2002
DOI: 10.1103/physrevd.65.064037
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Numerical tests of evolution systems, gauge conditions, and boundary conditions for 1D colliding gravitational plane waves

Abstract: We investigate how the accuracy and stability of numerical relativity simulations of 1D colliding plane waves depends on choices of equation formulations, gauge conditions, boundary conditions, and numerical methods, all in the context of a first-order 3+1 approach to the Einstein equations, with basic variables some combination of first derivatives of the spatial metric and components of the extrinsic curvature tensor. Hyperbolic schemes, specifically variations on schemes proposed by Bona and Massó and Ander… Show more

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Cited by 56 publications
(81 citation statements)
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References 33 publications
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“…With the lowest one corresponding to m π as low as 180 MeV, it is found that, when the quark mass is smaller than that of the strange, a 0 mass levels off, in contrast to those of a 1 and other hadrons that have been calculated on the lattice. This confirms the trend that has been observed in earlier works at higher quark masses in both the quenched and unquenched calculations [7,8,9,10]. The chiral extrapolated mass a 0 = 1.42 ± 0.13 GeV suggests that a 0 (1450) is a qq state.…”
Section: Introductionsupporting
confidence: 79%
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“…With the lowest one corresponding to m π as low as 180 MeV, it is found that, when the quark mass is smaller than that of the strange, a 0 mass levels off, in contrast to those of a 1 and other hadrons that have been calculated on the lattice. This confirms the trend that has been observed in earlier works at higher quark masses in both the quenched and unquenched calculations [7,8,9,10]. The chiral extrapolated mass a 0 = 1.42 ± 0.13 GeV suggests that a 0 (1450) is a qq state.…”
Section: Introductionsupporting
confidence: 79%
“…However, there are several serious problems with this scenario. First, the isovector scalar meson a 0 (1450) is confirmed to be a qq meson in lattice calculations [6,7,8,9, 10] which will be discussed later. As such, the degeneracy of a 0 (1450) and K * 0 (1430), which has a strange quark, cannot be explained if M S is larger than M N by ∼ 250 MeV.…”
Section: Introductionmentioning
confidence: 99%
“…These quantities are evaluated atQ, whereQ is the same quantity as computed in step (3). (11) De-orthonormalize at the cell edge:…”
Section: The Algorithmmentioning
confidence: 99%
“…If the solution domain is a flat manifold but contains complicated internal or external boundaries, it is often possible to introduce a curvilinear grid that conforms to the boundaries [41]. A fundementally different situation arises when the solution domain is a curved manifold, such as the surface of a sphere of radius r embedded in lR 3 . In this situation, the curvature of the manifold modifies the underlying dynamics.…”
Section: Introductionmentioning
confidence: 99%
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