1,017 research outputs found
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
On the Buchdahl inequality for spherically symmetric static shells
A classical result by Buchdahl \cite{Bu1} shows that for static solutions of the spherically symmetric Einstein-matter system, the total ADM mass M and the area radius R of the boundary of the body, obey the inequality The proof of this inequality rests on the hypotheses that the energy density is non-increasing outwards and that the pressure is isotropic. In this work neither of Buchdahl's hypotheses are assumed. We consider non-isotropic spherically symmetric shells, supported in of matter models for which the energy density and the radial- and tangential pressures and satisfy We show a Buchdahl type inequality for shells which are thin; given an such that when It is also shown that for a sequence of solutions such that the limit supremum of of the sequence is bounded by In particular if which is the case for Vlasov matter, the boumd is The latter result is motivated by numerical simulations \cite{AR2} which indicate that for non-isotropic shells of Vlasov matter and moreover, that the value 8/9 is approached for shells with . In \cite{An2} a sequence of shells of Vlasov matter is constructed with the properties that and that equals 8/9 in the limit. We emphasize that in the present paper no field equations for the matter are used, whereas in \cite{An2} the Vlasov equation is important
Control of MTDC Transmission Systems under Local Information
High-voltage direct current (HVDC) is a commonly used technology for
long-distance electric power transmission, mainly due to its low resistive
losses. In this paper a distributed controller for multi-terminal high-voltage
direct current (MTDC) transmission systems is considered. Sufficient conditions
for when the proposed controller renders the closed-loop system asymptotically
stable are provided. Provided that the closed loop system is asymptotically
stable, it is shown that in steady-state a weighted average of the deviations
from the nominal voltages is zero. Furthermore, a quadratic cost of the current
injections is minimized asymptotically
Distributed PI-Control with Applications to Power Systems Frequency Control
This paper considers a distributed PI-controller for networked dynamical
systems. Sufficient conditions for when the controller is able to stabilize a
general linear system and eliminate static control errors are presented. The
proposed controller is applied to frequency control of power transmission
systems. Sufficient stability criteria are derived, and it is shown that the
controller parameters can always be chosen so that the frequencies in the
closed loop converge to nominal operational frequency. We show that the load
sharing property of the generators is maintained, i.e., the input power of the
generators is proportional to a controller parameter. The controller is
evaluated by simulation on the IEEE 30 bus test network, where its
effectiveness is demonstrated
File Fragmentation over an Unreliable Channel
It has been recently discovered that heavy-tailed
file completion time can result from protocol interaction even
when file sizes are light-tailed. A key to this phenomenon is
the RESTART feature where if a file transfer is interrupted
before it is completed, the transfer needs to restart from the
beginning. In this paper, we show that independent or bounded
fragmentation guarantees light-tailed file completion time as long
as the file size is light-tailed, i.e., in this case, heavy-tailed file
completion time can only originate from heavy-tailed file sizes.
If the file size is heavy-tailed, then the file completion time is
necessarily heavy-tailed. For this case, we show that when the
file size distribution is regularly varying, then under independent
or bounded fragmentation, the completion time tail distribution
function is asymptotically upper bounded by that of the original
file size stretched by a constant factor. We then prove that if the
failure distribution has non-decreasing failure rate, the expected
completion time is minimized by dividing the file into equal sized
fragments; this optimal fragment size is unique but depends on
the file size. We also present a simple blind fragmentation policy
where the fragment sizes are constant and independent of the
file size and prove that it is asymptotically optimal. Finally, we
bound the error in expected completion time due to error in
modeling of the failure process
Distributed Primary Frequency Control through Multi-Terminal HVDC Transmission Systems
This paper presents a decentralized controller for sharing primary AC
frequency control reserves through a multi-terminal HVDC grid. By using
Lyapunov arguments, the proposed controller is shown to stabilize the
equilibrium of the closed-loop system consisting of the interconnected AC and
HVDC grids, given any positive controller gains. The static control errors
resulting from the proportional controller are quantified and bounded by
analyzing the equilibrium of the closed-loop system. The proposed controller is
applied to a test grid consisting of three asynchronous AC areas interconnected
by an HVDC grid, and its effectiveness is validated through simulation
Distributed Secondary Frequency Control through MTDC Transmission Systems
In this paper, we present distributed controllers for sharing primary and
secondary frequency control reserves for asynchronous AC transmission systems,
which are connected through a multi-terminal HVDC grid. By using Lyapunov
arguments, the equilibria of the closed-loop system are shown to be globally
asymptotically stable. We quantify the static errors of the voltages and
frequencies, and give upper bounds for these errors. It is also shown that the
controllers have the property of power sharing, i.e., primary and secondary
frequency control reserves are shared fairly amongst the AC systems. The
proposed controllers are applied to a high-order dynamic model of of a power
system consisting of asynchronous AC grids connected through a six-terminal
HVDC grid.Comment: arXiv admin note: text overlap with arXiv:1409.801
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