38,840 research outputs found
Analysis of stochastic fluid queues driven by local time processes
We consider a stochastic fluid queue served by a constant rate server and
driven by a process which is the local time of a certain Markov process. Such a
stochastic system can be used as a model in a priority service system,
especially when the time scales involved are fast. The input (local time) in
our model is always singular with respect to the Lebesgue measure which in many
applications is ``close'' to reality. We first discuss how to rigorously
construct the (necessarily) unique stationary version of the system under some
natural stability conditions. We then consider the distribution of performance
steady-state characteristics, namely, the buffer content, the idle period and
the busy period. These derivations are much based on the fact that the inverse
of the local time of a Markov process is a L\'evy process (a subordinator)
hence making the theory of L\'evy processes applicable. Another important
ingredient in our approach is the Palm calculus coming from the point process
point of view.Comment: 32 pages, 6 figure
Club-guessing, stationary reflection, and coloring theorems
We obtain strong coloring theorems at successors of singular cardinals from
failures of certain instances of simultaneous reflection of stationary sets.
Along the way, we establish new results in club-guessing and in the general
theory of ideals.Comment: Initial public versio
Effect of electron heating on self-induced transparency in relativistic intensity laser-plasma interaction
The effective increase of the critical density associated with the
interaction of relativistically intense laser pulses with overcritical plasmas,
known as self-induced transparency, is revisited for the case of circular
polarization. A comparison of particle-in-cell simulations to the predictions
of a relativistic cold-fluid model for the transparency threshold demonstrates
that kinetic effects, such as electron heating, can lead to a substantial
increase of the effective critical density compared to cold-fluid theory. These
results are interpreted by a study of separatrices in the single-electron phase
space corresponding to dynamics in the stationary fields predicted by the
cold-fluid model. It is shown that perturbations due to electron heating
exceeding a certain finite threshold can force electrons to escape into the
vacuum, leading to laser pulse propagation. The modification of the
transparency threshold is linked to the temporal pulse profile, through its
effect on electron heating.Comment: 13 pages, 12 figures; fixed some typos and improved discussion of
review materia
Epsilon-regularity for p-harmonic maps at a free boundary on a sphere
We prove an -regularity theorem for vector-valued p-harmonic maps,
which are critical with respect to a partially free boundary condition, namely
that they map the boundary into a round sphere.
This does not seem to follow from the reflection method that Scheven used for
harmonic maps with free boundary (i.e., the case ): the reflected equation
can be interpreted as a -harmonic map equation into a manifold, but the
regularity theory for such equations is only known for round targets.
Instead, we follow the spirit of the last-named author's recent work on free
boundary harmonic maps and choose a good frame directly at the free boundary.
This leads to growth estimates, which, in the critical regime , imply
H\"older regularity of solutions. In the supercritical regime, , we
combine the growth estimate with the geometric reflection argument: the
reflected equation is super-critical, but, under the assumption of growth
estimates, solutions are regular.
In the case , for stationary -harmonic maps with free boundary, as a
consequence of a monotonicity formula we obtain partial regularity up to the
boundary away from a set of -dimensional Hausdorff measure.Comment: Minor corrections, accepted to APD
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