectral energy density patterns. However, the role played by magnetization in such high-energy emission is still not entirely understood. With the aid of \\emph{Fermi}'s second LAT AGN catalog, a comparison with observations in the $\\gamma$-ray band was performed, in order to identify the effects of the magnetic field.
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Rueda-Becerril Jesús M.
2013-12-01
Full Text Available The internal-shocks scenario in relativistic jets has been used to explain the variability of blazars’ outflow emission. Recent simulations have shown that the magnetic field alters the dynamics of these shocks producing a whole zoo of spectral energy density patterns. However, the role played by magnetization in such high-energy emission is still not entirely understood. With the aid of Fermi’s second LAT AGN catalog, a comparison with observations in the γ-ray band was performed, in order to identify the effects of the magnetic field.
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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
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Vacaru, Olivia [National College of Iasi (Romania); Vacaru, Sergiu I. [Quantum Gravity Research, Topanga, CA (United States); University ' ' Al.I. Cuza' ' Iasi, Project IDEI, Iasi (Romania); Werner-Heisenberg-Institute, Max-Planck-Institute for Physics, Munich (Germany); Leibniz University of Hannover, Institute for Theoretical Physics (Germany); Ruchin, Vyacheslav
2017-03-15
Using double 2 + 2 and 3 + 1 nonholonomic fibrations on Lorentz manifolds, we extend the concept of W-entropy for gravitational fields in general relativity (GR). Such F- and W-functionals were introduced in the Ricci flow theory of three dimensional (3-d) Riemannian metrics by Perelman (the entropy formula for the Ricci flow and its geometric applications. arXiv:math.DG/0211159). Non-relativistic 3-d Ricci flows are characterized by associated statistical thermodynamical values determined by W-entropy. Generalizations for geometric flows of 4-d pseudo-Riemannian metrics are considered for models with local thermodynamical equilibrium and separation of dissipative and non-dissipative processes in relativistic hydrodynamics. The approach is elaborated in the framework of classical field theories (relativistic continuum and hydrodynamic models) without an underlying kinetic description, which will be elaborated in other work. The 3 + 1 splitting allows us to provide a general relativistic definition of gravitational entropy in the Lyapunov-Perelman sense. It increases monotonically as structure forms in the Universe. We can formulate a thermodynamic description of exact solutions in GR depending, in general, on all spacetime coordinates. A corresponding 2 + 2 splitting with nonholonomic deformation of linear connection and frame structures is necessary for generating in very general form various classes of exact solutions of the Einstein and general relativistic geometric flow equations. Finally, we speculate on physical macrostates and microstate interpretations of the W-entropy in GR, geometric flow theories and possible connections to string theory (a second unsolved problem also contained in Perelman's work) in Polyakov's approach. (orig.)
Kopeikin, S M; Kopeikin, Sergei; Fomalont, Ed
2002-01-01
A relativistic sub-picosecond model of gravitational time delay in radio astronomical observations is worked out and a new experimental test of general relativity is discussed in which the effect of retardation of gravity associated with its finite speed can be observed. As a consequence, the speed of gravity can be measured by differential VLBI observations. Retardation in propagation of gravity is a central part of the Einstein theory of general relativity which has not been tested directly so far. The idea of the proposed gravitational experiment is based on the fact that gravity in general relativity propagates with finite speed so that the deflection of light caused by the body must be sensitive to the ratio of the body's velocity to the speed of gravity. The interferometric experiment can be performed, for example, during the very close angular passage of a quasar by Jupiter. Due to the finite speed of gravity and orbital motion of Jupiter, the variation in its gravitational field reaches observer on Ea...
Relativistic thermodynamics, a Lagrangian field theory for general flows including rotation
Frønsdal, Christian
Any theory that is based on an action principle has a much greater predictive power than one that does not have such a formulation. The formulation of a dynamical theory of General Relativity, including matter, is here viewed as a problem of coupling Einstein’s theory of pure gravity to an independently chosen and well-defined field theory of matter. It is well known that this is accomplished in a most natural way when both theories are formulated as relativistic, Lagrangian field theories, as is the case with Einstein-Maxwell theory. Special matter models of this type have been available; here a more general thermodynamical model that allows for vortex flows is presented. In a wider context, the problem of subjecting hydrodynamics and thermodynamics to an action principle is one that has been pursued for at least 150 years. A solution to this problem has been known for some time, but only under the strong restriction to potential flows. A variational principle for general flows has become available. It represents a development of the Navier-Stokes-Fourier approach to fluid dynamics. The principal innovation is the recognition that two kinds of flow velocity fields are needed, one the gradient of a scalar field and the other the time derivative of a vector field, the latter closely associated with vorticity. In the relativistic theory that is presented here, the latter is the Hodge dual of an exact 3-form, well known as the notoph field of Ogievetskij and Palubarinov, the B-field of Kalb and Ramond and the vorticity field of Lund and Regge. The total number of degrees of freedom of a unary system, including the density and the two velocity fields is 4, as expected — as in classical hydrodynamics. In this paper, we do not reduce Einstein’s dynamical equation for the metric to phenomenology, which would have denied the relevance of any intrinsic dynamics for the matter sector, nor do we abandon the equation of continuity - the very soul of hydrodynamics.
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Decker, J.; Peysson, Y
2004-12-01
A new original code for solving the 3-D relativistic and bounce-averaged electron drift kinetic equation is presented. It designed for the current drive problem in tokamak with an arbitrary magnetic equilibrium. This tool allows self-consistent calculations of the bootstrap current in presence of other external current sources. RF current drive for arbitrary type of waves may be used. Several moments of the electron distribution function are determined, like the exact and effective fractions of trapped electrons, the plasma current, absorbed RF power, runaway and magnetic ripple loss rates and non-thermal Bremsstrahlung. Advanced numerical techniques have been used to make it the first fully implicit (reverse time) 3-D solver, particularly well designed for implementation in a chain of code for realistic current drive calculations in high {beta}{sub p} plasmas. All the details of the physics background and the numerical scheme are presented, as well a some examples to illustrate main code capabilities. Several important numerical points are addressed concerning code stability and potential numerical and physical limitations. (authors)
Troxel, M A; Ishak, Mustapha
2013-01-01
We study the effects and implications of anisotropies at the scale of galaxy clusters by building an exact general relativistic model of a cluster using the inhomogeneous and anisotropic Szekeres metric. The model is built from a modified Navarro-Frenk-White (NFW) density profile. We compare this to a corresponding spherically symmetric structure in the Lemaitre-Tolman (LT) model and quantify the impact of introducing varying levels of anisotropy. We examine two physical measures of gravitational infall -- the growth rate of density and the velocity of the source dust in the model. We introduce a generalization of the LT dust velocity profile for the Szekeres metric and demonstrate its consistency with the growth rate of density. We find that the growth rate of density in one substructure increases by 0.5%, 1.5%, and 3.75% for 5%, 10%, and 15% levels of introduced anisotropy, which is measured as the fractional displaced mass relative to the spherically symmetric case. The infall velocity of the dust is found...
Generalized Lagrangian-Path Representation of Non-Relativistic Quantum Mechanics
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.
Stefańska, Patrycja
2016-01-01
The Sturmian expansion of the generalized Dirac--Coulomb Green function [R.\\/~Szmytkowski, J.\\ Phys.\\ B \\textbf{30}, 825 (1997); \\textbf{30}, 2747(E) (1997)] is exploited to derive a closed-form expression for the magnetizability of the relativistic one-electron atom in an arbitrary discrete state, with a point-like, spinless and motionless nucleus of charge $Ze$. The result has the form of a double finite sum involving the generalized hypergeometric functions ${}_3F_2$ of the unit argument. Our general expression agrees with formulas obtained analytically earlier by other authors for some particular states of the atom. We present also numerical values of the magnetizability for some excited states of selected hydrogenlike ions with $1 \\leqslant Z \\leqslant 137$ and compare them with data available in the literature.
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Mueller, Bernhard; Janka, Hans-Thomas; Marek, Andreas, E-mail: bjmuellr@mpa-garching.mpg.de, E-mail: thj@mpa-garching.mpg.de [Max-Planck-Institut fuer Astrophysik, Karl-Schwarzschild-Str. 1, D-85748 Garching (Germany)
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.
Luciano, Rezzolla
2013-01-01
Relativistic hydrodynamics is a very successful theoretical framework to describe the dynamics of matter from scales as small as those of colliding elementary particles, up to the largest scales in the universe. This book provides an up-to-date, lively, and approachable introduction to the mathematical formalism, numerical techniques, and applications of relativistic hydrodynamics. The topic is typically covered either by very formal or by very phenomenological books, but is instead presented here in a form that will be appreciated both by students and researchers in the field. The topics covered in the book are the results of work carried out over the last 40 years, which can be found in rather technical research articles with dissimilar notations and styles. The book is not just a collection of scattered information, but a well-organized description of relativistic hydrodynamics, from the basic principles of statistical kinetic theory, down to the technical aspects of numerical methods devised for the solut...
Arzeliès, Henri
1972-01-01
Relativistic Point Dynamics focuses on the principles of relativistic dynamics. The book first discusses fundamental equations. The impulse postulate and its consequences and the kinetic energy theorem are then explained. The text also touches on the transformation of main quantities and relativistic decomposition of force, and then discusses fields of force derivable from scalar potentials; fields of force derivable from a scalar potential and a vector potential; and equations of motion. Other concerns include equations for fields; transfer of the equations obtained by variational methods int
Sourie, Aurélien; Novak, Jérôme
2016-01-01
We present a numerical model for uniformly rotating superfluid neutron stars, for the first time with realistic microphysics including entrainment, in a fully general relativistic framework. We compute stationary and axisymmetric configurations of neutron stars composed of two fluids, namely superfluid neutrons and charged particles (protons and electrons), rotating with different rates around a common axis. Both fluids are coupled by entrainment, a non-dissipative interaction which in case of a non-vanishing relative velocity between the fluids, causes the fluid momenta being not aligned with the respective fluid velocities. We extend the formalism by Comer and Joynt (2003) in order to calculate the equation of state (EoS) and entrainment parameters for an arbitrary relative velocity. The resulting entrainment matrix fulfills all necessary sum rules and in the limit of small relative velocity our results agree with Fermi liquid theory ones, derived to lowest order in the velocity. This formalism is applied t...
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.
Endrizzi, Andrea; Giacomazzo, Bruno; Kastaun, Wolfgang; Kawamura, Takumu
2016-01-01
We present new results of fully general relativistic magnetohydrodynamic (GRMHD) 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 (EOS) 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 (BH) 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 electro...
The general relativistic instability supernova of a supermassive population III star
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Chen, Ke-Jung; Woosley, Stan [Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064 (United States); Heger, Alexander [Monash Centre for Astrophysics, Monash University, Victoria 3800 (Australia); Almgren, Ann [Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Whalen, Daniel J. [T-2, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Johnson, Jarrett L., E-mail: kchen@ucolick.org [XTD-PRI, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States)
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.
Odyssey: A Public GPU-Based Code for General-Relativistic Radiative Transfer in Kerr Spacetime
Pu, Hung-Yi; Younsi, Ziri; Yoon, Suk-Jin
2016-01-01
General-relativistic radiative transfer (GRRT) 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 (mm/sub-mm) Very Long Baseline Interferometry (VLBI) observations of the supermassive black holes at the centres 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 nanosecond 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 (GUI) powered by a video-accelerated display architecture, we also present an educational software tool, Odyssey_Edu, for showing in real time h...
Odyssey: A Public GPU-based Code for General Relativistic Radiative Transfer in Kerr Spacetime
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.
General relativistic modelling of the negative reverberation X-ray time delays in AGN
Emmanoulopoulos, D; Dovciak, M; McHardy, I M
2014-01-01
We present the first systematic physical modelling of the time-lag spectra between the soft (0.3-1 keV) and the hard (1.5-4 keV) X-ray energy bands, as a function of Fourier frequency, in a sample of 12 active galactic nuclei which have been observed by XMM-Newton. We concentrate particularly on the negative X-ray time-lags (typically seen above $10^{-4}$ Hz) i.e. soft band variations lag the hard band variations, and we assume that they are produced by reprocessing and reflection by the accretion disc within a lamp-post X-ray source geometry. We also assume that the response of the accretion disc, in the soft X-ray bands, is adequately described by the response in the neutral iron line (Fe k$\\alpha$) at 6.4 keV for which we use fully general relativistic ray-tracing simulations to determine its time evolution. These response functions, and thus the corresponding time-lag spectra, yield much more realistic results than the commonly-used, but erroneous, top-hat models. Additionally we parametrize the positive ...
Penna, Robert F; Sadowski, Aleksander
2013-01-01
Recently it has been observed that the scaling of jet power with black hole spin in galactic X-ray binaries is consistent with the predictions of the Blandford-Znajek (BZ) jet model. These observations motivate us to revisit the BZ model using general relativistic magnetohydrodynamic simulations of magnetized jets from accreting (h/r ~ 0.3), spinning (0 < a_* < 0.98) black holes. We have three main results. First, we quantify the discrepancies between the BZ jet power and our simulations: assuming maximum efficiency and uniform fields on the horizon leads to a ~10% overestimate of jet power, while ignoring the accretion disk leads to a further ~50% overestimate. Simply reducing the standard BZ jet power prediction by 60% gives a good fit to our simulation data. Our second result is to show that the membrane formulation of the BZ model correctly describes the physics underlying simulated jets: torques, dissipation, and electromagnetic fields on the horizon. This provides intuitive yet rigorous pictures f...
A General Relativistic Magnetohydrodynamics Simulation of Jet Formation with a State Transition
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.
Pinpointing the base of the AGN jets through general relativistic X-ray reverberation studies
Emmanoulopoulos, D
2014-01-01
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 clos...
Cattaneo, Carlo
2011-01-01
This title includes: Pham Mau Quam: Problemes mathematiques en hydrodynamique relativiste; A. Lichnerowicz: Ondes de choc, ondes infinitesimales et rayons en hydrodynamique et magnetohydrodynamique relativistes; A.H. Taub: Variational principles in general relativity; J. Ehlers: General relativistic kinetic theory of gases; K. Marathe: Abstract Minkowski spaces as fibre bundles; and, G. Boillat: Sur la propagation de la chaleur en relativite.
Dubus, Guillaume; Fromang, Sébastien
2015-01-01
Detailed modeling of the high-energy emission from gamma-ray binaries has been propounded as a path to pulsar wind physics. Fulfilling this ambition requires a coherent model of the flow and its emission in the region where the pulsar wind interacts with the stellar wind of its companion. We developed a code that follows the evolution and emission of electrons in the shocked pulsar wind based on inputs from a relativistic hydrodynamical simulation. The code is used to model the well-documented spectral energy distribution and orbital modulations from LS 5039. The pulsar wind is fully confined by a bow shock and a back shock. The particles are distributed into a narrow Maxwellian, emitting mostly GeV photons, and a power law radiating very efficiently over a broad energy range from X-rays to TeV gamma rays. Most of the emission arises from the apex of the bow shock. Doppler boosting shapes the X-ray and VHE lightcurves, constraining the system inclination to $i\\approx 35^{\\rm o}$. There is a tension between th...
On a Generalization of the c-numerical Range
Institute of Scientific and Technical Information of China (English)
雷天刚; 邬晶华
2002-01-01
@@ Let Cn×n be the set of n × n complex matrices and An the set of orthonormal n-tuples of vectors in Cn. For a vector c in Cn and a matrix A in Cn×n, the c-numerical range of A is the set Wc(A)={n∑i=1 Ci(Axi,xi):(x1,…xn)∈∧n} When c = (1,0,…,0), Wc(A) is reduced to the classical numerical range W(A) (see [1]). For the classical numerical range and its generalizations, one may see the survey article[2].
Cotner, Eric
2016-01-01
Scalar particles are a common prediction of many beyond the Standard Model theories. If they are light and cold enough, there is a possibility they may form Bose-Einstein condensates, which will then become gravitationally bound. These boson stars are solitonic solutions to the Einstein-Klein-Gordon equations, but may be approximated in the non-relativistic regime with a coupled Schr\\"odinger-Poisson system. General properties of single soliton states are derived, including the possibility of quartic self-interactions. Binary collisions between two solitons are then studied, and the effects of different mass ratios, relative phases, self-couplings, and separation distances are characterized, leading to an easy conceptual understanding of how these parameters affect the collision outcome in terms of conservation of energy. Applications to dark matter are discussed.
Directory of Open Access Journals (Sweden)
O. Ye. Hentosh
2016-01-01
Full Text Available The possibility of applying the method of reducing upon finite-dimensional invariant subspaces, generated by the eigenvalues of the associated spectral problem, to some two-dimensional generalization of the relativistic Toda lattice with the triple matrix Lax type linearization is investigated. The Hamiltonian property and Lax-Liouville integrability of the vector fields, given by this system, on the invariant subspace related with the Bargmann type reduction are found out.
Beneke, M.; Hellmann, C.; Ruiz-Femenia, P.
2012-01-01
We compute analytically the tree-level annihilation rates of a collection of non-relativistic neutralino and chargino two-particle states in the general MSSM, including the previously unknown off-diagonal rates. The results are prerequisites to the calculation of the Sommerfeld enhancement in the MSSM, which will be presented in subsequent work. They can also be used to obtain concise analytic expressions for MSSM dark matter pair annihilation in the present Universe for a large number of exc...
General relativistic modelling of the negative reverberation X-ray time delays in AGN
Emmanoulopoulos, D.; Papadakis, I. E.; Dovčiak, M.; McHardy, I. M.
2014-04-01
We present the first systematic physical modelling of the time-lag spectra between the soft (0.3-1 keV) and the hard (1.5-4 keV) X-ray energy bands, as a function of Fourier frequency, in a sample of 12 active galactic nuclei which have been observed by XMM-Newton. We concentrate particularly on the negative X-ray time-lags (typically seen above 10-4 Hz), i.e. soft-band variations lag the hard-band variations, and we assume that they are produced by reprocessing and reflection by the accretion disc within a lamp-post X-ray source geometry. We also assume that the response of the accretion disc, in the soft X-ray bands, is adequately described by the response in the neutral Fe Kα line at 6.4 keV for which we use fully general relativistic ray-tracing simulations to determine its time evolution. These response functions, and thus the corresponding time-lag spectra, yield much more realistic results than the commonly used, but erroneous, top-hat models. Additionally, we parametrize the positive part of the time-lag spectra (typically seen below 10-4 Hz) by a power law. We find that the best-fitting black hole (BH) masses, M, agree quite well with those derived by other methods, thus providing us with a new tool for BH mass determination. We find no evidence for any correlation between M and the BH spin parameter, α, the viewing angle, θ, or the height of the X-ray source above the disc, h. Also on average, the X-ray source lies only around 3.7 gravitational radii above the accretion disc and θ is distributed uniformly between 20° and 60°. Finally, there is a tentative indication that the distribution of α may be bimodal above and below 0.62.
Numerical Calculation of Coupling Impedances in Kicker Modules for Non-Relativistic Particle Beams
Doliwa, B
2004-01-01
In the context of heavy-ion synchrotrons, coupling impedances in ferrite-loaded structures (e.g. fast kicker modules) are known to have a significant influence on beam stability. While bench measurements are feasible today, it is desirable to have the coupling impedances in hands already during the design process of the respective components. To achieve this goal, as a first step, we have carried out numerical analyses of simple ferrite-containing test systems within the framework of the Finite Integration Technique[1]. This amounts to solving the full set of Maxwell's equations in frequency domain, the particle beam being represented by an appropriate excitation current. With the resulting electromagnetic fields, one may then readily compute the corresponding coupling impedances. Despite the complicated material properties of ferrites, our results show that their numerical treatment is possible, thus opening up a way to determine a crucial parameter of kicker devices before construction.
A general numerical method to solve for dislocation configurations
Xin, X. J.; Wagoner, R. H.; Daehn, G. S.
1999-08-01
The shape of a mechanically equilibrated dislocation line is of considerable interest in the study of plastic deformation of metals and alloys. A general numerical method for finding such configurations in arbitrary stress fields has been developed. Analogous to the finite-element method (FEM), a general dislocation line is approximated by a series of straight segments (elements) bounded by nodes. The equilibrium configuration is found by minimizing the system energy with respect to nodal positions using a Newton-Raphson procedure. This approach, termed the finite-segment method (FSM), confers several advantages relative to segment-based, explicit formulations. The utility, generality, and robustness of the FSM is demonstrated by analyzing the Orowan bypass mechanism and a model of dislocation generation and equilibration at misfitting particles. Energy differences from previous analytical methods based on simple loop shapes are significant, up to 80 pct. Explicit expressions for the coordinate transformations, energies, and forces required for numerical implementation are presented.
Dynamical Relativistic Systems and the Generalized Gauge Fields of Manifestly Covariant Theories
Horwitz, L P
1998-01-01
The problem of the classical non-relativistic electromagnetically kicked oscillator can be cast into the form of an iterative map on phase space. The original work of Zaslovskii et al showed that the resulting evolution contains a stochastic flow in phase space to unbounded energy. Subsequent studies have formulated the problem in terms of a relativistically charged particle in interaction with the electromagnetic field. We review the standard derivation of the covariant Lorentz force, and review the structure of the relativistic equations used to study this problem. We show that the Lorentz force equation can be derived as well from the manifestly covariant mechanics of Stueckelberg in the presence of a standard Maxwell field. We show how this agreement is achieved, and criticize some of the fundamental assumptions underlying these derivations. We argue that a more complete theory, involving ``off-shell'' electromagnetic fields should be utilized. We then discuss the formulation of the off-shell electromagne...
Troxel, M A; Peel, Austin
2013-01-01
The study of relativistic, higher order and nonlinear effects has become necessary in recent years in the pursuit of precision cosmology. We develop and apply here a framework to study gravitational lensing in exact models in general relativity that are not restricted to homogeneity and isotropy, and where full nonlinearity and relativistic effects are included. We apply the framework to a specific, anisotropic galaxy cluster model which is based on a modified NFW halo density profile and described by the Szekeres metric. We examine the effects of increasing levels of anisotropy in the galaxy cluster on lensing observables like the convergence and shear for various lensing geometries, finding a strong nonlinear response in both the convergence and shear for rays passing through anisotropic regions of the cluster. Deviation from the expected values in a spherically symmetric structure are asymmetric with respect to path direction and thus will persist as a statistical effect when averaged over some ensemble of...
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%.
Baiotti, Luca; Yamamoto, Tetsuro
2010-01-01
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%.
Arabshahi, S.; Dwyer, J. R.; Nag, A.; Rakov, V. A.; Rassoul, H. K.
2014-01-01
Compact intracloud discharges (CIDs) are sources of the powerful, often isolated radio pulses emitted by thunderstorms. The VLF-LF radio pulses are called narrow bipolar pulses (NBPs). It is still not clear how CIDs are produced, but two categories of theoretical models that have previously been considered are the Transmission Line (TL) model and the Relativistic Runaway Electron Avalanche-Extensive Air Showers (RREA-EAS) model. In this paper, we perform numerical calculations of RREA-EASs for various electric field configurations inside thunderstorms. The results of these calculations are compared to results from the other models and to the experimental data. Our analysis shows that different theoretical models predict different fundamental characteristics for CIDs. Therefore, many previously published properties of CIDs are highly model dependent. This is because of the fact that measurements of the radiation field usually provide information about the current moment of the source, and different physical models with different discharge currents could have the same current moment. We have also found that although the RREA-EAS model could explain the current moments of CIDs, the required electric fields in the thundercloud are rather large and may not be realistic. Furthermore, the production of NBPs from RREA-EAS requires very energetic primary cosmic ray particles, not observed in nature. If such ultrahigh-energy particles were responsible for NBPs, then they should be far less frequent than is actually observed.
Numerical computation of gravitational field for general axisymmetric objects
Fukushima, Toshio
2016-10-01
We developed a numerical method to compute the gravitational field of a general axisymmetric object. The method (i) numerically evaluates a double integral of the ring potential by the split quadrature method using the double exponential rules, and (ii) derives the acceleration vector by numerically differentiating the numerically integrated potential by Ridder's algorithm. Numerical comparison with the analytical solutions for a finite uniform spheroid and an infinitely extended object of the Miyamoto-Nagai density distribution confirmed the 13- and 11-digit accuracy of the potential and the acceleration vector computed by the method, respectively. By using the method, we present the gravitational potential contour map and/or the rotation curve of various axisymmetric objects: (i) finite uniform objects covering rhombic spindles and circular toroids, (ii) infinitely extended spheroids including Sérsic and Navarro-Frenk-White spheroids, and (iii) other axisymmetric objects such as an X/peanut-shaped object like NGC 128, a power-law disc with a central hole like the protoplanetary disc of TW Hya, and a tear-drop-shaped toroid like an axisymmetric equilibrium solution of plasma charge distribution in an International Thermonuclear Experimental Reactor-like tokamak. The method is directly applicable to the electrostatic field and will be easily extended for the magnetostatic field. The FORTRAN 90 programs of the new method and some test results are electronically available.
Numerical Hydrodynamics in Special Relativity
Directory of Open Access Journals (Sweden)
Martí José Maria
2003-01-01
Full Text Available This review is concerned with a discussion of numerical methods for the solution of the equations of special relativistic hydrodynamics (SRHD. Particular emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods in SRHD. Results of a set of demanding test bench simulations obtained with different numerical SRHD methods are compared. Three applications (astrophysical jets, gamma-ray bursts and heavy ion collisions of relativistic flows are discussed. An evaluation of various SRHD methods is presented, and future developments in SRHD are analyzed involving extension to general relativistic hydrodynamics and relativistic magneto-hydrodynamics. The review further provides FORTRAN programs to compute the exact solution of a 1D relativistic Riemann problem with zero and nonzero tangential velocities, and to simulate 1D relativistic flows in Cartesian Eulerian coordinates using the exact SRHD Riemann solver and PPM reconstruction.
Numerical Hydrodynamics in Special Relativity.
Martí, José Maria; Müller, Ewald
2003-01-01
This review is concerned with a discussion of numerical methods for the solution of the equations of special relativistic hydrodynamics (SRHD). Particular emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods in SRHD. Results of a set of demanding test bench simulations obtained with different numerical SRHD methods are compared. Three applications (astrophysical jets, gamma-ray bursts and heavy ion collisions) of relativistic flows are discussed. An evaluation of various SRHD methods is presented, and future developments in SRHD are analyzed involving extension to general relativistic hydrodynamics and relativistic magneto-hydrodynamics. The review further provides FORTRAN programs to compute the exact solution of a 1D relativistic Riemann problem with zero and nonzero tangential velocities, and to simulate 1D relativistic flows in Cartesian Eulerian coordinates using the exact SRHD Riemann solver and PPM reconstruction.
Relativistic Hydrodynamics in Heavy-Ion Collisions: General Aspects and Recent Developments
Directory of Open Access Journals (Sweden)
Amaresh Jaiswal
2016-01-01
Full Text Available Relativistic hydrodynamics has been quite successful in explaining the collective behaviour of the QCD matter produced in high energy heavy-ion collisions at RHIC and LHC. We briefly review the latest developments in the hydrodynamical modeling of relativistic heavy-ion collisions. Essential ingredients of the model such as the hydrodynamic evolution equations, dissipation, initial conditions, equation of state, and freeze-out process are reviewed. We discuss observable quantities such as particle spectra and anisotropic flow and effect of viscosity on these observables. Recent developments such as event-by-event fluctuations, flow in small systems (proton-proton and proton-nucleus collisions, flow in ultracentral collisions, longitudinal fluctuations, and correlations and flow in intense magnetic field are also discussed.
The proper generalized decomposition for advanced numerical simulations a primer
Chinesta, Francisco; Leygue, Adrien
2014-01-01
Many problems in scientific computing are intractable with classical numerical techniques. These fail, for example, in the solution of high-dimensional models due to the exponential increase of the number of degrees of freedom. Recently, the authors of this book and their collaborators have developed a novel technique, called Proper Generalized Decomposition (PGD) that has proven to be a significant step forward. The PGD builds by means of a successive enrichment strategy a numerical approximation of the unknown fields in a separated form. Although first introduced and successfully demonstrated in the context of high-dimensional problems, the PGD allows for a completely new approach for addressing more standard problems in science and engineering. Indeed, many challenging problems can be efficiently cast into a multi-dimensional framework, thus opening entirely new solution strategies in the PGD framework. For instance, the material parameters and boundary conditions appearing in a particular mathematical mod...
A general numerical analysis of time-domain NQR experiments.
Harel, Elad; Cho, Herman
2006-12-01
We introduce a general numerical approach for solving the Liouville equation of an isolated quadrupolar nuclide that can be used to analyze the unitary dynamics of time-domain NQR experiments. A numerical treatment is necessitated by the dimensionality of the Liouville space, which precludes analytical, closed form solutions for I > 3/2. Accurate simulations of experimental nutation curves, forbidden transition intensities, powder and single crystal spectra, and off-resonance irradiation dynamics can be computed with this method. We also examine the validity of perturbative approximations where the signal intensity of a transition is proportional to the transition moment between the eigenstates of the system, thus providing a simple basis for determining selection rules. Our method allows us to calculate spectra for all values of the asymmetry parameter, eta, and sample orientations relative to the coil axis. We conclude by demonstrating the methodology for calculating the response of the quadrupole system to amplitude- and frequency-modulated pulses.
