Holographic Spherically Symmetric Metrics
Petri, Michael
The holographic principle (HP) conjectures, that the maximum number of degrees of freedom of any realistic physical system is proportional to the system's boundary area. The HP has its roots in the study of black holes. It has recently been applied to cosmological solutions. In this article we apply the HP to spherically symmetric static space-times. We find that any regular spherically symmetric object saturating the HP is subject to tight constraints on the (interior) metric, energy-density, temperature and entropy-density. Whenever gravity can be described by a metric theory, gravity is macroscopically scale invariant and the laws of thermodynamics hold locally and globally, the (interior) metric of a regular holographic object is uniquely determined up to a constant factor and the interior matter-state must follow well defined scaling relations. When the metric theory of gravity is general relativity, the interior matter has an overall string equation of state (EOS) and a unique total energy-density. Thus the holographic metric derived in this article can serve as simple interior 4D realization of Mathur's string fuzzball proposal. Some properties of the holographic metric and its possible experimental verification are discussed. The geodesics of the holographic metric describe an isotropically expanding (or contracting) universe with a nearly homogeneous matter-distribution within the local Hubble volume. Due to the overall string EOS the active gravitational mass-density is zero, resulting in a coasting expansion with Ht = 1, which is compatible with the recent GRB-data.
Shearfree Spherically Symmetric Fluid Models
Sharif, M
2013-01-01
We try to find some exact analytical models of spherically symmetric spacetime of collapsing fluid under shearfree condition. We consider two types of solutions: one is to impose a condition on the mass function while the other is to restrict the pressure. We obtain totally of five exact models, and some of them satisfy the Darmois conditions.
A charged spherically symmetric solution
Indian Academy of Sciences (India)
K Moodley; S D Maharaj; K S Govinder
2003-09-01
We ﬁnd a solution of the Einstein–Maxwell system of ﬁeld equations for a class of accelerating, expanding and shearing spherically symmetric metrics. This solution depends on a particular ansatz for the line element. The radial behaviour of the solution is fully speciﬁed while the temporal behaviour is given in terms of a quadrature. By setting the charge contribution to zero we regain an (uncharged) perfect ﬂuid solution found previously with the equation of state =+ constant, which is a generalisation of a stiff equation of state. Our class of charged shearing solutions is characterised geometrically by a conformal Killing vector.
Spherically symmetric scalar field collapse
Indian Academy of Sciences (India)
Koyel Ganguly; Narayan Banerjee
2013-03-01
It is shown that a scalar field, minimally coupled to gravity, may have collapsing modes even when the energy condition is violated, that is, for ( + 3) < 0. This result may be useful in the investigation of the possible clustering of dark energy. All the examples dealt with have apparent horizons formed before the formation of singularity. The singularities formed are shell focussing in nature. The density of the scalar field distribution is seen to diverge at singularity. The Ricci scalar also diverges at the singularity. The interior spherically symmetric metric is matched with exterior Vaidya metric at the hypersurface and the appropriate junction conditions are obtained.
Spherically symmetric brane spacetime with bulk gravity
Chakraborty, Sumanta; SenGupta, Soumitra
2015-01-01
Introducing term in the five-dimensional bulk action we derive effective Einstein's equation on the brane using Gauss-Codazzi equation. This effective equation is then solved for different conditions on dark radiation and dark pressure to obtain various spherically symmetric solutions. Some of these static spherically symmetric solutions correspond to black hole solutions, with parameters induced from the bulk. Specially, the dark pressure and dark radiation terms (electric part of Weyl curvature) affect the brane spherically symmetric solutions significantly. We have solved for one parameter group of conformal motions where the dark radiation and dark pressure terms are exactly obtained exploiting the corresponding Lie symmetry. Various thermodynamic features of these spherically symmetric space-times are studied, showing existence of second order phase transition. This phenomenon has its origin in the higher curvature term with gravity in the bulk.
Onthe static and spherically symmetric gravitational field
Gottlieb, Ioan; Maftei, Gheorghe; Mociutchi, Cleopatra
Starting from a generalization of Einstein 's theory of gravitation, proposed by one of the authors (Cleopatra Mociutchi), the authors study a particular spherical symmetric case. Among other one obtain the compatibility conditions for the existence of the static and spherically symmetruic gravitational filed in the case of extended Einstein equation.
Acik, O; Önder, M; Vercin, A
2008-01-01
Killing-Yano (KY) two and three forms of a class of spherically symmetric space-times that includes the well-known Minkowski, Schwarzschild, Reissner-Nordstrom, Robertson-Walker and six different forms of de Sitter space-times as special cases are derived in a unified and exhaustive manner. It is directly proved that while the Schwarzschild and Reissner-Nordstrom space-times do not accept any KY 3-form and they accept only one 2-form, the Robertson-Walker space-time admits four KY 2-forms and only one KY 3-form. Maximal number of KY-forms are obtained for Minkowski and all known forms of de Sitter space-times. Complete lists comprising explicit expressions of KY-forms are given.
On noncommutative spherically symmetric spaces
Energy Technology Data Exchange (ETDEWEB)
Buric, Maja [University of Belgrade, Faculty of Physics, P.O. Box 44, Belgrade (Serbia); Madore, John [Laboratoire de Physique Theorique, Orsay (France)
2014-03-15
Two families of noncommutative extensions are given of a general space-time metric with spherical symmetry, both based on the matrix truncation of the functions on the sphere of symmetry. The first family uses the truncation to foliate space as an infinite set of spheres, and it is of dimension four and necessarily time-dependent; the second can be time-dependent or static, is of dimension five, and uses the truncation to foliate the internal space. (orig.)
On noncommutative spherically symmetric spaces
Buric, Maja
2014-01-01
Two families of noncommutative extensions are given of a general space-time metric with spherical symmetry, both based on the matrix truncation of the functions on the sphere of symmetry. The first family uses the truncation to foliate space as an infinite set of spheres, is of dimension four and necessarily time-dependent; the second can be time-dependent or static, is of dimension five and uses the truncation to foliate the internal space.
Inflation in spherically symmetric inhomogeneous models
Energy Technology Data Exchange (ETDEWEB)
Stein-Schabes, J.A.
1986-11-01
Exact analytical solutions of Einstein's equations are found for a spherically symmetric inhomogeneous metric in the presence of a massless scalar field with a flat potential. The process of isotropization and homogenization is studied in detail. It is found that the time dependence of the metric becomes de Sitter for large times. Two cases are studied. The first deals with a homogeneous scalar field, while the second with a spherically symmetric inhomogeneous scalar field. In the former case the metric is of the Robertson-Walker form, while the latter is intrinsically inhomogeneous. 16 refs.
Noncommutative spherically symmetric spacetimes at semiclassical order
Fritz, Christopher
2016-01-01
Working within the recent formalism of Poisson-Riemannian geometry, we completely solve the case of generic spherically symmetric metric and spherically symmetric Poisson-bracket to find a unique answer for the quantum differential calculus, quantum metric and quantum Levi-Civita connection at semiclassical order $O(\\lambda)$. Here $\\lambda$ is the deformation parameter, plausibly the Planck scale. We find that $r,t,dr,dt$ are all forced to be central, i.e. undeformed at order $\\lambda$, while for each value of $r,t$ we are forced to have a fuzzy sphere of radius $r$ with a unique differential calculus which is necessarily nonassociative at order $\\lambda^2$. We give the spherically symmetric quantisation of the FLRW cosmology in detail and also recover a previous analysis for the Schwarzschild black hole, now showing that the quantum Ricci tensor for the latter vanishes at order $\\lambda$. The quantum Laplace-Beltrami operator for spherically symmetric models turns out to be undeformed at order $\\lambda$ whi...
Realizability of stationary spherically symmetric transonic accretion
Ray, A K; Ray, Arnab K.
2002-01-01
The spherically symmetric stationary transonic (Bondi) flow is considered a classic example of an accretion flow. This flow, however, is along a separatrix, which is usually not physically realizable. We demonstrate, using a pedagogical example, that it is the dynamics which selects the transonic flow.
Static spherically symmetric wormholes with isotropic pressure
Cataldo, Mauricio; Rodríguez, Pablo
2016-01-01
In this paper we study static spherically symmetric wormhole solutions sustained by matter sources with isotropic pressure. We show that such spherical wormholes do not exist in the framework of zero-tidal-force wormholes. On the other hand, it is shown that for the often used power-law shape function there is no spherically symmetric traversable wormholes sustained by sources with a linear equation of state $p=\\omega \\rho$ for the isotropic pressure, independently of the form of the redshift function $\\phi(r)$. We consider a solution obtained by Tolman at 1939 for describing static spheres of isotropic fluids, and show that it also may describe wormhole spacetimes with a power-law redshift function, which leads to a polynomial shape function, generalizing a power-law shape function, and inducing a solid angle deficit.
Spherically Symmetric, Self-Similar Spacetimes
Wagh, S M; Wagh, Sanjay M.; Govinder, Keshlan S.
2001-01-01
Self-similar spacetimes are of importance to cosmology and to gravitational collapse problems. We show that self-similarity or the existence of a homothetic Killing vector field for spherically symmetric spacetimes implies the separability of the spacetime metric in terms of the co-moving coordinates and that the metric is, uniquely, the one recently reported in [cqg1]. The spacetime, in general, has non-vanishing energy-flux and shear. The spacetime admits matter with any equation of state.
Design of spherical symmetric gradient index lenses
Miñano, Juan C.; Grabovičkić, Dejan; Benítez, Pablo; González, Juan C.; Santamaría, Asunción
2012-10-01
Spherical symmetric refractive index distributions also known as Gradient Index lenses such as the Maxwell-Fish-Eye (MFE), the Luneburg or the Eaton lenses have always played an important role in Optics. The recent development of the technique called Transformation Optics has renewed the interest in these gradient index lenses. For instance, Perfect Imaging within the Wave Optics framework has recently been proved using the MFE distribution. We review here the design problem of these lenses, classify them in two groups (Luneburg moveable-limits and fixed-limits type), and establish a new design techniques for each type of problem.
Diakogiannis, Foivos I; Ibata, Rodrigo A
2014-01-01
The spherical Jeans equation is widely used to estimate the mass content of a stellar systems with apparent spherical symmetry. However, this method suffers from a degeneracy between the assumed mass density and the kinematic anisotropy profile, $\\beta(r)$. In a previous work, we laid the theoretical foundations for an algorithm that combines smoothing B-splines with equations from dynamics to remove this degeneracy. Specifically, our method reconstructs a unique kinematic profile of $\\sigma_{rr}^2$ and $\\sigma_{tt}^2$ for an assumed free functional form of the potential and mass density $(\\Phi,\\rho)$ and given a set of observed line-of-sight velocity dispersion measurements, $\\sigma_{los}^2$. In Paper I (submitted to MNRAS: MN-14-0101-MJ) we demonstrated the efficiency of our algorithm with a very simple example and we commented on the need for optimum smoothing of the B-spline representation; this is in order to avoid unphysical variational behaviour when we have large uncertainty in our data. In the curren...
Critical behavior of spherically symmetric domain wall collapse
Ikeda, Taishi
2016-01-01
Critical collapse of a spherically symmetric domain wall is investigated. The domain wall is made of a minimally coupled scalar field with a double well potential. We consider a sequence of the initial data which describe a momentarily static domain wall characterized by its initial radius. The time evolution is performed by a full general relativistic numerical code for spherically symmetric systems. In this paper, we use the maximal slice gauge condition, in which spacelike time slices may penetrate the black hole horizon differently from other widely used procedures. In this paper, we consider two specific shapes of the double well potential, and observe the Type II critical behavior in both cases. The mass scaling, sub-critical curvature scaling, and those fine structures are confirmed. The index of the scaling behavior agrees with the massless scalar case.
Exact Spherically Symmetric Solutions in Massive Gravity
Berezhiani, Z; Nesti, F; Pilo, L
2008-01-01
A phase of massive gravity free from pathologies can be obtained by coupling the metric to an additional spin-two field. We study the gravitational field produced by a static spherically symmetric body, by finding the exact solution that generalizes the Schwarzschild metric to the case of massive gravity. Besides the usual 1/r term, the main effects of the new spin-two field are a shift of the total mass of the body and the presence of a new power-like term, with sizes determined by the mass and the shape (the radius) of the source. These modifications, being source dependent, give rise to a dynamical violation of the Strong Equivalence Principle. Depending on the details of the coupling of the new field, the power-like term may dominate at large distances or even in the ultraviolet. The effect persists also when the dynamics of the extra field is decoupled.
Dynamical systems and spherically symmetric cosmological models
He, Yanjing
2006-06-01
In this thesis we present a study of the timelike self-similar spherically symmetric cosmological models with two scalar fields with exponential potentials. We first define precisely the timelike self-similar spherically symmetric (TSS) spacetimes. We write the TSS metric in a conformally isometric form in a coordinate system adapted to the geometry of the spacetime manifold. In this coordinate system, both the metric functions of the TSS spacetimes and the potential functions of the scalar fields can be simplified to four undetermined functions of a single coordinate. As a result, the Einstein field equations reduce to an autonomous system of first-order ODEs and polynomial constraints in terms of these undetermined functions. By introducing new bounded variables as well as a new independent variable and solving the constraints, we are able to apply the theory of dynamical systems to study the properties of the TSS solutions. By finding invariant sets and associated monotonic functions, by applying the LaSalle Invariance Principle and the Monotonicity Principle, by applying the [straight phi] t -connected property of a limit set, and using other theorems, we prove that all of the TSS trajectories are heteroclinic trajectories. In addition, we conduct numerical simulations to confirm and support the qualitative analysis. We obtain all possible types of TSS solutions, by analyzing the qualitative behavior of the original system of ODES from those of the reduced one. We obtain asymptotic expressions for the TSS solutions (e.g., the asymptotic expressions for the metric functions, the source functions and the Ricci scalar). In particular, self-similar flat Friedmann-Robertson-Walker spacetimes are examined in order to obtain insights into the issues related to the null surface in general TSS spacetimes in these coordinates. A discussion of the divergence of the spacetime Ricci scalar and the possible extension of the TSS solutions across the null boundary is presented
Spherically symmetric conformal gravity and "gravitational bubbles"
Berezin, V A; Eroshenko, Yu N
2016-01-01
The general structure of the spherically symmetric solutions in the Weyl conformal gravity is described. The corresponding Bach equation are derived for the special type of metrics, which can be considered as the representative of the general class. The complete set of the pure vacuum solutions is found. It consists of two classes. The first one contains the solutions with constant two-dimensional curvature scalar of our specific metrics, and the representatives are the famous Robertson-Walker metrics. One of them we called the "gravitational bubbles", which is compact and with zero Weyl tensor. The second class is more general, with varying curvature scalar. We found its representative as the one-parameter family. It appears that it can be conformally covered by the thee-parameter Mannheim-Kazanas solution. We also investigated the general structure of the energy-momentum tensor in the spherical conformal gravity and constructed the vectorial equation that reveals clearly the same features of non-vacuum solu...
Transport coefficients for rigid spherically symmetric polymers or aggregates
Strating, P.; Wiegel, F.W.
1994-01-01
In this paper we investigate the transport properties for rigid spherically symmetric macromolecules, having a segment density distribution falling off as r- lambda . We calculate the rotational and translational diffusion coefficient for a spherically symmetric polymer and the shear viscosity for a
Complete classification of spherically symmetric static spacetimes via Noether symmetries
Ali, Farhad; Ali, Sajid
2013-01-01
In this paper we give a complete classification of spherically symmetric static space-times by their Noether symmetries. The determining equations for Noether symmetries are obtained by using the usual Lagrangian of a general spherically symmetric static spacetime which are integrated for each case. In particular we observe that spherically symmetric static spacetimes are categorized into six distinct classes corresponding to Noether algebra of dimensions 5, 6, 7, 9, 11 and 17. Using Noether`s theorem we also write down the first integrals for each class of such spacetimes corresponding to their Noether symmetries.
Spherically symmetric brane spacetime with bulk f(R) gravity
Energy Technology Data Exchange (ETDEWEB)
Chakraborty, Sumanta [IUCAA, Ganeshkhind, Pune University Campus, Post Bag 4, Pune (India); SenGupta, Soumitra [Indian Association for the Cultivation of Science, Department of Theoretical Physics, Kolkata (India)
2015-01-01
Introducing f(R) term in the five-dimensional bulk action we derive effective Einstein's equation on the brane using Gauss-Codazzi equation. This effective equation is then solved for different conditions on dark radiation and dark pressure to obtain various spherically symmetric solutions. Some of these static spherically symmetric solutions correspond to black hole solutions, with parameters induced from the bulk. Specially, the dark pressure and dark radiation terms (electric part of Weyl curvature) affect the brane spherically symmetric solutions significantly. We have solved for one parameter group of conformal motions where the dark radiation and dark pressure terms are exactly obtained exploiting the corresponding Lie symmetry. Various thermodynamic features of these spherically symmetric space-times are studied, showing existence of second order phase transition. This phenomenon has its origin in the higher curvature term with f(R) gravity in the bulk. (orig.)
Bayesian variable selection with spherically symmetric priors
De Kock, M. B.; Eggers, H. C.
2014-01-01
We propose that Bayesian variable selection for linear parametrisations with Gaussian iid likelihoods be based on the spherical symmetry of the diagonalised parameter space. Our r-prior results in closed forms for the evidence for four examples, including the hyper-g prior and the Zellner-Siow prior, which are shown to be special cases. Scenarios of a single variable dispersion parameter and of fixed dispersion are studied, and asymptotic forms comparable to the traditional information criter...
Spherically symmetric black-hole entropy without brick walls
Ren, Zhao; Yue-Qin, Wu; Li-Chun, Zhang
2003-11-01
Properties of the thermal radiation of black holes are discussed using a new equation of state density motivated by the generalized uncertainty relation in quantum gravity. There is no burst at the last stage of emission from a spherically symmetric black hole. When the new equation of state density is used to investigate the entropy of a bosonic field and fermionic field outside the horizon of a static spherically symmetric black hole, the divergence that appears in the brick-wall model is removed without any cutoff. The entropy proportional to the horizon area is derived from the contribution from the vicinity of the horizon.
Accretion processes for general spherically symmetric compact objects
Energy Technology Data Exchange (ETDEWEB)
Bahamonde, Sebastian [University College London, Department of Mathematics, London (United Kingdom); Jamil, Mubasher [National University of Sciences and Technology (NUST), H-12, Department of Mathematics, School of Natural Sciences (SNS), Islamabad (Pakistan)
2015-10-15
We investigate the accretion process for different spherically symmetric space-time geometries for a static fluid. We analyze this procedure using the most general black hole metric ansatz. After that, we examine the accretion process for specific spherically symmetric metrics obtaining the velocity of the sound during the process and the critical speed of the flow of the fluid around the black hole. In addition, we study the behavior of the rate of change of the mass for each chosen metric for a barotropic fluid. (orig.)
Accretion Processes for General Spherically Symmetric Compact Objects
Bahamonde, Sebastian
2015-01-01
We investigate the accretion process for different spherically symmetric space-time geometries for a static fluid. We analyse this procedure using the most general black hole metric ansatz. After that, we examine the accretion process for specific spherically symmetric metrics obtaining the velocity of the sound during the process and the critical speed of the flow of the fluid around the black hole. In addition, we study the behaviour of the rate of change of the mass for each chosen metric for a barotropic fluid.
Geometric inequalities in spherically symmetric spacetimes
Csukás, Károly Zoltán
2016-01-01
ADM mass is usually preferred against using quasi-local notions of mass in deriving geometric inequalities. We are interested in testing if usage of quasi-local mass provide any benefits. In spherical symmetry there is a highly accepted notion: the Misner-Sharp mass. It is closely related to the energy contained within a 2-surface and its null-expansions, which are used to determine if a surface is trapped. We use it to investigate inequalities between black hole's, Cauchy surface's and normal body's measurable parameters. There are investigations involving quasi-local charge and area. Our aim is to involv quasi-local mass too. This method support wide range of known inequalities and provide some new ones involving mass.
Thermodynamic motivations of spherically symmetric static metrics
Moradpour, H
2015-01-01
Bearing the thermodynamic arguments together with the two definitions of mass in mind, we try to find metrics with spherical symmetry. We consider the adiabatic condition along with the Gong-Wang mass, and evaluate the $g_{rr}$ element which points to a null hypersurface. In addition, we generalize the thermodynamics laws to this hypersurface to find its temperature and thus the corresponding surface gravity which enables us to get a relation for the $g_{tt}$ element. Finally, we investigate the mathematical and physical properties of the discovered metric in the Einstein relativity framework which shows that the primary mentioned null hypersurface is an event horizon. We also show that if one considers the Misner-Sharp mass in the calculations, the Schwarzschild metric will be got. The relationship between the two mass definitions in each metric is studied. The results of considering the geometrical surface gravity are also addressed.
Naked Singularities in Spherically Symmetric, Self-Similar Spacetimes
Wagh, S M; Wagh, Sanjay M.; Govinder, Keshlan S.
2001-01-01
We show that all known naked singularities in spherically symmetric self-similar spacetimes arise as a result of singular initial matter distribution. This is a result of the peculiarity of the coordinate transformation that takes these spacetimes into a separable form. Therefore, these examples of naked singularities are of no apparent consequence to astrophysical observations or theories.
Composite spherically symmetric configurations in Jordan-Brans-Dicke theory
Kozyrev, S
2010-01-01
In this article, a study of the scalar field shells in relativistic spherically symmetric configurations has been performed. We construct the composite solution of Jordan-Brans-Dicke field equation by matching the conformal Brans solutions at each junction surfaces. This approach allows us to associate rigorously with all solutions as a single glued "space", which is a unique differentiable manifold M^4.
Spacelike spherically symmetric CMC foliation in the extended Schwarzschild spacetime
Lee, Kuo-Wei
2015-01-01
We first summarize the characterization of smooth spacelike spherically symmetric constant mean curvature (SS-CMC) hypersurfaces in the Schwarzschild spacetime and Kruskal extension. Then use the characterization to prove special SS-CMC foliation property, and verify part of the conjecture by Malec and \\'{O} Murchadha in their 2003 paper.
Axially and spherically symmetric solitons in warm plasma
Dvornikov, Maxim
2010-01-01
We study the existence of stable axially and spherically symmetric plasma structures on the basis of the new nonlinear Schrodinger equation (NLSE) accounting for nonlocal electron nonlinearities. The numerical solutions of NLSE having the form of spatial solitions are obtained and their stability is analyzed. We discuss the possible application of the obtained results to the theoretical description of natural plasmoids in the atmosphere.
Thermodynamic Volume Product in Spherically Symmetric and Axisymmetric Spacetime
Pradhan, Parthapratim
2016-01-01
In this Letter, we compute particularly thermodynamic \\emph{volume product, volume sum, volume minus and volume division} for wide variety of spherically symmetric spacetime and axisymmetric spacetime in the frame work of \\emph{extended phase space}. We consider Einstein gravity as well as other than Einstein gravity i.e. \\emph{Ho\\v{r}ava Lifshitz} gravity. We speculate that for spherically symmetric black holes the volume product is mass-independent both in Einstein gravity as well as Ho\\v{r}ava Lifshitz gravity while the other combination is mass-dependent. For axisymmetric black hole spacetime in Einstein gravity all the combination is \\emph{mass-dependent}. There has been no chance to generate any combination of volume product is mass-independent. Interestingly, \\emph{only rotating BTZ black hole} in 3D provides the volume product formula is mass-independent i.e. \\emph{universal} and hence it is quantized.
The inverse spatial Laplacian of spherically symmetric spacetimes
Fernandes, Karan
2016-01-01
In this paper we derive the inverse spatial Laplacian for static, spherically symmetric backgrounds by solving Poisson's equation for a point source. This is different from the electrostatic Green function, which is defined on the four dimensional static spacetime, while the equation we consider is defined on the spatial hypersurface of such spacetimes. This Green function is relevant in the Hamiltonian dynamics of theories defined on spherically symmetric backgrounds, and closed form expressions for the solutions we find are absent in the literature. We derive an expression in terms of elementary functions for the Schwarzschild spacetime, and comment on the relation of this solution with the known Green function of the spacetime Laplacian operator. We also find an expression for the Green function on the static pure de Sitter space in terms of hypergeometric functions.
Relativistic electromagnetic mass models in spherically symmetric spacetime
Maurya, S K; Ray, Saibal; Chatterjee, Vikram
2015-01-01
Under the static spherically symmetric Einstein-Maxwell spacetime of embedding class one we explore possibility of electromagnetic mass model where mass and other physical parameters have purely electromagnetic origin (Tiwari 1984, Gautreau 1985, Gron 1985). This work is in continuation of our earlier investigation (Maurya 2015a) where we developed an algorithm and found out three new solutions of electromagnetic mass models. In the present letter we consider different metric potentials $\
An introduction to spherically symmetric loop quantum gravity black holes
Energy Technology Data Exchange (ETDEWEB)
Gambini, Rodolfo [Instituto de Física, Facultad de Ciencias, Iguá 4-225, esq. Mataojo, 11400 Montevideo (Uruguay); Pullin, Jorge [Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803-4001 (United States)
2015-03-26
We review recent developments in the treatment of spherically symmetric black holes in loop quantum gravity. In particular, we discuss an exact solution to the quantum constraints that represents a black hole and is free of singularities. We show that new observables that are not present in the classical theory arise in the quantum theory. We also discuss Hawking radiation by considering the quantization of a scalar field on the quantum spacetime.
Constrained field theories on spherically symmetric spacetimes with horizons
Fernandes, Karan; Lahiri, Amitabha; Ghosh, Suman
2017-02-01
We apply the Dirac-Bergmann algorithm for the analysis of constraints to gauge theories defined on spherically symmetric black hole backgrounds. We find that the constraints for a given theory are modified on such spacetimes through the presence of additional contributions from the horizon. As a concrete example, we consider the Maxwell field on a black hole background, and determine the role of the horizon contributions on the dynamics of the theory.
Constrained field theories on spherically symmetric spacetimes with horizons
Fernandes, Karan; Lahiri, Amitabha
2016-01-01
We apply the Dirac-Bergmann algorithm for the analysis of constraints to gauge theories defined on spherically symmetric black hole backgrounds. As a concrete example, we consider the Maxwell field on a black hole background, and determine the role of the horizon contributions on the dynamics of the theory. We find that the constraints are modified on such spacetimes through the presence of additional contributions from the horizon.
Gyroid phase of fluids with spherically symmetric competing interactions.
Edelmann, Markus; Roth, Roland
2016-06-01
We study the phase diagram of a fluid with spherically symmetric competing pair interactions that consist of a short-ranged attraction and a longer-ranged repulsion in addition to a hard core. To this end we perform free minimizations of three-dimensional triple periodic structures within the framework of classical density functional theory. We compare our results to those from Landau theory. Our main finding is that the double gyroid phase can exist as a thermodynamically stable phase.
Revisiting the quantum scalar field in spherically symmetric quantum gravity
Borja, Enrique F; Strobel, Eckhard
2012-01-01
We extend previous results in spherically symmetric gravitational systems coupled with a massless scalar field within the loop quantum gravity framework. As starting point, we take the Schwarzschild spacetime. The results presented here rely on the uniform discretization method. We are able to minimize the associated discrete master constraint using a variational method. The trial state for the vacuum consists of a direct product of a Fock vacuum for the matter part and a Gaussian centered around the classical Schwarzschild solution. This paper follows the line of research presented by Gambini, Pullin and Rastgoo and a comparison between their result and the one given in this work is made.
Minimal Length Effects on Tunnelling from Spherically Symmetric Black Holes
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Benrong Mu
2015-01-01
Full Text Available We investigate effects of the minimal length on quantum tunnelling from spherically symmetric black holes using the Hamilton-Jacobi method incorporating the minimal length. We first derive the deformed Hamilton-Jacobi equations for scalars and fermions, both of which have the same expressions. The minimal length correction to the Hawking temperature is found to depend on the black hole’s mass and the mass and angular momentum of emitted particles. Finally, we calculate a Schwarzschild black hole's luminosity and find the black hole evaporates to zero mass in infinite time.
Energy of Gravitational Field of Static Spherically Symmetric Neutron Stars
Institute of Scientific and Technical Information of China (English)
WENDe-Hua; CHENWei; WANGXian-Ju; AIBao-Quan; LIUGuo-Tao; LIULiang-Gang
2003-01-01
By using the Einstein-Tolman expression of the energy-momentum pseudo-tensor, the energy density of the gravitational field of the static spherically symmetric neutron stars is calculated in the Cartesian coordinate system.It is exciting that the energy density of gravitational field is positive and rational The xmmerical results of the energy density of gravitational field of neutron stars are calculated. For neutron stars with M=2M, the ratio of the energy density of gravitational field to the energy density of pure matters would be up to 0.54 at the surface.
All spherically symmetric charged anisotropic solutions for compact stars
Energy Technology Data Exchange (ETDEWEB)
Maurya, S.K. [University of Nizwa, Department of Mathematical and Physical Sciences, College of Arts and Science, Nizwa (Oman); Gupta, Y.K. [Raj Kumar Goel Institute of Technology, Department of Mathematics, Ghaziabad, UP (India); Ray, Saibal [Government College of Engineering and Ceramic Technology, Department of Physics, Kolkata, West Bengal (India)
2017-06-15
In the present paper we develop an algorithm for all spherically symmetric anisotropic charged fluid distributions. Considering a new source function ν(r) we find a set of solutions which is physically well behaved and represents compact stellar models. A detailed study specifically shows that the models actually correspond to strange stars in terms of their mass and radius. In this connection we investigate several physical properties like energy conditions, stability, mass-radius ratio, electric charge content, anisotropic nature and surface redshift through graphical plots and mathematical calculations. All the features from these studies are in excellent agreement with the already available evidence in theory as well as observations. (orig.)
Labeling spherically symmetric spacetimes with the Ricci tensor
Ferrando, Joan Josep; Sáez, Juan Antonio
2017-02-01
We complete the intrinsic characterization of spherically symmetric solutions partially accomplished in a previous paper (Ferrando and Sáez 2010 Class. Quantum Grav. 27 205024). In this approach we consider every compatible algebraic type of the Ricci tensor, and we analyze specifically the conformally flat case for perfect fluid and Einstein–Maxwell solutions. As a direct application we obtain the ideal labeling (exclusively involving explicit concomitants of the metric tensor) of the Schwarzschild interior metric and the Vaidya solution. The Stephani universes and some significative subfamilies are also characterized.
Spherically symmetric solution in a space-time with torsion
Farfan, Filemon; Loaiza-Brito, Oscar; Moreno, Claudia; Yakhno, Alexander
2011-01-01
By using the analysis group method, we obtain a new exact evolving and spherically symmetric solution of the Einstein-Cartan equations of motion, corresponding to a space-time threaded with a three-form Kalb-Ramond field strength. The solution describes in its more generic form, a space-time which scalar curvature vanishes for large distances and for large time. In static conditions, it reduces to a classical wormhole solution already reported in literature. In the process we have found evidence towards the construction of more new solutions.
Multihorizon spherically symmetric spacetimes with several scales of vacuum energy
Bronnikov, Kirill; Dymnikova, Irina; Galaktionov, Evgeny
2012-05-01
We present a family of spherically symmetric multihorizon spacetimes with a vacuum dark fluid, associated with a time-dependent and spatially inhomogeneous cosmological term. The vacuum dark fluid is defined in a model-independent way by the symmetry of its stress-energy tensor, i.e. its invariance under Lorentz boosts in a distinguished spatial direction (pr = -ρ for the spherically symmetric fluid), which makes dark fluid essentially anisotropic and allows its density to evolve. The related cosmological models belong to the Lemaître class of models with anisotropic fluids and describe evolution of a universe with several scales of vacuum energy related to phase transitions during its evolution. The typical behavior of solutions and the number of spacetime horizons are determined by the number of vacuum scales. We study in detail the model with three vacuum scales: GUT, QCD and that responsible for the present accelerated expansion. The model parameters are fixed by the observational data and by conditions of analyticity and causality. We find that our Universe has three horizons. During the first inflation, the Universe enters a T-region, which makes expansion irreversible. After second phase transition at the QCD scale, the Universe enters R-region, where for a long time its geometry remains almost pseudo-Euclidean. After crossing the third horizon related to the present vacuum density, the Universe should have to enter the next T-region with the inevitable expansion.
Revisiting the quantum scalar field in spherically symmetric quantum gravity
Borja, Enrique F.; Garay, Iñaki; Strobel, Eckhard
2012-07-01
We extend previous results in spherically symmetric gravitational systems coupled with a massless scalar field within the loop quantum gravity framework. As a starting point, we take the Schwarzschild spacetime. The results presented here rely on the uniform discretization method. We are able to minimize the associated discrete master constraint using a variational method. The trial state for the vacuum consists of a direct product of a Fock vacuum for the matter part and a Gaussian centered around the classical Schwarzschild solution. This paper follows the line of research presented by Gambini et al (2009 Class. Quantum Grav. 26 215011 (arXiv:0906.1774v1)) and a comparison between their result and the one given in this work is made.
Spherically symmetric Einstein-aether perfect fluid models
Coley, Alan A; Sandin, Patrik; Latta, Joey
2015-01-01
We investigate spherically symmetric cosmological models in Einstein-aether theory with a tilted (non-comoving) perfect fluid source. We use a 1+3 frame formalism and adopt the comoving aether gauge to derive the evolution equations, which form a well-posed system of first order partial differential equations in two variables. We then introduce normalized variables. The formalism is particularly well-suited for numerical computations and the study of the qualitative properties of the models, which are also solutions of Horava gravity. We study the local stability of the equilibrium points of the resulting dynamical system corresponding to physically realistic inhomogeneous cosmological models and astrophysical objects with values for the parameters which are consistent with current constraints. In particular, we consider dust models in ($\\beta-$) normalized variables and derive a reduced (closed) evolution system and we obtain the general evolution equations for the spatially homogeneous Kantowski-Sachs model...
Static spherically symmetric wormholes in f(R, T) gravity
Energy Technology Data Exchange (ETDEWEB)
Zubair, M.; Ahmad, Yasir [Institute Of Information Technology, Department of Mathematics, COMSATS, Lahore (Pakistan); Waheed, Saira [Prince Mohammad Bin Fahd University, Al Khobar (Saudi Arabia)
2016-08-15
In this work, we explore wormhole solutions in f(R, T) theory of gravity, where R is the scalar curvature and T is the trace of stress-energy tensor of matter. To investigate this, we consider a static spherically symmetric geometry with matter contents as anisotropic, isotropic, and barotropic fluids in three separate cases. By taking into account the Starobinsky f(R) model, we analyze the behavior of energy conditions for these different kinds of fluids. It is shown that the wormhole solutions can be constructed without exotic matter in few regions of space-time. We also give the graphical illustration of the results obtained and discuss the equilibrium picture for the anisotropic case only. It is concluded that the wormhole solutions with anisotropic matter are realistic and stable in this theory of gravity. (orig.)
Information entropy for static spherically symmetric black holes
Institute of Scientific and Technical Information of China (English)
Jiang Ji-Jian; Li Chuan-An
2009-01-01
By using the new equation of state density derived from the generalized uncertainty relation, the number of the quantum states near event horizon is obtained, with which then the information entropy of static spherically symmetric black holes has been discussed. It is found that the divergent integral of quantum states near the event horizon can be naturally avoided if using the new equation of state density without introducing the ultraviolet cut-off. The information entropy of black holes can be obtained precisely by the residue theorem, which is shown to be proportional to the horizon area. The information entropy of black holes obtained agrees with the Bechenstein-Hawking entropy when the suitable cutoff factor is adopted.
Timelike geodesics around a charged spherically symmetric dilaton black hole
Directory of Open Access Journals (Sweden)
Blaga C.
2015-01-01
Full Text Available In this paper we study the timelike geodesics around a spherically symmetric charged dilaton black hole. The trajectories around the black hole are classified using the effective potential of a free test particle. This qualitative approach enables us to determine the type of orbit described by test particle without solving the equations of motion, if the parameters of the black hole and the particle are known. The connections between these parameters and the type of orbit described by the particle are obtained. To visualize the orbits we solve numerically the equation of motion for different values of parameters envolved in our analysis. The effective potential of a free test particle looks different for a non-extremal and an extremal black hole, therefore we have examined separately these two types of black holes.
Entropy of N-Dimensional Spherically Symmetric Charged Black Hole
Institute of Scientific and Technical Information of China (English)
ZHAO Ren; WU Yue-Qin; ZHANG Li-Chun
2003-01-01
By using the method of quantum statistics, we derive directly the partition functions of bosonic andfermionic fields in the N-dimensional spherically symmetric charged black hole space-time. The statistical entropy ofblack hole is obtained by an improved brick-wall method. When we choose proper parameters in our results, we canobtain that the entropy of black hole is proportional to the area of horizon. In our result, there do not exist neglectedterm and divergent logarithmic term given in the original brick-wall method. We avoid the difficulty in solving the waveequation of scalar and Dirac fields. We offer a simple and direct way of studying entropy of the higher-dimensional black hole.
Triple-horizon spherically symmetric spacetime and holographic principle
Dymnikova, Irina
2012-01-01
We present a family of spherically symmetric spacetimes, specified by the density profile of a vacuum dark energy, which have the same global structure as the de Sitter spacetime but the reduced symmetry which leads to a time-evolving and spatially inhomogeneous cosmological term. It connects smoothly two de Sitter vacua with different values of cosmological constant and corresponds to anisotropic vacuum dark fluid defined by symmetry of its stress-energy tensor which is invariant under the radial boosts. This family contains a special class distinguished by dynamics of evaporation of a cosmological horizon which evolves to the triple horizon with the finite entropy, zero temperature, zero curvature, infinite positive specific heat, and infinite scrambling time. Non-zero value of the cosmological constant in the triple-horizon spacetime is tightly fixed by quantum dynamics of evaporation of the cosmological horizon.
Spherically Symmetric Solutions in Higher-Derivative Gravity
Lü, H; Pope, C N; Stelle, K S
2015-01-01
Extensions of Einstein gravity with quadratic curvature terms in the action arise in most effective theories of quantised gravity, including string theory. This article explores the set of static, spherically symmetric and asymptotically flat solutions of this class of theories. An important element in the analysis is the careful treatment of a Lichnerowicz-type `no-hair' theorem. From a Frobenius analysis of the asymptotic small-radius behaviour, the solution space is found to split into three asymptotic families, one of which contains the classic Schwarzschild solution. These three families are carefully analysed to determine the corresponding numbers of free parameters in each. One solution family is capable of arising from coupling to a distributional shell of matter near the origin; this family can then match on to an asymptotically flat solution at spatial infinity without encountering a horizon. Another family, with horizons, contains the Schwarzschild solution but includes also non-Schwarzschild black...
On the quantum levels of isolated spherically symmetric gravitational systems
Kastrup, H A
1996-01-01
The known canonical quantum theory of a spherically symmetric pure (Schwarzschild) gravitational system describes isolated black holes by plane waves exp(-iMc^2\\tau/\\hbar) with respect to their continuous masses M and the proper time \\tau of observers at spatial infinity. On the other hand Bekenstein and Mukhanov postulated discrete mass levels for such black holes in the spirit of the Bohr- Sommerfeld quantisation in atomic physics. The two approaches can be related by postulating periodic boundary conditions in time for the plane waves and by iden- tifying the period \\Delta in real time with the period \\Delta_H = 8\\pi GM/c^3 in Euclidean time. This yields the mass spectrum M_n = (1/2)\\sqrt{n}m_P, n=1,2,...
Static spherically symmetric metrics and their cosmological interpretation
Velez, Camilo Santa
2016-01-01
We find the transformation between static coordinates and the Newton gauge for the Schwarzschild-De-Sitter (SDS) solution, confirming it coincides with the weak field limit of the McVittie solution. We then consider different generalized classes of static spherically symmetric (SSS) metrics and using the same method we transform them to the Newton gauge, which could be used to test these modifications of the SDS solution using physical observables which are more conveniently computed within the framework of cosmological perturbation theory. Using the gauge invariance of the Bardeen potentials we then obtain a gauge invariant definition of the turn around radius, checking it is consistent with the result obtained in static coordinates for the SDS metric and for other SSS metrics.
Relativistic electromagnetic mass models in spherically symmetric spacetime
Maurya, S. K.; Gupta, Y. K.; Ray, Saibal; Chatterjee, Vikram
2016-10-01
Under the static spherically symmetric Einstein-Maxwell spacetime of embedding class one we explore possibility of constructing electromagnetic mass model where mass and other physical parameters have purely electromagnetic origin (Lorentz in Proc. Acad. Sci. Amst. 6, 1904). This work is in continuation of our earlier investigation of Maurya et al. (Eur. Phys. J. C 75:389, 2015a) where we developed an algorithm and found out three new solutions of electromagnetic mass model. In the present work we consider different metric potentials ν and λ and have analyzed them in a systematic way. It is observed that some of the previous solutions related to electromagnetic mass model are nothing but special cases of the presently obtained generalized solution set. We further verify the solution set and especially show that these are extremely applicable in the case of compact stars.
Static Spherically Symmetric Wormholes in $f(R,T)$ Gravity
Zubair, M; Ahmad, Yasir
2016-01-01
In this work, we explore wormhole solutions in $f(R,T)$ theory of gravity, where $R$ is the scalar curvature and $T$ is the trace of stress-energy tensor of matter. To investigate this, we consider static spherically symmetric geometry with matter contents as anisotropic, isotropic and barotropic fluids in three separate cases. By taking into account Starobinsky $f(R)$ model , we analyze the behavior of energy conditions for these different kind of fluids. It is shown that the wormhole solutions can be constructed without exotic matter in few regions of spacetime. We also give the graphical illustration of obtained results and discuss the equilibrium picture for anisotropic case only. It is concluded that the wormhole solutions with anisotropic matter are realistic and stable in this gravity.
Spherical Symmetric Gravitational Collapse in Chern-Simon Modified Gravity
Amir, Muhammad Jamil
2014-01-01
This paper is devoted to investigate the gravitational perfect fluid collapse in the framework of Chern-Simon modified gravity. For this purpose, we assume the spherically symmetric metric as an interior region and the Schwarzchild spacetime is considered as an exterior region of the star. The Israel junction conditions are used to match the interior and exterior spacetimes. For the sake of simplicity, we take the external field $\\Theta$ as a function of time parameter $t$ and obtain the solution of the field equations of Chern-Simon modified gravity. Junction conditions have been used to calculate the gravitational mass. We discuss the apparent horizons and their physical consequences. It is mentioning here that our results will reduce to those of general relativity, available in literature, if the external field is taken to be constant.
Spherically symmetric steady states of elastic bodies in general relativity
Andréasson, Håkan
2014-01-01
We study the properties of static spherically symmetric elastic bodies in general relativity using both analytical and numerical tools. The materials considered belong to the class of John elastic materials and reduce to perfect fluids when the rigidity parameter is set to zero. We find numerical support that such elastic bodies exist with different possible shapes (balls, single shells and multiple shells) and that their gravitational redshift can be very large ($z\\approx 2.8$) without violating the dominant energy condition. Moreover we show that the elastic body has finite radius even in the case when the constitutive equation of the elastic material is a perturbation of a polytropic fluid without finite radius, thereby concluding that such fluids are structurally unstable within the larger class of elastic matter models under study.
Self Tuning Scalar Fields in Spherically Symmetric Spacetimes
Appleby, Stephen
2015-01-01
We search for self tuning solutions to the Einstein-scalar field equations for the simplest class of `Fab-Four' models with constant potentials. We first review the conditions under which self tuning occurs in a cosmological spacetime, and by introducing a small modification to the original theory - introducing the second and third Galileon terms - show how one can obtain de Sitter states where the expansion rate is independent of the vacuum energy. We then consider whether the same self tuning mechanism can persist in a spherically symmetric inhomogeneous spacetime. We show that there are no asymptotically flat solutions to the field equations in which the vacuum energy is screened, other than the trivial one (Minkowski space). We then consider the possibility of constructing Schwarzschild de Sitter spacetimes for the modified Fab Four plus Galileon theory. We argue that the only model that can successfully screen the vacuum energy in both an FLRW and Schwarzschild de Sitter spacetime is one containing `John...
Spherically Symmetric Solutions in Ghost-Free Massive Gravity
Comelli, D; Nesti, F; Pilo, L
2011-01-01
Recently, a class of theories of massive gravity has been shown to be ghost-free. We study the spherically symmetric solutions in the bigravity formulation of such theories. In general, the solutions admit both a Lorentz invariant and a Lorentz breaking asymptotically flat behaviour and also fall in two branches. In the first branch, all solutions can be found analitycally and are Schwarzschild-like, with no modification as is found for other classes of theories. In the second branch, exact solutions are hard to find, and relying on perturbation theory, Yukawa-like modifications of the static potential are found. The general structure of the solutions suggests that the bigravity formulation of massive gravity is crucial and more than a tool.
Trajectories in a space with a spherically symmetric dislocation
Andrade, Alcides F
2012-01-01
We consider a new type of defect in the scope of linear elasticity theory, using geometrical methods. This defect is produced by a spherically symmetric dislocation, or ball dislocation. We derive the induced metric as well as the affine connections and curvature tensors. Since the induced metric is discontinuous, one can expect ambiguity coming from these quantities, due to products between delta functions or its derivatives, plaguing a description of ball dislocations based on the Geometric Theory of Defects. However, exactly as in the previous case of cylindric defect, one can obtain some well-defined physical predictions of the induced geometry. In particular, we explore some properties of test particle trajectories around the defect and show that these trajectories are curved but can not be circular orbits.
Spherically symmetric solutions in higher-derivative gravity
Lü, H.; Perkins, A.; Pope, C. N.; Stelle, K. S.
2015-12-01
Extensions of Einstein gravity with quadratic curvature terms in the action arise in most effective theories of quantized gravity, including string theory. This article explores the set of static, spherically symmetric and asymptotically flat solutions of this class of theories. An important element in the analysis is the careful treatment of a Lichnerowicz-type "no-hair" theorem. From a Frobenius analysis of the asymptotic small-radius behavior, the solution space is found to split into three asymptotic families, one of which contains the classic Schwarzschild solution. These three families are carefully analyzed to determine the corresponding numbers of free parameters in each. One solution family is capable of arising from coupling to a distributional shell of matter near the origin; this family can then match onto an asymptotically flat solution at spatial infinity without encountering a horizon. Another family, with horizons, contains the Schwarzschild solution but includes also non-Schwarzschild black holes. The third family of solutions obtained from the Frobenius analysis is nonsingular and corresponds to "vacuum" solutions. In addition to the three families identified from near-origin behavior, there are solutions that may be identified as "wormholes," which can match symmetrically onto another sheet of spacetime at finite radius.
Stable Event-Driven Particle Dynamics: Spherically Symmetric Potentials
Bannerman, Marcus N
2012-01-01
Event-Driven Particle Dynamics is a fast and precise method to simulate particulate systems of all scales. These advantages arise from the analytical solution of the dynamics required by the discrete-potential models used. Despite the high precision solution, the finite calculation-precision of computers will still cause the simulation to enter invalid states which, if left unchecked, can lead to unresolvable errors. In this work, the treatment of these marginal invalid-states is discussed and a general event-detection algorithm is proposed which stably handles these situations. This requires a definition of the dynamics of invalid states and leads to improved algorithms for event-detection in spherically symmetric systems, including the well-established hard-sphere and square-well models. Finally, the Event-Driven Particle Dynamics technique is extended to allow the study of systems with complex spherical-mesh boundary conditions and distance constraints as a demonstration of the generality of the proposed a...
Institute of Scientific and Technical Information of China (English)
Mohammed Ashraful Islam
2000-01-01
The analytic cosmological solutions of Einstein's field equations for a type of static metric representing plane, spherical and hyperbolic symmetric spaces are presented and their properties are discussed separately. A general type of solution is obtained which represents the plane, spherical and hyperbolic symmetric cosmological models. Its physical properties are also discussed in details.
Spherical Symmetric Gravitational Collapse in Chern-Simon Modified Gravity
Amir, M. Jamil; Ali, Sarfraz
2016-04-01
This paper is devoted to investigate the gravitational collapse in the framework of Chern-Simon (CS) modified gravity. For this purpose, we assume the spherically symmetric metric as an interior region and the Schwarzchild spacetime is considered as an exterior region of the star. Junction conditions are used to match the interior and exterior spacetimes. In dynamical formulation of CS modified gravity, we take the scalar field Θ as a function of radial parameter r and obtain the solution of the field equations. There arise two cases where in one case the apparent horizon forms first and then singularity while in second case the order of the formation is reversed. It means the first case results a black hole which supports the cosmic censorship hypothesis (CCH). Obviously, the second case yields a naked singularity. Further, we use Junction conditions have to calculate the gravitational mass. In non-dynamical formulation, the canonical choice of scalar field Θ is taken and it is shown that the obtained results of CS modified gravity simply reduce to those of the general relativity (GR). It is worth mentioning here that the results of dynamical case will reduce to those of GR, available in literature, if the scalar field is taken to be constant.
Rovibrational states of Wigner molecules in spherically symmetric confining potentials
Cioslowski, Jerzy
2016-08-01
The strong-localization limit of three-dimensional Wigner molecules, in which repulsively interacting particles are confined by a weak spherically symmetric potential, is investigated. An explicit prescription for computation of rovibrational wavefunctions and energies that are asymptotically exact at this limit is presented. The prescription is valid for systems with arbitrary angularly-independent interparticle and confining potentials, including those involving Coulombic and screened (i.e., Yukawa/Debye) interactions. The necessary derivations are greatly simplified by explicit constructions of the Eckart frame and the parity-adapted primitive wavefunctions. The performance of the new formalism is illustrated with the three- and four-electron harmonium atoms at their strong-correlation limits. In particular, the involvement of vibrational modes with the E symmetry is readily pinpointed as the origin of the "anomalous" weak-confinement behavior of the 1S+ state of the four-electron species that is absent in its 1D+ companion of the strong-confinement regime.
