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