Sekhar, Aswin; Valsecchi, Giovanni B.; Asher, David; Werner, Stephanie; Vaubaillon, Jeremie; Li, Gongjie
2017-06-01
One of the greatest successes of Einstein's General Theory of Relativity (GR) was the correct prediction of the perihelion precession of Mercury. The closed form expression to compute this precession tells us that substantial GR precession would occur only if the bodies have a combination of both moderately small perihelion distance and semi-major axis. Minimum Orbit Intersection Distance (MOID) is a quantity which helps us to understand the closest proximity of two orbits in space. Hence evaluating MOID is crucial to understand close encounters and collision scenarios better. In this work, we look at the possible scenarios where a small GR precession in argument of pericentre can create substantial changes in MOID for small bodies ranging from meteoroids to comets and asteroids.Previous works have looked into neat analytical techniques to understand different collision scenarios and we use those standard expressions to compute MOID analytically. We find the nature of this mathematical function is such that a relatively small GR precession can lead to drastic changes in MOID values depending on the initial value of argument of pericentre. Numerical integrations were done with the MERCURY package incorporating GR code to test the same effects. A numerical approach showed the same interesting relationship (as shown by analytical theory) between values of argument of pericentre and the peaks or dips in MOID values. There is an overall agreement between both analytical and numerical methods.We find that GR precession could play an important role in the calculations pertaining to MOID and close encounter scenarios in the case of certain small solar system bodies (depending on their initial orbital elements) when long term impact risk possibilities are considered. Previous works have looked into impact probabilities and collision scenarios on planets from different small body populations. This work aims to find certain sub-sets of small bodies where GR could play an
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{\
Improved Numerical Generalization of Bethe- Weizsacker Mass Formula
Mavrodiev, Strachimir
2016-01-01
In this paper is presented explicit improved numerical generalization of Bethe-Weizsacker mass formulae which describes the values of measured 2654 nuclear mass in AME2012 nuclear database with accuracy less than 2.2 MeV, starting from the number of protons Z=1 and number of neutrons N=1. In the obtained generazation of the Bethe-Weizsacker formula the influence of magic numbers and boundaries of their influence between them is defined for nine proton (2, 8, 14, 20, 28, 50, 82, 108, 124) and ten neutron (2, 8, 14, 20, 28, 50, 82, 124, 152, 202) magic numbers.
Hayata, Tomoya; Hongo, Masaru; Noumi, Toshifumi
2015-01-01
We derive relativistic hydrodynamics from quantum field theories by assuming that the density operator is given by a local Gibbs distribution at initial time. We decompose the energy-momentum tensor and particle current into nondissipative and dissipative parts, and analyze their time-evolution in detail. Performing the path-integral formulation of the local Gibbs distribution, we microscopically derive the generating functional for the nondissipative hydrodynamics. We also construct a basis to study dissipative corrections. In particular, we derive the first-order dissipative hydrodynamic equations without choice of frame such as the Landau-Lifshitz or Eckart frame.
Einstein Toolkit for Relativistic Astrophysics
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.
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.
General Relativistic Radiant Shock Waves in the Post-Quasistatic Approximation
Energy Technology Data Exchange (ETDEWEB)
H, Jorge A Rueda [Centro de Fisica Fundamental, Universidad de Los Andes, Merida 5101, Venezuela Escuela de Fisica, Universidad Industrial de Santander, A.A. 678, Bucaramanga (Colombia); Nunez, L A [Centro de Fisica Fundamental, Universidad de Los Andes, Merida 5101, Venezuela Centro Nacional de Calculo Cientifico, Universidad de Los Andes, CeCalCULA, Corporacion Parque Tecnologico de Merida, Merida 5101, Venezuela (Venezuela)
2007-05-15
An evolution of radiant shock wave front is considered in the framework of a recently presented method to study self-gravitating relativistic spheres, whose rationale becomes intelligible and finds full justification within the context of a suitable definition of the post-quasistatic approximation. The spherical matter configuration is divided into two regions by the shock and each side of the interface having a different equation of state and anisotropic phase. In order to simulate dissipation effects due to the transfer of photons and/or neutrinos within the matter configuration, we introduce the flux factor, the variable Eddington factor and a closure relation between them. As we expected the strong of the shock increases the speed of the fluid to relativistic ones and for some critical values is larger than light speed. In addition, we find that energy conditions are very sensible to the anisotropy, specially the strong energy condition. As a special feature of the model, we find that the contribution of the matter and radiation to the radial pressure are the same order of magnitude as in the mant as in the core, moreover, in the core radiation pressure is larger than matter pressure.
General Relativistic Hydrodynamic Simulation of Accretion Flow from a Stellar Tidal Disruption
Shiokawa, Hotaka; Cheng, Roseanne M; Piran, Tsvi; Noble, Scott C
2015-01-01
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 tidal debris motion, we track 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 the characteristic radius comparable to the semi-major axis of the most-bound material, not the tidal radius as previously thought. The outer shocks are caused by post-Newtonian effects, both on the stellar orbit during its disruption and on the tidal forces. Accumulation of mass into the accretion flow is non-monotonic and slow, requiring ~3--10x 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 accu...
Directory of Open Access Journals (Sweden)
J Ghanbari
2009-12-01
Full Text Available Dynamics of stationary axisymmetric configuration of the viscous accreting fluids surrounding a non-rotating compact object in final stages of accretion flow is presented here. For the special case of thin disk approximation, the relativistic fluid equations ignoring self-gravity of the disk are derived in Schwarzschild geometry. For two different state equations, two sets of self-consistent analytical solutions of fully relativistic fluid equations are obtained separately. The effect of bulk viscosity coefficient on the physical functions are investigated for each state equation, as well as the bounds that exert on the free parameters due to the condition of accretion flow in the last stages. The solutions found show that the radial and azimuthal velocities, density and pressure of the fluid increase inwards for both state equations. Also, viscosity has no effect on the velocities and density distributions in both state equations. Two state equations show different types of behavior with respect to the bulk viscosity coefficient. For p=K state equation, if there is no bulk viscosity, the pressure remains constant throughout the disk, whereas with increasing bulk viscosity the pressure falls off in the inner regions but soon stabilizes at an almost constant value. However, for p=ρc2 state equation, the pressure is never constant, even in the absence of bulk viscosity. The larger the value of ηb, the higher the value of pressure in the inner regions.
Nobili, Anna M.
2016-12-01
The universality of free fall and the weak equivalence principle, which are at the basis of general relativity, have been confirmed to 1 part in 1 013. Space experiments with macroscopic test masses of different composition orbiting Earth inside a low altitude satellite aim to improve this precision by 2 orders of magnitude (with the Microscope satellite launched on April 25, 2016) and up to 4 orders of magnitude (with the Galileo Galilei satellite). At such a high precision, many tiny effects must be taken into account in order to be ruled out as the source of a spurious violation signal. In this work, we investigate the general relativistic effects, including those which involve the rotation of both Earth and the test masses, and show that they are by far too small to be considered even in the most challenging experiment.
Nobili, Anna M
2016-01-01
The Universality of Free Fall and the Weak Equivalence Principle, which are at the basis of General Relativity, have been confirmed to 1 part in 10^13. Space experiments with macroscopic test masses of different composition orbiting the Earth inside a low altitude satellite aim at improving this precision by two orders of magnitude (with the Microscope satellite, launched on 25 April 2016) and up to four orders of magnitude (with the 'Galileo Galilei' - GG satellite). At such a high precision many tiny effects must be taken into account in order to be ruled out as the source of a spurious violation signal. In this work we investigate the general relativistic effects, including those which involve the rotation of both the source body and the test masses, and show that they are by far too small to be considered even in the most challenging experiment.
A numerical approach to finding general stationary vacuum black holes
Adam, Alexander; Wiseman, Toby
2011-01-01
The Harmonic Einstein equation is the vacuum Einstein equation supplemented by a gauge fixing term which we take to be that of DeTurck. For static black holes analytically continued to Riemannian manifolds without boundary at the horizon this equation has previously been shown to be elliptic, and Ricci flow and Newton's method provide good numerical algorithms to solve it. Here we extend these techniques to the arbitrary cohomogeneity stationary case which must be treated in Lorentzian signature. For stationary spacetimes with globally timelike Killing vector the Harmonic Einstein equation is elliptic. In the presence of horizons and ergo-regions it is less obviously so. Motivated by the Rigidity theorem we study a class of stationary black hole spacetimes, considered previously by Harmark, general enough to include the asymptotically flat case in higher dimensions. We argue the Harmonic Einstein equation consistently truncates to this class of spacetimes giving an elliptic problem. The Killing horizons and a...
The special relativistic shock tube
Thompson, Kevin W.
1986-01-01
The shock-tube problem has served as a popular test for numerical hydrodynamics codes. The development of relativistic hydrodynamics codes has created a need for a similar test problem in relativistic hydrodynamics. The analytical solution to the special relativistic shock-tube problem is presented here. The relativistic shock-jump conditions and rarefaction solution which make up the shock tube are derived. The Newtonian limit of the calculations is given throughout.
Relativistic spherical plasma waves
Bulanov, S. S.; Maksimchuk, A.; Schroeder, C. B.; Zhidkov, A. G.; Esarey, E.; Leemans, W. P.
2012-02-01
Tightly focused laser pulses that diverge or converge in underdense plasma can generate wake waves, having local structures that are spherical waves. Here we study theoretically and numerically relativistic spherical wake waves and their properties, including wave breaking.
Solving 3D relativistic hydrodynamical problems with WENO discontinuous Galerkin methods
Bugner, Marcus; Bernuzzi, Sebastiano; Weyhausen, Andreas; Bruegmann, Bernd
2015-01-01
Discontinuous Galerkin (DG) methods coupled to WENO algorithms allow high order convergence for smooth problems and for the simulation of discontinuities and shocks. In this work, we investigate WENO-DG algorithms in the context of numerical general relativity, in particular for general relativistic hydrodynamics. We implement the standard WENO method at different orders, a compact (simple) WENO scheme, as well as an alternative subcell evolution algorithm. To evaluate the performance of the different numerical schemes, we study non-relativistic, special relativistic, and general relativistic testbeds. We present the first three-dimensional simulations of general relativistic hydrodynamics, albeit for a fixed spacetime background, within the framework of WENO-DG methods. The most important testbed is a single TOV-star in three dimensions, showing that long term stable simulations of single isolated neutron stars can be obtained with WENO-DG methods.
Reisswig, C; Ott, C D; Abdikamalov, E; Moesta, P; Pollney, D; Schnetter, E
2013-01-01
We present a new three-dimensional general-relativistic hydrodynamic evolution scheme coupled to dynamical spacetime evolutions which is capable of efficiently simulating stellar collapse, isolated neutron stars, black hole formation, and binary neutron star coalescence. We make use of a set of adapted curvi-linear grids (multipatches) coupled with flux-conservative cell-centered adaptive mesh refinement. This allows us to significantly enlarge our computational domains while still maintaining high resolution in the gravitational-wave extraction zone, the exterior layers of a star, or the region of mass ejection in merging neutron stars. The fluid is evolved with a high-resolution shock capturing finite volume scheme, while the spacetime geometry is evolved using fourth-order finite differences. We employ a multi-rate Runge-Kutta time integration scheme for efficiency, evolving the fluid with second-order and the spacetime geometry with fourth-order integration, respectively. We validate our code by a number ...
Fokas, Athanassios S; Grigoriou, D
2015-01-01
Let $r(\\varphi)$ denote the orbit of Mercury and other planets. We compare the formula of General Relativity (GR) for $r(\\varphi)$, as well as the formula for the corresponding perihelion precession angle $\\Delta \\varphi$, with the formulae obtained via the relativistic gravitational law, $F=GMm\\gamma^3/r^2$. The latter law can be derived from Newton's gravitational law by employing the gravitational rather than the rest mass of the rotating body and using special relativity (SR) together with the equivalence principle to compute the inertial and hence the gravitational, mass. Remarkably, it is found that the two expressions for $r(\\varphi)$ differ only by a factor of 2 and by an additive constant. This constant does not affect the formula for the $\\Delta \\varphi$, thus the two expressions for $\\Delta\\varphi$ differ only by a factor of 2.
Murad, Mohammad Hassan; Pant, Neeraj
2014-03-01
In this paper we have studied a particular class of exact solutions of Einstein's gravitational field equations for spherically symmetric and static perfect fluid distribution in isotropic coordinates. The Schwarzschild compactness parameter, GM/ c 2 R, can attain the maximum value 0.1956 up to which the solution satisfies the elementary tests of physical relevance. The solution also found to have monotonic decreasing adiabatic sound speed from the centre to the boundary of the fluid sphere. A wide range of fluid spheres of different mass and radius for a given compactness is possible. The maximum mass of the fluid distribution is calculated by using stellar surface density as parameter. The values of different physical variables obtained for some potential strange star candidates like Her X-1, 4U 1538-52, LMC X-4, SAX J1808.4-3658 given by our analytical model demonstrate the astrophysical significance of our class of relativistic stellar models in the study of internal structure of compact star such as self-bound strange quark star.
General relativistic considerations of the field shedding model of fast radio bursts
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.
General Relativistic Considerations of the Field Shedding Model of Fast Radio Bursts
Punsly, Brian
2016-01-01
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 $B = 10^{11} - 10^{13}$ G and a long rotation period, $>1$ s this is not a ...
Heller, René
2017-09-01
As new concepts of sending interstellar spacecraft to the nearest stars are now being investigated by various research teams, crucial questions about the timing of such a vast financial and labour investment arise. If humanity could build high-speed interstellar lightsails and reach α Centauri 20 yr after launch, would it be better to wait a few years, then take advantage of further technology improvements and arrive earlier despite waiting? The risk of being overtaken by a future, faster probe has been described earlier as the incentive trap. Based on 211 yr of historical data, we find that the speed growth of artificial vehicles, from steam-driven locomotives to Voyager 1, is much faster than previously believed, about 4.72 per cent annually or a doubling every 15 yr. We derive the mathematical framework to calculate the minimum of the wait time to launch t plus travel time τ(t) and extend it into the relativistic regime. We show that the t + τ(t) minimum disappears for nearby targets. There is no use of waiting once we can reach an object within about 20 yr of travel, irrespective of the actual speed. In terms of speed, the t + τ(t) minimum for a travel to α Centauri occurs at 19.6 per cent the speed of light (c), in agreement with the 20 per cent c proposed by the Breakthrough Starshot initiative. If interstellar travel at 20 per cent c could be achieved within 45 yr from today and the kinetic energy be increased at a rate consistent with the historical record, then humans can reach the 10 most nearby stars within 100 yr from today.
Relativistic radiative transfer in relativistic spherical flows
Fukue, Jun
2017-02-01
Relativistic radiative transfer in relativistic spherical flows is numerically examined under the fully special relativistic treatment. We first derive relativistic formal solutions for the relativistic radiative transfer equation in relativistic spherical flows. We then iteratively solve the relativistic radiative transfer equation, using an impact parameter method/tangent ray method, and obtain specific intensities in the inertial and comoving frames, as well as moment quantities, and the Eddington factor. We consider several cases; a scattering wind with a luminous central core, an isothermal wind without a core, a scattering accretion on to a luminous core, and an adiabatic accretion on to a dark core. In the typical wind case with a luminous core, the emergent intensity is enhanced at the center due to the Doppler boost, while it reduces at the outskirts due to the transverse Doppler effect. In contrast to the plane-parallel case, the behavior of the Eddington factor is rather complicated in each case, since the Eddington factor depends on the optical depth, the flow velocity, and other parameters.
Numeric data services and sources for the general reference librarian
Kellam, Lynda
2011-01-01
The proliferation of online access to social science statistical and numeric data sources, such as the U.S. Census Bureau's American Fact Finder, has lead to an increased interest in supporting these sources in academic libraries. Many large libraries have been able to devote staff to data services for years, and recently smaller academic libraries have recognized the need to provide numeric data services and support. This guidebook serves as a primer to developing and supporting social science statistical and numerical data sources in the academic library. It provides strategies for the estab
Relativistic Remnants of Non-Relativistic Electrons
Kashiwa, Taro
2015-01-01
Electrons obeying the Dirac equation are investigated under the non-relativistic $c \\mapsto \\infty$ limit. General solutions are given by derivatives of the relativistic invariant functions whose forms are different in the time- and the space-like region, yielding the delta function of $(ct)^2 - x^2$. This light-cone singularity does survive to show that the charge and the current density of electrons travel with the speed of light in spite of their massiveness.
Energy Technology Data Exchange (ETDEWEB)
Rowland, D R [Student Support Services, University of Queensland, Brisbane QLD 4072 (Australia)
2006-01-01
Introductory courses covering modern physics sometimes introduce some elementary ideas from general relativity, though the idea of a geodesic is generally limited to shortest Euclidean length on a curved surface of two spatial dimensions rather than extremal aging in spacetime. It is shown that Epstein charts provide a simple geometric picture of geodesics in one space and one time dimension and that for a hypothetical uniform gravitational field, geodesics are straight lines on a planar diagram. This means that the properties of geodesics in a uniform field can be calculated with only a knowledge of elementary geometry and trigonometry, thus making the calculation of some basic results of general relativity accessible to students even in an algebra-based survey course on physics.
General relativistic simulations of compact binary mergers as engines of short gamma-ray bursts
Paschalidis, Vasileios
2016-01-01
Black hole - neutron star (BHNS) and neutron star - neutron star (NSNS) binaries are among the favored candidates for the progenitors of the black hole - disk systems that may be the engines powering short-hard gamma ray bursts. After almost two decades of simulations of binary NSNSs and BHNSs in full general relativity we are now beginning to understand the ingredients that may be necessary for these systems to launch incipient jets. Here, we review our current understanding, and summarize the surprises and lessons learned from state-of-the-art (magnetohydrodynamic) simulations in full general relativity of BHNS and NSNS mergers as jet engines for short-hard gamma-ray bursts.
General relativistic massive vector field effects in Gamma Ray Burst production
Tamburini, Fabrizio; Amati, Lorenzo; Thidé, Bo
2016-01-01
To explain the extremely high energy release, $>10^{53}$~erg, suggested by the observations of some Gamma Ray Bursts (GRBs) we propose a new energy extraction mechanism from the rotation energy of a Kerr-Newman black hole (BH) by a massive photon field. Numerical results show that this mechanism is stable with respect to the black hole rotation parameter, $a$, with a clear dependence on the BH mass, $M$, and charge, $Q$, and can extract energies up to $10^{54}$ erg. The controversial "energy crisis" problem of GRBs that does not show evidence for collimated emission may benefit of this energy extraction mechanism. With these results we set a lower bound on the coupling between electromagnetic and gravitational fields.
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.
Numerical simulations of the relativistic Langmuir turbulence%数值模拟相对论性朗缪尔湍动
Institute of Scientific and Technical Information of China (English)
刘笑兰; 范洪鸣; 熊慧勇; 黄悦阳
2014-01-01
In order to study the characteristics of relativistic Langmuir turbulence,we numerically calculated the relativistic Zakharov Equations which had the nonlinear coupling process of Langmuir wave and ion sounds wave.A series of the evolution images of Langmuir waves and ion sound waves were obtained.From these figures,The process of relativistic strong Langmuir turbulence and the maximal intensity of Lang-muir turbulence are were offered from these figures.Our studies have shown that the stronger the relativis-tic electron moved,the longer the evolution time of the Langmuir waves were,and the stronger the intensi-ty of Langmuir was.The research conld provide some reference for turbulent acceleration or plasma heat-ing,which should be significative to the generation mechanism of extremely hot electron (or fast ion flow) from the super laser plasma (or astrophysics).%为研究相对论性朗缪尔湍动特性，采用描述朗缪尔波与离声波非线性耦合过程的相对论性萨哈罗夫方程组，进行数值模拟，获得一系列朗缪尔波的时间演化图。图组形象地模拟出相对论性强朗缪尔湍动过程，图中给出不同相对论参数下朗缪尔波场强的最大值。研究表明，电子运动相对论性越强，朗缪尔波的演化耗时更长，朗缪尔波场越强，湍动越剧烈。这可为湍动加速或等离子体加热提供参考数据，对超强激光等离子体（或天体物理）中出现超热电子（或快离子流）的产生机制研究有一定的参考价值。
General relativistic simulations of compact binary mergers as engines for short gamma-ray bursts
Paschalidis, Vasileios
2017-04-01
Black hole—neutron star (BHNS) and neutron star—neutron star (NSNS) binaries are among the favored candidates for the progenitors of the black hole—disk systems that may be the engines powering short-hard gamma ray bursts. After almost two decades of simulations of binary NSNSs and BHNSs in full general relativity we are now beginning to understand the ingredients that may be necessary for these systems to launch incipient jets. Here, we review our current understanding, and summarize the surprises and lessons learned from state-of-the-art (magnetohydrodynamic) simulations in full general relativity of BHNS and NSNS mergers as jet engines for short-hard gamma-ray bursts. We also propose a new approach to probing the nuclear equation of state by virtue of multimessenger observations.
General Relativistic Energy Conditions The Hubble expansion in the epoch of galaxy formation
Visser, M
1997-01-01
The energy conditions of Einstein gravity (classical general relativity) are designed to extract as much information as possible from classical general relativity without enforcing a particular equation of state for the stress-energy. This systematic avoidance of the need to specify a particular equation of state is particularly useful in a cosmological setting --- since the equation of state for the cosmological fluid in a Friedmann-Robertson-Walker type universe is extremely uncertain. I shall show that the energy conditions provide simple and robust bounds on the behaviour of both the density and look-back time as a function of red-shift. I shall show that current observations suggest that the so-called strong energy condition (SEC) is violated sometime between the epoch of galaxy formation and the present. This implies that no possible combination of ``normal'' matter is capable of fitting the observational data.
Handbook of relativistic quantum chemistry
Energy Technology Data Exchange (ETDEWEB)
Liu, Wenjian (ed.) [Peking Univ., Beijing (China). Center for Computational Science and Engineering
2017-03-01
This handbook focuses on the foundations of relativistic quantum mechanics and addresses a number of fundamental issues never covered before in a book. For instance: How can many-body theory be combined with quantum electrodynamics? How can quantum electrodynamics be interfaced with relativistic quantum chemistry? What is the most appropriate relativistic many-electron Hamiltonian? How can we achieve relativistic explicit correlation? How can we formulate relativistic properties? - just to name a few. Since relativistic quantum chemistry is an integral component of computational chemistry, this handbook also supplements the ''Handbook of Computational Chemistry''. Generally speaking, it aims to establish the 'big picture' of relativistic molecular quantum mechanics as the union of quantum electrodynamics and relativistic quantum chemistry. Accordingly, it provides an accessible introduction for readers new to the field, presents advanced methodologies for experts, and discusses possible future perspectives, helping readers understand when/how to apply/develop the methodologies.
Energy Technology Data Exchange (ETDEWEB)
Li, Xiaoze; Ye, Hu; Zhang, Yuchuan; Song, Wei; Su, Jiancang; Zhang, Ligang; Tan, Weibing; Hu, Xianggang; Zhu, Xiaoxin; Shen, Zhiyuan; Zhang, Min [Science and Technology on High Power Microwave Laboratory, Northwest Institute of Nuclear Technology, Xi' an 710024 (China)
2016-05-15
A high power capacity relativistic backward wave oscillator with an electron collection cavity (ECC) placed at the downstream of the slow wave structure (SWS) is presented. The breakdown threshold is increased, and the density of seed electron is suppressed by preventing the secondary electron, plasma, and powder generated from the bombardment of spent electron beam on the surface of the collector drifting to the extractor and beam-wave interaction region. The maximum longitudinal electric field in the device is reduced through extension of the span between electron beam and slow wave structure and weakening the Cerenkov radiation. The conversion efficiency reaches up to 52% owing to enhanced transit time radiation taking place at the entrance of the ECC. The maximum longitudinal electric field is 1.1 MV/cm on the surface of SWSs when the output power is 7.3 GW and the power capacity improves significantly.
Numerical implementation of generalized Coddington equations for ophthalmic lens design
Rojo Badenas, Pilar; Royo Royo, Santiago; RAMÍREZ,JORGE; Madariaga, Inés
2014-01-01
A method for general implementation in any software platform of the generalized Coddington equations is presented, developed, and validated within a Matlab environment. The ophthalmic lens design strategy is presented thoroughly, and the basic concepts of generalized ray tracing are introduced. The methodology for ray tracing is shown to include two inter-related processes. Firstly, finite ray tracing is used to provide the main direction of propagation of the considered ray at the incidence ...
A public code for general relativistic, polarised radiative transfer around spinning black holes
Dexter, Jason
2016-10-01
Ray tracing radiative transfer is a powerful method for comparing theoretical models of black hole accretion flows and jets with observations. We present a public code, GRTRANS, for carrying out such calculations in the Kerr metric, including the full treatment of polarised radiative transfer and parallel transport along geodesics. The code is written in FORTRAN 90 and efficiently parallelises with OPENMP, and the full code and several components have PYTHON interfaces. We describe several tests which are used for verifiying the code, and we compare the results for polarised thin accretion disc and semi-analytic jet problems with those from the literature as examples of its use. Along the way, we provide accurate fitting functions for polarised synchrotron emission and transfer coefficients from thermal and power-law distribution functions, and compare results from numerical integration and quadrature solutions of the polarised radiative transfer equations. We also show that all transfer coefficients can play an important role in predicted images and polarisation maps of the Galactic centre black hole, Sgr A*, at submillimetre wavelengths.
Mueller, B
2014-01-01
Considering general relativistic, two-dimensional (2D) supernova (SN) explosion models of progenitor stars between 8.1 and 27 solar masses, 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 of electron antineutrinos and heavy-lepton neutrinos and even their crossing during the accretion phase for stars with M>10 M_sun as observed in previous 1D and 2D simulations with state-of-the-art neutrino transport. We establish a roughly linear scaling of the electron antineutrino mean energy 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 abru...
Takahashi, Hiroyuki R; Kawashima, Tomohisa; Sekiguchi, Yuichiro
2016-01-01
Using three-dimensional general relativistic radiation magnetohydrodynamics simulations of accretion flows around stellar mass black holes, we report that the relatively cold disk ($\\gtrsim 10^{7}$K) is truncated near the black hole. Hot and less-dense regions, of which the gas temperature is $ \\gtrsim 10^9$K and more than ten 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, and sandwich the cold disk, leading to the effective Compton upscattering. The truncation radius is $\\sim 30 r_{\\rm g}$ for $\\dot{M} \\sim L_{\\rm Edd}/c^2$, where $r_{\\rm g}, \\dot M, L_\\mathrm{Edd}, c$ are the gravitational radius, mass accretion rate, Eddington luminosity, and light speed. Our results are consistent with observations of very high state, whereby the truncated disk is thought to be embedded in the hot rarefied regions. The truncation radius shifts inward to $\\sim 10 r_{\\rm g}$ with increasing mass accret...
Relativistic Self-similar Dynamic Collapses of Black Holes in General Polytropic Spherical Clouds
Lian, Biao
2013-01-01
We study the hydrodynamic self-similar mass collapses of general polytropic (GP) spherical clouds to central Schwarzschild black holes and void evolution with or without shocks. In order to grossly capture characteristic effects of general relativity (GR) outside yet close to the event horizon of a Schwarzschild black hole and to avoid mathematical complexity, we adopt the approximation of the Paczynski-Wiita gravity to replace the simple Newtonian gravity in our model formulation. A new dimensionless parameter s appears with the physical meaning of the square of the ratio of the sound speed to the speed of light $c$. Various self-similar dynamic solutions are constructed for a polytropic index $\\gamma>4/3$. Two (for small enough $s4/3$, representing the collapse of static singular GP spheres towards the central singularity of spacetime. Such GP spherical dynamic mass collapse is shown to be highly efficient for the rapid formation of supermassive black holes (SMBHs; mass range of $10^6-10^{10}M_{\\odot}$) in ...
Some numerical studies of the evolution of generalized parton distributions
Energy Technology Data Exchange (ETDEWEB)
Diehl, M.; Kugler, W.
2007-11-15
We study the evolution behavior of generalized parton distributions at small longitudinal momentum fraction. Particular attention is paid to the ratio of a generalized parton distribution and its forward limit, to the mixing between quarks and gluons, and to the dependence on the squared momentum transfer t. (orig.)
Relativistic quantum revivals.
Strange, P
2010-03-26
Quantum revivals are now a well-known phenomena within nonrelativistic quantum theory. In this Letter we display the effects of relativity on revivals and quantum carpets. It is generally believed that revivals do not occur within a relativistic regime. Here we show that while this is generally true, it is possible, in principle, to set up wave packets with specific mathematical properties that do exhibit exact revivals within a fully relativistic theory.
Energy Technology Data Exchange (ETDEWEB)
Psaltis, Dimitrios; Özel, Feryal; Chan, Chi-Kwan; Marrone, Daniel P. [Astronomy Department, University of Arizona, 933 N. Cherry Ave, Tucson, AZ 85721 (United States)
2015-12-01
The half opening angle of a Kerr black hole shadow is always equal to (5 ± 0.2)GM/Dc{sup 2}, 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%.
Kuroda, Takami; Takiwaki, Tomoya
2012-01-01
We present results from the first generation of multi-dimensional hydrodynamic core-collapse simulations in full general relativity (GR) that include an approximate treatment of neutrino transport. Using a M1 closure scheme with an analytic variable Eddington factor, we solve the energy-independent set of radiation energy and momentum based on the Thorne's momentum formalism. To simplify the source terms of the transport equations, a methodology of multiflavour neutrino leakage scheme is partly employed. Our newly developed code is designed to evolve the Einstein field equation together with the GR radiation hydrodynamic equations. We follow the dynamics starting from the onset of gravitational core-collapse of a 15 $M_{\\odot}$ star, through bounce, up to about 100 ms postbounce in this study to study how the spacial multi-dimensionality and GR would affect the dynamics in the early postbounce phase. Our 3D results support the anticipation in previous 1D results that the neutrino luminosity and average neutri...
General relativistic models for rotating magnetized neutron stars in conformally flat space-time
Pili, A. G.; Bucciantini, N.; Del Zanna, L.