Directional Lya Equivalent Boosting I: Spherically Symmetric Distributions of Clumps
Gronke, Max
2014-01-01
We quantify the directional dependence of the escape fraction of Lyman-$\\alpha$ (Ly$\\alpha$) and non-ionising UV-continuum photons from a multiphase medium, and investigate whether there exist directional enhancements in the Ly$\\alpha$ equivalent width (EW). Our multiphase medium consists of spherically symmetric distributions of cold, dusty clumps embedded within a hot dust-free medium. We focus on three models from the analysis presented by Laursen et al. (2013). We find that for a Ly$\\alpha$ and UV-continuum point source, it is possible to find an EW boost $b(\\theta,\\phi) > 5 \\bar{b}$ in a few per cent of sight lines, where $\\bar{b}$ denotes the boost averaged over all photons. For spatially extended sources this directional dependence vanishes quickly when the size of the UV emitting region exceeds the mean distance between cold dusty clumps. Our analysis suggests that directional EW boosting can occur, and that this is mostly driven by reduced escape fractions of UV photons (which gives rise to UV-contin...
Generation of spherically symmetric metrics in f( R) gravity
Amirabi, Z.; Halilsoy, M.; Mazharimousavi, S. Habib
2016-06-01
In D-dimensional spherically symmetric f( R) gravity there are three unknown functions to be determined from the fourth order differential equations. It is shown that the system remarkably may be integrated to relate two functions through the third one to provide a reduction to second order equations accompanied with a large class of potential solutions. The third function, which acts as the generator of the process, is F(R) =mathrm{d}f(R)/dR. We recall that our generating function has been employed as a scalar field with an accompanying self-interacting potential previously, which is entirely different from our approach. Reduction of f( R) theory into a system of equations seems to be efficient enough to generate a solution corresponding to each generating function. As particular examples, besides the known ones, we obtain new black hole solutions in any dimension D. We further extend our analysis to cover non-zero energy-momentum tensors. Global monopole and Maxwell sources are given as examples.
Generation of spherically symmetric metrics in f(R) gravity
Energy Technology Data Exchange (ETDEWEB)
Amirabi, Z.; Halilsoy, M.; Mazharimousavi, S.H. [Eastern Mediterranean University, Department of Physics, Gazimagusa (Turkey)
2016-06-15
In D-dimensional spherically symmetric f(R) gravity there are three unknown functions to be determined from the fourth order differential equations. It is shown that the system remarkably may be integrated to relate two functions through the third one to provide a reduction to second order equations accompanied with a large class of potential solutions. The third function, which acts as the generator of the process, is F(R) = (df(R))/(dR). We recall that our generating function has been employed as a scalar field with an accompanying self-interacting potential previously, which is entirely different from our approach. Reduction of f(R) theory into a system of equations seems to be efficient enough to generate a solution corresponding to each generating function. As particular examples, besides the known ones, we obtain new black hole solutions in any dimension D. We further extend our analysis to cover non-zero energy-momentum tensors. Global monopole and Maxwell sources are given as examples. (orig.)
A static spherically symmetric thin shell wormhole colliding with a spherical thin shell
Gao, Sijie
2015-01-01
We consider a static spherically symmetric thin shell wormhole collides with another thin shell consisting of ordinary matter. By employing the geometrical constraint, which leads to the conservation of energy and momentum, we show that the state after the collision can be solved from the initial data. In the low speed approximation, the solutions are rather simple. The shell may either bounce back or pass through the wormhole. In either case, the wormhole shrinks right after the collision. In the ``bouncing'' case, a surprising result is that the radial speeds before and after the collision satisfy an addition law, which is independent of the masses of the wormhole and the shell. Once the shell passes through the wormhole, we find that the shell always expands. However, the expansion rate is the same as its collapsing rate right before the collision. Finally, we find out the solution for the shell moving together with the wormhole.
Spherically Symmetric Space Time with Regular de Sitter Center
Dymnikova, Irina
We formulate the requirements which lead to the existence of a class of globally regular solutions of the minimally coupled GR equations asymptotically de Sitter at the center.REFID="S021827180300358XFN001"> The source term for this class, invariant under boosts in the radial direction, is classified as spherically symmetric vacuum with variable density and pressure Tμ ν vac associated with an r-dependent cosmological term Λ μ ν = 8π GTμ ν vac, whose asymptotic at the origin, dictated by the weak energy condition, is the Einstein cosmological term Λgμν, while asymptotic at infinity is de Sitter vacuum with λ < Λ or Minkowski vacuum. For this class of metrics the mass m defined by the standard ADM formula is related to both the de Sitter vacuum trapped at the origin and the breaking of space time symmetry. In the case of the flat asymptotic, space time symmetry changes smoothly from the de Sitter group at the center to the Lorentz group at infinity through radial boosts in between. Geometry is asymptotically de Sitter as r → 0 and asymptotically Schwarzschild at large r. In the range of masses m ≥ mcrit, the de Sitter Schwarzschild geometry describes a vacuum nonsingular black hole (ΛBH), and for m < mcrit it describes G-lump — a vacuum selfgravitating particle-like structure without horizons. In the case of de Sitter asymptotic at infinity, geometry is asymptotically de Sitter as r → 0 and asymptotically Schwarzschild de Sitter at large r. Λμν geometry describes, dependently on parameters m and q = √ {Λ /λ } and choice of coordinates, a vacuum nonsingular cosmological black hole, self-gravitating particle-like structure at the de Sitter background λgμν, and regular cosmological models with cosmological constant evolving smoothly from Λ to λ.
Free boundary value problem to 3D spherically symmetric compressible Navier-Stokes-Poisson equations
Kong, Huihui; Li, Hai-Liang
2017-02-01
In the paper, we consider the free boundary value problem to 3D spherically symmetric compressible isentropic Navier-Stokes-Poisson equations for self-gravitating gaseous stars with γ -law pressure density function for 6/5 <γ ≤ 4/3. For stress-free boundary condition and zero flow density continuously across the free boundary, the global existence of spherically symmetric weak solutions is shown, and the regularity and long time behavior of global solution are investigated for spherically symmetric initial data with the total mass smaller than a critical mass.
Akbar, M. M.
2017-06-01
It is well known that static spherically symmetric spacetimes can admit foliations by flat spacelike hypersurfaces, which are best described in terms of the Painlevè-Gullstrand coordinates. The uniqueness and existence of such foliations were addressed earlier. In this paper, we prove, purely geometrically, that any possible foliation of a static spherically symmetric spacetime by an arbitrary codimension-one spherical spacelike geometry, up to time translation and rotation, is unique, and we find the algebraic condition under which it exists. This leads us to what can be considered as the most natural generalization of the Painlevè-Gullstrand coordinate system for static spherically symmetric metrics, which, in turn, makes it easy to derive generic conclusions on foliation and to study specific cases as well as to easily reproduce previously obtained generalizations as special cases. In particular, we note that the existence of foliation by flat hypersurfaces guarantees the existence of foliation by hypersurfaces whose Ricci curvature tensor is everywhere non-positive (constant negative curvature is a special case). The study of uniqueness and the existence concurrently solves the question of embeddability of a spherical spacelike geometry in one-dimensional higher static spherically symmetric spacetimes, and this produces known and new results geometrically, without having to go through the momentum and Hamiltonian constraints.
Noundjeu, P
2003-01-01
Using the iterative Scheme we prove the local existence and uniqueness of solutions of the spherically symmetric Einstein-Vlasov-Maxwell system with small initial data. We prove a continuation criterion to global in-time solutions.
Institute of Scientific and Technical Information of China (English)
陈光
2001-01-01
The static spherically symmetric solution of Einstein gravity coupled to electromagnetic and scalar fields is obtained under the consideration of the self-gravitational interaction of the electromagnetic and scalar fields, which is singularityfree and stable.
National Research Council Canada - National Science Library
Sergey V. Buldyrev; Pradeep Kumar; Pablo G. Debenedetti; Peter J. Rossky; H. Eugene Stanley
2007-01-01
We examine by molecular dynamics simulation the solubility of small apolar solutes in a solvent whose particles interact via the Jagla potential, a spherically symmetric ramp potential with two characteristic lengths...
Dvornikov, Maxim
2011-01-01
I reply here to the comment of Dr Shmatov on my recent work and demonstrate the invalidity of his criticism of the classical physics description of the formation of bound states of electrons participating in spherically symmetric oscillations of plasma.
Indian Academy of Sciences (India)
K D Patil; S H Ghate; R V Saraykar
2001-04-01
We consider a collapsing spherically symmetric inhomogeneous dust cloud in higher dimensional space-time. We show that the central singularity of collapse can be a strong curvature or a weak curvature naked singularity depending on the initial density distribution.
Static Spherically Symmetric Solutions of the SO(5) Einstein Yang-Mills Equations
Bartnik, Robert A.; Fisher, Mark; Oliynyk, Todd A.
2009-01-01
Globally regular (ie. asymptotically flat and regular interior), spherically symmetric and localised ("particle-like") solutions of the coupled Einstein Yang-Mills (EYM) equations with gauge group SU(2) have been known for more than 20 years, yet their properties are still not well understood. Spherically symmetric Yang--Mills fields are classified by a choice of isotropy generator and SO(5) is distinguished as the simplest model with a \\emph{non-Abelian} residual (little) group, $SU(2)\\times...
Montero, Pedro J
2012-01-01
Brown has recently introduced a covariant formulation of the BSSN equations which is well suited for curvilinear coordinate systems. This is particularly desirable as many astrophysical phenomena are symmetric with respect to the rotation axis or are such that curvilinear coordinates adapt better to their geometry. However, the singularities associated with such coordinate systems are known to lead to numerical instabilities unless special care is taken (e.g., regularization at the origin). Cordero-Carrion will present a rigorous derivation of partially implicit Runge-Kutta methods in forthcoming papers, with the aim of treating numerically the stiff source terms in wave-like equations that may appear as a result of the choice of the coordinate system. We have developed a numerical code solving the BSSN equations in spherical symmetry and the general relativistic hydrodynamic equations written in flux-conservative form. A key feature of the code is that it uses a second-order partially implicit Runge-Kutta me...
Fourier transforms of spherical distributions on compact symmetric spaces
Olafsson, Gestur; Schlichtkrull, Henrik
2008-01-01
In our previous articles "A local Paley-Wiener theorem for compact symmetric spaces", Adv. Math. 218 (2008), 202--215, and "Fourier series on compact symmetric spaces" (submitted) we studied Fourier series on a compact symmetric space M=U/K. In particular, we proved a Paley-Wiener type theorem for the smooth functions on M, which have sufficiently small support and are K-invariant, respectively K-finite. In this article we extend those results to K-invariant distributions on M. We show that t...
Formation of bound states of electrons in spherically symmetric oscillations of plasma
Dvornikov, Maxim
2010-01-01
We study spherically symmetric oscillations of electrons in plasma in frames of the classical electrodynamics. First we analyze the electromagnetic potentials for the system of radially oscillating charged particles. Then we consider both free and forced spherically symmetric oscillations of electrons. Finally we discuss the interaction between radially oscillating electrons through the exchange of ion acoustic waves. It is obtained that the effective potential of this interaction can be attractive and can transcend the Debye-Hueckel potential. We suggest that oscillating electrons can form bound states at the initial staged of the spherical plasma structure evolution. The application of the obtained results to the theory of natural plasmoids are considered.
Spherically symmetric vacuum solutions arising from trace dynamics modifications to gravitation
Adler, Stephen L.; Ramazanoğlu, Fethi M.
2015-12-01
We derive the equations governing static, spherically symmetric vacuum solutions to the Einstein equations, as modified by the frame-dependent effective action (derived from trace dynamics) that gives an alternative explanation of the origin of "dark energy". We give analytic and numerical results for the solutions of these equations, first in polar coordinates, and then in isotropic coordinates. General features of the static case are that: (i) there is no horizon, since g00 is nonvanishing for finite values of the polar radius, and only vanishes (in isotropic coordinates) at the internal singularity, (ii) the Ricci scalar R vanishes identically, and (iii) there is a physical singularity at cosmological distances. The large distance singularity may be an artifact of the static restriction, since we find that the behavior at large distances is altered in a time-dependent solution using the McVittie Ansatz.
Spherically symmetric inhomogeneous bianisotropic media: Wave propagation and light scattering
DEFF Research Database (Denmark)
Novitsky, Andrey; Shalin, Alexander S.; Lavrinenko, Andrei
2017-01-01
We develop a technique for finding closed-form expressions for electromagnetic fields in radially inhomogeneous bianisotropic media, both the solutions of the Maxwell equations and material tensors being defined by the set of auxiliary two-dimensional matrices. The approach is applied to determine...... the scattering cross-sections by spherical particles, the fields inside which correspond to the Airy-exponential waves....
On spherically symmetric singularity-free models in relativistic cosmology
Indian Academy of Sciences (India)
Ramesh Tikekar
2000-10-01
The introduction of time dependence through a scale factor in a non-conformally ﬂat static cosmological model whose spacetime can be embedded in a ﬁve demensional ﬂat spacetime is shown to give rise to two spherical models of universe ﬁlled with perfect ﬂuid acompannied with radial heat ﬂux without any Big Bang type singularity. The ﬁrst model describes an ever existing universe which witnesses a transition from state of contraction to that of ever expansion. The second model represents a universe oscillating between two regular states.
Spherically symmetric potential in noncommutative spacetime with a compactified extra dimensions
Energy Technology Data Exchange (ETDEWEB)
Guedezounme, Secloka Lazare [University of Abomey-Calavi, International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), Cotonou (Benin); Kanfon, Antonin Danvide [University of Abomey-Calavi, International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), Cotonou (Benin); University of d' Abomey-Calavi, Faculte des Sciences et Techniques, Cotonou (Benin); Samary, Dine Ousmane [University of Abomey-Calavi, International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), Cotonou (Benin); University of d' Abomey-Calavi, Faculte des Sciences et Techniques, Cotonou (Benin); Albert Einstein Institute, Max Planck Institute for Gravitational Physics, Potsdam (Germany)
2016-09-15
The Schroedinger equation of the spherically symmetrical quantum models such as the hydrogen atom problem seems to be analytically non-solvable in higher dimensions. When we try compactifying one or several dimensions this question can maybe solved. This paper presents a study of the spherically symmetrical quantum models on noncommutative spacetime with compactified extra dimensions. We provide analytically the resulting spectrum of the hydrogen atom and Yukawa problem in 4 + 1 dimensional noncommutative spacetime in the first order approximation of the noncommutative parameter. The case of higher dimensions D ≥ 4 is also discussed. (orig.)
Self-Gravitating Spherically Symmetric Solutions in Scalar-Torsion Theories
Kofinas, Georgios; Saridakis, Emmanuel N
2015-01-01
We studied spherically symmetric solutions in scalar-torsion gravity theories in which a scalar field is coupled to torsion with a derivative coupling. We obtained the general field equations from which we extracted a decoupled master equation, the solution of which leads to the specification of all other unknown functions. We first obtained an exact solution which represents a new wormhole-like solution dressed with a regular scalar field. Then, we found large distance linearized spherically symmetric solutions in which the space asymptotically is AdS.
Li, Ping; Li, Xin-zhou; Xi, Ping
2016-06-01
We present a detailed study of the spherically symmetric solutions in Lorentz-breaking massive gravity. There is an undetermined function { F }(X,{w}1,{w}2,{w}3) in the action of Stückelberg fields {S}φ ={{{Λ }}}4\\int {{{d}}}4x\\sqrt{-g}{ F }, which should be resolved through physical means. In general relativity, the spherically symmetric solution to the Einstein equation is a benchmark and its massive deformation also plays a crucial role in Lorentz-breaking massive gravity. { F } will satisfy the constraint equation {T}01=0 from the spherically symmetric Einstein tensor {G}01=0, if we maintain that any reasonable physical theory should possess the spherically symmetric solutions. The Stückelberg field {φ }i is taken as a ‘hedgehog’ configuration {φ }i=φ (r){x}i/r, whose stability is guaranteed by the topological one. Under this ansätz, {T}01=0 is reduced to d{ F }=0. The functions { F } for d{ F }=0 form a commutative ring {R}{ F }. We obtain an expression of the solution to the functional differential equation with spherical symmetry if { F }\\in {R}{ F }. If { F }\\in {R}{ F } and \\partial { F }/\\partial X=0, the functions { F } form a subring {S}{ F }\\subset {R}{ F }. We show that the metric is Schwarzschild, Schwarzschild-AdS or Schwarzschild-dS if { F }\\in {S}{ F }. When { F }\\in {R}{ F } but { F }\
Spherically Symmetric Waves of a Reaction-Diffusion Equation.
1980-02-01
The space A c M x [0,1] of chapter 4, section II inherited it.- semiflow from M x [0.11 which comes from the equation in cuestion . In this chapter we...have the property that an open neighbourhood of the solution whose stability is in cuestion with the inherited topology should be effectively the same
Wagh, S M; Muktibodh, P S; Govinder, K S
2001-01-01
In this paper, we find all the Conformal Killing Vectors (CKVs) and their Lie Algebra for the recently reported [cqg1] spherically symmetric, shear-free separable metric spacetimes with non-vanishing energy or heat flux. We also solve the geodesic equatios of motion for the spacetime under consideration.
On the local existence of maximal slicings in spherically symmetric spacetimes
Cordero-Carrión, Isabel; Morales-Lladosa, Juan Antonio
2010-01-01
In this talk we show that any spherically symmetric spacetime admits locally a maximal spacelike slicing. The above condition is reduced to solve a decoupled system of first order quasi-linear partial differential equations. The solution may be accomplished analytical or numerically. We provide a general procedure to construct such maximal slicings.
On the local existence of maximal slicings in spherically symmetric spacetimes
Energy Technology Data Exchange (ETDEWEB)
Cordero-Carrion, Isabel; Ibanez, Jose MarIa; Morales-Lladosa, Juan Antonio, E-mail: isabel.cordero@uv.e, E-mail: jose.m.ibanez@uv.e, E-mail: antonio.morales@uv.e [Departamento de AstronomIa y Astrofisica, Universidad de Valencia, C/ Dr. Moliner 50, E-46100 Burjassot, Valencia (Spain)
2010-05-01
In this talk we show that any spherically symmetric spacetime admits locally a maximal spacelike slicing. The above condition is reduced to solve a decoupled system of first order quasi-linear partial differential equations. The solution may be accomplished analytical or numerically. We provide a general procedure to construct such maximal slicings.
No nonminimally coupled massless scalar hair for spherically symmetric neutral black holes
Hod, Shahar
2017-08-01
We provide a remarkably compact proof that spherically symmetric neutral black holes cannot support static nonminimally coupled massless scalar fields. The theorem is based on causality restrictions imposed on the energy-momentum tensor of the fields near the regular black-hole horizon.
Generalized scalar tensor theory in four and higher dimensional spherically symmetric space-time
Indian Academy of Sciences (India)
Subenoy Chakraborty; Arabinda Ghosh
2001-05-01
In this paper, we have studied generalized scalar tensor theory for spherically symmetric models, both in four and higher dimensions with a bulk viscous fluid. We have considered both exponential and power law solutions with some assumptions among the physical parameters and solutions have been discussed.
Directory of Open Access Journals (Sweden)
Yu.V. Kalyuzhnyi
2013-01-01
Full Text Available Thermodynamic perturbation theory for cetral-force (TPT-CF type of associating potential is used to study the phase behavior of symmetric binary mixture of associating particles with spherically symmetric interaction. The model is represented by the binary Yukawa hard-sphere mixture with additional spherically symmetric square-well associative interaction located inside the hard-core region and valid only between dissimilar species. To account for the change of the system packing fraction due to association we propose an extended version of the TPT-CF approach. In addition to already known four types of the phase diagram for binary mixtures we were able to identify the fifth type, which is characterized by the absence of the intersection of the λ-line with the liquid-vapour binodals and by the appearance of the closed- loop liquid-liquid immiscibility with upper and lower critical solution temperatures.
A spherically-symmetric charged-dS solution in f(T) gravity theories
Nashed, Gamal G L
2013-01-01
A tetrad field with spherical symmetry is applied to the charged field equations of $f(T)$ gravity theory. A special spherically-symmetric charged-dS solution is obtained. The scalar torsion of this solution is a vanishing quantity. The spacetime of the derived solution is rewritten as a multiplication of three matrices: The first matrix is a special case of Euler$'$s angle "so(3)", the second matrix represents a boost transformation, while the third matrix is the square root of the spherically-symmetric charged-dS metric. It is shown that the boost matrix is important because it plays an essential role in adjusting the spacetime to become a solution for $f(T)$ theory.
Static spherically symmetric solutions in the IR limit of nonrelativistic quantum gravity
Harada, Tomohiro; Tsukamoto, Naoki
2009-01-01
We investigate static spherically symmetric vacuum solutions in the IR limit of projectable nonrelativistic quantum gravity, including the renormalisable quantum gravity recently proposed by Ho\\v{r}ava. It is found that the projectability condition plays an important role. Without the cosmological constant, the spacetime is uniquely given by the Schwarzschild solution. With the cosmological constant, the spacetime is uniquely given by the Kottler (Schwarzschild-(anti) de Sitter) solution for the entirely vacuum spacetime. However, the ``ultra-static'' metric of spherical and hyperbolic spaces can be also admissible for the locally empty region, for the positive and negative cosmological constants, respectively, if its nonvanishing contribution to the global Hamiltonian constraint can be compensated by that from the nonempty or nonstatic region. This implies that static spherically symmetric entirely vacuum solutions would not admit the freedom to reproduce the observed flat rotation curves of galaxies. On the...
The double-power approach to spherically symmetric astrophysical systems
Lingam, Manasvi
2013-01-01
In this paper, we present a simple approach to deriving a wide range of anisotropic distribution functions. We rely on constructing a basic augmented density that can be generated from a suitable double power distribution function, and proceeding to multiply and divide this augmented density with functions of r. After such an augmented density is determined, we express it as a series and proceed to construct the corresponding series for the distribution function. We use this method to generate three distinct classes of double power distribution functions, each of which possesses differing properties. The Class I models feature a finite number of double power components and have an arbitrary number of freely specifiable parameters. The Class II models allow one to generate constant anisotropy via an infinite series of double power distribution functions. The Class III models merge properties of these two families to give rise to distribution functions with a non-constant anisotropy parameter that involves thre...
Spherically symmetric scalar vacuum no-go theorems, black holes and solitons
Bronnikov, K A
2001-01-01
We prove some theorems characterizing the global properties of static, spherically symmetric configurations of a self-gravitating real scalar field in general relativity (GR) in various dimensions, with an arbitrary potential $V$, not necessarily positive-definite. The results are extended to sigma models, scalar-tensor and curvature-nonlinear theories of gravity. We show that the list of all possible types of space-time causal structure in the models under study is the same as for a constant scalar field, namely, Minkowski (or AdS), Schwarzschild, de Sitter and Schwarzschild - de Sitter, and all horizons are simple. In particular, these theories do not admit regular black holes with any asymptotics. Some special features of (2+1)D gravity are revealed. We give examples of two types of asymptotically flat configurations with positive mass in GR, admitted by the above theorems: (i) a black hole with nontrivial ``scalar hair'' and (ii) a particlelike solution with a regular centre; in both cases, the potential ...
Stability of spherically symmetric, charged black holes and multipole moments for stationary systems
Energy Technology Data Exchange (ETDEWEB)
Gursel, H.Y.
1983-01-01
This dissertation is written in two parts. Part I deals with the question of stability of a spherically symmetric, charged black hole against scalar, electromagnetic, and gravitational perturbations. It consists of two papers written in collaboration with Igor D. Novikov, Vernon D. Sandberg and A.A. Starobinsky. In these papers the dynamical evolution of these perturbations on the interior of a Reissner-Nordstrom black hole is described. The instability of the hole's Cauchy horizon is discussed in detail in terms of the energy densities of the test fields as measured by a freely falling observer approaching the Cauchy horizon. It is concluded that the Cauchy horizon of the analytically extended Reissner-Nordstrom solution is highly unstable and not a physical feature of a realistic gravitational collapse. Part II of this dissertation addresses two problems closely connected with multipole structure of stationary, asymptotically flat spacetimes. It consists of two papers written in collaboration with Kip S. Thorne. The first one shows the equivalence of the moments defined by Kip S. Thorne and the moments defined by Robert Geroch and Richard Hansen. The second proves a conjecture by Kip S. Thorne: In the limit of ''slow'' motion, general relativistic gravity produces no changes whatsoever in the classical Euler equations of rigid body motion. This conjecture is proved by giving an algorithm for generating rigidly rotating solutions of Einstein's equation from nonrotating, static solutions.
Sheet-like assemblies of spherical particles with point-symmetrical patches.
Mani, Ethayaraja; Sanz, Eduardo; Roy, Soumyajit; Dijkstra, Marjolein; Groenewold, Jan; Kegel, Willem K
2012-04-14
We report a computational study on the spontaneous self-assembly of spherical particles into two-dimensional crystals. The experimental observation of such structures stabilized by spherical objects appeared paradoxical so far. We implement patchy interactions with the patches point-symmetrically (icosahedral and cubic) arranged on the surface of the particle. In these conditions, preference for self-assembly into sheet-like structures is observed. We explain our findings in terms of the inherent symmetry of the patches and the competition between binding energy and vibrational entropy. The simulation results explain why hollow spherical shells observed in some Keplerate-type polyoxometalates (POM) appear. Our results also provide an explanation for the experimentally observed layer-by-layer growth of apoferritin--a quasi-spherical protein.
Ivanovski, S. L.; Zakharov, V. V.; Della Corte, V.; Crifo, J.-F.; Rotundi, A.; Fulle, M.
2017-01-01
In-situ measurements of individual dust grain parameters in the immediate vicinity of a cometary nucleus are being carried by the Rosetta spacecraft at comet 67P/Churyumov-Gerasimenko. For the interpretations of these observational data, a model of dust grain motion as realistic as possible is requested. In particular, the results of the Stardust mission and analysis of samples of interplanetary dust have shown that these particles are highly aspherical, which should be taken into account in any credible model. The aim of the present work is to study the dynamics of ellipsoidal shape particles with various aspect ratios introduced in a spherically symmetric expanding gas flow and to reveal the possible differences in dynamics between spherical and aspherical particles. Their translational and rotational motion under influence of the gravity and of the aerodynamic force and torque is numerically integrated in a wide range of physical parameters values including those of comet 67P/Churyumov-Gerasimenko. The main distinctions of the dynamics of spherical and ellipsoidal particles are discussed. The aerodynamic characteristics of the ellipsoidal particles, and examples of their translational and rotational motion in the postulated gas flow are presented.
Thermodynamic Properties of Spherically-Symmetric, Uniformly-Accelerated Reference Frames
Institute of Scientific and Technical Information of China (English)
ZHANG Jian-Bao; HUANG Chao-Guang; LIU Zeng-Rong; SUN Jia-Rui; LI Ying
2008-01-01
We aim to study the thermodynamic properties of the spherically symmetric reference frames with uniform acceleration, including the spherically symmetric generalization of Rindler reference frame and the new kind of uniformly accelerated reference frame. We find that, unlike the general studies about the horizon thermodynamics, one cannot obtain the laws of thermodynamics for their horizons in the usual approaches, despite that one can formally define an area entropy (Bekenstein-Hawking entropy). In fact, the common horizon for a set of uniformly accelerated observers does not always exist, even though the Hawking-Unruh temperature is still well-defined. This result indicates that the Hawking-Unruh temperature is only a kinematic effect, and to gain the laws of thermodynamics for the horizon, one needs the help of dynamics. Our result is in accordance with those from the various studies about the acoustic black holes.
External stability for Spherically Symmetric Solutions in Lorentz Breaking Massive Gravity
Addazi, Andrea
2014-01-01
We discuss spherically symmetric solutions for Stars and Black Holes in a class of Lorentz-breaking massive gravity theories. This analysis is valid both for St\\"uckelberg's effective field theory formulation and for Lorentz Breaking Massive Bigravity. The approach consists in analyzing the stability of the geodesic equations out to the star radius, at the first order (deviation equation). The main result is a strong constrain in the the space of parameters of the theory. This strongly motivates an higher order geodetic analysis of perturbations, to understand if it exists a class of spherically symmetric Lorentz-breaking massive gravity solutions for stars, black holes, and, in general, self-gravitating systems stable and phenomenologically acceptable.
Multidimensional Cosmological and Spherically Symmetric Solutions with Intersecting p-branes
Ivashchuk, V D
1999-01-01
Multidimensional model describing the cosmological evolution and/or spherically symmetric configuration with n+1 Einstein spaces in the theory with several scalar fields and forms is considered. When electro-magnetic composite p-brane ansatz is adopted, n "internal" spaces are Ricci-flat, one space M_0 has a non-zero curvature, and all p-branes do not "live" in M_0, a class of exact solutions is obtained if certain block-orthogonality relations on p-brane vectors are imposed. A subclass of spherically-symmetric solutions containing non-extremal p-brane black holes is considered. Post-Newtonian parameters are calculated and some examples are considered.
General Stationary, Spherically-Symmetric Solutions in the Gauge Theory of Gravity
Francis, M R; Francis, Matthew R.; Kosowsky, Arthur
2003-01-01
This paper provides a concise overview of the gauge theory of gravity, as recently formulated by Lasenby, Doran, and Gull. Instead of representing gravitation via spacetime curvature, the effects of gravity are given by gauge fields in flat spacetime; the gauge group is that of Lorentz transformations plus covariance under diffeomorphisms. The resulting theory is formally similar to the Cartan formulation of general relativity, and we make detailed comparisons with conventional representations of general relativity. We provide a constructive method for solving the field equations in gauge theory gravity, and apply this method to the spherically symmetric case. The most general vacuum solution results, which explicitly displays all coordinate freedom in terms of free functions of radius. Through particular choices of these functions, our general solution reduces to all known metric representations of spherically symmetric, stationary vacuum spacetime. We also obtain the corresponding generalization of the Reis...
General theory of spherically symmetric boundary-value problems of the linear transport theory.
Kanal, M.
1972-01-01
A general theory of spherically symmetric boundary-value problems of the one-speed neutron transport theory is presented. The formulation is also applicable to the 'gray' problems of radiative transfer. The Green's function for the purely absorbing medium is utilized in obtaining the normal mode expansion of the angular densities for both interior and exterior problems. As the integral equations for unknown coefficients are regular, a general class of reduction operators is introduced to reduce such regular integral equations to singular ones with a Cauchy-type kernel. Such operators then permit one to solve the singular integral equations by the standard techniques due to Muskhelishvili. We discuss several spherically symmetric problems. However, the treatment is kept sufficiently general to deal with problems lacking azimuthal symmetry. In particular the procedure seems to work for regions whose boundary coincides with one of the coordinate surfaces for which the Helmholtz equation is separable.
An investigation of embeddings for spherically symmetric spacetimes into Einstein manifolds
Indian Academy of Sciences (India)
Jothi Moodley; Gareth Amery
2011-09-01
Embeddings into higher dimensions are very important in the study of higherdimensional theories of our Universe and in high-energy physics. Theorems which have been developed recently guarantee the existence of embeddings of pseudo-Riemannian manifolds into Einstein spaces and more general pseudo-Riemannian spaces. These results provide a technique that can be used to determine solutions for such embeddings. Here we consider local isometric embeddings of four-dimensional spherically symmetric spacetimes into ﬁve-dimensional Einstein manifolds. Difﬁculties in solving the ﬁve-dimensional equations for given four-dimensional spaces motivate us to investigate embedded spaces that admit bulks of a speciﬁc type. We show that the general Schwarzschild–de Sitter spacetime and Einstein Universe are the only spherically symmetric spacetimes that can be embedded into an Einstein space of a particular form, and we discuss their ﬁve-dimensional solutions.
On heat conduction in multicomponent, non-Maxwellian spherically symmetric solar wind plasmas
Cuperman, S.; Dryer, M.
1985-01-01
A generalized expression for the steady-state heat flux in multicomponent, moderately non-Maxwellian spherically symmetric plasmas is presented and discussed. The work was motivated by the inability of the simple, Fourier-type formula for the thermal conductivity to explain the observed correlations in the solar wind. The results hold for situations not far from local thermodynamic equilibrium. The generalized expression includes not only correlations that have been observed but also correlations not sought for previously.
Spherically Symmetric Static Solution for a Schwarzschild Black Hole with Its Hawking Radiation
Institute of Scientific and Technical Information of China (English)
HUANG Chao-Guang
2000-01-01
A black hole and its Hawking radiation may be in stable thermal equilibrium. In this letter, the static spherically symmetric numerical solution for a Schwarzschild black hole with its Hawking radiation are obtained. In the calculation, the equilibrium system is supposed to consist of a black hole, thermal radiation and a two-dimensional surface layer. The solutions obtained are compared with the York's back-reaction approach and the Zhao-Liu thermodynamic approach.
Unified treatment of a class of spherically symmetric potentials: quasi-exact solution
Panahi, Hossein
2016-01-01
In this paper, we investigate the Schr\\"odinger equation for a class of spherically symmetric potentials in a simple and unified manner using the Lie algebraic approach within the framework of quasi-exact solvability. We illustrate that all models give rise to the same basic differential equation, which is expressible as an element of the universal enveloping algebra of sl(2). Then, we obtain the general exact solutions of the problem by employing the representation theory of sl(2) Lie algebra.
Nashed, Gamal G L
2012-01-01
Applying a non-diagonal spherically symmetric tetrad field having arbitrary function, $S(r)$, that is corresponding to local Lorentz transformation, to the field equations of f(T) gravity theories. An analytic vacuum solutions with constants of integration are derived. These constants are studied by calculating the total conserved charge associated to each solution. The study has shown that the obtained solutions represent Schwarzschild-Ads spacetime.
Energy Technology Data Exchange (ETDEWEB)
Nashed, Gamal G.L. [The British University in Egypt, Centre for Theoretical Physics, P.O. Box 43, Sherouk City (Egypt); Ain Shams University, Mathematics Department, Faculty of Science, Cairo (Egypt)
2013-04-15
In this paper a non-diagonal, spherically symmetric, tetrad field that contains an arbitrary function, S(r), which corresponds to a local Lorentz transformation, is applied to the field equations of f(T) gravity theories. Analytic vacuum solutions with integration constants are derived. These constants are studied by calculating the total conserved charge associated with each solution. The study shows that the obtained solutions represent the Schwarzschild-Ads spacetime. (orig.)
Functional derivative of the kinetic energy functional for spherically symmetric systems.
Nagy, Á
2011-07-28
Ensemble non-interacting kinetic energy functional is constructed for spherically symmetric systems. The differential virial theorem is derived for the ensemble. A first-order differential equation for the functional derivative of the ensemble non-interacting kinetic energy functional and the ensemble Pauli potential is presented. This equation can be solved and a special case of the solution provides the original non-interacting kinetic energy of the density functional theory.
No nonminimally coupled massless scalar hair for spherically symmetric neutral reflecting stars
Hod, Shahar
2017-07-01
It has recently been proved that horizonless compact stars with reflecting boundary conditions cannot support spatially regular matter configurations made of minimally coupled scalar fields, vector fields, and tensor fields. In the present paper we extend this intriguing no-hair property to the physically interesting regime of scalar fields with nonminimal coupling to gravity. In particular, we prove that static spherically symmetric configurations made of nonminimally coupled massless scalar fields cannot be supported by compact reflecting stars.
Institute of Scientific and Technical Information of China (English)
QIAN Shang-Wu
2006-01-01
This paper briefly discusses some interesting features for the external region of the spherical symmetric mass in the new theory of gravitation VGM, Le. The theory of gravitation by considering the vector graviton field and the metric field, such as pseudo-singularity, curvature tensor, static limit, event horizon, and the radial motion of a particle. All these features are different from the corresponding features obtained from general relativity.
Non-spherically symmetric black string perturbations in the large D limit
Sadhu, Amruta
2016-01-01
We consider non-spherically symmetric perturbations of the uncharged black string/flat black brane in the large dimension (D) limit of general relativity. We express the perturbations in a simplified form using variables introduced by Ishibashi and Kodama. We apply the large D limit to the equations, and show that this leads to decoupling of the equations in the near-horizon and asymptotic regions. It also enables use of matched asymptotic expansions to obtain approximate analytical solutions and to analyze stability of the black string/brane. For a large class of non-spherically symmetric perturbations, we prove that there are no instabilities in the large D limit. For the rest, we provide additional matching arguments that indicate that the black string/brane is stable. In the \\emph{static} limit, we show that for \\emph{all} non-spherically symmetric perturbations, there is no instability. This is proof that the Gross-Perry-Yaffe mode for semiclassical black hole perturbations is the unique unstable mode ev...
Spherically symmetric brane in a bulk of f(R) and Gauss-Bonnet gravity
Chakraborty, Sumanta; SenGupta, Soumitra
2016-11-01
Effective gravitational field equations on a four-dimensional brane embedded in a five-dimensional bulk have been considered. Using the Einstein-Hilbert action along with the Gauss-Bonnet correction term, we have derived static spherically symmetric vacuum solution to the effective field equations, first order in the Gauss-Bonnet coupling parameter. The solution so obtained, has one part corresponding to general relativity with an additional correction term, proportional to the Gauss-Bonnet coupling parameter. The correction term modifies the spacetime structure, in particular, the location of the event horizon. Proceeding further, we have derived effective field equations for f(R) gravity with Gauss-Bonnet correction term and a static spherically symmetric solution has been obtained. In this case the Gauss-Bonnet term modifies both the event and cosmological horizon of the spacetime. There exists another way of obtaining the brane metric—expanding the bulk gravitational field equations in the ratio of bulk to brane curvature scale and assuming a separable bulk metric ansatz. It turns out that static, spherically symmetric solutions obtained from this perturbative method can be matched exactly, with the solutions derived earlier. This will hold for Einstein-Hilbert plus Gauss-Bonnet as well as for f(R) with the Gauss-Bonnet correction. Implications of these results are discussed.
Ortiz, Néstor; Sarbach, Olivier
2014-04-01
A spherical dust cloud which is initially at rest and which has a monotonously decaying density profile collapses and forms a shell-focusing singularity. Provided the density profile is not too flat, meaning that its second radial derivative is negative at the centre, this singularity is visible to local, and sometimes even to global observers. According to the strong cosmic censorship conjecture, such naked singularities should be unstable under generic, non-spherical perturbations of the initial data or when more realistic matter models are considered. In an attempt to gain further insight into this stability issue, in this work we initiate the analysis of a simpler but related problem. We discuss the stability of test fields propagating in the vicinity of the Cauchy horizon associated to the naked central singularity. We first study the high-frequency limit and show that the fields undergo a blueshift as they approach the Cauchy horizon. However, in contrast to what occurs at inner horizons of black holes, we show that the blueshift is uniformly bounded along incoming and outgoing null rays. Motivated by this boundedness result, we take a step beyond the geometric optics approximation and consider the Cauchy evolution of spherically symmetric test scalar fields. We prove that under reasonable conditions on the initial data a suitable rescaled field can be continuously extended to the Cauchy horizon. In particular, this result implies that the physical field is everywhere finite on the Cauchy horizon away from the central singularity.
Asymptotic behavior of marginally trapped tubes in spherically symmetric black hole spacetimes
Williams, Catherine M.
We begin by reviewing some fundamental features of general relativity, then outline the mathematical definitions of black holes, trapped surfaces, and marginally trapped tubes, first in general terms, then rigorously in the context of spherical symmetry. We describe explicitly the reduction of Einstein's equation on a spherically symmetric 4-dimensional Lorentzian manifold to a system of partial differential equations on a subset of 2-dimensional Minkowski space. We discuss the asymptotic behavior of marginally trapped tubes in the Schwarzschild, Vaidya, and Reisner-Nordstrom solutions to Einstein's equations in spherical symmetry, as well as in Einstein-Maxwell-scalar field black hole spacetimes generated by evolving certain classes of asymptotically flat initial data. Our first main result gives conditions on a general stress-energy tensor Talphabeta in a spherically symmetric black hole spacetime that are sufficient to guarantee that the black hole will contain a marginally trapped tube which is eventually achronal, connected, and asymptotic to the event horizon. Here "general" means that the matter model is arbitrary, subject only to a certain positive energy condition. A certain matter field decay rate, known as Price law decay in the literature, is not required per se for this asymptotic result, but such decay does imply that the marginally trapped tube has finite length with respect to the induced metric. In our second main result, we give two separate applications of the first theorem to self-gravitating Higgs field spacetimes, one using weak Price law decay, the other certain strong smallness and monotonicity assumptions.
Burtscher, Annegret Y
2014-01-01
We study the evolution of a self-gravitating compressible fluid in spherical symmetry and we prove the existence of weak solutions with bounded variation for the Einstein-Euler equations of general relativity. We formulate the initial value problem in Eddington-Finkelstein coordinates and prescribe spherically symmetric data on a characteristic initial hypersurface. We introduce here a broad class of initial data which contain no trapped surfaces, and we then prove that their Cauchy development contains trapped surfaces. We therefore establish the formation of trapped surfaces in weak solutions to the Einstein equations. This result generalizes a theorem by Christodoulou for regular vacuum spacetimes (but without symmetry restriction). Our method of proof relies on a generalization of the "random choice" method for nonlinear hyperbolic systems and on a detailed analysis of the nonlinear coupling between the Einstein equations and the relativistic Euler equations in spherical symmetry.
Stability of spherically symmetric, charged black holes and multipole moments for stationary systems
Gursel, Yekta
This dissertation is written in two parts. Part I deals with the question of stability of a spherically symmetric, charged black hole against scalar, electromagnetic, and gravitational perturbations. It consists of two papers written in collaboration with Igor D. NoVikov, Vernon D. Sandberg and A. A. Starobinsky. In these papers we describe the dynamical evolution of these perturbations on the interior of a Reissner-Nordstrom black hole. The instability of the hole's Cauchy horizon is discussed in detail in terms of the energy densities of the test fields as measured by a freely falling observer approaching the Cauchy horizon. We conclude that the Cauchy horizon of the analytically extended Reissner-Nordstrom solution is highly unstable and not a physical feature of a realistic gravitational collapse. Part II of this dissertation addresses two problems closely connected with muitipole structure of stationary, asymptotically flat spacetimes. It consists of two papers written in collaboration with Kip S. Thorne despite the fact that his name does not appear on one of them. The first one (Paper III in this thesis) shows the equivalence of the moments defined by Kip S. Thorne and the moments defined by Robert Geroch and Richard Hansen. The second (Paper IV in this thesis) proves a conjecture by Kip S. Thorne: In the limit of "slow" motion, general relativistic gravity produces no changes whatsoever in the classical Euler equations of rigid body motion. We prove this conjecture by giving an algorithm for generating rigidly rotating solutions of Einstein's equations from nonrotating, static solutions.
Ono, Toshiaki; Fushimi, Naomasa; Yamada, Kei; Asada, Hideki
2015-01-01
In terms of Sturm's theorem, we reexamine a marginal stable circular orbit (MSCO) such as the innermost stable circular orbit (ISCO) of a timelike geodesic in any spherically symmetric and static spacetime. MSCOs for some of exact solutions to the Einstein's equation are discussed. Strum's theorem is explicitly applied to the Kottler (often called Schwarzschild-de Sitter) spacetime. Moreover, we analyze MSCOs for a spherically symmetric, static and vacuum solution in Weyl conformal gravity.
Some Aspects of Spherical Symmetric Extremal Dyonic Black Holes in 4d N=1 Supergravity
Gunara, Bobby E; Suroso, Agus; Arianto,
2013-01-01
In this paper we study several aspects of extremal spherical symmetric black hole solutions of for four dimensional N=1 supergravity coupled to vector and chiral multiplets with the scalar potential turned on. In the asymptotic region the complex scalars are fixed and regular which can be viewed as the critical points of the black hole and the scalar potential with vanishing scalar charges. It follows that the asymptotic geometries are of a constant and non-zero scalar curvature which further deform to the symmetric spaces, namely anti-de Sitter and de Sitter spaces. These spaces correspond to the near horizon geometries which are the product spaces of a two surface and the two sphere. We finally give some simple ${\\lC}^{n}$-models with both linear superpotential and gauge couplings.
Beyond Extreme Ultra Violet (BEUV) Radiation from Spherically symmetrical High-Z plasmas
Yoshida, Kensuke; Fujioka, Shinsuke; Higashiguchi, Takeshi; Ugomori, Teruyuki; Tanaka, Nozomi; Kawasaki, Masato; Suzuki, Yuhei; Suzuki, Chihiro; Tomita, Kentaro; Hirose, Ryouichi; Eshima, Takeo; Ohashi, Hayato; Nishikino, Masaharu; Scally, Enda; Nshimura, Hiroaki; Azechi, Hiroshi; O'Sullivan, Gerard
2016-03-01
Photo-lithography is a key technology for volume manufacture of high performance and compact semiconductor devices. Smaller and more complex structures can be fabricated by using shorter wavelength light in the photolithography. One of the most critical issues in development of the next generation photo-lithography is to increase energy conversion efficiency (CE) from laser to shorter wavelength light. Experimental database of beyond extreme ultraviolet (BEUV) radiation was obtained by using spherically symmetrical high-Z plasmas generated with spherically allocated laser beams. Absolute energy and spectra of BEUV light emitted from Tb, Gd, and Mo plasmas were measured with a absolutely calibrated BEUV calorimeter and a transmission grating spectrometer. 1.0 x 1012 W/cm2 is the optimal laser intensity to produced efficient BEUV light source plasmas with Tb and Gd targets. Maximum CE is achieved at 0.8% that is two times higher than the published CEs obtained with planar targets.
Coherent control for the spherical symmetric box potential in short and intensive XUV laser fields
Barna, I F
2007-01-01
Coherent control calculations are presented for a spherically symmetric box potential for non-resonant two photon transition probabilities. With the help of a genetic algorithm (GA) the population of the excited states are maximized and minimized. The external driving field is a superposition of three intensive extreme ultraviolet (XUV) linearly polarized laser pulses with different frequencies in the femtosecond duration range. We solved the quantum mechanical problem within the dipole approximation. Our investigation clearly shows that the dynamics of the electron current has a strong correlation with the optimized and neutralizing pulse shape.
Classic tests of General Relativity described by brane-based spherically symmetric solutions
Energy Technology Data Exchange (ETDEWEB)
Cuzinatto, R.R. [Universidade Federal de Alfenas, Instituto de Ciencia e Tecnologia, Pocos de Caldas, MG (Brazil); Pompeia, P.J. [Departamento de Ciencia e Tecnologia Aeroespacial, Instituto de Fomento e Coordenacao Industrial, Sao Jose dos Campos, SP (Brazil); Departamento de Ciencia e Tecnologia Aeroespacial, Instituto Tecnologico de Aeronautica, Sao Jose dos Campos, SP (Brazil); De Montigny, M. [University of Alberta, Theoretical Physics Institute, Edmonton, AB (Canada); University of Alberta, Campus Saint-Jean, Edmonton, AB (Canada); Khanna, F.C. [University of Alberta, Theoretical Physics Institute, Edmonton, AB (Canada); TRIUMF, Vancouver, BC (Canada); University of Victoria, Department of Physics and Astronomy, PO box 1700, Victoria, BC (Canada); Silva, J.M.H. da [Universidade Estadual Paulista, Departamento de Fisica e Quimica, Guaratingueta, SP (Brazil)
2014-08-15
We discuss a way to obtain information about higher dimensions from observations by studying a brane-based spherically symmetric solution. The three classic tests of General Relativity are analyzed in detail: the perihelion shift of the planet Mercury, the deflection of light by the Sun, and the gravitational redshift of atomic spectral lines. The braneworld version of these tests exhibits an additional parameter b related to the fifth-coordinate. This constant b can be constrained by comparison with observational data for massive and massless particles. (orig.)
Classic tests of General Relativity described by brane-based spherically symmetric solutions
Cuzinatto, R R; de Montigny, M; Khanna, F C; da Silva, J M Hoff
2014-01-01
We discuss a way to obtain information about higher dimensions from observations by studying a brane-based spherically symmetric solution. The three classic tests of General Relativity are analyzed in details: the perihelion shift of the planet Mercury, the deflection of light by the Sun, and the gravitational redshift of atomic spectral lines. The braneworld version of these tests exhibits an additional parameter $b$ related to the fifth-coordinate. This constant $b$ can be constrained by comparison with observational data for massive and massless particles.
Unified Treatment of a Class of Spherically Symmetric Potentials: Quasi-Exact Solution
Directory of Open Access Journals (Sweden)
H. Panahi
2016-01-01
Full Text Available We investigate the Schrödinger equation for a class of spherically symmetric potentials in a simple and unified manner using the Lie algebraic approach within the framework of quasi-exact solvability. We illustrate that all models give rise to the same basic differential equation, which is expressible as an element of the universal enveloping algebra of sl(2. Then, we obtain the general exact solutions of the problem by employing the representation theory of sl(2 Lie algebra.
Spherically symmetric solution in higher-dimensional teleparallel equivalent of general relativity
Institute of Scientific and Technical Information of China (English)
Gamal G.L.Nashed
2013-01-01
A theory of (N + 1)-dimensional gravity is developed on the basis of the teleparallel equivalent of general relativity (TEGR).The fundamental gravitational field variables are the (N + 1)-dimensional vector fields,defined globally on a manifold M,and the gravitational field is attributed to the torsion.The form of Lagrangian density is quadratic in torsion tensor.We then give an exact five-dimensional spherically symmetric solution (Schwarzschild (4 + 1)-dimensions).Finally,we calculate energy and spatial momentum using gravitational energy-momentum tensor and superpotential 2-form.
