7,302 research outputs found
A Method for Calculating the Structure of (Singular) Spacetimes in the Large
A formalism and its numerical implementation is presented which allows to
calculate quantities determining the spacetime structure in the large directly.
This is achieved by conformal techniques by which future null infinity
(\Scri{}^+) and future timelike infinity () are mapped to grid points on
the numerical grid. The determination of the causal structure of singularities,
the localization of event horizons, the extraction of radiation, and the
avoidance of unphysical reflections at the outer boundary of the grid, are
demonstrated with calculations of spherically symmetric models with a scalar
field as matter and radiation model.Comment: 29 pages, AGG2
General Relativistic Scalar Field Models in the Large
For a class of scalar fields including the massless Klein-Gordon field the
general relativistic hyperboloidal initial value problems are equivalent in a
certain sense. By using this equivalence and conformal techniques it is proven
that the hyperboloidal initial value problem for those scalar fields has an
unique solution which is weakly asymptotically flat. For data sufficiently
close to data for flat spacetime there exist a smooth future null infinity and
a regular future timelike infinity.Comment: 22 pages, latex, AGG 1
The Nature of Physical Knowledge
https://epublications.marquette.edu/mupress-book/1020/thumbnail.jp
First-order symmetrizable hyperbolic formulations of Einstein's equations including lapse and shift as dynamical fields
First-order hyperbolic systems are promising as a basis for numerical
integration of Einstein's equations. In previous work, the lapse and shift have
typically not been considered part of the hyperbolic system and have been
prescribed independently. This can be expensive computationally, especially if
the prescription involves solving elliptic equations. Therefore, including the
lapse and shift in the hyperbolic system could be advantageous for numerical
work. In this paper, two first-order symmetrizable hyperbolic systems are
presented that include the lapse and shift as dynamical fields and have only
physical characteristic speeds.Comment: 11 page
Persistence of Problematic Sexual Behaviors in Children
The purpose of this study was to identify personal and family predictors and correlates of persistence of problematic sexual behaviors (PSB) in children. Participants were the families of 49 children (ages 4–11 years) referred by Child Protective Services in 4 administrative districts of Quebec. Caregivers completed interviews and questionnaires twice at a 1-year interval. Results showed that 43% of children persisted with PSB. When age was controlled, greater exposure to sexualized behaviors in the family proved both a correlate and a predictor of PSB persistence in children 12 months later.\ud
Externalizing problems and somatic complaints emerged as correlates of PSB as well. Maltreatment subtypes did not predict PSB persistence
A formal framework for a nonlocal generalization of Einstein's theory of gravitation
The analogy between electrodynamics and the translational gauge theory of
gravity is employed in this paper to develop an ansatz for a nonlocal
generalization of Einstein's theory of gravitation. Working in the linear
approximation, we show that the resulting nonlocal theory is equivalent to
general relativity with "dark matter". The nature of the predicted "dark
matter", which is the manifestation of the nonlocal character of gravity in our
model, is briefly discussed. It is demonstrated that this approach can provide
a basis for the Tohline-Kuhn treatment of the astrophysical evidence for dark
matter.Comment: 13 pages RevTex, no figures; v2: minor corrections, reference added,
matches published versio
Retinal oscillations carry visual information to cortex
Thalamic relay cells fire action potentials that transmit information from
retina to cortex. The amount of information that spike trains encode is usually
estimated from the precision of spike timing with respect to the stimulus.
Sensory input, however, is only one factor that influences neural activity. For
example, intrinsic dynamics, such as oscillations of networks of neurons, also
modulate firing pattern. Here, we asked if retinal oscillations might help to
convey information to neurons downstream. Specifically, we made whole-cell
recordings from relay cells to reveal retinal inputs (EPSPs) and thalamic
outputs (spikes) and analyzed these events with information theory. Our results
show that thalamic spike trains operate as two multiplexed channels. One
channel, which occupies a low frequency band (<30 Hz), is encoded by average
firing rate with respect to the stimulus and carries information about local
changes in the image over time. The other operates in the gamma frequency band
(40-80 Hz) and is encoded by spike time relative to the retinal oscillations.
Because these oscillations involve extensive areas of the retina, it is likely
that the second channel transmits information about global features of the
visual scene. At times, the second channel conveyed even more information than
the first.Comment: 21 pages, 10 figures, submitted to Frontiers in Systems Neuroscienc
Lattice calculations on the spectrum of Dirac and Dirac-K\"ahler operators
We present a matrix technique to obtain the spectrum and the analytical index
of some elliptic operators defined on compact Riemannian manifolds. The method
uses matrix representations of the derivative which yield exact values for the
derivative of a trigonometric polynomial. These matrices can be used to find
the exact spectrum of an elliptic operator in particular cases and in general,
to give insight into the properties of the solution of the spectral problem. As
examples, the analytical index and the eigenvalues of the Dirac operator on the
torus and on the sphere are obtained and as an application of this technique,
the spectrum of the Dirac-Kahler operator on the sphere is explored.Comment: 11 page
Numerical Relativity Using a Generalized Harmonic Decomposition
A new numerical scheme to solve the Einstein field equations based upon the
generalized harmonic decomposition of the Ricci tensor is introduced. The
source functions driving the wave equations that define generalized harmonic
coordinates are treated as independent functions, and encode the coordinate
freedom of solutions. Techniques are discussed to impose particular gauge
conditions through a specification of the source functions. A 3D, free
evolution, finite difference code implementing this system of equations with a
scalar field matter source is described. The second-order-in-space-and-time
partial differential equations are discretized directly without the use first
order auxiliary terms, limiting the number of independent functions to
fifteen--ten metric quantities, four source functions and the scalar field.
This also limits the number of constraint equations, which can only be enforced
to within truncation error in a numerical free evolution, to four. The
coordinate system is compactified to spatial infinity in order to impose
physically motivated, constraint-preserving outer boundary conditions. A
variant of the Cartoon method for efficiently simulating axisymmetric
spacetimes with a Cartesian code is described that does not use interpolation,
and is easier to incorporate into existing adaptive mesh refinement packages.
Preliminary test simulations of vacuum black hole evolution and black hole
formation via scalar field collapse are described, suggesting that this method
may be useful for studying many spacetimes of interest.Comment: 18 pages, 6 figures; updated to coincide with journal version, which
includes some expanded discussions and a new appendix with a stability
analysis of a simplified problem using the same discretization scheme
described in the pape
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