2017-09-01
The extraordinary energetic activity of magnetars is usually explained in terms of dissipation of a huge internal magnetic field of the order of 1015-16 G. How such a strong magnetic field can originate during the formation of a neutron star (NS) is still subject of active research. An important role can be played by fast rotation: if magnetars are born as millisecond rotators dynamo mechanisms may efficiently amplify the magnetic field inherited from the progenitor star during the collapse. In this case, the combination of rapid rotation and strong magnetic field determine the right physical condition not only for the development of a powerful jet-driven explosion, manifesting as a gamma-ray burst, but also for a copious gravitational waves emission. Strong magnetic fields are indeed able to induce substantial quadrupolar deformations in the star. In this paper, we analyse the joint effect of rotation and magnetization on the structure of a polytropic and axisymmetric NS, within the ideal magneto-hydrodynamic regime. We will consider either purely toroidal or purely poloidal magnetic field geometries. Through the sampling of a large parameter space, we generalize previous results in literature, inferring new quantitative relations that allow for a parametrization of the induced deformation, that takes into account also the effects due to the stellar compactness and the current distribution. Finally, in the case of purely poloidal field, we also discuss how different prescription on the surface charge distribution (a gauge freedom) modify the properties of the surrounding electrosphere and its physical implications.
GRAVITAS : General Relativistic Astrophysics VIa Timing And Spectroscopy: An ESA M3 mission proposal
Nandra, Kirpal; Fabian, Andy; Strueder, Lothar; Willingale, Richard; Watson, Mike; Jonker, Peter; Kunieda, Hideyo; Miniutti, Giovanni; Motch, Christian; Predehl, Peter
2011-01-01
GRAVITAS is an X-ray observatory, designed and optimised to address the ESA Cosmic Vision theme of "Matter under extreme conditions". It was submitted as a response to the call for M3 mission proposals. The concept centres around an X-ray telescope of unprecedented effective area, which will focus radiation emitted from close to the event horizon of black holes or the surface of neutron stars. To reveal the nature and behaviour of matter in the most extreme astrophysical environments, GRAVITAS targets a key feature in the X-ray spectra of compact objects: the iron Kalpha line at ~6.5 keV. The energy, profile, and variability of this emission line, and the properties of the surrounding continuum emission, shaped by General Relativity (GR) effects, provide a unique probe of gravity in its strong field limit. Among its prime targets are hundreds of supermassive black holes in bright Active Galactic Nuclei (AGN), which form the perfect laboratory to help understand the physical processes behind black hole growth....
Numerical methods for a general class of porous medium equations
Energy Technology Data Exchange (ETDEWEB)
Rose, M. E.
1980-03-01
The partial differential equation par. deltau/par. deltat + par. delta(f(u))/par. deltax = par. delta(g(u)par. deltau/par. deltax)/par. deltax, where g(u) is a non-negative diffusion coefficient that may vanish for one or more values of u, was used to model fluid flow through a porous medium. Error estimates for a numerical procedure to approximate the solution are derived. A revised version of this report will appear in Computers and Mathematics with Applications.
Numerical implementation of generalized Coddington equations for ophthalmic lens design
Rojo, P.; Royo, S.; Ramírez, J.; Madariaga, I.
2014-02-01
A method for general implementation in any software platform of the generalized Coddington equations is presented, developed, and validated within a Matlab environment. The ophthalmic lens design strategy is presented thoroughly, and the basic concepts of generalized ray tracing are introduced. The methodology for ray tracing is shown to include two inter-related processes. Firstly, finite ray tracing is used to provide the main direction of propagation of the considered ray at the incidence point of interest. Afterwards, generalized ray tracing provides the principal curvatures of the local wavefront at that point, and its orientation after being refracted by the lens. The curvature values of the local wavefront are interpreted as the sagital and tangential powers of the lens at the point of interest. The proposed approach is validated using a double-check of the calculated lens performance in the spherical lens case: while finite ray tracing is validated using a commercial ray tracing software, generalized ray tracing is validated using a software application for ophthalmic lens design based on the classical version of Coddington equations. Equations of the complete tracing process are developed in detail for the case of generic astigmatic ophthalmic lenses as an example. Three-dimensional representation of the sagital and tangential powers of the ophthalmic lens at all directions of gaze then becomes possible, and results are presented for lenses with different geometries.
Bugner, Marcus; Dietrich, Tim; Bernuzzi, Sebastiano; Weyhausen, Andreas; Brügmann, Bernd
2016-10-01
Discontinuous Galerkin (DG) methods coupled to weighted essentially nonoscillatory (WENO) algorithms allow high order convergence for smooth problems and for the simulation of discontinuities and shocks. In this work, we investigate WENO-DG algorithms in the context of numerical general relativity, in particular for general relativistic hydrodynamics. We implement the standard WENO method at different orders, a compact (simple) WENO scheme, as well as an alternative subcell evolution algorithm. To evaluate the performance of the different numerical schemes, we study nonrelativistic, special relativistic, and general relativistic test beds. We present the first three-dimensional simulations of general relativistic hydrodynamics, albeit for a fixed spacetime background, within the framework of WENO-DG methods. The most important test bed is a single Tolman-Oppenheimer-Volkoff star in three dimensions, showing that long term stable simulations of single isolated neutron stars can be obtained with WENO-DG methods.
Numerical simulation of generalized Langevin equation with arbitrary correlated noise.
Lü, Kun; Bao, Jing-Dong
2005-12-01
A generalized Langevin equation with arbitrary correlated noise and associated frequency-dependent friction is simulated, which can lead to anomalous diffusion. The algorithm is realized by using the Fourier transform technique to generate noise and the stochastic Runge-Kutta method to solve the whole equation. Application to an acoustic phonon model, initial preparation-dependent ballistic diffusion, is shown.
The general Penrose inequality: lessons from numerical evidence
Karkowski, J; Karkowski, Janusz; Malec, Edward
2004-01-01
Formulation of the Penrose inequality becomes ambiguous when the past and future apparent horizons do cross. We test numerically several natural possibilities of stating the inequality in punctured and boosted single- and double- black holes, in a Dain-Friedrich class of initial data and in conformally flat spheroidal data.The Penrose inequality holds true in vacuum configurations for the outermost element amongst the set of disjoint future and past apparent horizons (as expected)and (unexpectedly) for each of the outermost past and future apparent horizons, whenever these two bifurcate from an outermost minimal surface, regardless of whether they intersect or remain disjoint. In systems with matter the conjecture breaks down only if matter does not obey the dominant energy condition.
Energy Technology Data Exchange (ETDEWEB)
Müller, Bernhard [Monash Center for Astrophysics, School of Mathematical Sciences, Building 28, Monash University, Victoria 3800 (Australia); Janka, Hans-Thomas, E-mail: bernhard.mueller@monash.edu, E-mail: bjmuellr@mpa-garching.mpg.de, E-mail: thj@mpa-garching.mpg.de [Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, D-85748 Garching (Germany)
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.
A Total Generalized Optimal Velocity Model and Its Numerical Tests
Institute of Scientific and Technical Information of China (English)
ZHU Wen-xing; LIU Yun-cai
2008-01-01
A car-following model named total generalized optimal velocity model (TGOVM) was developed with a consideration of an arbitrary number of preceding vehicles before current one based on analyzing the previous models such as optimal velocity model (OVM), generalized OVM (GOVM) and improved GOVM (IGOVM). This model describes the physical phenomena of traffic flow more exactly and realistically than previous models. Also the performance of this model was checked out by simulating the acceleration and de- celeration process for a small delay time. On a single circular lane, the evolution of the traffic congestion was studied for a different number of headways and relative velocities of the preceding vehicles being taken into account. The simulation results show that TGOVM is reasonable and correct.
GANDALF - A Generally Applicable Numerical Data Acquisition Laboratory Facility
DEFF Research Database (Denmark)
Lynov, Jens-Peter; Michelsen, Poul
This report contains a description of an interactive computer program, GANDALF, for general purpose data handling. GANDALF is designed for different types of data input, it has flexible data processing possibilities, and it can produce various kinds of data output. The program is written for an H......-9825 desk-top computer in HPL-language. However, the fundamental program structure can also be applied to other computer systems with other computer languages....
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
In this paper,authors discuss the numerical methods of general discontinuous boundary value problems for elliptic complex equations of first order.They first give the well posedness of general discontinuous boundary value problems,reduce the discontinuousboundary value problems to a variation problem,and then find the numerical solutions ofabove problem by the finite element method.Finally authors give some error-estimates of the foregoing numerical solutions.
Relativistic GLONASS and geodesy
Mazurova, E. M.; Kopeikin, S. M.; Karpik, A. P.
2016-12-01
GNSS technology is playing a major role in applications to civil, industrial and scientific areas. Nowadays, there are two fully functional GNSS: American GPS and Russian GLONASS. Their data processing algorithms have been historically based on the Newtonian theory of space and time with only a few relativistic effects taken into account as small corrections preventing the system from degradation on a fairly long time. Continuously growing accuracy of geodetic measurements and atomic clocks suggests reconsidering the overall approach to the GNSS theoretical model based on the Einstein theory of general relativity. This is essentially more challenging but fundamentally consistent theoretical approach to relativistic space geodesy. In this paper, we overview the basic principles of the relativistic GNSS model and explain the advantages of such a system for GLONASS and other positioning systems. Keywords: relativistic GLONASS, Einstein theory of general relativity.
Generalized propagation of light through optical systems. II. Numerical implications.
Tessmer, Manuel; Gross, Herbert
2015-12-01
We present an algorithm implemented in a MATLAB toolbox that is able to compute the wave propagation of coherent visible light through macroscopic lenses. The mathematical operations that complete the status at the end of the first paper of this sequence, where only limited configurations of the propagation direction were allowed toward arbitrarily directed input beam computations, are provided. With their help, high numerical aperture (NA) field tracing is made possible that is based on fast Fourier routines and is Maxwell exact in the limit of macroscopic structures and large curvature radii, including reflection and transmission. Whereas the curvature-dependent terms in the Helmholtz equation are under analytical control through the first perturbation order in the curvature, they are only included in the propagation distance in the current investigation for the sake of reasonable time consumption. We give a number of examples that demonstrate the strengths of our approach, describe essential differences from other approaches that were not obvious when Paper 1 was written, and list a number of drawbacks and possible simplifications to overcome them.
Status of numerical relativity
Indian Academy of Sciences (India)
Masaru Shibata
2004-10-01
I describe the current status of numerical relativity from my personal point of view. Here, I focus mainly on explaining the numerical implementations necessary for simulating general relativistic phenomena such as the merger of compact binaries and stellar collapse, emphasizing the well-developed current status of such implementations that enable simulations for several astrophysical phenomena. Some of our latest results for simulation of binary neutron star mergers are briefly presented.
Brun-Battistini, D; Sandoval-Villalbazo, A
2016-01-01
Richard C. Tolman analyzed the relation between a temperature gradient and a gravitational field in an equilibrium situation. In 2012, Tolman\\textquoteright s law was generalized to a non-equilibrium situation for a simple dilute relativistic fluid. The result in that scenario, obtained by introducing the gravitational force through the molecular acceleration, couples the heat flux with the metric coefficients and the gradients of the state variables. In the present paper it is shown, by \\textquotedblleft suppressing\\textquotedblright{} the molecular acceleration in Boltzmann\\textquoteright s equation, that a gravitational field drives a heat flux. This procedure corresponds to the description of particle motion through geodesics, in which a Newtonian limit to the Schwarzschild metric is assumed. The effect vanishes in the non-relativistic regime, as evidenced by the direct evaluation of the corresponding limit.
Mohammadi, Vahid; Chenaghlou, Alireza
2017-09-01
The two-dimensional Dirac equation with spin and pseudo-spin symmetries is investigated in the presence of the maximally superintegrable potentials. The integrals of motion and the quadratic algebras of the superintegrable quantum E3‧, anisotropic oscillator and the Holt potentials are studied. The corresponding Casimir operators and the structure functions of the mentioned superintegrable systems are found. Also, we obtain the relativistic energy spectra of the corresponding superintegrable systems. Finally, the relativistic energy eigenvalues of the generalized Yang-Coulomb monopole (YCM) superintegrable system (a SU(2) non-Abelian monopole) are calculated by the energy spectrum of the eight-dimensional oscillator which is dual to the former system by Hurwitz transformation.
Designing generalized statistical ensembles for numerical simulations of biopolymers
Energy Technology Data Exchange (ETDEWEB)
La Penna, G. [Consiglio Nazionale delle Ricerche, Genoa (Italy). Ist. per lo Studio delle Macromolecole ISMac]|[Florence Univ. (Italy). Magnetic Resonance Center; Morante, S. [Rome Univ. (Italy). Dipartimento di Fisica; Perico, A. [Consiglio Nazionale delle Ricerche, Genoa (Italy). Ist. per lo Studio delle Macromolecole ISMac; Rossi, G.C. [Rome Univ. (Italy). Dipartimento di Fisica]|[Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2004-08-01
Conformational properties of polymers, like average dihedral angles or molecular {alpha}-helicity, display a rather weak dependence on the detailed arrangement of the elementary constituents (atoms). We propose a computer simulation method to explore the polymer phase-space using a variant of the standard multi-canonical method, in which the density of states associated to suitably chosen configurational variables is considered in place of the standard energy density of states. This configurational density of states is used in the metropolis acceptance/rejection test when configurations are generated with the help of a hybrid monte carlo algorithm. The resulting configurational probability distribution is then modulated by exponential factors derived from the general principle of the maximal constrained entropy by requiring that certain average configurational quantities take preassigned (possibly temperature dependent) values. Thermal averages of other configurational quantities can be computed by using the probability distributions obtained in this way. Moments of the energy distribution require an extra canonical sampling of the system phase-space at the desired temperature, in order to locally thermalize the configurational degrees of freedom. As an application of these ideas we present the study of the structural properties of two simple models: a bead-and-spring model of polyethylene with independent hindered torsions and an all-atom model of alanine and glycine oligomers with 12 aminoacids in vacuum. (orig.)
Relativistic viscoelastic fluid mechanics.
Fukuma, Masafumi; Sakatani, Yuho
2011-08-01
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.
Colombeau, J. F.
2007-01-01
We present numerical techniques based on generalized functions adapted to nonlinear calculations. They concern main numerical engineering problems ruled by-or issued from-nonlinear equations of continuum mechanics. The aim of this text is to invite the readers in applying these techniques in their own work without significant prerequisites by presenting their use on a sample of elementary applications from engineering. Pure mathematicians can read it easily since the numerical techniques are ...
Relativistic theories of materials
Bressan, Aldo
1978-01-01
The theory of relativity was created in 1905 to solve a problem concerning electromagnetic fields. That solution was reached by means of profound changes in fundamental concepts and ideas that considerably affected the whole of physics. Moreover, when Einstein took gravitation into account, he was forced to develop radical changes also in our space-time concepts (1916). Relativistic works on heat, thermodynamics, and elasticity appeared as early as 1911. However, general theories having a thermodynamic basis, including heat conduction and constitutive equations, did not appear in general relativity until about 1955 for fluids and appeared only after 1960 for elastic or more general finitely deformed materials. These theories dealt with materials with memory, and in this connection some relativistic versions of the principle of material indifference were considered. Even more recently, relativistic theories incorporating finite deformations for polarizable and magnetizable materials and those in which couple s...
An analytic toy model for relativistic accretion in Kerr spacetime
Tejeda, Emilio; Miller, John C
2013-01-01
We present a relativistic model for the stationary axisymmetric accretion flow of a rotating cloud of non-interacting particles falling onto a Kerr black hole. Based on a ballistic approximation, streamlines are described analytically in terms of timelike geodesics, while a simple numerical scheme is introduced for calculating the density field. A novel approach is presented for describing all of the possible types of orbit by means of a single analytic expression. This model is a useful tool for highlighting purely relativistic signatures in the accretion flow dynamics coming from a strong gravitational field with frame-dragging. In particular, we explore the coupling due to this between the spin of the black hole and the angular momentum of the infalling matter. Moreover, we demonstrate how this analytic solution may be used for benchmarking general relativistic numerical hydrodynamics codes by comparing it against results of smoothed particle hydrodynamics simulations for a collapsar-like setup. These simu...
Iorio, Lorenzo
2005-01-01
The general relativistic Lense-Thirring precessions of the perihelia of the inner planets of the Solar System are about 10^-3 arcseconds per century. Recent improvements in planetary orbit determination may yield the first observational evidence of such a tiny effect. Indeed, corrections to the known perihelion rates of -0.0036 +/- 0.0050, -0.0002 +/- 0.0004 and 0.0001 +/- 0.0005 arcseconds per century were recently estimated by E.V. Pitjeva for Mercury, the Earth and Mars, respectively, on t...
A relativistic model of electron cyclotron current drive efficiency in tokamak plasmas
Lin-Liu Y.R.; Hu Y.J.; Hu Y.M.
2012-01-01
A fully relativistic model of electron cyclotron current drive (ECCD) efficiency based on the adjoint function techniques is considered. Numerical calculations of the current drive efficiency in a tokamak by using the variational approach are performed. A fully relativistic extension of the variational principle with the modified basis functions for the Spitzer function with momentum conservation in the electron-electron collision is described in general tokamak geometry. The model developed ...
Energy Extraction from Spinning Black Holes via Relativistic Jets
Narayan, Ramesh; Tchekhovskoy, Alexander
2013-01-01
It has for long been an article of faith among astrophysicists that black hole spin energy is responsible for powering the relativistic jets seen in accreting black holes. Two recent advances have strengthened the case. First, numerical general relativistic magnetohydrodynamic simulations of accreting spinning black holes show that relativistic jets form spontaneously. In at least some cases, there is unambiguous evidence that much of the jet energy comes from the black hole, not the disk. Second, spin parameters of a number of accreting stellar-mass black holes have been measured. For ballistic jets from these systems, it is found that the radio luminosity of the jet correlates with the spin of the black hole. This suggests a causal relationship between black hole spin and jet power, presumably due to a generalized Penrose process.
Fast lattice Boltzmann solver for relativistic hydrodynamics.
Mendoza, M; Boghosian, B M; Herrmann, H J; Succi, S
2010-07-01
A lattice Boltzmann formulation for relativistic fluids is presented and numerically validated through quantitative comparison with recent hydrodynamic simulations of relativistic fluids. In order to illustrate its capability to handle complex geometries, the scheme is also applied to the case of a three-dimensional relativistic shock wave, generated by a supernova explosion, impacting on a massive interstellar cloud. This formulation opens up the possibility of exporting the proven advantages of lattice Boltzmann methods, namely, computational efficiency and easy handling of complex geometries, to the context of (mildly) relativistic fluid dynamics at large, from quark-gluon plasmas up to supernovae with relativistic outflows.
Relativistic cosmological hydrodynamics
Hwang, J
1997-01-01
We investigate the relativistic cosmological hydrodynamic perturbations. We present the general large scale solutions of the perturbation variables valid for the general sign of three space curvature, the cosmological constant, and generally evolving background equation of state. The large scale evolution is characterized by a conserved gauge invariant quantity which is the same as a perturbed potential (or three-space curvature) in the comoving gauge.
Stefańska, Patrycja
2016-01-01
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); 30, 2747(E) (1997)], 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.
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.
A molecular dynamics approach to dissipative relativistic hydrodynamics: propagation of fluctuations
Shahsavar, Leila; Montakhab, Afshin
2016-01-01
Relativistic generalization of hydrodynamic theory has attracted much attention from a theoretical point of view. However, it has many important practical applications in high energy as well as astrophysical contexts. Despite various attempts to formulate relativistic hydrodynamics, no definitive consensus has been achieved. In this work, we propose to test the predictions of four types of \\emph{first-order} hydrodynamic theories for non-perfect fluids in the light of numerically exact molecular dynamics simulations of a fully relativistic particle system in the low density regime. In this regard, we study the propagation of density, velocity and heat fluctuations in a wide range of temperatures using extensive simulations and compare them to the corresponding analytic expressions we obtain for each of the proposed theories. As expected in the low temperature classical regime all theories give the same results consistent with the numerics. In the high temperature extremely relativistic regime, not all conside...
Relativistic cosmology; Cosmologia Relativista
Energy Technology Data Exchange (ETDEWEB)
Bastero-Gil, M.
2015-07-01
Relativistic cosmology is nothing but the study of the evolution of our universe expanding from the General Theory of Relativity, which describes the gravitational interaction at any scale and given its character far-reaching is the force that dominate the evolution of the universe. (Author)
Fabian, A C; Parker, M L
2014-01-01
Broad emission lines, particularly broad iron-K lines, are now commonly seen in the X-ray spectra of luminous AGN and Galactic black hole binaries. Sensitive NuSTAR spectra over the energy range of 3-78 keV and high frequency reverberation spectra now confirm that these are relativistic disc lines produced by coronal irradiation of the innermost accretion flow around rapidly spinning black holes. General relativistic effects are essential in explaining the observations. Recent results are briefly reviewed here.
Instability of Extremal Relativistic Charged Spheres
Anninos, P; Anninos, Peter; Rothman, Tony
2002-01-01
With the question, ``Can relativistic charged spheres form extremal black holes?" in mind, we investigate the properties of such spheres from a classical point of view. The investigation is carried out numerically by integrating the Oppenheimer-Volkov equation for relativistic charged fluid spheres and finding interior Reissner-Nordstr\\"om solutions for these objects. We consider both constant density and adiabatic equations of state, as well as several possible charge distributions, and examine stability by both a normal mode and an energy analysis. In all cases, the stability limit for these spheres lies between the extremal ($Q = M$) limit and the black hole limit ($R = R_+$). That is, we find that charged spheres undergo gravitational collapse before they reach $Q = M$, suggesting that extremal Reissner-Nordtr\\"om black holes produced by collapse are ruled out. A general proof of this statement would support a strong form of the cosmic censorship hypothesis, excluding not only stable naked singularities, ...
A general numerical solution of dispersion relations for the nuclear optical model
Capote, R; Quesada, J M; Capote, Roberto; Molina, Alberto; Quesada, Jose Manuel
2001-01-01
A general numerical solution of the dispersion integral relation between the real and the imaginary parts of the nuclear optical potential is presented. Fast convergence is achieved by means of the Gauss-Legendre integration method, which offers accuracy, easiness of implementation and generality for dispersive optical model calculations. The use of this numerical integration method in the optical-model parameter search codes allows for a fast and accurate dispersive analysis. PACS number(s): 11.55.Fv, 24.10.Ht, 02.60.Jh
Iorio, L
2005-01-01
The post-Newtonian general relativistic gravitomagnetic Lense-Thirring precessions of the perihelia of the inner planets of the Solar System amount to 10^-3 arcseconds per century. Up to now they were always retained too small to be detected. Recent improvements in the planetary ephemerides determination yield the first observational evidence of such a tiny effect. Indeed, extra-corrections to the known perihelion advances of -0.0036\\pm 0.0050, -0.0002\\pm 0.0004 and 0.0001\\pm 0.0005 arcseconds per century were recently determined by E.V. Pitjeva for Mercury, the Earth and Mars, respectively. They were based on the EPM2004 ephemerides and a set of more than 317 000 observations of various kinds. The predicted relativistic Thirring-Lense precessions for these planets are -0.0020, -0.0001 and -3\\times 10^-5 arcseconds per century, respectively and are compatible with the measured perihelia corrections, although the experimental errors are still large. The data from the forthcoming BepiColombo mission to Mercury ...
Mueller, B; Dimmelmeier, H
2010-01-01
We present a new general relativistic (GR) code for hydrodynamic supernova simulations with neutrino transport in spherical and azimuthal symmetry (1D/2D). 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, energy-dependent neutrino transport scheme VERTEX. VERTEX integrates the neutrino moment equations with a variable Eddington factor closure computed from a model Boltzmann equation and uses the ray-by-ray plus approximation in 2D, assuming the neutrino distribution to be axially symmetric around the radial direction, and thus the neutrino flux to be radial. Our spacetime treatment employs the ADM 3+1 formalism with the conformal flatness condition for the spatial three-metric. This approach is exact in 1D and has been shown to yield very accurate results also for rotational stellar collapse. We introduce new formulations of the energy equation to improve total energy conservation in relativistic and Newtonian...
Macías-Díaz, J. E.; Medina-Ramírez, I. E.; Puri, A.
2009-09-01
In the present work, the connection of the generalized Fisher-KPP equation to physical and biological fields is noted. Radially symmetric solutions to the generalized Fisher-KPP equation are considered, and analytical results for the positivity and asymptotic stability of solutions to the corresponding time-independent elliptic differential equation are quoted. An energy analysis of the generalized theory is carried out with further physical applications in mind, and a numerical method that consistently approximates the energy of the system and its rate of change is presented. The method is thoroughly tested against analytical and numerical results on the classical Fisher-KPP equation, the Heaviside equation, and the generalized Fisher-KPP equation with logistic nonlinearity and Heaviside initial profile, obtaining as a result that our method is highly stable and accurate, even in the presence of discontinuities. As an application, we establish numerically that, under the presence of suitable initial conditions, there exists a threshold for the relaxation time with the property that solutions to the problems considered are nonnegative if and only if the relaxation time is below a critical value. An analytical prediction is provided for the Heaviside equation, against which we verify the validity of our computational code, and numerical approximations are provided for several generalized Fisher-KPP problems.
Rotem, Avital; Henik, Avishai
2015-01-01
We examined the development of sensitivity to general and specific numerical features in typical achievers and in 6th and 8th graders with mathematics learning disability (MLD), using two effects in mental multiplication: operand-relatedness (i.e., difficulty in avoiding errors that are related to the operands via a shared multiplication row) and decade-consistency (i.e., difficulty in avoiding errors that are operand related and also share a decade with the true result). Responses to decade-consistent products were quick but erroneous. In line with the processing sequence in adults, children first became sensitive to the general numerical feature of operand-relatedness (typical achievers--from 3rd grade; children with MLD in 8th grade) and only later to the specific feature of decade-consistency (typical achievers--from 4th grade, but only from 6th grade in a mature pattern). Implications of the numerical sensitivity in children with MLD are discussed.
Relativistic formulation and reference frame
Klioner, Sergei A.
2004-01-01
After a short review of experimental foundations of metric theories of gravity, the choice of general relativity as a theory to be used for the routine modeling of Gaia observations is justified. General principles of relativistic modeling of astronomical observations are then sketched and compared to the corresponding Newtonian principles. The fundamental reference system -- Barycentric Celestial Reference System, which has been chosen to be the relativistic reference system underlying the f...
Fractional Dynamics of Relativistic Particle
Tarasov, Vasily E
2011-01-01
Fractional dynamics of relativistic particle is discussed. Derivatives of fractional orders with respect to proper time describe long-term memory effects that correspond to intrinsic dissipative processes. Relativistic particle subjected to a non-potential four-force is considered as a nonholonomic system. The nonholonomic constraint in four-dimensional space-time represents the relativistic invariance by the equation for four-velocity u_{\\mu} u^{\\mu}+c^2=0, where c is a speed of light in vacuum. In the general case, the fractional dynamics of relativistic particle is described as non-Hamiltonian and dissipative. Conditions for fractional relativistic particle to be a Hamiltonian system are considered.
ORDMET: A General Algorithm for Constructing All Numerical Solutions to Ordered Metric Data
McClelland, Gary; Coombs, Clyde H.
1975-01-01
ORDMET is applicable to structures obtained from additive conjoint measurement designs, unfolding theory, general Fechnerian scaling, types of multidimensional scaling, and ordinal multiple regression. A description is obtained of the space containing all possible numerical representations which can satisfy the structure, size, and shape of which…
ORDMET: A General Algorithm for Constructing All Numerical Solutions to Ordered Metric Data
McClelland, Gary; Coombs, Clyde H.
1975-01-01
ORDMET is applicable to structures obtained from additive conjoint measurement designs, unfolding theory, general Fechnerian scaling, types of multidimensional scaling, and ordinal multiple regression. A description is obtained of the space containing all possible numerical representations which can satisfy the structure, size, and shape of which…
Relativistic impulse dynamics.
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.
Wuthrich, Christian
2014-01-01
There exists a growing literature on the so-called physical Church-Turing thesis in a relativistic spacetime setting. The physical Church-Turing thesis is the conjecture that no computing device that is physically realizable (even in principle) can exceed the computational barriers of a Turing machine. By suggesting a concrete implementation of a beyond-Turing computer in a spacetime setting, Istv\\'an N\\'emeti and Gyula D\\'avid (2006) have shown how an appreciation of the physical Church-Turing thesis necessitates the confluence of mathematical, computational, physical, and indeed cosmological ideas. In this essay, I will honour Istv\\'an's seventieth birthday, as well as his longstanding interest in, and his seminal contributions to, this field going back to as early as 1987 by modestly proposing how the concrete implementation in N\\'emeti and D\\'avid (2006) might be complemented by a quantum-information-theoretic communication protocol between the computing device and the logician who sets the beyond-Turing ...
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.
Sahoo, Raghunath
2016-01-01
This lecture note covers Relativistic Kinematics, which is very useful for the beginners in the field of high-energy physics. A very practical approach has been taken, which answers "why and how" of the kinematics useful for students working in the related areas.
Minimal relativistic three-particle equations
Energy Technology Data Exchange (ETDEWEB)
Lindesay, J.
1981-07-01
A minimal self-consistent set of covariant and unitary three-particle equations is presented. Numerical results are obtained for three-particle bound states, elastic scattering and rearrangement of bound pairs with a third particle, and amplitudes for breakup into states of three free particles. The mathematical form of the three-particle bound state equations is explored; constraints are set upon the range of eigenvalues and number of eigenstates of these one parameter equations. The behavior of the number of eigenstates as the two-body binding energy decreases to zero in a covariant context generalizes results previously obtained non-relativistically by V. Efimov.
