1,036 research outputs found
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
Modelling sulphate stream concentrations in the Black Forest catchments Schluchsee and Villingen
International audienceThe sulphate (SO4) released by mineralisation and desorption from soil can play an important role in determining concentrations of SO4 in streams. The MAGIC model was calibrated for two catchments in the Black Forest, Germany (Schluchsee and Villingen) and SO4 concentrations in the streams for the years 2016 and 2030 were predicted. Special emphasis was placed on the dynamics of soil sulphur (S) pools. At Schluchsee, 90% of soil S is stored in the organic S (Sorg) pool, whereas at Villingen, 54% is in the inorganic (Sinorg) pool. The Villingen stream chemistry was modelled successfully by measured Langmuir isotherm parameters (LIPs) for Sinorg. Schluchsee data could not be modelled satisfactorily using measured or freely adapted LIPs only, as the Sinorg pool would have to be more than five times larger than what was measured. With 60.5 mmolc SO4 m-2 yr-1 as internal soil source by mineralisation and the measured LIPs, stream data was modelled successfully. The modelling shows that in these two catchments pre-industrial concentrations of SO4 in runoff can be reached in the next two decades if S deposition decreases as intended under currently agreed national and international legislation. Sorg is the most likely dominant source of SO4 released at Schluchsee. Mineralization from the Sorg pool must be included when modelling SO4 concentrations in the stream. As the dynamics and the controlling factors of S release by mineralisation are not yet clear, this process remains a source of uncertainty for predictions of SO4 concentrations in streams. Future research should concentrate on dynamics of S mineralisation in the field, such that mathematical descriptions of long-term S-mineralisation can be incorporated into biogeochemical models. Keywords: sulphate release, organic S, mineralisation, acidification, recovery, modelling, MAGIC, catchments, predictions, Germany, fores
Approximate Analytical Solutions to the Initial Data Problem of Black Hole Binary Systems
We present approximate analytical solutions to the Hamiltonian and momentum
constraint equations, corresponding to systems composed of two black holes with
arbitrary linear and angular momentum. The analytical nature of these initial
data solutions makes them easier to implement in numerical evolutions than the
traditional numerical approach of solving the elliptic equations derived from
the Einstein constraints. Although in general the problem of setting up initial
conditions for black hole binary simulations is complicated by the presence of
singularities, we show that the methods presented in this work provide initial
data with and norms of violation of the constraint equations
falling below those of the truncation error (residual error due to
discretization) present in finite difference codes for the range of grid
resolutions currently used. Thus, these data sets are suitable for use in
evolution codes. Detailed results are presented for the case of a head-on
collision of two equal-mass M black holes with specific angular momentum 0.5M
at an initial separation of 10M. A straightforward superposition method yields
data adequate for resolutions of , and an "attenuated" superposition
yields data usable to resolutions at least as fine as . In addition, the
attenuated approximate data may be more tractable in a full (computational)
exact solution to the initial value problem.Comment: 6 pages, 5 postscript figures. Minor changes and some points
clarified. Accepted for publication in Phys. Rev.
Analysis of ``Gauge Modes'' in Linearized Relativity
By writing the complete set of (ADM) equations for linearized waves,
we are able to demonstrate the properties of the initial data and of the
evolution of a wave problem set by Alcubierre and Schutz. We show that the
gauge modes and constraint error modes arise in a straightforward way in the
analysis, and are of a form which will be controlled in any well specified
convergent computational discretization of the differential equations.Comment: 11pages LaTe
On the Role of Disks in the Formation of Stellar Systems: A Numerical Parameter Study of Rapid Accretion
We study rapidly accreting, gravitationally unstable disks with a series of
global, three dimensional, numerical experiments using the code ORION. In this
paper we conduct a numerical parameter study focused on protostellar disks, and
show that one can predict disk behavior and the multiplicity of the accreting
star system as a function of two dimensionless parameters which compare the
disk's accretion rate to its sound speed and orbital period. Although
gravitational instabilities become strong, we find that fragmentation into
binary or multiple systems occurs only when material falls in several times
more rapidly than the canonical isothermal limit. The disk-to-star accretion
rate is proportional to the infall rate, and governed by gravitational torques
generated by low-m spiral modes. We also confirm the existence of a maximum
stable disk mass: disks that exceed ~50% of the total system mass are subject
to fragmentation and the subsequent formation of binary companions.Comment: 16 pages, 12 figures, submitte
Binary Black Holes: Spin Dynamics and Gravitational Recoil
We present a study of spinning black hole binaries focusing on the spin
dynamics of the individual black holes as well as on the gravitational recoil
acquired by the black hole produced by the merger. We consider two series of
initial spin orientations away from the binary orbital plane. In one of the
series, the spins are anti-aligned; for the second series, one of the spins
points away from the binary along the line separating the black holes. We find
a remarkable agreement between the spin dynamics predicted at 2nd
post-Newtonian order and those from numerical relativity. For each
configuration, we compute the kick of the final black hole. We use the kick
estimates from the series with anti-aligned spins to fit the parameters in the
\KKF{,} and verify that the recoil along the direction of the orbital angular
momentum is and on the orbital plane ,
with the angle between the spin directions and the orbital angular
momentum. We also find that the black hole spins can be well estimated by
evaluating the isolated horizon spin on spheres of constant coordinate radius.Comment: 15 pages, 10 figures, replaced with version accepted for publication
in PR
Gravitational recoil from spinning binary black hole mergers
The inspiral and merger of binary black holes will likely involve black holes
with both unequal masses and arbitrary spins. The gravitational radiation
emitted by these binaries will carry angular as well as linear momentum. A net
flux of emitted linear momentum implies that the black hole produced by the
merger will experience a recoil or kick. Previous studies have focused on the
recoil velocity from unequal mass, non-spinning binaries. We present results
from simulations of equal mass but spinning black hole binaries and show how a
significant gravitational recoil can also be obtained in these situations. We
consider the case of black holes with opposite spins of magnitude
aligned/anti-aligned with the orbital angular momentum, with the
dimensionless spin parameters of the individual holes. For the initial setups
under consideration, we find a recoil velocity of V = 475 \KMS a.
Supermassive black hole mergers producing kicks of this magnitude could result
in the ejection from the cores of dwarf galaxies of the final hole produced by
the collision.Comment: 8 pages, 8 figures, replaced with version accepted for publication in
Ap
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