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(24 Apr 2013)
posted to no-tag
by BenWhale
on 2013-05-14 23:13:18
Abstract
The linearised general conformal field equations in their first and second order form are used to study the behaviour of the spin-2 zero-rest-mass equation on Minkowski background in the vicinity of space-like infinity. ...
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(14 June 2009)
posted to no-tag
by BenWhale
on 2013-04-16 05:11:28
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posted to no-tag
by BenWhale
on 2013-04-14 01:19:03
Abstract
We give an up-to-date perspective with a general overview of the theory of causal properties, the derived causal structures, their classification and applications and the definition and construction of causal boundaries and of causal symmetries, mostly for Lorentzian manifolds but also in more abstract settings. ...
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(1 Feb 2013)
posted to no-tag
by BenWhale
on 2013-02-17 10:50:07
Abstract
Linear perturbations on Minkowski space are used to probe numerically the remote region of an asymptotically flat space-time close to spatial infinity. The study is undertaken within the framework of Friedrich's conformal field equations and the corresponding conformal representation of spatial infinity as a cylinder. The system under consideration is the (linear) zero-rest-mass equation for a spin-2 field. The spherical symmetry of the underlying background is used to decompose the field into separate non-interacting multipoles. It is demonstrated that it is possible to reach null-infinity from initial data on ...
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Annals of Global Analysis and Geometry In Annals of Global Analysis and Geometry, Vol. 14, No. 3. (1 August 1996), pp. 301-312, doi:10.1007/bf00054475
posted to no-tag
by BenWhale
on 2012-12-19 21:50:37
Abstract
Splitting theorems for stable causal spacetimes admitting certain metric related reference frames are obtained in connection to timelike geodesic incompletenes. ...
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ArXiv Mathematics e-prints (22 Oct 2001)
Abstract
We prove some Bernstein theorems for entire space-like submanifolds in pseudo-Euclidean spaces and, as a corollary, we obtain a new proof of the Calabi-Pogorelov theorem on global solutions of Monge-Ampere equations. ...
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Abstract
The boundary-value problem is discretized on several grids (or finite-element spaces) of widely different mesh sizes. Interactions between these levels enable us (i) to solve the possibly nonlinear system of $n$ discrete equations in $O(n)$ operations ($40n$ additions and shifts for Poisson problems); (ii) to conveniently adapt the discretization (the local mesh size, local order of approximation, etc.) to the evolving solution in a nearly optimal way, obtaining "$∞$-order" approximations and low $n$, even when singularities are present. General theoretical analysis ...
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Abstract
We find candidate macroscopic gravity duals for scale-invariant but non-Lorentz invariant fixed points, which do not have particle number as a conserved quantity. We compute two-point correlation functions which exhibit novel behavior relative to their AdS counterparts, and find holographic renormalization group flows to conformal field theories. Our theories are characterized by a dynamical critical exponent z, which governs the anisotropy between spatial and temporal scaling t→λzt, x→λx; we focus on the case with z=2. Such theories describe multicritical points in ...
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posted to no-tag
by BenWhale
on 2012-12-18 01:29:56
Abstract
I find a class of black hole solutions to a (3+1) dimensional theory gravity coupled to abelian gauge fields with negative cosmological constant that has been proposed as the dual theory to a Lifshitz theory describing critical phenomena in (2+1) dimensions. These black holes are all asymptotic to a Lifshitz fixed point geometry and depend on a single parameter that determines both their area (or size) and their charge. Most of the solutions are obtained numerically, but an ...
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Abstract
I summarize results from a numerical study of spherically symmetric collapse of a massless scalar field. I consider families of solutions, scrS[p], with the property that a critical parameter value, p*, separates solutions containing black holes from those which do not. I present evidence in support of conjectures that (1) the strong-field evolution in the p→p* limit is universal and generates structure on arbitrarily small spatiotemporal scales and (2) the masses of black holes which form satisfy a power law MBH∝‖p-p*‖γ, ...
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posted to no-tag
by BenWhale
on 2012-12-18 01:18:43
Abstract
Cauchy problems for Einstein's conformal vacuum field equations are reduced to Cauchy problems for first order quasilinear symmetric hyperbolic systems. The “hyperboloidal initial value” problem, where Cauchy data are given on a spacelike hypersurface which intersects past null infinity at a spacelike two-surface, is discussed and translated into the conformally related picture. It is shown that for conformal hyperboloidal initial data of classH ...
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posted to no-tag
by BenWhale
on 2012-12-18 01:15:22
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posted to no-tag
by BenWhale
on 2012-12-18 01:10:27
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posted to no-tag
by BenWhale
on 2012-12-18 01:08:02
Abstract
A calculus for general relativity is developed in which the basic role of tensors is taken over by spinors. The Riemann-Christoffel tensor is written in a spinor form according to a scheme of Witten. It is shown that the curvature of empty space can be uniquely characterized by a totally symmetric four-index spinor which satisfies a first order equation formally identical with one for a zero rest-mass particle of spin two. However, the derivatives used here are covariant, so that on ...