Numerical validation of the generalized Harvey-Shack surface scatter theory
Choi, Narak; Harvey, James E.
2013-11-01
The generalized Harvey-Shack (GHS) surface scatter theory is numerically compared to the classical small perturbation method, the Kirchhoff approximation method, and the rigorous method of moments for one-dimensional ideally conducting surfaces whose surface power spectral density function is Gaussian or exhibits an inverse power law (fractal) behavior. In spite of its simple analytic form, our numerical comparison shows that the new GHS theory is valid (with reasonable accuracy) over a broader range of surface parameter space than either of the two classical surface scatter theories.
Frontiers in Numerical Relativity
Evans, Charles R.; Finn, Lee S.; Hobill, David W.
2011-06-01
Preface; Participants; Introduction; 1. Supercomputing and numerical relativity: a look at the past, present and future David W. Hobill and Larry L. Smarr; 2. Computational relativity in two and three dimensions Stuart L. Shapiro and Saul A. Teukolsky; 3. Slowly moving maximally charged black holes Robert C. Ferrell and Douglas M. Eardley; 4. Kepler's third law in general relativity Steven Detweiler; 5. Black hole spacetimes: testing numerical relativity David H. Bernstein, David W. Hobill and Larry L. Smarr; 6. Three dimensional initial data of numerical relativity Ken-ichi Oohara and Takashi Nakamura; 7. Initial data for collisions of black holes and other gravitational miscellany James W. York, Jr.; 8. Analytic-numerical matching for gravitational waveform extraction Andrew M. Abrahams; 9. Supernovae, gravitational radiation and the quadrupole formula L. S. Finn; 10. Gravitational radiation from perturbations of stellar core collapse models Edward Seidel and Thomas Moore; 11. General relativistic implicit radiation hydrodynamics in polar sliced space-time Paul J. Schinder; 12. General relativistic radiation hydrodynamics in spherically symmetric spacetimes A. Mezzacappa and R. A. Matzner; 13. Constraint preserving transport for magnetohydrodynamics John F. Hawley and Charles R. Evans; 14. Enforcing the momentum constraints during axisymmetric spacelike simulations Charles R. Evans; 15. Experiences with an adaptive mesh refinement algorithm in numerical relativity Matthew W. Choptuik; 16. The multigrid technique Gregory B. Cook; 17. Finite element methods in numerical relativity P. J. Mann; 18. Pseudo-spectral methods applied to gravitational collapse Silvano Bonazzola and Jean-Alain Marck; 19. Methods in 3D numerical relativity Takashi Nakamura and Ken-ichi Oohara; 20. Nonaxisymmetric rotating gravitational collapse and gravitational radiation Richard F. Stark; 21. Nonaxisymmetric neutron star collisions: initial results using smooth particle hydrodynamics
Parker, Edward
2017-08-01
A nonrelativistic particle released from rest at the edge of a ball of uniform charge density or mass density oscillates with simple harmonic motion. We consider the relativistic generalizations of these situations where the particle can attain speeds arbitrarily close to the speed of light; generalizing the electrostatic and gravitational cases requires special and general relativity, respectively. We find exact closed-form relations between the position, proper time, and coordinate time in both cases, and find that they are no longer harmonic, with oscillation periods that depend on the amplitude. In the highly relativistic limit of both cases, the particle spends almost all of its proper time near the turning points, but almost all of the coordinate time moving through the bulk of the ball. Buchdahl's theorem imposes nontrivial constraints on the general-relativistic case, as a ball of given density can only attain a finite maximum radius before collapsing into a black hole. This article is intended to be pedagogical, and should be accessible to those who have taken an undergraduate course in general relativity.
What is "Relativistic Canonical Quantization"?
Arbatsky, D. A.
2005-01-01
The purpose of this review is to give the most popular description of the scheme of quantization of relativistic fields that was named relativistic canonical quantization (RCQ). I do not give here the full exact account of this scheme. But with the help of this review any physicist, even not a specialist in the relativistic quantum theory, will be able to get a general view of the content of RCQ, of its connection with other known approaches, of its novelty and of its fruitfulness.
Andrew, Keith; Taylor, Lisa
2013-01-01
Using survey data and numerical LCDM modeling we establish an optimized fit to the generalized Reduced Void Probability Function, RVPF, of Mikjian used to establish a statistical foundation to any physical process associated with hierarchical clustering. We use a numerical N-body cosmological simulation code, GADGET-2, to investigate the sensitivity of the distribution of voids characterized by the RVPF to a general hierarchical reduced void parameter, a. The void parameter is related to the Levy stability index of the distribution and Fischer critical exponent used in clustering models. We numerically simulate the evolution of the universe from a redshift of z=50 to the current epoch at z=0 in order to generate RVPFs. GADGET-2 is an N-body/smoothed particle hydrodynamics, SPH, code that we ran in MPI parallelizable mode on an HPC Beowulf cluster. The numerical data sets are compared to observational data from the Sloan digital sky Survey, SDSS, CfA, the Deep2 Galaxy Redshift Survey, and the 2dF Survey. We fi...
Institute of Scientific and Technical Information of China (English)
R.Mokhtari; A.Samadi Toodar; N.G.Chegini
2011-01-01
@@ We the extend application of the generalized differential quadrature method (GDQM) to solve some coupled nonlinear Schr(o)dinger equations.The cosine-based GDQM is employed and the obtained system of ordinary differential equations is solved via the fourth order Runge-Kutta method.The numerical solutions coincide with the exact solutions in desired machine precision and invariant quantities are conserved sensibly.Some comparisons with the methods applied in the literature are carried out.%We the extend application of the generalized differential quadrature method (GDQM) to solve some coupled nonlinear Schrodinger equations. The cosine-based GDQM is employed and the obtained system of ordinary differential equations is solved via the fourth order Runge-Kutta method. The numerical solutions coincide with the exact solutions in desired machine precision and invariant quantities are conserved sensibly. Some comparisons with the methods applied in the literature are carried out.
Numerical solution of shock and ramp compression for general material properties
Energy Technology Data Exchange (ETDEWEB)
Swift, D C
2009-01-28
A general formulation was developed to represent material models for applications in dynamic loading. Numerical methods were devised to calculate response to shock and ramp compression, and ramp decompression, generalizing previous solutions for scalar equations of state. The numerical methods were found to be flexible and robust, and matched analytic results to a high accuracy. The basic ramp and shock solution methods were coupled to solve for composite deformation paths, such as shock-induced impacts, and shock interactions with a planar interface between different materials. These calculations capture much of the physics of typical material dynamics experiments, without requiring spatially-resolving simulations. Example calculations were made of loading histories in metals, illustrating the effects of plastic work on the temperatures induced in quasi-isentropic and shock-release experiments, and the effect of a phase transition.
Baczewski, Andrew D
2013-01-01
Generalized Langevin dynamics (GLD) arise in the modeling of a number of systems, ranging from structured fluids that exhibit a viscoelastic mechanical response, to biological systems, and other media that exhibit anomalous diffusive phenomena. Molecular dynamics (MD) simulations that include GLD in conjunction with external and/or pairwise forces require the development of numerical integrators that are efficient, stable, and have known convergence properties. In this article, we derive a family of extended variable integrators for the Generalized Langevin equation (GLE) with a positive Prony series memory kernel. Using stability and error analysis, we identify a superlative choice of parameters and implement the corresponding numerical algorithm in the LAMMPS MD software package. Salient features of the algorithm include exact conservation of the first and second moments of the equilibrium velocity distribution in some important cases, stable behavior in the limit of conventional Langevin dynamics, and the ...
Relativistic effects in atom gravimeters
Tan, Yu-Jie; Shao, Cheng-Gang; Hu, Zhong-Kun
2017-01-01
Atom interferometry is currently developing rapidly, which is now reaching sufficient precision to motivate laboratory tests of general relativity. Thus, it is extremely significant to develop a general relativistic model for atom interferometers. In this paper, we mainly present an analytical derivation process and first give a complete vectorial expression for the relativistic interferometric phase shift in an atom interferometer. The dynamics of the interferometer are studied, where both the atoms and the light are treated relativistically. Then, an appropriate coordinate transformation for the light is performed crucially to simplify the calculation. In addition, the Bordé A B C D matrix combined with quantum mechanics and the "perturbation" approach are applied to make a methodical calculation for the total phase shift. Finally, we derive the relativistic phase shift kept up to a sensitivity of the acceleration ˜1 0-14 m/s 2 for a 10 -m -long atom interferometer.
Relativistic Hydrodynamics with Wavelets
DeBuhr, Jackson; Anderson, Matthew; Neilsen, David; Hirschmann, Eric W
2015-01-01
Methods to solve the relativistic hydrodynamic equations are a key computational kernel in a large number of astrophysics simulations and are crucial to understanding the electromagnetic signals that originate from the merger of astrophysical compact objects. Because of the many physical length scales present when simulating such mergers, these methods must be highly adaptive and capable of automatically resolving numerous localized features and instabilities that emerge throughout the computational domain across many temporal scales. While this has been historically accomplished with adaptive mesh refinement (AMR) based methods, alternatives based on wavelet bases and the wavelet transformation have recently achieved significant success in adaptive representation for advanced engineering applications. This work presents a new method for the integration of the relativistic hydrodynamic equations using iterated interpolating wavelets and introduces a highly adaptive implementation for multidimensional simulati...
Hakim, Rémi
1994-01-01
Il existe à l'heure actuelle un certain nombre de théories relativistes de la gravitation compatibles avec l'expérience et l'observation. Toutefois, la relativité générale d'Einstein fut historiquement la première à fournir des résultats théoriques corrects en accord précis avec les faits.
Chinyoka, T.; Makinde, O. D.
2013-01-01
The thermodynamic second law analysis is utilized to investigate the inherent irreversibility in an unsteady hydromagnetic generalized Couette flow with variable electrical conductivity in the presence of induced electric field. Based on some simplified assumption, the model nonlinear governing equations are obtained and solved numerically using semidiscretization finite difference techniques. Effects of various thermophysical parameters on the fluid velocity, temperature, current density, skin friction, the Nusselt number, entropy generation number, and the Bejan number are presented graphically and discussed quantitatively. PMID:23956691
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.
Relativistic suppression of wave packet spreading.
Su, Q; Smetanko, B; Grobe, R
1998-03-30
We investigate numerically the solution of Dirac equation and analytically the Klein-Gordon equation and discuss the relativistic motion of an electron wave packet in the presence of an intense static electric field. In contrast to the predictions of the (non-relativistic) Schroedinger theory, the spreading rate in the field's polarization direction as well as in the transverse directions is reduced.
Baczewski, Andrew D; Bond, Stephen D
2013-07-28
Generalized Langevin dynamics (GLD) arise in the modeling of a number of systems, ranging from structured fluids that exhibit a viscoelastic mechanical response, to biological systems, and other media that exhibit anomalous diffusive phenomena. Molecular dynamics (MD) simulations that include GLD in conjunction with external and/or pairwise forces require the development of numerical integrators that are efficient, stable, and have known convergence properties. In this article, we derive a family of extended variable integrators for the Generalized Langevin equation with a positive Prony series memory kernel. Using stability and error analysis, we identify a superlative choice of parameters and implement the corresponding numerical algorithm in the LAMMPS MD software package. Salient features of the algorithm include exact conservation of the first and second moments of the equilibrium velocity distribution in some important cases, stable behavior in the limit of conventional Langevin dynamics, and the use of a convolution-free formalism that obviates the need for explicit storage of the time history of particle velocities. Capability is demonstrated with respect to accuracy in numerous canonical examples, stability in certain limits, and an exemplary application in which the effect of a harmonic confining potential is mapped onto a memory kernel.
Baczewski, Andrew D.; Bond, Stephen D.
2013-07-01
Generalized Langevin dynamics (GLD) arise in the modeling of a number of systems, ranging from structured fluids that exhibit a viscoelastic mechanical response, to biological systems, and other media that exhibit anomalous diffusive phenomena. Molecular dynamics (MD) simulations that include GLD in conjunction with external and/or pairwise forces require the development of numerical integrators that are efficient, stable, and have known convergence properties. In this article, we derive a family of extended variable integrators for the Generalized Langevin equation with a positive Prony series memory kernel. Using stability and error analysis, we identify a superlative choice of parameters and implement the corresponding numerical algorithm in the LAMMPS MD software package. Salient features of the algorithm include exact conservation of the first and second moments of the equilibrium velocity distribution in some important cases, stable behavior in the limit of conventional Langevin dynamics, and the use of a convolution-free formalism that obviates the need for explicit storage of the time history of particle velocities. Capability is demonstrated with respect to accuracy in numerous canonical examples, stability in certain limits, and an exemplary application in which the effect of a harmonic confining potential is mapped onto a memory kernel.
On the Numerical Modelling and Error Compensation for General Gough-Stewart Platform
Directory of Open Access Journals (Sweden)
Eusebio Hernandez
2014-11-01
Full Text Available Parallel robots are specially designed to perform high-precision tasks. Nevertheless, manufacturing, assembling and control issues can reduce their capacity to perform adequately. Observing the acquired measurement data with high-precision devices - such as laser-based instruments - it is not surprising that the error data follows patterns or have a structure because, in many cases, the greatest error comes from a mechanical bias introduced by manufacturing issues. Even though we cannot determine with certainty where the error comes from, a pattern in the measured data suggests that it is feasible that it can be modelled and corrected - in a significant proportion - by purely software applications, without the need of disassembling or re-manufacturing any component. This work deals with the problem of finding a mathematical model which adequately fits the error data from the legs of a general Gough-Stewart platform. Hence, we obtain an expression which can be subtracted from the control parameters in order to compensate the inherent mechanical error in the legs. The purpose of this article is two-fold: 1 to present numerical results of the beneficial effects of the error compensation in the legs as well as in the end-effector, and 2 to introduce a numerical methodology to find a model for error compensation and to numerically simulate its effects. Numerical, graphical and statistical evidence of the error improvements, according this methodology, is provided.
Identifying generalized Fitzhugh-Nagumo equation from a numerical solution of Hodgkin-Huxley model
Directory of Open Access Journals (Sweden)
Nikola V. Georgiev
2003-01-01
Full Text Available An analytic time series in the form of numerical solution (in an appropriate finite time interval of the Hodgkin-Huxley current clamped (HHCC system of four differential equations, well known in the neurophysiology as an exact empirical model of excitation of a giant axon of Loligo, is presented. Then we search for a second-order differential equation of generalized Fitzhugh-Nagumo (GFN type, having as a solution the given single component (action potential of the numerical solution. The given time series is used as a basis for reconstructing orders, powers, and coefficients of the polynomial right-hand sides of GFN equation approximately governing the process of action potential. For this purpose, a new geometrical method for determining phase space dimension of the unknown dynamical system (GFN equation and a specific modification of least squares method for identifying unknown coefficients are developed and applied.
Relativistic Radiation Mediated Shocks
Budnik, Ran; Sagiv, Amir; Waxman, Eli
2010-01-01
The structure of relativistic radiation mediated shocks (RRMS) propagating into a cold electron-proton plasma is calculated and analyzed. A qualitative discussion of the physics of relativistic and non relativistic shocks, including order of magnitude estimates for the relevant temperature and length scales, is presented. Detailed numerical solutions are derived for shock Lorentz factors $\\Gamma_u$ in the range $6\\le\\Gamma_u\\le30$, using a novel iteration technique solving the hydrodynamics and radiation transport equations (the protons, electrons and positrons are argued to be coupled by collective plasma processes and are treated as a fluid). The shock transition (deceleration) region, where the Lorentz factor $ \\Gamma $ drops from $ \\Gamma_u $ to $ \\sim 1 $, is characterized by high plasma temperatures $ T\\sim \\Gamma m_ec^2 $ and highly anisotropic radiation, with characteristic shock-frame energy of upstream and downstream going photons of a few~$\\times\\, m_ec^2$ and $\\sim \\Gamma^2 m_ec^2$, respectively.P...
Directory of Open Access Journals (Sweden)
M. Boumaza
2015-07-01
Full Text Available Transient convection heat transfer is of fundamental interest in many industrial and environmental situations, as well as in electronic devices and security of energy systems. Transient fluid flow problems are among the more difficult to analyze and yet are very often encountered in modern day technology. The main objective of this research project is to carry out a theoretical and numerical analysis of transient convective heat transfer in vertical flows, when the thermal field is due to different kinds of variation, in time and space of some boundary conditions, such as wall temperature or wall heat flux. This is achieved by the development of a mathematical model and its resolution by suitable numerical methods, as well as performing various sensitivity analyses. These objectives are achieved through a theoretical investigation of the effects of wall and fluid axial conduction, physical properties and heat capacity of the pipe wall on the transient downward mixed convection in a circular duct experiencing a sudden change in the applied heat flux on the outside surface of a central zone.
Generalization Evaluation of Machine Learning Numerical Observers for Image Quality Assessment.
Kalayeh, Mahdi M; Marin, Thibault; Brankov, Jovan G
2013-06-01
In this paper, we present two new numerical observers (NO) based on machine learning for image quality assessment. The proposed NOs aim to predict human observer performance in a cardiac perfusion-defect detection task for single-photon emission computed tomography (SPECT) images. Human observer (HumO) studies are now considered to be the gold standard for task-based evaluation of medical images. However such studies are impractical for use in early stages of development for imaging devices and algorithms, because they require extensive involvement of trained human observers who must evaluate a large number of images. To address this problem, numerical observers (also called model observers) have been developed as a surrogate for human observers. The channelized Hotelling observer (CHO), with or without internal noise model, is currently the most widely used NO of this kind. In our previous work we argued that development of a NO model to predict human observers' performance can be viewed as a machine learning (or system identification) problem. This consideration led us to develop a channelized support vector machine (CSVM) observer, a kernel-based regression model that greatly outperformed the popular and widely used CHO. This was especially evident when the numerical observers were evaluated in terms of generalization performance. To evaluate generalization we used a typical situation for the practical use of a numerical observer: after optimizing the NO (which for a CHO might consist of adjusting the internal noise model) based upon a broad set of reconstructed images, we tested it on a broad (but different) set of images obtained by a different reconstruction method. In this manuscript we aim to evaluate two new regression models that achieve accuracy higher than the CHO and comparable to our earlier CSVM method, while dramatically reducing model complexity and computation time. The new models are defined in a Bayesian machine-learning framework: a channelized
Leiter, D; Robertson, S; Leiter, Darryl; Mitra, Abhas; Robertson, Stanley
2001-01-01
It has been recently shown (Mitra, 2000 - astro-ph/9910408) that the timelike spherical collapse of a radiating, physical fluid in General Relativity, as seen by an interior co-moving observer at rest in the physical fluid, does not permit formation of ``trapped surfaces''. This followed from the fact that the formation of a trapped surface in a physical fluid would cause the timelike world lines of the collapsing fluid to become null at the would be trapped surface, thus violating the Principle of Equivalence in General Theory of Relativity. In this paper we generalize and extend this result by studying the problem from the point of view of the exterior Vaidya metric of a collapsing radiating fluid as seen by an exterior stationary observer, and find that the "no trapped surface condition" becomes g00 > 0 consistent with that obtained for the interior co-moving metric. Since we have shown that the Principle of Equivalence prevents trapped surfaces from being formed in collapsing, radiating objects, then true...
Relativistic gravity gradiometry
Bini, Donato; Mashhoon, Bahram
2016-12-01
In general relativity, relativistic gravity gradiometry involves the measurement of the relativistic tidal matrix, which is theoretically obtained from the projection of the Riemann curvature tensor onto the orthonormal tetrad frame of an observer. The observer's 4-velocity vector defines its local temporal axis and its local spatial frame is defined by a set of three orthonormal nonrotating gyro directions. The general tidal matrix for the timelike geodesics of Kerr spacetime has been calculated by Marck [Proc. R. Soc. A 385, 431 (1983)]. We are interested in the measured components of the curvature tensor along the inclined "circular" geodesic orbit of a test mass about a slowly rotating astronomical object of mass M and angular momentum J . Therefore, we specialize Marck's results to such a "circular" orbit that is tilted with respect to the equatorial plane of the Kerr source. To linear order in J , we recover the gravitomagnetic beating phenomenon [B. Mashhoon and D. S. Theiss, Phys. Rev. Lett. 49, 1542 (1982)], where the beat frequency is the frequency of geodetic precession. The beat effect shows up as a special long-period gravitomagnetic part of the relativistic tidal matrix; moreover, the effect's short-term manifestations are contained in certain post-Newtonian secular terms. The physical interpretation of this effect is briefly discussed.
Indian Academy of Sciences (India)
M H Mkwizu; O D Makinde; Yaw Nkansah-Gyekye
2015-10-01
This work investigates the effects of convective cooling on entropy generation in a transient generalized Couette flow of water-based nanofluids containing Copper (Cu) and Alumina (Al2O3) as nanoparticles. Both First and Second Laws of thermodynamics are utilised to analyse the problem. The model partial differential equations for momentum and energy balance are tackled numerically using a semidiscretization finite difference method together with Runge–Kutta Fehlberg integration scheme. Graphical results on the effects of parameter variation on velocity, temperature, skin friction, Nusselt number, entropy generation rate, irreversibility ratio and Bejan number are presented and discussed.
Knecht, Stefan; Jensen, Hans Jorgen Aa; Fleig, Timo
2008-01-07
We present a parallel implementation of a string-driven general active space configuration interaction program for nonrelativistic and scalar-relativistic electronic-structure calculations. The code has been modularly incorporated in the DIRAC quantum chemistry program package. The implementation is based on the message passing interface and a distributed data model in order to efficiently exploit key features of various modern computer architectures. We exemplify the nearly linear scalability of our parallel code in large-scale multireference configuration interaction (MRCI) calculations, and we discuss the parallel speedup with respect to machine-dependent aspects. The largest sample MRCI calculation includes 1.5x10(9) Slater determinants. Using the new code we determine for the first time the full short-range electronic potentials and spectroscopic constants for the ground state and for eight low-lying excited states of the weakly bound molecular system (Rb-Ba)+ with the spin-orbit-free Dirac formalism and using extensive uncontracted basis sets. The time required to compute to full convergence these electronic states for (Rb-Ba)+ in a single-point MRCI calculation correlating 18 electrons and using 16 cores was reduced from more than 10 days to less than 1 day.
Redkov, V M
1998-01-01
Some attention in the literature has been given to the case of a particle of spin 1/2 on the background of the external monopole potential. Some aspects of this problem are reexamined here. The primary technical novelty is that the tetrad generally relativistic method of Tetrode-Weyl-Fock-Ivanenko for describing a spinor particle is exploited. The choice of the formalism has turned out to be of great fruitfulness for examining the system. It is matter that, as known, the use of a special spherical tetrad in the theory of a spin 1/2 particle had led Schrodinger to a basis of remarkable features. The basis has been used with great efficiency by Pauli in his investigation on the pro- blem of allowed spherically symmetric wave functions in quantum mechanics. For our purposes, just several simple rules extracted from the much more com- prehensive Pauli's analysis will be quite sufficient; those are almost mnemo- nic working regulations. So, one may remember some very primary facts of D- functions theory and then p...
Relativistic and non-relativistic geodesic equations
Energy Technology Data Exchange (ETDEWEB)
Giambo' , R.; Mangiarotti, L.; Sardanashvily, G. [Camerino Univ., Camerino, MC (Italy). Dipt. di Matematica e Fisica
1999-07-01
It is shown that any dynamic equation on a configuration space of non-relativistic time-dependent mechanics is associated with connections on its tangent bundle. As a consequence, every non-relativistic dynamic equation can be seen as a geodesic equation with respect to a (non-linear) connection on this tangent bundle. Using this fact, the relationships between relativistic and non-relativistic equations of motion is studied.
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
Muronga, A
2007-01-01
Relativistic non-ideal fluid dynamics is formulated in 3+1 space--time dimensions. The equations governing dissipative relativistic hydrodynamics are given in terms of the time and the 3-space quantities which correspond to those familiar from non-relativistic physics. Dissipation is accounted for by applying the causal theory of relativistic dissipative fluid dynamics. As a special case we consider a fluid without viscous/heat couplings in the causal system of transport/relaxation equations. For the study of physical systems we consider pure (1+1)-dimensional expansion in planar geometry, (1+1)-dimensional spherically symmetric ({\\em fireball}) expansion, (1+1)-dimensional cylindrically symmetric expansion and a (2+1)-dimensional expansion with cylindrical symmetry in the transverse plane ({\\em firebarell} expansion). The transport/relaxation equations are given in terms of the spatial components of the dissipative fluxes, since these are not independent. The choice for the independent components is analogou...
Scattering in Relativistic Particle Mechanics.
de Bievre, Stephan
The problem of direct interaction in relativistic particle mechanics has been extensively studied and a variety of models has been proposed avoiding the conclusions of the so-called no-interaction theorems. In this thesis we study scattering in the relativistic two-body problem. We use our results to analyse gauge invariance in Hamiltonian constraint models and the uniqueness of the symplectic structure in manifestly covariant relativistic particle mechanics. We first present a general geometric framework that underlies approaches to relativistic particle mechanics. This permits a model-independent and geometric definition of the notions of asymptotic completeness and of Moller and scattering operators. Subsequent analysis of these concepts divides into two parts. First, we study the kinematic properties of the scattering transformation, i.e. those properties that arise solely from the invariance of the theory under the Poincare group. We classify all canonical (symplectic) scattering transformations on the relativistic phase space for two free particles in terms of a single function of the two invariants of the theory. We show how this function is determined by the center of mass time delay and scattering angle and vice versa. The second part of our analysis of the relativistic two-body scattering problem is devoted to the dynamical properties of the scattering process. Hence, we turn to two approaches to relativistic particle mechanics: the Hamiltonian constraint models and the manifestly covariant formalism. Using general geometric arguments, we prove "gauge invariance" of the scattering transformation in the Todorov -Komar Hamiltonian constraint model. We conclude that the scattering cross sections of the Todorov-Komar models have the same angular dependence as their non-relativistic counterpart, irrespective of a choice of gauge. This limits the physical relevance of those models. We present a physically non -trivial Hamiltonian constraint model, starting from
A general finite element model for numerical simulation of structure dynamics
Institute of Scientific and Technical Information of China (English)
WANG Fujun; LI Yaojun; Han K.; Feng Y.T.
2006-01-01
A finite element model used to simulate the dynamics with continuum and discontinuum is presented. This new approach is conducted by constructing the general contact model. The conventional discrete element is treated as a standard finite element with one node in this new method. The one-node element has the same features as other finite elements, such as element stress and strain. Thus, a general finite element model that is consistent with the existed finite element model is set up. This new model is simple in mathematical concept and is straightforward to be combined into the existing standard finite element code. Numerical example demonstrates that this new approach is more effective to perform the dynamic process analysis in which the interactions among a large number of discrete bodies and continuum objects are included.
Global numerical simulations of vortex-mediated pulsar glitches in full general relativity
Sourie, Aurélie; Novak, Jérôme; Oertel, Micaela
2016-01-01
In this paper, we study in detail the role of general relativity on the global dynamics of giant pulsar glitches as exemplified by Vela. For this purpose, we carry out numerical simulations of the spin up triggered by the sudden unpinning of superfluid vortices. In particular, we compute the exchange of angular momentum between the core neutron superfluid and the rest of the star within a two-fluid model including both (non-dissipative) entrainment effects and (dissipative) mutual friction forces. Our simulations are based on a quasi-stationary approach using realistic equations of state (EoSs) following \\cite{sourie2016numerical}. We show that the evolution of the angular velocities of both fluids can be accurately described by an exponential law. The associated characteristic rise time $\\tau_{\\text{r}}$, which can be precisely computed from stationary configurations only, has a form similar to that obtained in the Newtonian limit. However, general relativity changes the structure of the star and leads to ad...
Numerical verification of similar Cam-clay model based on generalized potential theory
Institute of Scientific and Technical Information of China (English)
钟志辉; 杨光华; 傅旭东; 温勇; 张玉成
2014-01-01
From the mathematical principles, the generalized potential theory can be employed to create constitutive model of geomaterial directly. The similar Cam-clay model, which is created based on the generalized potential theory, has less assumptions, clearer mathematical basis, and better computational accuracy. Theoretically, it is more scientific than the traditional Cam-clay models. The particle flow code PFC3D was used to make numerical tests to verify the rationality and practicality of the similar Cam-clay model. The verification process was as follows: 1) creating the soil sample for numerical test in PFC3D, and then simulating the conventional triaxial compression test, isotropic compression test, and isotropic unloading test by PFC3D; 2) determining the parameters of the similar Cam-clay model from the results of above tests; 3) predicting the sample’s behavior in triaxial tests under different stress paths by the similar Cam-clay model, and comparing the predicting results with predictions by the Cam-clay model and the modified Cam-clay model. The analysis results show that the similar Cam-clay model has relatively high prediction accuracy, as well as good practical value.
Equation of State in Relativistic Magnetohydrodynamics: variable versus constant adiabatic index
Mignone, A
2007-01-01
The role of the equation of state for a perfectly conducting, relativistic magnetized fluid is the main subject of this work. The ideal constant $\\Gamma$-law equation of state, commonly adopted in a wide range of astrophysical applications, is compared with a more realistic equation of state that better approximates the single-specie relativistic gas. The paper focus on three different topics. First, the influence of a more realistic equation of state on the propagation of fast magneto-sonic shocks is investigated. This calls into question the validity of the constant $\\Gamma$-law equation of state in problems where the temperature of the gas substantially changes across hydromagnetic waves. Second, we present a new inversion scheme to recover primitive variables (such as rest-mass density and pressure) from conservative ones that allows for a general equation of state and avoids catastrophic numerical cancellations in the non-relativistic and ultrarelativistic limits. Finally, selected numerical tests of ast...
