1,011 research outputs found
Hyperbolicity and Constrained Evolution in Linearized Gravity
Solving the 4-d Einstein equations as evolution in time requires solving
equations of two types: the four elliptic initial data (constraint) equations,
followed by the six second order evolution equations. Analytically the
constraint equations remain solved under the action of the evolution, and one
approach is to simply monitor them ({\it unconstrained} evolution). Since
computational solution of differential equations introduces almost inevitable
errors, it is clearly "more correct" to introduce a scheme which actively
maintains the constraints by solution ({\it constrained} evolution). This has
shown promise in computational settings, but the analysis of the resulting
mixed elliptic hyperbolic method has not been completely carried out. We
present such an analysis for one method of constrained evolution, applied to a
simple vacuum system, linearized gravitational waves.
We begin with a study of the hyperbolicity of the unconstrained Einstein
equations. (Because the study of hyperbolicity deals only with the highest
derivative order in the equations, linearization loses no essential details.)
We then give explicit analytical construction of the effect of initial data
setting and constrained evolution for linearized gravitational waves. While
this is clearly a toy model with regard to constrained evolution, certain
interesting features are found which have relevance to the full nonlinear
Einstein equations.Comment: 18 page
Effective non-intercommutation of local cosmic strings at high collision speeds
We present evidence that Abrikosov-Nielsen-Olesen (ANO) strings pass through
each other for very high speeds of approach due to a double intercommutation.
In near-perpendicular collisions numerical simulations give threshold speeds
bounded above by for type I, and by for deep type
II strings. The second intercommutation occurs because at ultra high collision
speeds, the connecting segments formed by the first intercommutation are nearly
static and almost antiparallel, which gives them time to interact and
annihilate. A simple model explains the rough features of the threshold
velocity dependence with the incidence angle. For deep type II strings and
large incidence angles a second effect becomes dominant, the formation of a
loop that catches up with the interpolating segments. The loop is related to
the observed vortex - antivortex reemergence in two-dimensions. In this case
the critical value for double intercommutation can become much lower.Comment: 5 pages, 4 figures. data points added, plots for deep type II regime
showing lower critical velocities, some minor changes in tex
Intercommutation of Semilocal Strings and Skyrmions
We study the intercommuting of semilocal strings and Skyrmions, for a wide
range of internal parameters, velocities and intersection angles by numerically
evolving the equations of motion. We find that the collisions of strings and
strings, strings and Skyrmions, and Skyrmions and Skyrmions, all lead to
intercommuting for a wide range of parameters. Even the collisions of unstable
Skyrmions and strings leads to intercommuting, demonstrating that the
phenomenon of intercommuting is very robust, extending to dissimilar field
configurations that are not stationary solutions. Even more remarkably, at
least for the semilocal U(2) formulation considered here, all intercommutations
trigger a reversion to U(1) Nielsen-Olesen strings.Comment: 4 pages, 4 figures. Fixed typos, added reference
Cosmic string Y-junctions: a comparison between field theoretic and Nambu-Goto dynamics
We explore the formation of cosmic string Y-junctions when strings of two
different types collide, which has recently become important since string
theory can yield cosmic strings of distinct types. Using a model containing two
types of local U(1) string and stable composites, we simulate the collision of
two straight strings and investigate whether the dynamics matches that
previously obtained using the Nambu-Goto action, which is not strictly valid
close to the junction. We find that the Nambu-Goto action performs only
moderately well at predicting when the collision results in the formation of a
pair of Y-junctions (with a composite string connecting them). However, we find
that when they do form, the late time dynamics matches those of the Nambu-Goto
approximation very closely. We also see little radiative emission from the
Y-junction system, which suggests that radiative decay due to bridge formation
does not appear to be a means via which a cosmological network of such string
would rapidly lose energy.Comment: 17 pages, 17 figures; typo correctio
Area Invariance of Apparent Horizons under Arbitrary Boosts
It is a well known analytic result in general relativity that the
2-dimensional area of the apparent horizon of a black hole remains invariant
regardless of the motion of the observer, and in fact is independent of the slice, which can be quite arbitrary in general relativity.
Nonetheless the explicit computation of horizon area is often substantially
more difficult in some frames (complicated by the coordinate form of the
metric), than in other frames. Here we give an explicit demonstration for very
restricted metric forms of (Schwarzschild and Kerr) vacuum black holes. In the
Kerr-Schild coordinate expression for these spacetimes they have an explicit
Lorentz-invariant form. We consider {\it boosted} versions with the black hole
moving through the coordinate system. Since these are stationary black hole
spacetimes, the apparent horizons are two dimensional cross sections of their
event horizons, so we compute the areas of apparent horizons in the boosted
space with (boosted) , and obtain the same result as in the
unboosted case. Note that while the invariance of area is generic, we deal only
with black holes in the Kerr-Schild form, and consider only one particularly
simple change of slicing which amounts to a boost. Even with these restrictions
we find that the results illuminate the physics of the horizon as a null
surface and provide a useful pedagogical tool. As far as we can determine, this
is the first explicit calculation of this type demonstrating the area
invariance of horizons. Further, these calculations are directly relevant to
transformations that arise in computational representation of moving black
holes. We present an application of this result to initial data for boosted
black holes.Comment: 19 pages, 3 figures. Added a new section and 2 plots along with a
coautho
Bipolar molecular outflows driven by hydromagnetic protostellar winds
We demonstrate that magnetically-collimated protostellar winds will sweep
ambient material into thin, radiative, momentum-conserving shells whose
features reproduce those commonly observed in bipolar molecular outflows. We
find the typical position-velocity and mass-velocity relations to occur in
outflows in a wide variety of ambient density distributions, regardless of the
time histories of their driving winds.Comment: 4 pages, 1 figure, submitted to ApJ
Ultra-fast Optical Network Throughput Prediction using Graph Neural Networks
One of the key performance metrics for optical networks is the maximum achievable throughput. Determining it however, is an NP-hard optimisation problem, often solved via computationally expensive integer linear programming (ILP) formulations. Heuristics, in conjunction with sequential loading, are scalable but non-exact. There is, thus, a need for ultra-fast performance evaluation of optical networks. For the first time, we propose message passing neural networks (MPNN), to learn the relationship between the structure and the maximum achievable throughput of optical networks. We demonstrate that MPNNs can accurately predict the maximum achievable throughput while reducing the computational time by 5-orders of magnitude compared to the ILP
Expanding Graph Neural Networks for Ultra-Fast Optical Core Network Throughput Prediction to Large Node Scales
Using maximum achievable throughput as an objective, message passing neural networks (MPNN) are applied to larger optical networks (25-100 nodes), enabling physical properties-aware large-scale topology optimisation in record time, reducing computation time by 5 orders of magnitude, with close to perfect throughput correlation (ρ = 0.986)
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