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Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, Vol. 378, No. 1774. (26 October 1981), pp. 401-421, doi:10.1098/rspa.1981.0159
posted to no-tag
by BenWhale
on 2012-12-18 01:04:25
Abstract
The asymptotic characteristic initial value problem for Einstein's vacuum field equations where data are given on an incoming null hypersurface and on part of past null infinity is reduced to a characteristic initial value problem for a first-order quasilinear symmetric hyperbolic system of differential equations for which existence and uniqueness of solutions can be shown. It is delineated how the same method can be applied to the standard Cauchy problems for Einstein's vacuum and conformal vacuum equations. ...
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posted to no-tag
by BenWhale
on 2012-12-18 01:01:10
Abstract
There has been significant interest in the last several years in studying possible gravitational duals, known as Lifshitz spacetimes, to anisotropically scaling field theories by adding matter to distort the asymptotics of an AdS spacetime. We point out that the putative ground state for the most heavily studied example of such a spacetime, that with a flat spatial section, suffers from a naked singularity. Furthermore, stringy effects can not resolve this singularity without producing significant quantum corrections to the entire spacetime, ...
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General Relativity and Gravitation In General Relativity and Gravitation, Vol. 43, No. 5. (5 November 2011), pp. 1391-1400, doi:10.1007/s10714-010-1117-y
posted to no-tag
by BenWhale
on 2012-12-18 00:59:19
Abstract
We generalize Penrose’s notion of conformal infinity of spacetime, to situations with anisotropic scaling. This is relevant not only for Lifshitz-type anisotropic gravity models, but also in standard general relativity and string theory, for spacetimes exhibiting a natural asymptotic anisotropy. Examples include the Lifshitz and Schrödinger spaces (proposed as AdS/CFT duals of nonrelativistic field theories), warped AdS ...
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(27 Sep 2012)
posted to no-tag
by BenWhale
on 2012-12-18 00:50:41
Abstract
In this paper we provide a global investigation of the geometry of parallelizable manifolds (or absolute parallelism geometry) frequently used for application. We discuss the different linear connections and curvature tensors from a global point of view. We give an existence and uniqueness theorem for a remarkable linear connection, called the canonical connection. Different curvature tensors are expressed in a compact form in terms of the torsion tensor of the canonical connection only. Using the Bianchi identities, some interesting identities are derived. An important special fourth order tensor, which ...
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(30 Aug 2012)
posted to no-tag
by BenWhale
on 2012-12-18 00:50:12
Abstract
When a lump of matter falls into a black hole it is expected that a marginally trapped tube when hit moves outwards everywhere, even in regions not yet in causal contact with the infalling matter. But to describe this phenomenon analytically in 3+1 dimensions is difficult since gravitational radiation is emitted. By considering a particle falling into a toy model of a black hole in 2+1 dimensions an exact description of this non-local behaviour of a marginally trapped tube is found. ...
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(26 Jul 2012)
Abstract
We present a short review of geometric and algebraic approach to causal cones and describe cone preserving transformations and their relationship with causal structure related to special and general theory of relativity. We describe Lie groups, especially matrix Lie groups, homogeneous and symmetric spaces and causal cones and certain implications of these concepts in special and general theory of relativity related to causal structure and topology of space-time. We compare and contrast the results on causal relations with those in the literature for general space-times and compare these ...
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(30 May 2012)
posted to no-tag
by BenWhale
on 2012-12-18 00:49:39
Abstract
We develop a method for evaluation of A. Einstein's strength of systems of partial differential and difference equations based on the computation of Hilbert-type dimension polynomials of the associated differential and difference field extensions. Also we present algorithms for such computations, which are based on the Gröbner basis method adjusted for the modules over rings of differential, difference and inversive difference operators. The developed technique is applied to some fundamental systems of PDEs of mathematical physics such as the diffusion equation, Maxwell equations and equations for an electromagnetic field ...
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(20 Aug 2012)
Abstract
We propose that the Standard Model (SM) Higgs is responsible for generating the cosmological perturbations of the universe by acting as an isocurvature mode during a de Sitter inflationary stage. In view of the recent ATLAS and CMS results for the Higgs mass, this can happen if the Hubble rate during inflation is in the range $(10^10- 10^14)$ GeV (depending on the SM parameters). Implications for the detection of primordial tensor perturbations through the $B$-mode of CMB polarization via the PLANCK satellite are discussed. For example, if the ...