Psaltis, Dimitrios; Chan, Chi-Kwan; Marrone, Daniel P
2014-01-01
(Abridged) In General Relativity, the shadow cast by a black hole has a size that depends very weakly on its spin or the orientation of the observer. The half opening angle of the shadow is always equal to 5+-0.2 GM/Dc^2, where M is the mass of the black hole and D is its distance from the Earth. Therefore, measuring the size of the shadow of a black hole of known mass-to-distance ratio and verifying whether it is within the 4% predicted range constitutes a null hypothesis test of GR. We show that Sgr A* is the optimal target for performing this test with the Event Horizon Telescope. We use the results of monitoring of stellar orbits to show that the ratio M/D for Sgr A* is already known to an accuracy of ~6%. We investigate our prior knowledge of the scattering screen towards Sgr A, the effects of which will need to be corrected for in order for the black-hole shadow to appear sharp against the background emission. We argue that, even though the properties of the scattering ellipse at longer wavelengths are ...
Relativistic magnetohydrodynamics
Hernandez, Juan; Kovtun, Pavel
2017-05-01
We present the equations of relativistic hydrodynamics coupled to dynamical electromagnetic fields, including the effects of polarization, electric fields, and the derivative expansion. We enumerate the transport coefficients at leading order in derivatives, including electrical conductivities, viscosities, and thermodynamic coefficients. We find the constraints on transport coefficients due to the positivity of entropy production, and derive the corresponding Kubo formulas. For the neutral state in a magnetic field, small fluctuations include Alfvén waves, magnetosonic waves, and the dissipative modes. For the state with a non-zero dynamical charge density in a magnetic field, plasma oscillations gap out all propagating modes, except for Alfvén-like waves with a quadratic dispersion relation. We relate the transport coefficients in the "conventional" magnetohydrodynamics (formulated using Maxwell's equations in matter) to those in the "dual" version of magnetohydrodynamics (formulated using the conserved magnetic flux).
Leardini, Fabrice
2013-01-01
This manuscript presents a problem on special relativity theory (SRT) which embodies an apparent paradox relying on the concept of simultaneity. The problem is represented in the framework of Greek epic poetry and structured in a didactic way. Owing to the characteristic properties of Lorenz transformations, three events which are simultaneous in a given inertial reference system, occur at different times in the other two reference frames. In contrast to the famous twin paradox, in the present case there are three, not two, different inertial observers. This feature provides a better framework to expose some of the main characteristics of SRT, in particular, the concept of velocity and the relativistic rule of addition of velocities.
Geometric Models of the Relativistic Harmonic Oscillator
Cotaescu, I I
1997-01-01
A family of relativistic geometric models is defined as a generalization of the actual anti-de Sitter (1+1) model of the relativistic harmonic oscillator. It is shown that all these models lead to the usual harmonic oscillator in the non-relativistic limit, even though their relativistic behavior is quite different. Among quantum models we find a set of models with countable energy spectra, and another one having only a finite number of energy levels and in addition a continuous spectrum.
Special Relativistic Hydrodynamics with Gravitation
Hwang, Jai-chan; Noh, Hyerim
2016-12-01
Special relativistic hydrodynamics with weak gravity has hitherto been unknown in the literature. Whether such an asymmetric combination is possible has been unclear. Here, the hydrodynamic equations with Poisson-type gravity, considering fully relativistic velocity and pressure under the weak gravity and the action-at-a-distance limit, are consistently derived from Einstein’s theory of general relativity. An analysis is made in the maximal slicing, where the Poisson’s equation becomes much simpler than our previous study in the zero-shear gauge. Also presented is the hydrodynamic equations in the first post-Newtonian approximation, now under the general hypersurface condition. Our formulation includes the anisotropic stress.
Special relativistic hydrodynamics with gravitation
Hwang, Jai-chan
2016-01-01
The special relativistic hydrodynamics with weak gravity is hitherto unknown in the literature. Whether such an asymmetric combination is possible was unclear. Here, the hydrodynamic equations with Poisson-type gravity considering fully relativistic velocity and pressure under the weak gravity and the action-at-a-distance limit are consistently derived from Einstein's general relativity. Analysis is made in the maximal slicing where the Poisson's equation becomes much simpler than our previous study in the zero-shear gauge. Also presented is the hydrodynamic equations in the first post-Newtonian approximation, now under the {\\it general} hypersurface condition. Our formulation includes the anisotropic stress.
Komissarov, S S; Lyutikov, M
2015-01-01
In this paper we describe a simple numerical approach which allows to study the structure of steady-state axisymmetric relativistic jets using one-dimensional time-dependent simulations. It is based on the fact that for narrow jets with v~c the steady-state equations of relativistic magnetohydrodynamics can be accurately approximated by the one-dimensional time-dependent equations after the substitution z=ct. Since only the time-dependent codes are now publicly available this is a valuable and efficient alternative to the development of a high-specialized code for the time-independent equations. The approach is also much cheaper and more robust compared to the relaxation method. We tested this technique against numerical and analytical solutions found in literature as well as solutions we obtained using the relaxation method and found it sufficiently accurate. In the process, we discovered the reason for the failure of the self-similar analytical model of the jet reconfinement in relatively flat atmospheres a...
Physico-mathematical foundations of relativistic cosmology
Soares, Domingos
2013-01-01
I briefly present the foundations of relativistic cosmology, which are, General Relativity Theory and the Cosmological Principle. I discuss some relativistic models, namely, "Einstein static universe" and "Friedmann universes". The classical bibliographic references for the relevant tensorial demonstrations are indicated whenever necessary, although the calculations themselves are not shown.
Fixtureless geometric inspection of nonrigid parts using "generalized numerical inspection fixture"
Radvar Esfahlan, Hassan
Free-form nonrigid parts form the substance of today's automotive and aerospace industries. These parts have different shapes in free state due to their dimensional and geometric variations, gravity and residual strains. For the geometric inspection of such compliant parts, special inspection fixtures, in combination with coordinate measuring systems (CMM) and/or optical data acquisition devices (scanners) are used. This inevitably causes additional costs and delays that result in a lack of competitiveness in the industry. The goal of this thesis is to facilitate the dimensional and geometrical inspection of flexible components from a point cloud without using a jig or secondary conformation operation. More specifically, we aim to develop a methodology to localize and quantify the profile defects in the case of thin shells which are typical to the aerospace and automotive industries. The presented methodology is based on the fact that the interpoint geodesic distance between any two points of a shape remains unchangeable during an isometric deformation. This study elaborates on the theory and general methods for the metrology of nonrigid parts. We have developed a Generalized Numerical Inspection Fixture (GNIF), a robust methodology which merges existing technologies in metric and computational geometry, nonlinear dimensionality reduction techniques, and finite element methods to introduce a general approach to the fixtureless geometrical inspection of nonrigid parts.
Pireaux, S
2008-01-01
The Relativistic Motion Integrator (RMI) consists in integrating numerically the EXACT relativistic equations of motion, with respect to the appropriate gravitational metric, instead of Newtonian equations plus relativistic corrections. The aim of the present paper is to validate the method, and to illustrate how RMI can be used for space missions to produce relativistic ephemerides of satellites. Indeed, nowadays, relativistic effects have to be taken into account, and comparing a RMI ephemeris with a classical keplerian one helps to quantify such effects. LISA is a relevant example to use RMI. This mission is an interferometer formed by three spacecraft which aims at the detection of gravitational waves. Precise ephemerides of LISA spacecraft are needed not only for the sake of the orbitography but also to compute the photon flight time in laser links between spacecraft, required in LISA data pre-processing in order to reach the gravitational wave detection level. Relativistic effects in LISA orbitography n...
Generalized monotone method and numerical approach for coupled reaction diffusion systems
Sowmya, M.; Vatsala, Aghalaya S.
2017-01-01
Study of coupled reaction diffusion systems are very useful in various branches of science and engineering. In this paper, we provide a methodology to construct the solution for the coupled reaction diffusion systems, with initial and boundary conditions, where the forcing function is the sum of an increasing and decreasing function. It is known that the generalized monotone method coupled with coupled lower and upper solutions yield monotone sequences which converges uniformly and monotonically to coupled minimal and maximal solutions. In addition, the interval of existence is guaranteed by the lower and upper solutions, which are relatively easy to compute. Using the lower and upper solutions as the initial approximation, we develop a method to compute the sequence of coupled lower and upper solutions on the interval or on the desired interval of existence. Further, if the uniqueness conditions are satisfied, the coupled minimal and maximal solutions converge to the unique solution of the reaction diffusion systems. We will provide some numerical results as an application of our numerical methodology.
Bayesian analysis of general failure data from an ageing distribution: advances in numerical methods
Energy Technology Data Exchange (ETDEWEB)
Procaccia, H.; Villain, B. [Electricite de France (EDF), 93 - Saint-Denis (France); Clarotti, C.A. [ENEA, Casaccia (Italy)
1996-12-31
EDF and ENEA carried out a joint research program for developing the numerical methods and computer codes needed for Bayesian analysis of component-lives in the case of ageing. Early results of this study were presented at ESREL`94. Since then the following further steps have been gone: input data have been generalized to the case that observed lives are censored both on the right and on the left; allowable life distributions are Weibull and gamma - their parameters are both unknown and can be statistically dependent; allowable priors are histograms relative to different parametrizations of the life distribution of concern; first-and-second-order-moments of the posterior distributions can be computed. In particular the covariance will give some important information about the degree of the statistical dependence between the parameters of interest. An application of the code to the appearance of a stress corrosion cracking in a tube of the PWR Steam Generator system is presented. (authors). 10 refs.
Energy Technology Data Exchange (ETDEWEB)
Mueller, Bernhard
2009-05-07
In this thesis, we have presented the first multi-dimensional models of core-collapse supernovae that combine a detailed, up-to-date treatment of neutrino transport, the equation of state, and - in particular - general relativistic gravity. Building on the well-tested neutrino transport code VERTEX and the GR hydrodynamics code CoCoNuT, we developed and implemented a relativistic generalization of a ray-by-ray-plus method for energy-dependent neutrino transport. The result of these effort, the VERTEX-CoCoNuT code, also incorporates a number of improved numerical techniques that have not been used in the code components VERTEX and CoCoNuT before. In order to validate the VERTEX-CoCoNuT code, we conducted several test simulations in spherical symmetry, most notably a comparison with the one-dimensional relativistic supernova code AGILE-BOLTZTRAN and the Newtonian PROMETHEUSVERTEX code. (orig.)
Piran, T.; Ruffini, R.
The following topics were dealt with: conservation laws; exact solutions; inertial forces in general relativity; alternative theories in four dimensions; alternative theories (Kaluza-Klein); hairy black holes; time machines; chaos in general relativity; Einstein Maxwell systems; mass inflation; critical phenomena; numerical relativity; algebraic computations; quantum fields in curved space time; time in quantum gravity; canonical quantum gravity; strings; the Casimir effect; black hole thermodynamics; quantum cosmology; gravitational wave detectors; general relativity in space; experimental tests; equivalence principle in space; observational cosmology; inflation; topological defects; early universe; cosmic microwave background; nonsingular cosmology; dark matter; astro-particles; gravitational lenses; extragalactic sources; astrophysical black holes; QPO's; binary neutron stars; microlenses; gamma ray bursts; boson stars.
Cheng, Roseanne M
2013-01-01
We consider tidal encounters between a white dwarf and an intermediate mass black hole. Both weak encounters and those at the threshold of disruption are modeled. The numerical code combines mesh-based (PPM) hydrodynamics, a spectral method (FFT) solution of the self-gravity, and a general relativistic Fermi normal coordinate (FNC) system that follows the star and debris. FNCs provide an expansion of the black hole tidal field that includes quadrupole and higher multipole moments and relativistic corrections. We compute the mass loss from the white dwarf that occurs in weak tidal encounters. Secondly, we compute carefully the energy deposition onto the star, examining the effects of non-radial and radial mode excitation, surface layer heating, mass loss, and relativistic orbital motion. We find evidence of a slight relativistic suppression in tidal energy transfer. Tidal energy deposition is compared to orbital energy loss due to gravitational bremsstrahlung and the combined losses are used to estimate tidal ...
Relativistic recursion relations for transition matrix elements
Martínez y Romero, R P; Salas-Brito, A L
2004-01-01
We review some recent results on recursion relations which help evaluating arbitrary non-diagonal, radial hydrogenic matrix elements of $r^\\lambda$ and of $\\beta r^\\lambda$ ($\\beta$ a Dirac matrix) derived in the context of Dirac relativistic quantum mechanics. Similar recursion relations were derived some years ago by Blanchard in the non relativistic limit. Our approach is based on a generalization of the second hypervirial method previously employed in the non-relativistic Schr\\"odinger case. An extension of the relations to the case of two potentials in the so-called unshifted case, but using an arbitrary radial function instead of a power one, is also given. Several important results are obtained as special instances of our recurrence relations, such as a generalization to the relativistic case of the Pasternack-Sternheimer rule. Our results are useful in any atomic or molecular calculation which take into account relativistic corrections.
From geometry to numerics: interdisciplinary aspects in mathematical and numerical relativity
Energy Technology Data Exchange (ETDEWEB)
Jaramillo, Jose Luis [Instituto de AstrofIsica de AndalucIa, CSIC, Apartado Postal 3004, Granada 18080 (Spain); Valiente Kroon, Juan Antonio [School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS (United Kingdom); Gourgoulhon, Eric [Laboratoire Univers et Theories, UMR 8102 du CNRS, Observatoire de Paris, Universite Paris Diderot, F-92190 Meudon (France)], E-mail: jarama@iaa.es, E-mail: j.a.valiente-kroon@qmul.ac.uk, E-mail: eric.gourgoulhon@obspm.fr
2008-05-07
This paper reviews some aspects in the current relationship between mathematical and numerical general relativity. Focus is placed on the description of isolated systems, with a particular emphasis on recent developments in the study of black holes. Ideas concerning asymptotic flatness, the initial-value problem, the constraint equations, evolution formalisms, geometric inequalities and quasi-local black hole horizons are discussed in light of the interaction between numerical and mathematical relativists. (topical review)
From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
Jaramillo, J L; Gourgoulhon, E
2007-01-01
This article reviews some aspects in the current relationship between mathematical and numerical General Relativity. Focus is placed on the description of isolated systems, with a particular emphasis on recent developments in the study of black holes. Ideas concerning asymptotic flatness, the initial value problem, the constraint equations, evolution formalisms, geometric inequalities and quasilocal black hole horizons are discussed on the light of the interaction between numerical and mathematical relativists.
Wie, Yong-Sun
1990-01-01
A procedure for calculating 3-D, compressible laminar boundary layer flow on general fuselage shapes is described. The boundary layer solutions can be obtained in either nonorthogonal 'body oriented' coordinates or orthogonal streamline coordinates. The numerical procedure is 'second order' accurate, efficient and independent of the cross flow velocity direction. Numerical results are presented for several test cases, including a sharp cone, an ellipsoid of revolution, and a general aircraft fuselage at angle of attack. Comparisons are made between numerical results obtained using nonorthogonal curvilinear 'body oriented' coordinates and streamline coordinates.
Sourie, A.; Chamel, N.; Novak, J.; Oertel, M.
2017-02-01
In this paper, we study in detail the role of general relativity on the global dynamics of giant pulsar glitches as exemplified by Vela. For this purpose, we carry out numerical simulations of the spin up triggered by the sudden unpinning of superfluid vortices. In particular, we compute the exchange of angular momentum between the core neutron superfluid and the rest of the star within a two-fluid model including both (non-dissipative) entrainment effects and (dissipative) mutual friction forces. Our simulations are based on a quasi-stationary approach using realistic equations of state (EoSs). We show that the evolution of the angular velocities of both fluids can be accurately described by an exponential law. The associated characteristic rise time τr, which can be precisely computed from stationary configurations only, has a form similar to that obtained in the Newtonian limit. However, general relativity changes the structure of the star and leads to additional couplings between the fluids due to frame-dragging effects. As a consequence, general relativity can have a large impact on the actual value of τr: the errors incurred by using Newtonian gravity are thus found to be as large as ˜40 per cent for the models considered. Values of the rise time are calculated for Vela and compared with current observational limits. Finally, we study the amount of gravitational waves emitted during a glitch. Simple expressions are obtained for the corresponding characteristic amplitudes and frequencies. The detectability of glitches through gravitational wave observatories is briefly discussed.
Frontiers in relativistic celestial mechanics
2014-01-01
Relativistic celestial mechanics – investigating the motion celestial bodies under the influence of general relativity – is a major tool of modern experimental gravitational physics. With a wide range of prominent authors from the field, this two-volume series consists of reviews on a multitude of advanced topics in the area of relativistic celestial mechanics – starting from more classical topics such as the regime of asymptotically-flat spacetime, light propagation and celestial ephemerides, but also including its role in cosmology and alternative theories of gravity as well as modern experiments in this area.
A general spectral method for the numerical simulation of one-dimensional interacting fermions
Clason, Christian; von Winckel, Gregory
2012-02-01
This work introduces a general framework for the direct numerical simulation of systems of interacting fermions in one spatial dimension. The approach is based on a specially adapted nodal spectral Galerkin method, where the basis functions are constructed to obey the antisymmetry relations of fermionic wave functions. An efficient MATLAB program for the assembly of the stiffness and potential matrices is presented, which exploits the combinatorial structure of the sparsity pattern arising from this discretization to achieve optimal run-time complexity. This program allows the accurate discretization of systems with multiple fermions subject to arbitrary potentials, e.g., for verifying the accuracy of multi-particle approximations such as Hartree-Fock in the few-particle limit. It can be used for eigenvalue computations or numerical solutions of the time-dependent Schrödinger equation. Program summaryProgram title: assembleFermiMatrix Catalogue identifier: AEKO_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKO_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.: 102 No. of bytes in distributed program, including test data, etc.: 2294 Distribution format: tar.gz Programming language: MATLAB Computer: Any architecture supported by MATLAB Operating system: Any supported by MATLAB; tested under Linux (x86-64) and Mac OS X (10.6) RAM: Depends on the data Classification: 4.3, 2.2 Nature of problem: The direct numerical solution of the multi-particle one-dimensional Schrödinger equation in a quantum well is challenging due to the exponential growth in the number of degrees of freedom with increasing particles. Solution method: A nodal spectral Galerkin scheme is used where the basis functions are constructed to obey the antisymmetry relations of the fermionic wave
A Signed Particle Formulation of Non-Relativistic Quantum Mechanics
Sellier, Jean Michel
2015-01-01
A formulation of non-relativistic quantum mechanics in terms of Newtonian particles is presented in the shape of a set of three postulates. In this new theory, quantum systems are described by ensembles of signed particles which behave as field-less classical objects which carry a negative or positive sign and interact with an external potential by means of creation and annihilation events only. This approach is shown to be a generalization of the signed particle Wigner Monte Carlo method which reconstructs the time-dependent Wigner quasi-distribution function of a system and, therefore, the corresponding Schroedinger time-dependent wave-function. Its classical limit is discussed and a physical interpretation, based on experimental evidences coming from quantum tomography, is suggested. Moreover, in order to show the advantages brought by this novel formulation, a straightforward extension to relativistic effects is discussed. To conclude, quantum tunnelling numerical experiments are performed to show the val...
The Einstein Toolkit: A Community Computational Infrastructure for Relativistic Astrophysics
Löffler, Frank; Bentivegna, Eloisa; Bode, Tanja; Diener, Peter; Haas, Roland; Hinder, Ian; Mundim, Bruno C; Ott, Christian D; Schnetter, Erik; Allen, Gabrielle; Campanelli, Manuela; Laguna, Pablo
2011-01-01
We describe the Einstein Toolkit, a community-driven, freely accessible computational infrastructure intended for use in numerical relativity, relativistic astrophysics, and other applications. The Toolkit, developed by a collaboration involving researchers from multiple institutions around the world, combines a core set of components needed to simulate astrophysical objects such as black holes, compact objects, and collapsing stars, as well as a full suite of analysis tools. The Einstein Toolkit is currently based on the Cactus Framework for high-performance computing and the Carpet adaptive mesh refinement driver. It implements spacetime evolution via the BSSN evolution system and general-relativistic hydrodynamics in a finite-volume discretization. The toolkit is under continuous development and contains many new code components that have been publicly released for the first time and are described in this article. We discuss the motivation behind the release of the toolkit, the philosophy underlying its de...
Anton, L; Marti, J M; Ibanez, J M; Aloy, M A; Mimica, P
2009-01-01
We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wavefront in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numeric...
Kalmykov, M Yu
2004-01-01
Generalized log-sine functions appear in higher order epsilon-expansion of different Feynman diagrams. We present an algorithm for numerical evaluation of these functions of real argument. This algorithm is implemented as C++ library with arbitrary-precision arithmetics for integer 0 1. Some new relations and representations for the generalized log-sine functions are given.
Empirical Foundations of Relativistic Gravity
Ni, W T
2005-01-01
In 1859, Le Verrier discovered the mercury perihelion advance anomaly. This anomaly turned out to be the first relativistic-gravity effect observed. During the 141 years to 2000, the precisions of laboratory and space experiments, and astrophysical and cosmological observations on relativistic gravity have been improved by 3 orders of magnitude. In 1999, we envisaged a 3-6 order improvement in the next 30 years in all directions of tests of relativistic gravity. In 2000, the interferometric gravitational wave detectors began their runs to accumulate data. In 2003, the measurement of relativistic Shapiro time-delay of the Cassini spacecraft determined the relativistic-gravity parameter gammaγ with a 1.5-order improvement. In October 2004, Ciufolini and Pavlis reported a measurement of the Lense-Thirring effect on the LAGEOS and LAGEOS2 satellites to 10 percent of the value predicted by general relativity. In April 2004, Gravity Probe B was launched and has been accumulating science data for more than ...
Relativistic causality and clockless circuits
Matherat, Philippe; 10.1145/2043643.2043650
2011-01-01
Time plays a crucial role in the performance of computing systems. The accurate modelling of logical devices, and of their physical implementations, requires an appropriate representation of time and of all properties that depend on this notion. The need for a proper model, particularly acute in the design of clockless delay-insensitive (DI) circuits, leads one to reconsider the classical descriptions of time and of the resulting order and causal relations satisfied by logical operations. This questioning meets the criticisms of classical spacetime formulated by Einstein when founding relativity theory and is answered by relativistic conceptions of time and causality. Applying this approach to clockless circuits and considering the trace formalism, we rewrite Udding's rules which characterize communications between DI components. We exhibit their intrinsic relation with relativistic causality. For that purpose, we introduce relativistic generalizations of traces, called R-traces, which provide a pertinent des...
Whittaker Order Reduction Method of Relativistic Birkhoffian Systems
Institute of Scientific and Technical Information of China (English)
LUOShao-Kai; HUANGFei-Jiang; LUYi-Bing
2004-01-01
The order reduction method of the relativistic Birkhollian equations is studied. For a relativistic autonomous Birkhotffian system, if the conservative law of the Birkhotffian holds, the conservative quantity can be called the generalized energy integral. Through the generalized energy integral, the order of the system can be reduced. If the relativisticBirkhoffian system has a generalized energy integral, then the Birkhoffian equations can be reduced by at least twodegrees and the Birkhoffian form can be kept. The relations among the relativistic Birkhoffian mechanics, the relativistic Hamiltonian mechanics and the relativistic Lagrangian mechanics are discussed, and the Whittaker order reduction method of the relativistic Lagrangian system is obtained. And an example is given to illustrate the application of theresult.
Whittaker Order Reduction Method of Relativistic Birkhoffian Systems
Institute of Scientific and Technical Information of China (English)
LUO Shao-Kai; HUANG Fei-Jiang; LU Yi-Bing
2004-01-01
The order reduction method of the relativistic Birkhoffian equations is studied. For a relativistic autonomous Birkhoffian system, if the conservative law of the Birkhoffian holds, the conservative quantity can be called the generalized energy integral. Through the generalized energy integral, the order of the system can be reduced. If the relativistic Birkhoffian system has a generalized energy integral, then the Birkhoffian equations can be reduced by at least two degrees and the Birkhoffian form can be kept. The relations among the relativistic Birkhoffian mechanics, the relativistic Hamiltonian mechanics and the relativistic Lagrangian mechanics are discussed, and the Whittaker order reduction method of the relativistic Lagrangian system is obtained. And an example is given to illustrate the application of the result.
Moscibrodzka, M; Dolence, J; Shiokawa, H; Leung, P K
2010-01-01
We review results from general relativistic axisymmetric magnetohydrodynamic simulations of accretion in Sgr A*. We use general relativistic radiative transfer methods and to produce a broad band (from millimeter to gamma-rays) spectrum. Using a ray tracing scheme we also model images of Sgr A* and compare the size of image to the VLBI observations at 230 GHz. We perform a parameter survey and study radiative properties of the flow models for various black hole spins, ion to electron temperature ratios, and inclinations. We scale our models to reconstruct the flux and the spectral slope around 230 GHz. The combination of Monte Carlo spectral energy distribution calculations and 230 GHz image modeling constrains the parameter space of the numerical models. Our models suggest rather high black hole spin ($a_*\\approx 0.9$), electron temperatures close to the ion temperature ($T_i/T_e \\sim 3$) and high inclination angles ($i \\approx 90 \\deg$).
Relativistic quantum information
Mann, R. B.; Ralph, T. C.
2012-11-01
Over the past few years, a new field of high research intensity has emerged that blends together concepts from gravitational physics and quantum computing. Known as relativistic quantum information, or RQI, the field aims to understand the relationship between special and general relativity and quantum information. Since the original discoveries of Hawking radiation and the Unruh effect, it has been known that incorporating the concepts of quantum theory into relativistic settings can produce new and surprising effects. However it is only in recent years that it has become appreciated that the basic concepts involved in quantum information science undergo significant revision in relativistic settings, and that new phenomena arise when quantum entanglement is combined with relativity. A number of examples illustrate that point. Quantum teleportation fidelity is affected between observers in uniform relative acceleration. Entanglement is an observer-dependent property that is degraded from the perspective of accelerated observers moving in flat spacetime. Entanglement can also be extracted from the vacuum of relativistic quantum field theories, and used to distinguish peculiar motion from cosmological expansion. The new quantum information-theoretic framework of quantum channels in terms of completely positive maps and operator algebras now provides powerful tools for studying matters of causality and information flow in quantum field theory in curved spacetimes. This focus issue provides a sample of the state of the art in research in RQI. Some of the articles in this issue review the subject while others provide interesting new results that will stimulate further research. What makes the subject all the more exciting is that it is beginning to enter the stage at which actual experiments can be contemplated, and some of the articles appearing in this issue discuss some of these exciting new developments. The subject of RQI pulls together concepts and ideas from
Presenting Numerical Modelling of Explosive Volcanic Eruption to a General Public
Demaria, C.; Todesco, M.; Neri, A.; Blasi, G.
2001-12-01
Numerical modeling of explosive volcanic eruptions has been widely applied, during the last decades, to study pyroclastic flows dispersion along volcano's flanks and to evaluate their impact on urban areas. Results from these transient multi-phase and multi-component simulations are often reproduced in form of computer animations, representing the spatial and temporal evolution of relevant flow variables (such as temperature, or particle concentration). Despite being a sophisticated, technical tool to analyze and share modeling results within the scientific community, these animations truly look like colorful cartoons showing an erupting volcano and are especially suited to be shown to a general public. Thanks to their particular appeal, and to the large interest usually risen by exploding volcanoes, these animations have been presented several times on television and magazines and are currently displayed in a permanent exposition, at the Vesuvius Observatory in Naples. This work represents an effort to produce an accompanying tool for these animations, capable of explaining to a large audience the scientific meaning of what can otherwise look as a graphical exercise. Dealing with research aimed at the study of dangerous, explosive volcanoes, improving the general understanding of these scientific results plays an important role as far as risk perception is concerned. An educated population has better chances to follow an appropriate behavior, i.e.: one that could lead, on the long period, to a reduction of the potential risk. In this sense, a correct divulgation of scientific results, while improving the confidence of the population in the scientific community, should belong to the strategies adopted to mitigate volcanic risk. Due to the relevance of the long term final goal of such divulgation experiment, this work represents an interdisciplinary effort, combining scientific expertise and specific competence from the modern communication science and risk
Numerical Generalization of the Bethe-Weizs\\"{a}cker Mass Formula
Mavrodiev, S Cht
2016-01-01
Based on the AME2012 nuclear database and the semi-empirical mass formula of Bethe and von Weizs\\"{a}cker we formulated and solved the inverse problem for its numerical generalization in step by step way. The established parametrization describes the measured nuclear masses of 2564 isotopes with an accuracy better than 2.6 MeV, starting from the number of protons $Z=1$ and number of neutrons $N=1$. The set of parameters $\\{a_{i}\\}$, $i=1,\\dots, {N}_{\\rm{total}}$ of our fit represent the solution of an overdetermined system of algebraic equations, which represent equalities between the binding energy $E_{B}^{\\rm{Expt}}(A_{j},Z_{j})$ and its model $E_{B}^{\\rm{Th}}(A_{j},Z_{j},\\{a_{i}\\})$, where $j=1,\\dots,2564$. The solution of the overdetermined system of equations has been obtained with the help of the Aleksandrov's auto-regularization method of Gauss-Newton type for ill-posed problems (Dubna FORTRAN code REGN). The explicit form of unknown functions was discovered in a step-by-step way using the LCH procedur...
