14,515 research outputs found
Exact Results for the Kuramoto Model with a Bimodal Frequency Distribution
We analyze a large system of globally coupled phase oscillators whose natural
frequencies are bimodally distributed. The dynamics of this system has been the
subject of long-standing interest. In 1984 Kuramoto proposed several
conjectures about its behavior; ten years later, Crawford obtained the first
analytical results by means of a local center manifold calculation.
Nevertheless, many questions have remained open, especially about the
possibility of global bifurcations. Here we derive the system's complete
stability diagram for the special case where the bimodal distribution consists
of two equally weighted Lorentzians. Using an ansatz recently discovered by Ott
and Antonsen, we show that in this case the infinite-dimensional problem
reduces exactly to a flow in four dimensions. Depending on the parameters and
initial conditions, the long-term dynamics evolves to one of three states:
incoherence, where all the oscillators are desynchronized; partial synchrony,
where a macroscopic group of phase-locked oscillators coexists with a sea of
desynchronized ones; and a standing wave state, where two counter-rotating
groups of phase-locked oscillators emerge. Analytical results are presented for
the bifurcation boundaries between these states. Similar results are also
obtained for the case in which the bimodal distribution is given by the sum of
two Gaussians.Comment: 28 pages, 7 figures; submitted to Phys. Rev. E Added comment
Rectenna system design
The function of the rectenna in the solar power satellite system is described and the basic design choices based on the desired microwave field concentration and ground clearance requirements are given. One important area of concern, from the EMI point of view, harmonic reradiation and scattering from the rectenna is also designed. An optimization of a rectenna system design to minimize costs was performed. The rectenna cost breakdown for a 56 w installation is given as an example
On the equality of Hausdorff and box counting dimensions
By viewing the covers of a fractal as a statistical mechanical system, the
exact capacity of a multifractal is computed. The procedure can be extended to
any multifractal described by a scaling function to show why the capacity and
Hausdorff dimension are expected to be equal.Comment: CYCLER Paper 93mar001 Latex file with 3 PostScript figures (needs
psfig.sty
Multifractal clustering of passive tracers on a surface flow
We study the anomalous scaling of the mass density measure of Lagrangian
tracers in a compressible flow realized on the free surface on top of a three
dimensional flow. The full two dimensional probability distribution of local
stretching rates is measured. The intermittency exponents which quantify the
fluctuations of the mass measure of tracers at small scales are calculated from
the large deviation form of stretching rate fluctuations. The results indicate
the existence of a critical exponent above which exponents
saturate, in agreement with what has been predicted by an analytically solvable
model. Direct evaluation of the multi-fractal dimensions by reconstructing the
coarse-grained particle density supports the results for low order moments.Comment: 7 pages, 4 figures, submitted to EP
Dynamics of Black Hole Pairs II: Spherical Orbits and the Homoclinic Limit of Zoom-Whirliness
Spinning black hole pairs exhibit a range of complicated dynamical behaviors.
An interest in eccentric and zoom-whirl orbits has ironically inspired the
focus of this paper: the constant radius orbits. When black hole spins are
misaligned, the constant radius orbits are not circles but rather lie on the
surface of a sphere and have acquired the name "spherical orbits". The
spherical orbits are significant as they energetically frame the distribution
of all orbits. In addition, each unstable spherical orbit is asymptotically
approached by an orbit that whirls an infinite number of times, known as a
homoclinic orbit. A homoclinic trajectory is an infinite whirl limit of the
zoom-whirl spectrum and has a further significance as the separatrix between
inspiral and plunge for eccentric orbits. We work in the context of two
spinning black holes of comparable mass as described in the 3PN Hamiltonian
with spin-orbit coupling included. As such, the results could provide a testing
ground of the accuracy of the PN expansion. Further, the spherical orbits could
provide useful initial data for numerical relativity. Finally, we comment that
the spinning black hole pairs should give way to chaos around the homoclinic
orbit when spin-spin coupling is incorporated.Comment: 16 pages, several figure
Magnetic domain fluctuations in an antiferromagnetic film observed with coherent resonant soft x-ray scattering
We report the direct observation of slow fluctuations of helical
antiferromagnetic domains in an ultra-thin holmium film using coherent resonant
magnetic x-ray scattering. We observe a gradual increase of the fluctuations in
the speckle pattern with increasing temperature, while at the same time a
static contribution to the speckle pattern remains. This finding indicates that
domain-wall fluctuations occur over a large range of time scales. We ascribe
this non-ergodic behavior to the strong dependence of the fluctuation rate on
the local thickness of the film.Comment: to appear in Phys. Rev. Let
Ordering of small particles in one-dimensional coherent structures by time-periodic flows
Small particles transported by a fluid medium do not necessarily have to
follow the flow. We show that for a wide class of time-periodic incompressible
flows inertial particles have a tendency to spontaneously align in
one-dimensional dynamic coherent structures. This effect may take place for
particles so small that often they would be expected to behave as passive
tracers and be used in PIV measurement technique. We link the particle tendency
to form one-dimensional structures to the nonlinear phenomenon of phase
locking. We propose that this general mechanism is, in particular, responsible
for the enigmatic formation of the `particle accumulation structures'
discovered experimentally in thermocapillary flows more than a decade ago and
unexplained until now
Dynamic transition and Shapiro-step melting in a frustrated Josephson-junction array
We consider a two-dimensional fully frustrated Josephson-junction array
driven by combined direct and alternating currents. Interplay between the mode
locking phenomenon, manifested by giant Shapiro steps in the current-voltage
characteristics, and the dynamic phase transition is investigated at finite
temperatures. Melting of Shapiro steps due to thermal fluctuations is shown to
be accompanied by the dynamic phase transition, the universality class of which
is also discussed
Classical diffusion in double-delta-kicked particles
We investigate the classical chaotic diffusion of atoms subjected to {\em
pairs} of closely spaced pulses (`kicks) from standing waves of light (the
-KP). Recent experimental studies with cold atoms implied an
underlying classical diffusion of type very different from the well-known
paradigm of Hamiltonian chaos, the Standard Map.
The kicks in each pair are separated by a small time interval , which together with the kick strength , characterizes the transport.
Phase space for the -KP is partitioned into momentum `cells' partially
separated by momentum-trapping regions where diffusion is slow. We present here
an analytical derivation of the classical diffusion for a -KP
including all important correlations which were used to analyze the
experimental data.
We find a new asymptotic () regime of `hindered' diffusion:
while for the Standard Map the diffusion rate, for , oscillates about the uncorrelated, rate , we find
analytically, that the -KP can equal, but never diffuses faster than,
a random walk rate.
We argue this is due to the destruction of the important classical
`accelerator modes' of the Standard Map.
We analyze the experimental regime , where
quantum localisation lengths are affected by fractal
cell boundaries. We find an approximate asymptotic diffusion rate , in correspondence to a regime in the Standard Map
associated with 'golden-ratio' cantori.Comment: 14 pages, 10 figures, error in equation in appendix correcte
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