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(2007)
posted to no-tag
by BenWhale
on 2012-11-27 21:21:21
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posted to no-tag
by BenWhale
on 2012-11-27 21:08:32
Abstract
We discuss properties of conformal geodesics on general, vacuum, and warped product space-times and derive a system of conformal deviation equations. It is then shown how to construct on the Schwarzschild-Kruskal space-time globally defined systems of conformal Gauss coordinates which extend smoothly and without degeneracy to future and past null infinity. ...
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Abstract
Stability for nonlinear convection problems using centered difference schemes require the addition of artificial dissipation. In this paper we present dissipation operators that preserve both stability and accuracy for high order finite difference approximations of initial boundary value problems. ...
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Abstract
A famous essay by Wigner is reexamined in view of more recent developments around its topic, together with some remarks on the metaphysical character of its main question about mathematics and natural sciences. ...
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Abstract
The spectral method with discrete spherical harmonics transform plays an important role in many applications. In spite of its advantages, the spherical harmonics transform has a drawback of high computational complexity, which is determined by that of the associated Legendre transform, and the direct computation requires time of O(N3) for cut-off frequency N. In this paper, we propose a fast approximate algorithm for the associated Legendre transform. Our algorithm evaluates the transform by means of polynomial interpolation accelerated by the Fast ...
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SIAM Journal on Scientific and Statistical Computing, Vol. 12, No. 1. (January 1991), pp. 158-179, doi:10.1137/0912009
posted to no-tag
by BenWhale
on 2012-11-23 03:49:19
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(1996)
posted to no-tag
by BenWhale
on 2012-11-23 00:24:40
Abstract
. In this paper, we propose an algorithm for the stable and efficient computation of Fourier expansions of square integrable functions on the unit sphere S ae R 3 , as well as for the evaluation of these Fourier expansions at special knots. The heart of the algorithm is an efficient realization of discrete Legendre function transforms based on a modified and stabilized version of the Driscoll--Healy algorithm. 1991 Mathematics Subject Classification. Primary 65T99, 33C35, 33C25, 42C10 Key ...
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In The Journal of Fourier Analysis and Applications (1996), pp. 341-385
posted to no-tag
by BenWhale
on 2012-11-23 00:18:37
Abstract
Earlier work by Driscoll and Healy [16] has produced an e#cient algorithm for computing the Fourier transform of band-limited functions on the 2-sphere. In this paper we present a reformulation and variation of the original algorithm which results in a greatly improved inverse transform, and consequent improved convolution algorithm for such functions. All require at most O(N log 2 N ) operations where N is the number of sample points. We also address implementation considerations and give heuristics for ...
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posted to no-tag
by BenWhale
on 2012-11-23 00:00:26
Abstract
In this paper we describe algorithms for the numerical computation of Fourier transforms of tensor fields on the two-sphere, S2. These algorithms reduce the computation of an expansion on tensor spherical harmonics to expansions in scalar spherical harmonics, and hence can take advantage of recent improvements in the efficiency of computation of scalar spherical harmonic transforms. ...
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In SIAM J. Sci. Comput (2004), pp. 1903-1928
posted to no-tag
by BenWhale
on 2012-11-22 22:28:37
Abstract
An algorithm is introduced for the rapid evaluation at appropriately chosen nodes on the two-dimensional sphere S 2 in � 3 of functions specified by their spherical harmonic expansions (known as the inverse spherical harmonic transform), and for the evaluation of the coefficients in spherical harmonic expansions of functions specified by their values at appropriately chosen points on S 2 (known as the forward spherical harmonic transform). The procedure is numerically stable and requires an amount of CPU time proportional to ...
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Acta crystallographica. Section D, Biological crystallography, Vol. 58, No. Pt 8. (August 2002), pp. 1282-1286
Abstract
A computationally efficient method is presented - 'fast rotational matching' or FRM - that significantly accelerates the search of the three rotational degrees of freedom (DOF) in biomolecular matching problems. This method uses a suitable parametrization of the three-dimensional rotation group along with spherical harmonics, which allows efficient computation of the Fourier Transform of the rotational correlation function. Previous methods have used Fourier techniques only ...
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In Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing (2003), pp. 156-164
Abstract
One of the challenges in 3D shape matching arises from the fact that in many applications, models should be considered to be the same if they differ by a rotation. Consequently, when comparing two models, a similarity metric implicitly provides the measure of similarity at the optimal alignment. Explicitly solving for the optimal alignment is usually impractical. So, two general methods have been proposed for addressing this issue: (1) Every model is represented using rotation invariant descriptors. (2) Every model is ...
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Abstract
As the number of 3D models available on the Web grows, there is an increasing need for a search engine to help people find them. Unfortunately, traditional text-based search techniques are not always effective for 3D data. In this article, we investigate new shape-based search methods. The key challenges are to develop query methods simple enough for novice users and matching algorithms robust enough to work for arbitrary polygonal models. We present a Web-based search engine system that supports queries based ...
