316 research outputs found

    Gravitational waveforms from unequal-mass binaries with arbitrary spins under leading order spin-orbit coupling

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    The paper generalizes the structure of gravitational waves from orbiting spinning binaries under leading order spin-orbit coupling, as given in the work by K\"onigsd\"orffer and Gopakumar [PRD 71, 024039 (2005)] for single-spin and equal-mass binaries, to unequal-mass binaries and arbitrary spin configurations. The orbital motion is taken to be quasi-circular and the fractional mass difference is assumed to be small against one. The emitted gravitational waveforms are given in analytic form.Comment: 13 pages, 2 figures, submitted to PRD on 11 Sep. 200

    Ultrarelativistic boost of the black ring

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    We investigate the ultrarelativistic boost of the five-dimensional Emparan-Reall non-rotating black ring. Following the classical method of Aichelburg and Sexl, we determine the gravitational field generated by a black ring moving ``with the speed of light'' in an arbitrary direction. In particular, we study in detail two different boosts along axes orthogonal and parallel to the plane of the ring circle, respectively. In both cases, after the limit one obtains a five-dimensional impulsive pp-wave propagating in Minkowski spacetime. The curvature singularity of the original static spacetime becomes a singular source within the wave front, in the shape of a ring or a rod according to the direction of the boost. In the case of an orthogonal boost, the wave front contains also a remnant of the original disk-shaped membrane as a component of the Ricci tensor (which is everywhere else vanishing). We also analyze the asymptotic properties of the boosted black ring at large spatial distances from the singularity, and its behaviour near the sources. In the limit when the singularity shrinks to a point, one recovers the well known five-dimensional analogue of the Aichelburg-Sexl ``monopole'' solution.Comment: 10 pages, 2 figures, REVTeX 4. v2: added boost in an arbitrary direction, one new figure, one new reference. To appear in Phys. Rev.

    Far-off-resonant wave interaction in one-dimensional photonic crystals with quadratic nonlinearity

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    We extend a recently developed Hamiltonian formalism for nonlinear wave interaction processes in spatially periodic dielectric structures to the far-off-resonant regime, and investigate numerically the three-wave resonance conditions in a one-dimensional optical medium with χ(2)\chi^{(2)} nonlinearity. In particular, we demonstrate that the cascading of nonresonant wave interaction processes generates an effective χ(3)\chi^{(3)} nonlinear response in these systems. We obtain the corresponding coupling coefficients through appropriate normal form transformations that formally lead to the Zakharov equation for spatially periodic optical media.Comment: 14 pages, 4 figure

    Algorithms for zero-dimensional ideals using linear recurrent sequences

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    Inspired by Faug\`ere and Mou's sparse FGLM algorithm, we show how using linear recurrent multi-dimensional sequences can allow one to perform operations such as the primary decomposition of an ideal, by computing the annihilator of one or several such sequences.Comment: LNCS, Computer Algebra in Scientific Computing CASC 201

    Construction of C 2 Pythagorean-hodograph interpolating splines by the homotopy method

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    The complex representation of polynomial Pythagorean-hodograph (PH) curves allows the problem of constructing a C 2 PH quintic “spline” that interpolates a given sequence of points p 0 , p 1 ,..., p N and end-derivatives d 0 and d N to be reduced to solving a “tridiagonal” system of N quadratic equations in N complex unknowns. The system can also be easily modified to incorporate PH-spline end conditions that bypass the need to specify end-derivatives. Homotopy methods have been employed to compute all solutions of this system, and hence to construct a total of 2 N +1 distinct interpolants for each of several different data sets. We observe empirically that all but one of these interpolants exhibits undesirable “looping” behavior (which may be quantified in terms of the elastic bending energy , i.e., the integral of the square of the curvature with respect to arc length). The remaining “good” interpolant, however, is invariably a fairer curve-having a smaller energy and a more even curvature distribution over its extent-than the corresponding “ordinary” C 2 cubic spline. Moreover, the PH spline has the advantage that its offsets are rational curves and its arc length is a polynomial function of the curve parameter.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41719/1/10444_2005_Article_BF02124754.pd

