1,250 research outputs found
Adaptive Mesh Refinement for Characteristic Grids
I consider techniques for Berger-Oliger adaptive mesh refinement (AMR) when
numerically solving partial differential equations with wave-like solutions,
using characteristic (double-null) grids. Such AMR algorithms are naturally
recursive, and the best-known past Berger-Oliger characteristic AMR algorithm,
that of Pretorius & Lehner (J. Comp. Phys. 198 (2004), 10), recurses on
individual "diamond" characteristic grid cells. This leads to the use of
fine-grained memory management, with individual grid cells kept in
2-dimensional linked lists at each refinement level. This complicates the
implementation and adds overhead in both space and time.
Here I describe a Berger-Oliger characteristic AMR algorithm which instead
recurses on null \emph{slices}. This algorithm is very similar to the usual
Cauchy Berger-Oliger algorithm, and uses relatively coarse-grained memory
management, allowing entire null slices to be stored in contiguous arrays in
memory. The algorithm is very efficient in both space and time.
I describe discretizations yielding both 2nd and 4th order global accuracy.
My code implementing the algorithm described here is included in the electronic
supplementary materials accompanying this paper, and is freely available to
other researchers under the terms of the GNU general public license.Comment: 37 pages, 15 figures (40 eps figure files, 8 of them color; all are
viewable ok in black-and-white), 1 mpeg movie, uses Springer-Verlag svjour3
document class, includes C++ source code. Changes from v1: revised in
response to referee comments: many references added, new figure added to
better explain the algorithm, other small changes, C++ code updated to latest
versio
The Singularity Threshold of the Nonlinear Sigma Model Using 3D Adaptive Mesh Refinement
Numerical solutions to the nonlinear sigma model (NLSM), a wave map from 3+1
Minkowski space to S^3, are computed in three spatial dimensions (3D) using
adaptive mesh refinement (AMR). For initial data with compact support the model
is known to have two regimes, one in which regular initial data forms a
singularity and another in which the energy is dispersed to infinity. The
transition between these regimes has been shown in spherical symmetry to
demonstrate threshold behavior similar to that between black hole formation and
dispersal in gravitating theories. Here, I generalize the result by removing
the assumption of spherical symmetry. The evolutions suggest that the
spherically symmetric critical solution remains an intermediate attractor
separating the two end states.Comment: 5 pages, 5 figures, 1 table; To be published in Phys. Rev. D.; Added
discussion of initial data; Added figure and reference
Fibers and global geometry of functions
Since the seminal work of Ambrosetti and Prodi, the study of global folds was
enriched by geometric concepts and extensions accomodating new examples. We
present the advantages of considering fibers, a construction dating to Berger
and Podolak's view of the original theorem. A description of folds in terms of
properties of fibers gives new perspective to the usual hypotheses in the
subject. The text is intended as a guide, outlining arguments and stating
results which will be detailed elsewhere
Critical Collapse of the Massless Scalar Field in Axisymmetry
We present results from a numerical study of critical gravitational collapse
of axisymmetric distributions of massless scalar field energy. We find
threshold behavior that can be described by the spherically symmetric critical
solution with axisymmetric perturbations. However, we see indications of a
growing, non-spherical mode about the spherically symmetric critical solution.
The effect of this instability is that the small asymmetry present in what
would otherwise be a spherically symmetric self-similar solution grows. This
growth continues until a bifurcation occurs and two distinct regions form on
the axis, each resembling the spherically symmetric self-similar solution. The
existence of a non-spherical unstable mode is in conflict with previous
perturbative results, and we therefore discuss whether such a mode exists in
the continuum limit, or whether we are instead seeing a marginally stable mode
that is rendered unstable by numerical approximation.Comment: 11 pages, 8 figure
Critical Collapse of Cylindrically Symmetric Scalar Field in Four-Dimensional Einstein's Theory of Gravity
Four-dimensional cylindrically symmetric spacetimes with homothetic
self-similarity are studied in the context of Einstein's Theory of Gravity, and
a class of exact solutions to the Einstein-massless scalar field equations is
found. Their local and global properties are investigated and found that they
represent gravitational collapse of a massless scalar field. In some cases the
collapse forms black holes with cylindrical symmetry, while in the other cases
it does not. The linear perturbations of these solutions are also studied and
given in closed form. From the spectra of the unstable eigen-modes, it is found
that there exists one solution that has precisely one unstable mode, which may
represent a critical solution, sitting on a boundary that separates two
different basins of attraction in the phase space.Comment: Some typos are corrected. The final version to appear in Phys. Rev.