Static Spherically Symmetric Kerr-Schild Metrics and Implications for the Classical Double Copy
Ridgway, Alexander K
2015-01-01
We discuss the physical interpretation of stress-energy tensors that source static spherically symmetric Kerr-Schild metrics. We find that the sources of such metrics with no curvature singularities or horizons do not simultaneously satisfy the weak and strong energy conditions. Sensible stress-energy tensors usually satisfy both of them. Under most circumstances these sources are not perfect fluids and contain shear stresses. We show that for these systems the classical double copy associates the electric charge density to the Komar energy density. In addition, we demonstrate that the stress-energy tensors are determined by the electric charge density and their conservation equations.
Static spherically symmetric Kerr-Schild metrics and implications for the classical double copy
Ridgway, Alexander K.; Wise, Mark B.
2016-08-01
We discuss the physical interpretation of stress-energy tensors that source static spherically symmetric Kerr-Schild metrics. We find that the sources of such metrics with no curvature singularities or horizons do not simultaneously satisfy the weak and strong energy conditions. Sensible stress-energy tensors usually satisfy both of them. Under most circumstances, these sources are not perfect fluids and contain shear stresses. We show that for these systems the classical double copy associates the electric charge density to the Komar energy density. In addition, we demonstrate that the stress-energy tensors are determined by the electric charge density and their conservation equations.
Spherically symmetric vacuum in covariant F (T )=T +α/2 T2+O (Tγ) gravity theory
DeBenedictis, Andrew; Ilijić, Saša
2016-12-01
Recently, a fully covariant version of the theory of F (T ) torsion gravity has been introduced by M. Kršśák and E. Saridakis [Classical Quantum Gravity 33, 115009 (2016)]. In covariant F (T ) gravity, the Schwarzschild solution is not a vacuum solution for F (T )≠T , and therefore determining the spherically symmetric vacuum is an important open problem. Within the covariant framework, we perturbatively solve the spherically symmetric vacuum gravitational equations around the Schwarzschild solution for the scenario with F (T )=T +(α /2 )T2 , representing the dominant terms in theories governed by Lagrangians analytic in the torsion scalar. From this, we compute the perihelion shift correction to solar system planetary orbits as well as perturbative gravitational effects near neutron stars. This allows us to set an upper bound on the magnitude of the coupling constant, α , which governs deviations from general relativity. We find the bound on this nonlinear torsion coupling constant by specifically considering the uncertainty in the perihelion shift of Mercury. We also analyze a bound from a similar comparison with the periastron orbit of the binary pulsar PSR J0045-7319 as an independent check for consistency. Setting bounds on the dominant nonlinear coupling is important in determining if other effects in the Solar System or greater universe could be attributable to nonlinear torsion.
Static Spherically Symmetric Solutions of the SO(5) Einstein Yang-Mills Equations
Bartnik, Robert A; Oliynyk, Todd A
2009-01-01
Globally regular (ie. asymptotically flat and regular interior), spherically symmetric and localised ("particle-like") solutions of the coupled Einstein Yang-Mills (EYM) equations with gauge group SU(2) have been known for more than 20 years, yet their properties are still not well understood. Spherically symmetric Yang--Mills fields are classified by a choice of isotropy generator and SO(5) is distinguished as the simplest model with a \\emph{non-Abelian} residual (little) group, $SU(2)\\times U(1)$, and which admits globally regular particle-like solutions. We exhibit an algebraic gauge condition which normalises the residual gauge freedom to a finite number of discrete symmetries. This generalises the well-known reduction to the real magnetic potential $w(r,t)$ in the original SU(2) YM model. Reformulating using gauge invariant polynomials dramatically simplifies the system and makes numerical search techniques feasible. We find three families of embedded SU(2) EYM equations within the SO(5) system, one of w...
An excision scheme for black holes in constrained evolution formulations: spherically symmetric case
Cordero-Carrión, Isabel; Novak, Jérôme; Jaramillo, José Luis
2013-01-01
Excision techniques are used in order to deal with black holes in numerical simulations of Einstein equations and consist in removing a topological sphere containing the physical singularity from the numerical domain, applying instead appropriate boundary conditions at the excised surface. In this work we present recent developments of this technique in the case of constrained formulations of Einstein equations and for spherically symmetric spacetimes. We present a new set of boundary conditions to apply to the elliptic system in the fully-constrained formalism of Bonazzola et al. (2004), at an arbitrary sphere inside the apparent horizon. Analytical properties of this system of boundary conditions are studied and, under some assumptions, an exponential convergence toward the stationary solution is exhibited for the vacuum spacetime. This is verified in numerical examples, together with the applicability in the case of the accretion of a scalar field onto a Schwarzschild black hole.
Static slightly non-spherically symmetric, and slowly rotating linearised vacuum spacetimes
Saw, Vee-Liem
2015-01-01
We apply the general method of constructing manifolds of revolution around a given curve to derive first order perturbations on the Schwarzschild metric. Two different perturbations are carried out separately: 1) Non-rotating 2-spheres are added along a plane curve slightly deviated from the "Schwarzschild line"; 2) Slow-rotating 2-spheres are added along the "Schwarzschild line". For (1), we obtain the first order vacuum solution, representing the exterior region of a static slightly non-spherically symmetric body. No higher order vacuum solution exists. For (2), we find that the first order vacuum solution is equivalent to the slowly rotating Kerr metric. This is hence a much simpler and geometrically insightful derivation as compared to the gravitomagnetic one, where this rotating-shells construction is a direct manifestation of the frame-dragging phenomenon. A (full non-perturbative) generalisation to this method is explored here, by adding rotating 2-ellipsoids. It turns out however, that this cannot pro...
Stability of Schwarzschild-AdS for the spherically symmetric Einstein-Klein-Gordon system
Holzegel, Gustav
2011-01-01
In this paper, we study the global behavior of solutions to the spherically symmetric coupled Einstein-Klein-Gordon (EKG) system in the presence of a negative cosmological constant. We prove that the Schwarzschild-AdS spacetimes (the trivial black hole solutions of the EKG system for which $\\phi=0$ identically) are asymptotically stable: Small perturbations of Schwarzschild-AdS initial data again lead to regular black holes, with the metric on the black hole exterior approaching a Schwarzschild-AdS spacetime. The main difficulties in the proof arise from the lack of monotonicity for the Hawking mass and the asymptotically AdS boundary conditions, which render even (part of) the orbital stability intricate. These issues are resolved in a bootstrap argument on the black hole exterior, with the redshift effect and weighted Hardy inequalities playing the fundamental role in the analysis. Both integrated decay and pointwise decay estimates are obtained.
Non-Singular Spherically Symmetric Solution in Einstein-Scalar-Tensor Gravity
Moffat, J W
2007-01-01
A static spherically symmetric metric in Einstein-scalar-tensor gravity theory with a scalar field potential is non-singular for all real values of the coordinates. It does not have a black hole event horizon and there is no essential singularity at the origin of coordinates. The weak energy condition $\\rho > 0$ is satisfied but the strong energy condition $\\rho+3p > 0$ is violated by a scalar field ``dark energy'' vacuum contribution with pressure $p_\\phi < -{1/3}\\rho_\\phi$. The collapse of a star with zero normal matter pressure and uniform matter density is solved for an interior constant scalar field vacuum energy and leads to a finite singularity free collapsed object called a ``grey star'' with a non-singular exterior gravitational field. The properties of hydrostatic stability of a grey star are obtained and compared to the black hole Schwarzschild solution in general relativity.
Shestakova, T P
2013-01-01
We construct Hamiltonian dynamics of the generalized spherically symmetric gravitational model in extended phase space. We start from the Faddeev - Popov effective action with gauge-fixing and ghost terms, making use of gauge conditions in differential form. It enables us to introduce missing velocities into the Lagrangian and then construct a Hamiltonian function according a usual rule which is applied for systems without constraints. The main feature of Hamiltonian dynamics in extended phase space is that it can be proved to be completely equivalent to Lagrangian dynamics derived from the effective action. The sets of Lagrangian and Hamiltonian equations are not gauge invariant in general. We demonstrate that solutions to the obtained equations include those of the gauge invariant Einstein equations, and also discuss a possible role of gauge-noninvariant terms. Then, we find a BRST invariant form of the effective action by adding terms not affecting Lagrangian equations. After all, we construct the BRST cha...
Coughlin, Eric R
2016-01-01
We present the exact solutions for the collapse of a spherically-symmetric, cold (i.e., pressureless) cloud under its own self-gravity, valid for arbitrary initial density profiles and not restricted to the realm of self-similarity. These solutions exhibit a number of remarkable features, including the self-consistent formation of and subsequent accretion onto a central point mass. A number of specific examples are provided, and we show that Penston's solution of pressureless, self-similar collapse is recovered for polytropic density profiles; importantly, however, we demonstrate that the time over which this solution holds is fleetingly narrow, implying that much of the collapse proceeds non-self-similarly. We show that our solutions can naturally incorporate turbulent pressure support, and we investigate the evolution of overdensities -- potentially generated by such turbulence -- as the collapse proceeds. Finally, we analyze the evolution of the angular velocity and magnetic fields in the limit that their ...
Higher spins tunneling from a time dependent and spherically symmetric black hole
Energy Technology Data Exchange (ETDEWEB)
Siahaan, Haryanto M. [Parahyangan Catholic University, Physics Department, Bandung (Indonesia)
2016-03-15
The discussions of Hawking radiation via tunneling method have been performed extensively in the case of scalar particles. Moreover, there are also several works in discussing the tunneling method for Hawking radiation by using higher spins, e.g. neutrino, photon, and gravitino, in the background of static black holes. Interestingly, it is found that the Hawking temperature for static black holes using the higher spins particles has no difference compared to the one computed using scalars. In this paper, we study the Hawking radiation for a spherically symmetric and time dependent black holes using the tunneling of Dirac particles, photon, and gravitino. We find that the obtained Hawking temperature is similar to the one derived in the tunneling method by using scalars. (orig.)
Spherically-symmetric Accretion onto a Black Hole at the Center of a Young Stellar Cluster
Silich, Sergiy; Hueyotl-Zahuantitla, Filiberto
2008-01-01
We present a self-consistent, bimodal stationary solution for spherically symmetric flows driven by young massive stellar clusters with a central supermassive black hole. We demonstrate that the hydrodynamic regime of the flow depends on the location of the cluster in the 3D (star cluster mechanical luminosity - BH mass - star cluster radius) parameter space. We show that a threshold mechanical luminosity (L_crit) separates clusters which evolve in the BH dominated regime frome those whose internal structure is strongly affected by the radiative cooling. In the first case(below the threshold energy) gravity of the BH separates the flow into two distinct zones: the inner accretion zone and the outer zone where the star cluster wind is formed. In the second case (above the critical luminosity), catastrophic cooling sets in inside the cluster. In this case the injected plasma becomes thermally unstable that inhibits a complete stationary solution. We compared the calculated accretion rates and the BH luminositie...
Field Equations and Radial Solution in a Noncommutative Spherically Symmetric Geometry
Yazdani, Aref
2014-01-01
We study a noncommutative theory of gravity in the framework of torsional spacetime. This theory is based on a Lagrangian obtained by applying the technique of dimensional reduction of noncommutative gauge theory and that the yielded diffeomorphism invariant field theory can be made equivalent to a teleparallel formulation of gravity. Field equations are derived in the framework of teleparallel gravity through Weitzenbock geometry. We solve these field equations by considering a mass that is distributed spherically symmetrically in a stationary static spacetime in order to obtain a noncommutative line element.This new line element interestingly reaffirms the coherent state theory for a noncommutative Schwarzschild black hole. For the first time, we derive the Newtonian gravitational force equation in the commutative relativity framework, and this result could provide the possibility to investigate examples in various topics in quantum and ordinary theories of gravity.
On spherically symmetric solutions with horizon in model with multicomponent anisotropic fluid
Dehnen, H
2003-01-01
A family of spherically symmetric solutions in the model with m-component anisotropic fluid is considered. The metric of the solution depends on parameters q_s, s = 1,...,m, relating radial pressures and the densities and contains (n -1)m parameters corresponding to Ricci-flat "internal space" metrics and obeying certain m(m-1)/2 ("orthogonality") relations. For q_s = 1 (for all s) and certian equations of state (p_i^s = \\pm \\rho^s) the metric coincides with the metric of intersecting black brane solution in the model with antisymmetric forms. A family of solutions with (regular) horizon corresponding to natural numbers q_s = 1,2,... is singled out. Certain examples of "generalized simulation" of intersecting M-branes in D=11 supergravity are considered. The post-Newtonian parameters \\beta and \\gamma corresponding to the 4-dimensional section of the metric are calculated.
A new model for spherically symmetric charged compact stars of embedding class 1
Energy Technology Data Exchange (ETDEWEB)
Maurya, S.K. [University of Nizwa, Department of Mathematical and Physical Sciences, College of Arts and Science, Nizwa (Oman); Gupta, Y.K. [Raj Kumar Goel Institute of Technology, Department of Mathematics, Ghaziabad, U.P. (India); Ray, Saibal [Government College of Engineering and Ceramic Technology, Department of Physics, Kolkata, West Bengal (India); Deb, Debabrata [Indian Institute of Engineering Science and Technology, Department of Physics, Howrah, West Bengal (India)
2017-01-15
In the present study we search for a new stellar model with spherically symmetric matter and a charged distribution in a general relativistic framework. The model represents a compact star of embedding class 1. The solutions obtained here are general in nature, having the following two features: first of all, the metric becomes flat and also the expressions for the pressure, energy density, and electric charge become zero in all the cases if we consider the constant A = 0, which shows that our solutions represent the so-called 'electromagnetic mass model' [17], and, secondly, the metric function ν(r), for the limit n tending to infinity, converts to ν(r) = Cr{sup 2}+ ln B, which is the same as considered by Maurya et al. [11]. We have investigated several physical aspects of the model and find that all the features are acceptable within the requirements of contemporary theoretical studies and observational evidence. (orig.)
Energy and momentum of a spherically symmetric dilaton frame as regularized by teleparallel gravity
Nashed, Gamal G L
2011-01-01
We calculate energy and momentum of a spherically symmetric dilaton frame using the gravitational energy-momentum 3-form within the tetrad formulation of general relativity (GR). The frame we use is characterized by an arbitrary function $\\Upsilon$ with the help of which all the previously found solutions can be reproduced. We show how the effect of inertia {\\it (which is mainly reproduced from $\\Upsilon$)} makes the total energy and momentum always different from the well known result when we use the Riemannian connection ${{\\widetilde \\Gamma}_\\alpha}^\\beta$. On the other hand, when use is made of the covariant formulation of teleparallel gravity, which implies to take into account the pure gauge connection, teleparallel gravity always yields the physically relevant result for the energy and momentum.
Generation of spherically symmetric metrics in $f\\left( R\\right) $ gravity
Amirabi, Z; Mazharimousavi, S Habib
2015-01-01
In $D-$dimensional spherically symmetric $f\\left( R\\right) $ gravity there are three unknown functions to be determined from the fourth order differential equations. It is shown that the system remarkably integrates to relate two functions through the third one to provide reduction to second order equations accompanied with a large class of potential solutions. The third function which acts as the generator of the process is $F\\left( R\\right) =\\frac{df\\left( R\\right) }{dR}.$ As particular examples, besides known ones, we obtain new black hole solutions in any dimension $D$. We further extend our analysis to cover particularly chosen non-zero energy-momentum tensors.
Energy eigenvalues of spherical symmetric potentials with relativistic corrections: analytic results
Energy Technology Data Exchange (ETDEWEB)
Dineykhan, M; Zhaugasheva, S A [Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna (Russian Federation); Toinbaeva, N Sh [al-Farabi Kazak National University, Almaty (Kazakhstan)
2010-01-14
Based on the investigation of the asymptotic behaviour of the polarization loop function for charged n scalar particles in an external gauge field, we determine the interaction Hamiltonian including the relativistic corrections. The energy eigenvalues of spherical symmetric potentials for two-particle bound state systems with relativistic corrections are analytically derived. The energy spectra of linear and funnel potentials with orbital and radial excitations are determined. The energy spectrum of a superposition of Coulomb and Yukawa potentials is also determined. Our result shows that the energy spectrum with the relativistic corrections for the linear, harmonic oscillator and funnel potentials is smaller than the upper boundaries for the energy spectrum established in the framework of the spinless Salpeter equation for the orbital and radial excited states. The relativistic corrections to the energy spectrum of a superposition of the attractive Coulomb potential and the Yukawa (exponentially screened Coulomb) potentials are very small.
A Simple General Solution of the Radial Schrodinger Equation for Spherically Symmetric Potentials
Erbil, H H
2003-01-01
By using a simple procedure the general solution of the time-independent radial Schrodinger Equation for spherical symmetric potentials was made without making any approximation. The wave functions are always periodic. It appears two diffucilties: one of them is the solution of the equation E= U(r), where E and U(r) are the total an effective potential energies, respectively, and the other is the calculation of the integral of the square root of U(r). If analytical calculations are not possible, one must apply numerical methods. To find the energy wave function of the ground state, there is no need for the calculation of this integral, it is sufficient to find the classical turning points, that is to solve the equation E=U(r).
A Model of Dust-like Spherically Symmetric Gravitational Collapse without Event Horizon Formation
Directory of Open Access Journals (Sweden)
Piñol M.
2015-10-01
Full Text Available Some dynamical aspects of gravitational collapse are explored in this paper. A time- dependent spherically symmetric metric is proposed and the corresponding Einstein field equations are derived. An ultrarelativistic dust-like stress-momentum tensor is considered to obtain analytical solutions of these equations, with the perfect fluid con- sisting of two purely radial fluxes — the inwards flux of collapsing matter and the outwards flux of thermally emitted radiation. Thermal emission is calculated by means of a simplistic but illustrative model of uninteracting collapsing shells. Our results show an asymptotic approach to a maximal space-time deformation without the formation of event horizons. The size of the body is slightly larger than the Schwarzschild radius during most of its lifetime, so that there is no contradiction with either observations or previous theorems on black holes. The relation of the latter with our results is scruti- nized in detail.
Jacobi stability of the vacuum in the static spherically symmetric brane world models
Harko, T
2008-01-01
We analyze the stability of the structure equations of the vacuum in the brane world models, by using both the linear (Lyapunov) stability analysis, and the Jacobi stability analysis, the Kosambi-Cartan-Chern (KCC) theory. In the brane world models the four dimensional effective Einstein equations acquire extra terms, called dark radiation and dark pressure, respectively, which arise from the embedding of the 3-brane in the bulk. Generally, the spherically symmetric vacuum solutions of the brane gravitational field equations, have properties quite distinct as compared to the standard black hole solutions of general relativity. We close the structure equations by assuming a simple linear equation of state for the dark pressure. In this case the vacuum is Jacobi stable only for a small range of values of the proportionality constant relating the dark pressure and the dark radiation. The unstable trajectories on the brane behave chaotically, in the sense that after a finite radial distance it would be impossible...
Spherically symmetric Jordan-Brans-Dicke quantum gravity with de Broglie Bohm pilot wave perspective
Ghaffarnejad, Hossein
2013-01-01
We obtain two dimensional analogue of the Jordan-Brans-Dicke (JBD) gravity action described in four dimensional spherically symmetric curved space time metric. There will be two scalar fields, namely, the Brans Dicke (BD) $\\phi$ and scale factor of 2-sphere part of the space time $\\psi.$ There is obtained a suitable duality transformation between $(\\psi,\\phi)$ and $(\\rho,S)$ where $\\rho$ and $S$ are respectively amplitude and phase part of the corresponding de Broglie pilot wave function $\\Psi(\\rho,S)=\\sqrt{\\rho}e^{iS}.$ There is established covariant conservation of mass-energy current density of particles ensemble $J_a=\\rho\\partial_aS,$ in a particular dynamical conformal frame described by $(\\rho,S).$
Huang, Xiangdi
2017-02-01
One of the most influential fundamental tools in harmonic analysis is the Riesz transforms. It maps Lp functions to Lp functions for any p ∈ (1 , ∞) which plays an important role in singular operators. As an application in fluid dynamics, the norm equivalence between ‖∇u‖Lp and ‖ div u ‖ Lp +‖ curl u ‖ Lp is well established for p ∈ (1 , ∞). However, since Riesz operators sent bounded functions only to BMO functions, there is no hope to bound ‖∇u‖L∞ in terms of ‖ div u ‖ L∞ +‖ curl u ‖ L∞. As pointed out by Hoff (2006) [11], this is the main obstacle to obtain uniqueness of weak solutions for isentropic compressible flows. Fortunately, based on new observations, see Lemma 2.2, we derive an exact estimate for ‖∇u‖L∞ ≤ (2 + 1 / N)‖ div u ‖ L∞ for any N-dimensional radially symmetric vector functions u. As a direct application, we give an affirmative answer to the open problem of uniqueness of some weak solutions to the compressible spherically symmetric flows in a bounded ball.
Energy and momentum of general spherically symmetric frames on the regularizing teleparallelism
Institute of Scientific and Technical Information of China (English)
Gamal G. L. Nashed
2012-01-01
In the context of the covariant teleparallel framework,we use the 2-form translational momentum to compute the total energy of two general spherically symmetric frames.The first one is characterized by an arbitrary function H(γ),which preserves the spherical symmetry and reproduces all the previous solutions,while the other one is characterized by a parameter ξ which ensures the vanishing of the axial of trace of the torsion.We calculate the total energy by using two procedures,i.e.,when the Weitzenb?ck connection Γαβ is trivial,and show how H(r) and ξ play the role of an inertia that leads the total energy to be unphysical.Therefore,we take into account Γαβ and show that although the spacetimes we use contain an arbitrary function and one parameter,they have no effect on the form of the total energy and momentum as it should be.
Multi-horizon spherically symmetric spacetimes with several scales of vacuum energy
Bronnikov, Kirill; Galaktionov, Evgeny
2012-01-01
We present a family of spherically symmetric multi-horizon spacetimes with a vacuum dark fluid, associated with a time-dependent and spatially inhomogeneous cosmological term. The vacuum dark fluid is defined in a model-independent way by the symmetry of its stress-energy tensor, i.e., its invariance under Lorentz boosts in a distinguished spatial direction ($p_r=-\\rho$ for spherical symmetry), which makes the dark fluid essentially anisotropic and allows its density to evolve. The related cosmological models belong to the Lemaitre class of models with anisotropic fluids and describe a universe with several scales of vacuum energy related to phase transitions during its evolution. The typical behavior of solutions and the number of spacetime horizons are determined by the number of vacuum scales. We study in detail a model with three vacuum scales: GUT, QCD and that responsible for the present accelerated expansion. The model parameters are fixed by the observational data and by analyticity and causality cond...
Aktosun, Tuncay; Gintides, Drossos; Papanicolaou, Vassilis G.
2011-11-01
The recovery of a spherically symmetric wave speed v is considered in a bounded spherical region of radius b from the set of the corresponding transmission eigenvalues for which the corresponding eigenfunctions are also spherically symmetric. If the integral of 1/v on the interval [0, b] is less than b, assuming that there exists at least one v corresponding to the data, it is shown that v is uniquely determined by the data consisting of such transmission eigenvalues and their ‘multiplicities’, where the ‘multiplicity’ is defined as the multiplicity of the transmission eigenvalue as a zero of a key quantity. When that integral is equal to b, the unique recovery is obtained when the data contain one additional piece of information. Some similar results are presented for the unique determination of the potential from the transmission eigenvalues with ‘multiplicities’ for a related Schrödinger equation.
Aktosun, Tuncay; Papanicolaou, Vassilis G.
2013-06-01
The unique reconstruction of a spherically symmetric wave speed v is considered in a bounded spherical region of radius b from the set of corresponding transmission eigenvalues for which the corresponding eigenfunctions are also spherically symmetric. If the integral of 1/v on the interval [0, b] is less than b, assuming that there exists at least one v corresponding to the data, then v is uniquely reconstructed from the data consisting of such transmission eigenvalues and their ‘multiplicities’, where the multiplicity is defined as the multiplicity of the transmission eigenvalue as a zero of a key quantity. When that integral is equal to b, the unique reconstruction is presented when the data set contains one additional piece of information. Some similar results are presented for the unique reconstruction of the potential from the transmission eigenvalues with multiplicities for a related Schrödinger equation.
An investigation of the Buchdahl inequality for spherically symmetric static shells
Energy Technology Data Exchange (ETDEWEB)
Andreasson, Haakan [Department of Mathematics, Chalmers, S-41296 Goeteborg (Sweden)
2007-05-15
A classical result by Buchdahl [9] shows that a class of static spherically symmetric solutions of the Einstein equations obey the inequality 2M/R {<=} 8/9, where M is the total ADM mass and R the area radius of the body. Buchdahl's proof rests on the hypotheses that the energy density is non-increasing outwards and that the pressure is isotropic. In this work neither of Buchdahl's hypotheses are assumed. We consider non-isotropic spherically symmetric shells, supported in [R{sub 0}, R{sub 1}], R{sub 0} > 0, of matter models for which the energy density {rho} {>=} 0, and the radial- and tangential pressures p {>=} 0 and q, satisfy p + q {<=} {omega}{rho}, {omega} {>=} 1. Note that this inequality holds with {omega} = 3 for any matter model which satisfies the dominant energy condition. We show a Buchdahl type inequality for shells which are thin; given an {epsilon} < 1/4 there is a {kappa} > 0 such that 2M/R{sub 1} {<=} 1 - {kappa} when R{sub 1}/R{sub 0} 1 + {epsilon}. It is also shown that for a sequence of solutions such that R{sub 1}/R{sub 0} {yields} 1, the limit supremum of 2M/R{sub 1} of the sequence is bounded by ((2{omega} + 1){sup 2} - 1)/(2{omega} + 1){sup 2} (which equals 8/9 if {omega} = 1). We emphasize that no field equations for the matter are used for this result. However, in the second part we consider the Einstein-Vlasov system and use the matter field equation to construct a family of static solutions with the property that R{sub 1}/R{sub 0} {yields} 1. We also show that for this sequence the value 8/9 of 2M/R{sub 1} is attained in the limit (note that {omega} = 1 for Vlasov matter). The energy density of this sequence get more and more peaked, which should be contrasted to the solution for which 2M/R = 8/9 in Buchdahl's original work where {rho} is constant and p blows up at r = 0. Clearly, this solution cannot satisfy the inequality p = q {<=} {omega}{rho}, in particular it violates the dominant energy condition.
Araujo, M E
2010-01-01
One of the continuing challenges in cosmology has been to determine the large-scale space-time metric from observations with a minimum of assumptions -- without, for instance, assuming that the universe is almost Friedmann-Lema\\^{i}tre-Robertson-Walker (FLRW). If we are lucky enough this would be a way of demonstrating that our universe is FLRW, instead of presupposing it or simply showing that the observations are consistent with FLRW. Showing how to do this within the more general spherically symmetric, inhomogeneous space-time framework takes us a long way towards fulfilling this goal. In recent work researchers have shown how this can be done both in the traditional Lema\\^{i}tre-Tolman-Bondi (LTB) 3 + 1 coordinate framework, and in the observational coordinate (OC) framework, in which the radial coordinate $y$ is null (light-like) and measured down the past lightcone of the observer. Here we give an elaborated account of this second approach, and compare it to the LTB 3 + 1 procedure with respect to the s...
Spherically symmetric black holes in $f(R)$ gravity: Is geometric scalar hair supported ?
Cañate, Pedro; Salgado, Marcelo
2015-01-01
We discuss with a rather critical eye the current situation of black hole (BH) solutions in $f(R)$ gravity and shed light about its geometrical and physical significance. We also argue about the meaning, existence or lack thereof of a Birkhoff's theorem in this kind of modified gravity. We focus then on the analysis and quest of $non-trivial$ (i.e. hairy) $asymptotically\\,\\,flat$ (AF) BH solutions in static and spherically symmetric (SSS) spacetimes in vacuum having the property that the Ricci scalar does $not$ vanish identically in the domain of outer communication. To do so, we provide and enforce the $regularity\\,\\,conditions$ at the horizon in order to prevent the presence of singular solutions there. Specifically, we consider several classes of $f(R)$ models like those proposed recently for explaining the accelerated expansion in the universe and which have been thoroughly tested in several physical scenarios. Finally, we report analytical and numerical evidence about the $absence$ of $geometric\\,\\,hair$...
Spherically Symmetric Gravitational Collapse of a Clump of Solids in a Gas
Shariff, Karim
2014-01-01
Several mechanisms have been identified that create dense particle clumps in the solar nebula. The present work is concerned with the gravitational collapse of such clumps, idealized as being spherically symmetric. Calculations using the two-fluid model are performed (almost) up to the time when a central density singularity forms. The end result of the study is a parametrization for this time, in order that it may be compared with timescales for various disruptive effects to which clumps may be subject. An important effect is that as the clump compresses, it also compresses the gas due to drag. This increases gas pressure which retards particle collapse and leads to oscillation in the size and density of the clump. The ratio of gravitational force to gas pressure gives a two-phase Jeans parameter, $J_t$, which is the classical Jeans parameter with the sound speed replaced by an the wave speed in a coupled two-fluid medium. Its use makes the results insensitive to the initial density ratio of particles to gas...
Non-linear effects in the post-Newtonian approximation of a spherically symmetric field
Energy Technology Data Exchange (ETDEWEB)
Gambi, J.M.; Zamorano, P. [Madrid Univ. Carlos 3, Madrid (Spain). Dept. de Matematicas; Romero, P.; Garcia del Pino, M.L. [Madrid Univ. Complutense, Madrid (Spain). Dept. de Astronomia y Geodesia
2000-02-01
Conditions for the compatibility of the exterior metric of a spherically symmetric object with the field equations for the empty space and equations of motion and of trajectories for test particles, written in polar Gaussian and Fermi coordinates, are obtained to show that, although their explicit exact solutions cannot be derived in these coordinates, the post-Newtonian limits of these solutions can, nevertheless, be obtained. With these limits, it is next shown that the cited post-Newtonian equations do not fit into the standard post-Newtonian approximation either. It is then shown that these coordinates can, nevertheless, be included in a more general formalism together with the usual post-Newtonian (standard, harmonic, Painleve and isotropic) coordinates so that their respective equations of motion may be compared to each other and, finally, it is demonstrated that the only non-linear term taken in the Christoffel symbols with these usual coordinates in the standard post-Newtonian equations of motion to explain some known perturbations is not needed when polar Gaussian or Fermi coordinates are used to explain also those perturbations. In fact, it is demonstrated that these are the only coordinates for which that term becomes zero.
Complete affine connection in the causal boundary: static, spherically symmetric spacetimes
Harris, Steven (Stacey) G.
2017-02-01
The boundary at I^+, future null infinity, for a standard static, spherically symmetric spactime is examined for possible linear connections. Two independent methods are employed, one for treating I^+ as the future causal boundary, and one for treating it as a conformal boundary (the latter is subsumed in the former, which is of greater generality). Both methods provide the same result: a constellation of various possible connections, depending on an arbitrary choice of a certain function, a sort of gauge freedom in obtaining a natural connection on I^+; choosing that function to be constant (for instance) results in a complete connection. Treating I^+ as part of the future causal boundary, the method is to impute affine connections on null hypersurfaces going out to I^+, in terms of a transverse vector field on each null hypersurface (there is much gauge freedom on choice of the transverse vector fields). Treating I^+ as part of a conformal boundary, the method is to make a choice of conformal factor that makes the boundary totally geodesic in the enveloping manifold (there is much gauge freedom in choice of that conformal factor). Similar examination is made of other boundaries, such as timelike infinity and timelike and spacelike singularities. These are much simpler, as they admit a unique connection from a similar limiting process (i.e., no gauge freedom); and that connection is complete.
Cyclic and heteroclinic flows near general static spherically symmetric black holes
Energy Technology Data Exchange (ETDEWEB)
Ahmed, Ayyesha K.; Jamil, Mubasher [National University of Sciences and Technology(NUST), Department of Mathematics, School of Natural Sciences (SNS), Islamabad (Pakistan); Azreg-Ainou, Mustapha [Baskent University, Engineering Faculty, Ankara (Turkey); Faizal, Mir [University of Lethbridge, Department of Physics and Astronomy, Alberta (Canada); University of Waterloo, Department of Physics and Astronomy, Waterloo, ON (Canada)
2016-05-15
We investigate the Michel-type accretion onto a static spherically symmetric black hole. Using a Hamiltonian dynamical approach, we show that the standard method employed for tackling the accretion problem has masked some properties of the fluid flow. We determine new analytical solutions that are neither transonic nor supersonic as the fluid approaches the horizon(s); rather, they remain subsonic for all values of the radial coordinate. Moreover, the three-velocity vanishes and the pressure diverges on the horizon(s), resulting in a flow-out of the fluid under the effect of its own pressure. This is in favor of the earlier prediction that pressure-dominant regions form near the horizon. This result does not depend on the form of the metric and it applies to a neighborhood of any horizon where the time coordinate is timelike. For anti-de Sitter-like f(R) black holes we discuss the stability of the critical flow and determine separatrix heteroclinic orbits. For de Sitter-like f(R) black holes, we construct polytropic cyclic, non-homoclinic, physical flows connecting the two horizons. These flows become non-relativistic for Hamiltonian values higher than the critical value, allowing for a good estimate of the proper period of the flow. (orig.)
Ziegler, Andy; Köhler, Thomas; Nielsen, Tim; Proksa, Roland
2006-12-01
In cone-beam transmission tomography the measurements are performed with a divergent beam of x-rays. The reconstruction with iterative methods is an approach that offers the possibility to reconstruct the corresponding images directly from these measurements. Another approach based on spherically symmetric basis functions (blobs) has been reported with results demonstrating a better image quality for iterative reconstruction algorithms. When combining the two approaches (i.e., using blobs in iterative cone-beam reconstruction of divergent rays) the problem of blob sampling without introducing aliasing must be addressed. One solution to this problem is to select a blob size large enough to ensure a sufficient sampling, but this prevents a high resolution reconstruction, which is not desired. Another solution is a heuristic low-pass filtering, which removes this aliasing, but neglects the different contributions of blobs to the absorption depending on the spatial position in the volume and, therefore, cannot achieve the best image quality. This article presents a model of sampling the blobs which is motivated by the beam geometry. It can be used for high resolution reconstruction and can be implementedefficiently.
Compact invariant sets of the static spherically symmetric Einstein-Yang-Mills equations
Energy Technology Data Exchange (ETDEWEB)
Starkov, Konstantin E., E-mail: konst@citedi.m [CITEDI-IPN, Av. del Parque 1310, Mesa de Otay, Tijuana, BC (Mexico)
2010-04-05
In this Letter we obtain results concerning compact invariant sets of the static spherically symmetric Einstein-Yang-Mills (EYM) equations with help of studies of its localization. Let a be a cosmological constant and s be another parameter entering into these equations which is used for considering the physical time as a temporal variable, with s=1, while s=-1 is used for considering the physical time as a spatial variable. We show that in case s=1; a<0 the location of any compact invariant set is described by some system of linear inequalities. Then we prove that in case s=1; a>0 the set of all compact invariant sets consists of two equilibrium points only. Further, we state that in cases s=-1; a<0 and s=-1; a>0 there are only two equilibrium points and there are no periodic orbits. In addition, we prove that in the last two cases there are neither homoclinic orbits nor heteroclinic orbits as well.
Spherically Symmetric Solution of the Weyl-Dirac Theory of Gravitation and its Consequences
Babourova, O. V.; Frolov, B. N.; Kudlaev, P. E.; Romanova, E. V.
2016-12-01
The Poincaré and Poincaré-Weyl gauge theories of gravitation with Lagrangians quadratic on curvature and torsion in post-Riemannian spaces with the Dirac scalar field is discussed in a historical aspect. The various hypotheses concerning the models of a dark matter with the help of a scalar field are considered. The new conformal Weyl-Dirac theory of gravitation is proposed, which is a gravitational theory in Cartan-Weyl spacetime with the Dirac scalar field representing the dark matter model. A static spherically symmetric solution of the field equations in vacuum for a central compact mass is obtained as the metrics conformal to the Yilmaz-Rosen metrics. On the base of this solution one considers a radial movement of an interplanetary spacecraft starting from the Earth. Using the Newton approximation one obtains that the asymptotic line-of-sight velocity in this case depends on the parameters of the solution, and therefore one can obtain, on basis of the observable data, the values of these parameters and then the value of a rest mass of the Dirac scalar field.
Brihaye, Yves; Hartmann, Betti
2005-01-01
We construct solutions of an Einstein Yang Mills system including a cosmological constant in 4 + n spacetime dimensions, where the n-dimensional manifold associated with the extra dimensions is taken to be Ricci flat. Assuming the matter and metric fields to be independent of the n extra coordinates, a spherical symmetric ansatz for the fields leads to a set of coupled ordinary differential equations. We find that for n > 1 only solutions with either one non-zero Higgs field or with all Higgs fields constant and zero gauge field function (corresponding to a Wu Yang-type ansatz) exist. We give the analytic solutions available in this model. These are 'embedded' Abelian solutions with a diverging size of the manifold associated with the extra n dimensions. Depending on the choice of parameters, these latter solutions either represent naked singularities or they possess a single horizon. We also present solutions of the effective four-dimensional Einstein Yang Mills Higgs-dilaton model, where the higher-dimensional cosmological constant induces a Liouville-type potential. The solutions are non-Abelian solutions with diverging Higgs fields, which exist only up to a maximal value of the cosmological constant.
Trampert, Patrick; Vogelgesang, Jonas; Schorr, Christian; Maisl, Michael; Bogachev, Sviatoslav; Marniok, Nico; Louis, Alfred; Dahmen, Tim; Slusallek, Philipp
2017-03-21
Laminography is a tomographic technique that allows three-dimensional imaging of flat and elongated objects that stretch beyond the extent of a reconstruction volume. Laminography images can be reconstructed using iterative algorithms based on the Kaczmarz method. This study aims to develop and demonstrate a new reconstruction algorithm that may provide superior image reconstruction quality for this challenged imaging application. The images are initially represented using the coefficients over basis functions, which are typically piecewise constant functions (voxels). By replacing voxels with spherically symmetric volume elements (blobs) based on the generalized Kaiser-Bessel window functions, the images are reconstructed using this new adapted version of the algebraic image reconstruction technique. Band-limiting properties of blob functions are beneficial particular in the case of noisy projections and with only a limited number of available projections. Study showed that using blob basis functions improved full-width-at-half-maximum resolution from 10.2±1.0 to 9.9±0.9 (p functions, especially if noisy data is expected.
Thermodynamic Analysis of the Static Spherically Symmetric Field Equations in Rastall Theory
Directory of Open Access Journals (Sweden)
Hooman Moradpour
2016-01-01
Full Text Available The restrictions on the Rastall theory due to application of the Newtonian limit to the theory are derived. In addition, we use the zero-zero component of the Rastall field equations as well as the unified first law of thermodynamics to find the Misner-Sharp mass content confined to the event horizon of the spherically symmetric static spacetimes in the Rastall framework. The obtained relation is calculated for the Schwarzschild and de-Sitter back holes as two examples. Bearing the obtained relation for the Misner-Sharp mass in mind together with recasting the one-one component of the Rastall field equations into the form of the first law of thermodynamics, we obtain expressions for the horizon entropy and the work term. Finally, we also compare the thermodynamic quantities of system, including energy, entropy, and work, with their counterparts in the Einstein framework to have a better view about the role of the Rastall hypothesis on the thermodynamics of system.
Complete Affine Connection in the Causal Boundary: Static, Spherically Symmetric Spacetimes
Steven,
2016-01-01
The boundary at $\\Cal I^+$, future null infinity, for a standard static, spherically symmetric spactime is examined for possible linear connections. Two independent methods are employed, one for treating $\\Cal I^+$ as the future causal boundary, and one for treating it as a conformal boundary (the latter is subsumed in the former, which is of greater generality). Both methods provide the same result: a constellation of various possible connections, depending on an arbitrary choice of a certain function, a sort of gauge freedom in obtaining a natural connection on $\\Cal I^+$; choosing that function to be constant (for instance) results in a complete connection. Treating $\\Cal I^+$ as part of the future causal boundary, the method is to impute affine connections on null hypersurfaces going out to $\\Cal I^+$, in terms of a transverse vector field on each null hypersurface (there is much gauge freedom on choice of the transverse vector fields). Treating $\\Cal I^+$ as part of a conformal boundary, the method is to...
Teyssandier, Pierre
2014-01-01
This paper is mainly devoted to the determination of the travel time of a photon as a function of the positions of the emitter and the receiver in a large class of static, spherically symmetric spacetimes. Such a function - often called time transfer function - is of crucial interest for testing metric theories of gravity in the solar system. Until very recently, this function was known only up to the second order in the Newtonian gravitational constant $G$ for a 3-parameter family of static, spherically symmetric metrics generalizing the Schwarzschild metric. We present here two procedures enabling to determine - at least in principle - the time transfer function at any order of approximation when the components of the metric are expressible in power series of the Schwarzschild radius of the central body divided by the radial coordinate. These procedures exclusively work for light rays which may be described as perturbations in power series in $G$ of a Minkowskian null geodesic passing through the positions ...
Spherically symmetric black holes in f (R) gravity: is geometric scalar hair supported?
Cañate, Pedro; Jaime, Luisa G.; Salgado, Marcelo
2016-08-01
We critically discuss current research on black hole (BH) solutions in f (R) gravity and shed light on its geometrical and physical significance. We also investigate the meaning, existence or lack thereof of Birkhoff’s theorem (BT) in this kind of modified gravity. We then focus on the analysis and search for non-trivial (i.e. hairy) asymptotically flat (AF) BH solutions in static and spherically symmetric (SSS) spacetimes in vacuum having the property that the Ricci scalar does not vanish identically in the domain of outer communication. To do so, we provide and enforce regularity conditions at the horizon in order to prevent the presence of singular solutions there. Specifically, we consider several classes of f (R) models like those proposed recently for explaining the accelerated expansion in the Universe and which have been thoroughly tested in several physical scenarios. Finally, we report analytical and numerical evidence about the absence of geometric hair in AFSSSBH solutions in those f (R) models. First, we submit the models to the available no-hair theorems (NHTs), and in the cases where the theorems apply, the absence of hair is demonstrated analytically. In the cases where the theorems do not apply, we resort to a numerical analysis due to the complexity of the non-linear differential equations. With that aim, a code to solve the equations numerically was built and tested using well-known exact solutions. In a future investigation we plan to analyze the problem of hair in de Sitter and anti-de Sitter backgrounds.
Horizon-less Spherically Symmetric Vacuum-Solutions in a Higgs Scalar-Tensor Theory of Gravity
Bezares-Roder, Nils M; Nandan, H; Bezares-Roder, Nils M.; Dehnen, Heinz; Nandan, Hemwati
2006-01-01
The exact static and spherically symmetric solutions of the vacuum field equations for a Higgs Scalar-Tensor theory (HSTT) are derived in Schwarzschild coordinates. It is shown that there exists no Schwarzschild horizon and that the massless scalar field acts like a massless field in the conventional theory of gravitation. Only in the center (point-particle) the fields are singular (as naked singularity). However, the Schwarzschild solution is obtained for the limit of vanishing excited Higgs fields.
Horizon-less Spherically Symmetric Vacuum-Solutions in a Higgs Scalar-Tensor Theory of Gravity
Bezares-Roder, Nils M.; Nandan, Hemwati; Dehnen, Heinz
2007-10-01
The exact static and spherically symmetric solutions of the vacuum field equations for a Higgs Scalar-Tensor theory (HSTT) are derived in Schwarzschild coordinates. It is shown that in general there exists no Schwarzschild horizon and that the fields are only singular (as naked singularity) at the center (i.e. for the case of a point-particle). However, the Schwarzschild solution as in usual general relativity (GR) is obtained for the vanishing limit of Higgs field excitations.
Hydrodynamic Analysis of the Spherical Underwater Robot SUR-II
Directory of Open Access Journals (Sweden)
Chunfeng Yue
2013-05-01
Full Text Available Abstract This paper describes the development of the second-generation Spherical Underwater Robot (SUR-II. The new SUR-II has an improved propulsion system structure, resulting in better performance compared with the original design. This paper focuses on the characteristics of the water-jet thruster and the spherical hull of the SUR-II. To analyse its hydrodynamic characteristics, the main hydrodynamic parameters of the SUR-II were estimated based on two reasonable assumptions and a reasonable dynamic equation was proposed to describe the relationship between force and velocity. Drag coefficients were calculated separately for vertical and horizontal motions due to the fin on the robot's equator and the holes in the robot's hull. The holes had a particularly adverse effect on the horizontal drag coefficient. A hydrodynamic analysis using computational fluid dynamics was then carried out to verify the estimated parameters. The velocity vectors, pressure contours and drag coefficient for each state of motion were obtained. Finally, the propulsive force was determined experimentally to verify the theoretical calculations and simulation results.
Wang, Tongjiang; Davila, Joseph M.
2014-01-01
Determining the coronal electron density by the inversion of white-light polarized brightness (pB) measurements by coronagraphs is a classic problem in solar physics. An inversion technique based on the spherically symmetric geometry (spherically symmetric inversion, SSI) was developed in the 1950s and has been widely applied to interpret various observations. However, to date there is no study of the uncertainty estimation of this method. We here present the detailed assessment of this method using a three-dimensional (3D) electron density in the corona from 1.5 to 4 solar radius as a model, which is reconstructed by a tomography method from STEREO/COR1 observations during the solar minimum in February 2008 (Carrington Rotation, CR 2066).We first show in theory and observation that the spherically symmetric polynomial approximation (SSPA) method and the Van de Hulst inversion technique are equivalent. Then we assess the SSPA method using synthesized pB images from the 3D density model, and find that the SSPA density values are close to the model inputs for the streamer core near the plane of the sky (POS) with differences generally smaller than about a factor of two; the former has the lower peak but extends more in both longitudinal and latitudinal directions than the latter. We estimate that the SSPA method may resolve the coronal density structure near the POS with angular resolution in longitude of about 50 deg. Our results confirm the suggestion that the SSI method is applicable to the solar minimum streamer (belt), as stated in some previous studies. In addition, we demonstrate that the SSPA method can be used to reconstruct the 3D coronal density, roughly in agreement with the reconstruction by tomography for a period of low solar activity (CR 2066). We suggest that the SSI method is complementary to the 3D tomographic technique in some cases, given that the development of the latter is still an ongoing research effort.
Ambrus, Victor E
2016-01-01
We consider rigidly rotating states in thermal equilibrium on static spherically symmetric spacetimes. Using the Maxwell-Juttner equilibrium distribution function, onstructed as a solution of the relativistic Boltzmann equation, the equilibrium particle flow four-vector, stress-energy tensor and the transport coefficients in the Marle model are computed. Their properties are discussed in view of the topology of the speed-of-light surface induced by the rotation for two classes of spacetimes: maximally symmetric (Minkowski, de Sitter and anti-de Sitter) and charged (Reissner-Nordstrom) black-hole spacetimes. To facilitate our analysis, we employ a non-holonomic comoving tetrad field, obtained unambiguously by applying a Lorentz boost on a fixed background tetrad.
Sokołowski, Leszek M
2014-01-01
We investigate local and global properties of timelike geodesics in three static spherically symmetric spacetimes. These properties are of its own mathematical relevance and provide a solution of the physical `twin paradox' problem. The latter means that we focus our studies on the search of the longest timelike geodesics between two given points. Due to problems with solving the geodesic deviation equation we restrict our investigations to radial and circular (if exist) geodesics. On these curves we find general Jacobi vector fields, determine by means of them sequences of conjugate points and with the aid of the comoving coordinate system and the spherical symmetry we determine the cut points. These notions identify segments of radial and circular gepdesics which are locally or globally of maximal length. In de Sitter spacetime all geodesics are globally maximal. In CAdS and Bertotti--Robinson spacetimes the radial geodesics which infinitely many times oscillate between antipodal points in the space contain...
Achour, Jibril Ben; Marciano, Antonino
2016-01-01
Using self dual Ashtekar variables, we investigate (at the effective level) the spherically symmetry reduced model of loop quantum gravity, both in vacuum and when coupled to a scalar field. Within the real Ashtekar-Barbero formulation, the system scalar field coupled to spherically symmetric gravity is known to possess a non closed (quantum) algebra of constraints once the holonomy corrections are introduced, which forbids the loop quantization of the model. Moreover, the vacuum case, while not anomalous, introduces modifications which are usually interpreted as a signature change of the metric in the deep quantum region. We show in this paper that both those difficulties disappear when working with self dual Ashtekar variables, both in the vacuum case and in the case of gravity minimally coupled to a scalar field. In this framework, the algebra of the holonomy corrected constraints is anomaly free and reproduces the classical hypersurface deformation algebra without any deformations. A possible path towards...
Marshall, B. D.; Chapman, W. G.
2013-01-01
In this paper we extend our previous theory [B. D. Marshall and W.G. Chapman, J. Chem. Phys. 139, 104904 (2013)] for mixtures of single patch colloids (p colloids) and colloids with spherically symmetric attractions (s colloids) to the case that the p colloids can have multiple patches. The theory is then applied to the case of a binary mixture of bi-functional p colloids which have an A and B type patch and s colloids which are not attracted to other s colloids and are attracted to only patc...
Marshall, B. D.; Chapman, W G
2013-01-01
In this paper we extend our previous theory [B. D. Marshall and W.G. Chapman, J. Chem. Phys. 139, 104904 (2013)] for mixtures of single patch colloids (p colloids) and colloids with spherically symmetric attractions (s colloids) to the case that the p colloids can have multiple patches. The theory is then applied to the case of a binary mixture of bi-functional p colloids which have an A and B type patch and s colloids which are not attracted to other s colloids and are attracted to only patc...
Barrios, Nahuel; Pullin, Jorge
2015-01-01
We consider a massive scalar field living on the recently found exact quantum space-time corresponding to vacuum spherically symmetric loop quantum gravity. The discreteness of the quantum space time naturally regularizes the scalar field, eliminating divergences. However, the resulting finite theory depends on the details of the micro physics. We argue that such dependence can be eliminated through a finite renormalization and discuss its nature. This is an example of how quantum field theories on quantum space times deal with the issues of divergences in quantum field theories.
