150 research outputs found
Long Time Evolution of Phase Oscillator Systems
It is shown, under weak conditions, that the dynamical evolution of an
important class of large systems of globally coupled, heterogeneous frequency,
phase oscillators is, in an appropriate physical sense, time-asymptotically
attracted toward a reduced manifold of system states. This manifold, which is
invariant under the system evolution, was previously known and used to
facilitate the discovery of attractors and bifurcations of such systems. The
result of this paper establishes that attractors for the order parameter
dynamics obtained by restriction to this reduced manifold are, in fact, the
only such attractors of the full system. Thus all long time dynamical behavior
of the order parameters of these systems can be obtained by restriction to the
reduced manifold.Comment: Improved discussion of Eqs. (28)- (30) Corrected typos. Made notation
consisten
Comment on "Long Time Evolution of Phase Oscillator Systems" [Chaos 19,023117 (2009), arXiv:0902.2773]
A previous paper (arXiv:0902.2773, henceforth referred to as I) considered a
general class of problems involving the evolution of large systems of globally
coupled phase oscillators. It was shown there that, in an appropriate sense,
the solutions to these problems are time asymptotically attracted toward a
reduced manifold of system states (denoted M). This result has considerable
utility in the analysis of these systems, as has been amply demonstrated in
recent papers. In this note, we show that the analysis of I can be modified in
a simple way that establishes significant extensions of the range of validity
of our previous result. In particular, we generalize I in the following ways:
(1) attraction to M is now shown for a very general class of oscillator
frequency distribution functions g(\omega), and (2) a previous restriction on
the allowed class of initial conditions is now substantially relaxed
A statistical model for the excitation of cavities through apertures
In this paper, a statistical model for the coupling of electromagnetic
radiation into enclosures through apertures is presented. The model gives a
unified picture bridging deterministic theories of aperture radiation, and
statistical models necessary for capturing the properties of irregular shaped
enclosures. A Monte Carlo technique based on random matrix theory is used to
predict and study the power transmitted through the aperture into the
enclosure. Universal behavior of the net power entering the aperture is found.
Results are of interest for predicting the coupling of external radiation
through openings in irregular enclosures and reverberation chambers.Comment: 12 pages, 11 figures, in press, IEEE Transactions on Electromagnetic
Compatibilit
Sensing Small Changes in a Wave Chaotic Scattering System
Classical analogs of the quantum mechanical concepts of the Loschmidt Echo
and quantum fidelity are developed with the goal of detecting small
perturbations in a closed wave chaotic region. Sensing techniques that employ a
one-recording-channel time-reversal-mirror, which in turn relies on time
reversal invariance and spatial reciprocity of the classical wave equation, are
introduced. In analogy with quantum fidelity, we employ Scattering Fidelity
techniques which work by comparing response signals of the scattering region,
by means of cross correlation and mutual information of signals. The
performance of the sensing techniques is compared for various perturbations
induced experimentally in an acoustic resonant cavity. The acoustic signals are
parametrically processed to mitigate the effect of dissipation and to vary the
spatial diversity of the sensing schemes. In addition to static boundary
condition perturbations at specified locations, perturbations to the medium of
wave propagation are shown to be detectable, opening up various real world
sensing applications in which a false negative cannot be tolerated.Comment: 14 pages, 11 figures, as published on J. Appl. Phy
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