51,015 research outputs found
Rotational Instabilities in Post-Collapse Stellar Cores
A core-collapse supernova might produce large amplitude gravitational waves
if, through the collapse process, the inner core can aquire enough rotational
energy to become dynamically unstable. In this report I present the results of
3-D numerical simulations of core collapse supernovae. These simulations
indicate that for some initial conditions the post-collapse inner core is
indeed unstable. However, for the cases considered, the instability does not
produce a large gravitational-wave signal.Comment: 12 pages, 10 figures; prepared for the proceedings of the workshop on
Astrophysical Sources of Gravitational Radiatio
Black Hole Thermodynamics in a Box
Simple calculations indicate that the partition function for a black hole is
defined only if the temperature is fixed on a finite boundary. Consequences of
this result are discussed. (Contribution to the Proceedings of the Lanczos
Centenary Conference.)Comment: 3 pages (plain TeX
Primitive Integral Solutions to x^2 + y^3 = z^{10}
We classify primitive integer solutions to x^2 + y^3 = z^10. The technique is
to combine modular methods at the prime 5, number field enumeration techniques
in place of modular methods at the prime 2, Chabauty techniques for elliptic
curves over number fields, and local methods.Comment: 11 pages; fixed typos, updated reference
Reference Fluids as Standards of Space and Time
The idea that spacetime points are to be identified by a fleet of
clock--carrying particles can be traced to the earliest days of general
relativity. Such a fleet of clocks can be described phenomenologically as a
reference fluid. One approach to the problem of time consists in coupling the
metric to a reference fluid and solving the super--Hamiltonian constraint for
the momentum conjugate to the clock time variable. The resolved constraint
leads to a functional Schr\"{o}dinger equation and formally to a conserved
inner product. The reference fluid that is described phenomenologically as
incoherent dust has the extraordinary property that the true Hamiltonian
density for the coupled system depends only on the gravitational variables. The
dust particles also endow space with a privileged system of coordinates that
allows the supermomentum constraint to be solved explicitly. (Contribution to
the Proceedings of the Lanczos Centenary Conference.)Comment: (plain TeX, 3 pages
Duality Invariance of Black Hole Creation Rates
Pair creation of electrically charged black holes and its dual process, pair
creation of magnetically charged black holes, are considered. It is shown that
the creation rates are equal provided the boundary conditions for the two
processes are dual to one another. This conclusion follows from a careful
analysis of boundary terms and boundary conditions for the Maxwell action.Comment: 8 pages, REVTE
Imaging Three-Dimensional Relative Sources from Nuclear Reactions
One can access the space-time development of a heavy-ion reaction directly by
imaging the source function from two particle correlation functions. In the
case of like-charged pions, this imaging can be recast as a Fourier inversion
problem. We will demonstrate how this inversion can be performed on full
three-dimensional (i.e. in long, side and out coordinates) experimentally
determined correlation functions. We will discuss the resulting three
dimensional images of the relative sources. Finally, we will discuss how to
perform the full three dimensional inversion for particles whose final state
interactions are more complicated than those of the pions.Comment: 5 pages, 2 figures. Uses modifed sprocl.sty (included). Centenial APS
Heavy-Ion Mini-Symposium proceedings contributio
Probing the puncture for black hole simulations
With the puncture method for black hole simulations, the second infinity of a
wormhole geometry is compactified to a single "puncture point" on the
computational grid. The region surrounding the puncture quickly evolves to a
trumpet geometry. The computational grid covers only a portion of the trumpet
throat. It ends at a boundary whose location depends on resolution. This raises
the possibility that perturbations in the trumpet geometry could propagate down
the trumpet throat, reflect from the puncture boundary, and return to the black
hole exterior with a resolution--dependent time delay. Such pathological
behavior is not observed. This is explained by the observation that some
perturbative modes propagate in the conformal geometry, others propagate in the
physical geometry. The puncture boundary exists only in the physical geometry.
The modes that propagate in the physical geometry are always directed away from
the computational domain at the puncture boundary. The finite difference
stencils ensure that these modes are advected through the boundary with no
coupling to the modes that propagate in the conformal geometry. These results
are supported by numerical experiments with a code that evolves spherically
symmetric gravitational fields with standard Cartesian finite difference
stencils. The code uses the Baumgarte--Shapiro--Shibata--Nakamura formulation
of Einstein's equations with 1+log slicing and gamma--driver shift conditions.Comment: Minor typos corrected and references updated. To be published in PR
MyCaffe: A Complete C# Re-Write of Caffe with Reinforcement Learning
Over the past few years Caffe, from Berkeley AI Research, has gained a strong
following in the deep learning community with over 15K forks on the
github.com/BLVC/Caffe site. With its well organized, very modular C++ design it
is easy to work with and very fast. However, in the world of Windows
development, C# has helped accelerate development with many of the enhancements
that it offers over C++, such as garbage collection, a very rich .NET
programming framework and easy database access via Entity Frameworks. So how
can a C# developer use the advances of C# to take full advantage of the
benefits offered by the Berkeley Caffe deep learning system? The answer is the
fully open source, 'MyCaffe' for Windows .NET programmers. MyCaffe is an open
source, complete C# language re-write of Berkeley's Caffe. This article
describes the general architecture of MyCaffe including the newly added
MyCaffeTrainerRL for Reinforcement Learning. In addition, this article
discusses how MyCaffe closely follows the C++ Caffe, while talking efficiently
to the low level NVIDIA CUDA hardware to offer a high performance, highly
programmable deep learning system for Windows .NET programmers.Comment: 13 pages, 9 figure
Puncture Evolution of Schwarzschild Black Holes
The moving puncture method is analyzed for a single, non-spinning black hole.
It is shown that the puncture region is not resolved by current numerical
codes. As a result, the geometry near the puncture appears to evolve to an
infinitely long cylinder of finite areal radius. The puncture itself actually
remains at spacelike infinity throughout the evolution. In the limit of
infinite resolution the data never become stationary. However, at any
reasonable finite resolution the grid points closest to the puncture are
rapidly drawn into the black hole interior by the Gamma-driver shift condition.
The data can then evolve to a stationary state. These results suggest that the
moving puncture technique should be viewed as a type of "natural excision".Comment: This is the final version to be published in PRD. One important
change: the phrase "excision by under resolution" is replaced by the more
appropriate phrase "natural excision
Is it possible to reconstruct the freeze-out duration of heavy-ion collisions using tomography?
We investigate what conditions allow us to extract the relative distribution
of freeze-out space and time points in an arbitrary reference frame using
tomography and source imaging. The source function may be extracted from the
two-particle correlation function measured in heavy-ion collisions using
imaging techniques. This imaged source function is related to the relative
distribution of freeze-out space and time points through a generalization of
the Radon transform found in tomography. Using tomography, the imaged source
function may be converted into the relative freeze-out distribution in the
frame of interest. We describe how the tomography may be performed in practice.Comment: 11 pages, uses RevTeX. Submitted to Phys. Rev. Let
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