Institute of Scientific and Technical Information of China (English)
ZHANG Hong-Bao; CAO Zhou-Jian; GAO Chong-Shou
2004-01-01
Si-Jie Gao has recently investigated Hawking radiation from spherically symmetrical gravitational collapse to an extremal R-N black hole for a real scalar field. Especially he estimated the upper bound for the expected number of particles in any wave packet belonging to Hout spontaneously produced from the state |0＞in, which confirms the traditional belief that extremal black holes do not radiate particles. Making some modifications, we demonstrate that the analysis can go through for a charged scalar field.
Horvat, D; Narancic, Z; Horvat, Dubravko; Ilijic, Sasa; Narancic, Zoran
2004-01-01
Spherically symmetric distributions of electrically counterpoised dust (ECD) are used to construct solutions to Einstein-Maxwell equations in Majumdar-Papapetrou formalism. Unexpected bifurcating behavior of regular and singular solutions with regard to source strength is found for localized, as well as for the delta-function ECD distributions. Unified treatment of general ECD distributions is accomplished and it is shown that for certain source strengths one class of regular solutions approaches Minkowski spacetime, while the other comes arbitrarily close to black hole solutions.
Ortiz, Néstor
2013-01-01
A spherical dust cloud which is initially at rest and which has a monotonously decaying density profile collapses and forms a shell-focussing singularity. Provided the density profile is not too flat, meaning that its second radial derivative is negative at the center, this singularity is visible to local, and sometimes even to global observers. According to the strong cosmic censorship conjecture, such naked singularities should be unstable under generic, nonspherical perturbations of the initial data or when more realistic matter models are considered. In an attempt to gain some understanding about this stability issue, in this work we initiate the analysis of a simpler but related problem. We discuss the stability of test fields propagating in the vicinity of the Cauchy horizon associated to the naked central singularity. We first study the high-frequency limit and show that the fields undergo a blueshift as they approach the Cauchy horizon. However, in contrast to what occurs at inner horizons of black ho...
The Thermal Response of a Pulsar Glitch The Non-spherical Symmetric Case
Cheng, K S
1999-01-01
We study the thermal evolution of a pulsar after a glitch in which the energy is released from a relative compact region. A set of relativistic thermal transport and energy balance equations is used to study the thermal evolution, without making the assumption of spherical symmetry. We use an exact cooling model to solve this set of differential equtions. Our results differ significantly from those obtained under the assumption of spherical symmetry. Even for young pulsars with a hot core like the Vela pulsar, we find that a detectable hot spot can be observed after a glitch. The results suggest that the intensity variation and the relative phases of hard X-ray emissions in different epoches can provide important information on the equation of state.
Lapiedra, Ramon
2016-01-01
The collapse of pressureless (dust) and non-homogeneous matter is analyzed under the following additional assumptions: spherical symmetry and existence of a spatially flat foliation of comoving 3-spaces (marginally bound collapse). The starting point is not, in this case, the integration of the Einstein equations from some suitable initial conditions. Instead, starting from the corresponding general exact solution of these equations, depending on two arbitrary functions of the radial coordinate, the fulfillment of the Lichnerowicz matching conditions of the interior collapsing metric and the exterior Schwarzschild one is ensured: the continuity of the metric and its first derivatives on the time-like hypersurface describing the evolution of the spherical 2-surface boundary of the collapsing cloud. The whole analytical family of resulting models is obtained and some of them are picked out as physical better models on the basis of the finite and stationary value of its {\\em intrinsic} energy.
Wrapping Brownian motion and heat kernels II: symmetric spaces
Maher, David G
2010-01-01
In this paper we extend our previous results on wrapping Brownian motion and heat kernels onto compact Lie groups to various symmetric spaces, where a global generalisation of Rouvi\\`ere's formula and the $e$-function are considered. Additionally, we extend some of our results to complex Lie groups, and certain non-compact symmetric spaces.
Explosion Dynamics of Parametrized Spherically Symmetric Core-Collapse Supernova Simulations
Ebinger, Kevin; Fröhlich, Carla; Perego, Albino; Hempel, Matthias; Eichler, Marius; Casanova, Jordi; Liebendörfer, Matthias; Thielemann, Friedrich-Karl
2016-01-01
We report on a method, PUSH, for triggering core-collapse supernova (CCSN) explosions of massive stars in spherical symmetry. This method provides a framework to study many important aspects of core collapse supernovae: the effects of the shock passage through the star, explosive supernova nucleosynthesis and the progenitor-remnant connection. Here we give an overview of the method, compare the results to multi-dimensional simulations and investigate the effects of the progenitor and the equation of state on black hole formation.
Study of the geodesic equations of a spherical symmetric spacetime in conformal Weyl gravity
Hoseini, Bahareh; Saffari, Reza; Soroushfar, Saheb
2017-03-01
A set of analytic solutions of the geodesic equation in a spherical conformal spacetime is presented. Solutions of this geodesics can be expressed in terms of the Weierstrass \\wp function and the Kleinian σ function. Using conserved energy and angular momentum we can characterize the different orbits. Also, considering parametric diagrams and effective potentials, we plot some possible orbits. Moreover, with the help of analytical solutions, we investigate the light deflection for such an escape orbit. Finally, by using periastron advance we get to an upper bound for magnitude of γ.
Tortoise Coordinates and Hawking Radiation in a Dynamical Spherically Symmetric Spacetime
Institute of Scientific and Technical Information of China (English)
YANG Jian; ZHAO Zheng; TIAN Gui-Hua; LIU Wen-Biao
2009-01-01
Hawking effect from dynamical spherical Vaidya black hole,Vaidya-Bonner black hole,and Vaidya-de Sitter black hole is investigated using the improved Damour-Ruffini method.After the new tortoise coordinate transformation in which the position τ of event horizon is an undetermined function and the temperature parameter κ is an undetermined constant,the Klein-Gordon equation can be written as the standard form at the event horizon,and both τ and κ can be determined automatically.Then extending the outgoing wave from outside to inside of the horizon analytically,the Hawking temperature can also be obtained automatically.
Institute of Scientific and Technical Information of China (English)
罗少盈; 刘琦
2014-01-01
In this article, we concern the motion of relativistic membranes and null mem-branes in the Reissner-Nordstr¨om space-time. The equation of relativistic membranes moving in the Reissner-Nordstr¨om space-time is derived and some properties are discussed. Spherical symmetric solutions for the motion are illustrated and some interesting physical phenomena are discovered. The equations of the null membranes are derived and the exact solutions are also given. Spherical symmetric solutions for null membranes are just the two horizons of Reissner-Nordstr¨om space-time.
Encounters between spherical galaxies - II. Systems with a dark halo
Gonzalez-Garcia, AC; van Albada, TS
2005-01-01
We perform N-body simulations of encounters between spherical systems surrounded by a spherical halo. Following a preceding paper with a similar aim, the initial systems include a spherical Jaffe model for the luminous matter and a Hernquist model for the halo. The merger remnants from this sample a
Directory of Open Access Journals (Sweden)
Khalaf A. M.
2015-04-01
Full Text Available The interacting boson model (sd-IBM1 with intrinsic coherent state is used to study the shape phase transitions from spherical U(5 to prolate deformed SU(3 shapes in Nd- Sm isotopic chains. The Hamiltonian is written in the creation and annihilation form with one and two body terms.For each nucleus a fitting procedure is adopted to get the best model parameters by fitting selected experimental energy levels, B(E2 transi- tion rates and two-neutron separation energies with the calculated ones.The U(5-SU(3 IBM potential energy surfaces (PES’s are analyzed and the critical phase transition points are identified in the space of model parameters.In Nd-Sm isotopic chains nuclei evolve from spherical to deformed shapes by increasing the boson number. The nuclei 150 Nd and 152 Sm have been found to be close to critical points.We have also studied the energy ratios and the B(E2 values for yrast band at the critical points.
The Plancherel decomposition for a reductive symmetric space II : representation theory
Ban, E.P. van den; Schlichtkrull, H.
2001-01-01
We obtain the Plancherel decomposition for a reductive symmetric space in the sense of representation theory. Our starting point is the Plancherel formula for spherical Schwartz functions, obtained in part I. The formula for Schwartz functions involves Eisenstein integrals obtained by a residual
Addition theorems for spin spherical harmonics: II. Results
Energy Technology Data Exchange (ETDEWEB)
Bouzas, Antonio O, E-mail: abouzas@mda.cinvestav.mx [Departamento de Fisica Aplicada, CINVESTAV-IPN, Carretera Antigua a Progreso Km. 6, Apdo. Postal 73 ' Cordemex' , Merida 97310, Yucatan (Mexico)
2011-04-22
Based on the results of part I (2011 J. Phys. A: Math. Theor. 44 165301), we obtain the general form of the addition theorem for spin spherical harmonics and give explicit results in the cases involving one spin-s' and one spin-s spherical harmonics with s', s = 1/2, 1, 3/2, and |s' - s| = 0, 1. We also obtain a fully general addition theorem for one scalar and one tensor spherical harmonic of arbitrary rank. A variety of bilocal sums of ordinary and spin spherical harmonics are given in explicit form, including a general explicit expression for bilocal spherical harmonics.
Rekier, Jeremy; Fuzfa, Andre
2014-01-01
We present a fully relativistic numerical method for the study of cosmological problems in spherical symmetry. This involves using the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formalism on a dynamical Friedmann-Lema\\^itre-Robertson-Walker (FLRW) background. The regular and smooth numerical solution at the center of coordinates proceeds in a natural way by relying on the Partially Implicit Runge-Kutta (PIRK) algorithm described in Montero and Cordero-Carri\\'on [arXiv:1211.5930]. We generalize the usual radiative outer boundary condition to the case of a dynamical background. We show the stability and convergence properties of the method in the study of pure gauge dynamics on a de Sitter background and present a simple application to cosmology by reproducing the Lema\\^itre-Tolman-Bondi (LTB) solution for the collapse of pressure-less matter.
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.
X-ray emission from Planetary Nebulae. I. Spherically symmetric numerical simulations
Stute, M; Stute, Matthias; Sahai, Raghvendra
2006-01-01
(abridged) The interaction of a fast wind with a spherical Asymptotic Giant Branch (AGB) wind is thought to be the basic mechanism for shaping Pre-Planetary Nebulae (PPN) and later Planetary Nebulae (PN). Due to the large speed of the fast wind, one expects extended X-ray emission from these objects, but X-ray emission has only been detected in a small fraction of PNs and only in one PPN. Using numerical simulations we investigate the constraints that can be set on the physical properties of the fast wind (speed, mass-flux, opening angle) in order to produce the observed X-ray emission properties of PPNs and PNs. We combine numerical hydrodynamical simulations including radiative cooling using the code FLASH with calculations of the X-ray properties of the resulting expanding hot bubble using the atomic database ATOMDB. In this first study, we compute X-ray fluxes and spectra using one-dimensional models. Comparing our results with analytical solutions, we find some agreements and many disagreements. In parti...
Qureshi, Muhammad Amer; Mahomed, K S
2016-01-01
A study of proper teleparallel conformal vector field in spherically symmetric static space-times is given using the direct integration technique and diagonal tetrads. In this study we show that the above space-times do not admit proper teleparallel conformal vector fields.
The Symmetric Group Defies Strong Fourier Sampling: Part II
Moore, Cristopher; Moore, Cristopher; Russell, Alexander
2005-01-01
Part I of this paper showed that the hidden subgroup problem over the symmetric group--including the special case relevant to Graph Isomorphism--cannot be efficiently solved by strong Fourier sampling, even if one may perform an arbitrary POVM on the coset state. In this paper, we extend these results to entangled measurements. Specifically, we show that the hidden subgroup problem on the symmetric group cannot be solved by any POVM applied to pairs of cosets states. In particular, these hidden subgroups cannot be determined by any polynomial number of one- or two-register experiments on coset states.
Sound wave generation by a spherically symmetric outburst and AGN feedback in galaxy clusters
Tang, Xiaping; Churazov, Eugene
2017-07-01
We consider the evolution of an outburst in a uniform medium under spherical symmetry, having in mind active galactic nucleus feedback in the intracluster medium. For a given density and pressure of the medium, the spatial structure and energy partition at a given time tage (since the onset of the outburst) are fully determined by the total injected energy Einj and the duration tb of the outburst. We are particularly interested in the late phase evolution when the strong shock transforms into a sound wave. We studied the energy partition during such transition with different combinations of Einj and tb. For an instantaneous outburst with tb → 0, which corresponds to the extension of classic Sedov-Taylor solution with counter-pressure, the fraction of energy that can be carried away by sound waves is ≲12 per cent of Einj. As tb increases, the solution approaches the 'slow piston' limit, with the fraction of energy in sound waves approaching zero. We then repeat the simulations using radial density and temperature profiles measured in Perseus and M87/Virgo clusters. We find that the results with a uniform medium broadly reproduce an outburst in more realistic conditions once proper scaling is applied. We also develop techniques to map intrinsic properties of an outburst (Einj, tb and tage) to the observables like the Mach number of the shock and radii of the shock and ejecta. For the Perseus cluster and M87, the estimated (Einj, tb and tage) agree with numerical simulations tailored for these objects with 20-30 per cent accuracy.
Finite symmetric trilinear integral transform of distributions. Part II
Directory of Open Access Journals (Sweden)
G. L. Waghmare
2006-01-01
Full Text Available The finite symmetric trilinear integral transform is extended to distributions by using quite different technique than Zemanian (1968 and Dube (1976 and an inversion formula is established using Parseval's identity. The operational calculus generated is applied to find the temperature inside an equilateral prism of semi-infinite length.
Gravitational acceleration and tidal effects in spherical-symmetric density profiles
Caimmi, R
2015-01-01
Pure power-law density profiles, $\\rho(r)\\propto r^{b-3}$, are classified in connection with the following reference cases: (i) isodensity, $b=3$, $\\rho=$ const; (ii) isogravity, $b=2$, $g=$ const; (iii) isothermal, $b=1$, $v=[GM(r)/r]^{1/2}=$ const; (iv) isomass, $b=0$, $M=$ const. A restricted number of different families of density profiles including, in addition, cored power-law, generalized power-law, polytropes, are studied in detail with regard to both one-component and two-component systems. Considerable effort is devoted to the existence of an extremum point (maximum absolute value) in the gravitational acceleration within the matter distribution. Predicted velocity curves are compared to the data inferred from observations. Tidal effects on an inner subsystem are investigated and an application is made to globular clusters within the Galaxy. To this aim, the tidal radius is defined by balancing the opposite gravitational forces from the Galaxy and the selected cluster on a special point of the clust...
Burikham, Piyabut; Harko, Tiberiu; Lake, Matthew J
2015-01-01
We obtain bounds for the minimum and maximum mass/radius ratio of a stable, charged, spherically symmetric compact object in a $D$-dimensional space-time in the framework of general relativity, and in the presence of a dark energy. The total energy, including the gravitational component, and the stability of objects with minimum mass/radius ratio is also investigated. The minimum energy condition leads to a representation of the mass and radius of the charged objects with minimum mass/radius ratio in terms of the charge and vacuum energy only. As applied to the electron in the four-dimensional case, this procedure allows to re-obtain the classical electron radius from purely general relativistic considerations. By combining the lower mass bound, in four space-time dimensions, with minimum length uncertainty relations (MLUR) motivated by quantum gravity, we obtain an alternative bound for the maximum charge/mass ratio of a stable, gravitating, charged quantum mechanical object, expressed in terms of fundamenta...
Harada, T; Iguchi, H; Harada, Tomohiro; Nakao, Ken-ichi; Iguchi, Hideo
1999-01-01
It was recently shown that the metric functions which describe a spherically symmetric space-time with vanishing radial pressure can be explicitly integrated. We investigate the nakedness and curvature strength of the shell-focusing singularity in that space-time. If the singularity is naked, the relation between the circumferential radius and the Misner-Sharp mass is given by $R\\approx 2y_{0} m^{\\beta}$ with $ 1/3<\\beta\\le 1$ along the first radial null geodesic from the singularity. The $\\beta$ is closely related to the curvature strength of the naked singularity. For example, for the outgoing or ingoing null geodesic, if the strong curvature condition (SCC) by Tipler holds, then $\\beta$ must be equal to 1. We define the ``gravity dominance condition'' (GDC) for a geodesic. If GDC is satisfied for the null geodesic, both SCC and the limiting focusing condition (LFC) by Królak hold for $\\beta=1$ and $y_{0}\
A New Open-Source Code for Spherically-Symmetric Stellar Collapse to Neutron Stars and Black Holes
O'Connor, Evan
2009-01-01
We present the new open-source spherically-symmetric general-relativistic (GR) hydrodynamics code GR1D. It is based on the Eulerian formulation of GR hydrodynamics (GRHD) put forth by Romero-Ibanez-Gourgoulhon and employs radial-gauge, polar-slicing coordinates in which the 3+1 equations simplify substantially. We discretize the GRHD equations with a finite-volume scheme, employing piecewise-parabolic reconstruction and an approximate Riemann solver. GR1D is intended for the simulation of stellar collapse to neutron stars and black holes and will also serve as a testbed for modeling technology to be incorporated in multi-D GR codes. Its GRHD part is coupled to various finite-temperature microphysical equations of state in tabulated form that we make available with GR1D. An approximate deleptonization scheme for the collapse phase and a neutrino-leakage/heating scheme for the postbounce epoch are included and described. We also derive the equations for effective rotation in 1D and implement them in GR1D. We pr...
Ignatyev, Yu G
2011-01-01
Exact linear retarding spherically symmetric solutions of Einstein equations linearized around Friedmann background for the ultrarelativistic equation of state are obtained and investigated. Uniqueness of the solutions in the $C^{1} $ class is proved.
Energy Technology Data Exchange (ETDEWEB)
Burikham, Piyabut [Chulalongkorn University, High Energy Physics Theory Group, Department of Physics, Faculty of Science, Bangkok (Thailand); Cheamsawat, Krai [Chulalongkorn University, High Energy Physics Theory Group, Department of Physics, Faculty of Science, Bangkok (Thailand); Imperial College, Theoretical Physics Group, Blackett Laboratory, London (United Kingdom); Harko, Tiberiu [Babes-Bolyai University, Department of Physics, Cluj-Napoca (Romania); University College London, Department of Mathematics, London (United Kingdom); Lake, Matthew J. [Naresuan University, The Institute for Fundamental Study, ' ' The Tah Poe Academia Institute' ' , Phitsanulok (Thailand); Ministry of Education, Thailand Center of Excellence in Physics, Bangkok (Thailand)
2016-03-15
We obtain bounds for the minimum and maximum mass/radius ratio of a stable, charged, spherically symmetric compact object in a D-dimensional space-time in the framework of general relativity, and in the presence of dark energy. The total energy, including the gravitational component, and the stability of objects with minimum mass/radius ratio is also investigated. The minimum energy condition leads to a representation of the mass and radius of the charged objects with minimum mass/radius ratio in terms of the charge and vacuum energy only. As applied to the electron in the four-dimensional case, this procedure allows one to re-obtain the classical electron radius from purely general relativistic considerations. By combining the lower mass bound, in four space-time dimensions, with minimum length uncertainty relations (MLUR) motivated by quantum gravity, we obtain an alternative bound for the maximum charge/mass ratio of a stable, gravitating, charged quantum mechanical object, expressed in terms of fundamental constants. Evaluating this limit numerically, we obtain again the correct order of magnitude value for the charge/mass ratio of the electron, as required by the stability conditions. This suggests that, if the electron were either less massive (with the same charge) or if its charge were any higher (for fixed mass), a combination of electrostatic and dark energy repulsion would destabilize the Compton radius. In other words, the electron would blow itself apart. Our results suggest the existence of a deep connection between gravity, the presence of the cosmological constant, and the stability of fundamental particles. (orig.)
Fibonacci or quasi-symmetric phyllotaxis. Part II: botanical observations
Directory of Open Access Journals (Sweden)
Stéphane Douady
2016-12-01
Full Text Available Historically, the study of phyllotaxis was greatly helped by the simple description of botanical patterns by only two integer numbers, namely the number of helices (parastichies in each direction tiling the plant stem. The use of parastichy numbers reduced the complexity of the study and created a proliferation of generalizations, among others the simple geometric model of lattices. Unfortunately, these simple descriptive method runs into difficulties when dealing with patterns presenting transitions or irregularities. Here, we propose several ways of addressing the imperfections of botanical reality. Using ontogenetic analysis, which follows the step-by-step genesis of the pattern, and crystallographic analysis, which reveal irregularity in its details, we show how to derive more information from a real botanical sample, in particular, about its irregularities and transitions. We present several examples, from the first explicit visualization of a normal Fibonacci parastichy number increase, to more exotic ones, including the quasi-symmetric patterns detected in simulations. We compare these observations qualitatively with the result of the disk-packing model, presenting evidence for the relevance of the model.
Gravitational Waves in Locally Rotationally Symmetric (LRS Class II Cosmologies
Directory of Open Access Journals (Sweden)
Michael Bradley
2017-10-01
Full Text Available In this work we consider perturbations of homogeneous and hypersurface orthogonal cosmological backgrounds with local rotational symmetry (LRS, using a method based on the 1 + 1 + 2 covariant split of spacetime. The backgrounds, of LRS class II, are characterised by that the vorticity, the twist of the 2-sheets, and the magnetic part of the Weyl tensor all vanish. They include the flat Friedmann universe as a special case. The matter contents of the perturbed spacetimes are given by vorticity-free perfect fluids, but otherwise the perturbations are arbitrary and describe gravitational, shear, and density waves. All the perturbation variables can be given in terms of the time evolution of a set of six harmonic coefficients. This set decouples into one set of four coefficients with the density perturbations acting as source terms, and another set of two coefficients describing damped source-free gravitational waves with odd parity. We also consider the flat Friedmann universe, which has been considered by several others using the 1 + 3 covariant split, as a check of the isotropic limit. In agreement with earlier results we find a second-order wavelike equation for the magnetic part of the Weyl tensor which decouples from the density gradient for the flat Friedmann universes. Assuming vanishing vector perturbations, including the density gradient, we find a similar equation for the electric part of the Weyl tensor, which was previously unnoticed.
Matyjasek, Jerzy
2016-10-01
In this paper, using the general Schwinger-DeWitt approach, we construct the approximate stress-energy tensor of the quantized massive scalar field with arbitrary curvature coupling in D =4 and D =5 classical spacetimes of the electrically charged static black holes with the cosmological constant. Depending on the sign of the cosmological constant we consider both spherically symmetric and topological spacetimes with the special emphasis put on the extremal and ultraextremal configurations. Moreover, we analyze the geometries of the closest vicinity of the degenerate horizons, which topologically are the product of the maximally symmetric subspaces. We solve the semiclassical Einstein field equations for such product spacetimes. Since the transformation k →-k and f''→-f'' leaves the equations unchanged, where k is the curvature of the (D -2 )-dimensional subspace and f'' is the second derivative of the metric potential at the degenerate horizon, it suffices to consider only the spherically symmetric case. It is shown that in four and five dimensions there are forbidden sectors of the parameter space.
Guven, Jemal; Murchadha, Niall O.'
1995-07-01
This is the first of a series of papers in which we examine the constraints of spherically symmetric general relativity with one asymptotically flat region. Our approach is manifestly invariant under spatial diffeomorphisms, exploiting both traditional metric variables as well as the optical scalar variables introduced recently in this context. With respect to the latter variables, there exist two linear combinations of the Hamiltonian and momentum constraints one of which is obtained from the other by time reversal. Boundary conditions on the spherically symmetric three-geometries and extrinsic curvature tensors are discussed. We introduce a one-parameter family of foliations of spacetime involving a linear combination of the two scalars characterizing a spherically symmetric extrinsic curvature tensor. We can exploit this gauge to express one of these scalars in terms of the other and thereby solve the radial momentum constraint uniquely in terms of the radial current. The values of the parameter yielding potentially globally regular gauges corresponding to the vanishing of a timelike vector in the superspace of spherically symmetric geometries. We define a quasilocal mass (QLM) on spheres of fixed proper radius which provides observables of the theory. When the constraints are satisfied the QLM can be expressed as a volume integral over the sources and is positive. We provide two proofs of the positivity of the QLM. If the dominant energy condition (DEC) and the constraints are satisfied positivity can be established in a manifestly gauge-invariant way. This is most easily achieved exploiting the optical scalars. In the second proof we specify the foliation. The payoff is that the weak energy condition replaces the DEC and the Hamiltonian constraint replaces the full constraints. Underpinning this proof is a bound on the derivative of the circumferential radius of the geometry with respect to its proper radius. We show that, when the DEC is satisfied, analogous
Chakrabarti, Soumya
2016-01-01
The gravitational collapse of a spherical distribution, in a class of f(R) theories of gravity, where f(R) is power function of R, is discussed. The spacetime is assumed to admit a homothetic Killing vector. In the collapsing modes, some of the situations indeed hit a singularity, but they are all covered with an apparent horizon. Some peculiar cases are observed where the collapsing body settles to a constant radius at a given value of the radial coordinate.
Shestakova, Tatyana P.
2015-01-01
Among theoretical issues in General Relativity the problem of constructing its Hamiltonian formulation is still of interest. The most of attempts to quantize Gravity are based upon Dirac generalization of Hamiltonian dynamics for system with constraints. At the same time there exists another way to formulate Hamiltonian dynamics for constrained systems guided by the idea of extended phase space. We have already considered some features of this approach in the previous MG12 Meeting by the example of a simple isotropic model. Now we apply the approach to a generalized spherically symmetric model which imitates the structure of General Relativity much better. In particular, making use of a global BRST symmetry and the Noether theorem, we construct the BRST charge that generates correct gauge transformations for all gravitational degrees of freedom.
Shestakova, T P
2013-01-01
Among theoretical issues in General Relativity the problem of constructing its Hamiltonian formulation is still of interest. The most of attempts to quantize Gravity are based upon Dirac generalization of Hamiltonian dynamics for system with constraints. At the same time there exists another way to formulate Hamiltonian dynamics for constrained systems guided by the idea of extended phase space. We have already considered some features of this approach in the previous MG12 Meeting by the example of a simple isotropic model. Now we apply the approach to a generalized spherically symmetric model which imitates the structure of General Relativity much better. In particular, making use of a global BRST symmetry and the Noether theorem, we construct the BRST charge that generates correct gauge transformations for all gravitational degrees of freedom.
Ghanem, Sari
2016-01-01
We prove uniform decay estimates in the entire exterior of the Schwarzschild black hole for gauge invariant norms on the Yang-Mills fields valued in the Lie algebra associated to the Lie group $SU(2)$. We assume that the initial data are spherically symmetric satisfying a certain Ansatz, and have small energy, which eliminates the stationary solutions which do not decay. We first prove a Morawetz type estimate that is stronger than the one assumed in previous work by the first author, without passing through the scalar wave equation on the Yang-Mills curvature, using the Yang-Mills equations directly. This allows one by then to adapt the proof constructed in this previous work to show local energy decay and uniform decay of the $L^{\\infty}$ norm of the middle components in the entire exterior of the Schwarzschild black hole, including the event horizon.
Directory of Open Access Journals (Sweden)
Ion BULAC
2016-05-01
Full Text Available The technological (geometrical deviations determine in the intermediate couples of the mechanism supplementary efforts due to restrained movement. The 4R asymmetrical spherical quadrilateral mechanism is multiple statically indeterminate, and for calculating the reactions from the kinematic pairs it is applied the elastic linear calculation using the relative displacements method. The equations of elastic balanced are written in the general system of reference.For this is necessary the knowledge the forms of the technical (geometrical deviations in the general system of reference.This paper presents the calculation modality these deviations .
Energy Technology Data Exchange (ETDEWEB)
El Ghazi, Haddou, E-mail: hadghazi@gmail.com [LPS, Faculty of Science, Dhar EL Mehrez, BP 1796 Fes-Atlas (Morocco); Special Mathematics, CPGE, 267 Quartier complémentaire Ennahda 1, Rabat (Morocco); Jorio, Anouar [LPS, Faculty of Science, Dhar EL Mehrez, BP 1796 Fes-Atlas (Morocco)
2014-01-01
Within the framework of effective-mass approximation and finite parabolic potential barrier, single particle and ground-state interband recombination energies in Core|well|shell based on GaN|(In,Ga)N|GaN spherical QDQW are investigated as a function of the inner and the outer radii. The temperature dependency of effective-mass, band-gap energy and potential barrier is taken into account. Particle eigenvalue and band-gap energy competing effects are speculated to explain our numerical results which show that the interband recombination energy increases when the temperature increases. The results we obtained are in quite good agreement with the findings.
Ben Achour, Jibril; Brahma, Suddhasattwa; Marcianò, Antonino
2017-07-01
Using self-dual Ashtekar variables, we investigate (at the effective level) the spherically symmetry reduced model of loop quantum gravity, both in vacuum and when coupled to a scalar field. Within the real Ashtekar-Barbero formulation, the system scalar field coupled to spherically symmetric gravity is known to possess a non closed (quantum) algebra of constraints once local (pointwise) holonomy corrections are introduced, which leads to several obstructions in the loop quantization of the model. Moreover, the vacuum case, while not anomalous, introduces modifications which have been suggested to be an effective signature change of the metric in the deep quantum region. We show in this paper that both those complications disappear when working with self-dual Ashtekar variables, both in the vacuum case and in the case of gravity minimally coupled to a scalar field. In this framework, the algebra of the holonomy corrected constraints is anomaly free and reproduces the classical hypersurface deformation algebra without any deformations. A possible path towards quantization of this model is briefly discussed.
Energy Technology Data Exchange (ETDEWEB)
Burikham, Piyabut; Cheamsawat, Krai [Chulalongkorn University, High Energy Physics Theory Group, Department of Physics, Faculty of Science, Bangkok (Thailand); Harko, Tiberiu [University College London, Department of Mathematics, London (United Kingdom); Lake, Matthew J. [Naresuan University, The Institute for Fundamental Study, ' ' The Tah Poe Academia Institute' ' , Phitsanulok (Thailand); Ministry of Education, Thailand Center of Excellence in Physics, Bangkok (Thailand)
2015-09-15
The existence of both a minimum mass and a minimum density in nature, in the presence of a positive cosmological constant, is one of the most intriguing results in classical general relativity. These results follow rigorously from the Buchdahl inequalities in four-dimensional de Sitter space. In this work, we obtain the generalized Buchdahl inequalities in arbitrary space-time dimensions with Λ ≠ 0 and consider both the de Sitter and the anti-de Sitter cases. The dependence on D, the number of space-time dimensions, of the minimum and maximum masses for stable spherical objects is explicitly obtained. The analysis is then extended to the case of dark energy satisfying an arbitrary linear barotropic equation of state. The Jeans instability of barotropic dark energy is also investigated, for arbitrary D, in the framework of a simple Newtonian model with and without viscous dissipation, and we determine the dispersion relation describing the dark energy-matter condensation process, along with estimates of the corresponding Jeans mass (and radius). Finally, the quantum mechanical implications of the mass limits are investigated, and we show that the existence of a minimum mass scale naturally leads to a model in which dark energy is composed of a 'sea' of quantum particles, each with an effective mass proportional to Λ{sup 1/4}. (orig.)
Babourova, O V; Kudlaev, P E; Romanova, E V
2016-01-01
The Poincare and Poincare-Weyl gauge theories of gravitation with Lagrangians quadratic on curvature and torsion in post-Riemannian spaces with the Dirac scalar field is discussed in a historical aspect. The various hypothesizes concerning the models of a dark matter with the help of a scalar field are considered. The new conformal Weyl-Dirac theory of gravitation is proposed, which is a gravitational theory in Cartan-Weyl space-time with the Dirac scalar field representing the dark matter model. A static spherically symmetric solution of the field equations in vacuum for a central compact mass is obtained as the metrics conformal to the Yilmaz-Rosen metrics. On the base of this solution one considers a radial movement of an interplanetary spacecraft starting from the Earth. Using the Newton approximation one obtains that the asymptotic line-of-sight velocity in this case depends from the parameters of the solution, and therefore one can obtain on basis of the observable data the values of these parameters.
Mezzacappa, A; Liebendörfer, M; Messer, O E; Hix, W R; Thielemann, F K; Bruenn, S W
2001-03-05
With exact three-flavor Boltzmann neutrino transport, we simulate the stellar core collapse, bounce, and postbounce evolution of a 13M star in spherical symmetry, the Newtonian limit, without invoking convection. In the absence of convection, prior spherically symmetric models, which implemented approximations to Boltzmann transport, failed to produce explosions. We consider exact transport to determine if these failures were due to the transport approximations made and to answer remaining fundamental questions in supernova theory. The model presented here is the first in a sequence of models beginning with different progenitors. In this model, a supernova explosion is not obtained.
Site distortions created by the stereoactive lone pair of Tin(II) in highly symmetric structures
Dénès, Georges; Madamba, M. Cecilia; Merazig, Hocine; Muntasar, Abdualhafed; Zhu, Zhimeng
2016-10-01
Several fluoride compounds containing divalent tin that have a fluorite (CaF2-type) unit cell have been prepared and studied. Some are stoichiometric compounds while others are solid solutions. The cubic symmetry of the unit-cell (no lattice distortion and no superstructure) and the unique metal ion site of the fluorite structure make it that tin and the other metal have to be disordered on the normal metal site of the fluorite unit-cell. However, that site has the m3m-Oh point symmetry, and the metal ion is located in the center of a cube having fluoride ions in all its corners. Therefore, the same coordination should apply to tin. However, tin(II) possesses a non-bonding pair of electrons called a "lone pair", and in order for tin(II) to have a cubic symmetry, its lone pair has to be located on the unhybridized 5s orbital, that is spherical and thus does not distort the coordination. In such a case, the lone pair is said to be "non-stereoactive". This would make tin present in the form of the Sn2+ stannous ion, and therefore Sn-F bonding must be ionic. However, tin(II) fluorides are known to be always covalent with a hybridized lone pair on tin, which has therefore a reduced coordination number and therefore a highly distorted polyhedron of coordination. Such a hybridized lone pair is said to be "stereoactive". Tin-119 Mössbauer spectroscopy was used to probe the bonding type and it showed that bonding is covalent, the lone pair is hybridized and the tin coordination is dramatically distorted. A model based on a double disorder was made that accounts for the apparent contradiction between the crystallographic and the Mössbauer results.
Kong, Qingzhao; Fan, Shuli; Mo, Y. L.; Song, Gangbing
2017-09-01
The newly developed spherical smart aggregate (SSA) based on a radially polarized spherical piezoceramic shell element has unique omnidirectional actuating and sensing capabilities that can greatly improve the detection aperture and provide additional functionalities in health monitoring applications in concrete structures. Detailed fabrication procedures and electrical characterization of the SSA have been previously studied (Part I). In this second paper (Part II), the functionalities of the SSA used in both active sensing and passive sensing approaches were investigated in experiments and numerical simulations. One SSA sample was embedded in a 1 ft3 concrete specimen. In the active sensing approach, the SSA was first utilized as an actuator to generate stress waves and six conventional smart aggregates (SA) mounted on the six faces of the concrete cube were utilized as sensors to detect the wave response. Conversely, the embedded SSA was then utilized as a sensor to successively detect the wave response from each SA. The experimentally obtained behavior of the SSA was then compared with the numerical simulation results. Further, a series of impact tests were conducted to verify the performance of the SSA in the detection of the impact events from different directions. Comparison with the wave response associated with different faces of the cube verified the omnidirectional actuating and sensing capabilities of the SSA.
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
The HIT-II Spherical Torus: Physics and Key Experimental Results
Redd, A. J.; Hamp, W. T.; Izzo, V. A.; Jarboe, T. R.; Nelson, B. A.; O'Neill, R. G.; Raman, R.; Sieck, P. E.; Smith, R. J.
2004-11-01
Discharges in the HIT-II spherical torus device [Redd et al., Phys. Plasmas 9, 2006 (2002)] can be driven by either Ohmic or Coaxial Helicity Injection (CHI) current drive. A new CHI operating regime has been explored, with toroidal plasma currents of up to 350 kA, I_p/I_TF ratios of up to 1.2, and internal probing data which may demonstrate the formation of a closed-flux core. The key to acheiving these results is the magnetic field shear in the CHI injector region, with a minimum shear necessary for current build-up. Ohmic plasma performance has also improved, with peak currents up to 300 kA, with and without transient CHI startup. The CHI startup technique [Raman et al., Phys. Plasmas 11, 2565 (2004)] provides more robust discharges, with a wider operating space and more efficient use of the transformer Volt-seconds, than unassisted Ohmic. Finally, CHI can be used to enhance an Ohmic plasma current without significantly degrading the quality of the discharge. Results will be presented for each HIT--II operating regime, including empirical performance scalings and applicable parametric operating spaces.
Chick, Kenneth M.; Gombosi, Tamas I.
1993-01-01
A numerical solution for the multiple light scattering in spherical axisymmetric geometry is applied to the simulation of images of a coma as it would appear to a near-flying satellite such as Giotto. The appearance of symmetric comas and dust jets is examined in detail; the nucleus visibility is studied; the effect of forward scattering is considered; and single and multiple scattering effects are quantified. Attention is given to simulated images of a coma with a hollow cone of dust, as predicted by dust-gas hydrodynamic modeling. The cone's appearance is very similar to the northern area of activity on Comet Halley, observed by the Giotto HMC.
Second-order symmetric Lorentzian manifolds II: structure and global properties
Blanco, O F; Senovilla, J M M
2011-01-01
We give a summary of recent results on the explicit local form of the second-order symmetric Lorentzian manifolds in arbitrary dimension, and its global version. These spacetimes turn out to be essentially a specific subclass of plane waves.
Second-order symmetric Lorentzian manifolds II: structure and global properties
Energy Technology Data Exchange (ETDEWEB)
Blanco, O F; Sanchez, M [Departamento de GeometrIa y TopologIa, Facultad de Ciencias, Universidad de Granada Campus Fuentenueva s/n, 18071 Granada (Spain); Senovilla, J M M, E-mail: oihane@ugr.es, E-mail: sanchezm@ugr.es, E-mail: josemm.senovilla@ehu.es [Fisica Teorica, Universidad del PaIs Vasco, Apartado 644, 48080 Bilbao (Spain)
2011-09-22
We give a summary of recent results on the explicit local form of the second-order symmetric Lorentzian manifolds in arbitrary dimension, and its global version. These spacetimes turn out to be essentially a specific subclass of plane waves.
The quantum free particle on spherical and hyperbolic spaces: A curvature dependent approach. II
Energy Technology Data Exchange (ETDEWEB)
Carinena, Jose F.; Ranada, Manuel F. [Departamento de Fisica Teorica and IUMA, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza (Spain); Santander, Mariano [Departamento de Fisica Teorica, Facultad de Ciencias, Universidad de Valladolid, 47011 Valladolid (Spain)
2012-10-15
This paper is the second part of a study of the quantum free particle on spherical and hyperbolic spaces by making use of a curvature-dependent formalism. Here we study the analogues, on the three-dimensional spherical and hyperbolic spaces, S{sub {kappa}}{sup 3} ({kappa} > 0) and H{sub k}{sup 3} ({kappa} < 0), to the standard spherical waves in E{sup 3}. The curvature {kappa} is considered as a parameter and for any {kappa} we show how the radial Schroedinger equation can be transformed into a {kappa}-dependent Gauss hypergeometric equation that can be considered as a {kappa}-deformation of the (spherical) Bessel equation. The specific properties of the spherical waves in the spherical case are studied with great detail. These have a discrete spectrum and their wave functions, which are related with families of orthogonal polynomials (both {kappa}-dependent and {kappa}-independent), and are explicitly obtained.
Symmetrization and Applications
Kesavan, S
2006-01-01
The study of isoperimetric inequalities involves a fascinating interplay of analysis, geometry and the theory of partial differential equations. Several conjectures have been made and while many have been resolved, a large number still remain open.One of the principal tools in the study of isoperimetric problems, especially when spherical symmetry is involved, is Schwarz symmetrization, which is also known as the spherically symmetric and decreasing rearrangement of functions. The aim of this book is to give an introduction to the theory of Schwarz symmetrization and study some of its applicat
Energy Technology Data Exchange (ETDEWEB)
Clarisse, J.M
2007-07-01
A numerical scheme for computing linear Lagrangian perturbations of spherically symmetric flows of gas dynamics is proposed. This explicit first-order scheme uses the Roe method in Lagrangian coordinates, for computing the radial spherically symmetric mean flow, and its linearized version, for treating the three-dimensional linear perturbations. Fulfillment of the geometric conservation law discrete formulations for both the mean flow and its perturbation is ensured. This scheme capabilities are illustrated by the computation of free-surface mode evolutions at the boundaries of a spherical hollow shell undergoing an homogeneous cumulative compression, showing excellent agreement with reference results. (author)
Peng, Jie; Zhu, Jianhua; Li, Tong
2016-06-01
The thermal lens effect of 2.1 μm Cr, Tm, Ho: YAG (CTH:YAG) solid-state laser under high pumping power condition is analyzed, and a symmetric spherical resonator which is insensitive to thermal focal length change is proposed to improve the beam quality of Fabry-Perot (F-P) resonator. Then the gradient-reflectivity mirror is introduced as output mirror to optimize the resonator mode and beam quality. Based on the scalar diffraction theory, the Fox-Li numerical iteration method and fast Fourier transform (FFT) algorithm are used to calculate the resonator mode and output power distribution of resonators with Gaussian, super-Gaussian and parabolic gradient mirror, respectively. By comparing the cavity loss and beam quality, one can find that the symmetric spherical resonator with a super-Gaussian mirror can provide the best output beam quality, it has the minimum cavity loss of 0.1907, the minimum far-field divergence angle of 1 mrad and the maximum power in the bucket (PIB) of 89.42%.
Maj, Omar
2008-01-01
This is the second part of a work aimed to study complex-phase oscillatory solutions of nonlinear symmetric hyperbolic systems. We consider, in particular, the case of one space dimension. That is a remarkable case, since one can always satisfy the \\emph{naive} coherence condition on the complex phases, which is required in the construction of the approximate solution. Formally the theory applies also in several space dimensions, but the \\emph{naive} coherence condition appears to be too restrictive; the identification of the optimal coherence condition is still an open problem.
Zhang, Zhao; Sahoo, Sharmistha; Teo, Jeffrey
We mimic the massless surface Majorana's of topological superconductors by coupled wire models in two spatial dimensions, and introduce many-body gapping interactions that preserve time reversal symmetry. Coupling with a Z2 gauge theory, the symmetric gapped surface generically carries a non-trivial GN topological order, where N is the number of Majorana species and GN is some SO(r)1 or SO(3)3 -like topological state. These form a 32-fold periodic class GN ≅GN + 32 , and a Z32 relative tensor product structure GN1⊗bGN2 ≅GN1 +N2 by anyon condensation. We present the anyon structures of these topological states, and understand the topological orders through bulk-boundary correspondence and the Wilson structures on a torus geometry.
Duality for symmetric second rank tensors. II. The linearized gravitational field
Casini, H; Urrutia, L F; Urrutia, Luis F.
2003-01-01
The construction of dual theories for linearized gravity in four dimensions is considered. Our approach is based on the parent Lagrangian method previously developed for the massive spin-two case, but now considered for the zero mass case. This leads to a dual theory described in terms of a rank two symmetric tensor, analogous to the usual gravitational field, and an auxiliary antisymmetric field. This theory has an enlarged gauge symmetry, but with an adequate partial gauge fixing it can be reduced to a gauge symmetry similar to the standard one of linearized gravitation. We present examples illustrating the general procedure and the physical interpretation of the dual fields. The zero mass case of the massive theory dual to the massive spin-two theory is also examined, but we show that it only contains a spin-zero excitation.
CSIR Research Space (South Africa)
Makgopa, K
2016-09-01
Full Text Available Pseudocapacitive properties of nickel (II) tetraaminophthalocyanine-modified graphene oxide sheets (GO/NiTAPc) composites have been studied. Microscopic and spectroscopic analysis of the GO/NiTAPc electrode material with its precursors (GO and Ni...
Yan, Wang-Ji; Ren, Wei-Xin
2016-12-01
In Part I of this study, some new theorems, corollaries and lemmas on circularly-symmetric complex normal ratio distribution have been mathematically proved. This part II paper is dedicated to providing a rigorous treatment of statistical properties of raw scalar transmissibility functions at an arbitrary frequency line. On the basis of statistics of raw FFT coefficients and circularly-symmetric complex normal ratio distribution, explicit closed-form probabilistic models are established for both multivariate and univariate scalar transmissibility functions. Also, remarks on the independence of transmissibility functions at different frequency lines and the shape of the probability density function (PDF) of univariate case are presented. The statistical structures of probabilistic models are concise, compact and easy-implemented with a low computational effort. They hold for general stationary vector processes, either Gaussian stochastic processes or non-Gaussian stochastic processes. The accuracy of proposed models is verified using numerical example as well as field test data of a high-rise building and a long-span cable-stayed bridge. This study yields new insights into the qualitative analysis of the uncertainty of scalar transmissibility functions, which paves the way for developing new statistical methodologies for modal analysis, model updating or damage detection using responses only without input information.
Nyambuya, G G
2010-01-01
This paper is part of a series on the Azimuthally Symmetric Theory of Gravitation (ASTG) which is built on Laplace-Poisson's well known equation. We show herein that the emergent equations from the ASTG, under some critical conditions determined by the spin, do possess repulsive gravitational fields in the polar regions of the gravitating body in question. This places the ASTG on an interesting pedestal to infer the origins of outflows as a repulsive gravitational phenomenon. Outflows are a ubiquitous phenomenon found in star forming systems and their true origin is a question yet to be settled. Given the current thinking on their origin, the direction that the present paper takes is nothing short of an asymptotic break from conventional wisdom; at the very least, it is a complete paradigm shift because gravitation is not at all associated with this process, but rather it is thought to be an all-attractive force that only tries to squash matter together onto a single point. Additionally, we show that the emer...
Energy Technology Data Exchange (ETDEWEB)
Aman, Noor [ACC Division, National Metallurgical Laboratory, CSIR (Council of Scientific and Industrial Research), Jamshedpur-831007 (India); Mishra, T., E-mail: drtmishra@yahoo.com [ACC Division, National Metallurgical Laboratory, CSIR (Council of Scientific and Industrial Research), Jamshedpur-831007 (India); Hait, J.; Jana, R.K. [ACC Division, National Metallurgical Laboratory, CSIR (Council of Scientific and Industrial Research), Jamshedpur-831007 (India)
2011-02-15
Graphical abstract: Spherical zirconia mixed titania materials can reduce 100 ppm of Cu(II) and Se(VI) mixture within 40 min of reaction under visible light. - Abstract: Waste water of copper mines and copper processing plant contains both copper and selenium ions with other contaminants. In this paper simultaneous photoreductive removal of copper (II) and selenium (IV) is studied for the first time using spherical binary oxide photocatalysts under visible light. All the synthesized materials are found to be mesoporous in nature with reasonably high surface area. Among a range of hole scavengers, only EDTA (ethylene diamine tetraacetic acid) and formic acid are found to be the most active for the reduction reaction. A comparative study is carried out using both the hole scavengers varying reaction time, concentration, pH etc. For a single contaminant, EDTA is found to be the best for Cu(II) reduction whereas formic acid is the best for Se(IV) reduction. In a mixed solution both EDTA and formic acid perform very well under visible light irradiation. Highest photocatalytic reduction in a mixed solution is observed at pH 3. Among all the synthesized materials, TiZr-10 performs as the best photocatalyst for both Cu(II) and Se(IV) reduction. However under UV light, Degussa P25 performs slightly better than TiZr-10. Present study shows that 100 ppm of mixed solution can be removed under visible light in 40 min of reaction using TiZr-10 as catalyst. Photodeposited material is found to be copper selenide rather than pure copper and selenium metal. This indicates that the waste water containing copper and selenium ions can be efficiently treated under visible or solar light.
Directory of Open Access Journals (Sweden)
R.O. Moreira
2007-02-01
Full Text Available The objective of the present study was to establish the frequency of psychiatric comorbidity in a sample of diabetic patients with symmetric distal polyneuropathy (SDPN. Sixty-five patients with type 2 diabetes mellitus were selected consecutively to participate in the study at Instituto Estadual de Diabetes e Endocrinologia. All patients were submitted to a complete clinical and psychiatric evaluation, including the Portuguese version of the structured clinical interview for DSM-IV, the Beck Depression Inventory, the Neuropathy Symptom Score, and Neuropathy Disability Score. SDPN was identified in 22 subjects (33.8%. Patients with and without SDPN did not differ significantly regarding sociodemographic characteristics. However, a trend toward a worse glycemic control was found in patients with SDPN in comparison to patients without SDPN (HbA1c = 8.43 ± 1.97 vs 7.48 ± 1.95; P = 0.08. Patients with SDPN exhibited axis I psychiatric disorders significantly more often than those without SDPN (especially anxiety disorders, in general (81.8 vs 60.0%; P = 0.01, and major depression - current episode, in particular (18.2 vs 7.7%; P = 0.04. The severity of the depressive symptoms correlated positively with the severity of SDPN symptoms (r = 0.38; P = 0.006, but not with the severity of SDPN signs (r = 0.07; P = 0.56. In conclusion, the presence of SDPN seems to be associated with a trend toward glycemic control. The diagnosis of SDPN in diabetic subjects seems also to be associated with relevant psychiatric comorbidity, including anxiety and current mood disorders.
