6,637 research outputs found
Critical collapse of rotating radiation fluids
We present results from the first fully relativistic simulations of the
critical collapse of rotating radiation fluids. We observe critical scaling
both in subcritical evolutions, in which case the fluid disperses to infinity
and leaves behind flat space, and in supercritical evolutions that lead to the
formation of black holes. We measure the mass and angular momentum of these
black holes, and find that both show critical scaling with critical exponents
that are consistent with perturbative results. The critical exponents are
universal; they are not affected by angular momentum, and are independent of
the direction in which the critical curve, which separates subcritical from
supercritical evolutions in our two-dimensional parameter space, is crossed. In
particular, these findings suggest that the angular momentum decreases more
rapidly than the square of the mass, so that, as criticality is approached, the
collapse leads to the formation of a non-spinning black hole. We also
demonstrate excellent agreement of our numerical data with new closed-form
extensions of power-law scalings that describe the mass and angular momentum of
rotating black holes formed close to criticality.Comment: 5 pages, 4 figures; version accepted for publication in PR
Eigenvalue Decomposition as a Generalized Synchronization Cluster Analysis
Motivated by the recent demonstration of its use as a tool for the detection
and characterization of phase-shape correlations in multivariate time series,
we show that eigenvalue decomposition can also be applied to a matrix of
indices of bivariate phase synchronization strength. The resulting method is
able to identify clusters of synchronized oscillators, and to quantify their
strength as well as the degree of involvement of an oscillator in a cluster.
Since for the case of a single cluster the method gives similar results as our
previous approach, it can be seen as a generalized Synchronization Cluster
Analysis, extending its field of application to more complex situations. The
performance of the method is tested by applying it to simulation data.Comment: Submitted Oct 2005, accepted Jan 2006, "published" Oct 2007, actually
available Jan 200
Robust Exponential Stability and Invariance Guarantees with General Dynamic O'Shea-Zames-Falb Multipliers
We propose novel time-domain dynamic integral quadratic constraints with a
terminal cost for exponentially weighted slope-restricted gradients of not
necessarily convex functions. This extends recent results for subdifferentials
of convex function and their link to so-called O'Shea-Zames-Falb multipliers.
The benefit of merging time-domain and frequency-domain techniques is
demonstrated for linear saturated systems.Comment: This paper will appear in the Proceedings of the IFAC World Congress
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