Relativistic Fractal Cosmologies
Ribeiro, Marcelo B
2009-01-01
This article reviews an approach for constructing a simple relativistic fractal cosmology whose main aim is to model the observed inhomogeneities of the distribution of galaxies by means of the Lemaitre-Tolman solution of Einstein's field equations for spherically symmetric dust in comoving coordinates. This model is based on earlier works developed by L. Pietronero and J.R. Wertz on Newtonian cosmology, whose main points are discussed. Observational relations in this spacetime are presented, together with a strategy for finding numerical solutions which approximate an averaged and smoothed out single fractal structure in the past light cone. Such fractal solutions are shown, with one of them being in agreement with some basic observational constraints, including the decay of the average density with the distance as a power law (the de Vaucouleurs' density power law) and the fractal dimension in the range 1 <= D <= 2. The spatially homogeneous Friedmann model is discussed as a special case of the Lemait...
The First Principle Formula of the Relativistic Heat Conductivity of Coulomb Electronic Plasmas
Institute of Scientific and Technical Information of China (English)
TIAN Chu-Shun; ZHANG Chi; LU Quan-Kang
2001-01-01
Making use of the relativistic BBGKY technique,the relativistic generalization of Landau collision integral is obtained.Furthermore,we calculate the relativistic hydrodynamic modes up to the second order in the hydrodynamic wave number.Combining Résibois' method,we present the first principle formula of the relativistic heat conductivity of Coulomb electronic plasmas for low-order corrections.
Chaos and Maps in Relativistic Dynamical Systems
Horwitz, L P
1999-01-01
The basic work of Zaslavskii et al showed that the classical non-relativistic electromagnetically kicked oscillator can be cast into the form of an iterative map on the phase space; the resulting evolution contains a stochastic flow to unbounded energy. Subsequent studies have formulated the problem in terms of a relativistic charged particle in interaction with the electromagnetic field. We review the structure of the covariant Lorentz force used to study this problem. We show that the Lorentz force equation can be derived as well from the manifestly covariant mechanics of Stueckelberg in the presence of a standard Maxwell field, establishing a connection between these equations and mass shell constraints. We argue that these relativistic generalizations of the problem are intrinsically inaccurate due to an inconsistency in the structure of the relativistic Lorentz force, and show that a reformulation of the relativistic problem, permitting variations (classically) in both the particle mass and the effective...
Properties of relativistically rotating quark stars
Zhou, Enping
2017-06-01
In this work, quasi-equilibrium models of rapidly rotating triaxially deformed quark stars are computed in general relativistic gravity, assuming a conformally flat spatial geometry (Isenberg-Wilson-Mathews formulation) and a polynomial equation of state. Especially, since we are using a full 3-D numerical relativity initial data code, we are able to consider the triaxially deformed rotating quark stars at very high spins. Such triaxially deformed stars are possible gravitational radiation sources detectable by ground based gravitational wave observatories. Additionally, the bifurcation from axisymmetric rotating sequence to triaxially rotating sequence hints a more realistic spin up limit for rotating compact stars compared with the mass-shedding limit. With future observations such as sub-millisecond pulsars, we could possibly distinguish between equation of states of compact stars, thus better understanding strong interaction in the low energy regime.
Microscopic picture of non-relativistic classicalons
Energy Technology Data Exchange (ETDEWEB)
Berkhahn, Felix; Müller, Sophia; Niedermann, Florian; Schneider, Robert, E-mail: felix.berkhahn@physik.lmu.de, E-mail: sophia.x.mueller@physik.uni-muenchen.de, E-mail: florian.niedermann@physik.lmu.de, E-mail: robert.bob.schneider@physik.uni-muenchen.de [Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität, Theresienstraße 37, 80333 Munich (Germany)
2013-08-01
A theory of a non-relativistic, complex scalar field with derivatively coupled interaction terms is investigated. This toy model is considered as a prototype of a classicalizing theory and in particular of general relativity, for which the black hole constitutes a prominent example of a classicalon. Accordingly, the theory allows for a non-trivial solution of the stationary Gross-Pitaevskii equation corresponding to a black hole in the case of GR. Quantum fluctuations on this classical background are investigated within the Bogoliubov approximation. It turns out that the perturbative approach is invalidated by a high occupation of the Bogoliubov modes. Recently, it was proposed that a black hole is a Bose-Einstein condensate of gravitons that dynamically ensures to stay at the verge of a quantum phase transition. Our result is understood as an indication for that claim. Furthermore, it motivates a non-linear numerical analysis of the model.
Transport coefficients of a relativistic plasma
Pike, O. J.; Rose, S. J.
2016-05-01
In this work, a self-consistent transport theory for a relativistic plasma is developed. Using the notation of Braginskii [S. I. Braginskii, in Reviews of Plasma Physics, edited by M. A. Leontovich (Consultants Bureau, New York, 1965), Vol. 1, p. 174], we provide semianalytical forms of the electrical resistivity, thermoelectric, and thermal conductivity tensors for a Lorentzian plasma in a magnetic field. This treatment is then generalized to plasmas with arbitrary atomic number by numerically solving the linearized Boltzmann equation. The corresponding transport coefficients are fitted by rational functions in order to make them suitable for use in radiation-hydrodynamic simulations and transport calculations. Within the confines of linear transport theory and on the assumption that the plasma is optically thin, our results are valid for temperatures up to a few MeV. By contrast, classical transport theory begins to incur significant errors above kBT ˜10 keV, e.g., the parallel thermal conductivity is suppressed by 15% at kBT =20 keV due to relativistic effects.
Nonlinear propagation of weakly relativistic ion-acoustic waves in electron–positron–ion plasma
Indian Academy of Sciences (India)
M G HAFEZ; M R TALUKDER; M HOSSAIN ALI
2016-11-01
This work presents theoretical and numerical discussion on the dynamics of ion-acoustic solitary wave for weakly relativistic regime in unmagnetized plasma comprising non-extensive electrons, Boltzmann positrons and relativistic ions. In order to analyse the nonlinear propagation phenomena, the Korteweg–de Vries(KdV) equation is derived using the well-known reductive perturbation method. The integration of the derived equation is carried out using the ansatz method and the generalized Riccati equation mapping method. The influenceof plasma parameters on the amplitude and width of the soliton and the electrostatic nonlinear propagation of weakly relativistic ion-acoustic solitary waves are described. The obtained results of the nonlinear low-frequencywaves in such plasmas may be helpful to understand various phenomena in astrophysical compact object and space physics.
Long wavelength unstable modes in the far upstream of relativistic collisionless shocks
Rabinak, Itay; Waxman, Eli
2010-01-01
The growth rate of long wavelength kinetic instabilities arising due to the interaction of a collimated beam of relativistic particles and a cold unmagnetized plasma are calculated in the ultra relativistic limit. For sufficiently culminated beams, all long wave-length modes are shown to be Weibel-unstable, and a simple analytic expression for their growth rate is derived. For large transverse velocity spreads, these modes become stable. An analytic condition for stability is given. These analytic results, which generalize earlier ones given in the literature, are shown to be in agreement with numerical solutions of the dispersion equation and with the results of novel PIC simulations in which the electro-magnetic fields are restricted to a given k-mode. The results may describe the interaction of energetic cosmic rays, propagating into the far upstream of a relativistic collisionless shock, with a cold unmagnetized upstream. The long wavelength modes considered may be efficient in deflecting particles and co...
Relativistic Gravothermal Instabilities
Roupas, Zacharias
2014-01-01
The thermodynamic instabilities of the self-gravitating, classical ideal gas are studied in the case of static, spherically symmetric configurations in General Relativity taking into account the Tolman-Ehrenfest effect. One type of instabilities is found at low energies, where thermal energy becomes too weak to halt gravity and another at high energies, where gravitational attraction of thermal pressure overcomes its stabilizing effect. These turning points of stability are found to depend on the total rest mass $\\mathcal{M}$ over the radius $R$. The low energy instability is the relativistic generalization of Antonov instability, which is recovered in the limit $G\\mathcal{M} \\ll R c^2$ and low temperatures, while in the same limit and high temperatures, the high energy instability recovers the instability of the radiation equation of state. In the temperature versus energy diagram of series of equilibria, the two types of gravothermal instabilities make themselves evident as a double spiral! The two energy l...
Mueller, Bernhard; Marek, Andreas
2012-01-01
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 (2D) 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 postshock 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 e...
TOUGH2: A general-purpose numerical simulator for multiphase nonisothermal flows
Energy Technology Data Exchange (ETDEWEB)
Pruess, K. [Lawrence Berkeley Lab., CA (United States)
1991-06-01
Numerical simulators for multiphase fluid and heat flows in permeable media have been under development at Lawrence Berkeley Laboratory for more than 10 yr. Real geofluids contain noncondensible gases and dissolved solids in addition to water, and the desire to model such `compositional` systems led to the development of a flexible multicomponent, multiphase simulation architecture known as MULKOM. The design of MULKOM was based on the recognition that the mass-and energy-balance equations for multiphase fluid and heat flows in multicomponent systems have the same mathematical form, regardless of the number and nature of fluid components and phases present. Application of MULKOM to different fluid mixtures, such as water and air, or water, oil, and gas, is possible by means of appropriate `equation-of-state` (EOS) modules, which provide all thermophysical and transport parameters of the fluid mixture and the permeable medium as a function of a suitable set of primary thermodynamic variables. Investigations of thermal and hydrologic effects from emplacement of heat-generating nuclear wastes into partially water-saturated formations prompted the development and release of a specialized version of MULKOM for nonisothermal flow of water and air, named TOUGH. TOUGH is an acronym for `transport of unsaturated groundwater and heat` and is also an allusion to the tuff formations at Yucca Mountain, Nevada. The TOUGH2 code is intended to supersede TOUGH. It offers all the capabilities of TOUGH and includes a considerably more general subset of MULKOM modules with added capabilities. The paper briefly describes the simulation methodology and user features.
Vaneeva, O. O.; Papanicolaou, N. C.; Christou, M. A.; Sophocleous, C.
2014-09-01
The exhaustive group classification of a class of variable coefficient generalized KdV equations is presented, which completes and enhances results existing in the literature. Lie symmetries are used for solving an initial and boundary value problem for certain subclasses of the above class. Namely, the found Lie symmetries are applied in order to reduce the initial and boundary value problem for the generalized KdV equations (which are PDEs) to an initial value problem for nonlinear third-order ODEs. The latter problem is solved numerically using the finite difference method. Numerical solutions are computed and the vast parameter space is studied.
Relativistic models of a class of compact objects
Indian Academy of Sciences (India)
Rumi Deb; Bikash Chandra Paul; Ramesh Tikekar
2012-08-01
A class of general relativistic solutions in isotropic spherical polar coordinates which describe compact stars in hydrostatic equilibrium are discussed. The stellar models obtained here are characterized by four parameters, namely, , , and of geometrical significance related to the inhomogeneity of the matter content of the star. The stellar models obtained using the solutions are physically viable for a wide range of values of the parameters. The physical features of the compact objects taken up here are studied numerically for a number of admissible values of the parameters. Observational stellar mass data are used to construct suitable models of the compact stars.
Relativistic MHD and excision: formulation and initial tests
Energy Technology Data Exchange (ETDEWEB)
Neilsen, David; Hirschmann, Eric W; Millward, R Steven [Department of Physics and Astronomy, Brigham Young University, Provo, UT 84602 (United States)
2006-08-21
A new algorithm for solving the general relativistic MHD equations is described in this paper. We design our scheme to incorporate black hole excision with smooth boundaries, and to simplify solving the combined Einstein and MHD equations with AMR. The fluid equations are solved using a finite difference convex ENO method. Excision is implemented using overlapping grids. Elliptic and hyperbolic divergence cleaning techniques allow for maximum flexibility in choosing coordinate systems, and we compare both methods for a standard problem. Numerical results of standard test problems are presented in two-dimensional flat space using excision, overlapping grids and elliptic and hyperbolic divergence cleaning.
Relativistic MHD and black hole excision: Formulation and initial tests
Neilsen, D; Millward, R S; Hirschmann, Eric W; Neilsen, David
2006-01-01
A new algorithm for solving the general relativistic MHD equations is described in this paper. We design our scheme to incorporate black hole excision with smooth boundaries, and to simplify solving the combined Einstein and MHD equations with AMR. The fluid equations are solved using a finite difference Convex ENO method. Excision is implemented using overlapping grids. Elliptic and hyperbolic divergence cleaning techniques allow for maximum flexibility in choosing coordinate systems, and we compare both methods for a standard problem. Numerical results of standard test problems are presented in two-dimensional flat space using excision, overlapping grids, and elliptic and hyperbolic divergence cleaning.
Relativistic Langevin equation for runaway electrons
Mier, J. A.; Martin-Solis, J. R.; Sanchez, R.
2016-10-01
The Langevin approach to the kinetics of a collisional plasma is developed for relativistic electrons such as runaway electrons in tokamak plasmas. In this work, we consider Coulomb collisions between very fast, relativistic electrons and a relatively cool, thermal background plasma. The model is developed using the stochastic equivalence of the Fokker-Planck and Langevin equations. The resulting Langevin model equation for relativistic electrons is an stochastic differential equation, amenable to numerical simulations by means of Monte-Carlo type codes. Results of the simulations will be presented and compared with the non-relativistic Langevin equation for RE electrons used in the past. Supported by MINECO (Spain), Projects ENE2012-31753, ENE2015-66444-R.
Holographic Aspects of a Relativistic Nonconformal Theory
Directory of Open Access Journals (Sweden)
Chanyong Park
2013-01-01
Full Text Available We study a general D-dimensional Schwarzschild-type black brane solution of the Einstein-dilaton theory and derive, by using the holographic renormalization, its thermodynamics consistent with the geometric results. Using the membrane paradigm, we calculate the several hydrodynamic transport coefficients and compare them with the results obtained by the Kubo formula, which shows the self-consistency of the gauge/gravity duality in the relativistic nonconformal theory. In order to understand more about the relativistic non-conformal theory, we further investigate the binding energy, drag force, and holographic entanglement entropy of the relativistic non-conformal theory.
Cowan, Richard; Powell, Daisy
2014-01-01
Explanations of the marked individual differences in elementary school mathematical achievement and mathematical learning disability (MLD or dyscalculia) have involved domain-general factors (working memory, reasoning, processing speed, and oral language) and numerical factors that include single-digit processing efficiency and multidigit skills…
Discrete Self-Similarity in Ultra-Relativistic Type-II Strong Explosions
Oren, Yonatan; 10.1063/1.3231838
2009-01-01
A solution to the ultra-relativistic strong explosion problem with a non-power law density gradient is delineated. We consider a blast wave expanding into a density profile falling off as a steep radial power-law with small, spherically symmetric, and log-periodic density perturbations. We find discretely self-similar solutions to the perturbation equations and compare them to numerical simulations. These results are then generalized to encompass small spherically symmetric perturbations with arbitrary profiles.
Theory and Applications of Non-Relativistic and Relativistic Turbulent Reconnection
Lazarian, A; Takamoto, M; Pino, E M de Gouveia Dal; Cho, J
2015-01-01
Realistic astrophysical environments are turbulent due to the extremely high Reynolds numbers. Therefore, the theories of reconnection intended for describing astrophysical reconnection should not ignore the effects of turbulence on magnetic reconnection. Turbulence is known to change the nature of many physical processes dramatically and in this review we claim that magnetic reconnection is not an exception. We stress that not only astrophysical turbulence is ubiquitous, but also magnetic reconnection itself induces turbulence. Thus turbulence must be accounted for in any realistic astrophysical reconnection setup. We argue that due to the similarities of MHD turbulence in relativistic and non-relativistic cases the theory of magnetic reconnection developed for the non-relativistic case can be extended to the relativistic case and we provide numerical simulations that support this conjecture. We also provide quantitative comparisons of the theoretical predictions and results of numerical experiments, includi...
Lock, Maximilian P E
2016-01-01
The conflict between quantum theory and the theory of relativity is exemplified in their treatment of time. We examine the ways in which their conceptions differ, and describe a semiclassical clock model combining elements of both theories. The results obtained with this clock model in flat spacetime are reviewed, and the problem of generalizing the model to curved spacetime is discussed, before briefly describing an experimental setup which could be used to test of the model. Taking an operationalist view, where time is that which is measured by a clock, we discuss the conclusions that can be drawn from these results, and what clues they contain for a full quantum relativistic theory of time.
Relativistic electron beams above thunderclouds
DEFF Research Database (Denmark)
Füellekrug, M.; Roussel-Dupre, R.; Symbalisty, E. M. D.;
2011-01-01
Non-luminous relativistic electron beams above thunderclouds have been detected by the radio signals of low frequency similar to 40-400 kHz which they radiate. The electron beams occur similar to 2-9 ms after positive cloud-to-ground lightning discharges at heights between similar to 22-72 km above...... thunderclouds. Intense positive lightning discharges can also cause sprites which occur either above or prior to the electron beam. One electron beam was detected without any luminous sprite which suggests that electron beams may also occur independently of sprites. Numerical simulations show that beams...... of electrons partially discharge the lightning electric field above thunderclouds and thereby gain a mean energy of similar to 7MeV to transport a total charge of similar to-10mC upwards. The impulsive current similar to 3 x 10(-3) Am-2 associated with relativistic electron beams above thunderclouds...
Relativistic electron beams above thunderclouds
Directory of Open Access Journals (Sweden)
M. Füllekrug
2011-05-01
Full Text Available Non-luminous relativistic electron beams above thunderclouds are detected by radio remote sensing with low frequency radio signals from 40–400 kHz. The electron beams occur 2–9 ms after positive cloud-to-ground lightning discharges at heights between 22–72 km above thunderclouds. The positive lightning discharges also cause sprites which occur either above or before the electron beam. One electron beam was detected without any luminous sprite occurrence which suggests that electron beams may also occur independently. Numerical simulations show that the beamed electrons partially discharge the lightning electric field above thunderclouds and thereby gain a mean energy of 7 MeV to transport a total charge of 10 mC upwards. The impulsive current associated with relativistic electron beams above thunderclouds is directed downwards and needs to be considered as a novel element of the global atmospheric electric circuit.
Double Relativistic Electron Accelerating Mirror
Directory of Open Access Journals (Sweden)
Saltanat Sadykova
2013-02-01
Full Text Available In the present paper, the possibility of generation of thin dense relativistic electron layers is shown using the analytical and numerical modeling of laser pulse interaction with ultra-thin layers. It was shown that the maximum electron energy can be gained by optimal tuning between the target width, intensity and laser pulse duration. The optimal parameters were obtained from a self-consistent system of Maxwell equations and the equation of motion of electron layer. For thin relativistic electron layers, the gaining of maximum electron energies requires a second additional overdense plasma layer, thus cutting the laser radiation off the plasma screen at the instant of gaining the maximum energy (DREAM-schema.
Ruder, Hanns; Nollert, Hans-Peter; Hehl, Friedrich
1998-01-01
This book summarizes the lectures given at the 162. WE-Heraeus Seminar which took place in the house of the German Physical Society in Bad Honnefin August 1996. Already the number 162 shows the activity and effectiveness of the WE-Heraeus Foundation. We would like to express our thanks to Jutta Adam and Dr. Volker Schafer for the almost incredibly simple and unbureaucratical procedure of funding, organization and realization, and, of course, to the founders. Similar to the 152. WE-Heraeus Seminar Relativity and Scientific Computing (Springer Verlag 1996), this seminar was a joint venture of the Astronomical Society (AG) and of the Section 'Gravitation und Relativity Theory' of the German Physical Society (DPG). Since Einstein has developed his Theory of General Relativity more than 80 years ago, the situation has changed dramatically. In the first decades main efforts were untertaken for a better understanding and for the experimental verification of the theory. Mean while General Relativity (GR) is one of ...
Khriplovich, I. B
2005-01-01
This book offers an alternative to other textbooks on the subject, providing a more specific discussion of numerous general relativistic effects for readers who have knowledge of classical mechanics and electrodynamics, including special relativity. Coverage includes gravitational lensing, signal retardation in the gravitational field of the Sun, the Reissner-Nordström solution, selected spin effects, the resonance transformation of an electromagnetic wave into a gravitational one, and the entropy and temperature of black holes. The book includes numerous problems at various levels of difficulty, making it ideal also for independent study by a broad readership of advanced students and researchers. I.B. Khriplovich is Chief Researcher, Budker Institute of Nuclear Physics, Novosibirsk, and Chair of Theoretical Physics at Novosibirsk University. Dr. Khriplovich is a Corresponding Member of the Russian Academy of Sciences. He has been awarded the Dirac Medal ``For the advancement of theoretical physics'' by Univ...
Similarity solutions for radiation in time-dependent relativistic flows
Lucy, L B
2004-01-01
Exact analytic solutions are derived for radiation in time-dependent relativistic flows. The flows are spherically-symmetric homologous explosions or implosions of matter with a grey extinction coefficient. The solutions are suitable for testing numerical transfer codes, and this is illustrated for a fully relativistic Monte Carlo code.
Al-Hashimi, M H; Shalaby, A M
2016-01-01
A general method has been developed to solve the Schr\\"odinger equation for an arbitrary derivative of the $\\delta$-function potential in 1-d using cutoff regularization. The work treats both the relativistic and nonrelativistic cases. A distinction in the treatment has been made between the case when the derivative $n$ is an even number from the one when $n$ is an odd number. A general gap equations for each case has been derived. The case of $\\delta^{(2)}$-function potential has been used as an example. The results from the relativistic case show that the $\\delta^{(2)}$-function system behaves exactly like the $\\delta$-function and the $\\delta'$-function potentials, which means it also shares the same features with quantum field theories, like being asymptotically free, in the massless limit, it undergoes dimensional transmutation and it possesses an infrared conformal fixed point. As a result the evidence of universality of contact interactions has been extended further to include the $\\delta^{(2)}$-functi...
New Developments in Relativistic Viscous Hydrodynamics
Romatschke, Paul
2009-01-01
Starting with a brief introduction into the basics of relativistic fluid dynamics, I discuss our current knowledge of a relativistic theory of fluid dynamics in the presence of (mostly shear) viscosity. Derivations based on the generalized second law of thermodynamics, kinetic theory, and a complete second-order gradient expansion are reviewed. The resulting fluid dynamic equations are shown to be consistent for all these derivations, when properly accounting for the respective region of appl...
Relativistic Celestial Mechanics of the Solar System
Kopeikin, Sergei; Efroimsky, Michael; Kaplan, George
2011-09-01
The general theory of relativity was developed by Einstein a century ago. Since then, it has become the standard theory of gravity, especially important to the fields of fundamental astronomy, astrophysics, cosmology, and experimental gravitational physics. Today, the application of general relativity is also essential for many practical purposes involving astrometry, navigation, geodesy, and time synchronization. Numerous experiments have successfully tested general relativity to a remarkable level of precision. Exploring relativistic gravity in the solar system now involves a variety of high-accuracy techniques, for example, very long baseline radio interferometry, pulsar timing, spacecraft Doppler tracking, planetary radio ranging, lunar laser ranging, the global positioning system (GPS), torsion balances and atomic clocks. Over the last few decades, various groups within the International Astronomical Union have been active in exploring the application of the general theory of relativity to the modeling and interpretation of high-accuracy astronomical observations in the solar system and beyond. A Working Group on Relativity in Celestial Mechanics and Astrometry was formed in 1994 to define and implement a relativistic theory of reference frames and time scales. This task was successfully completed with the adoption of a series of resolutions on astronomical reference systems, time scales, and Earth rotation models by the 24th General Assembly of the IAU, held in Manchester, UK, in 2000. However, these resolutions only form a framework for the practical application of relativity theory, and there have been continuing questions on the details of the proper application of relativity theory to many common astronomical problems. To ensure that these questions are properly addressed, the 26th General Assembly of the IAU, held in Prague in August 2006, established the IAU Commission 52, "Relativity in Fundamental Astronomy". The general scientific goals of the new
Relativistic quantum mechanics
Wachter, Armin
2010-01-01
Which problems do arise within relativistic enhancements of the Schrödinger theory, especially if one adheres to the usual one-particle interpretation, and to what extent can these problems be overcome? And what is the physical necessity of quantum field theories? In many books, answers to these fundamental questions are given highly insufficiently by treating the relativistic quantum mechanical one-particle concept very superficially and instead introducing field quantization as soon as possible. By contrast, this monograph emphasizes relativistic quantum mechanics in the narrow sense: it extensively discusses relativistic one-particle concepts and reveals their problems and limitations, therefore motivating the necessity of quantized fields in a physically comprehensible way. The first chapters contain a detailed presentation and comparison of the Klein-Gordon and Dirac theory, always in view of the non-relativistic theory. In the third chapter, we consider relativistic scattering processes and develop the...
Numerical Evolution of Black Holes with a Hyperbolic Formulation of General Relativity
Scheel, M A; Cook, G B; Shapiro, S L; Teukolsky, S A; Scheel, Mark A.; Baumgarte, Thomas W.; Cook, Gregory B.; Shapiro, Stuart L.; Teukolsky, Saul A.
1997-01-01
We describe a numerical code that solves Einstein's equations for a Schwarzschild black hole in spherical symmetry, using a hyperbolic formulation introduced by Choquet-Bruhat and York. This is the first time this formulation has been used to evolve a numerical spacetime containing a black hole. We excise the hole from the computational grid in order to avoid the central singularity. We describe in detail a causal differencing method that should allow one to stably evolve a hyperbolic system of equations in three spatial dimensions with an arbitrary shift vector, to second-order accuracy in both space and time. We demonstrate the success of this method in the spherically symmetric case.
Institute of Scientific and Technical Information of China (English)
ZHANG Peng-Fei; RUAN Tu-Nan
2001-01-01
A systematic theory on the appropriate spin operators for the relativistic states is developed. For a massive relativistic particle with arbitrary nonzero spin, the spin operator should be replaced with the relativistic one, which is called in this paper as moving spin. Further the concept of moving spin is discussed in the quantum field theory. A new is constructed. It is shown that, in virtue of the two operators, problems in quantum field concerned spin can be neatly settled.
Relativistic Guiding Center Equations
Energy Technology Data Exchange (ETDEWEB)
White, R. B. [PPPL; Gobbin, M. [Euratom-ENEA Association
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.
Relativistic Linear Restoring Force
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…
Relativistic Interpretation of Newtonian Simulations for Cosmic Structure Formation
Fidler, Christian; Rampf, Cornelius; Crittenden, Robert; Koyama, Kazuya; Wands, David
2016-01-01
The standard numerical tools for studying non-linear collapse of matter are Newtonian $N$-body simulations. Previous work has shown that these simulations are in accordance with General Relativity (GR) up to first order in perturbation theory, provided that the effects from radiation can be neglected. In this paper we show that the present day matter density receives more than 1% corrections from radiation on large scales if Newtonian simulations are initialised before $z=50$. We provide a relativistic framework in which unmodified Newtonian simulations are compatible with linear GR even in the presence of radiation. Our idea is to use GR perturbation theory to keep track of the evolution of relativistic species and the relativistic spacetime consistent with the Newtonian trajectories computed in $N$-body simulations. If metric potentials are sufficiently small, they can be computed using a first-order Einstein-Boltzmann code such as CLASS. We make this idea rigorous by defining a class of GR gauges, the Newt...
Directory of Open Access Journals (Sweden)
Ioana Opriș
2017-02-01
Full Text Available A general and simple numerical model is presented to calculate the uncontrolled steam flows extracted from a turbine to preheat the feed-water of a steam generator. For a user-defined technological scheme, a set of clear rules is given to complete the elements of the augmented matrix of the linear system that solves the problem. The model avoids writing of the heat balance equations for each heat exchanger. The steam extractions to the heaters are determined as related to the flow rate at the condenser. A numerical example is given to show the results.
A Relativistic Long-term Precession of the Earth
Tang, K.
2016-05-01
et al. (2003), they explain how to calculate the relativistic inertial torque, and discuss how to deal with different relativistic reference systems as well as various time scales and relativistic scalings. The geodetic precession and nutation are also taken into account in a natural way. This theory of Earth's rotation is consistent with General Relativity. This approach allows us to obtain the long-term precession of the Earth in a more rigorous relativistic framework. Our goal is to obtain the relativistic Earth's precession from -1 Myr to 1 Myr around J2000.0. The precession of the ecliptic is obtained by numerical integration as in most previous works. The precession of the equator, which is calculated with the relativistic theory of Earth's rotation as mentioned above, is also derived numerically. This part of work starts with a post-Newtonian rigid-multipole formalism that has been published by Klioner et al. (2003). Then the equations are integrated numerically, and the results are modified due to the effect of tidal dissipation. Approximations for the precession are derived and expressed in form of a linear term plus 20--30 periodic terms. Compared with P03, the difference is only several arcseconds in an interval of 2000 years around J2000.0. The results are consistent with other long-term precession theories. Finally, the relativistic effects of precession are analyzed. In this thesis, the models for the relativistic long-term precession of the Earth are given. Chapter 1 briefly introduces some historical background and the aim of our work. Chapters 2 to 5 give the way to calculate the precession in detail. Chapter 2 is about the structure of a quasi symplectic integrator which was developed by ourselves. According to our dynamical model of the solar system, the numerical integrator is based on the symplectic SABA4 scheme, and some tricks are used to treat the problems of tidal dissipation, close encounters, and round-off errors. The first-order post
MALFLIET, R
1993-01-01
We discuss the present status of relativistic transport theory. Special emphasis is put on problems of topical interest: hadronic features, thermodynamical consistent approximations and spectral properties.
Ye, Ai; Hansen, Nicole; Resnick, Ilyse; Carrique, Jessica; Jordan, Nancy
2016-01-01
The purpose of the present study was to reveal the developmental pathway from third grade cognitive competencies to sixth grade conceptual and procedural fraction knowledge through the intervening whole numerical skills at fifth grade. The study used empirical data that come from 536 students in nine schools across two Delaware public school…
A Collocation Method for Numerical Solution of the Generalized Burgers-Huxley Equation
Directory of Open Access Journals (Sweden)
Mohammad ZAREBNIA
2014-08-01
Full Text Available In this paper, we use a collocation method to solve the Burgers-Huxley equation. To achieve this aim, we use mesh free technique based on sinc functions. The stability analysis is discussed. Some numerical examples are provided to illustrate the accuracy and fluency of the method.