Moreira, R O; Papelbaum, M; Fontenelle, L F; Appolinario, J C; Ellinger, V C M; Coutinho, W F; Zagury, L
2007-02-01
The objective of the present study was to establish the frequency of psychiatric comorbidity in a sample of diabetic patients with symmetric distal polyneuropathy (SDPN). Sixty-five patients with type 2 diabetes mellitus were selected consecutively to participate in the study at Instituto Estadual de Diabetes e Endocrinologia. All patients were submitted to a complete clinical and psychiatric evaluation, including the Portuguese version of the structured clinical interview for DSM-IV, the Beck Depression Inventory, the Neuropathy Symptom Score, and Neuropathy Disability Score. SDPN was identified in 22 subjects (33.8%). Patients with and without SDPN did not differ significantly regarding sociodemographic characteristics. However, a trend toward a worse glycemic control was found in patients with SDPN in comparison to patients without SDPN (HbA1c = 8.43 +/- 1.97 vs 7.48 +/- 1.95; P = 0.08). Patients with SDPN exhibited axis I psychiatric disorders significantly more often than those without SDPN (especially anxiety disorders, in general (81.8 vs 60.0%; P = 0.01), and major depression--current episode, in particular (18.2 vs 7.7%; P = 0.04)). The severity of the depressive symptoms correlated positively with the severity of SDPN symptoms (r = 0.38; P = 0.006), but not with the severity of SDPN signs (r = 0.07; P = 0.56). In conclusion, the presence of SDPN seems to be associated with a trend toward glycemic control. The diagnosis of SDPN in diabetic subjects seems also to be associated with relevant psychiatric comorbidity, including anxiety and current mood disorders.
Kotnik, T; Miklavcic, D; Mir, L M
2001-08-01
The paper presents a comparative study of the contamination of a cell suspension by ions released from aluminum cuvettes (Al(3+)) and stainless steel electrodes (Fe(2+)/Fe(3+)) during cell membrane electropermeabilization by unipolar and by symmetrical bipolar rectangular electric pulses. A single pulse and a train of eight pulses were delivered to electrodes at a 2-mm distance, with 100-micros and 1-ms pulse durations, and amplitudes ranging from 0 to 400 V for unipolar, and from 0 to 280 V for bipolar pulses. We found that the released concentrations of Al(3+) and Fe(2+)/Fe(3+) were always more than one order of magnitude lower with bipolar pulses than with unipolar pulses of the same amplitude and duration. We then investigated the viability of DC-3F cells after 1 h of incubation in the medium containing different concentrations of Al(3+) or Fe(2+)/Fe(3+) within the range of measured released concentrations (up to 2.5 mM for both ions), thus separating the effects of electrolytic contamination from the effects of electropermeabilization itself. For Fe(2+)/Fe(3+), loss of cell viability became significant at concentrations above 1.5 mM, while for Al(3+), no effect on cell survival was detected within the investigated range. Still, reports on the biochemical effects of released Al(3+) also suggest that with aluminum cuvettes, electrolytic contamination can be detrimental. Our study shows that electrolytic contamination and its detrimental effects can be largely reduced with no loss in efficiency of electropermeabilization, if bipolar rectangular pulses of the same amplitude and duration are used instead of the commonly applied unipolar pulses.
Daul, J M; Daul, Jean-Marc; Grangier, Philippe
2003-01-01
We consider the situation where a two-level atom is placed in the vicinity of the center of a spherical cavity with a large numerical aperture. The vacuum field at the center of the cavity is actually equivalent to the one obtained in a microcavity, and both the dissipative and the reactive parts of the atom's spontaneous emission are significantly modified. Using an explicit calculation of the spatial dependence of the radiative relaxation rate and of the associated level shift, we show that for a weakly excitating light field, the atom can be attracted to the center of the cavity by vacuum-induced light shifts.
Asari, Yusuke; Takeda, Kyozaburo; Tamura, Hiroyuki
2005-04-01
We theoretically studied the electronic structure of the three-dimensional spherical parabolic quantum dot (3D-SPQD) under a magnetic field. We obtained the quantum dot orbitals (QDOs) and determined the ground state by using the extended UHF approach where the expectation values of the z component of the total orbital angular momentum are conserved during the scf-procedure. The single-electron treatment predicts that the applied magnetic field (B) creates k-th new shells at the magnetic field of Bk=k(k+2)/(k+1)ω0 with the shell-energy interval of \\hbarω0/(k+1), where ω0(=\\hbar/m*l02) is the characteristic frequency originating from the spherical parabolic confinement potential. These shells are formed by the level crossing among multiple QDOs. The interelectron interaction breaks the simple level crossing but causes complicated dependences among the total energy, the chemical potential and their differences (magic numbers) with the magnetic field or the number of confinement electrons. The ground state having a higher spin multiplicity is theoretically predicted on the basis of the \\textit{quasi}-degeneracies of the QDOs around these shells.
Time-symmetric initial data of large brane-localized black hole in RS-II model
Tanahashi, Norihiro
2008-01-01
In the aim of shedding a new light on the classical black hole evaporation conjecture stating that a static brane-localized black hole (BH) larger than the bulk curvature scale does not exist in Randall-Sundrum II (RS-II) model, we investigate time-symmetric initial data with a brane-localized apparent horizon (AH) and analyzed its properties. We find that a three-parameter family of such initial data can be constructed by simply placing a brane on a constant time surface of Schwarzschild anti-de Sitter space. By this method, we unambiguously confirm that initial data with an arbitrarily large AH area do exist. We compare the ADM mass and the horizon area of our initial data with that of the black string (BS) solution, and find that any initial data constructed by this method do not have a smaller mass than the BS solution when the horizon area is larger than the size determined by the bulk curvature scale. We further investigate what kind of configuration realizes the minimum mass for the same AH area. The c...
Energy Technology Data Exchange (ETDEWEB)
Gregori, A.; Kounnas, C.; Rizos, J
1999-05-31
Using free world-sheet fermions, we construct and classify all the N = 2, Z{sub 2} x Z{sub 2} four-dimensional orbifolds of the type IIA/B strings for which the orbifold projections act symmetrically on the left- and right-movers. We study the deformations of these models out of the fermionic point, deriving the partition functions at a generic point in the moduli of the internal tours T{sup 6} = T{sup 2} x T{sup 2} x T{sup 2}. We investigate some of their perturbative and non-perturbative dualities and construct new dual pairs of type IIA/type II asymmetric orbifolds, which are related non-perturbatively and allow us to gain insight into some of the non-perturbative properties of the type IIA/B strings in four dimensions. In particular, we consider some of the (non)-perturbative gravitational corrections.
Gregori, A; Rizos, J
1999-01-01
Using free world-sheet fermions, we construct and classify all the N = 2, Z sub 2 x Z sub 2 four-dimensional orbifolds of the type IIA/B strings for which the orbifold projections act symmetrically on the left- and right-movers. We study the deformations of these models out of the fermionic point, deriving the partition functions at a generic point in the moduli of the internal tours T sup 6 = T sup 2 x T sup 2 x T sup 2. We investigate some of their perturbative and non-perturbative dualities and construct new dual pairs of type IIA/type II asymmetric orbifolds, which are related non-perturbatively and allow us to gain insight into some of the non-perturbative properties of the type IIA/B strings in four dimensions. In particular, we consider some of the (non)-perturbative gravitational corrections.
Energy Technology Data Exchange (ETDEWEB)
Panicker, Nisha S. [School of Pure and Applied Physics, Mahatma Gandhi University, Kottayam, Kerala 686560 (India); Gopinathan, T.G. [KE College, Mannanam, Kottayam, Kerala (India); Dhanya, I. [School of Pure and Applied Physics, Mahatma Gandhi University, Kottayam, Kerala 686560 (India); Menon, C.S., E-mail: prof.menoncs@gmail.co [School of Pure and Applied Physics, Mahatma Gandhi University, Kottayam, Kerala 686560 (India)
2010-11-01
Vacuum deposited tin(II)2,3-naphthalocyanine (SnNc) crystalline thin films were produced. The structural properties of the thin films were characterized using Fourier transform infrared spectroscopy (FTIR), which reveals traces of organic compounds within the as-deposited films. Surface morphological studies by scanning electron microscopy (SEM) were done and the films were found to be grainy in nature, comprising of small agglomerated spherical particles. Heat treatment decreased the optical band gap of the films due to the dependence of dilatation of the lattice and/or electron-lattice interaction. The electrical conductivity of the films at various heat treated stages shows that SnNc has a better conductivity by 10-50 times that of its earlier reported phthalocyanine counterpart and the activation energy was found to increase with annealing temperature.
Tidal dissipation in a homogeneous spherical body. II. Three examples: Io, Mercury, and Kepler-10 b
Makarov, Valeri V
2014-01-01
In Efroimsky & Makarov (2014), we derived from the first principles a formula for the tidal heating rate in a tidally perturbed homogeneous sphere. We compared it with the formulae used in the literature, and pointed out the differences. Using this result, we now present three case studies - Mercury, Kepler-10b, and a triaxial Io. A very sharp frequency-dependence of k2/Q near spin-orbit resonances yields a similarly sharp dependence of k2/Q on the spin rate. This indicates that physical libration may play a major role in tidal heating of synchronously rotating bodies. The magnitude of libration in the spin rate being defined by the planet's triaxiality, the latter should be a factor determining the dissipation rate. Other parameters equal, a synchronously rotating body with a stronger triaxiality should generate more heat than a similar body of a more symmetrical shape. Further in the paper, we discuss scenarios where initially triaxial objects melt and lose their triaxiality. Thereafter, dissipation in ...
Arfaoui, A.; Mahdouani, M.; Bourguiga, R.
2017-08-01
The two-band model effective mass approximation has been adopted to explain the energy spectra in type-I CdSe core-only and type-II CdSe/CdTe core/shell quantum dots (QDs). As optical properties, the emission wavelength, the electron-hole overlap integral and the radiative recombination lifetime have been investigated. The simulated emission spectra are in good agreement with available experimental results for both core-only and core/shell QDs. The radiative recombination lifetime (τrad) has been investigated in different carrier localization regimes and compared to that corresponding to core-only QDs. We have found a sudden increase in τrad at around r1 1.1 nm suggesting the transition of the heterostructure from the quasi-type-II to the type-II regime. A monotonic increase in τrad with the core and shell sizes (geometric parameters) was observed. Also found is the possibility of increasing τrad over two orders of magnitude with a suitable change in the geometric parameters. The long radiative lifetime produced by increasing the geometric parameters is found due to spatial separation of the carriers, which makes the type-II core/shell QDs made from large core and shell sizes promising for photovoltaic applications.
Tidal dissipation in a homogeneous spherical body. II. Three examples: Mercury, Io, and Kepler-10 b
Energy Technology Data Exchange (ETDEWEB)
Makarov, Valeri V.; Efroimsky, Michael, E-mail: vvm@usno.navy.mil, E-mail: michael.efroimsky@usno.navy.mil [US Naval Observatory, 3450 Massachusetts Avenue NW, Washington, DC 20392 (United States)
2014-11-01
In Efroimsky and Makarov (Paper I), we derived from the first principles a formula for the tidal heating rate in a homogeneous sphere, compared it with the previously used formulae, and noted the differences. Now we present case studies: Mercury, Kepler-10 b, and a triaxial Io. A sharp frequency dependence of k {sub 2}/Q near spin-orbit resonances yields a sharp dependence of k {sub 2}/Q (and, therefore, of tidal heating) upon the spin rate. Thereby physical libration plays a major role in tidal heating of synchronously rotating planets. The magnitude of libration in the spin rate being defined by the planet's triaxiality, the latter becomes a factor determining the dissipation rate. Other parameters equal, a strongly triaxial synchronized body generates more heat than a similar body of a more symmetrical shape. After an initially triaxial object melts and loses its triaxiality, dissipation becomes less intensive; the body can solidify, with the tidal bulge becoming a new figure with triaxiality lower than the original. We derive approximate expressions for the dissipation rate in a Maxwell planet with the Maxwell time longer than the inverse tidal frequency. The expressions derived pertain to the 1:1 and 3:2 resonances and a nonresonant case; so they are applicable to most close-in super-Earths detected. In these planets, the heating outside synchronism is weakly dependent on the eccentricity and obliquity, provided both these parameters's values are moderate. According to our calculation, Kepler-10 b could hardly survive the intensive tidal heating without being synchronized, circularized, and reshaped through a complete or partial melt-down.
Aman, Noor; Mishra, T; Hait, J; Jana, R K
2011-02-15
Waste water of copper mines and copper processing plant contains both copper and selenium ions with other contaminants. In this paper simultaneous photoreductive removal of copper (II) and selenium (IV) is studied for the first time using spherical binary oxide photocatalysts under visible light. All the synthesized materials are found to be mesoporous in nature with reasonably high surface area. Among a range of hole scavengers, only EDTA (ethylene diamine tetraacetic acid) and formic acid are found to be the most active for the reduction reaction. A comparative study is carried out using both the hole scavengers varying reaction time, concentration, pH etc. For a single contaminant, EDTA is found to be the best for Cu(II) reduction whereas formic acid is the best for Se(IV) reduction. In a mixed solution both EDTA and formic acid perform very well under visible light irradiation. Highest photocatalytic reduction in a mixed solution is observed at pH 3. Among all the synthesized materials, TiZr-10 performs as the best photocatalyst for both Cu(II) and Se(IV) reduction. However under UV light, Degussa P25 performs slightly better than TiZr-10. Present study shows that 100 ppm of mixed solution can be removed under visible light in 40 min of reaction using TiZr-10 as catalyst. Photodeposited material is found to be copper selenide rather than pure copper and selenium metal. This indicates that the waste water containing copper and selenium ions can be efficiently treated under visible or solar light.
Directory of Open Access Journals (Sweden)
C. Risso-Pascotto
2005-11-01
Full Text Available Microsporogenesis and pollen development were analyzed in a tetraploid (2n = 4x = 36 accession of the forage grass Brachiaria jubata (BRA 007820 from the Embrapa Beef Cattle Brachiaria collection that showed partial male sterility. Microsporocytes and pollen grains were prepared by squashing and staining with 0.5% propionic carmine. The meiotic process was typical of polyploids, with precocious chromosome migration to the poles and laggards in both meiosis I and II, resulting in tetrads with micronuclei in some microspores. After callose dissolution, microspores were released into the anther locule and appeared to be normal. Although each microspore initiated its differentiation into a pollen grain, in 11.1% of them nucleus polarization was not observed, i.e., pollen mitosis I was symmetric and the typical hemispherical cell plate was not detected. After a central cytokinesis, two equal-sized cells showing equal chromatin condensation and the same nuclear shape and size were formed. Generative cells and vegetative cells could not be distinguished. These cells did not undergo the second pollen mitosis and after completion of pollen wall synthesis each gave rise to a sterile and uninucleate pollen grain. The frequency of abnormal pollen mitosis varied among flowers and also among inflorescences. All plants were equally affected. The absence of fertile sperm cells in a considerable amount of pollen grains in this accession of B. jubata may compromise its use in breeding and could explain, at least in part, why seed production is low when compared with the amount of flowers per raceme.
Central MONDian spike in spherically symmetric systems
Hernandez, X.
2017-08-01
Under a MONDian view, astrophysical systems are expected to follow Newtonian dynamics whenever the local acceleration is above the critical a0 = 1.2 × 10-10 m s-2, and enter a modified regime for accelerations below this critical value. Indeed, the dark matter phenomenology on galactic and subgalactic scales appears always, and only, at low accelerations. It is standard to find the a core, and numerically for a cored isothermal profile. Under a Newtonian interpretation, such a central MONDian region will be interpreted as extra mass, analogous to the controversial black holes sometimes inferred to lie at the centres of globular clusters, despite an absence of nuclear activity detected to date. We calculate this effect and give predictions for the 'central black hole' mass to be expected under Newtonian interpretations of low density Galactic globular clusters.
What is the spacetime of {\\em physically realizable} spherical collapse?
Wagh, S M; Govinder, K S; Wagh, Sanjay M.; Saraykar, Ravindra V.; Govinder, Keshlan S.
2002-01-01
We argue that a particular spacetime, a spherically symmetric spacetime with hyper-surface orthogonal, radial, homothetic Killing vector, is a physically meaningful spacetime that describes the problem of spherical gravitational collapse in its full "physical" generality.
Directory of Open Access Journals (Sweden)
Tom H. Koornwinder
2008-06-01
Full Text Available This paper builds on the previous paper by the author, where a relationship between Zhedanov's algebra AW(3 and the double affine Hecke algebra (DAHA corresponding to the Askey-Wilson polynomials was established. It is shown here that the spherical subalgebra of this DAHA is isomorphic to AW(3 with an additional relation that the Casimir operator equals an explicit constant. A similar result with q-shifted parameters holds for the antispherical subalgebra. Some theorems on centralizers and centers for the algebras under consideration will finally be proved as corollaries of the characterization of the spherical and antispherical subalgebra.
A quantum symmetric key cipher(Y-00) and key generation (Quantum stream cipher-Part II)
Hirota, O; Sohma, M; Fuse, M; Hirota, Osamu; Kato, Kentaro; Sohma, Masaki; Fuse, Masaru
2004-01-01
What obstructs the realization of useful quantum cryptography is single photon scheme, or entanglement which is not applicable to the current infrastructure of optical communication network. We are concerned with the following question: Can we realize the information theoretically secure symmetric key cipher under "the finite secret key" based on quantum-optical communications? A role of quantum information theory is to give an answer for such a question. As an answer for the question, a new quantum cryptography was proposed by H.P.Yuen, which can realize a secure symmetric key cipher with high speeds(Gbps) and for long distance(1000 Km). Although some researchers claim that Yuen protocol(Y-00) is equivalent to the classical cryptography, they are all mistaken. Indeed it has no classical analogue, and also provides a generalization even in the conventional cryptography. At present, it is proved that a basic model of Y-00 has at least the security such as $H(X|Y_E)=H(K|Y_E)=H(K)$, $H(K|Y_E,X)\\sim 0$ under the ...
Burke, Jan
2009-03-01
This paper complements our previous study on testing a 25.4 mm diameter diamond-turned 90 masculine off-axis commercial-quality parabolic mirror with a spherical test wave in a phase-shifting Fizeau interferometer (Opt. Express 17, 3196-3210 (2009). In this study I reverse the optical system and use the Fizeau interferometer with a planar reference surface, auxiliary components, and the surface of the transmission sphere as a reflecting spherical return surface. As in the previous paper, I present a description of the necessary steps for alignment and measurement validation. The reversal of the optical system, and associated co-ordinate systems, necessitates some changes of hardware and analysis that provide insight into the underlying symmetries, and may prove useful in a wider context.
Milking the spherical cow: on aspherical dynamics in spherical coordinates
Pontzen, Andrew; Teyssier, Romain; Governato, Fabio; Gualandris, Alessia; Roth, Nina; Devriendt, Julien
2015-01-01
Galaxies and the dark matter halos that host them are not spherically symmetric, yet spherical symmetry is a helpful simplifying approximation for idealised calculations and analysis of observational data. The assumption leads to an exact conservation of angular momentum for every particle, making the dynamics unrealistic. But how much does that inaccuracy matter in practice for analyses of stellar distribution functions, collisionless relaxation, or dark matter core-creation? We provide a general answer to this question for a wide class of aspherical systems; specifically, we consider distribution functions that are "maximally stable", i.e. that do not evolve at first order when external potentials (which arise from baryons, large scale tidal fields or infalling substructure) are applied. We show that a spherically-symmetric analysis of such systems gives rise to the false conclusion that the density of particles in phase space is ergodic (a function of energy alone). Using this idea we are able to demonstra...
ODF Maxima Extraction in Spherical Harmonic Representation via Analytical Search Space Reduction
2010-05-01
by expressing the ODF, or any antipodally symmetric spherical function, in the common fourth order real and symmetric spherical harmonic basis, the...propose an analytical dimension reduction approach to ODF maxima extraction. We show that by expressing the ODF, or any antipodally symmetric...or any antipodally symmetric spherical function – without compromising the precision. Contrary to [14]–[16], our method works directly in the RSSH
Energy spectrum of an exciton in a CdSe/ZnTe type-II core/shell spherical quantum dot
Chafai, A.; Dujardin, F.; Essaoudi, I.; Ainane, A.
2017-01-01
The binding energy of an exciton inside a CdSe/ZnTe core/shell spherical quantum dot was theoretically examined taking into account the dependence of the dielectric constant and charge carriers effective mass on radius, and using the envelope function approximation. Such a structure presents original optical and electronic properties because of the spatial separation of electrons and holes caused by the type-II alignment of energy states. The mean distance between the electron and hole was calculated variationally using a trial function taking into account the coulomb interaction between charge carriers. Our numerical results provide a description to the size dependence of the binding energy of an exciton inside a core/shell nanoheterostructure type-II. Indeed, by controlling the inner and outer radii, we can precisely control the energy spectrum of the exciton.
Bahaffi, Saleh O.; Abdel Aziz, Ayman A.; El-Naggar, Maher M.
2012-08-01
A novel series of four copper(II) complexes were synthesized by thermal reaction of copper acetate salt with symmetrical tetradentate Schiff bases, N,N'bis(o-vanillin)4,5-dimethyl-l,2-phenylenediamine (H2L1), N,N'bis(salicylaldehyde)4,5-dimethyl-1,2-phenylenediamine (H2L2), N,N'bis(o-vanillin)4,5-dichloro-1,2-phenylenediamine (H2L3) and N,N'bis(salicylaldehyde)4,5-dichloro-1,2-phenylenediamine (H2L4), respectively. All the new synthesized complexes were characterized by using of microanalysis, FT-IR, UV-Vis, magnetic measurements, ESR, and conductance measurements, respectively. The data revealed that all the Schiff bases (H2L1-4) coordinate in their deprotonated forms and behave as tetradentate NOON coordinated ligands. Moreover, their copper(II) complexes have square planar geometry with general formula [CuL1-4]. The binding of the complexes with calf thymus DNA (CT-DNA) was investigated by UV-Vis spectrophotometry, fluorescence quenching and viscosity measurements. The results indicated that the complexes bind to CT-DNA through an intercalative mode. From the biological activity view, the copper(II) complexes and their parent ligands were screened for their in vitro antibacterial activity against the bacterial species Staphylococcus aureus, Staphylococcus epidermidis, Escherichia coli and Pseudomonas aeruginosai by well diffusion method. The complexes showed an increased activity in comparison to some standard drugs.
Keypour, Hassan; Shayesteh, Maryam; Rezaeivala, Majid; Chalabian, Firoozeh; Valencia, Laura
2013-01-15
A new symmetrical [N4O2] hexadentate Schiff base ligand, (E)-N-(pyridin-2-ylmethylene)-2-(3-(2-((E)-pyridin-2-lmethyleneamino)phenoxy)naphthalen-2-yloxy)benzenamine, abbreviated to L, and its complexes of Ni(II), Cu(II), Zn(II), Co(II), Cd(II) and Mn(II) have been synthesized in the presence of metal ions. The complexes were structurally characterized by elemental analyses, IR, UV-Vis, NMR and molar conductivity. The crystal structures of two complexes, [NiL(ONO2)2]·2H2O and [CoLCl2]CH3OH·0.5H2O, have been determined by a single crystal X-ray diffraction study. In these complexes, the ligand is coordinated in a neutral form via pyridine and azomethine nitrogen atoms. The metal ions complete their six coordination with two coordinated nitrate or chloride ions, forming a distorted octahedral geometry. The synthesized compounds have antibacterial activity against the three Gram-positive bacteria: Enterococcus faecalis, Bacillus cereus and Staphylococcus epid and also against the three Gram-negative bacteria: Citrobacter freundii, Enterobacter aerogenes and Salmonella typhi. The activity data show that the complexes are more potent antibacterials than the parent Schiff base.
Keypour, Hassan; Shayesteh, Maryam; Rezaeivala, Majid; Chalabian, Firoozeh; Valencia, Laura
2013-01-01
A new symmetrical [N4O2] hexadentate Schiff base ligand, (E)-N-(pyridin-2-ylmethylene)-2-(3-(2-((E)-pyridin-2-lmethyleneamino)phenoxy)naphthalen-2-yloxy)benzenamine, abbreviated to L, and its complexes of Ni(II), Cu(II), Zn(II), Co(II), Cd(II) and Mn(II) have been synthesized in the presence of metal ions. The complexes were structurally characterized by elemental analyses, IR, UV-Vis, NMR and molar conductivity. The crystal structures of two complexes, [NiL(ONO2)2]·2H2O and [CoLCl2]CH3OH·0.5H2O, have been determined by a single crystal X-ray diffraction study. In these complexes, the ligand is coordinated in a neutral form via pyridine and azomethine nitrogen atoms. The metal ions complete their six coordination with two coordinated nitrate or chloride ions, forming a distorted octahedral geometry. The synthesized compounds have antibacterial activity against the three Gram-positive bacteria: Enterococcus faecalis, Bacillus cereus and Staphylococcus epid and also against the three Gram-negative bacteria: Citrobacter freundii, Enterobacter aerogenes and Salmonella typhi. The activity data show that the complexes are more potent antibacterials than the parent Schiff base.
Vasiljević, Gorazd
2014-01-01
This BSc thesis deals with certain topics from graph theory. When we talk about studying graphs, we usually mean studying their structure and their structural properties. By doing that, we are often interested in automorphisms of a graph (symmetries), which are permutations of its vertex set, preserving adjacency. There exist graphs, which are symmetric enough, so that automorhism group acts transitively on their vertex set. This means that for any pair of vertices of the graph, there is an a...
Wenninger, Magnus J
2012-01-01
Well-illustrated, practical approach to creating star-faced spherical forms that can serve as basic structures for geodesic domes. Complete instructions for making models from circular bands of paper with just a ruler and compass. Discusses tessellation, or tiling, and how to make spherical models of the semiregular solids and concludes with a discussion of the relationship of polyhedra to geodesic domes and directions for building models of domes. "". . . very pleasant reading."" - Science. 1979 edition.
Reese, D; Rieutord, M
2004-01-01
We carry out numerical and mathematical investigations of shear Alfven waves inside of a spherical shell filled with an incompressible conducting fluid, and bathed in a strong dipolar magnetic field. We focus on axisymmetric toroidal and non-axisymmetric modes, in continuation of a previous work by Rincon & Rieutord (2003). Analytical expressions are obtained for toroidal eigenmodes and their corresponding frequencies at low diffusivities. These oscillations behave like magnetic shear layers, in which the magnetic poles play a key role, and hence become singular when diffusivities vanish. It is also demonstrated that non-axisymmetric modes are split into two categories, namely poloidal or toroidal types, following similar asymptotic behaviours as their axisymmetric counterparts when the diffusivities become arbitrarily small.
Yu, C; Yu, Cong; Lou, Yu-Qing
2005-01-01
We investigate self-similar magnetohydrodynamic (MHD) processes in an isothermal self-gravitating fluid with a quasi-spherical symmetry and extend the envelope expansion with core collapse (EECC) solutions of Lou & Shen by incorporating a random magnetic field. Stagnation surfaces of EECC solutions that seperate core collapse and envelope expansion propagate at constant speeds either sub-magnetosonically or super-magnetosonically. Crossing the magnetosonic line twice analytically, there exists an infinite number of discrete magnetized EECC and ECCC solutions. In addition to the EECC shock solution which could change the central accretion rate, the magnetic field can also affect the core accretion rate. As the magnetic parameter $\\lambda$ increases, the core accretion rate appropriate for the MHD EWCS becomes larger. Under the frozen-in approximation, magnetic fields in the envelope expansion portion would scale as $B\\propto r^{-1}$, while in the core collapse portion they would scale as $B\\propto r^{-1/2}...
Directory of Open Access Journals (Sweden)
C. León Llerena
2007-12-01
Full Text Available Presentamos el caso de un varón de 56 años de edad con historia de 35 años de abuso de alcohol y sin otra patología asociada, que presentaba masas en hombros, mamas y flancos que habían aumentado de tamaño de forma progresiva durante los últimos dos años y medio, y que dificultaban su movilidad y su actividad laboral. El estudio mediante Tomografía Axial Computerizada apreció un exceso de deposito graso de distribución homogénea no encapsulado (difuso sobre los hombros, mamas y cintura abdominal, sin afectación de estructuras profundas. Consideramos importante conocer los dos tipos existentes de Lipomatosis Simétrica Benigna, por sus diferencias tanto en la localización de las masas lipomatosas como en la afectación de estructuras profundas. Es por ello que aportamos este caso de Lipomatosis Simétrica Benigna tipo II sin afectación cervical ni de estructuras profundas.We report the case of a 56 years-old man with a 35-years history of alcohol abuse, but no other illness. The patient presented masses on shoulders, breasts and flanks that had enlarged progressively over the previous two and a half years, and that hindered his work by restricting mobility. Computed Tomography revealed non-encapsulated excess fat deposits evenlydistributed on shoulders, breasts and abdomen, without affecting the deep structures. Awareness of the two types of Benign symmetric lipomatosis is necessary because of their differences, both in location of the lipomatous masses and in the involvement of the deep structures. We therefore report this case of type II Benign symmetric lipomatosis without cervical or deep structure involvement.
Foliation dependence of black hole apparent horizons in spherical symmetry
Faraoni, Valerio; Firouzjaee, Javad T; Helou, Alexis; Musco, Ilia
2016-01-01
Numerical studies of gravitational collapse to black holes make use of apparent horizons, which are intrinsically foliation-dependent. We expose the problem and discuss possible solutions using the Hawking quasilocal mass. In spherical symmetry, we present a physically sensible approach to the problem by restricting to spherically symmetric spacetime slicings. In spherical symmetry the apparent horizons are gauge-independent in any spherically symmetric foliation but physical quantities associated with them, such as surface gravity and temperature, are not. The widely used comoving and Kodama foliations, which are of particular interest, are discussed in detail.
Foliation dependence of black hole apparent horizons in spherical symmetry
Faraoni, Valerio; Ellis, George F. R.; Firouzjaee, Javad T.; Helou, Alexis; Musco, Ilia
2017-01-01
Numerical studies of gravitational collapse to black holes make use of apparent horizons, which are intrinsically foliation dependent. We expose the problem and discuss possible solutions using the Hawking-Hayward quasilocal mass. In spherical symmetry, we present a physically sensible approach to the problem by restricting to spherically symmetric spacetime slicings. In spherical symmetry, the apparent horizons enjoy a restricted gauge independence in any spherically symmetric foliation, but physical quantities associated with them, such as surface gravity and temperature, are fully gauge dependent. The widely used comoving and Kodama foliations, which are of particular interest, are discussed in detail as examples.
Kordy, M.; Wannamaker, P.; Maris, V.; Cherkaev, E.; Hill, G.
2016-01-01
Following the creation described in Part I of a deformable edge finite-element simulator for 3-D magnetotelluric (MT) responses using direct solvers, in Part II we develop an algorithm named HexMT for 3-D regularized inversion of MT data including topography. Direct solvers parallelized on large-RAM, symmetric multiprocessor (SMP) workstations are used also for the Gauss-Newton model update. By exploiting the data-space approach, the computational cost of the model update becomes much less in both time and computer memory than the cost of the forward simulation. In order to regularize using the second norm of the gradient, we factor the matrix related to the regularization term and apply its inverse to the Jacobian, which is done using the MKL PARDISO library. For dense matrix multiplication and factorization related to the model update, we use the PLASMA library which shows very good scalability across processor cores. A synthetic test inversion using a simple hill model shows that including topography can be important; in this case depression of the electric field by the hill can cause false conductors at depth or mask the presence of resistive structure. With a simple model of two buried bricks, a uniform spatial weighting for the norm of model smoothing recovered more accurate locations for the tomographic images compared to weightings which were a function of parameter Jacobians. We implement joint inversion for static distortion matrices tested using the Dublin secret model 2, for which we are able to reduce nRMS to ˜1.1 while avoiding oscillatory convergence. Finally we test the code on field data by inverting full impedance and tipper MT responses collected around Mount St Helens in the Cascade volcanic chain. Among several prominent structures, the north-south trending, eruption-controlling shear zone is clearly imaged in the inversion.
An axially symmetric solution of metric-affine gravity
Vlachynsky, E J; Obukhov, Yu N; Hehl, F W
1996-01-01
We present an exact stationary {\\it axially symmetric} vacuum solution of metric-affine gravity (MAG) which generalises the recently reported spherically symmetric solution. Besides the metric, it carries nonmetricity and torsion as post-Riemannian geometrical structures. The parameters of the solution are interpreted as mass and angular momentum and as dilation, shear and spin charges.
Axially symmetric solutions in f(R)-gravity
Capozziello, Salvatore; Stabile, Arturo
2009-01-01
Axially symmetric solutions for f(R)-gravity can be derived starting from exact spherically symmetric solutions. The method takes advantage of a complex coordinate transformation previously developed by Newman and Janis in General Relativity. An example is worked out to show the general validity of the approach.
Axially symmetric solutions in f(R)-gravity
Energy Technology Data Exchange (ETDEWEB)
Capozziello, Salvatore; De Laurentis, Mariafelicia [Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' (Italy); Stabile, Arturo, E-mail: capozziello@na.infn.i [Dipartimento di Ingegneria, Universita del Sannio, Benevento, C.so Garibaldi 107, I-80125 Benevento (Italy)
2010-08-21
Axially symmetric solutions for f(R)-gravity can be derived starting from exact spherically symmetric solutions achieved by Noether symmetries. The method takes advantage of a complex coordinate transformation previously developed by Newman and Janis in general relativity. An example is worked out to show the general validity of the approach. The physical properties of the solution are also considered.
Hawking Radiation from Plane Symmetric Black Hole Covariant Anomaly
Institute of Scientific and Technical Information of China (English)
ZENG Xiao-Xiong; HAN Yi-Wen; YANG Shu-Zheng
2009-01-01
Based on the covariant anomaly cancellation method, which is believed to be more refined than the initial approach of Robinson and Wilczek, we discuss Hawking radiation from the plane symmetric black hole. The result shows that Hawking radiation from the non-spherical symmetric black holes also can be derived from the viewpoint of anomaly.
Dynamics of a Spherical Null Shell within the Distributional Formalism
Khakshournia, Samad; Mansouri, Reza
2004-01-01
Dynamics of a null thin shell immersed in a generic spherically symmetric spacetime is obtained within the distributional formalism. It has been shown that the distributional formalism leads to the same result as in the conventional formalism.
Bounce-free Spherical Hydrodynamic Implosion
Kagan, Grigory; Hsu, Scott C; Awe, Thomas J
2011-01-01
In a bounce-free spherical hydrodynamic implosion, the post-stagnation hot core plasma does not expand against the imploding flow. Such an implosion scheme has the advantage of improving the dwell time of the burning fuel, resulting in a higher fusion burn-up fraction. The existence of bounce-free spherical implosions is demonstrated by explicitly constructing a family of self-similar solutions to the spherically symmetric ideal hydrodynamic equations. When applied to a specific example of plasma liner driven magneto-inertial fusion, the bounce-free solution is found to produce at least a factor of four improvement in dwell time and fusion energy gain.
Spherical harmonics in texture analysis
Schaeben, Helmut; van den Boogaart, K. Gerald
2003-07-01
The objective of this contribution is to emphasize the fundamental role of spherical harmonics in constructive approximation on the sphere in general and in texture analysis in particular. The specific purpose is to present some methods of texture analysis and pole-to-orientation probability density inversion in a unifying approach, i.e. to show that the classic harmonic method, the pole density component fit method initially introduced as a distinct alternative, and the spherical wavelet method for high-resolution texture analysis share a common mathematical basis provided by spherical harmonics. Since pole probability density functions and orientation probability density functions are probability density functions defined on the sphere Ω3⊂ R3 or hypersphere Ω4⊂ R4, respectively, they belong at least to the space of measurable and integrable functions L1( Ωd), d=3, 4, respectively. Therefore, first a basic and simplified method to derive real symmetrized spherical harmonics with the mathematical property of providing a representation of rotations or orientations, respectively, is presented. Then, standard orientation or pole probability density functions, respectively, are introduced by summation processes of harmonic series expansions of L1( Ωd) functions, thus avoiding resorting to intuition and heuristics. Eventually, it is shown how a rearrangement of the harmonics leads quite canonically to spherical wavelets, which provide a method for high-resolution texture analysis. This unified point of view clarifies how these methods, e.g. standard functions, apply to texture analysis of EBSD orientation measurements.
Salom, Igor; Dmitrašinović, V.
2017-07-01
We construct the three-body permutation symmetric hyperspherical harmonics to be used in the non-relativistic three-body Schrödinger equation in three spatial dimensions (3D). We label the state vectors according to the S3 ⊗ SO(3)rot ⊂ O (2) ⊗ SO(3)rot ⊂ U (3) ⋊S2 ⊂ O (6) subgroup chain, where S3 is the three-body permutation group and S2 is its two element subgroup containing transposition of first two particles, O (2) is the ;democracy transformation;, or ;kinematic rotation; group for three particles; SO(3)rot is the 3D rotation group, and U (3) , O (6) are the usual Lie groups. We discuss the good quantum numbers implied by the above chain of algebras, as well as their relation to the S3 permutation properties of the harmonics, particularly in view of the SO(3)rot ⊂ SU (3) degeneracy. We provide a definite, practically implementable algorithm for the calculation of harmonics with arbitrary finite integer values of the hyper angular momentum K, and show an explicit example of this construction in a specific case with degeneracy, as well as tables of K ≤ 6 harmonics. All harmonics are expressed as homogeneous polynomials in the Jacobi vectors (λ , ρ) with coefficients given as algebraic numbers unless the ;operator method; is chosen for the lifting of the SO(3)rot ⊂ SU (3) multiplicity and the dimension of the degenerate subspace is greater than four - in which case one must resort to numerical diagonalization; the latter condition is not met by any K ≤ 15 harmonic, or by any L ≤ 7 harmonic with arbitrary K. We also calculate a certain type of matrix elements (the Gaunt integrals of products of three harmonics) in two ways: 1) by explicit evaluation of integrals and 2) by reduction to known SU (3) Clebsch-Gordan coefficients. In this way we complete the calculation of the ingredients sufficient for the solution to the quantum-mechanical three-body bound state problem.
Collapsing spherical null shells in general relativity
Directory of Open Access Journals (Sweden)
S Khakshournia
2011-03-01
Full Text Available In this work, the gravitational collapse of a spherically symmetric null shell with the flat interior and a charged Vaidya exterior spacetimes is studied. There is no gravitational impulsive wave present on the null hypersurface which is shear-free and contracting. It follows that there is a critical radius at which the shell bounces and starts expanding.
Homogeneous spacelike singularities inside spherical black holes
Burko, L M
1997-01-01
Recent numerical simulations have found that the Cauchy horizon inside spherical charged black holes, when perturbed nonlinearly by a self-gravitating, minimally-coupled, massless, spherically-symmetric scalar field, turns into a null weak singularity which focuses monotonically to $r=0$ at late times, where the singularity becomes spacelike. Our main objective is to study this spacelike singularity. We study analytically the spherically-symmetric Einstein-Maxwell-scalar equations asymptotically near the singularity. We obtain a series-expansion solution for the metric functions and for the scalar field near $r=0$ under the simplifying assumption of homogeneity. Namely, we neglect spatial derivatives and keep only temporal derivatives. We find that there indeed exists a generic spacelike singularity solution for these equations (in the sense that the solution depends on enough free parameters), with similar properties to those found in the numerical simulations. This singularity is strong in the Tipler sense,...
Plane symmetric cosmological models
Yadav, Anil Kumar; Ray, Saibal; Mallick, A
2016-01-01
In this work, we perform the Lie symmetry analysis on the Einstein-Maxwell field equations in plane symmetric spacetime. Here Lie point symmetries and optimal system of one dimensional subalgebras are determined. The similarity reductions and exact solutions are obtained in connection to the evolution of universe. The present study deals with the electromagnetic energy of inhomogeneous universe where $F_{12}$ is the non-vanishing component of electromagnetic field tensor. To get a deterministic solution, it is assumed that the free gravitational field is Petrov type-II non-degenerate. The electromagnetic field tensor $F_{12}$ is found to be positive and increasing function of time. As a special case, to validate the solution set, we discuss some physical and geometric properties of a specific sub-model.
Symmetric Powers of Symmetric Bilinear Forms
Institute of Scientific and Technical Information of China (English)
Se(a)n McGarraghy
2005-01-01
We study symmetric powers of classes of symmetric bilinear forms in the Witt-Grothendieck ring of a field of characteristic not equal to 2, and derive their basic properties and compute their classical invariants. We relate these to earlier results on exterior powers of such forms.
Coning, symmetry and spherical frameworks
Schulze, Bernd
2011-01-01
In this paper, we combine separate works on (a) the transfer of infinitesimal rigidity results from an Euclidean space to the next higher dimension by coning, (b) the further transfer of these results to spherical space via associated rigidity matrices, and (c) the prediction of finite motions from symmetric infinitesimal motions at regular points of the symmetry-derived orbit rigidity matrix. Each of these techniques is reworked and simplified to apply across several metrics, including the Minkowskian metric $\\M^{d}$ and the hyperbolic metric $\\H^{d}$. This leads to a set of new results transferring infinitesimal and finite motions associated with corresponding symmetric frameworks among $\\E^{d}$, cones in $E^{d+1}$, $\\SS^{d}$, $\\M^{d}$, and $\\H^{d}$. We also consider the further extensions associated with the other Cayley-Klein geometries overlaid on the shared underlying projective geometry.
Directory of Open Access Journals (Sweden)
Morteza Montazerozohori
2013-01-01
Full Text Available Synthesis of zinc(II/cadmium(II/mercury(II thiocyanate and azide complexes of a new bidentate Schiff-base ligand (L with general formula of MLX2 (M = Zn(II, Cd(II, and Hg(II in ethanol solution at room temperature is reported. The ligand and metal complexes were characterized by using ultraviolet-visible (UV-visible, Fourier transform infrared (FT-IR, 1H- and 13C-NMR spectroscopy and physical characterization, CHN analysis, and molar conductivity. 1H- and 13C-NMR spectra have been studied in DMSO-d6. The reasonable shifts of FT-IR and NMR spectral signals of the complexes with respect to the free ligand confirm well coordination of Schiff-base ligand and anions in an inner sphere coordination space. The conductivity measurements as well as spectral data indicated that the complexes are nonelectrolyte. Theoretical optimization on the structure of ligand and its complexes was performed at the Becke’s three-parameter hybrid functional (B3 with the nonlocal correlation of Lee-Yang-Parr (LYP level of theory with double-zeta valence (LANL2DZ basis set using GAUSSIAN 03 suite of program, and then some theoretical structural parameters such as bond lengths, bond angles, and torsion angles were obtained. Finally, electrochemical behavior of ligand and its complexes was investigated. Cyclic voltammograms of metal complexes showed considerable changes with respect to free ligand.
Jiang, Haiyong
2016-04-11
We present an automatic algorithm for symmetrizing facade layouts. Our method symmetrizes a given facade layout while minimally modifying the original layout. Based on the principles of symmetry in urban design, we formulate the problem of facade layout symmetrization as an optimization problem. Our system further enhances the regularity of the final layout by redistributing and aligning boxes in the layout. We demonstrate that the proposed solution can generate symmetric facade layouts efficiently. © 2015 IEEE.
Symmetrization of Facade Layouts
Jiang, Haiyong
2016-02-26
We present an automatic approach for symmetrizing urban facade layouts. Our method can generate a symmetric layout through minimally modifying the original input layout. Based on the principles of symmetry in urban design, we formulate facade layout symmetrization as an optimization problem. Our method further enhances the regularity of the final layout by redistributing and aligning elements in the layout. We demonstrate that the proposed solution can effectively generate symmetric facade layouts.
Chambler, A F; Chapman-Sheath, P J; Pearse, M F; Hollingdale, J
1997-10-01
Chronic recurrent multifocal osteomyelitis is often confused with symmetrical Brodie's abscess as it has a similar pathogenesis. We report an otherwise healthy 17-year-old boy presenting with a true symmetrical Brodie's abscess. We conclude that a symmetrical Brodie's abscess presenting in an otherwise healthy patient is a separate clinical condition with a different management protocol.
A new model for spherically symmetric anisotropic compact star
Maurya, S K; Dayanandan, Baiju; Ray, Saibal
2016-01-01
In this article we obtain a new anisotropic solution for Einstein's field equation of embedding class one metric. The solution is representing the realistic objects such as $Her~X-1$ and $RXJ~1856-37$. We perform detailed investigation of both objects by solving numerically the Einstein field equations under with anisotropic pressure. The physical features of the parameters depend on the anisotropic factor i.e. if anisotropy is zero everywhere inside the star then the density and pressures will become zero and metric turns out to be flat. We report our results and compare with the above mentioned two compact objects on a number of key aspects: the central density, the surface density onset and the critical scaling behavior, the effective mass and radius ratio, the anisotropization with isotropic initial conditions, adiabatic index and red shift. Along with this we have also made a comparison between the classical limit and theoretical model treatment of the compact objects. Finally we discuss the implications...
A new model for spherically symmetric anisotropic compact star
Maurya, S. K.; Gupta, Y. K.; Dayanandan, Baiju; Ray, Saibal
2016-05-01
In this article we obtain a new anisotropic solution for Einstein's field equations of embedding class one metric. The solution represents realistic objects such as Her X-1 and RXJ 1856-37. We perform a detailed investigation of both objects by solving numerically the Einstein field equations with anisotropic pressure. The physical features of the parameters depend on the anisotropic factor i.e. if the anisotropy is zero everywhere inside the star then the density and pressures will become zero and the metric turns out to be flat. We report our results and compare with the above mentioned two compact objects as regards a number of key aspects: the central density, the surface density onset and the critical scaling behaviour, the effective mass and radius ratio, the anisotropization with isotropic initial conditions, adiabatic index and red shift. Along with this we have also made a comparison between the classical limit and theoretical model treatment of the compact objects. Finally we discuss the implications of our findings for the stability condition in a relativistic compact star.
A new model for spherically symmetric anisotropic compact star
Energy Technology Data Exchange (ETDEWEB)
Maurya, S.K.; Dayanandan, Baiju [University of Nizwa, Department of Mathematical and Physical Sciences, College of Arts and Science, Nizwa (Oman); Gupta, Y.K. [Raj Kumar Goel Institute of Technology, Department of Mathematics, Ghaziabad, UP (India); Ray, Saibal [Government College of Engineering and Ceramic Technology, Department of Physics, Kolkata, West Bengal (India)
2016-05-15
In this article we obtain a new anisotropic solution for Einstein's field equations of embedding class one metric. The solution represents realistic objects such as Her X-1 and RXJ 1856-37. We perform a detailed investigation of both objects by solving numerically the Einstein field equations with anisotropic pressure. The physical features of the parameters depend on the anisotropic factor i.e. if the anisotropy is zero everywhere inside the star then the density and pressures will become zero and the metric turns out to be flat. We report our results and compare with the above mentioned two compact objects as regards a number of key aspects: the central density, the surface density onset and the critical scaling behaviour, the effective mass and radius ratio, the anisotropization with isotropic initial conditions, adiabatic index and red shift. Along with this we have also made a comparison between the classical limit and theoretical model treatment of the compact objects. Finally we discuss the implications of our findings for the stability condition in a relativistic compact star. (orig.)
SMBH Spherically Symmetric Accretion Regulated by Violent Star Formation Feedback
Silich, S; Tenorio-Tagle, G
2008-01-01
The mounting evidence for violent nuclear star formation in Seyfert galaxies has led us to consider the hydrodynamics of the matter reinserted by massive stars through strong stellar winds and supernovae, under the presence of a central massive BH. We show that in all cases there is a bimodal solution strongly weighted by the location of the stagnation radius (Rst), which splits the star cluster into two different zones. Matter reinserted within the stagnation volume is to be accreted by the BH while its outer counterpart would composed a star cluster wind. The mechanical power of the latter, ensures that there is no accretion of the ISM into the BH and thus the BH accretion and its luminosity is regulated by the star formation feedback. The location of the stagnation radius is a function of three parameters: the BH mass, the mechanical power (or mass) of the star formation event and the size of the star forming region. Here we present our self-consistent, stationary solution, discuss the accretion rates and ...
Spherically Symmetric and Rotating Wormholes Produced by Lightlike Branes
Guendelman, Eduardo; Nissimov, Emil; Pacheva, Svetlana
2009-01-01
Lightlike p-branes (LL-branes) with dynamical (variable) tension allow simple and elegant Polyakov-type and dual to it Nambu-Goto-like world-volume action formulations. Here we first briefly describe the dynamics of LL-branes as test objects in various physically interesting gravitational backgrounds of black hole type, including rotating ones. Next we show that LL-branes are the appropriate gravitational sources that provide proper matter energy momentum tensors in the Einstein equations of motion needed to generate traversable wormhole solutions, in particular, self-consistent cylindrical rotating wormholes, with the LL-branes occupying their throats. Here a major role is being played by the dynamical LL-brane tension which turns out to be negative but may be of arbitrary small magnitude. As a particular solution we obtain traversable wormhole with Schwarzschild geometry generated by a LL-brane positioned at the wormhole throat, which represents the correct consistent realization of the original Einstein-Ro...
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.
Spherical Black Holes cannot Support Scalar Hair
Sudarsky, D
1998-01-01
The static spherically symmetric ``black hole solution" of the Einstein - conformally invariant massless scalar field equations known as the BBMB ( Bocharova, , Bronikov, Melinkov, Bekenstein) black hole is critically examined. It is shown that the stress energy tensor is ill-defined at the horizon, and that its evaluation through suitable regularization yields ambiguous results. Consequently, the configuration fails to represent a genuine black hole solution. With the removal of this solution as a counterexample to the no hair conjecture, we argue that the following appears to be true: Spherical black holes cannot carry any kind of classical scalar hair.
Canteaut, Anne; Videau, Marion
2005-01-01
http://www.ieee.org/; We present an extensive study of symmetric Boolean functions, especially of their cryptographic properties. Our main result establishes the link between the periodicity of the simplified value vector of a symmetric Boolean function and its degree. Besides the reduction of the amount of memory required for representing a symmetric function, this property has some consequences from a cryptographic point of view. For instance, it leads to a new general bound on the order of...
DÍaz, R.; Rivas, M.