    A New Method of Generating Exact Inflationary Solutions

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    The mechanism of the initial inflation of the universe is based on gravitationally coupled scalar fields Ď•\phi. Various scenarios are distinguished by the choice of an {\it effective self--interaction potential} U(Ď•)U(\phi) which simulates a {\it temporarily} non--vanishing {\em cosmological term}. Using the Hubble expansion parameter HH as a new ``time" coordinate, we can formally derive the {\it general} Robertson--Walker metric for a {\em spatially flat} cosmos. Our new method provides a classification of allowed inflationary potentials and is broad enough to embody all known {\it exact} solutions involving one scalar field as special cases. Moreover, we present new inflationary and deflationary exact solutions and can easily predict the influence of the form of U(Ď•)U(\phi) on density perturbations.Comment: 32 pages, REVTeX, 9 postscript figures (or hardcopy) available upon request, Cologne-thp-1994-H

    Chaotic eigenfunctions in momentum space

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    We study eigenstates of chaotic billiards in the momentum representation and propose the radially integrated momentum distribution as useful measure to detect localization effects. For the momentum distribution, the radially integrated momentum distribution, and the angular integrated momentum distribution explicit formulae in terms of the normal derivative along the billiard boundary are derived. We present a detailed numerical study for the stadium and the cardioid billiard, which shows in several cases that the radially integrated momentum distribution is a good indicator of localized eigenstates, such as scars, or bouncing ball modes. We also find examples, where the localization is more strongly pronounced in position space than in momentum space, which we discuss in detail. Finally applications and generalizations are discussed.Comment: 30 pages. The figures are included in low resolution only. For a version with figures in high resolution see http://www.physik.uni-ulm.de/theo/qc/ulm-tp/tp99-2.htm

    Harmonic Sums and Mellin Transforms up to two-loop Order

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    A systematic study is performed on the finite harmonic sums up to level four. These sums form the general basis for the Mellin transforms of all individual functions fi(x)f_i(x) of the momentum fraction xx emerging in the quantities of massless QED and QCD up to two--loop order, as the unpolarized and polarized splitting functions, coefficient functions, and hard scattering cross sections for space and time-like momentum transfer. The finite harmonic sums are calculated explicitly in the linear representation. Algebraic relations connecting these sums are derived to obtain representations based on a reduced set of basic functions. The Mellin transforms of all the corresponding Nielsen functions are calculated.Comment: 44 pages Latex, contract number adde

    Opposing Tumor-Promoting and -Suppressive Functions of Rictor/mTORC2 Signaling in Adult Glioma and Pediatric SHH Medulloblastoma.

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    Most human cancers arise from stem and progenitor cells by the sequential accumulation of genetic and epigenetic alterations, while cancer modeling typically requires simultaneous multiple oncogenic events. Here, we show that a single p53 mutation, despite causing no defect in the mouse brain, promoted neural stem and progenitor cells to spontaneously accumulate oncogenic alterations, including loss of multiple chromosomal (chr) regions syntenic to human chr10 containing Pten, forming malignant gliomas with PI3K/Akt activation. Rictor/mTORC2 loss inhibited Akt signaling, greatly delaying and reducing glioma formation by suppressing glioma precursors within the subventricular zone stem cell niche. Rictor/mTORC2 loss delayed timely differentiation of granule cell precursors (GCPs) during cerebellar development, promoting sustained GCP proliferation and medulloblastoma formation, which recapitulated critical features of TP53 mutant sonic hedgehog (SHH) medulloblastomas with GLI2 and/or N-MYC amplification. Our study demonstrates that Rictor/mTORC2 has opposing functions in neural stem cells and GCPs in the adult and the developing brain, promoting malignant gliomas and suppressing SHH-medulloblastoma formation, respectively
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