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posted to no-tag
by BenWhale
on 2012-11-22 21:59:54
Abstract
Astronomy is entering a new era as multiple, large area, digital sky surveys are in production. The resulting datasets are truly remarkable in their own right; however, a revolutionary step arises in the aggregation of complimentary multi-wavelength surveys (i.e. the cross-identification of a billion sources). Federating these different datasets, however, is an extremely challenging task. With this task in mind, we have identified several areas where community standardization can provide enormous benefits in order to develop the techniques and technologies necessary ...
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SIAM Journal on Numerical Analysis, Vol. 22, No. 6. (December 1985), pp. 1107-1115, doi:10.1137/0722066
posted to no-tag
by BenWhale
on 2012-11-22 21:51:56
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posted to no-tag
by BenWhale
on 2012-11-22 21:40:16
Abstract
We present a fast algorithm for generating full-sky, high-resolution (~5') simulations of the cosmic microwave background anisotropy pattern. We also discuss the inverse problem, that of evaluating from such a map the full set of a <IMG SRC="http://ej.iop.org/images/1538-4357/488/2/L63/img1.gif" ALIGN="MIDDLE" ALT="_lm" /> lm values and the spectral coefficients C <IMG SRC="http://ej.iop.org/images/1538-4357/488/2/L63/img2.gif" ALIGN="MIDDLE" ALT="_l" /> l . We show that using an equidistant cylindrical projection of the sky substantially speeds up the calculations. Thus, generating and/or ...
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In Astronomical Data Analysis Software and Systems I (Astronomical Society of the Pacific Conference Series), Vol. 25 (1992), 379
posted to no-tag
by BenWhale
on 2012-11-22 21:30:46
Abstract
The quadrilateralized spherical cube (Chan & O'Neill 1975 and O'Neill & Laubscher 1976) is a geometrical projection well suited for mapping all sky data, as well as to the use of the quad-tree nearest neighbor (rather than rasterized) storage scheme for the the archiving and retrieval of data. The celestial sphere is projected onto the six faces of a cube in a tangent plane projection. The lines of latitude and longitude on each face are then curved such that, when the ...
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posted to no-tag
by BenWhale
on 2012-11-22 21:30:42
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No. DAMTP-1998-78. (29 Jun 1998)
posted to no-tag
by BenWhale
on 2012-11-22 21:14:22
Abstract
We investigate various pixelizations of the sky which allow for fast spherical transforms, for implementation in full sky CMB experiments such as Planck and MAP. We study the effect of varying pixel shape and area on the extraction of the CMB power spectrum. We argue for the benefits of having a truly azimuthal, or `igloo' pixelization. Such pixelizations are simple and allow for fast, exact simulations of pixelized skies. They also allow for precise correction to be made which accounts for the effects of pixel smoothing on extracted ...
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posted to no-tag
by BenWhale
on 2012-11-22 21:10:25
Abstract
For power spectrum estimation, it's important that the pixelization of a CMB sky map be smooth and regular to high degree. With this criterion in mind, the " COBE sky cube" was defined. This Letter has as central theme to further improve on this elegant scheme that uses a cube as projective base —here an icosahedron is used in its place. Although the sky cube is excellent, a further ...
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(06 May 2002)
Abstract
New edition of successful and unique textbook for students in mathematics or theoretical computer science. ...
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posted to no-tag
by BenWhale ✚
on 2012-11-21 22:07:17
along with 1 person
nschaeff
Abstract
A method for numerically expanding an arbitrary function on the sphere in a series of spherical harmonics which makes use of the speed of a fast Fourier transform is described. Discussions of the operation count, storage requirements, accuracy, and an algebraic and a numerical example are included. A comparison with straightforward integration is made throughout. Also, a new method for evaluating the spherical harmonics is discussed. ...
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All Res. J. Phys., Vol. 1, No. 1. (25 May 2011)
posted to no-tag
by BenWhale
on 2012-11-21 22:04:12
Abstract
In many applications data are measured or defined on a spherical manifold; spherical harmonic transforms are then required to access the frequency content of the data. We derive algorithms to perform forward and inverse spin spherical harmonic transforms for functions of arbitrary spin number. These algorithms involve recasting the spin transform on the two-sphere S^2 as a Fourier transform on the two-torus T^2. Fast Fourier transforms are then used to compute Fourier coefficients, which are related to spherical harmonic coefficients through a linear transform. By recasting the problem ...
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posted to no-tag
by BenWhale
on 2012-11-21 21:12:53
Abstract
The concept of orthogonality lies at the very heart of the method of least squares. The normal equations of least squares in their simplest expression state that the residual vector is orthogonal to all of the basis vectors used in the approximating ...
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(1971)
posted to no-tag
by BenWhale
on 2012-11-21 21:01:53
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posted to no-tag
by BenWhale
on 2012-11-21 20:57:41
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