2010-01-01
In order to study Boolean algebras in the category of vector spaces we introduce a prop whose algebras in set are Boolean algebras. A probabilistic logical interpretation for linear Boolean algebras is provided. An advantage of defining Boolean algebras in the linear category is that we are able to study its symmetric powers. We give explicit formulae for products in symmetric and cyclic Boolean algebras of various dimensions and formulate symmetric forms of the inclusion-exclusion principle.
Dynamics and statics of flexible axially symmetric shallow shells
2006-01-01
In this work, we propose the method for the investigation of stochastic vibrations of deterministic mechanical systems represented by axially symmetric spherical shells. These structure members are widely used as sensitive elements of pressure measuring devices in various branches of measuring and control industry, machine design, and so forth. The proposed method can be easily extended for the investigation of shallow spherical shells, goffer-type membranes, and so on. T...
New mathematical framework for spherical gravitational collapse
Giambo, R; Magli, G; Piccione, P; Giambo', Roberto; Giannoni, Fabio; Magli, Giulio; Piccione, Paolo
2003-01-01
A theorem, giving necessary and sufficient condition for naked singularity formation in spherically symmetric non static spacetimes under hypotheses of physical acceptability, is formulated and proved. The theorem relates existence of singular null geodesics to existence of regular curves which are super-solutions of the radial null geodesic equation, and allows us to treat all the known examples of naked singularities from a unified viewpoint. New examples are also found using this approach, and perspectives are discussed.
New mathematical framework for spherical gravitational collapse
Energy Technology Data Exchange (ETDEWEB)
Giambo, Roberto [Dipartimento di Matematica e Informatica, Universita di Camerino (Italy); Giannoni, Fabio [Dipartimento di Matematica e Informatica, Universita di Camerino (Italy); Magli, Giulio [Dipartimento di Matematica, Politecnico di Milano (Italy); Piccione, Paolo [Dipartimento di Matematica e Informatica, Universita di Camerino (Italy)
2003-03-21
A theorem, giving necessary and sufficient condition for naked singularity formation in spherically symmetric non-static spacetimes under hypotheses of physical acceptability, is formulated and proved. The theorem relates the existence of singular null geodesics to the existence of regular curves which are supersolutions of the radial null geodesic equation, and allows us to treat all the known examples of naked singularities from a unified viewpoint. New examples are also found using this approach, and perspectives are discussed. (letter to the editor)
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.
Inverse Symmetric Inflationary Attractors
Odintsov, S D
2016-01-01
We present a class of inflationary potentials which are invariant under a special symmetry, which depends on the parameters of the models. As we show, in certain limiting cases, the inverse symmetric potentials are qualitatively similar to the $\\alpha$-attractors models, since the resulting observational indices are identical. However, there are some quantitative differences which we discuss in some detail. As we show, some inverse symmetric models always yield results compatible with observations, but this strongly depends on the asymptotic form of the potential at large $e$-folding numbers. In fact when the limiting functional form is identical to the one corresponding to the $\\alpha$-attractors models, the compatibility with the observations is guaranteed. Also we find the relation of the inverse symmetric models with the Starobinsky model and we highlight the differences. In addition, an alternative inverse symmetric model is studied and as we show, not all the inverse symmetric models are viable. Moreove...
Symmetric cryptographic protocols
Ramkumar, Mahalingam
2014-01-01
This book focuses on protocols and constructions that make good use of symmetric pseudo random functions (PRF) like block ciphers and hash functions - the building blocks for symmetric cryptography. Readers will benefit from detailed discussion of several strategies for utilizing symmetric PRFs. Coverage includes various key distribution strategies for unicast, broadcast and multicast security, and strategies for constructing efficient digests of dynamic databases using binary hash trees. • Provides detailed coverage of symmetric key protocols • Describes various applications of symmetric building blocks • Includes strategies for constructing compact and efficient digests of dynamic databases
Spherical cows in dark matter indirect detection
Bernal, Nicolás; Necib, Lina; Slatyer, Tracy R.
2016-12-01
Dark matter (DM) halos have long been known to be triaxial, but in studies of possible annihilation and decay signals they are often treated as approximately spherical. In this work, we examine the asymmetry of potential indirect detection signals of DM annihilation and decay, exploiting the large statistics of the hydrodynamic simulation Illustris. We carefully investigate the effects of the baryons on the sphericity of annihilation and decay signals for both the case where the observer is at 8.5 kpc from the center of the halo (exemplified in the case of Milky Way-like halos), and for an observer situated well outside the halo. In the case of Galactic signals, we find that both annihilation and decay signals are expected to be quite symmetric, with axis ratios very different from 1 occurring rarely. In the case of extragalactic signals, while decay signals are still preferentially spherical, the axis ratio for annihilation signals has a much flatter distribution, with elongated profiles appearing frequently. Many of these elongated profiles are due to large subhalos and/or recent mergers. Comparing to gamma-ray emission from the Milky Way and X-ray maps of clusters, we find that the gamma-ray background appears less spherical/more elongated than the expected DM signal from the large majority of halos, and the Galactic gamma ray excess appears very spherical, while the X-ray data would be difficult to distinguish from a DM signal by elongation/sphericity measurements alone.
Random matrix theory and symmetric spaces
Energy Technology Data Exchange (ETDEWEB)
Caselle, M.; Magnea, U
2004-05-01
In this review we discuss the relationship between random matrix theories and symmetric spaces. We show that the integration manifolds of random matrix theories, the eigenvalue distribution, and the Dyson and boundary indices characterizing the ensembles are in strict correspondence with symmetric spaces and the intrinsic characteristics of their restricted root lattices. Several important results can be obtained from this identification. In particular the Cartan classification of triplets of symmetric spaces with positive, zero and negative curvature gives rise to a new classification of random matrix ensembles. The review is organized into two main parts. In Part I the theory of symmetric spaces is reviewed with particular emphasis on the ideas relevant for appreciating the correspondence with random matrix theories. In Part II we discuss various applications of symmetric spaces to random matrix theories and in particular the new classification of disordered systems derived from the classification of symmetric spaces. We also review how the mapping from integrable Calogero-Sutherland models to symmetric spaces can be used in the theory of random matrices, with particular consequences for quantum transport problems. We conclude indicating some interesting new directions of research based on these identifications.
Sphaleron glueballs in NBI theory with symmetrized trace
Dyadichev, V V
2000-01-01
We derive a closed expression for the SU(2) Born-Infeld action with the symmetrized trace for static spherically symmetric purely magnetic configurations. The lagrangian is obtained in terms of elementary functions. Using it, we investigate glueball solutions to the flat space NBI theory and their self-gravitating counterparts. Such solutions, found previously in the NBI model with the 'square root - ordinary trace' lagrangian, are shown to persist in the theory with the symmetrized trace lagrangian as well. Although the symmetrized trace NBI equations differ substantially from those of the theory with the ordinary trace, a qualitative picture of glueballs remains essentially the same. Gravity further reduces the difference between solutions in these two models, and, for sufficiently large values of the effective gravitational coupling, solutions tends to the same limiting form. The black holes in the NBI theory with the symmetrized trace are also discussed.
Geometric Entanglement of Symmetric States and the Majorana Representation
Aulbach, Martin; Murao, Mio
2010-01-01
Permutation-symmetric quantum states appear in a variety of physical situations, and they have been proposed for quantum information tasks. This article builds upon the results of [New J. Phys. 12, 073025 (2010)], where the maximally entangled symmetric states of up to twelve qubits were explored, and their amount of geometric entanglement determined by numeric and analytic means. For this the Majorana representation, a generalization of the Bloch sphere representation, can be employed to represent symmetric n qubit states by n points on the surface of a unit sphere. Symmetries of this point distribution simplify the determination of the entanglement, and enable the study of quantum states in novel ways. Here it is shown that the duality relationship of Platonic solids has a counterpart in the Majorana representation, and that in general maximally entangled symmetric states neither correspond to anticoherent spin states nor to spherical designs. The usability of symmetric states as resources for measurement-b...
Transitions in a magnetized quasi-laminar spherical Couette Flow
Kaprzyk, C; Seilmayer, M; Stefani, F
2016-01-01
First results of a new spherical Couette experiment are presented. The liquid metal flow in a spherical shell is exposed to a homogeneous axial magnetic field. For a Reynolds number Re=1000, we study the effect of increasing Hartmann number Ha. The resulting flow structures are inspected by ultrasound Doppler velocimetry. With a weak applied magnetic field, we observe an equatorially anti-symmetric jet instability with azimuthal wave number m=3. As the magnetic field strength increases, this instability vanishes. When the field is increased further, an equatorially symmetric return flow instability arises. Our observations are shown to be in good agreement with linear stability analysis and non-linear flow simulations.
Energy Technology Data Exchange (ETDEWEB)
Tipler, F.J.
1977-08-01
Causally symmetric spacetimes are spacetimes with J/sup +/(S) isometric to J/sup -/(S) for some set S. We discuss certain properties of these spacetimes, showing for example that, if S is a maximal Cauchy surface with matter everywhere on S, then the spacetime has singularities in both J/sup +/(S) and J/sup -/(S). We also consider totally vicious spacetimes, a class of causally symmetric spacetimes for which I/sup +/(p) =I/sup -/(p) = M for any point p in M. Two different notions of stability in general relativity are discussed, using various types of causally symmetric spacetimes as starting points for perturbations.
Rotationally symmetric numerical solutions to the sine-Gordon equation
DEFF Research Database (Denmark)
Olsen, O. H.; Samuelsen, Mogens Rugholm
1981-01-01
We examine numerically the properties of solutions to the spherically symmetric sine-Gordon equation given an initial profile which coincides with the one-dimensional breather solution and refer to such solutions as ring waves. Expanding ring waves either exhibit a return effect or expand towards...
Knapp-Stein type intertwining operators for symmetric pairs
DEFF Research Database (Denmark)
Möllers, Jan; Ørsted, Bent; Oshima, Yoshiki
2015-01-01
For a symmetric pair $(G,H)$ we construct a family of intertwining operators between spherical principal series representations of $G$ and $H$ that are induced from parabolic subgroups satisfying certain compatibility conditions. The operators are given explicitly in terms of their integral kernels...
Discrete Self-Similarity in Type-II Strong Explosions
Oren, Yonatan; 10.1063/1.3139307
2009-01-01
We present new solutions to the strong explosion problem in a non-power law density profile. The unperturbed self-similar solutions discovered by Waxman & Shvarts describe strong Newtonian shocks propagating into a cold gas with a density profile falling off as $r^{-\\omega}$, where $\\omega>3$ (Type-II solutions). The perturbations we consider are spherically symmetric and log-periodic with respect to the radius. While the unperturbed solutions are continuously self-similar, the log-periodicity of the density perturbations leads to a discrete self-similarity of the perturbations, i.e. the solution repeats itself up to a scaling at discrete time intervals. We discuss these solutions and verify them against numerical integrations of the time dependent hydrodynamic equations. Finally we show that this method can be generalized to treat any small, spherically symmetric density perturbation by employing Fourier decomposition.
Dunajewski, Adam; Dusza, Jacek J.; Rosado Muñoz, Alfredo
2014-11-01
The article presents a proposal for the description of human gait as a periodic and symmetric process. Firstly, the data for researches was obtained in the Laboratory of Group SATI in the School of Engineering of University of Valencia. Then, the periodical model - Mean Double Step (MDS) was made. Finally, on the basis of MDS, the symmetrical models - Left Mean Double Step and Right Mean Double Step (LMDS and RMDS) could be created. The method of various functional extensions was used. Symmetrical gait models can be used to calculate the coefficients of asymmetry at any time or phase of the gait. In this way it is possible to create asymmetry, function which better describes human gait dysfunction. The paper also describes an algorithm for calculating symmetric models, and shows exemplary results based on the experimental data.
Newtonian wormholes with spherical symmetry and tidal forces on test particles
Luz, Paulo
2015-01-01
A spherically symmetric wormhole in Newtonian gravitation in curved space, enhanced with a connection between the mass density and the Ricci scalar, is presented. The wormhole, consisting of two connected asymptotically flat regions, inhabits a spherically symmetric curved space. The gravitational potential, gravitational field and the pressure that supports the fluid that permeates the Newtonian wormhole are computed. Particle dynamics and tidal effects in this geometry are studied. The possibility of having Newtonian black holes in this theory is sketched.
Fukushima, Toshio
2012-11-01
We confirm that the first-, second-, and third-order derivatives of fully-normalized Legendre polynomial (LP) and associated Legendre function (ALF) of arbitrary degree and order can be correctly evaluated by means of non-singular fixed-degree formulas (Bosch in Phys Chem Earth 25:655-659, 2000) in the ordinary IEEE754 arithmetic when the values of fully-normalized LP and ALF are obtained without underflow problems, for e.g., using the extended range arithmetic we recently developed (Fukushima in J Geod 86:271-285, 2012). Also, we notice the same correctness for the popular but singular fixed-order formulas unless (1) the order of differentiation is greater than the order of harmonics and (2) the point of evaluation is close to the poles. The new formulation using the fixed-order formulas runs at a negligible extra computational time, i.e., 3-5 % increase in computational time per single ALF when compared with the standard algorithm without the exponent extension. This enables a practical computation of low-order derivatives of spherical harmonics of arbitrary degree and order.
Analytical calculation of the wake potential of a spherical resonator
Directory of Open Access Journals (Sweden)
Sebastian Ratschow
2002-05-01
Full Text Available An analytical formula for the wake potential of a closed spherical resonator with perfectly conducting walls is presented. Mode analysis is used for the calculation. For every rotationally symmetric TM mode the loss parameter is calculated and the formula for the determination of the corresponding frequency is given. The final wake potential is an infinite sum over all modes mentioned above.
N>=2 symmetric superpolynomials
Alarie-Vézina, L; Mathieu, P
2015-01-01
The theory of symmetric functions has been extended to the case where each variable is paired with an anticommuting one. The resulting expressions, dubbed superpolynomials, provide the natural N=1 supersymmetric version of the classical bases of symmetric functions. Here we consider the case where two independent anticommuting variables are attached to each ordinary variable. The N=2 super-version of the monomial, elementary, homogeneous symmetric functions, as well as the power sums, are then constructed systematically (using an exterior-differential formalism for the multiplicative bases), these functions being now indexed by a novel type of superpartitions. Moreover, the scalar product of power sums turns out to have a natural N=2 generalization which preserves the duality between the monomial and homogeneous bases. All these results are then generalized to an arbitrary value of N. Finally, for N=2, the scalar product and the homogenous functions are shown to have a one-parameter deformation, a result that...
Counting with symmetric functions
Mendes, Anthony
2015-01-01
This monograph provides a self-contained introduction to symmetric functions and their use in enumerative combinatorics. It is the first book to explore many of the methods and results that the authors present. Numerous exercises are included throughout, along with full solutions, to illustrate concepts and also highlight many interesting mathematical ideas. The text begins by introducing fundamental combinatorial objects such as permutations and integer partitions, as well as generating functions. Symmetric functions are considered in the next chapter, with a unique emphasis on the combinatorics of the transition matrices between bases of symmetric functions. Chapter 3 uses this introductory material to describe how to find an assortment of generating functions for permutation statistics, and then these techniques are extended to find generating functions for a variety of objects in Chapter 4. The next two chapters present the Robinson-Schensted-Knuth algorithm and a method for proving Pólya’s enu...
Symmetric tensor decomposition
Brachat, Jerome; Mourrain, Bernard; Tsigaridas, Elias
2009-01-01
We present an algorithm for decomposing a symmetric tensor, of dimension n and order d as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We recall the correspondence between the decomposition of a homogeneous polynomial in n variables of total degree d as a sum of powers of linear forms (Waring's problem), incidence properties on secant varieties of the Veronese Variety and the representation of linear forms as a linear combination of evaluations at distinct points. Then we reformulate Sylvester's approach from the dual point of view. Exploiting this duality, we propose necessary and sufficient conditions for the existence of such a decomposition of a given rank, using the properties of Hankel (and quasi-Hankel) matrices, derived from multivariate polynomials and normal form computations. This leads to the resolution of polynomial equations of small degree in non-generic cases. We propose a new algorithm for symmetric tensor decomposition, based on th...
Multiparty Symmetric Sum Types
DEFF Research Database (Denmark)
Nielsen, Lasse; Yoshida, Nobuko; Honda, Kohei
2010-01-01
This paper introduces a new theory of multiparty session types based on symmetric sum types, by which we can type non-deterministic orchestration choice behaviours. While the original branching type in session types can represent a choice made by a single participant and accepted by others...... determining how the session proceeds, the symmetric sum type represents a choice made by agreement among all the participants of a session. Such behaviour can be found in many practical systems, including collaborative workflow in healthcare systems for clinical practice guidelines (CPGs). Processes...... with the symmetric sums can be embedded into the original branching types using conductor processes. We show that this type-driven embedding preserves typability, satisfies semantic soundness and completeness, and meets the encodability criteria adapted to the typed setting. The theory leads to an efficient...
Progressive symmetric erythrokeratoderma
Directory of Open Access Journals (Sweden)
Gharpuray Mohan
1990-01-01
Full Text Available Four patients had symmetrically distributed hyperkeratotic plaques on the trunk and extremities; The lesions in all of them had appeared during infancy, and after a brief period of progression, had remained static, All of them had no family history of similar skin lesions. They responded well to topical applications of 6% salicylic acid in 50% propylene glycol. Unusual features in these cases of progressive symmetric erythrokeratoderma were the sparing of palms and soles, involvement of the trunk and absence of erythema.
Symmetric Spaces in Supergravity
Ferrara, Sergio
2008-01-01
We exploit the relation among irreducible Riemannian globally symmetric spaces (IRGS) and supergravity theories in 3, 4 and 5 space-time dimensions. IRGS appear as scalar manifolds of the theories, as well as moduli spaces of the various classes of solutions to the classical extremal black hole Attractor Equations. Relations with Jordan algebras of degree three and four are also outlined.
Distributed Searchable Symmetric Encryption
Bösch, Christoph; Peter, Andreas; Leenders, Bram; Lim, Hoon Wei; Tang, Qiang; Wang, Huaxiong; Hartel, Pieter; Jonker, Willem
2014-01-01
Searchable Symmetric Encryption (SSE) allows a client to store encrypted data on a storage provider in such a way, that the client is able to search and retrieve the data selectively without the storage provider learning the contents of the data or the words being searched for. Practical SSE schemes
Energy Technology Data Exchange (ETDEWEB)
Amore, Paolo, E-mail: paolo.amore@gmail.com [Facultad de Ciencias, CUICBAS, Universidad de Colima, Bernal Díaz del Castillo 340, Colima, Colima (Mexico); Fernández, Francisco M., E-mail: fernande@quimica.unlp.edu.ar [INIFTA (UNLP, CCT La Plata-CONICET), División Química Teórica, Diag. 113 y 64 (S/N), Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina); Garcia, Javier [INIFTA (UNLP, CCT La Plata-CONICET), División Química Teórica, Diag. 113 y 64 (S/N), Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina); Gutierrez, German [Facultad de Ciencias, CUICBAS, Universidad de Colima, Bernal Díaz del Castillo 340, Colima, Colima (Mexico)
2014-04-15
We study both analytically and numerically the spectrum of inhomogeneous strings with PT-symmetric density. We discuss an exactly solvable model of PT-symmetric string which is isospectral to the uniform string; for more general strings, we calculate exactly the sum rules Z(p)≡∑{sub n=1}{sup ∞}1/E{sub n}{sup p}, with p=1,2,… and find explicit expressions which can be used to obtain bounds on the lowest eigenvalue. A detailed numerical calculation is carried out for two non-solvable models depending on a parameter, obtaining precise estimates of the critical values where pair of real eigenvalues become complex. -- Highlights: •PT-symmetric Hamiltonians exhibit real eigenvalues when PT symmetry is unbroken. •We study PT-symmetric strings with complex density. •They exhibit regions of unbroken PT symmetry. •We calculate the critical parameters at the boundaries of those regions. •There are exact real sum rules for some particular complex densities.
Spontaneous spherical symmetry breaking in atomic confinement
Sveshnikov, Konstantin; Tolokonnikov, Andrey
2017-07-01
The effect of spontaneous breaking of initial SO(3) symmetry is shown to be possible for an H-like atom in the ground state, when it is confined in a spherical box under general boundary conditions of "not going out" through the box surface (i.e. third kind or Robin's ones), for a wide range of physically reasonable values of system parameters. The most novel and nontrivial result, which has not been reported previously, is that such an effect takes place not only for attractive, but also for repulsive interactions of atomic electrons with the cavity environment. Moreover, in the limit of a large box size R ≫ aB the regime of an atom, soaring over a plane with boundary condition of "not going out", is reproduced, rather than a spherically symmetric configuration, which would be expected on the basis of the initial SO(3) symmetry of the problem.
Spherical Gravitating Systems of Arbitrary Dimension
Das, A
2001-01-01
We study spherically symmetric solutions to the Einstein field equations under the assumption that the space-time may possess an arbitrary number of spatial dimensions. The general solution of Synge is extended to describe systems of any dimension. Arbitrary dimension analogues of known four dimensional solutions are also presented, derived using the above scheme. Finally, we discuss the requirements for the existence of Birkhoff's theorems in space-times of arbitrary dimension with or without matter fields present. Cases are discussed where the assumptions of the theorem are considerably weakened yet the theorem still holds. We also discuss where the weakening of certain conditions may cause the theorem to fail.
Directory of Open Access Journals (Sweden)
Muhammad Jamil
2013-01-01
Full Text Available A series of some novel N3,N3′-bis(disubstitutedisophthalyl-bis(thioureas compounds with general formula [C6H4· {CONHCSNHR}2], where R = 2-ClC6H4S (L1, 3,5-(Cl2C6H3 (L2, 2,4-(Cl2C6H3 (L3, 2,5-(Cl2C6H3 (L4, and 2-NH2C6H4 (L5, and their Cu(II and Ni(II complexes (C1–C10 have been synthesized. These compounds (L1–L5 and their metal(II complexes (C1–C10 have been characterized by elemental analysis, infrared spectroscopy, 1H NMR and 13C NMR spectroscopy, magnetic moments, and electronic spectral measurements. The ligands are coordinated to metal atom in a bidentate pattern producing a neutral complex of the type [ML]2. These compounds (L1–L5 and their metal(II complexes (C1–C10 were also screened for their antibacterial and cytotoxic activities.
Serial Symmetrical Relocation Algorithm for the Equal Sphere Packing Problem
Huang, WenQi
2012-01-01
For dealing with the equal sphere packing problem, we propose a serial symmetrical relocation algorithm, which is effective in terms of the quality of the numerical results. We have densely packed up to 200 equal spheres in spherical container and up to 150 equal spheres in cube container. All results are rigorous because of a fake sphere trick. It was conjectured impossible to pack 68 equal spheres of radius 1 into a sphere of radius 5. The serial symmetrical relocation algorithm has proven wrong this conjecture by finding one such packing.
Stable black holes in shift-symmetric Horndeski theories
Tretyakova, Daria A.; Takahashi, Kazufumi
2017-09-01
In shift-symmetric Horndeski theories, a static and spherically symmetric black hole can support linearly time-dependent scalar hair. However, it was shown that such a solution generically suffers from ghost or gradient instability in the vicinity of the horizon. In the present paper, we explore the possibility to avoid the instability, and present a new example of theory and its black hole solution with a linearly time-dependent scalar configuration. We also discuss the stability of solutions with static scalar hair for a special case where nonminimal derivative coupling to the Einstein tensor appears.
Conformally symmetric traversable wormholes in f( G) gravity
Sharif, M.; Fatima, H. Ismat
2016-11-01
We discuss non-static conformally symmetric traversable wormholes for spherically symmetric spacetime using the model f(G)=α Gn, where n>0 and α is an arbitrary constant. We investigate wormhole solutions by taking two types of shape function and found that physically realistic wormholes exist only for even values of n. We also check the validity of flare-out condition, required for wormhole construction, for the shape functions deduced from two types of equation of state. It is found that this condition is satisfied by these functions in all cases except phantom case with non-static conformal symmetry.
Generating functions for symmetric and shifted symmetric functions
Jing, Naihuan; Rozhkovskaya, Natasha
2016-01-01
We describe generating functions for several important families of classical symmetric functions and shifted Schur functions. The approach is originated from vertex operator realization of symmetric functions and offers a unified method to treat various families of symmetric functions and their shifted analogues.
Generating functions for symmetric and shifted symmetric functions
Jing, Naihuan; Rozhkovskaya, Natasha
2016-01-01
We describe generating functions for several important families of classical symmetric functions and shifted Schur functions. The approach is originated from vertex operator realization of symmetric functions and offers a unified method to treat various families of symmetric functions and their shifted analogues.
Relativistic spherical plasma waves
Bulanov, S S; Schroeder, C B; Zhidkov, A G; Esarey, E; Leemans, W P
2011-01-01
Tightly focused laser pulses as they diverge or converge in underdense plasma can generate wake waves, having local structures that are spherical waves. Here we report on theoretical study of relativistic spherical wake waves and their properties, including wave breaking. These waves may be suitable as particle injectors or as flying mirrors that both reflect and focus radiation, enabling unique X-ray sources and nonlinear QED phenomena.
EQUIFOCAL HYPERSURFACES IN SYMMETRIC SPACES
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
This note investigates the multiplicity problem of principal curvatures of equifocal hyper surfaces in simply connected rank 1 symmetric spaces. Using Clifford representation theory, and the author also constructs infinitely many equifocal hypersurfaces in the symmetric spaces.
Homogenous finitary symmetric groups
Directory of Open Access Journals (Sweden)
Otto. H. Kegel
2015-03-01
Full Text Available We characterize strictly diagonal type of embeddings of finitary symmetric groups in terms of cardinality and the characteristic. Namely, we prove the following. Let kappa be an infinite cardinal. If G=underseti=1stackrelinftybigcupG i , where G i =FSym(kappan i , (H=underseti=1stackrelinftybigcupH i , where H i =Alt(kappan i , is a group of strictly diagonal type and xi=(p 1 ,p 2 ,ldots is an infinite sequence of primes, then G is isomorphic to the homogenous finitary symmetric group FSym(kappa(xi (H is isomorphic to the homogenous alternating group Alt(kappa(xi , where n 0 =1,n i =p 1 p 2 ldotsp i .
Chen, Yan; Feng, Huijuan; Ma, Jiayao; Peng, Rui; You, Zhong
2016-06-01
The traditional waterbomb origami, produced from a pattern consisting of a series of vertices where six creases meet, is one of the most widely used origami patterns. From a rigid origami viewpoint, it generally has multiple degrees of freedom, but when the pattern is folded symmetrically, the mobility reduces to one. This paper presents a thorough kinematic investigation on symmetric folding of the waterbomb pattern. It has been found that the pattern can have two folding paths under certain circumstance. Moreover, the pattern can be used to fold thick panels. Not only do the additional constraints imposed to fold the thick panels lead to single degree of freedom folding, but the folding process is also kinematically equivalent to the origami of zero-thickness sheets. The findings pave the way for the pattern being readily used to fold deployable structures ranging from flat roofs to large solar panels.
Symmetric Extended Ockham Algebras
Institute of Scientific and Technical Information of China (English)
T.S. Blyth; Jie Fang
2003-01-01
The variety eO of extended Ockham algebras consists of those algealgebra with an additional endomorphism k such that the unary operations f and k commute. Here, we consider the cO-algebras which have a property of symmetry. We show that there are thirty two non-isomorphic subdirectly irreducible symmetric extended MS-algebras and give a complete description of them.2000 Mathematics Subject Classification: 06D15, 06D30
Symmetrization Selection Rules, 1
Page, P R
1996-01-01
We introduce a category of strong and electromagnetic interaction selection rules for the two-body connected decay and production of exotic J^{PC} = 0^{+-}, 1^{-+}, 2^{+-}, 3^{-+}, ... hybrid and four-quark mesons. The rules arise from symmetrization in states in addition to Bose symmetry and CP invariance. Examples include various decays to \\eta'\\eta, \\eta\\pi, \\eta'\\pi and four-quark interpretations of a 1^{-+} signal.
Symmetrization Selection Rules, 2
Page, P R
1996-01-01
We introduce strong interaction selection rules for the two-body decay and production of hybrid and conventional mesons coupling to two S-wave hybrid or conventional mesons. The rules arise from symmetrization in states in the limit of non-relativistically moving quarks. The conditions under which hybrid coupling to S-wave states is suppressed are determined by the rules, and the nature of their breaking is indicated.
Overview of spherical tokamak research in Japan
Takase, Y.; Ejiri, A.; Fujita, T.; Fukumoto, N.; Fukuyama, A.; Hanada, K.; Idei, H.; Nagata, M.; Ono, Y.; Tanaka, H.; Uchida, M.; Horiuchi, R.; Kamada, Y.; Kasahara, H.; Masuzaki, S.; Nagayama, Y.; Oishi, T.; Saito, K.; Takeiri, Y.; Tsuji-Iio, S.
2017-10-01
Nationally coordinated research on spherical tokamak is being conducted in Japan. Recent achievements include: (i) plasma current start-up and ramp-up without the use of the central solenoid by RF waves (in electron cyclotron and lower hybrid frequency ranges), (ii) plasma current start-up by AC Ohmic operation and by coaxial helicity injection, (iii) development of an advanced fuelling technique by compact toroid injection, (iv) ultra-long-pulse operation and particle control using a high temperature metal wall, (v) access to the ultra-high-β regime by high-power reconnection heating, and (vi) improvement of spherical tokamak plasma stability by externally applied helical field.
Spherical coverage verification
Petkovic, Marko D; Latecki, Longin Jan
2011-01-01
We consider the problem of covering hypersphere by a set of spherical hypercaps. This sort of problem has numerous practical applications such as error correcting codes and reverse k-nearest neighbor problem. Using the reduction of non degenerated concave quadratic programming (QP) problem, we demonstrate that spherical coverage verification is NP hard. We propose a recursive algorithm based on reducing the problem to several lower dimension subproblems. We test the performance of the proposed algorithm on a number of generated constellations. We demonstrate that the proposed algorithm, in spite of its exponential worst-case complexity, is applicable in practice. In contrast, our results indicate that spherical coverage verification using QP solvers that utilize heuristics, due to numerical instability, may produce false positives.
Spherical geodesic mesh generation
Energy Technology Data Exchange (ETDEWEB)
Fung, Jimmy [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Kenamond, Mark Andrew [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Burton, Donald E. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Shashkov, Mikhail Jurievich [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-02-27
In ALE simulations with moving meshes, mesh topology has a direct influence on feature representation and code robustness. In three-dimensional simulations, modeling spherical volumes and features is particularly challenging for a hydrodynamics code. Calculations on traditional spherical meshes (such as spin meshes) often lead to errors and symmetry breaking. Although the underlying differencing scheme may be modified to rectify this, the differencing scheme may not be accessible. This work documents the use of spherical geodesic meshes to mitigate solution-mesh coupling. These meshes are generated notionally by connecting geodesic surface meshes to produce triangular-prismatic volume meshes. This mesh topology is fundamentally different from traditional mesh topologies and displays superior qualities such as topological symmetry. This work describes the geodesic mesh topology as well as motivating demonstrations with the FLAG hydrocode.
Symmetric Tensor Decomposition
DEFF Research Database (Denmark)
Brachat, Jerome; Comon, Pierre; Mourrain, Bernard
2010-01-01
of polynomial equations of small degree in non-generic cases. We propose a new algorithm for symmetric tensor decomposition, based on this characterization and on linear algebra computations with Hankel matrices. The impact of this contribution is two-fold. First it permits an efficient computation...... of total degree d as a sum of powers of linear forms (Waring’s problem), incidence properties on secant varieties of the Veronese variety and the representation of linear forms as a linear combination of evaluations at distinct points. Then we reformulate Sylvester’s approach from the dual point of view...
Symmetrically Constrained Compositions
Beck, Matthias; Lee, Sunyoung; Savage, Carla D
2009-01-01
Given integers $a_1, a_2, ..., a_n$, with $a_1 + a_2 + ... + a_n \\geq 1$, a symmetrically constrained composition $\\lambda_1 + lambda_2 + ... + lambda_n = M$ of $M$ into $n$ nonnegative parts is one that satisfies each of the the $n!$ constraints ${\\sum_{i=1}^n a_i \\lambda_{\\pi(i)} \\geq 0 : \\pi \\in S_n}$. We show how to compute the generating function of these compositions, combining methods from partition theory, permutation statistics, and lattice-point enumeration.
The Spherical Deformation Model
DEFF Research Database (Denmark)
Hobolth, Asgar
2003-01-01
Miller et al. (1994) describe a model for representing spatial objects with no obvious landmarks. Each object is represented by a global translation and a normal deformation of a sphere. The normal deformation is defined via the orthonormal spherical-harmonic basis. In this paper we analyse...... the spherical deformation model in detail and describe how it may be used to summarize the shape of star-shaped three-dimensional objects with few parameters. It is of interest to make statistical inference about the three-dimensional shape parameters from continuous observations of the surface and from...
Symmetric spaces and the Kashiwara-Vergne method
Rouvière, François
2014-01-01
Gathering and updating results scattered in journal articles over thirty years, this self-contained monograph gives a comprehensive introduction to the subject. Its goal is to: - motivate and explain the method for general Lie groups, reducing the proof of deep results in invariant analysis to the verification of two formal Lie bracket identities related to the Campbell-Hausdorff formula (the "Kashiwara-Vergne conjecture"); - give a detailed proof of the conjecture for quadratic and solvable Lie algebras, which is relatively elementary; - extend the method to symmetric spaces; here an obstruction appears, embodied in a single remarkable object called an "e-function"; - explain the role of this function in invariant analysis on symmetric spaces, its relation to invariant differential operators, mean value operators and spherical functions; - give an explicit e-function for rank one spaces (the hyperbolic spaces); - construct an e-function for general symmetric spaces, in the spirit of Kashiwara and Vergne's or...
The hydrodynamics analysis for the underwater robot with a spherical hull
Lan, Xiaojuan; Sun, Hanxu; Jia, Qingxuan
2009-05-01
The underwater spherical robot has a spherical pressure hull which contains power modules, sensors, and so on. It lacks robot arms or end effectors but is highly maneuverable, for the simplest symmetrical geometry is the sphere. This paper analyzes the spherical robot's hydrodynamic model with CFD software, concludes the spherical robot's hydrodynamic characteristics, and compares these characteristics with the hydrodynamic model of another underwater robot which has a streamlined hull. The effect of sphere hydraulic resistance on the control of the robot is analyzed with some examples.
Construction of Aesthetic Spherical Patterns from Planar IFSs
Chen, Ning; Zhang, Yuting; Chung, K. W.
2016-07-01
To construct symmetrical patterns on the unit sphere from the planar iterative function systems (IFSs), we present a method of constructing IFSs with D3 symmetry which is composed of three-fold rotational symmetries together with reflections. An algorithm is developed to generate strange attractors with D3 symmetry on a triangular face and then project it onto the surface of the unit sphere to form aesthetics patterns with spherical symmetry. As an illustrative example, we consider the regular inscribed icosahedron in the unit sphere which contains 20 triangular faces. This method is valid to randomly generate aesthetic spherical patterns using planar IFSs.
Sirsi, Swarnamala; Hegde, Subramanya
2011-01-01
Quantum computation on qubits can be carried out by an operation generated by a Hamiltonian such as application of a pulse as in NMR, NQR. Quantum circuits form an integral part of quan- tum computation. We investigate the nonlocal operations generated by a given Hamiltonian. We construct and study the properties of perfect entanglers, that is, the two-qubit operations that can generate maximally entangled states from some suitably chosen initial separable states in terms of their entangling power. Our work addresses the problem of analyzing the quantum evolution in the special case of two qubit symmetric states. Such a symmetric space can be considered to be spanned by the angular momentum states {|j = 1,m>;m = +1, 0,-1}. Our technique relies on the decomposition of a Hamiltonian in terms of newly defined Hermitian operators Mk's (k= 0.....8) which are constructed out of angular momentum operators Jx, Jy, Jz. These operators constitute a linearly independent set of traceless matrices (except for M0). Further...
Directory of Open Access Journals (Sweden)
Giuseppe Di Maio
2008-04-01
Full Text Available The subject of hyperspace topologies on closed or closed and compact subsets of a topological space X began in the early part of the last century with the discoveries of Hausdorff metric and Vietoris hit-and-miss topology. In course of time, several hyperspace topologies were discovered either for solving some problems in Applied or Pure Mathematics or as natural generalizations of the existing ones. Each hyperspace topology can be split into a lower and an upper part. In the upper part the original set inclusion of Vietoris was generalized to proximal set inclusion. Then the topologization of the Wijsman topology led to the upper Bombay topology which involves two proximities. In all these developments the lower topology, involving intersection of finitely many open sets, was generalized to locally finite families but intersection was left unchanged. Recently the authors studied symmetric proximal topology in which proximity was used for the first time in the lower part replacing intersection with its generalization: nearness. In this paper we use two proximities also in the lower part and we obtain the lower Bombay hypertopology. Consequently, a new hypertopology arises in a natural way: the symmetric Bombay topology which is the join of a lower and an upper Bombay topology.
Spherical Accretion in a Uniformly Expanding Universe
Colpi, Monica; Shapiro, Stuart L.; Wasserman, Ira
1996-10-01
We consider spherically symmetric accretion of material from an initially homogeneous, uniformly expanding medium onto a Newtonian point mass M. The gas is assumed to evolve adiabatically with a constant adiabatic index F, which we vary over the range Γ ɛ [1, 5/3]. We use a one-dimensional Lagrangian code to follow the spherical infall of material as a function of time. Outflowing shells gravitationally bound to the point mass fall back, giving rise to a inflow rate that, after a rapid rise, declines as a power law in time. If there were no outflow initially, Bondi accretion would result, with a characteristic accretion time-scale ta,0. For gas initially expanding at a uniform rate, with a radial velocity U = R/t0 at radius R, the behavior of the flow at all subsequent times is determined by ta,0/t0. If ta,0/t0 ≫ 1, the gas has no time to respond to pressure forces, so the fluid motion is nearly collisionless. In this case, only loosely bound shells are influenced by pressure gradients and are pushed outward. The late-time evolution of the mass accretion rate Mdot is close to the result for pure dust, and we develop a semianalytic model that accurately accounts for the small effect of pressure gradients in this limit. In the opposite regime, ta,0/t0 ≪ 1, pressure forces significantly affect the motion of the gas. At sufficiently early times, t ≤ ttr, the flow evolved along a sequence of quasi-stationary, Bondi-like states, with a time-dependent Mdot determined by the slowly varying gas density at large distances. However, at later times, t ≥ ttr, the fluid flow enters a dustllke regime; ttr is the time when the instantaneous Bondi accretion radius reaches the marginally bound radius. The transition time ttr depends sensitively on ta,0/t0 for a given Γ and can greatly exceed t0. We show that there exists a critical value Γ = 11/9, below which the transition from fluid to ballistic motion disappears. As one application of our calculations, we consider the
The Symmetricity of Normal Modes in Symmetric Complexes
Song, Guang
2016-01-01
In this work, we look at the symmetry of normal modes in symmetric structures, particularly structures with cyclic symmetry. We show that normal modes of symmetric structures have different levels of symmetry, or symmetricity. One novel theoretical result of this work is that, for a ring structure with $m$ subunits, the symmetricity of the normal modes falls into $m$ groups of equal size, with normal modes in each group having the same symmetricity. The normal modes in each group can be computed separately, using a much smaller amount of memory and time (up to $m^3$ less), thus making it applicable to larger complexes. We show that normal modes with perfect symmetry or anti-symmetry have no degeneracy while the rest of the modes have a degeneracy of two. We show also how symmetry in normal modes correlates with symmetry in structure. While a broken symmetry in structure generally leads to a loss of symmetricity in symmetric normal modes, the symmetricity of some symmetric normal modes is preserved even when s...
Spherical distributions : Schoenberg revisited
Steerneman, AGM; van Perlo-ten Kleij, F
2005-01-01
An in-dimensional random vector X is said to have a spherical distribution if and only if its characteristic function is of the form phi(parallel to t parallel to), where t is an element of R-m, parallel to.parallel to denotes the usual Euclidean norm, and phi is a characteristic function on R. A mo
Spherical colloidal photonic crystals.
Zhao, Yuanjin; Shang, Luoran; Cheng, Yao; Gu, Zhongze
2014-12-16
CONSPECTUS: Colloidal photonic crystals (PhCs), periodically arranged monodisperse nanoparticles, have emerged as one of the most promising materials for light manipulation because of their photonic band gaps (PBGs), which affect photons in a manner similar to the effect of semiconductor energy band gaps on electrons. The PBGs arise due to the periodic modulation of the refractive index between the building nanoparticles and the surrounding medium in space with subwavelength period. This leads to light with certain wavelengths or frequencies located in the PBG being prohibited from propagating. Because of this special property, the fabrication and application of colloidal PhCs have attracted increasing interest from researchers. The most simple and economical method for fabrication of colloidal PhCs is the bottom-up approach of nanoparticle self-assembly. Common colloidal PhCs from this approach in nature are gem opals, which are made from the ordered assembly and deposition of spherical silica nanoparticles after years of siliceous sedimentation and compression. Besides naturally occurring opals, a variety of manmade colloidal PhCs with thin film or bulk morphology have also been developed. In principle, because of the effect of Bragg diffraction, these PhC materials show different structural colors when observed from different angles, resulting in brilliant colors and important applications. However, this angle dependence is disadvantageous for the construction of some optical materials and devices in which wide viewing angles are desired. Recently, a series of colloidal PhC materials with spherical macroscopic morphology have been created. Because of their spherical symmetry, the PBGs of spherical colloidal PhCs are independent of rotation under illumination of the surface at a fixed incident angle of the light, broadening the perspective of their applications. Based on droplet templates containing colloidal nanoparticles, these spherical colloidal PhCs can be
Perturbations on steady spherical accretion in Schwarzschild geometry
Naskar, Tapan; Bhattacharjee, Jayanta K; Ray, Arnab K
2007-01-01
The stationary background flow in the spherically symmetric infall of a compressible fluid, coupled to the space-time defined by the static Schwarzschild metric, has been subjected to linearized perturbations. The perturbative procedure is based on the continuity condition and it shows that the coupling of the flow with the geometry of space-time brings about greater stability for the flow, to the extent that the amplitude of the perturbation, treated as a standing wave, decays in time, as opposed to the amplitude remaining constant in the Newtonian limit. In qualitative terms this situation simulates the effect of a dissipative mechanism in the classical Bondi accretion flow, defined in the Newtonian construct of space and time. As a result of this approach it becomes impossible to define an acoustic metric for a conserved spherically symmetric flow, described within the framework of Schwarzschild geometry. In keeping with this view, the perturbation, considered separately as a high-frequency travelling wave...
Institute of Scientific and Technical Information of China (English)
傅育熙
1998-01-01
An alternative presentation of the π－calculus is given.This version of the π-calculus is symmetric in the sense that communications are symmetric and there is no difference between input and output prefixes.The point of the symmetric π-calculus is that it has no abstract names.The set of closed names is therefore homogeneous.The π－calculus can be fully embedded into the symmetric π-calculus.The symmetry changes the emphasis of the communication mechanism of the π-calculus and opens up possibility for further variations.
Spherical Gravitational Collapse with Heat Flux and Cosmic Censorship
Wagh, S M; Muktibodh, P S; Govinder, K S
2001-01-01
In this paper, we investigate the nature of the singularity in the spherically symmetrical, shear-free, gravitational collapse of a star with heat flux using a separable metric [cqg1]. For any non-singular, regular, radial density profile for a star described by this metric, eq. (2.1), the singularity of the gravitational collapse is not naked locally. Our results here unequivocally support the Strong Cosmic Censorship Hypothesis.
Spherical coordinate descriptions of cylindrical and spherical Bessel beams.
Poletti, M A
2017-03-01
This paper derives a generalized spherical harmonic description of Bessel beams. The spherical harmonic description of the well-known cylindrical Bessel beams is reviewed and a family of spherical Bessel beams are introduced which can provide a number of azimuthal phase variations for a single beam radial amplitude. The results are verified by numerical simulations.
de Rham, Claudia
2016-01-01
We study the development of caustics in shift-symmetric scalar field theories by focusing on simple waves with an $SO(p)$-symmetry in an arbitrary number of space dimensions. We show that the Galileon and the DBI-Galileon naturally emerge as the unique set of caustic-free theories, highlighting a link between the caustic-free condition for simple $SO(p)$-waves and the existence of either a global galilean symmetry or a global relativistic galilean symmetry.
Lee, M. C.; Kendall, J. M., Jr.; Bahrami, P. A.; Wang, T. G.
1986-01-01
Fluid-dynamic and capillary forces can be used to form nearly perfect, very small spherical shells when a liquid that can solidify is passed through an annular die to form an annular jet. Gravity and certain properties of even the most ideal materials, however, can cause slight asymmetries. The primary objective of the present work is the control of this shell formation process in earth laboratories rather than space microgravity, through the development of facilities and methods that minimize the deleterious effects of gravity, aerodynamic drag, and uncontrolled cooling. The spherical shells thus produced can be used in insulation, recyclable filter materials, fire retardants, explosives, heat transport slurries, shock-absorbing armor, and solid rocket motors.
Representation of Fuzzy Symmetric Relations
1986-03-19
Std Z39-18 REPRESENTATION OF FUZZY SYMMETRIC RELATIONS L. Valverde Dept. de Matematiques i Estadistica Universitat Politecnica de Catalunya Avda...REPRESENTATION OF FUZZY SYMMETRIC RELATIONS L. "Valverde* Dept. de Matematiques i Estadistica Universitat Politecnica de Catalunya Avda. Diagonal, 649
Parallel Symmetric Eigenvalue Problem Solvers
2015-05-01
Plemmons G. Golub and A. Sameh. High-speed computing : scientific appli- cations and algorithm design. University of Illinois Press, Champaign, Illinois , 1988...16. SECURITY CLASSIFICATION OF: Sparse symmetric eigenvalue problems arise in many computational science and engineering applications such as...Eigenvalue Problem Solvers Report Title Sparse symmetric eigenvalue problems arise in many computational science and engineering applications such as
Multiphase, non-spherical gas accretion onto a black hole
Barai, Paramita; Nagamine, Kentaro
2011-01-01
(Abridged) We investigate non-spherical behavior of gas accreting onto a central supermassive black hole performing simulations using the SPH code GADGET-3 including radiative cooling and heating by the central X-ray source. As found in earlier 1D studies, our 3D simulations show that the accretion mode depends on the X-ray luminosity (L_X) for a fixed density at infinity and accretion efficiency. In the low L_X limit, gas accretes in a stable, spherically symmetric fashion. In the high L_X limit, the inner gas is significantly heated up and expands, reducing the central mass inflow rate. The expanding gas can turn into a strong enough outflow capable of expelling most of the gas at larger radii. For some intermediate L_X, the accretion flow becomes unstable developing prominent non-spherical features, the key reason for which is thermal instability (TI) as shown by our analyses. Small perturbations of the initially spherically symmetric accretion flow that is heated by the intermediate L_X quickly grow to fo...
The space-time outside a source of gravitational radiation: the axially symmetric null fluid
Energy Technology Data Exchange (ETDEWEB)
Herrera, L. [Universidad Central de Venezuela, Escuela de Fisica, Facultad de Ciencias, Caracas (Venezuela, Bolivarian Republic of); Universidad de Salamanca, Instituto Universitario de Fisica Fundamental y Matematicas, Salamanca (Spain); Di Prisco, A. [Universidad Central de Venezuela, Escuela de Fisica, Facultad de Ciencias, Caracas (Venezuela, Bolivarian Republic of); Ospino, J. [Universidad de Salamanca, Departamento de Matematica Aplicada and Instituto Universitario de Fisica Fundamental y Matematicas, Salamanca (Spain)
2016-11-15
We carry out a study of the exterior of an axially and reflection symmetric source of gravitational radiation. The exterior of such a source is filled with a null fluid produced by the dissipative processes inherent to the emission of gravitational radiation, thereby representing a generalization of the Vaidya metric for axially and reflection symmetric space-times. The role of the vorticity, and its relationship with the presence of gravitational radiation is put in evidence. The spherically symmetric case (Vaidya) is, asymptotically, recovered within the context of the 1 + 3 formalism. (orig.)
The spacetime outside a source of gravitational radiation: The axially symmetric null fluid
Herrera, L; Ospino, J
2016-01-01
We carry out a study of the exterior of an axially and reflection symmetric source of gravitational radiation. The exterior of such a source is filled with a null fluid produced by the dissipative processes inherent to the emission of gravitational radiation, thereby representing a generalization of the Vaidya metric for axially and reflection symmetric spacetimes. The role of the vorticity, and its relationship with the presence of gravitational radiation is put in evidence. The spherically symmetric case (Vaidya) is, asymptotically, recovered within the context of the $1+3$ formalism.
CSIR Research Space (South Africa)
Khawula, TNY
2016-03-01
Full Text Available Molybdenum disulfide-modified carbon nanospheres (MoS(sub2)/CNS) with two different morphologies (spherical and flower-like) have been synthesized using hydrothermal techniques and investigated as symmetric pseudocapacitors in an aqueous electrolyte...
Degenerate Neutrinos in Left Right Symmetric Theory
Joshipura, Anjan S.
1994-01-01
Various hints on the neutrino masses namely, ({\\em i}) the solar neutrino deficit ({\\em ii}) the atmospheric neutrino deficit ({\\em iii}) the need for the dark matter and/or ({\\em iv}) the non-zero neutrinoless double beta decay collectively imply that all the three neutrinos must be nearlty degenerate. This feature can be understood in the left right symmetric theory. We present a model based on the group $SU(2)_{L}\\times SU(2)_R\\times U(1)_{B-L}\\times SU(2)_H$ which can explain the required...