Institute of Scientific and Technical Information of China (English)
黄思训; 杜华栋; 韩威
2004-01-01
The generalized variational data assimilation for non-differential dynamical systems is studied.There is no tangent linear model for non-differential systems and thus the general adjoint model can not be derived in the traditional way.The weak form of the original system was introduced, and then the generalized adjoint model was derived. The generalized variational data assimilation methods were developed for non-differential low dimensional system and non-differential high dimensional system with global and local observations. Furthermore, ideas in inverse problems are introduced to 4DVAR (Four-dimensional variational) of non-differential partial differential system with local observations.
1980-11-01
generalized nodel described by Eykhoff [1, 2], Astrom and Eykhoff [3], and on pages 209-220 of Eykhoff [4]. The origin of the general- ized model can be...aspects of process-parameter estimation," IEEE Trans. Auto. Control, October 1963, pp. 347-357. 3. K. J. Astrom and P. Eykhoff, "System
Relativistic Runaway Electrons
Breizman, Boris
2014-10-01
This talk covers recent developments in the theory of runaway electrons in a tokamak with an emphasis on highly relativistic electrons produced via the avalanche mechanism. The rapidly growing population of runaway electrons can quickly replace a large part of the initial current carried by the bulk plasma electrons. The magnetic energy associated with this current is typically much greater than the particle kinetic energy. The current of a highly relativistic runaway beam is insensitive to the particle energy, which separates the description of the runaway current evolution from the description of the runaway energy spectrum. A strongly anisotropic distribution of fast electrons is generally prone to high-frequency kinetic instabilities that may cause beneficial enhancement of runaway energy losses. The relevant instabilities are in the frequency range of whistler waves and electron plasma waves. The instability thresholds reported in earlier work have been revised considerably to reflect strong dependence of collisional damping on the wave frequency and the role of plasma non-uniformity, including radial trapping of the excited waves in the plasma. The talk also includes a discussion of enhanced scattering of the runaways as well as the combined effect of enhanced scattering and synchrotron radiation. A noteworthy feature of the avalanche-produced runaway current is a self-sustained regime of marginal criticality: the inductive electric field has to be close to its critical value (representing avalanche threshold) at every location where the runaway current density is finite, and the current density should vanish at any point where the electric field drops below its critical value. This nonlinear Ohm's law enables complete description of the evolving current profile. Work supported by the U.S. Department of Energy Contract No. DEFG02-04ER54742 and by ITER contract ITER-CT-12-4300000273. The views and opinions expressed herein do not necessarily reflect those of
Numerical convergence of the block-maxima approach to the Generalized Extreme Value distribution
Faranda, Davide; Turchetti, Giorgio; Vaienti, Sandro
2011-01-01
In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems. In this setting, recent works have shown how to get a statistics of extremes in agreement with the classical Extreme Value Theory. We pursue these investigations by giving analytical expressions of Extreme Value distribution parameters for maps that have an absolutely continuous invariant measure. We compare these analytical results with numerical experiments in which we study the convergence to limiting distributions using the so called block-maxima approach, pointing out in which cases we obtain robust estimation of parameters. In regular maps for which mixing properties do not hold, we show that the fitting procedure to the classical Extreme Value Distribution fails, as expected. However, we obtain an empirical distribution that can be explained starting from a different observable function for which Nicolis et al. [2006] have found analytical results.
Institute of Scientific and Technical Information of China (English)
Zhang Lizhen; Wang Xiaoming; Miguel A.González Hernández; Wang Jun
2008-01-01
This paper was to validate the effects of airfoil thickness ratio on the characteristics of a family of airfoils.Re-search was carried out in different ways.First,tests were conducted in the wind tunnel.And numerical simulation was performed on the basis of tests.Results from calculation were consistent with tests,indicating that numerical method could help evaluate characteristics of airfoils.Then the results were confirmed by compared with empirical data.The study also showed that the determining factor of lift is not only the thickness ratio,but the angle of attack,the relative camber and the camber line.The thickness ratio appears to have little effect on lift coefficient at zero angle of attack,since the angle of zero llft is largely determined by the airfoil camber.According to the research,numerical simulation can be used to determine the aerodynamic characteristics of airfoils in different environment such as in the dusty or hu-mid air.
Energy Technology Data Exchange (ETDEWEB)
Aviles, B.N.; Sutton, T.M.; Kelly, D.J. III.
1991-09-01
A generalized Runge-Kutta method has been employed in the numerical integration of the stiff space-time diffusion equations. The method is fourth-order accurate, using an embedded third-order solution to arrive at an estimate of the truncation error for automatic timestep control. The efficiency of the Runge-Kutta method is enhanced by a block-factorization technique that exploits the sparse structure of the matrix system resulting from the space and energy discretized form of the time-dependent neutron diffusion equations. Preliminary numerical evaluation using a one-dimensional finite difference code shows the sparse matrix implementation of the generalized Runge-Kutta method to be highly accurate and efficient when compared to an optimized iterative theta method. 12 refs., 5 figs., 4 tabs.
Relativistic calculations of coalescing binary neutron stars
Indian Academy of Sciences (India)
Joshua Faber; Phillippe Grandclément; Frederic Rasio
2004-10-01
We have designed and tested a new relativistic Lagrangian hydrodynamics code, which treats gravity in the conformally flat approximation to general relativity. We have tested the resulting code extensively, finding that it performs well for calculations of equilibrium single-star models, collapsing relativistic dust clouds, and quasi-circular orbits of equilibrium solutions. By adding a radiation reaction treatment, we compute the full evolution of a coalescing binary neutron star system. We find that the amount of mass ejected from the system, much less than a per cent, is greatly reduced by the inclusion of relativistic gravitation. The gravity wave energy spectrum shows a clear divergence away from the Newtonian point-mass form, consistent with the form derived from relativistic quasi-equilibrium fluid sequences.
Relabeling symmetry in relativistic fluids and plasmas
Kawazura, Yohei; Fukumoto, Yasuhide
2014-01-01
The conservation of the recently formulated relativistic canonical helicity [Yoshida Z, Kawazura Y, and Yokoyama T 2014 J. Math. Phys. 55 043101] is derived from Noether's theorem by constructing an action principle on the relativistic Lagrangian coordinates (we obtain general cross helicities that include the helicity of the canonical vorticity). The conservation law is, then, explained by the relabeling symmetry pertinent to the Lagrangian label of fluid elements. Upon Eulerianizing the Noether current, the purely spatial volume integral on the Lagrangian coordinates is mapped to a space-time mixed three-dimensional integral on the four-dimensional Eulerian coordinates. The relativistic conservation law in the Eulerian coordinates is no longer represented by any divergence-free current; hence, it is not adequate to regard the relativistic helicity (represented by the Eulerian variables) as a Noether charge, and this stands the reason why the "conventional helicity" is no longer a constant of motion. We have...
Relativistic diffusion equation from stochastic quantization
Kazinski, P O
2007-01-01
The new scheme of stochastic quantization is proposed. This quantization procedure is equivalent to the deformation of an algebra of observables in the manner of deformation quantization with an imaginary deformation parameter (the Planck constant). We apply this method to the models of nonrelativistic and relativistic particles interacting with an electromagnetic field. In the first case we establish the equivalence of such a quantization to the Fokker-Planck equation with a special force. The application of the proposed quantization procedure to the model of a relativistic particle results in a relativistic generalization of the Fokker-Planck equation in the coordinate space, which in the absence of the electromagnetic field reduces to the relativistic diffusion (heat) equation. The stationary probability distribution functions for a stochastically quantized particle diffusing under a barrier and a particle in the potential of a harmonic oscillator are derived.
Goloviznin, V. M.; Karabasov, S. A.; Kozubskaya, T. K.; Maksimov, N. V.
2009-12-01
A generalization of the CABARET finite difference scheme is proposed for linearized one-dimensional Euler equations based on the characteristic decomposition into local Riemann invariants. The new method is compared with several central finite difference schemes that are widely used in computational aeroacoustics. Numerical results for the propagation of an acoustic wave in a homogeneous field and the refraction of this wave through a contact discontinuity obtained on a strongly nonuniform grid are presented.
Numerical expression of general relationships in hierarchical data base management systems
Energy Technology Data Exchange (ETDEWEB)
Hall, R. C.
1980-01-01
The need for a means to express general relationships among entity occurrences in hierarchical data bases is addressed. Integer expression of general path segments is described as a means to meet this need. Operations on the expressions are also described. Two possible implementations are discussed. Both implementations are compatible with the hierarchical data model, and provide a logical extension that permits representation of many-to-many relationships. 4 figures.
Acceleration and Collimation of Relativistic Magnetohydrodynamic Disk Winds
Porth, Oliver; Fendt, Christian
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 × 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
Relativistic quantum mechanics; Mecanique quantique relativiste
Energy Technology Data Exchange (ETDEWEB)
Ollitrault, J.Y. [CEA Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique]|[Universite Pierre et Marie Curie, 75 - Paris (France)
1998-12-01
These notes form an introduction to relativistic quantum mechanics. The mathematical formalism has been reduced to the minimum in order to enable the reader to calculate elementary physical processes. The second quantification and the field theory are the logical followings of this course. The reader is expected to know analytical mechanics (Lagrangian and Hamiltonian), non-relativistic quantum mechanics and some basis of restricted relativity. The purpose of the first 3 chapters is to define the quantum mechanics framework for already known notions about rotation transformations, wave propagation and restricted theory of relativity. The next 3 chapters are devoted to the application of relativistic quantum mechanics to a particle with 0,1/5 and 1 spin value. The last chapter deals with the processes involving several particles, these processes require field theory framework to be thoroughly described. (A.C.) 2 refs.
Stable discrete representation of relativistically drifting plasmas
Kirchen, Manuel; Godfrey, Brendan B; Dornmair, Irene; Jalas, Soeren; Peters, Kevin; Vay, Jean-Luc; Maier, Andreas R
2016-01-01
Representing the electrodynamics of relativistically drifting particle ensembles in discrete, co-propagating Galilean coordinates enables the derivation of a Particle-in-Cell algorithm that is intrinsically free of the Numerical Cherenkov Instability, for plasmas flowing at a uniform velocity. Application of the method is shown by modeling plasma accelerators in a Lorentz-transformed optimal frame of reference.
Solitary Waves in Relativistic Electromagnetic Plasma
Institute of Scientific and Technical Information of China (English)
XIE Bai-Song; HUA Cun-Cai
2005-01-01
Solitary waves in relativistic electromagnetic plasmas are obtained numerically. The longitudinal momentum of electrons has been taken into account in the problem. It is found that in the moving frame with electromagnetic field propagating the solitary waves can exist in both cases, where the vector potential frequency is larger or smaller than the plasma characteristic frequency.
Towards relativistic quantum geometry
Energy Technology Data Exchange (ETDEWEB)
Ridao, Luis Santiago [Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina); Bellini, Mauricio, E-mail: mbellini@mdp.edu.ar [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata (Argentina); Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina)
2015-12-17
We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner–Nordström black-hole is studied.
Relativistic stars in bigravity theory
Aoki, Katsuki; Tanabe, Makoto
2016-01-01
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 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.
A general method for numerical Green's function in arbitrarily layered soils
Institute of Scientific and Technical Information of China (English)
ZOU Jun; HE Jinliang; ZENG Rong; SUN Weiming; YU Gang
2003-01-01
A straightforward approach is developed to calculate Green's function of a point current source in horizontal multi-layer soils. The sampling value of the coefficient of Green's function is obtained in an iterative way in terms of the equation group satisfying the pertinent boundary value problem. Further, the closed-form expression of multilayered soil Green's function can be given by the vector matrix pencil technology. The numerical results are in agreement with those by using other softwares. The approach proposed here is applicable to grounding problems with the structure of arbitrarily layered soil without needing the analytical expression of Green's function.
A novel numerical flux for the 3D Euler equations with general equation of state
Toro, Eleuterio F.
2015-09-30
Here we extend the flux vector splitting approach recently proposed in (E F Toro and M E Vázquez-Cendón. Flux splitting schemes for the Euler equations. Computers and Fluids. Vol. 70, Pages 1-12, 2012). The scheme was originally presented for the 1D Euler equations for ideal gases and its extension presented in this paper is threefold: (i) we solve the three-dimensional Euler equations on general meshes; (ii) we use a general equation of state; and (iii) we achieve high order of accuracy in both space and time through application of the semi-discrete ADER methodology on general meshes. The resulting methods are systematically assessed for accuracy, robustness and efficiency on a carefully selected suite of test problems. Formal high accuracy is assessed through convergence rates studies for schemes of up to 4th order of accuracy in both space and time on unstructured meshes.
Density perturbations with relativistic thermodynamics
Maartens, R
1997-01-01
We investigate cosmological density perturbations in a covariant and gauge- invariant formalism, incorporating relativistic causal thermodynamics to give a self-consistent description. The gradient of density inhomogeneities splits covariantly into a scalar part, a rotational vector part that is determined by the vorticity, and a tensor part that describes the shape. We give the evolution equations for these parts in the general dissipative case. Causal thermodynamics gives evolution equations for viswcous stress and heat flux, which are coupled to the density perturbation equation and to the entropy and temperature perturbation equations. We give the full coupled system in the general dissipative case, and simplify the system in certain cases.
Relativistic collapse and explosion of rotating supermassive stars with thermonuclear effects
Montero, Pedro J; Mueller, Ewald
2011-01-01
We present results of general relativistic simulations of collapsing supermassive stars with and without rotation using the two-dimensional general relativistic numerical code Nada, which solves the Einstein equations written in the BSSN formalism and the general relativistic hydrodynamics equations with high resolution shock capturing schemes. These numerical simulations use an equation of state which includes effects of gas pressure, and in a tabulated form those associated with radiation and the electron-positron pairs. We also take into account the effect of thermonuclear energy released by hydrogen and helium burning. We find that objects with a mass of 5x10^{5} solar mass and an initial metallicity greater than Z_{CNO}~0.007 do explode if non-rotating, while the threshold metallicity for an explosion is reduced to Z_{CNO}~0.001 for objects uniformly rotating. The critical initial metallicity for a thermonuclear explosion increases for stars with mass ~10^{6} solar mass. For those stars that do not explo...
An HLLC Solver for Relativistic Flows
Mignone, A
2005-01-01
We present an extension of the HLLC approximate Riemann solver by Toro, Spruce and Speares to the relativistic equations of fluid dynamics. The solver retains the simplicity of the original two-wave formulation proposed by Harten, Lax and van Leer (HLL) but it restores the missing contact wave in the solution of the Riemann problem. The resulting numerical scheme is computationally efficient, robust and positively conservative. The performance of the new solver is evaluated through numerical testing in one and two dimensions.
Relativistic and Non-relativistic Equations of Motion
Mangiarotti, L
1998-01-01
It is shown that any second order dynamic equation on a configuration space $X$ of non-relativistic time-dependent mechanics can be seen as a geodesic equation with respect to some (non-linear) connection on the tangent bundle $TX\\to X$ of relativistic velocities. Using this fact, the relationship between relativistic and non-relativistic equations of motion is studied.
Solutions of Conformal Israel-Stewart Relativistic Viscous Fluid Dynamics
Marrochio, Hugo; Denicol, Gabriel S; Luzum, Matthew; Jeon, Sangyong; Gale, Charles
2013-01-01
We use symmetry arguments developed by Gubser to construct the first radially-expanding explicit solutions of the Israel-Stewart formulation of hydrodynamics. Along with a general semi-analytical solution, an exact analytical solution is given which is valid in the cold plasma limit where viscous effects from shear viscosity and the relaxation time coefficient are important. The radially expanding solutions presented in this paper can be used as nontrivial checks of numerical algorithms employed in hydrodynamic simulations of the quark-gluon plasma formed in ultra-relativistic heavy ion collisions. We show this explicitly by comparing such analytic and semi-analytic solutions with the corresponding numerical solutions obtained using the MUSIC viscous hydrodynamics simulation code.
Directory of Open Access Journals (Sweden)
Michiko Yoshitake
2014-01-01
Full Text Available Interface termination between alumina and aluminum-containing alloys is discussed from a viewpoint of thermodynamics by extending the authors’ previous discussion on the interface termination between alumina and pure metal. A numerical formula to predict interface bonding at alumina-aluminum-containing alloys is proposed. The effectiveness of the formula is examined by extracting information on interface termination from experimental results and first-principle calculations in references. It is revealed that the prediction by the formula agrees quite well with the results reported in the references. According to the formula, a terminating species can be switched from oxygen to aluminum, which had been actually demonstrated experimentally. The formula uses only basic quantities of pure elements and the formation enthalpy of oxides. Therefore it can be applied for most of aluminum-containing alloys in the periodic table and is useful for material screening in developing interfaces with particular functions.
Numeric promoter description - A comparative view on concepts and general application.
Beier, Rico; Labudde, Dirk
2016-01-01
Nucleic acid molecules play a key role in a variety of biological processes. Starting from storage and transfer tasks, this also comprises the triggering of biological processes, regulatory effects and the active influence gained by target binding. Based on the experimental output (in this case promoter sequences), further in silico analyses aid in gaining new insights into these processes and interactions. The numerical description of nucleic acids thereby constitutes a bridge between the concrete biological issues and the analytical methods. Hence, this study compares 26 descriptor sets obtained by applying well-known numerical description concepts to an established dataset of 38 DNA promoter sequences. The suitability of the description sets was evaluated by computing partial least squares regression models and assessing the model accuracy. We conclude that the major importance regarding the descriptive power is attached to positional information rather than to explicitly incorporated physico-chemical information, since a sufficient amount of implicit physico-chemical information is already encoded in the nucleobase classification. The regression models especially benefited from employing the information that is encoded in the sequential and structural neighborhood of the nucleobases. Thus, the analyses of n-grams (short fragments of length n) suggested that they are valuable descriptors for DNA target interactions. A mixed n-gram descriptor set thereby yielded the best description of the promoter sequences. The corresponding regression model was checked and found to be plausible as it was able to reproduce the characteristic binding motifs of promoter sequences in a reasonable degree. As most functional nucleic acids are based on the principle of molecular recognition, the findings are not restricted to promoter sequences, but can rather be transferred to other kinds of functional nucleic acids. Thus, the concepts presented in this study could provide
Alternative gauge for the description of the light-matter interaction in a relativistic framework
Kjellsson, Tor; Førre, Morten; Simonsen, Aleksander Skjerlie; Selstø, Sølve; Lindroth, Eva
2017-08-01
We present a generalized velocity gauge form of the relativistic laser-matter interaction. In comparison with the (equivalent) regular minimal coupling description, this form of light-matter interaction results in superior convergence properties for the numerical solution of the time-dependent Dirac equation. This applies both to the numerical treatment and, more importantly, to the multipole expansion of the laser field. The advantages of the alternative gauge is demonstrated in hydrogen by studies of the dynamics following the impact of superintense laser pulses of extreme ultraviolet wavelengths and subfemtosecond duration.
Introduction to 3+1 numerical relativity
Alcubierre, Miguel
2008-01-01
This book introduces the modern field of 3+1 numerical relativity. The book has been written in a way as to be as self-contained as possible, and only assumes a basic knowledge of special relativity. Starting from a brief introduction to general relativity, it discusses the different concepts and tools necessary for the fully consistent numerical simulation of relativistic astrophysical systems, with strong and dynamical gravitational fields. Among the topics discussed in detail arethe following: the initial data problem, hyperbolic reductions of the field equations, gauge conditions, the evol
Rubin, Jacques
2014-01-01
Relativistic stereometric coordinates supplied by relativistic auto-locating positioning systems made up of four satellites supplemented by a fifth one are defined in addition to the well-known emission and reception coordinates. Such a constellation of five satellites defines a so-called relativistic localizing system. The determination of such systems is motivated by the need to not only locate (within a grid) users utilizing receivers but, more generally, to localize any spacetime event. The angles measured on the celestial spheres of the five satellites enter into the definition. Therefore, there are, up to scalings, intrinsic physical coordinates related to the underlying conformal structure of spacetime. Moreover, they indicate that spacetime must be endowed everywhere with a local projective geometry characteristic of a so-called generalized Cartan space locally modeled on four-dimensional, real projective space. The particular process of localization providing the relativistic stereometric coordinates...
Fermion confinement by a relativistic flux tube
Olsson, M G; Williams, K; Olsson, M G; Veseli, S; Williams, K
1996-01-01
We formulate the description of the dynamic confinement of a single fermion by a flux tube. The range of validity extends from the relativistic corrections of a slowly moving quark to the ultra-relativistic motion in a heavy-light meson. The reduced Salpeter equation, also known as the no-pair equation, provides the framework for our discussion. The Regge structure is that of a Nambu string with one end fixed. Numerical solutions are found giving very good fits to heavy-light meson masses. The Isgur-Wise function with a zero recoil slope of \\xi'(1)\\simeq -1.23 is obtained.
Absolute Stability Limit for Relativistic Charged Spheres
Giuliani, Alessandro
2007-01-01
We find an exact solution for the stability limit of relativistic charged spheres for the case of constant gravitational mass density and constant charge density. We argue that this provides an absolute stability limit for any relativistic charged sphere in which the gravitational mass density decreases with radius and the charge density increases with radius. We then provide a cruder absolute stability limit that applies to any charged sphere with a spherically symmetric mass and charge distribution. We give numerical results for all cases. In addition, we discuss the example of a neutral sphere surrounded by a thin, charged shell.
Relativistic wave equations: an operational approach
Dattoli, G.; Sabia, E.; Górska, K.; Horzela, A.; Penson, K. A.
2015-03-01
The use of operator methods of an algebraic nature is shown to be a very powerful tool to deal with different forms of relativistic wave equations. The methods provide either exact or approximate solutions for various forms of differential equations, such as relativistic Schrödinger, Klein-Gordon, and Dirac. We discuss the free-particle hypotheses and those relevant to particles subject to non-trivial potentials. In the latter case we will show how the proposed method leads to easily implementable numerical algorithms.
Nasser, Mohamed M. S.; Murid, Ali H. M.; Sangawi, Ali W. K.
2013-01-01
This paper presents a new uniquely solvable boundary integral equation for computing the conformal mapping, its derivative and its inverse from bounded multiply connected regions onto the five classical canonical slit regions. The integral equation is derived by reformulating the conformal mapping as an adjoint Riemann-Hilbert problem. From the adjoint Riemann-Hilbert problem, we derive a boundary integral equation with the adjoint generalized Neumann kernel for the derivative of the boundary...
Convexity and symmetrization in relativistic theories
Ruggeri, T.
1990-09-01
There is a strong motivation for the desire to have symmetric hyperbolic field equations in thermodynamics, because they guarantee well-posedness of Cauchy problems. A generic quasi-linear first order system of balance laws — in the non-relativistic case — can be shown to be symmetric hyperbolic, if the entropy density is concave with respect to the variables. In relativistic thermodynamics this is not so. This paper shows that there exists a scalar quantity in relativistic thermodynamics whose concavity guarantees a symmetric hyperbolic system. But that quantity — we call it —bar h — is not the entropy, although it is closely related to it. It is formed by contracting the entropy flux vector — ha with a privileged time-like congruencebar ξ _α . It is also shown that the convexity of h plus the requirement that all speeds be smaller than the speed of light c provide symmetric hyperbolic field equations for all choices of the direction of time. At this level of generality the physical meaning of —h is unknown. However, in many circumstances it is equal to the entropy. This is so, of course, in the non-relativistic limit but also in the non-dissipative relativistic fluid and even in relativistic extended thermodynamics for a non-degenerate gas.
The relativistic geoid: redshift and acceleration potential
Philipp, Dennis; Lämmerzahl, Claus; Puetzfeld, Dirk; Hackmann, Eva; Perlick, Volker
2017-04-01
We construct a relativistic geoid based on a time-independent redshift potential, which foliates the spacetime into isochronometric surfaces. This relativistic potential coincides with the acceleration potential for isometric congruences. We show that the a- and u- geoid, defined in a post-Newtonian framework, coincide also in a more general setup. Known Newtonian and post-Newtonian results are recovered in the respective limits. Our approach offers a relativistic definition of the Earth's geoid as well as a description of the Earth itself (or observers on its surface) in terms of an isometric congruence. Being fully relativistic, this notion of a geoid can also be applied to other compact objects such as neutron stars. By definition, this relativistic geoid can be determined by a congruence of Killing observers equipped with standard clocks by comparing their frequencies as well as by measuring accelerations of objects that follow the congruence. The redshift potential gives the correct result also for frequency comparison through optical fiber links as long as the fiber is at rest w.r.t. the congruence. We give explicit expressions for the relativistic geoid in the Kerr spacetime and the Weyl class of spacetimes. To investigate the influence of higher order mass multipole moments we compare the results for the Schwarzschild case to those obtained for the Erez-Rosen and q-metric spacetimes.
Extended Galilean symmetries of non-relativistic strings
Batlle, Carles; Gomis, Joaquim; Not, Daniel
2017-02-01
We consider two non-relativistic strings and their Galilean symmetries. These strings are obtained as the two possible non-relativistic (NR) limits of a relativistic string. One of them is non-vibrating and represents a continuum of non-relativistic massless particles, and the other one is a non-relativistic vibrating string. For both cases we write the generator of the most general point transformation and impose the condition of Noether symmetry. As a result we obtain two sets of non-relativistic Killing equations for the vector fields that generate the symmetry transformations. Solving these equations shows that NR strings exhibit two extended, infinite dimensional space-time symmetries which contain, as a subset, the Galilean symmetries. For each case, we compute the associated conserved charges and discuss the existence of non-central extensions.
Extended Galilean symmetries of non-relativistic strings
Batlle, Carles; Not, Daniel
2016-01-01
We consider two non-relativistic strings and their Galilean symmetries. These strings are obtained as the two possible non-relativistic (NR) limits of a relativistic string. One of them is non-vibrating and represents a continuum of non-relativistic massless particles, and the other one is a non-relativistic vibrating string. For both cases we write the generator of the most general point transformation and impose the condition of Noether symmetry. As a result we obtain two sets of non-relativistic Killing equations for the vector fields that generate the symmetry transformations. Solving these equations shows that NR strings exhibit two extended, infinite dimensional space-time symmetries which contain, as a subset, the Galilean symmetries. For each case, we compute the associated conserved charges and discuss the existence of non-central extensions.
Unification of Relativistic and Quantum Mechanics from Elementary Cycles Theory
Dolce, Donatello
2016-01-01
In Elementary Cycles theory elementary quantum particles are consistently described as the manifestation of ultra-fast relativistic spacetime cyclic dynamics, classical in the essence. The peculiar relativistic geometrodynamics of Elementary Cycles theory yields de facto a unification of ordinary relativistic and quantum physics. In particular its classical-relativistic cyclic dynamics reproduce exactly from classical physics first principles all the fundamental aspects of Quantum Mechanics, such as all its axioms, the Feynman path integral, the Dirac quantisation prescription (second quantisation), quantum dynamics of statistical systems, non-relativistic quantum mechanics, atomic physics, superconductivity, graphene physics and so on. Furthermore the theory allows for the explicit derivation of gauge interactions, without postulating gauge invariance, directly from relativistic geometrodynamical transformations, in close analogy with the description of gravitational interaction in general relativity. In thi...
Relativistic effects in elastic scattering of electrons in TEM.
Rother, Axel; Scheerschmidt, Kurt
2009-01-01
Transmission electron microscopy typically works with highly accelerated thus relativistic electrons. Consequently the scattering process is described within a relativistic formalism. In the following, we will examine three different relativistic formalisms for elastic electron scattering: Dirac, Klein-Gordon and approximated Klein-Gordon, the standard approach. This corresponds to a different consideration of spin effects and a different coupling to electromagnetic potentials. A detailed comparison is conducted by means of explicit numerical calculations. For this purpose two different formalisms have been applied to the approaches above: a numerical integration with predefined boundary conditions and the multislice algorithm, a standard procedure for such simulations. The results show a negligibly small difference between the different relativistic equations in the vicinity of electromagnetic potentials, prevailing in the electron microscope. The differences between the two numeric approaches are found to be small for small-angle scattering but eventually grow large for large-angle scattering, recorded for instance in high-angle annular dark field.
INTRACLUSTER MEDIUM REHEATING BY RELATIVISTIC JETS
Energy Technology Data Exchange (ETDEWEB)
Perucho, Manel; Quilis, Vicent; Marti, Jose-Maria [Departament d' Astronomia i Astrofisica, Universitat de Valencia, c/Dr. Moliner 50, E-46100 Burjassot (Valencia) (Spain)
2011-12-10
Galactic jets are powerful energy sources reheating the intracluster medium in galaxy clusters. Their crucial role in the cosmic puzzle, motivated by observations, has been established by a great number of numerical simulations excluding the relativistic nature of these jets. We present the first relativistic simulations of the very long-term evolution of realistic galactic jets. Unexpectedly, our results show no buoyant bubbles, but large cocoon regions compatible with the observed X-ray cavities. The reheating is more efficient and faster than in previous scenarios, and it is produced by the shock wave driven by the jet, that survives for several hundreds of Myr. Therefore, the X-ray cavities in clusters produced by powerful relativistic jets would remain confined by weak shocks for extremely long periods and their detection could be an observational challenge.
