2,852 research outputs found
Protocol-Safe Workflow Support for Santa Claus
Practical software analysis techniques exploit a form a process description, mostly in some \ud
avour of state diagram. Unlike typing information, these process structures are usually not passed down to the implementation level, and neither are they exploited in any form of consistency check. It is our belief that the information in most designs suffices to perform all sorts of consistency checks. This workshop paper studies a simple case where work\ud
ow processes interact with `actual' objects at the implementation level, and demonstrates how useful protocol checking can be in making and keeping these processes consistent with each other
On Practical Verification of Processes
The integration of a formal process theory with a practically usable notation is not straightforward, but it is necessary for practical verification of process specifications. Given such an intermediate language, a verification process that gives useful feedback is not trivial either: Model checkers are not powerful enough to deal with object models, and theorem provers provide insu#cient feedback and are not certain to find a proof
On the steady states of the spherically symmetric Einstein-Vlasov system
Using both numerical and analytical tools we study various features of
static, spherically symmetric solutions of the Einstein-Vlasov system. In
particular, we investigate the possible shapes of their mass-energy density and
find that they can be multi-peaked, we give numerical evidence and a partial
proof for the conjecture that the Buchdahl inequality , the quasi-local mass, holds for all such steady states--both
isotropic {\em and} anisotropic--, and we give numerical evidence and a partial
proof for the conjecture that for any given microscopic equation of state--both
isotropic {\em and} anisotropic--the resulting one-parameter family of static
solutions generates a spiral in the radius-mass diagram.Comment: 34 pages, 18 figures, LaTe
Formation of trapped surfaces for the spherically symmetric Einstein-Vlasov system
We consider the spherically symmetric, asymptotically flat, non-vacuum
Einstein equations, using as matter model a collisionless gas as described by
the Vlasov equation. We find explicit conditions on the initial data which
guarantee the formation of a trapped surface in the evolution which in
particular implies that weak cosmic censorship holds for these data. We also
analyze the evolution of solutions after a trapped surface has formed and we
show that the event horizon is future complete. Furthermore we find that the
apparent horizon and the event horizon do not coincide. This behavior is
analogous to what is found in certain Vaidya spacetimes. The analysis is
carried out in Eddington-Finkelstein coordinates.Comment: 2
Home-grown CASE tools with XML and XSLT
This paper demonstrates an approach to software generation where xml representations of models are transformed to implementations by XSLT style sheets. Although XSLT was not primarily intended for this use, it serves quite well. There are only few problems in this approach, and we identify these based on our examples
Global existence for the spherically symmetric Einstein-Vlasov system with outgoing matter
We prove a new global existence result for the asymptotically flat,
spherically symmetric Einstein-Vlasov system which describes in the framework
of general relativity an ensemble of particles which interact by gravity. The
data are such that initially all the particles are moving radially outward and
that this property can be bootstrapped. The resulting non-vacuum spacetime is
future geodesically complete.Comment: 16 page
REBOUND: An open-source multi-purpose N-body code for collisional dynamics
REBOUND is a new multi-purpose N-body code which is freely available under an
open-source license. It was designed for collisional dynamics such as planetary
rings but can also solve the classical N-body problem. It is highly modular and
can be customized easily to work on a wide variety of different problems in
astrophysics and beyond.
REBOUND comes with three symplectic integrators: leap-frog, the symplectic
epicycle integrator (SEI) and a Wisdom-Holman mapping (WH). It supports open,
periodic and shearing-sheet boundary conditions. REBOUND can use a Barnes-Hut
tree to calculate both self-gravity and collisions. These modules are fully
parallelized with MPI as well as OpenMP. The former makes use of a static
domain decomposition and a distributed essential tree. Two new collision
detection modules based on a plane-sweep algorithm are also implemented. The
performance of the plane-sweep algorithm is superior to a tree code for
simulations in which one dimension is much longer than the other two and in
simulations which are quasi-two dimensional with less than one million
particles.
In this work, we discuss the different algorithms implemented in REBOUND, the
philosophy behind the code's structure as well as implementation specific
details of the different modules. We present results of accuracy and scaling
tests which show that the code can run efficiently on both desktop machines and
large computing clusters.Comment: 10 pages, 9 figures, accepted by A&A, source code available at
https://github.com/hannorein/reboun
On the Einstein-Vlasov system with hyperbolic symmetry
It is shown that a spacetime with collisionless matter evolving from data on a compact Cauchy surface with hyperbolic symmetry can be globally covered by compact hypersurfaces on which the mean curvature is constant and by compact hypersurfaces on which the area radius is constant. Results for the related cases of spherical and plane symmetry are reviewed and extended. The prospects of using the global time coordinates obtained in this way to investigate the global geometry of the spacetimes concerned are discusse
Global existence and asymptotic behaviour in the future for the Einstein-Vlasov system with positive cosmological constant
The behaviour of expanding cosmological models with collisionless matter and
a positive cosmological constant is analysed. It is shown that under the
assumption of plane or hyperbolic symmetry the area radius goes to infinity,
the spacetimes are future geodesically complete, and the expansion becomes
isotropic and exponential at late times. This proves a form of the cosmic no
hair theorem in this class of spacetimes
Stochastic orbital migration of small bodies in Saturn's rings
Many small moonlets, creating propeller structures, have been found in
Saturn's rings by the Cassini spacecraft. We study the dynamical evolution of
such 20-50m sized bodies which are embedded in Saturn's rings. We estimate the
importance of various interaction processes with the ring particles on the
moonlet's eccentricity and semi-major axis analytically. For low ring surface
densities, the main effects on the evolution of the eccentricity and the
semi-major axis are found to be due to collisions and the gravitational
interaction with particles in the vicinity of the moonlet. For large surface
densities, the gravitational interaction with self-gravitating wakes becomes
important.
We also perform realistic three dimensional, collisional N-body simulations
with up to a quarter of a million particles. A new set of pseudo shear periodic
boundary conditions is used which reduces the computational costs by an order
of magnitude compared to previous studies. Our analytic estimates are confirmed
to within a factor of two.
On short timescales the evolution is always dominated by stochastic effects
caused by collisions and gravitational interaction with self-gravitating ring
particles. These result in a random walk of the moonlet's semi-major axis. The
eccentricity of the moonlet quickly reaches an equilibrium value due to
collisional damping. The average change in semi-major axis of the moonlet after
100 orbital periods is 10-100m. This translates to an offset in the azimuthal
direction of several hundred kilometres. We expect that such a shift is easily
observable.Comment: 13 pages, 6 figures, submitted to A&A, comments welcom
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