Spherical Boson Stars as Black Hole mimickers
Guzman, F S; 10.1103/PhysRevD.80.084023
2010-01-01
We present spherically symmetric boson stars as black hole mimickers based on the power spectrum of a simple accretion disk model. The free parameters of the boson star are the mass of the boson and the fourth order self-interaction coefficient in the scalar field potential. We show that even if the mass of the boson is the only free parameter it is possible to find a configuration that mimics the power spectrum of the disk due to a black hole of the same mass. We also show that for each value of the self-interaction a single boson star configuration can mimic a black hole at very different astrophysical scales in terms of the mass of the object and the accretion rate. In order to show that it is possible to distinguish one of our mimickers from a black hole we also study the deflection of light.
Spherical Accretion in Nearby Weakly Active Galaxies
Moscibrodzka, M A
2005-01-01
We consider the sample of weakly active galaxies situated in 'Local Universe' collected in the paper of Pellegrini (2005) with inferred accretion efficiencies from $10^{-2}$ to $10^{-7}$. We apply a model of spherically symmetrical Bondi accretion for given parameters ($M_{BH}$,$T_{\\infty}$,$\\rho_{\\infty}$,) taken from observation. We calculate spectra emitted by the gas accreting onto its central objects using Monte Carlo method including synchrotron and bremsstrahlung photons as seed photons. We compare our results with observed nuclear X-ray luminosities $L_{X,nuc}$ (0.3-10 keV) of the sample. Model is also tested for different external medium parameters ($\\rho_{\\infty}$ and $T_{\\infty}$) and different free parameters of the model. Our model is able to explain most of the observed nuclear luminosities $L_X$ under an assumption that half of the compresion energy is transfered directly to the electrons.
Georgiev, G. H.; Dinkova, C. L.
2013-10-01
Long spirals in the Euclidean plane have been introduced by A. Kurnosenko five years ago. Using a natural map of the shape sphere into the extended Gaussian plane we study spherical curves that are pre-images of plane long spirals. Loxodromes and spherical spiral antennas are typical examples of such spherical long spirals. The set of all planar spirals leaves invariant under an arbitrary similarity transformation. This set is divided in two disjoint classes by A. Kirnosenko. The first class is consist of the so-called short spirals which are widely used in geometric modeling. The second class of planar long spirals contains well-known logarithmic spiral and Archimedean spirals which have many applications in mathematics, astrophysics and industry. The notion of simplicial shape space is due to D. Kendall. The most popular simplicial shape space of order (2,3) is the set of equivalence classes of similar triangles in the plane. The sphere of radius 1/2 centered at the origin can be considered as a model of this quotient space, so-called the shape sphere. F. Bookstein and J. Lester showed that the one-point extension of the Euclidean plane, so-called the extended Gaussian plane, is another model of the same simplicial shape space. The present paper gives a description of long spirals on the shape sphere by the use a natural conformal mapping between two models. First, we examine long spirals in the extended Gaussian plane. After that, we describe some differential geometric properties of the shape sphere. Finally, we discuss parameterizations of long spirals on the shape sphere.
Directory of Open Access Journals (Sweden)
M. A. Navascués
2013-01-01
Full Text Available This paper tackles the construction of fractal maps on the unit sphere. The functions defined are a generalization of the classical spherical harmonics. The methodology used involves an iterated function system and a linear and bounded operator of functions on the sphere. For a suitable choice of the coefficients of the system, one obtains classical maps on the sphere. The different values of the system parameters provide Bessel sequences, frames, and Riesz fractal bases for the Lebesgue space of the square integrable functions on the sphere. The Laplace series expansion is generalized to a sum in terms of the new fractal mappings.
MINIMIZATION PROBLEM FOR SYMMETRIC ORTHOGONAL ANTI-SYMMETRIC MATRICES
Institute of Scientific and Technical Information of China (English)
Yuan Lei; Anping Liao; Lei Zhang
2007-01-01
By applying the generalized singular value decomposition and the canonical correlation decomposition simultaneously, we derive an analytical expression of the optimal approximate solution (X), which is both a least-squares symmetric orthogonal anti-symmetric solution of the matrix equation ATXA ＝ B and a best approximation to a given matrix X*.Moreover, a numerical algorithm for finding this optimal approximate solution is described in detail, and a numerical example is presented to show the validity of our algorithm.
On integrability of strings on symmetric spaces
Energy Technology Data Exchange (ETDEWEB)
Wulff, Linus [Blackett Laboratory, Imperial College,London SW7 2AZ (United Kingdom)
2015-09-17
In the absence of NSNS three-form flux the bosonic string on a symmetric space is described by a symmetric space coset sigma-model. Such models are known to be classically integrable. We show that the integrability extends also to cases with non-zero NSNS flux (respecting the isometries) provided that the flux satisfies a condition of the form H{sub abc}H{sup cde}∼R{sub ab}{sup de}. We then turn our attention to the type II Green-Schwarz superstring on a symmetric space. We prove that if the space preserves some supersymmetry there exists a truncation of the full superspace to a supercoset space and derive the general form of the superisometry algebra. In the case of vanishing NSNS flux the corresponding supercoset sigma-model for the string is known to be integrable. We prove that the integrability extends to the full string by augmenting the supercoset Lax connection with terms involving the fermions which are not captured by the supercoset model. The construction is carried out to quadratic order in these fermions. This proves the integrability of strings on symmetric spaces supported by RR flux which preserve any non-zero amount of supersymmetry. Finally we also construct Lax connections for some supercoset models with non-zero NSNS flux describing strings in AdS{sub 2,3}×S{sup 2,3}×S{sup 2,3}×T{sup 2,3,4} backgrounds preserving eight supersymmetries.
Mostert, W.
2017-01-27
We present numerical simulations of ideal magnetohydrodynamics showing suppression of the Richtmyer-Meshkov instability in spherical implosions in the presence of an octahedrally symmetric magnetic field. This field configuration is of interest owing to its high degree of spherical symmetry in comparison with previously considered dihedrally symmetric fields. The simulations indicate that the octahedral field suppresses the instability comparably to the other previously considered candidate fields for light-heavy interface accelerations while retaining a highly symmetric underlying flow even at high field strengths. With this field, there is a reduction in the root-mean-square perturbation amplitude of up to approximately 50% at representative time under the strongest field tested while maintaining a homogeneous suppression pattern compared to the other candidate fields.
The Role of Orthogonal Polynomials in Tailoring Spherical Distributions to Kurtosis Requirements
Directory of Open Access Journals (Sweden)
Luca Bagnato
2016-08-01
Full Text Available This paper carries out an investigation of the orthogonal-polynomial approach to reshaping symmetric distributions to fit in with data requirements so as to cover the multivariate case. With this objective in mind, reference is made to the class of spherical distributions, given that they provide a natural multivariate generalization of univariate even densities. After showing how to tailor a spherical distribution via orthogonal polynomials to better comply with kurtosis requirements, we provide operational conditions for the positiveness of the resulting multivariate Gram–Charlier-like expansion, together with its kurtosis range. Finally, the approach proposed here is applied to some selected spherical distributions.
The ETE spherical Tokamak project
Energy Technology Data Exchange (ETDEWEB)
Ludwig, Gerson Otto; Andrade, Maria Celia Ramos de; Barbosa, Luis Filipe Wiltgen [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil). Lab. Associado de Plasma] [and others]. E-mail: ludwig@plasma.inpe.br
1999-07-01
This paper describes the general characteristics of spherical tokamaks, with a brief overview of work in the area of spherical torus already performed or in progress at several institutions. The paper presents also the historical development of the ETE (Spherical Tokamak Experiment) project, its research program, technical characteristics and status of construction in September, 1998 at the Associated plasma Laboratory (LAP) of the National Institute for Space Research (INPE) in Brazil. (author)
Spherical tokamak development in Brazil
Energy Technology Data Exchange (ETDEWEB)
Ludwig, Gerson Otto; Bosco, Edson Del; Ferreira, Julio Guimaraes [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil). Lab. Associado de Plasma] (and others)
2003-07-01
The general characteristics of spherical tokamaks, or spherical tori, with a brief view of work in this area already performed or in progress at several institutions worldwide are described. The paper presents also the steps in the development of the ETE (Experiment Tokamak spheric) project, its research program, technical characteristics and operating conditions as of December, 2002 a the Associated Plasma Laboratory (LAP) of the National Space Research Institute (INPE) in Brazil. (author)
Spherical artifacts on ferrograms
Jones, W. R., Jr.
1976-01-01
In the past, hollow spheres detected on ferrograms have been interpreted as being due to fretting, abrasion, cavitation erosion, and fatigue-related processes. Here it is reported that such spheres were found to result from the fact that a routine grinding operation on a steel plate was carried out about 20 feet away from the ferrograph. A similar grinding operation was performed on a piece of low carbon steel a few feet from the ferrograph, and after a few minutes of grinding, the resulting ferrogram contained thousands of particles of which more than 90% were spherical. Because of the widespread occurrence of ordinary grinding operations, it seems prudent that those utilizing the ferrograph be cognizant of this type of artifact.
Spherical grating spectrometers
O'Donoghue, Darragh; Clemens, J. Christopher
2014-07-01
We describe designs for spectrometers employing convex dispersers. The Offner spectrometer was the first such instrument; it has almost exclusively been employed on satellite platforms, and has had little impact on ground-based instruments. We have learned how to fabricate curved Volume Phase Holographic (VPH) gratings and, in contrast to the planar gratings of traditional spectrometers, describe how such devices can be used in optical/infrared spectrometers designed specifically for curved diffraction gratings. Volume Phase Holographic gratings are highly efficient compared to conventional surface relief gratings; they have become the disperser of choice in optical / NIR spectrometers. The advantage of spectrometers with curved VPH dispersers is the very small number of optical elements used (the simplest comprising a grating and a spherical mirror), as well as illumination of mirrors off axis, resulting in greater efficiency and reduction in size. We describe a "Half Offner" spectrometer, an even simpler version of the Offner spectrometer. We present an entirely novel design, the Spherical Transmission Grating Spectrometer (STGS), and discuss exemplary applications, including a design for a double-beam spectrometer without any requirement for a dichroic. This paradigm change in spectrometer design offers an alternative to all-refractive astronomical spectrometer designs, using expensive, fragile lens elements fabricated from CaF2 or even more exotic materials. The unobscured mirror layout avoids a major drawback of the previous generation of catadioptric spectrometer designs. We describe laboratory measurements of the efficiency and image quality of a curved VPH grating in a STGS design, demonstrating, simultaneously, efficiency comparable to planar VPH gratings along with good image quality. The stage is now set for construction of a prototype instrument with impressive performance.
Spherical wave rotation in spherical near-field antenna measurements
DEFF Research Database (Denmark)
Wu, Jian; Larsen, Flemming Holm; Lemanczyk, J.
1991-01-01
The rotation of spherical waves in spherical near-field antenna measurement is discussed. Considering the many difficult but interesting features of the rotation coefficients, an efficient rotation scheme is derived. The main feature of the proposed scheme is to ignore the calculation of the very...
Institute of Scientific and Technical Information of China (English)
ZHU Yong-an; WANG Fan; LIU Ren-huai
2008-01-01
The nonlinear thermal buckling of symmetrically laminated cylindrically orthotropic shallow spherical shell under temperature field and uniform pressure including transverse shear is studied.Also the analytic formulas for determining the critical buckling loads under different temperature fields are obtained by using the modified iteration method.The effect of transverse shear deformation and different temperature fields on critical buckling load is discussed.
Directory of Open Access Journals (Sweden)
Igor Salom
2017-07-01
Full Text Available We construct the three-body permutation symmetric hyperspherical harmonics to be used in the non-relativistic three-body Schrödinger equation in three spatial dimensions (3D. We label the state vectors according to the S3⊗SO(3rot⊂O(2⊗SO(3rot⊂U(3⋊S2⊂O(6 subgroup chain, where S3 is the three-body permutation group and S2 is its two element subgroup containing transposition of first two particles, O(2 is the “democracy transformation”, or “kinematic rotation” group for three particles; SO(3rot is the 3D rotation group, and U(3,O(6 are the usual Lie groups. We discuss the good quantum numbers implied by the above chain of algebras, as well as their relation to the S3 permutation properties of the harmonics, particularly in view of the SO(3rot⊂SU(3 degeneracy. We provide a definite, practically implementable algorithm for the calculation of harmonics with arbitrary finite integer values of the hyper angular momentum K, and show an explicit example of this construction in a specific case with degeneracy, as well as tables of K≤6 harmonics. All harmonics are expressed as homogeneous polynomials in the Jacobi vectors (λ,ρ with coefficients given as algebraic numbers unless the “operator method” is chosen for the lifting of the SO(3rot⊂SU(3 multiplicity and the dimension of the degenerate subspace is greater than four – in which case one must resort to numerical diagonalization; the latter condition is not met by any K≤15 harmonic, or by any L≤7 harmonic with arbitrary K. We also calculate a certain type of matrix elements (the Gaunt integrals of products of three harmonics in two ways: 1 by explicit evaluation of integrals and 2 by reduction to known SU(3 Clebsch–Gordan coefficients. In this way we complete the calculation of the ingredients sufficient for the solution to the quantum-mechanical three-body bound state problem.
Particle-vortex symmetric liquid
Mulligan, Michael
2016-01-01
We introduce an effective theory with manifest particle-vortex symmetry for disordered thin films undergoing a magnetic field-tuned superconductor-insulator transition. The theory may enable one to access both the critical properties of the strong-disorder limit, which has recently been confirmed [Breznay et al., PNAS 113, 280 (2016)] to exhibit particle-vortex symmetric electrical response, and the metallic phase discovered earlier [Mason and Kapitulnik, Phys. Rev. Lett. 82, 5341 (1999)] in less disordered samples. Within the effective theory, the Cooper-pair and field-induced vortex degrees of freedom are simultaneously incorporated into an electrically-neutral Dirac fermion minimally coupled to an (emergent) Chern-Simons gauge field. A derivation of the theory follows upon mapping the superconductor-insulator transition to the integer quantum Hall plateau transition and the subsequent use of Son's particle-hole symmetric composite Fermi liquid. Remarkably, particle-vortex symmetric response does not requir...
Harmonic analysis on symmetric spaces
Terras, Audrey
This text explores the geometry and analysis of higher rank analogues of the symmetric spaces introduced in volume one. To illuminate both the parallels and differences of the higher rank theory, the space of positive matrices is treated in a manner mirroring that of the upper-half space in volume one. This concrete example furnishes motivation for the general theory of noncompact symmetric spaces, which is outlined in the final chapter. The book emphasizes motivation and comprehensibility, concrete examples and explicit computations (by pen and paper, and by computer), history, and, above all, applications in mathematics, statistics, physics, and engineering. The second edition includes new sections on Donald St. P. Richards’s central limit theorem for O(n)-invariant random variables on the symmetric space of GL(n, R), on random matrix theory, and on advances in the theory of automorphic forms on arithmetic groups.
Symmetric autocompensating quantum key distribution
Walton, Zachary D.; Sergienko, Alexander V.; Levitin, Lev B.; Saleh, Bahaa E. A.; Teich, Malvin C.
2004-08-01
We present quantum key distribution schemes which are autocompensating (require no alignment) and symmetric (Alice and Bob receive photons from a central source) for both polarization and time-bin qubits. The primary benefit of the symmetric configuration is that both Alice and Bob may have passive setups (neither Alice nor Bob is required to make active changes for each run of the protocol). We show that both the polarization and the time-bin schemes may be implemented with existing technology. The new schemes are related to previously described schemes by the concept of advanced waves.
Clark, Robin J. H.; Michael, David J.
1988-10-01
Resonance Raman spectra of the linear-chain, mixed-valence, halogen-bridged complexes [Pt(pn) 2] [Pt(pn) 2X 2] (ClO 4) 4, where X = Cl or Br, and [Pd(pn) 2] [Pd(pn) 2Br 2] (ClO 4) 4 have been obtained over the range of excitation wavelengths 457.9 to 647.1 nm. Of particular interest is the symmetric metal—halogen stretch, ν 1, which has several components. The relative intensities of these components change with variation of the wavenumber of excitation within the intervalence electronic absorption. This effect and the origin of the different components are discussed.
Optimal tests for the two-sample spherical location problem
Ley, Christophe; Verdebout, Thomas
2012-01-01
We tackle the classical two-sample spherical location problem for directional data by having recourse to the Le Cam methodology, habitually used in classical "linear" multivariate analysis. More precisely we construct locally and asymptotically optimal (in the maximin sense) parametric tests, which we then turn into semi-parametric ones in two distinct ways. First, by using a studentization argument; this leads to so-called pseudo-FvML tests. Second, by resorting to the invariance principle; this leads to efficient rank-based tests. Within each construction, the semi-parametric tests inherit optimality under a given distribution (the FvML in the first case, any rotationally symmetric one in the second) from their parametric counterparts and also improve on the latter by being valid under the whole class of rotationally symmetric distributions. Asymptotic relative efficiencies are calculated and the finite-sample behavior of the proposed tests is investigated by means of a Monte Carlo simulation.
Spherical 3D isotropic wavelets
Lanusse, F.; Rassat, A.; Starck, J.-L.
2012-04-01
Context. Future cosmological surveys will provide 3D large scale structure maps with large sky coverage, for which a 3D spherical Fourier-Bessel (SFB) analysis in spherical coordinates is natural. Wavelets are particularly well-suited to the analysis and denoising of cosmological data, but a spherical 3D isotropic wavelet transform does not currently exist to analyse spherical 3D data. Aims: The aim of this paper is to present a new formalism for a spherical 3D isotropic wavelet, i.e. one based on the SFB decomposition of a 3D field and accompany the formalism with a public code to perform wavelet transforms. Methods: We describe a new 3D isotropic spherical wavelet decomposition based on the undecimated wavelet transform (UWT) described in Starck et al. (2006). We also present a new fast discrete spherical Fourier-Bessel transform (DSFBT) based on both a discrete Bessel transform and the HEALPIX angular pixelisation scheme. We test the 3D wavelet transform and as a toy-application, apply a denoising algorithm in wavelet space to the Virgo large box cosmological simulations and find we can successfully remove noise without much loss to the large scale structure. Results: We have described a new spherical 3D isotropic wavelet transform, ideally suited to analyse and denoise future 3D spherical cosmological surveys, which uses a novel DSFBT. We illustrate its potential use for denoising using a toy model. All the algorithms presented in this paper are available for download as a public code called MRS3D at http://jstarck.free.fr/mrs3d.html
AdS nonlinear instability: moving beyond spherical symmetry
Dias, Oscar J C
2016-01-01
Anti-de Sitter (AdS) is conjectured to be nonlinear unstable to a weakly turbulent mechanism that develops a cascade towards high frequencies, leading to black hole formation [1,2]. We give evidence that the gravitational sector of perturbations behaves differently from the scalar one studied in [2]. In contrast with [2], we find that not all gravitational normal modes of AdS can be nonlinearly extended into periodic horizonless smooth solutions of the Einstein equation. In particular, we show that even seeds with a single normal mode can develop secular resonances, unlike the spherically symmetric scalar field collapse studied in [2]. Moreover, if the seed has two normal modes, more than one resonance can be generated at third order, unlike the spherical collapse of [2]. We also show that weak turbulent perturbative theory predicts the existence of direct and inverse cascades, with the former dominating the latter for equal energy two-mode seeds.
Maximal slicings in spherical symmetry: local existence and construction
Cordero-Carrión, Isabel; Morales-Lladosa, Juan Antonio; 10.1063/1.3658864
2011-01-01
We show that any spherically symmetric spacetime locally admits a maximal spacelike slicing and we give a procedure allowing its construction. The construction procedure that we have designed is based on purely geometrical arguments and, in practice, leads to solve a decoupled system of first order quasi-linear partial differential equations. We have explicitly built up maximal foliations in Minkowski and Friedmann spacetimes. Our approach admits further generalizations and efficient computational implementation. As by product, we suggest some applications of our work in the task of calibrating Numerical Relativity complex codes, usually written in Cartesian coordinates.
Full light absorption in single arrays of spherical nanoparticles
Ra'di, Y; Kosulnikov, S U; Omelyanovich, M M; Morits, D; Osipov, A V; Simovski, C R; Tretyakov, S A
2015-01-01
In this paper we show that arrays of core-shell nanoparticles function as effective thin absorbers of light. In contrast to known metamaterial absorbers, the introduced absorbers are formed by single planar arrays of spherical inclusions and enable full absorption of light incident on either or both sides of the array. We demonstrate possibilities for realizing different kinds of symmetric absorbers, including resonant, ultra-broadband, angularly selective, and all-angle absorbers. The physical principle behind these designs is explained considering balanced electric and magnetic responses of unit cells. Photovoltaic devices and thermal emitters are the two most important potential applications of the proposed designs.
General Equilibrium Property of Spherical Torus Configurations with Large Triangularity
Institute of Scientific and Technical Information of China (English)
SHIBingren
2003-01-01
In magnetic fusion research, two sorts of axi-symmetric toroidal equilibrium configuration are mostly interested. One is the conventional tokamak that has an aspect ratio 2. 8spherical torus (the ST configuration) with A≤1.4.For tokamaks, it is generally observed that equilibrium configurations with large triangular deformation usually has the merit of stabilizing higher beta plasma and better confinement scaling so that higher βN/li value can be attained. This was also verified theoretically in the ballooning mode analysis.
Optimization of spherical facets for parabolic solar concentrators
White, J. E.; Erikson, R. J.; Sturgis, J. D.; Elfe, T. B.
1986-01-01
Solar concentrator designs which employ deployable hexagonal panels are being developed for space power systems. An offset optical configuration has been developed which offers significant system level advantages over previously proposed collector designs for space applications. Optical analyses have been performed which show offset reflector intercept factors to be only slightly lower than those for symmetric reflectors with the same slope error. Fluxes on the receiver walls are asymmetric but manageable by varying the tilt angle of the receiver. Greater producibility is achieved by subdividing the hexagonal panels into triangular mirror facets of spherical contour. Optical analysis has been performed upon these to yield near-optimum sizes and radii.
Topological Lensing in Spherical Spaces
Gausmann, E; Luminet, Jean Pierre; Uzan, J P; Weeks, J; Gausmann, Evelise; Lehoucq, Roland; Luminet, Jean-Pierre; Uzan, Jean-Philippe; Weeks, Jeffrey
2001-01-01
This article gives the construction and complete classification of all three-dimensional spherical manifolds, and orders them by decreasing volume, in the context of multiconnected universe models with positive spatial curvature. It discusses which spherical topologies are likely to be detectable by crystallographic methods using three-dimensional catalogs of cosmic objects. The expected form of the pair separation histogram is predicted (including the location and height of the spikes) and is compared to computer simulations, showing that this method is stable with respect to observational uncertainties and is well suited for detecting spherical topologies.
Axially Symmetric, Spatially Homothetic Spacetimes
Wagh, S M; Wagh, Sanjay M.; Govinder, Keshlan S.
2002-01-01
We show that the existence of appropriate spatial homothetic Killing vectors is directly related to the separability of the metric functions for axially symmetric spacetimes. The density profile for such spacetimes is (spatially) arbitrary and admits any equation of state for the matter in the spacetime. When used for studying axisymmetric gravitational collapse, such solutions do not result in a locally naked singularity.
Particle-vortex symmetric liquid
Mulligan, Michael
2017-01-01
We introduce an effective theory with manifest particle-vortex symmetry for disordered thin films undergoing a magnetic field-tuned superconductor-insulator transition. The theory may enable one to access both the critical properties of the strong-disorder limit, which has recently been confirmed by Breznay et al. [Proc. Natl. Acad. Sci. USA 113, 280 (2016), 10.1073/pnas.1522435113] to exhibit particle-vortex symmetric electrical response, and the nearby metallic phase discovered earlier by Mason and Kapitulnik [Phys. Rev. Lett. 82, 5341 (1999), 10.1103/PhysRevLett.82.5341] in less disordered samples. Within the effective theory, the Cooper-pair and field-induced vortex degrees of freedom are simultaneously incorporated into an electrically neutral Dirac fermion minimally coupled to a (emergent) Chern-Simons gauge field. A derivation of the theory follows upon mapping the superconductor-insulator transition to the integer quantum Hall plateau transition and the subsequent use of Son's particle-hole symmetric composite Fermi liquid. Remarkably, particle-vortex symmetric response does not require the introduction of disorder; rather, it results when the Dirac fermions exhibit vanishing Hall effect. The theory predicts approximately equal (diagonal) thermopower and Nernst signal with a deviation parameterized by the measured electrical Hall response at the symmetric point.
Symmetric relations of finite negativity
Kaltenbaeck, M.; Winkler, H.; Woracek, H.; Forster, KH; Jonas, P; Langer, H
2006-01-01
We construct and investigate a space which is related to a symmetric linear relation S of finite negativity on an almost Pontryagin space. This space is the indefinite generalization of the completion of dom S with respect to (S.,.) for a strictly positive S on a Hilbert space.
Vassiliev Invariants from Symmetric Spaces
DEFF Research Database (Denmark)
Biswas, Indranil; Gammelgaard, Niels Leth
We construct a natural framed weight system on chord diagrams from the curvature tensor of any pseudo-Riemannian symmetric space. These weight systems are of Lie algebra type and realized by the action of the holonomy Lie algebra on a tangent space. Among the Lie algebra weight systems, they are ......, they are exactly characterized by having the symmetries of the Riemann curvature tensor....
Thermophoresis of Axially Symmetric Bodies
2007-11-02
Sweden Abstract. Thermophoresis of axially symmetric bodies is investigated to first order in the Knudsen-mimber, Kn. The study is made in the limit...derived. Asymptotic solutions are studied. INTRODUCTION Thermophoresis as a phenomenon has been known for a long time, and several authors have approached
Axiomatizations of symmetrically weighted solutions
Kleppe, John; Reijnierse, Hans; Sudhölter, P.
2013-01-01
If the excesses of the coalitions in a transferable utility game are weighted, then we show that the arising weighted modifications of the well-known (pre)nucleolus and (pre)kernel satisfy the equal treatment property if and only if the weight system is symmetric in the sense that the weight of a su
Computationally Efficient Searchable Symmetric Encryption
Liesdonk, van Peter; Sedghi, Saeed; Doumen, Jeroen; Hartel, Pieter; Jonker, Willem; Jonker, Willem; Petkovic, Milan
2010-01-01
Searchable encryption is a technique that allows a client to store documents on a server in encrypted form. Stored documents can be retrieved selectively while revealing as little information as possible to the server. In the symmetric searchable encryption domain, the storage and the retrieval are
Symmetrical progressive erythro-keratoderma
Directory of Open Access Journals (Sweden)
Sunil Gupta
1999-01-01
Full Text Available A 13-year-old male child had gradually progressive, bilaterall, symmetrical, erythematous hyperkeratotic plaques over knees, elbows, natal cleft, dorsa of hands and feet with palmoplantar keratoderma. High arched palate, fissured tongue and sternal depression (pectus-excavatum were unusual associations.
Plastic instabilities in statically and dynamically loaded spherical vessels
Energy Technology Data Exchange (ETDEWEB)
Duffey, Thomas A [Los Alamos National Laboratory; Rodriguez, Edward A [Los Alamos National Laboratory
2010-01-01
Significant changes were made in design limits for pressurized vessels in the 2007 version of the ASME Code (Section VIII, Div. 3) and 2008 and 2009 Addenda. There is now a local damage-mechanics based strain-exhaustion limit as well as the well-known global plastic collapse limit. Moreover, Code Case 2564 (Section VIII, Div. 3) has recently been approved to address impulsively loaded vessels. It is the purpose of this paper to investigate the plastic collapse limit as it applies to dynamically loaded spherical vessels. Plastic instabilities that could potentially develop in spherical shells under symmetric loading conditions are examined for a variety of plastic constitutive relations. First, a literature survey of both static and dynamic instabilities associated with spherical shells is presented. Then, a general plastic instability condition for spherical shells subjected to displacement controlled and impulsive loading is given. This instability condition is evaluated for six plastic and visco-plastic constitutive relations. The role of strain-rate sensitivity on the instability point is investigated. Calculations for statically and dynamically loaded spherical shells are presented, illustrating the formation of instabilities as well as the role of imperfections. Conclusions of this work are that there are two fundamental types of instabilities associated with failure of spherical shells. In the case of impulsively loaded vessels, where the pulse duration is short compared to the fundamental period of the structure, one instability type is found not to occur in the absence of static internal pressure. Moreover, it is found that the specific role of strain-rate sensitivity on the instability strain depends on the form of the constitutive relation assumed.
Degenerate Neutrinos in Left Right Symmetric Theory
Joshipura, A S
1995-01-01
Various hints on the neutrino masses namely, ({\\em i}) the solar neutrino deficit ({\\em ii}) the atmospheric neutrino deficit ({\\em iii}) the need for the dark matter and/or ({\\em iv}) the non-zero neutrinoless double beta decay collectively imply that all the three neutrinos must be nearlty degenerate. This feature can be understood in the left right symmetric theory. We present a model based on the group $SU(2)_{L}\\times SU(2)_R\\times U(1)_{B-L}\\times SU(2)_H$ which can explain the required departures from degeneracy in neutrino masses and large mixing among them without assuming any of the mixing in the quark or charged lepton sector to be large as would be expected in a typical $SO(10)$ model.
Understanding symmetrical components for power system modeling
Das, J C
2017-01-01
This book utilizes symmetrical components for analyzing unbalanced three-phase electrical systems, by applying single-phase analysis tools. The author covers two approaches for studying symmetrical components; the physical approach, avoiding many mathematical matrix algebra equations, and a mathematical approach, using matrix theory. Divided into seven sections, topics include: symmetrical components using matrix methods, fundamental concepts of symmetrical components, symmetrical components –transmission lines and cables, sequence components of rotating equipment and static load, three-phase models of transformers and conductors, unsymmetrical fault calculations, and some limitations of symmetrical components.
Spherical tokamak development in Brazil
Energy Technology Data Exchange (ETDEWEB)
Ludwig, G.O.; Del Bosco, E.; Ferreira, J.G.; Berni, L.A.; Oliveira, R.M.; Andrade, M.C.R.; Shibata, C.S.; Ueda, M.; Barroso, J.J.; Castro, P.J. [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil). Lab. Associado de Plasma; Barbosa, L.F.W. [Universidade do Vale do Paraiba (UNIVAP), Sao Jose dos Campos, SP (Brazil). Faculdade de Engenharia, Arquitetura e Urbanismo; Patire Junior, H. [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil). Div. de Mecanica Espacial e Controle; The high-power microwave sources group
2003-12-01
This paper describes the general characteristics of spherical tokamaks, or spherical tori, with a brief overview of work in this area already performed or in progress at several institutions worldwide. The paper presents also the steps in the development of the ETE (Experimento Tokamak Esferico) project, its research program, technical characteristics and operating conditions as of December, 2002 at the Associated Plasma Laboratory (LAP) of the National Space Research Institute (INPE) in Brazil. (author)
SPHERICAL SHOCK WAVES IN SOLIDS
Differential Equation of Self-Similar Motion; Application of the Theory of Self-Similar Motion to the Problem of Expansion of a Spherical...Self-Similar Solutions of the Problem of Cratering Due to Hypervelocity Impact, and Numerical Integration of the Differential Equation of Spherical...Aluminum, Blast Waves in Other Metals; and Consideration of the Non-Similar Aspects of the Blast Wave Problem ; Experimental Procedure and Results; Singular Point of Ordinary Differential Equations; Numerical Program-Fortran
Symmetric Teleparallel Gravity: Some Exact Solutions and Spinor Couplings
Adak, Muzaffer; Sert, Özcan; Kalay, Mestan; Sari, Murat
2013-12-01
In this paper, we elaborate on the symmetric teleparallel gravity (STPG) written in a non-Riemannian space-time with nonzero nonmetricity, but zero torsion and zero curvature. First, we give a prescription for obtaining the nonmetricity from the metric in a peculiar gauge. Then, we state that under a novel prescription of parallel transportation of a tangent vector in this non-Riemannian geometry, the autoparallel curves coincide with those of the Riemannian space-times. Subsequently, we represent the symmetric teleparallel theory of gravity by the most general quadratic and parity conserving Lagrangian with lagrange multipliers for vanishing torsion and curvature. We show that our Lagrangian is equivalent to the Einstein-Hilbert Lagrangian for certain values of coupling coefficients. Thus, we arrive at calculating the field equations via independent variations. Then, we obtain in turn conformal, spherically symmetric static, cosmological and pp-wave solutions exactly. Finally, we discuss a minimal coupling of a spin-1/2 field to STPG.
Spherical 3D Isotropic Wavelets
Lanusse, F; Starck, J -L
2011-01-01
Future cosmological surveys will provide 3D large scale structure maps with large sky coverage, for which a 3D Spherical Fourier-Bessel (SFB) analysis in is natural. Wavelets are particularly well-suited to the analysis and denoising of cosmological data, but a spherical 3D isotropic wavelet transform does not currently exist to analyse spherical 3D data. The aim of this paper is to present a new formalism for a spherical 3D isotropic wavelet, i.e. one based on the Fourier-Bessel decomposition of a 3D field and accompany the formalism with a public code to perform wavelet transforms. We describe a new 3D isotropic spherical wavelet decomposition based on the undecimated wavelet transform (UWT) described in Starck et al. 2006. We also present a new fast Discrete Spherical Fourier-Bessel Transform (DSFBT) based on both a discrete Bessel Transform and the HEALPIX angular pixelisation scheme. We test the 3D wavelet transform and as a toy-application, apply a denoising algorithm in wavelet space to the Virgo large...
Hellaby, C; Hellaby, Charles; Krasinski, Andrzej
2002-01-01
The spherically symmetric dust model of Lemaitre-Tolman can describe wormholes, but the causal communication between the two asymptotic regions through the neck is even less than in the vacuum (Schwarzschild-Kruskal-Szekeres) case. We investigate the anisotropic generalisation of the wormhole topology in the Szekeres model. The function E(r, p, q) describes the deviation from spherical symmetry if \\partial_r E \
Dynamics and statics of flexible axially symmetric shallow shells
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available In this work, we propose the method for the investigation of stochastic vibrations of deterministic mechanical systems represented by axially symmetric spherical shells. These structure members are widely used as sensitive elements of pressure measuring devices in various branches of measuring and control industry, machine design, and so forth. The proposed method can be easily extended for the investigation of shallow spherical shells, goffer-type membranes, and so on. The so-called charts of control parameters for a shell subjected to a transversal uniformly distributed and local harmonic loading force and resistance moment are constructed. The scenarios of the transition of vibration of shallow-type system into chaotic state are investigated with the use of the theory of differential equations and the theory of nonlinear dynamics. The method of the control of chaotic vibrations of flexible spherical shells subjected to a transversal harmonic load through a synchronized action of either harmonic resistance moment or force is proposed, illustrated, and discussed.
The antipodal sets of compact symmetric spaces
National Research Council Canada - National Science Library
Liu, Xingda; Deng, Shaoqiang
2014-01-01
We study the antipodal set of a point in a compact Riemannian symmetric space. It turns out that we can give an explicit description of the antipodal set of a point in any connected simply connected compact Riemannian symmetric space...
Symmetric normalisation for intuitionistic logic
DEFF Research Database (Denmark)
Guenot, Nicolas; Straßburger, Lutz
2014-01-01
, but using a non-local rewriting. The second system is the symmetric completion of the first, as normally given in deep inference for logics with a DeMorgan duality: all inference rules have duals, as cut is dual to the identity axiom. We prove a generalisation of cut elimination, that we call symmetric...... normalisation, where all rules dual to standard ones are permuted up in the derivation. The result is a decomposition theorem having cut elimination and interpolation as corollaries.......We present two proof systems for implication-only intuitionistic logic in the calculus of structures. The first is a direct adaptation of the standard sequent calculus to the deep inference setting, and we describe a procedure for cut elimination, similar to the one from the sequent calculus...
Symmetric two-coordinate photodiode
Directory of Open Access Journals (Sweden)
Dobrovolskiy Yu. G.
2008-12-01
Full Text Available The two-coordinate photodiode is developed and explored on the longitudinal photoeffect, which allows to get the coordinate descriptions symmetric on the steepness and longitudinal resistance great exactness. It was shown, that the best type of the coordinate description is observed in the case of scanning by the optical probe on the central part of the photosensitive element. The ways of improvement of steepness and linear of its coordinate description were analyzed.
Rotationally symmetric viscous gas flows
Weigant, W.; Plotnikov, P. I.
2017-03-01
The Dirichlet boundary value problem for the Navier-Stokes equations of a barotropic viscous compressible fluid is considered. The flow region and the data of the problem are assumed to be invariant under rotations about a fixed axis. The existence of rotationally symmetric weak solutions for all adiabatic exponents from the interval (γ*,∞) with a critical exponent γ* < 4/3 is proved.
Dynamics of non-spherical colloidal particles near and at oil-water interfaces
Wang, Anna; Dimiduk, Thomas G.; Fung, Jerome; Chaudhary, Kundan; Lewis, Jennifer A.; Razavi, Sepideh; Kretzschmar, Ilona; Manoharan, Vinothan N.
2014-03-01
Whereas much is known about how spherical colloidal particles interact with and at oil-water interfaces, not much is known about their non-spherical counterparts. The rotation of non-spherically symmetric particles adds extra degrees of freedom to how such particles interact with each other and the interface, so to study their three-dimensional dynamics we must first be able to image the rotation which has so far only been possible in viscous fluids or for particles with large aspect ratios. Here we track both the three-dimensional translation and the rotation of non-spherical colloidal particles at high speeds using the discrete dipole approximation in conjunction with digital holographic microscopy. We study the dynamics of such particles at an oil-water interface to determine interactions and dynamics prior to or after attachment. We aim to connect these measurements to the formation and stability of Pickering emulsions.
Normal range of facial asymmetry in spherical coordinates: a CBCT study
Energy Technology Data Exchange (ETDEWEB)
Yoon, Suk Ja [Dept. of Oral and Maxillofacial Radiology, School of Dentistry, Dental Science Research Institute, Chonnam National University, Gwangju (Korea, Republic of); Wang, Rui Feng [Research Laboratory Specialist Intermediate, Department of Biologic and Material Sciences, School of Dentistry, University of Michigan, Ann Arbor, MI (United States); Na, Hee Ja [Dept. ofDental Hygiene, Honam University, Gwangju (Korea, Republic of); Palomo, Juan Matin [Dept. of Orthodontics, School of Dental Medicine, Case Western Reserve University, Cleveland (United States)
2013-03-15
This study aimed to measure the bilateral differences of facial lines in spherical coordinates from faces within a normal range of asymmetry utilizing cone-beam computed tomography (CBCT). CBCT scans from 22 females with normal symmetric-looking faces (mean age 24 years and 8 months) were selected for the study. The average menton deviation was 1.01{+-}0.66 mm. The spherical coordinates, length, and midsagittal and coronal inclination angles of the ramal and mandibular lines were calculated from CBCT. The bilateral differences in the facial lines were determined. All of the study subjects had minimal bilateral differences of facial lines. The normal range of facial asymmetry of the ramal and mandibular lines was obtained in spherical coordinates. The normal range of facial asymmetry in the spherical coordinate system in this study should be useful as a reference for diagnosing facial asymmetry.
Bender, Carl M.
2015-07-01
The average quantum physicist on the street would say that a quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under combined matrix transposition and complex conjugation) in order to guarantee that the energy eigenvalues are real and that time evolution is unitary. However, the Hamiltonian H = p2 + ix3, which is obviously not Dirac Hermitian, has a positive real discrete spectrum and generates unitary time evolution, and thus it defines a fully consistent and physical quantum theory. Evidently, the axiom of Dirac Hermiticity is too restrictive. While H = p2 + ix3 is not Dirac Hermitian, it is PT symmetric; that is, invariant under combined parity P (space reflection) and time reversal T. The quantum mechanics defined by a PT-symmetric Hamiltonian is a complex generalization of ordinary quantum mechanics. When quantum mechanics is extended into the complex domain, new kinds of theories having strange and remarkable properties emerge. In the past few years, some of these properties have been verified in laboratory experiments. A particularly interesting PT-symmetric Hamiltonian is H = p2 - x4, which contains an upside-down potential. This potential is discussed in detail, and it is explained in intuitive as well as in rigorous terms why the energy levels of this potential are real, positive, and discrete. Applications of PT-symmetry in quantum field theory are also discussed.
Energy Technology Data Exchange (ETDEWEB)
Imai, T.; Iwano, K.; Hotta, H.; Takano, S.; Tsutsumi, H. (Kao Corporation, Tokyo (Japan))
1991-12-20
The previous report explained that an excellent spherical particulate pigment with a grain size of 0.5 mm or less can be obtained by preparing multinuclear aluminum lakes from acidic dyes and multinuclear aluminum salt using water droplets in a W/O emulsion as reaction fields. This paper describes preparing pigments varying the charging concentrations of the pigments in a W/O emulsion and the droplet particle size to discuss the mechanism of forming the pigments. As a result, it was found that the particle sizes in the produced pigments have a clear correlation with the charging concentrations of the pigments and the droplet particle sizes in the W/O emulsion. A pigment produced in the W/O emulsion forms only in its own droplets, and reflects its particle sizes. Films dispersed with pigments having different particle sizes were prepared to discuss their tinting abilities, whereas it was clarified that the smaller the particle size, the higher the tinting ability and the higher saturation in colored paint films. 6 refs., 9 figs., 3 tabs.
Degenerate neutrinos in left-right symmetric theory
Energy Technology Data Exchange (ETDEWEB)
Joshipura, A.S. (Theory Group, Physical Research Laboratory, Navrangpura, Ahmedabad 380009 (India))
1995-02-01
Various hints on the neutrino masses, namely, (i) the solar neutrino deficit, (ii) the atmospheric neutrino deficit, (iii) the need for the dark matter, and/or (iv) the nonzero neutrinoless double [beta] decay collectively imply that all the three neutrinos must be nearly degenerate. This feature can be understood in the left-right symmetric theory. We present a model based on the group SU(2)[sub [ital L
Addition theorems for spin spherical harmonics: I. Preliminaries
Energy Technology Data Exchange (ETDEWEB)
Bouzas, Antonio O, E-mail: abouzas@mda.cinvestav.mx [Departamento de Fisica Aplicada, CINVESTAV-IPN, Carretera Antigua a Progreso Km. 6, Apdo. Postal 73 ' Cordemex' , Merida 97310, Yucatan (Mexico)
2011-04-22
We develop a systematic approach to deriving addition theorems for, and some other bilocal sums of, spin spherical harmonics. In this first part we establish some necessary technical results. We discuss the factorization of orbital and spin degrees of freedom in certain products of Clebsch-Gordan coefficients, and obtain general explicit results for the matrix elements in configuration space of tensor products of arbitrary rank of the position and angular-momentum operators. These results are the basis of the addition theorems for spin spherical harmonics obtained in part II (2011 J. Phys. A: Math. Theor. 44 165302).
Chen, Yong; Yan, Zhenya
2017-01-01
The effect of derivative nonlinearity and parity-time-symmetric (PT -symmetric) potentials on the wave propagation dynamics is explored in the derivative nonlinear Schrödinger equation, where the physically interesting Scarf-II and harmonic-Hermite-Gaussian potentials are chosen. We study numerically the regions of unbroken and broken linear PT -symmetric phases and find some stable bright solitons of this model in a wide range of potential parameters even though the corresponding linear PT -symmetric phases are broken. The semielastic interactions between particular bright solitons and exotic incident waves are illustrated such that we find that particular nonlinear modes almost keep their shapes after interactions even if the exotic incident waves have evidently been changed. Moreover, we exert the adiabatic switching on PT -symmetric potential parameters such that a stable nonlinear mode with the unbroken linear PT -symmetric phase can be excited to another stable nonlinear mode belonging to the broken linear PT -symmetric phase.
Yoon, Jungjoo; Mirica, Liviu M; Stack, T Daniel P; Solomon, Edward I
2004-10-06
The magnetic and electronic properties of a spin-frustrated ground state of an antiferromagnetically coupled 3-fold symmetric trinuclear copper complex (TrisOH) is investigated using a combination of variable-temperature variable-field magnetic circular dichroism (VTVH MCD) and powder/single-crystal EPR. Direct evidence for a low-lying excited S = (1)/(2) state from the zero-field split ground (2)E state is provided by the nonlinear dependence of the MCD intensity on 1/T and the nesting of the VTVH MCD isotherms. A consistent zero-field splitting (Delta) value of approximately 65 cm(-1) is obtained from both approaches. In addition, the strong angular dependence of the single-crystal EPR spectrum, with effective g-values from 2.32 down to an unprecedented 1.2, requires in-state spin-orbit coupling of the (2)E state via antisymmetric exchange. The observable EPR intensities also require lowering of the symmetry of the trimer structure, likely reflecting a magnetic Jahn-Teller effect. Thus, the Delta of the ground (2)E state is shown to be governed by the competing effects of antisymmetric exchange (G = 36.0 +/- 0.8 cm(-1)) and symmetry lowering (delta = 17.5 +/- 5.0 cm(-1)). G and delta have opposite effects on the spin distribution over the three metal sites where the former tends to delocalize and the latter tends to localize the spin of the S(tot) = (1)/(2) ground state on one metal center. The combined effects lead to partial delocalization, reflected by the observed EPR parallel hyperfine splitting of 74 x 10(-4) cm(-1). The origin of the large G value derives from the efficient superexchange pathway available between the ground d(x2-y2) and excited d(xy) orbitals of adjacent Cu sites, via strong sigma-type bonds with the in-plane p-orbitals of the bridging hydroxy ligands. This study provides significant insight into the orbital origin of the spin Hamiltonian parameters of a spin-frustrated ground state of a trigonal copper cluster.
2014-01-01
afloat as a surface warfare officer trained in naval nuclear propulsion, including Assistant Reactor Officer on USS ENTERPRISE (CVN-65) and Chief Staff...integer sequences, were formulated based on coprime modular systems. Symmetrical number systems include the symmetrical number system (SNS), the optimum...real number x we write log x for the maximum between 2 and the natural logarithm of x. II. ROBUST SYMMETRICAL NUMBER SYSTEM The RSNS is a modular based
Symmetric products of mixed Hodge modules
Maxim, Laurentiu; Schuermann, Joerg
2010-01-01
Generalizing a theorem of Macdonald, we show a formula for the mixed Hodge structure on the cohomology of the symmetric products of bounded complexes of mixed Hodge modules by showing the existence of the canonical action of the symmetric group on the multiple external self-products of complexes of mixed Hodge modules. We also generalize a theorem of Hirzebruch and Zagier on the signature of the symmetric products of manifolds to the case of the symmetric products of symmetric parings on bounded complexes with constructible cohomology sheaves where the pairing is not assumed to be non-degenerate.
Singular Value Decomposition for Unitary Symmetric Matrix
Institute of Scientific and Technical Information of China (English)
ZOUHongxing; WANGDianjun; DAIQionghai; LIYanda
2003-01-01
A special architecture called unitary sym-metric matrix which embodies orthogonal, Givens, House-holder, permutation, and row (or column) symmetric ma-trices as its special cases, is proposed, and a precise corre-spondence of singular values and singular vectors between the unitary symmetric matrix and its mother matrix is de-rived. As an illustration of potential, it is shown that, for a class of unitary symmetric matrices, the singular value decomposition (SVD) using the mother matrix rather than the unitary symmetric matrix per se can save dramatically the CPU time and memory without loss of any numerical precision.
On the gradient of Schwarz symmetrization of functions in Sobolev spaces
Bramanti, Marco
2010-01-01
Let S be a Sobolev or Orlicz-Sobolev space of functions not necessarily vanishing at the boundary of the domain. We give sufficient conditions on a nonnegative function in S in order that its spherical rearrangement ("Schwartz symmetrization") still belongs to S. These results are obtained via relative isoperimetric inequalities and somewhat generalize a well-known Polya-Szego's theorem. We also prove that the rearrangement of any function in S is locally in S.
Spherical membranes in Matrix theory
Kabat, D; Kabat, Daniel; Taylor, Washington
1998-01-01
We consider membranes of spherical topology in uncompactified Matrix theory. In general for large membranes Matrix theory reproduces the classical membrane dynamics up to 1/N corrections; for certain simple membrane configurations, the equations of motion agree exactly at finite N. We derive a general formula for the one-loop Matrix potential between two finite-sized objects at large separations. Applied to a graviton interacting with a round spherical membrane, we show that the Matrix potential agrees with the naive supergravity potential for large N, but differs at subleading orders in N. The result is quite general: we prove a pair of theorems showing that for large N, after removing the effects of gravitational radiation, the one-loop potential between classical Matrix configurations agrees with the long-distance potential expected from supergravity. As a spherical membrane shrinks, it eventually becomes a black hole. This provides a natural framework to study Schwarzschild black holes in Matrix theory.
Spherical Demons: Fast Surface Registration
Yeo, B.T. Thomas; Sabuncu, Mert; Vercauteren, Tom; Ayache, Nicholas; Fischl, Bruce; Golland, Polina
2009-01-01
We present the fast Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizers for the modified demons objective function can be efficiently implemented on the sphere using convolution. Based on the one parameter subgroups of diffeomorphisms, the resulting registration is diffeomorphic and fast – registration of two cortical mesh models with more than 100k nodes takes less than 5 minutes, comparable to the fastest surface registration algorithms. Moreover, the accuracy of our method compares favorably to the popular FreeSurfer registration algorithm. We validate the technique in two different settings: (1) parcellation in a set of in-vivo cortical surfaces and (2) Brodmann area localization in ex-vivo cortical surfaces. PMID:18979813
Directory of Open Access Journals (Sweden)
Kurt Hornik
2012-09-01
Full Text Available Clustering text documents is a fundamental task in modern data analysis, requiring approaches which perform well both in terms of solution quality and computational efficiency. Spherical k-means clustering is one approach to address both issues, employing cosine dissimilarities to perform prototype-based partitioning of term weight representations of the documents.This paper presents the theory underlying the standard spherical k-means problem and suitable extensions, and introduces the R extension package skmeans which provides a computational environment for spherical k-means clustering featuring several solvers: a fixed-point and genetic algorithm, and interfaces to two external solvers (CLUTO and Gmeans. Performance of these solvers is investigated by means of a large scale benchmark experiment.