Superdeformed rotational bands in the Mercury region; A Cranked Skyrme-Hartree-Fock-Bogoliubov study
A study of rotational properties of the ground superdeformed bands in \Hg{0},
\Hg{2}, \Hg{4}, and \Pb{4} is presented. We use the cranked
Hartree-Fock-Bogoliubov method with the {\skm} parametrization of the Skyrme
force in the particle-hole channel and a seniority interaction in the pairing
channel. An approximate particle number projection is performed by means of the
Lipkin-Nogami prescription. We analyze the proton and neutron quasiparticle
routhians in connection with the present information on about thirty presently
observed superdeformed bands in nuclei close neighbours of \Hg{2}.Comment: 26 LaTeX pages, 14 uuencoded postscript figures included, Preprint
IPN-TH 93-6
The Similarity Hypothesis in General Relativity
Self-similar models are important in general relativity and other fundamental
theories. In this paper we shall discuss the ``similarity hypothesis'', which
asserts that under a variety of physical circumstances solutions of these
theories will naturally evolve to a self-similar form. We will find there is
good evidence for this in the context of both spatially homogenous and
inhomogeneous cosmological models, although in some cases the self-similar
model is only an intermediate attractor. There are also a wide variety of
situations, including critical pheneomena, in which spherically symmetric
models tend towards self-similarity. However, this does not happen in all cases
and it is it is important to understand the prerequisites for the conjecture.Comment: to be submitted to Gen. Rel. Gra
Measurements of inclusive W+jets production rates as a function of jet transverse momentum in ppbar collisions at sqrt{s}=1.96 TeV
This Letter describes measurements of inclusive W (--> e nu) + n jet cross
sections (n = 1-4), presented as total inclusive cross sections and
differentially in the nth jet transverse momentum. The measurements are made
using data corresponding to an integrated luminosity of 4.2 fb-1 collected by
the D0 detector at the Fermilab Tevatron Collider, and achieve considerably
smaller uncertainties on W +jets production cross sections than previous
measurements. The measurements are compared to next-to-leading order
perturbative QCD (pQCD) calculations in the n =1-3 jet multiplicity bins and to
leading order pQCD calculations in the 4-jet bin. The measurements are
generally in agreement with pQCD predictions, although certain regions of phase
space are identified where the calculations could be improved
Proton-Antiproton Pair Production in Two-Photon Collisions at LEP
The reaction e^+e^- -> e^+e^- proton antiproton is studied with the L3
detector at LEP. The analysis is based on data collected at e^+e^-
center-of-mass energies from 183 GeV to 209 GeV, corresponding to an integrated
luminosity of 667 pb^-1. The gamma gamma -> proton antiproton differential
cross section is measured in the range of the two-photon center-of-mass energy
from 2.1 GeV to 4.5 GeV. The results are compared to the predictions of the
three-quark and quark-diquark models
Measurement of Exclusive rho+rho- Production in Mid-Virtuality Two-Photon Interactions and Study of the gamma gamma* -> rho rho Process at LEP
Exclusive rho+rho- production in two-photon collisions between a quasi-real
photon, gamma, and a mid-virtuality photon, gamma*, is studied with data
collected at LEP at centre-of-mass energies root(s)=183-209GeV with a total
integrated luminosity of 684.8pb^-1. The cross section of the gamma gamma* ->
rho+ rho- process is determined as a function of the photon virtuality, Q^2,
and the two-photon centre-of-mass energy, W_gg, in the kinematic region:
0.2GeV^2 < Q^2 <0.85GeV^2 and 1.1GeV < W_gg < 3GeV. These results, together
with previous L3 measurements of rho0 rho0 and rho+ rho- production, allow a
study of the gamma gamma* -> rho rho process over the Q^2-region 0.2GeV^2 < Q^2
< 30 GeV^2
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