3,611,936 research outputs found
Phase mixing in MOND
Dissipationless collapses in Modified Newtonian Dynamics (MOND) have been
studied by using our MOND particle-mesh N-body code, finding that the projected
density profiles of the final virialized systems are well described by Sersic
profiles with index m<4 (down to m~2 for a deep-MOND collapse). The simulations
provided also strong evidence that phase mixing is much less effective in MOND
than in Newtonian gravity. Here we describe "ad hoc" numerical simulations with
the force angular components frozen to zero, thus producing radial collapses.
Our previous findings are confirmed, indicating that possible differences in
radial orbit instability under Newtonian and MOND gravity are not relevant in
the present context.Comment: 10 pages, 3 figures. To appear in the Proceedings of the
International Workshop "Collective Phenomena in Macroscopic Systems", G.
Bertin, R. Pozzoli, M. Rome, and K.R. Sreenivasan, eds., World Scientific,
Singapor
Perfect Simulation of Queues
In this paper we describe a perfect simulation algorithm for the stable
queue. Sigman (2011: Exact Simulation of the Stationary Distribution of
the FIFO M/G/c Queue. Journal of Applied Probability, 48A, 209--213) showed how
to build a dominated CFTP algorithm for perfect simulation of the super-stable
queue operating under First Come First Served discipline, with
dominating process provided by the corresponding queue (using Wolff's
sample path monotonicity, which applies when service durations are coupled in
order of initiation of service), and exploiting the fact that the workload
process for the queue remains the same under different queueing
disciplines, in particular under the Processor Sharing discipline, for which a
dynamic reversibility property holds. We generalize Sigman's construction to
the stable case by comparing the queue to a copy run under Random
Assignment. This allows us to produce a naive perfect simulation algorithm
based on running the dominating process back to the time it first empties. We
also construct a more efficient algorithm that uses sandwiching by lower and
upper processes constructed as coupled queues started respectively from
the empty state and the state of the queue under Random Assignment. A
careful analysis shows that appropriate ordering relationships can still be
maintained, so long as service durations continue to be coupled in order of
initiation of service. We summarize statistical checks of simulation output,
and demonstrate that the mean run-time is finite so long as the second moment
of the service duration distribution is finite.Comment: 28 pages, 5 figure
Four-dimensional Riemannian manifolds with two circulant structures
We consider a class (M, g, q) of four-dimensional Riemannian manifolds M,
where besides the metric g there is an additional structure q, whose fourth
power is the unit matrix. We use the existence of a local coordinate system
such that there the coordinates of g and q are circulant matrices. In this
system q has constant coordinates and q is an isometry with respect to g. By
the special identity for the curvature tensor R generated by the Riemannian
connection of g we define a subclass of (M, g, q). For any (M, g, q) in this
subclass we get some assertions for the sectional curvatures of two-planes. We
get the necessary and sufficient condition for g such that q is parallel with
respect to the Riemannian connection of g
On strong rainbow connection number
A path in an edge-colored graph, where adjacent edges may be colored the
same, is a rainbow path if no two edges of it are colored the same. For any two
vertices and of , a rainbow geodesic in is a rainbow
path of length , where is the distance between and .
The graph is strongly rainbow connected if there exists a rainbow
geodesic for any two vertices and in . The strong rainbow connection
number of , denoted , is the minimum number of colors that are
needed in order to make strong rainbow connected. In this paper, we first
investigate the graphs with large strong rainbow connection numbers. Chartrand
et al. obtained that is a tree if and only if , we will show that
, so is not a tree if and only if , where
is the number of edge of . Furthermore, we characterize the graphs
with . We next give a sharp upper bound for according to
the number of edge-disjoint triangles in graph , and give a necessary and
sufficient condition for the equality.Comment: 16 page
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