[Spherical crystallization in pharmaceutical technology].
Szabóné, R P; Pintyéné, H K; Kása, P; Erös, I; Hasznosné, N M; Farkas, B
1998-03-01
Physical properties of crystals, such as size, crystal size distribution and morphology, may predetermine the usefulness of crystalline materials in many pharmaceutical application. The above properties can be regulated with the crystallization process. The spherical crystals are suitable for direct tablet-making because of their better flowability and compressibility properties. These crystals can be used in the filling of the capsule. In this work, the spherical crystals such as "single crystal", "poly-crystals" and agglomerates with other excipients are collected from the literature and the experimental results of the authors. A close cooperation between chemists and the pharmaceutical technologists can help for doing steps in this field.
Spherical agglomeration of acetylsalicylic acid
Directory of Open Access Journals (Sweden)
Polowczyk Izabela
2016-01-01
Full Text Available In this paper spherical agglomeration of acetylsalicylic acid was described. In the first step, the system of good and poor solvents as well as bridging liquid was selected. As a result of a preliminary study, ethyl alcohol, water and carbon tetrachloride were used as the good solvent, poor one, and bridging liquid, respectively. Then, the amount of acetylsalicylic acid and the ratio of the solvents as well as the volume of the bridging liquid were examined. In the last step, the agglomeration conditions, such as mixing intensity and time, were investigated. The spherical agglomerates obtained under optimum conditions could be subjected to a tableting process afterwards.
Basketballs as spherical acoustic cavities
Russell, Daniel A.
2010-06-01
The sound field resulting from striking a basketball is found to be rich in frequency content, with over 50 partials in the frequency range of 0-12 kHz. The frequencies are found to closely match theoretical expectations for standing wave patterns inside a spherical cavity. Because of the degenerate nature of the mode shapes, explicit identification of the modes is not possible without internal investigation with a microphone probe. A basketball proves to be an interesting application of a boundary value problem involving spherical coordinates.
A Non-axisymmetric Spherical α2-Dynamo
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Using the Chebyshev-tau method, the generation of oscillatory nonaxisymmetric stellar magnetic fields by the α2-dynamo is studied in spherical geometry. Following the boundary conditions given by Schubert & Zhang, the spherical α2-dynamo consists of a fully convective spherical shell with inner radius ri and outer radius ro. A comparison of the critical dynamo numbers of axisymmetric and φ-dependent modes for different thicknesses of the convective shell and different α-profiles leads to the following qualitative results: (I) when the angular factor of α-profile is sinnθ cosθ (n = 1, 2, 4) the solutions of the α2-dynamo are oscillatory and non-axisymmetric, (ii) the thinner the convective shell, the more easily is the nonaxisymmetric mode excited and the higher is the latitudinal wave number, (iii) the thickness of the outer convective shell has an effect on the symmetries of the magnetic fields.
Mechanisms of Stochastic Diffusion of Energetic Ions in Spherical Tori
Energy Technology Data Exchange (ETDEWEB)
Ya.I. Kolesnichenko; R.B. White; Yu.V. Yakovenko
2001-01-18
Stochastic diffusion of the energetic ions in spherical tori is considered. The following issues are addressed: (I) Goldston-White-Boozer diffusion in a rippled field; (ii) cyclotron-resonance-induced diffusion caused by the ripple; (iii) effects of non-conservation of the magnetic moment in an axisymmetric field. It is found that the stochastic diffusion in spherical tori with a weak magnetic field has a number of peculiarities in comparison with conventional tokamaks; in particular, it is characterized by an increased role of mechanisms associated with non-conservation of the particle magnetic moment. It is concluded that in current experiments on National Spherical Torus eXperiment (NSTX) the stochastic diffusion does not have a considerable influence on the confinement of energetic ions.
Discrete Torsion and Symmetric Products
Dijkgraaf, R
1999-01-01
In this note we point out that a symmetric product orbifold CFT can be twisted by a unique nontrivial two-cocycle of the permutation group. This discrete torsion changes the spins and statistics of corresponding second-quantized string theory making it essentially ``supersymmetric.'' The long strings of even length become fermionic (or ghosts), those of odd length bosonic. The partition function and elliptic genus can be described by a sum over stringy spin structures. The usual cubic interaction vertex is odd and nilpotent, so this construction gives rise to a DLCQ string theory with a leading quartic interaction.
Immanant Conversion on Symmetric Matrices
Directory of Open Access Journals (Sweden)
Purificação Coelho M.
2014-01-01
Full Text Available Letr Σn(C denote the space of all n χ n symmetric matrices over the complex field C. The main objective of this paper is to prove that the maps Φ : Σn(C -> Σn (C satisfying for any fixed irre- ducible characters X, X' -SC the condition dx(A +aB = dχ·(Φ(Α + αΦ(Β for all matrices A,В ε Σ„(С and all scalars a ε C are automatically linear and bijective. As a corollary of the above result we characterize all such maps Φ acting on ΣИ(С.
Eigenvalues of the static, spherically-symmetric Einstein-Proca equations
Vuille, Chris
2016-01-01
The Proca potential has been used in many contexts in flat spacetime, but not so often in curved spacetime. Here, the static Proca potentials are derived on a Schwarzschild background, and are found to have very different forms from those in flat space. In addition, the coupling of the two fields leads to a quantum condition on the particle mass, which is found to be quantized and inversely proportional to the range parameter, $\\mu$. This suggests that gravity may induce quantization in other physical fields.
Mass bounds for compact spherically symmetric objects in generalized gravity theories
Burikham, Piyabut; Lake, Matthew J
2016-01-01
We derive upper and lower bounds on the mass-radius ratio of stable compact objects in extended gravity theories, in which modifications of the gravitational dynamics via-{\\' a}-vis standard general relativity are described by an effective contribution to the matter energy-momentum tensor. Our results include the possibility of a variable coupling between the matter sector and the gravitational field and are valid for a large class of generalized gravity models. The generalized continuity and Tolman-Oppenheimer-Volkoff equations are expressed in terms of the effective mass, density and pressure, given by the bare values plus additional contributions from the total energy-momentum tensor, and general theoretical limits for the maximum and minimum mass-radius ratios are explicitly obtained. As an applications of the formalism developed herein, we consider compact bosonic objects, described by scalar-tensor gravitational theories with self-interacting scalar field potentials, and charged compact objects, respect...
On the spherically symmetric Einstein-Yang-Mills-Higgs equations in Bondi coordinates
Tadmon, Calvin
2012-01-01
We revisit and generalize, to the Einstein-Yang-Mills-Higgs system, previous results of D. Christodoulou and D. Chae concerning global solutions for the Einstein-scalar field and the Einstein-Maxwell-Higgs equations. The novelty of the present work is twofold. For one thing the assumption on the self-interaction potential is improved. For another thing explanation is furnished why the solutions obtained here and those proved by Chae for the Einstein-Maxwell-Higgs decay more slowly than those established by Christodoulou in the case of self-gravitating scalar fields. Actually this latter phenomenon stems from the non-vanishing local charge in Einstein-Maxwell-Higgs and Einstein-Yang-Mills-Higgs models.
Motion of a thin spherically symmetric Shell of Dust in the Schwarzschild field
Schmidt, H -J
2014-01-01
The equation of motion announced in the title was already deduced for the cases the inner metric being flat and the shell being negligibly small (test matter), using surface layers and geodesic trajectories resp. Here we derive the general equation of motion and solve it in closed form for the case of parabolic motion. Especially the motion near the horizon and near the singularity are examined.
Mass bounds for compact spherically symmetric objects in generalized gravity theories
Burikham, Piyabut; Harko, Tiberiu; Lake, Matthew J.
2016-09-01
We derive upper and lower bounds on the mass-radius ratio of stable compact objects in extended gravity theories, in which modifications of the gravitational dynamics via-á-vis standard general relativity are described by an effective contribution to the matter energy-momentum tensor. Our results include the possibility of a variable coupling between the matter sector and the gravitational field and are valid for a large class of generalized gravity models. The generalized continuity and Tolman-Oppenheimer-Volkoff equations are expressed in terms of the effective mass, density, and pressure, given by the bare values plus additional contributions from the total energy-momentum tensor, and general theoretical limits for the maximum and minimum mass-radius ratios are explicitly obtained. As applications of the formalism developed herein, we consider compact bosonic objects, described by scalar-tensor gravitational theories with self-interacting scalar field potentials, and charged compact objects, respectively. For Higgs-type models, we find that these bounds can be expressed in terms of the value of the potential at the surface of the compact object. Minimizing the energy with respect to the radius, we obtain explicit upper and lower bounds on the mass, which admits a Chandrasekhar-type representation. For charged compact objects, we consider the effects of the Poincaré stresses on the equilibrium structure and obtain bounds on the radial and tangential stresses. As a possible astrophysical test of our results, we obtain the general bound on the gravitational redshift for compact objects in extended gravity theories and explicitly compute the redshift restrictions for objects with nonzero effective surface pressure. General implications of minimum mass bounds for the gravitational stability of fundamental particles and for the existence of holographic duality between bulk and boundary degrees of freedom are also considered.
Solution of the spherically symmetric linear thermoviscoelastic problem in the inertia-free limit
DEFF Research Database (Denmark)
Christensen, Tage Emil; Dyre, J. C.
2008-01-01
paper-the thermoviscoelastic problem may be solved analytically in the inertia-free limit, i.e., the limit where the sample is much smaller than the wavelength of sound waves at the frequencies of interest. As for the one-dimensional thermoviscoelastic problem [Christensen et al., Phys. Rev. E 75......, 041502 (2007)], the solution is conveniently formulated in terms of the so-called transfer matrix, which directly links to the boundary conditions that can be experimentally controlled. Once the transfer matrix has been calculated, it is fairly easy to deduce the equations describing various...
Point kinetic model of the early phase of a spherically symmetric nuclear explosion
Aste, Andreas
2016-01-01
A concise point kinetic model of the explosion of a prompt supercritical sphere driven by a nuclear fission chain reaction is presented. The findings are in good agreement with the data available for Trinity, the first detonation of a nuclear weapon conducted by the United States Army as part of the Manhattan project. Results are presented for an implosion device containing pure plutonium-239, although the model can be easily applied to, e.g., uranium-235. The fizzle probability and corresponding yield of a fission bomb containing plutonium recovered from reactor fuel and therefore containing significant amounts of spontaneously fissioning plutonium-240 which can induce a predetonation of the device is illustrated by adding a corresponding source term in the presented model. Related questions whether a bomb could be made by developing countries or terrorist organizations can be tackled this way. Although the information needed to answer such questions is in the public domain, it is difficult to extract a cons...
Wang, Peng; Ying, Shuxuan
2015-01-01
We compute the black hole horizon entanglement entropy for a massless scalar field in the brick wall model by incorporating the minimal length. Taking the minimal length effects on the occupation number $n(\\omega,l)$ and the Hawking temperature into consideration, we obtain the leading UV divergent term and the subleading logarithmic term in the entropy. The leading divergent term scales with the horizon area. The subleading logarithmic term is the same as that in the usual brick wall model without the minimal length.
On the Stability of Spherically Symmetric Self-Gravitating Classical and Quantum Systems
DEFF Research Database (Denmark)
Makedonski, Mathias
on to the description of the corresponding systems in the setting of general relativity, it is shown, that the Tolman-Oppenheimer-Volko equation can be obtained from a suitable variation of the total energy. We prove a previously unnoticed energetic instability of the model. Staying in the general relativistic setting......, we examine the self-gravitating massive free scalar eld. It is shown, by proving suitable dierentiability properties of the occurring functionals, that Einstein's equations in this setting can again be obtained by a constrained variation of the total mass as dened by Arnowitt, Deser and Misner...
Sharp bounds on $2m/r$ of general spherically symmetric static objects
Andreasson, H
2007-01-01
where $m$ is the quasi-local mass, so that in particular $M=m(R).$ We also show that the inequality is sharp. Note that when $\\Omega=1$ the original bound by Buchdahl is recovered. The assumptions on the matter model are very general and in particular any model with $p\\geq 0$ which satisfies the dominant energy condition satisfies the hypotheses with $\\Omega=3.$
The T-domain and extreme matter phases inside spherically symmetric black holes
De Benedictis, A; Das, A
2002-01-01
Black hole interiors (the $T$-domain) are studied here in great detail. Both the {\\em general} and particular $T$-domain solutions are presented including non-singular ones. Infinitely many local $T$-domain solutions may be modeled with this scheme. The duality between the $T$ and $R$ domains is presented. It is demonstrated how generally well behaved $R$-domain solutions will give rise to exotic phases of matter when collapsed inside the event horizon. However, as seen by an external observer, the field is simply that of the Schwarzschild vacuum with well behaved mass term and no evidence of this behaviour may be observed. A singularity theorem is also presented which is independent of energy conditions.
Ulhoa, S C; Capistrano, Abraão J S
2016-01-01
In this paper we investigate scalar perturbations of black holes embedded in a five dimensional bulk space. It is calculated the quasinormal frequencies of a such black holes using the third order of Wentzel, Kramers, Brillouin (WKB) approximation for scalar perturbations. The results are presented in tables along the text.
Comment on "Spherically symmetric perfect fluid in area-radial coordinates" by Iguchi et al
Giambo', R; Magli, G; Piccione, P; Giambo', Roberto; Giannoni, Fabio; Magli, Giulio; Piccione, Paolo
2004-01-01
In this short note we comment about some criticisms - appeared in a recent paper by Iguchi et al - to our previous works on gravitational collapse of perfect fluids. We show that those criticisms are incorrect on their own.
Collapse of a nanoscopic void triggered by a spherically symmetric traveling sound wave.
Hołyst, Robert; Litniewski, Marek; Garstecki, Piotr
2012-05-01
Molecular-dynamics simulations of the Lennard-Jones fluid (up to 10(7) atoms) are used to analyze the collapse of a nanoscopic bubble. The collapse is triggered by a traveling sound wave that forms a shock wave at the interface. The peak temperature T(max) in the focal point of the collapse is approximately ΣR(0)(a), where Σ is the surface density of energy injected at the boundary of the container of radius R(0) and α ≈ 0.4-0.45. For Σ = 1.6 J/m(2) and R(0) = 51 nm, the shock wave velocity, which is proportional to √Σ, reaches 3400 m/s (4 times the speed of sound in the liquid); the pressure at the interface, which is proportional to Σ, reaches 10 GPa; and T(max) reaches 40,000 K. The Rayleigh-Plesset equation together with the time of the collapse can be used to estimate the pressure at the front of the shock wave.
Veiled singularities for the spherically symmetric massless Einstein-Vlasov system
Rendall, Alan D
2016-01-01
This paper continues the investigation of the formation of naked singularities in the collapse of collisionless matter initiated in [RV]. There the existence of certain classes of non-smooth solutions of the Einstein-Vlasov system was proved. Those solutions are self-similar and hence not asymptotically flat. To obtain solutions which are more physically relevant it makes sense to attempt to cut off these solutions in a suitable way so as to make them asymptotically flat. This task, which turns out to be technically challenging, will be carried out in this paper. [RV] A. D. Rendall and J. J. L. Vel\\'{a}zquez, A class of dust-like self-similar solutions of the massless Einstein-Vlasov system. Annales Henri Poincare 12, 919-964, (2011).
Study of the electric capacitance spectra on symmetric quantum-dot pattern
Institute of Scientific and Technical Information of China (English)
DAI; Zhenhong(戴振宏); SUN; Jinzuo(孙金祚); ZHANG; Lide; (张立德); SUI; Pengfei(隋鹏飞); HUANG; Shiyong(黄士勇); LU; Maowang(卢卯旺)
2003-01-01
We have calculated the ground-state energy of the symmetric quantum-dot pattern by the ab initio calculation method, i.e. unrestricted Hartree-Fock-Roothaan (UHFR) method based on the Gaussian basis, and studied their electric capacitance spectra, assuming each quantum dot of quantum-dot pattern to be confined in a three-dimensional spherical potential well of finite depth. For the systems in question, our results show that our method and theoretical model not only give the electric capacitance peaks similar to s-shell and p-shell atom-like quantum dot, but also show some new fine-structure of electric capacitance in the symmetric quantum-dot pattern system. This method might be a feasible tool to study few-electron problems on the symmetric quantum-dot pattern system.
Spherical Pendulum, Actions, and Spin
Richter, Peter H.; Dullin, Holger R.; Waalkens, Holger; Wiersig, Jan
1996-01-01
The classical and quantum mechanics of a spherical pendulum are worked out, including the dynamics of a suspending frame with moment of inertia θ. The presence of two separatrices in the bifurcation diagram of the energy-momentum mapping has its mathematical expression in the hyperelliptic nature of
Study of the apsidal precession of the Physical Symmetrical Pendulum
Maya, Hector R; Herrera, William J
2013-01-01
We study the apsidal precession of a Physical Symmetrical Pendulum (Allais' precession) as a generalization of the precession corresponding to the Ideal Spherical Pendulum (Airy's Precession). Based on the Hamilton-Jacobi formalism and using the technics of variation of parameters along with the averaging method, we obtain approximate solutions, in terms of which the motion of both systems admits a simple geometrical description. The method developed in this paper is considerably simpler than the standard one in terms of elliptical functions and the numerical agreement with the exact solutions is excellent. In addition, the present procedure permits to show clearly the origin of the Airy's and Allais' precession, as well as the effect of the spin of the Physical Pendulum on the Allais' precession. Further, the method can be extended to the study of the asymmetrical pendulum in which an exact solution is not possible anymore.
Schwarz Methods: To Symmetrize or Not to Symmetrize
Holst, Michael
2010-01-01
A preconditioning theory is presented which establishes sufficient conditions for multiplicative and additive Schwarz algorithms to yield self-adjoint positive definite preconditioners. It allows for the analysis and use of non-variational and non-convergent linear methods as preconditioners for conjugate gradient methods, and it is applied to domain decomposition and multigrid. It is illustrated why symmetrizing may be a bad idea for linear methods. It is conjectured that enforcing minimal symmetry achieves the best results when combined with conjugate gradient acceleration. Also, it is shown that absence of symmetry in the linear preconditioner is advantageous when the linear method is accelerated by using the Bi-CGstab method. Numerical examples are presented for two test problems which illustrate the theory and conjectures.
Novel Spherical Robot with Hybrid Pendulum Driving Mechanism
Directory of Open Access Journals (Sweden)
Sung-Su Ahn
2014-11-01
Full Text Available As regards omnidirectional driving, conventional one- and two-pendulum spherical robots have a limited capability due to a limited pendulum motion range. In particular, such robots cannot move from a stationary state in a parallel direction to the center horizontal axis to which the pendulums are attached. Thus, to overcome the limited driving capability of one- and two-pendulum driven spherical robots, a passive version of a spherical robot, called KisBot II, was developed with a curved two-pendulum driving mechanism operated by a joystick. However, this paper presents an active upgraded version of KisBot II that includes a DSP-based control system and Task-based software architecture for driving control and data communication, respectively. A dynamic model for two-pendulum driving is derived using the Lagrange equation method, and a feedback controller for linear driving using two pendulums is then constructed based on the dynamic model. Experiments with several motions verify the driving efficiency of the proposed novel spherical robot.
Kallman, T. R.; Wilkes, B. J.; Krolik, J. H.; Green, Richard
1993-01-01
Line profile data are used to test a simple kinematic model - spherically symmetric gravitational free fall - in which the number of free parameters is limited by requiring physical self-consistency. The predictions of this model are fitted to high-resolution spectra of the stronger rest-frame UV emission lines in 12 quasars with z of about 2. It is found that if all the lines are radiated predominantly from the illuminated faces of the emission-line clouds, the profiles of Ly-alpha, N V 1240 A, and C IV 1549 A can be simultaneously well fitted with very similar parameters for all 12 quasars. It is concluded that spherically symmetric gravitational free fall does not correctly describe the dynamics of quasar broad emission-line regions.
Non-adiabatic spherical collapse with a two-fluid atmosphere
Govender, M
2014-01-01
In this work we present an exact model of a spherically symmetric star undergoing dissipative collapse in the form of a radial heat flux. The interior of the star is matched smoothly to the generalised Vaidya line element representing a two-fluid atmosphere comprising null radiation and a string fluid. The influence of the string density on the thermal behaviour of the model is investigated by employing a causal heat transport equation of Maxwell-Cattaneo form.
Theoretical Study of a Spherical Plasma Focus
Ay, Yasar
A theoretical model is developed for two concentric electrodes spherical plasma focus device in order to investigate the plasma sheath dynamics, radiative emission, and the ion properties. The work focuses on the model development of the plasma sheath dynamics and its validation, followed by studying of the radiation effects and the beam-ion properties in such unique geometry as a pulsed source for neutrons, soft and hard x-rays, and electron and ion beams. Chapter 1 is an introduction on fusion systems including plasma focus. Chapter 2 is an extensive literature survey on plasma focus modeling and experiments including the various radiations and their mechanism. Chapter 3 details modeling and validation of the plasma sheath dynamics model with comparison between hydrogen, deuterium, tritium and deuterium-tritium mixture for the production of pulsed neutrons. Chapter 4 is a study of the radiative phase, in which neutron yield is investigated, as well as the predicted beam-ion properties. Chapter 5 summarizes and discusses the results. Chapter 6 provides concluding remarks and proposed future works. The phases of the developed model are the rundown phase I, rundown phase II, the reflected phase and a radiative phase. The rundown phase I starts immediately after the completion of the gas breakdown and ends when the current sheath reaches the equator point of the spherical shape. Then immediately followed by rundown phase II to start and it ends when the shock front hits the axis, which is the beginning of the reflected shock phase. Reflected shock front moves towards the incoming current sheath and meets it which is both the end of the reflected shock phase and the beginning of the radiative phase. After the reflected shock front and the current sheath meet, the current sheath continues to move radially inward by compressing the produced plasma column until it reaches the axis. Since the discharge current contains important information about the plasma dynamic
Hydrogenic Donor in a Spherical Quantum Dot with Different Confinements
Institute of Scientific and Technical Information of China (English)
A. John Peter; K. Navaneethakrishnan
2009-01-01
Binding energies of a hydrogenic donor in a spherical GaAs quantum dot surrounded by Ga1-xAlxAs matrix are calculated. The results are presented for realistic barrier heights corresponding to different values of x (x < 0.4). The calculations are performed under two different conditions: (i) a spherical dot with square well confinement and (ii) a dot with parabolic potential well confinement. The results show that (i) the donor ionization energies are always higher under parabolic confinement as compared to a dot of the same radius under square well confinement and (ii) the oscillator strengths coupling ground state with excited states are two orders larger under parabolic confinement. Our results are in agreement with the results of other researchers.
Fine Spectra of Symmetric Toeplitz Operators
Directory of Open Access Journals (Sweden)
Muhammed Altun
2012-01-01
Full Text Available The fine spectra of 2-banded and 3-banded infinite Toeplitz matrices were examined by several authors. The fine spectra of n-banded triangular Toeplitz matrices and tridiagonal symmetric matrices were computed in the following papers: Altun, “On the fine spectra of triangular toeplitz operators” (2011 and Altun, “Fine spectra of tridiagonal symmetric matrices” (2011. Here, we generalize those results to the (2+1-banded symmetric Toeplitz matrix operators for arbitrary positive integer .
Classification of symmetric toroidal orbifolds
Energy Technology Data Exchange (ETDEWEB)
Fischer, Maximilian; Ratz, Michael; Torrado, Jesus [Technische Univ. Muenchen, Garching (Germany). Physik-Department; Vaudrevange, Patrick K.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-09-15
We provide a complete classification of six-dimensional symmetric toroidal orbifolds which yield N{>=}1 supersymmetry in 4D for the heterotic string. Our strategy is based on a classification of crystallographic space groups in six dimensions. We find in total 520 inequivalent toroidal orbifolds, 162 of them with Abelian point groups such as Z{sub 3}, Z{sub 4}, Z{sub 6}-I etc. and 358 with non-Abelian point groups such as S{sub 3}, D{sub 4}, A{sub 4} etc. We also briefly explore the properties of some orbifolds with Abelian point groups and N=1, i.e. specify the Hodge numbers and comment on the possible mechanisms (local or non-local) of gauge symmetry breaking.
Classification of symmetric toroidal orbifolds
Energy Technology Data Exchange (ETDEWEB)
Fischer, Maximilian; Ratz, Michael; Torrado, Jesus [Technische Univ. Muenchen, Garching (Germany). Physik-Department; Vaudrevange, Patrick K.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-09-15
We provide a complete classification of six-dimensional symmetric toroidal orbifolds which yield N{>=}1 supersymmetry in 4D for the heterotic string. Our strategy is based on a classification of crystallographic space groups in six dimensions. We find in total 520 inequivalent toroidal orbifolds, 162 of them with Abelian point groups such as Z{sub 3}, Z{sub 4}, Z{sub 6}-I etc. and 358 with non-Abelian point groups such as S{sub 3}, D{sub 4}, A{sub 4} etc. We also briefly explore the properties of some orbifolds with Abelian point groups and N=1, i.e. specify the Hodge numbers and comment on the possible mechanisms (local or non-local) of gauge symmetry breaking.
Symmetric functions and Hall polynomials
MacDonald, Ian Grant
1998-01-01
This reissued classic text is the acclaimed second edition of Professor Ian Macdonald's groundbreaking monograph on symmetric functions and Hall polynomials. The first edition was published in 1979, before being significantly expanded into the present edition in 1995. This text is widely regarded as the best source of information on Hall polynomials and what have come to be known as Macdonald polynomials, central to a number of key developments in mathematics and mathematical physics in the 21st century Macdonald polynomials gave rise to the subject of double affine Hecke algebras (or Cherednik algebras) important in representation theory. String theorists use Macdonald polynomials to attack the so-called AGT conjectures. Macdonald polynomials have been recently used to construct knot invariants. They are also a central tool for a theory of integrable stochastic models that have found a number of applications in probability, such as random matrices, directed polymers in random media, driven lattice gases, and...
A Minimally Symmetric Higgs Boson
Low, Ian
2014-01-01
Models addressing the naturalness of a light Higgs boson typically employ symmetries, either bosonic or fermionic, to stabilize the Higgs mass. We consider a setup with the minimal amount of symmetries: four shift symmetries acting on the four components of the Higgs doublet, subject to the constraints of linearly realized SU(2)xU(1) electroweak symmetry. Up to terms that explicitly violate the shift symmetries, the effective lagrangian can be derived, irrespective of the spontaneously broken group G in the ultraviolet, and is universal in all models where the Higgs arises as a pseudo-Nambu-Goldstone boson (PNGB). Very high energy scatterings of vector bosons could provide smoking gun signals of a minimally symmetric Higgs boson.
Computing symmetric colorings of the dihedral group
Zelenyuk, Yuliya
2016-06-01
A symmetry on a group G is a mapping G ∋ x ↦ gx-1 g ∈ G, where g ∈ G. A subset A ⊆ G is symmetric if it is invariant under some symmetry, that is, A = gA-1g. The notion of symmetry has interesting relations to enumerative combinatorics. A coloring is symmetric if χ(gx-1g) = χ(x) for some g ∈ G. We discuss an approach how to compute the number of symmetric r-colorings for any finite group. Using this approach we derive the formula for the number of symmetric r-colorings of the dihedral group D3.
Radially Symmetric Motions of Nonlinearly Viscoelastic Bodies Under Live Loads
Stepanov, Alexey B.; Antman, Stuart S.
2017-08-01
This paper treats radially symmetric motions of nonlinearly viscoelastic circular-cylindrical and spherical shells subjected to the live loads of centrifugal force and (time-dependent) hydrostatic pressures. The governing equations are exact versions of those for 3-dimensional continuum mechanics (so shell does not connote an approximate via some shell theory). These motions are governed by quasilinear third-order parabolic-hyperbolic equations having but one independent spatial variable. The principal part of such a partial differential equation is determined by a general family of nonlinear constitutive equations. The presence of strains in two orthogonal directions requires a careful treatment of constitutive restrictions that are physically natural and support the analysis. The interaction of geometrically exact formulations, the compatible use of general constitutive equations for material response, and the presence of live loads show how these factors play crucial roles in the behavior of solutions. In particular, for different kinds of live loads there are thresholds separating materials that produce qualitatively different dynamical behavior. The analysis (using classical methods) covers infinite-time blowup for cylindrical shells subject to centrifugal forces, infinite-time blowup for cylindrical shells subject to steady and time-dependent hydrostatic pressures, finite-time blowup for spherical shells subject to steady and time-dependent hydrostatic pressures, and the preclusion of total compression. This paper concludes with a sketch (using some modern methods) of the existence of regular solutions until the time of blowup.
Developement of Spherical Polyurethane Beads
Institute of Scientific and Technical Information of China (English)
K. Maeda; H. Ohmori; H. Gyotoku
2005-01-01
@@ 1Results and Discussion We established a new method to produce the spherical polyurethane beads which have narrower distribution of particle size. This narrower distribution was achieved by the polyurethane prepolymer which contains ketimine as a blocked chain-extending agent. Firstly, the prepolymer is dispersed into the aqueous solution containing surfactant. Secondaly, water comes into the inside of prepolymer as oil phase. Thirdly, ketimine is hydrolyzed to amine, and amine reacts with prepolymer immediately to be polyurethane.Our spherical polyurethane beads are very suitable for automotive interior parts especially for instrument panel cover sheet producing under the slush molding method, because of good process ability, excellent durability to the sunlight and mechanical properties at low temperature. See Fig. 1 ,Fig. 2 and Fig. 3 (Page 820).
Miniaturization of Spherical Magnetodielectric Antennas
DEFF Research Database (Denmark)
Hansen, Troels Vejle
The fundamental limitations in performance of electrically small antennas (ESAs) - and how far these may be approached - have been of great interest for over a century. Particularly over the past few decades, it has become increasingly relevant and important, to approach these limits in view...... to the important antenna parameters of radiation efficiency e and impedance bandwidth. For single-mode antennas the fundamental minimum Q is the Chu lower bound. In this Ph.D. dissertation, the topic is miniaturization of spherical antennas loaded by an internal magnetodielectric core. The goal is to determine......, quantify, and assess the effects of an internal material loading upon antenna performance, including its potentials towards miniaturization. Emphasis have been upon performing an exhaustive and exact analysis of rigorous validity covering a large class of spherical antennas. In the context of this study...
Geodesics of Spherical Dilaton Spacetimes
Institute of Scientific and Technical Information of China (English)
ZENG Yi; L(U) Jun-Li; WANG Yong-Jiu
2006-01-01
The properties of spherical dilaton black hole spacetimes are investigated through a study of their geodesies. The closed and non-closed orbits of test particles are analysed using the effective potential and phase-plane method. The stability and types of orbits are determined in terms of the energy and angular momentum of the test particles. The conditions of the existence of circular orbits for a spherical dilaton spacetime with an arbitrary dilaton coupling constant a are obtained. The properties of the orbits and in particular the position of the innermost stable circular orbit are compared to those of the Reissner-Nordstrom spacetime. The circumferential radius of innermost stable circular orbit and the corresponding angular momentum of the test particles increase for a≠0.
Molecular Simulations using Spherical Harmonics
Institute of Scientific and Technical Information of China (English)
CAI, Wen-Sheng; XU, Jia-Wei; SHAO, Xue-Guang; MAIGRET, Bernard
2003-01-01
Computer-aided drug design is to develop a chemical that binds to a target macromolecule known to play a key role in a disease state. In recognition of ligands by their protein receptors,molecular surfaces are often used because they represent the interacting part of molecules and they should reflex the complementarity between ligand and receptor. However, assessing the surface complementarity by searching all relative position of two surfaces is often computationally expensive. The complementarity of lobe-hole is very important in protein-ligand interactions. Spherical harmonic models based on expansions of spherical harmonic functions were used as a fingerprint to approximate the binding cavity and the ligand, respectively. This defines a new way to identify the complementarity between lobes and holes. The advantage of this method is that two spherical harmonic surfaces to be compared can be defined separately. This method can be used as a filter to eliminate candidates among a large number of conformations, and it will speed up the docking procedure. Therefore, it is possible to select complementary ligands or complementary conformations of a ligand and the macromoleeules, by comparing their fingerprints previously stored in a database.
Automorphism groups of causal symmetric spaces of Cayley type and bounded symmetric domains
Institute of Scientific and Technical Information of China (English)
Soji; Kaneyuki
2005-01-01
Symmetric spaces of Cayley type are a higher dimensional analogue of a onesheeted hyperboloid in R3. They form an important class of causal symmetric spaces. To a symmetric space of Cayley type M, one can associate a bounded symmetric domain of tube type D. We determine the full causal automorphism group of M. This clarifies the relation between the causal automorphism group and the holomorphic automorphism group of D.
Discontinuous Galerkin finite element methods for radiative transfer in spherical symmetry
Kitzmann, D; Patzer, A B C
2016-01-01
The discontinuous Galerkin finite element method (DG-FEM) is successfully applied to treat a broad variety of transport problems numerically. In this work, we use the full capacity of the DG-FEM to solve the radiative transfer equation in spherical symmetry. We present a discontinuous Galerkin method to directly solve the spherically-symmetric radiative transfer equation as a two-dimensional problem. The transport equation in spherical atmospheres is more complicated than in the plane-parallel case due to the appearance of an additional derivative with respect to the polar angle. The DG-FEM formalism allows for the exact integration of arbitrarily complex scattering phase functions, independent of the angular mesh resolution. We show that the discontinuous Galerkin method is able to describe accurately the radiative transfer in extended atmospheres and to capture discontinuities or complex scattering behaviour which might be present in the solution of certain radiative transfer tasks and can, therefore, cause...
Partially locally rotationally symmetric perfect fluid cosmologies
Mustapha, N; Van Elst, H; Marklund, M; Mustapha, Nazeem; Ellis, George F R; Elst, Henk van; Marklund, Mattias
2000-01-01
We show that there are no new consistent perfect fluid cosmologies with the kinematic variables and the electric and magnetic parts of the Weyl curvature all rotationally symmetric about a common axis in an open neighbourhood ${\\cal U}$ of an event. The consistent solutions of this kind are either locally rotationally symmetric, or are subcases of the Szekeres model.
CANONICAL EXTENSIONS OF SYMMETRIC LINEAR RELATIONS
Sandovici, Adrian; Davidson, KR; Gaspar, D; Stratila, S; Timotin, D; Vasilescu, FH
2006-01-01
The concept of canonical extension of Hermitian operators has been recently introduced by A. Kuzhel. This paper deals with a generalization of this notion to the case of symmetric linear relations. Namely, canonical regular extensions of symmetric linear relations in Hilbert spaces are studied. The
Symmetric products, permutation orbifolds and discrete torsion
Bántay, P
2000-01-01
Symmetric product orbifolds, i.e. permutation orbifolds of the full symmetric group S_{n} are considered by applying the general techniques of permutation orbifolds. Generating functions for various quantities, e.g. the torus partition functions and the Klein-bottle amplitudes are presented, as well as a simple expression for the discrete torsion coefficients.
Inversion-symmetric topological insulators
Hughes, Taylor L.; Prodan, Emil; Bernevig, B. Andrei
2011-06-01
We analyze translationally invariant insulators with inversion symmetry that fall outside the current established classification of topological insulators. These insulators exhibit no edge or surface modes in the energy spectrum and hence they are not edge metals when the Fermi level is in the bulk gap. However, they do exhibit protected modes in the entanglement spectrum localized on the cut between two entangled regions. Their entanglement entropy cannot be made to vanish adiabatically, and hence the insulators can be called topological. There is a direct connection between the inversion eigenvalues of the Hamiltonian band structure and the midgap states in the entanglement spectrum. The classification of protected entanglement levels is given by an integer N, which is the difference between the negative inversion eigenvalues at inversion symmetric points in the Brillouin zone, taken in sets of 2. When the Hamiltonian describes a Chern insulator or a nontrivial time-reversal invariant topological insulator, the entirety of the entanglement spectrum exhibits spectral flow. If the Chern number is zero for the former, or time reversal is broken in the latter, the entanglement spectrum does not have spectral flow, but, depending on the inversion eigenvalues, can still exhibit protected midgap bands similar to impurity bands in normal semiconductors. Although spectral flow is broken (implying the absence of real edge or surface modes in the original Hamiltonian), the midgap entanglement bands cannot be adiabatically removed, and the insulator is “topological.” We analyze the linear response of these insulators and provide proofs and examples of when the inversion eigenvalues determine a nontrivial charge polarization, a quantum Hall effect, an anisotropic three-dimensional (3D) quantum Hall effect, or a magnetoelectric polarization. In one dimension, we establish a link between the product of the inversion eigenvalues of all occupied bands at all inversion
Joglekar, Yogesh N
2010-01-01
We study the properties of a parity- and time-reversal- (PT) symmetric tight-binding chain of size N with position-dependent hopping amplitude. In contrast to the fragile PT-symmetric phase of a chain with constant hopping and imaginary impurity potentials, we show that, under very general conditions, our model is {\\it always} in the PT-symmetric phase. We numerically obtain the energy spectrum and the density of states of such a chain, and show that they are widely tunable. By studying the size-dependence of inverse participation ratios, we show that although the chain is not translationally invariant, most of its eigenstates are extended. Our results indicate that tight-binding models with non-Hermitian PT-symmetric hopping have a robust PT-symmetric phase and rich dynamics.
Classification of Entanglement in Symmetric States
Aulbach, Martin
2011-01-01
Quantum states that are symmetric with respect to permutations of their subsystems appear in a wide range of physical settings, and they have a variety of promising applications in quantum information science. In this thesis the entanglement of symmetric multipartite states is categorised, with a particular focus on the pure multi-qubit case and the geometric measure of entanglement. An essential tool for this analysis is the Majorana representation, a generalisation of the single-qubit Bloch sphere representation, which allows for a unique representation of symmetric n qubit states by n points on the surface of a sphere. Here this representation is employed to search for the maximally entangled symmetric states of up to 12 qubits in terms of the geometric measure, and an intuitive visual understanding of the upper bound on the maximal symmetric entanglement is given. Furthermore, it will be seen that the Majorana representation facilitates the characterisation of entanglement equivalence classes such as Stoc...
Exact EGB models for spherical static perfect fluids
Hansraj, Sudan; Maharaj, Sunil D
2015-01-01
We obtain a new exact solution to the field equations in the EGB modified theory of gravity for a 5-dimensional spherically symmetric static distribution. By using a transformation, the study is reduced to the analysis of a single second order nonlinear differential equation. In general the condition of pressure isotropy produces a first order differential equation which is an Abel equation of the second kind. An exact solution is found. The solution is examined for physical admissability. In particular a set of constants is found which ensures that a pressure-free hypersurface exists which defines the boundary of the distribution. Additionally the isotropic pressure and the energy density are shown to be positive within the radius of the sphere. The adiabatic sound speed criterion is also satisfied within the fluid ensuring a subluminal sound speed. Furthermore, the weak, strong and dominant conditions hold throughout the distribution. On setting the Gauss-Bonnet coupling to zero, an exact solution for 5-dim...
Self-similar spherical metrics with tangential pressure
Gair, J R
2002-01-01
A family of spherically symmetric spacetimes is discussed, which have anisotropic pressure and possess a homothetic Killing vector. The spacetimes are composed of dust with a tangential pressure provided by angular momentum of the dust particles. The solution is given implicitly by an elliptic integral and depends on four arbitrary functions. These represent the initial configurations of angular momentum, mass, energy and position of the shells. The solution is derived by imposing self-similarity in the coordinates R, the shell label, and tau, the proper time experienced by the dust. Conditions for evolution without shell crossing and a description of singularity formation are given and types of solution discussed. General properties of the solutions are illustrated by reference to a particular case, which represents a universe that exists for an infinite time, but in which every shell expands and recollapses in a finite time.
Covariance in models of loop quantum gravity: Spherical symmetry
Bojowald, Martin; Reyes, Juan D
2015-01-01
Spherically symmetric models of loop quantum gravity have been studied recently by different methods that aim to deal with structure functions in the usual constraint algebra of gravitational systems. As noticed by Gambini and Pullin, a linear redefinition of the constraints (with phase-space dependent coefficients) can be used to eliminate structure functions, even Abelianizing the more-difficult part of the constraint algebra. The Abelianized constraints can then easily be quantized or modified by putative quantum effects. As pointed out here, however, the method does not automatically provide a covariant quantization, defined as an anomaly-free quantum theory with a classical limit in which the usual (off-shell) gauge structure of hypersurface deformations in space-time appears. The holonomy-modified vacuum theory based on Abelianization is covariant in this sense, but matter theories with local degrees of freedom are not. Detailed demonstrations of these statements show complete agreement with results of ...
Spherical Cows in the Sky with Fab Four
Kaloper, Nemanja
2013-01-01
We explore spherically symmetric static solutions in a subclass of unitary scalar-tensor theories of gravity, called the `Fab Four' models. The weak field large distance solutions may be phenomenologically viable, but only if the Gauss-Bonnet term is negligible. Only in this limit will the Vainshtein mechanism work consistently. Further, classical constraints and unitarity bounds constrain the models quite tightly. Nevertheless, in the limits where the range of individual terms at large scales is respectively Kinetic Braiding, Horndeski, and Gauss-Bonnet, the horizon scale effects may occur while the theory satisfies Solar system constraints and, marginally, unitarity bounds. On the other hand, to bring the cutoff down to below a millimeter constrains all the couplings scales such that `Fab Fours' can't be heard outside of the Solar system.
Measurement of Poloidal Velocity on the National Spherical Torus Experiment
Energy Technology Data Exchange (ETDEWEB)
Ronald E. Bell and Russell Feder
2010-06-04
A diagnostic suite has been developed to measure impurity poloidal flow using charge exchange recombination spectroscopy on the National Spherical Torus Experiment. Toroidal and poloidal viewing systems measure all quantities required to determine the radial electric field. Two sets of up/down symmetric poloidal views are used to measure both active emission in the plane of the neutral heating beams and background emission in a radial plane away from the neutral beams. Differential velocity measurements isolate the line-integrated poloidal velocity from apparent flows due to the energy-dependent chargeexchange cross section. Six f/1.8 spectrometers measure 276 spectra to obtain 75 active and 63 background channels every 10 ms. Local measurements from a similar midplane toroidal viewing system are mapped into two dimensions to allow the inversion of poloidal line-integrated measurements to obtain local poloidal velocity profiles. Radial resolution after inversion is 0.6-1.8 cm from the plasma edge to the center.
Baryon symmetric big bang cosmology
Stecker, F. W.
1978-01-01
Both the quantum theory and Einsteins theory of special relativity lead to the supposition that matter and antimatter were produced in equal quantities during the big bang. It is noted that local matter/antimatter asymmetries may be reconciled with universal symmetry by assuming (1) a slight imbalance of matter over antimatter in the early universe, annihilation, and a subsequent remainder of matter; (2) localized regions of excess for one or the other type of matter as an initial condition; and (3) an extremely dense, high temperature state with zero net baryon number; i.e., matter/antimatter symmetry. Attention is given to the third assumption, which is the simplest and the most in keeping with current knowledge of the cosmos, especially as pertains the universality of 3 K background radiation. Mechanisms of galaxy formation are discussed, whereby matter and antimatter might have collided and annihilated each other, or have coexisted (and continue to coexist) at vast distances. It is pointed out that baryon symmetric big bang cosmology could probably be proved if an antinucleus could be detected in cosmic radiation.
Symmetric Structure in Logic Programming
Institute of Scientific and Technical Information of China (English)
Jin-Zhao Wu; Harald Fecher
2004-01-01
It is argued that some symmetric structure in logic programs could be taken into account when implementing semantics in logic programming. This may enhance the declarative ability or expressive power of the semantics. The work presented here may be seen as representative examples along this line. The focus is on the derivation of negative information and some other classic semantic issues. We first define a permutation group associated with a given logic program. Since usually the canonical models used to reflect the common sense or intended meaning are minimal or completed models of the program, we expose the relationships between minimal models and completed models of the original program and its so-called G-reduced form newly-derived via the permutation group defined. By means of this G-reduced form, we introduce a rule to assume negative information termed G-CWA, which is actually a generalization of the GCWA. We also develop the notions of G-definite, G-hierarchical and G-stratified logic programs, which are more general than definite, hierarchical and stratified programs, and extend some well-known declarative and procedural semantics to them, respectively.
PT-Symmetric Quantum Electrodynamics
Bender, C M; Milton, K A; Shajesh, K V; Bender, Carl M.; Cavero-Pelaez, Ines; Milton, Kimball A.
2005-01-01
The Hamiltonian for quantum electrodynamics becomes non-Hermitian if the unrenormalized electric charge $e$ is taken to be imaginary. However, if one also specifies that the potential $A^\\mu$ in such a theory transforms as a pseudovector rather than a vector, then the Hamiltonian becomes PT symmetric. The resulting non-Hermitian theory of electrodynamics is the analog of a spinless quantum field theory in which a pseudoscalar field $\\phi$ has a cubic self-interaction of the form $i\\phi^3$. The Hamiltonian for this cubic scalar field theory has a positive spectrum, and it has recently been demonstrated that the time evolution of this theory is unitary. The proof of unitarity requires the construction of a new operator called C, which is then used to define an inner product with respect to which the Hamiltonian is self-adjoint. In this paper the corresponding C operator for non-Hermitian quantum electrodynamics is constructed perturbatively. This construction demonstrates the unitarity of the theory. Non-Hermit...
Substring-Searchable Symmetric Encryption
Directory of Open Access Journals (Sweden)
Chase Melissa
2015-06-01
Full Text Available In this paper, we consider a setting where a client wants to outsource storage of a large amount of private data and then perform substring search queries on the data – given a data string s and a search string p, find all occurrences of p as a substring of s. First, we formalize an encryption paradigm that we call queryable encryption, which generalizes searchable symmetric encryption (SSE and structured encryption. Then, we construct a queryable encryption scheme for substring queries. Our construction uses suffix trees and achieves asymptotic efficiency comparable to that of unencrypted suffix trees. Encryption of a string of length n takes O(λn time and produces a ciphertext of size O(λn, and querying for a substring of length m that occurs k times takes O(λm+k time and three rounds of communication. Our security definition guarantees correctness of query results and privacy of data and queries against a malicious adversary. Following the line of work started by Curtmola et al. (ACM CCS 2006, in order to construct more efficient schemes we allow the query protocol to leak some limited information that is captured precisely in the definition. We prove security of our substring-searchable encryption scheme against malicious adversaries, where the query protocol leaks limited information about memory access patterns through the suffix tree of the encrypted string.
A method of spherical harmonic analysis in the geosciences via hierarchical Bayesian inference
Muir, J. B.; Tkalčić, H.
2015-11-01
The problem of decomposing irregular data on the sphere into a set of spherical harmonics is common in many fields of geosciences where it is necessary to build a quantitative understanding of a globally varying field. For example, in global seismology, a compressional or shear wave speed that emerges from tomographic images is used to interpret current state and composition of the mantle, and in geomagnetism, secular variation of magnetic field intensity measured at the surface is studied to better understand the changes in the Earth's core. Optimization methods are widely used for spherical harmonic analysis of irregular data, but they typically do not treat the dependence of the uncertainty estimates on the imposed regularization. This can cause significant difficulties in interpretation, especially when the best-fit model requires more variables as a result of underestimating data noise. Here, with the above limitations in mind, the problem of spherical harmonic expansion of irregular data is treated within the hierarchical Bayesian framework. The hierarchical approach significantly simplifies the problem by removing the need for regularization terms and user-supplied noise estimates. The use of the corrected Akaike Information Criterion for picking the optimal maximum degree of spherical harmonic expansion and the resulting spherical harmonic analyses are first illustrated on a noisy synthetic data set. Subsequently, the method is applied to two global data sets sensitive to the Earth's inner core and lowermost mantle, consisting of PKPab-df and PcP-P differential traveltime residuals relative to a spherically symmetric Earth model. The posterior probability distributions for each spherical harmonic coefficient are calculated via Markov Chain Monte Carlo sampling; the uncertainty obtained for the coefficients thus reflects the noise present in the real data and the imperfections in the spherical harmonic expansion.
Cooperative effects in spherical spasers
DEFF Research Database (Denmark)
Bordo, Vladimir
2017-01-01
a shell/core contains an arbitrarily large number of active molecules in the vicinity of a metallic core/shell. An essential aspect of the theory is an ab initio account of the feedback from the core/shell boundaries which significantly modifies the molecular dynamics. The theory provides rigorous, albeit......A fully analytical semiclassical theory of cooperative optical processes which occur in an ensemble of molecules embedded in a spherical core-shell nanoparticle is developed from first principles. Both the plasmonic Dicke effect and spaser generation are investigated for the designs in which...
Intermittency in spherical Couette dynamos
Raynaud, Raphaël; 10.1103/PhysRevE.87.033011
2013-01-01
We investigate dynamo action in three-dimensional numerical simulations of turbulent spherical Couette flows. Close to the onset of dynamo action, the magnetic field exhibits an intermittent behavior, characterized by a series of short bursts of the magnetic energy separated by low-energy phases. We show that this behavior corresponds to the so-called on-off intermittency. This behavior is here reported for dynamo action with realistic boundary conditions. We investigate the role of magnetic boundary conditions in this phenomenon.
Spherical Orbifolds for Cosmic Topology
Kramer, Peter
2012-01-01
Harmonic analysis is a tool to infer cosmic topology from the measured astrophysical cosmic microwave background CMB radiation. For overall positive curvature, Platonic spherical manifolds are candidates for this analysis. We combine the specific point symmetry of the Platonic manifolds with their deck transformations. This analysis in topology leads from manifolds to orbifolds. We discuss the deck transformations of the orbifolds and give basis functions for the harmonic analysis as linear combinations of Wigner polynomials on the 3-sphere. They provide new tools for detecting cosmic topology from the CMB radiation.