Thermodynamics of Relativistic Fermions with Chern-Simons Coupling
Bralic, N; Schaposnik, F A
1994-01-01
We study the thermodynamics of the relativistic Quantum Field Theory of massive fermions in three space-time dimensions coupled to an Abelian Maxwell-Chern-Simons gauge field. We evaluate the specific heat at finite temperature and density and find that the variation with the statistical angle is consistent with the non-relativistic ideas on generalized statistics.
Meson-Meson Scattering in Relativistic Constraint Dynamics
Crater, H W; Crater, Horace W.
2004-01-01
Dirac's relativistic constraint dynamics have been successfully applied to obtain a covariant nonperturbative description of QED and QCD bound states. We use this formalism to describe a microscopic theory of meson-meson scattering as a relativistic generalization of the nonrelativistic quark-interchange model developed by Barnes and Swanson.
Zeng, S.; Wesseling, P.
1993-01-01
The performance of a linear multigrid method using four smoothing methods, called SCGS (Symmetrical Coupled GauBeta-Seidel), CLGS (Collective Line GauBeta-Seidel), SILU (Scalar ILU), and CILU (Collective ILU), is investigated for the incompressible Navier-Stokes equations in general coordinates, in association with Galerkin coarse grid approximation. Robustness and efficiency are measured and compared by application to test problems. The numerical results show that CILU is the most robust, SILU the least, with CLGS and SCGS in between. CLGS is the best in efficiency, SCGS and CILU follow, and SILU is the worst.
Institute of Scientific and Technical Information of China (English)
Bai Jing-Song; Zhang Zhan-Ji; Li Ping; Zhong Min
2006-01-01
Based on the classical Roe method, we develop an interface capture method according to the general equation of state, and extend the single-fluid Roe method to the two-dimensional (2D) multi-fluid flows, as well as construct the continuous Roe matrix for the whole flow field. The interface capture equations and fluid dynamic conservative equations are coupled together and solved by using any high-resolution schemes that usually suit for the single-fluid flows. Some numerical examples are given to illustrate the solution of 1D and 2D multi-fluid Riemann problems.
Directory of Open Access Journals (Sweden)
Klusák J.
2009-12-01
Full Text Available The study of bi-material notches becomes a topical problem as they can model efficiently geometrical or material discontinuities. When assessing crack initiation conditions in the bi-material notches, the generalized stress intensity factors H have to be calculated. Contrary to the determination of the K-factor for a crack in an isotropic homogeneous medium, for the ascertainment of the H-factor there is no procedure incorporated in the calculation systems. The calculation of these fracture parameters requires experience. Direct methods of estimation of H-factors need choosing usually length parameter entering into calculation. On the other hand the method combining the application of the reciprocal theorem (Ψ-integral and FEM does not require entering any length parameter and is capable to extract the near-tip information directly from the far-field deformation.
Applying Relativistic Reconnection to Blazar Jets
Nalewajko, Krzysztof
2016-01-01
Rapid and luminous flares of non-thermal radiation observed in blazars require an efficient mechanism of energy dissipation and particle acceleration in relativistic active galactic nuclei (AGN) jets. Particle acceleration in relativistic magnetic reconnection is being actively studied by kinetic numerical simulations. Relativistic reconnection produces hard power-law electron energy distributions N(gamma) = N_0 gamma^(-p) exp(-gamma/gamma_max) with index p -> 1 and exponential cut-off Lorentz factor gamma_max ~ sigma in the limit of magnetization sigma = B^2/(4 pi w) >> 1 (where w is the relativistic enthalpy density). Reconnection in electron-proton plasma can additionally boost gamma_max by the mass ratio m_p/m_e. Hence, in order to accelerate particles to gamma_max ~ 10^6 in the case of BL Lacs, reconnection should proceed in plasma of very high magnetization sigma_max >~ 10^3. On the other hand, moderate mean jet magnetization values are required for magnetic bulk acceleration of relativistic jets, sigma...
Bliokh, Konstantin Y
2011-01-01
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 correct Lorentz transformations of the AM tensor. We examine manifestations of the relativistic Hall effect in quantum vortices, mechanical flywheel, and discuss various fundamental aspects of the 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.
On the convexity of Relativistic Ideal Magnetohydrodynamics
Ibáñez, José-María; Aloy, Miguel-Ángel; Martí, José-María; Miralles, Juan-Antonio
2015-01-01
We analyze the influence of the magnetic field in the convexity properties of the relativistic magnetohydrodynamics system of equations. To this purpose we use the approach of Lax, based on the analysis of the linearly degenerate/genuinely non-linear nature of the characteristic fields. Degenerate and non-degenerate states are discussed separately and the non-relativistic, unmagnetized limits are properly recovered. The characteristic fields corresponding to the material and Alfv\\'en waves are linearly degenerate and, then, not affected by the convexity issue. The analysis of the characteristic fields associated with the magnetosonic waves reveals, however, a dependence of the convexity condition on the magnetic field. The result is expressed in the form of a generalized fundamental derivative written as the sum of two terms. The first one is the generalized fundamental derivative in the case of purely hydrodynamical (relativistic) flow. The second one contains the effects of the magnetic field. The analysis ...
Exact Relativistic 'Antigravity' Propulsion
Felber, F 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.
Exact Relativistic `Antigravity' Propulsion
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.
Saini, N. S.; Singh, Kuldeep
2016-10-01
A head-on collision between two dust ion acoustic solitary waves (DIASWs) travelling in the opposite direction in a weakly relativistic plasma composed of four distinct particle populations, namely, weakly relativistic ion fluid, superthermal electrons as well as positrons, and immobile dust, is investigated. By employing extended Poincaré-Lighthill-Kuo method, two Korteweg-de Vries (KdV) equations are derived. The analytical phase shift after a head-on collision of two dust ion acoustic (DIA) solitary waves is also obtained. The combined effects of relativistic factor (β), electron to positron temperature ratio (α), ion to electron temperature ratio (σ), positron to electron density ratio (P), dust density ratio (d), and superthermality of electrons as well as positrons (via κ) on the phase shifts are numerically studied. All these physical parameters have also changed the potential amplitude and the width of colliding solitary waves. It is found that the presence of superthermal electrons as well as positrons and dust grains has emphatic influence on the phase shifts and potential pulse profiles of compressive DIA solitons. Our results are general and may be helpful in understanding a head-on collision between two DIASWs in astrophysical and laboratory plasmas, especially the interaction of pulsar relativistic winds with supernova ejecta that produces the superthermal particles and relativistic ions.
Energy Technology Data Exchange (ETDEWEB)
Hussain, S.; Mahmood, S.; Rehman, Aman-ur- [Theoretical Physics Division (TPD), PINSTECH, P.O. Nilore, Islamabad 44000, Pakistan and Pakistan Institute of Engineering and Applied Sciences (PIEAS), P.O. Nilore, Islamabad 44000 (Pakistan)
2014-11-15
Linear and nonlinear propagation of magnetosonic waves in the perpendicular direction to the ambient magnetic field is studied in dense plasmas for non-relativistic and ultra-relativistic degenerate electrons pressure. The sources of nonlinearities are the divergence of the ions and electrons fluxes, Lorentz forces on ions and electrons fluids and the plasma current density in the system. The Korteweg-de Vries equation for magnetosonic waves propagating in the perpendicular direction of the magnetic field is derived by employing reductive perturbation method for non-relativistic as well as ultra-relativistic degenerate electrons pressure cases in dense plasmas. The plots of the magnetosonic wave solitons are also shown using numerical values of the plasma parameters such a plasma density and magnetic field intensity of the white dwarfs from literature. The dependence of plasma density and magnetic field intensity on the magnetosonic wave propagation is also pointed out in dense plasmas for both non-relativistic and ultra-relativistic degenerate electrons pressure cases.
Vanbinst, K; De Smedt, B
2016-01-01
This contribution reviewed the available evidence on the domain-specific and domain-general neurocognitive determinants of children's arithmetic development, other than nonsymbolic numerical magnitude processing, which might have been overemphasized as a core factor of individual differences in mathematics and dyscalculia. We focused on symbolic numerical magnitude processing, working memory, and phonological processing, as these determinants have been most researched and their roles in arithmetic can be predicted against the background of brain imaging data. Our review indicates that symbolic numerical magnitude processing is a major determinant of individual differences in arithmetic. Working memory, particularly the central executive, also plays a role in learning arithmetic, but its influence appears to be dependent on the learning stage and experience of children. The available evidence on phonological processing suggests that it plays a more subtle role in children's acquisition of arithmetic facts. Future longitudinal studies should investigate these factors in concert to understand their relative contribution as well as their mediating and moderating roles in children's arithmetic development.
Energy Technology Data Exchange (ETDEWEB)
Bast, Radovan; Juselius, Jonas [Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Tromso, N-9037 Tromso (Norway); Saue, Trond [Institut de Chimie de Strasbourg, CNRS et Universite Louis Pasteur, Laboratoire de Chimie Quantique, 4, rue Blaise Pascal, BP 1032, F-67070 Strasbourg (France)], E-mail: tsaue@chimie.u-strasbg.fr
2009-02-17
We present a 4-component relativistic implementation for calculating the magnetically induced current density within Hartree-Fock and Kohn-Sham linear response theory using a common gauge origin. We demonstrate how the current density can be decomposed into paramagnetic and diamagnetic contributions by calculating separately the contributions from rotations between positive-energy orbitals and contributions from rotations between the occupied positive-energy orbitals and the virtual negative-energy orbitals, respectively. This methodology is applied to the study of the magnetically induced current density in benzene and the group 15 heteroaromatic compounds C{sub 5}H{sub 5}E (E = N, P, As, Sb, Bi). Quantitative values for the magnetically induced ring currents are obtained by numerical integration over the current flow. We have found that the diatropic ring current is sustained for the entire series of the group 15 heteroaromatic compounds-the induced ring current susceptibility of bismabenzene being 76% of the benzene result. Having employed two hybrid and two nonhybrid generalized gradient approximation functionals, the results are found to be rather insensitive to the choice of the density functional approximation. The relativistic effect is relatively small, reaching its maximum of 8% for bismabenzene. The presented 4-component relativistic methodology opens up the possibility to visualize magnetically induced current densities of aromatic heavy-element systems with both scalar relativistic and spin-orbit effects included.
Newton-Cartan (super)gravity as a non-relativistic limit
Bergshoeff, Eric; Rosseel, Jan; Zojer, Thomas
2015-01-01
We define a procedure that, starting from a relativistic theory of supergravity, leads to a consistent, non-relativistic version thereof. As a first application we use this limiting procedure to show how the Newton-Cartan formulation of non-relativistic gravity can be obtained from general relativit
On the relativistic anisotropic configurations
Energy Technology Data Exchange (ETDEWEB)
Shojai, F. [University of Tehran, Department of Physics, Tehran (Iran, Islamic Republic of); Institute for Research in Fundamental Sciences (IPM), Foundations of Physics Group, School of Physics, Tehran (Iran, Islamic Republic of); Kohandel, M. [Alzahra University, Department of Physics and Chemistry, Tehran (Iran, Islamic Republic of); Stepanian, A. [University of Tehran, Department of Physics, Tehran (Iran, Islamic Republic of)
2016-06-15
In this paper we study anisotropic spherical polytropes within the framework of general relativity. Using the anisotropic Tolman-Oppenheimer-Volkov equations, we explore the relativistic anisotropic Lane-Emden equations. We find how the anisotropic pressure affects the boundary conditions of these equations. Also we argue that the behavior of physical quantities near the center of star changes in the presence of anisotropy. For constant density, a class of exact solution is derived with the aid of a new ansatz and its physical properties are discussed. (orig.)
Fukushima, Toshio
2017-06-01
Reviewed are recently developed methods of the numerical integration of the gravitational field of general two- or three-dimensional bodies with arbitrary shape and mass density distribution: (i) an axisymmetric infinitely-thin disc (Fukushima 2016a, MNRAS, 456, 3702), (ii) a general infinitely-thin plate (Fukushima 2016b, MNRAS, 459, 3825), (iii) a plane-symmetric and axisymmetric ring-like object (Fukushima 2016c, AJ, 152, 35), (iv) an axisymmetric thick disc (Fukushima 2016d, MNRAS, 462, 2138), and (v) a general three-dimensional body (Fukushima 2016e, MNRAS, 463, 1500). The key techniques employed are (a) the split quadrature method using the double exponential rule (Takahashi and Mori, 1973, Numer. Math., 21, 206), (b) the precise and fast computation of complete elliptic integrals (Fukushima 2015, J. Comp. Appl. Math., 282, 71), (c) Ridder's algorithm of numerical differentiaion (Ridder 1982, Adv. Eng. Softw., 4, 75), (d) the recursive computation of the zonal toroidal harmonics, and (e) the integration variable transformation to the local spherical polar coordinates. These devices succesfully regularize the Newton kernel in the integrands so as to provide accurate integral values. For example, the general 3D potential is regularly integrated as Φ (\\vec{x}) = - G \\int_0^∞ ( \\int_{-1}^1 ( \\int_0^{2π} ρ (\\vec{x}+\\vec{q}) dψ ) dγ ) q dq, where \\vec{q} = q (√{1-γ^2} cos ψ, √{1-γ^2} sin ψ, γ), is the relative position vector referred to \\vec{x}, the position vector at which the potential is evaluated. As a result, the new methods can compute the potential and acceleration vector very accurately. In fact, the axisymmetric integration reproduces the Miyamoto-Nagai potential with 14 correct digits. The developed methods are applied to the gravitational field study of galaxies and protoplanetary discs. Among them, the investigation on the rotation curve of M33 supports a disc-like structure of the dark matter with a double-power-law surface
Induced Compton Scattering by Relativistic Electrons in Magnetized Astrophysical Plasmas.
Sincell, Mark William
1994-01-01
The effects of stimulated scattering on high brightness temperature radiation are studied in two important contexts. In the first case, we assume that the radiation is confined to a collimated beam traversing a relativistically streaming magnetized plasma. When the plasma is cold in the bulk frame, stimulated scattering is only significant if the angle between the photon motion and the plasma velocity is less than gamma^{-1} , where gamma is the bulk Lorentz factor. Under the assumption that the center of the photon beam is parallel to the bulk motion, we calculate the scattering rate as a function of the angular spread of the beam and gamma. Magnetization changes the photon recoil, without which stimulated scattering has no effect. It also introduces a strong dependence on frequency and polarization: if the photon frequency matches the electron cyclotron frequency, the scattering rate of photons polarized perpendicular to the magnetic field can be substantially enhanced relative to Thomson, and if the photon frequency is much less than the cyclotron frequency the scattering is suppressed. Applying these calculations to pulsars, we find that stimulated scattering of the radio beam in the magnetized wind believed to exist outside the light cylinder can substantially alter the spectrum and polarization state of the radio signal. We suggest that the scattering rate is so high in some pulsars that the ability of the radio signal to penetrate the pulsar magnetosphere requires modification of either the conventional model of the magnetosphere or assumptions about the effects of stimulated scattering upon a beam. In the second case, we present a model of the radio emission from synchrotron self-absorbed sources, including the effects of induced Compton scattering by the relativistic electrons in the source. Order of magnitude estimates show that stimulated scattering becomes the dominant absorption process when (kTB/m ec^2)tau_{T }_sp{~}> 0.1. Numerical simulations
Stream instabilities in relativistically hot plasma
Shaisultanov, Rashid; Eichler, David
2011-01-01
The instabilities of relativistic ion beams in a relativistically hot electron background are derived for general propagation angles. It is shown that the Weibel instability in the direction perpendicular to the streaming direction is the fastest growing mode, and probably the first to appear, consistent with the aligned filaments that are seen in PIC simulations. Oblique, quasiperpendicular modes grow almost as fast, as the growth rate varies only moderately with angle, and they may distort or corrugate the filaments after the perpendicular mode saturates.
Relativistic Celestial Mechanics of the Solar System
Kopeikin, Sergei; Kaplan, George
2011-01-01
This authoritative book presents the theoretical development of gravitational physics as it applies to the dynamics of celestial bodies and the analysis of precise astronomical observations. In so doing, it fills the need for a textbook that teaches modern dynamical astronomy with a strong emphasis on the relativistic aspects of the subject produced by the curved geometry of four-dimensional spacetime. The first three chapters review the fundamental principles of celestial mechanics and of special and general relativity. This background material forms the basis for understanding relativistic r
Theory of Relativistic Reference Frames for High-Precision Astrometric Space Missions
Kopeikin, S M
2000-01-01
Recent modern space missions deliver invaluable information about origin of our universe, physical processes in the vicinity of black holes and other exotic astrophysical objects, stellar dynamics of our galaxy, etc. On the other hand, space astrometric missions make it possible to determine with unparalleled precision distances to stars and cosmological objects as well as their physical characteristics and positions on the celestial sphere. Permanently growing accuracy of space astronomical observations and the urgent need for adequate data processing algorithms require corresponding development of an adequate theory of reference frames along with unambiguous description of propagation of light rays from a source of light to observer. Such a theory must be based on the Einstein's general relativity and account for numerous relativistic effects both in the solar system and outside of its boundary. The main features of the relativistic theory of reference frames are presented in this work. A hierarchy of the f...
Kikuchi, Daiki; Yamada, Kei; Asada, Hideki
2014-01-01
Toward a test of parity violation in a gravity theory, possible effects of Chern-Simons (CS) gravity on an interferometer have been recently discussed. Continuing work initiated in an earlier publication [Okawara, Yamada and Asada, Phys. Rev. Lett. 109, 231101 (2012)], we study possible altitudinal and directional dependence of relativistic Sagnac effect in CS modified gravity. We compare the CS effects on Sagnac interferometers with the general relativistic Lense-Thirring (LT) effects. Numerical calculations show that the eastbound Sagnac interferometer might be preferred for testing CS separately, because LT effects on this interferometer cancel out. The size of the phase shift induced in the CS model might have an oscillatory dependence also on the altitude of the interferometer through the CS mass parameter $m_{CS}$. Therefore, the international space station site as well as a ground-based experiment is also discussed.
Ways to constrain neutron star equation of state models using relativistic disc lines
Bhattacharyya, Sudip
2011-01-01
Relativistic spectral lines from the accretion disc of a neutron star low-mass X-ray binary can be modelled to infer the disc inner edge radius. A small value of this radius tentatively implies that the disc terminates either at the neutron star hard surface, or at the innermost stable circular orbit (ISCO). Therefore an inferred disc inner edge radius either provides the stellar radius, or can directly constrain stellar equation of state (EoS) models using the theoretically computed ISCO radius for the spacetime of a rapidly spinning neutron star. However, this procedure requires numerical computation of stellar and ISCO radii for various EoS models and neutron star configurations using an appropriate rapidly spinning stellar spacetime. We have fully general relativistically calculated about 16000 stable neutron star structures to explore and establish the above mentioned procedure, and to show that the Kerr spacetime is inadequate for this purpose. Our work systematically studies the methods to constrain Eo...
Moroz, O
2014-01-01
Using Mathematica package, we derive analytical closed-form expressions for the shear and the bulk viscosity coefficients in multicomponent relativistic gases with constant cross sections, being the relativistic generalization for the hard spheres model. Some of them are cumbersome and require symbolic manipulations in an algebraic package. The constant cross sections are of the elastic processes, while the inelastic (or number-changing) processes (collisions or decays) are considered only partly. As examples, we find explicit expressions of the correct single-component first-order shear viscosity coefficient and some explicit analytical results for the binary mixture. These formulas have numerous applications in approximate nonequilibrium descriptions of gases of particles or quasiparticles with averaged (temperature dependent) cross sections. In addition to this, we present formulas for collision rates and some other related formulas. This paper is a shortened version of a previous one.
Relativistic electron beams above thunderclouds
Directory of Open Access Journals (Sweden)
M. Füllekrug
2011-08-01
Full Text Available Non-luminous relativistic electron beams above thunderclouds have been detected by the radio signals of low frequency ∼40–400 kHz which they radiate. The electron beams occur ∼2–9 ms after positive cloud-to-ground lightning discharges at heights between ∼22–72 km above thunderclouds. Intense positive lightning discharges can also cause sprites which occur either above or prior to the electron beam. One electron beam was detected without any luminous sprite which suggests that electron beams may also occur independently of sprites. Numerical simulations show that beams of electrons partially discharge the lightning electric field above thunderclouds and thereby gain a mean energy of ∼7 MeV to transport a total charge of ∼−10 mC upwards. The impulsive current ∼3 × 10^{−3} Am^{−2} associated with relativistic electron beams above thunderclouds is directed downwards and needs to be considered as a novel element of the global atmospheric electric circuit.
Entropy-limited hydrodynamics: a novel approach to relativistic hydrodynamics
Guercilena, Federico; Radice, David; Rezzolla, Luciano
2017-07-01
We present entropy-limited hydrodynamics (ELH): a new approach for the computation of numerical fluxes arising in the discretization of hyperbolic equations in conservation form. ELH is based on the hybridisation of an unfiltered high-order scheme with the first-order Lax-Friedrichs method. The activation of the low-order part of the scheme is driven by a measure of the locally generated entropy inspired by the artificial-viscosity method proposed by Guermond et al. (J. Comput. Phys. 230(11):4248-4267, 2011, doi: 10.1016/j.jcp.2010.11.043). Here, we present ELH in the context of high-order finite-differencing methods and of the equations of general-relativistic hydrodynamics. We study the performance of ELH in a series of classical astrophysical tests in general relativity involving isolated, rotating and nonrotating neutron stars, and including a case of gravitational collapse to black hole. We present a detailed comparison of ELH with the fifth-order monotonicity preserving method MP5 (Suresh and Huynh in J. Comput. Phys. 136(1):83-99, 1997, doi: 10.1006/jcph.1997.5745), one of the most common high-order schemes currently employed in numerical-relativity simulations. We find that ELH achieves comparable and, in many of the cases studied here, better accuracy than more traditional methods at a fraction of the computational cost (up to {˜}50% speedup). Given its accuracy and its simplicity of implementation, ELH is a promising framework for the development of new special- and general-relativistic hydrodynamics codes well adapted for massively parallel supercomputers.
Chaos and maps in relativistic rynamical systems
Directory of Open Access Journals (Sweden)
L. P. Horwitz
2000-01-01
Full Text Available The basic work of Zaslavskii et al showed that the classical non-relativistic electromagnetically kicked oscillator can be cast into the form of an iterative map on the phase space; the resulting evolution contains a stochastic flow to unbounded energy. Subsequent studies have formulated the problem in terms of a relativistic charged particle in interaction with the electromagnetic field. We review the structure of the covariant Lorentz force used to study this problem. We show that the Lorentz force equation can be derived as well from the manifestly covariant mechanics of Stueckelberg in the presence of a standard Maxwell field, establishing a connection between these equations and mass shell constraints. We argue that these relativistic generalizations of the problem are intrinsically inaccurate due to an inconsistency in the structure of the relativistic Lorentz force, and show that a reformulation of the relativistic problem, permitting variations (classically in both the particle mass and the effective “mass” of the interacting electromagnetic field, provides a consistent system of classical equations for describing such processes.
Gravitational mass of relativistic matter and antimatter
Directory of Open Access Journals (Sweden)
Tigran Kalaydzhyan
2015-12-01
Full Text Available The universality of free fall, the weak equivalence principle (WEP, is a cornerstone of the general theory of relativity, the most precise theory of gravity confirmed in all experiments up to date. The WEP states the equivalence of the inertial, m, and gravitational, mg, masses and was tested in numerous occasions with normal matter at relatively low energies. However, there is no confirmation for the matter and antimatter at high energies. For the antimatter the situation is even less clear – current direct observations of trapped antihydrogen suggest the limits −65
Gravitational mass of relativistic matter and antimatter
Kalaydzhyan, Tigran
2015-01-01
The universality of free fall, the so-called weak equivalence principle (WEP), is a cornerstone of the general theory of relativity, the most precise theory of gravity confirmed in all experiments up to date. The WEP states the equivalence of the inertial and gravitational masses and was tested in numerous occasions with normal matter at relatively low energies. However, there is no proof for the matter and antimatter at high energies. %coming from ground-based experiments. For the antimatter the situation is even less clear -- current direct observations of trapped antihydrogen suggest the limits -65 < m_g / m < 110 not ruling out antigravity, i.e. repulsion of the antimatter by Earth. Here we demonstrate a bound 1 - 4x10^{-7} < m_g/m < 1 + 2x10^{-7} on the gravitational mass of relativistic electrons and positrons in the potential of the Local Supercluster (LS) coming from the Large Electron-Positron Collider (LEP) and Tevatron accelerator experiments. By considering annual variations of the sol...
Relativistic Scott correction for atoms and molecules
DEFF Research Database (Denmark)
Solovej, Jan Philip; Sørensen, Thomas Østergaard; Spitzer, Wolfgang Ludwig
2010-01-01
We prove the first correction to the leading Thomas-Fermi energy for the ground state energy of atoms and molecules in a model where the kinetic energy of the electrons is treated relativistically. The leading Thomas-Fermi energy, established in [25], as well as the correction given here, are of ......We prove the first correction to the leading Thomas-Fermi energy for the ground state energy of atoms and molecules in a model where the kinetic energy of the electrons is treated relativistically. The leading Thomas-Fermi energy, established in [25], as well as the correction given here......, are of semiclassical nature. Our result on atoms and molecules is proved from a general semiclassical estimate for relativistic operators with potentials with Coulomb-like singularities. This semiclassical estimate is obtained using the coherent state calculus introduced in [36]. The paper contains a unified treatment...
Exact quantisation of the relativistic Hopfield model
Belgiorno, F; Piazza, F Dalla; Doronzo, M
2016-01-01
We investigate the quantisation in the Heisenberg representation of a relativistically covariant version of the Hopfield model for dielectric media, which entails the interaction of the quantum electromagnetic field with the matter dipole fields. The matter fields are represented by a mesoscopic polarization field. A full quantisation of the model is provided in a covariant gauge, with the aim of maintaining explicit relativistic covariance. Breaking of the Lorentz invariance due to the intrinsic presence in the model of a preferred reference frame is also taken into account. Relativistic covariance forces us to deal with the unphysical (scalar and longitudinal) components of the fields, furthermore it introduces, in a more tricky form, the well-known dipole ghost of standard QED in a covariant gauge. In order to correctly dispose of this contribution, we implement a generalized Lautrup trick. Furthermore, causality and the relation of the model with the Wightman axioms are also discussed.
Packo, Pawel; Uhl, Tadeusz; Staszewski, Wieslaw J
2014-09-01
The paper presents an efficient and accurate method for dispersion curve calculation and analysis of numerical models for guided waves. The method can be used for any arbitrarily selected anisotropic material. The proposed approach utilizes the wave equation and through-thickness-only discretization of anisotropic, layered plates to obtain the Lamb wave characteristics. Thus, layered structures, such as composites, can be analyzed in a straightforward manner. A general framework for the proposed analysis is given, along with application examples. Although these examples are based on the local interaction simulation approach for elastic waves propagation, the proposed methodology can be easily adopted for other methods (e.g., finite elements). The method can be also used to study the influence of discretization parameters on dispersion curves estimates.
Energy Technology Data Exchange (ETDEWEB)
Debry, E.
2005-01-15
Chemical-transport models are now able to describe in a realistic way gaseous pollutants behavior in the atmosphere. Nevertheless atmospheric pollution also exists as fine suspended particles, called aerosols, which interact with gaseous phase, solar radiation, and have their own dynamic behavior. The goal of this thesis is the modelling and numerical simulation of the General Dynamic Equation of aerosols (GDE). Part I deals with some theoretical aspects of aerosol modelling. Part II is dedicated to the building of one size resolved aerosol model (SIREAM). In part III we perform the reduction of this model in order to use it in dispersion models as POLAIR3D. Several modelling issues are still opened: organic aerosol matter, externally mixed aerosols, coupling with turbulent mixing, and nano-particles. (author)
Multidimensional electron beam-plasma instabilities in the relativistic regime
BRET, ANTOINE; Gremillet, Laurent; Dieckmann, Mark Eric
2010-01-01
The interest in relativistic beam-plasma instabilities has been greatly rejuvenated over the past two decades by novel concepts in laboratory and space plasmas. Recent advances in this long-standing field are here reviewed from both theoretical and numerical points of view. The primary focus is on the two-dimensional spectrum of unstable electromagnetic waves growing within relativistic, unmagnetized, and uniform electron beam-plasma systems. Although the goal is to provide a unified picture ...
Relativistic Jet Dynamics and Calorimetry of Gamma-Ray Bursts
Wygoda, N; Frail, D
2011-01-01
We present numerical solutions of the 2D relativistic hydrodynamics equations describing the deceleration and expansion of highly relativistic conical jets, of opening angles 0.05R/c the emission of radiation from the jet blast wave is similar to that of a spherical blast wave carrying the same energy. Thus, the total (calorimetric) energy of GRB blast waves may be estimated with only a small fractional error based on t>R/c observations.
Relativistic modeling capabilities in PERSEUS extended MHD simulation code for HED plasmas
Energy Technology Data Exchange (ETDEWEB)
Hamlin, Nathaniel D., E-mail: nh322@cornell.edu [438 Rhodes Hall, Cornell University, Ithaca, NY, 14853 (United States); Seyler, Charles E., E-mail: ces7@cornell.edu [Cornell University, Ithaca, NY, 14853 (United States)
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.
Energy Technology Data Exchange (ETDEWEB)
Blair, D.G.; Buckingham, M.J. (Western Australia Univ., Nedlands (Australia). Dept. of Physics)
1989-01-01
The Marcel Grossmann Meetings have been conceived with the aim of reviewing recent developments in gravitation and general relativity, with major emphasis on mathematical foundations and physical predictions. Their main object is to elicit contributions which deepen our understanding of spacetime structure as well as to review the status of experiments testing Einstein's theory of gravitation.
Relativistic Quantum Communication
Hosler, Dominic
2013-01-01
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 tend...