158 research outputs found
Herman's Theory Revisited
We prove that a -smooth orientation-preserving circle
diffeomorphism with rotation number in Diophantine class ,
, is -smoothly conjugate to a rigid
rotation. We also derive the most precise version of Denjoy's inequality for
such diffeomorphisms.Comment: 10 page
Cooperative oscillation of non-degenerate transverse modes in an optical system: multimode operation in parametric oscillators
We show experimentally that parametric interaction can induce a cooperative
oscillation of non simultaneously resonant transverse modes in an optical
parametric oscillator. More generally, this effect is expected to occur in any
spatially extended system subjected to boundary conditions where nonlinear wave
mixing of two nonresonant spatial modes can generate a resonant oscillation
The Continuum Directed Random Polymer
Motivated by discrete directed polymers in one space and one time dimension,
we construct a continuum directed random polymer that is modeled by a
continuous path interacting with a space-time white noise. The strength of the
interaction is determined by an inverse temperature parameter beta, and for a
given beta and realization of the noise the path evolves in a Markovian way.
The transition probabilities are determined by solutions to the one-dimensional
stochastic heat equation. We show that for all beta > 0 and for almost all
realizations of the white noise the path measure has the same Holder continuity
and quadratic variation properties as Brownian motion, but that it is actually
singular with respect to the standard Wiener measure on C([0,1]).Comment: 21 page
Oscillation regimes of a solid-state ring laser with active beat note stabilization : from a chaotic device to a ring laser gyroscope
We report experimental and theoretical study of a rotating diode-pumped
Nd-YAG ring laser with active beat note stabilization. Our experimental setup
is described in the usual Maxwell-Bloch formalism. We analytically derive a
stability condition and some frequency response characteristics for the
solid-state ring laser gyroscope, illustrating the important role of mode
coupling effects on the dynamics of such a device. Experimental data are
presented and compared with the theory on the basis of realistic laser
parameters, showing a very good agreement. Our results illustrate the duality
between the very rich non linear dynamics of the diode-pumped solid-state ring
laser (including chaotic behavior) and the possibility to obtain a very stable
beat note, resulting in a potentially new kind of rotation sensor
Coherent instabilities in a semiconductor laser with fast gain recovery
We report the observation of a coherent multimode instability in quantum
cascade lasers (QCLs), which is driven by the same fundamental mechanism of
Rabi oscillations as the elusive Risken-Nummedal-Graham-Haken (RNGH)
instability predicted 40 years ago for ring lasers. The threshold of the
observed instability is significantly lower than in the original RNGH
instability, which we attribute to saturable-absorption nonlinearity in the
laser. Coherent effects, which cannot be reproduced by standard laser rate
equations, can play therefore a key role in the multimode dynamics of QCLs, and
in lasers with fast gain recovery in general.Comment: 5 pages, 4 figure
Low-frequency dynamics of disordered XY spin chains and pinned density waves: from localized spin waves to soliton tunneling
A long-standing problem of the low-energy dynamics of a disordered XY spin
chain is re-examined. The case of a rigid chain is studied where the quantum
effects can be treated quasiclassically. It is shown that as the frequency
decreases, the relevant excitations change from localized spin waves to
two-level systems to soliton-antisoliton pairs. The linear-response correlation
functions are calculated. The results apply to other periodic glassy systems
such as pinned density waves, planar vortex lattices, stripes, and disordered
Luttinger liquids.Comment: (v2) Major improvements in presentation style. One figure added (v3)
Another minor chang
The extreme vulnerability of interdependent spatially embedded networks
Recent studies show that in interdependent networks a very small failure in
one network may lead to catastrophic consequences. Above a critical fraction of
interdependent nodes, even a single node failure can invoke cascading failures
that may abruptly fragment the system, while below this "critical dependency"
(CD) a failure of few nodes leads only to small damage to the system. So far,
the research has been focused on interdependent random networks without space
limitations. However, many real systems, such as power grids and the Internet,
are not random but are spatially embedded. Here we analytically and numerically
analyze the stability of systems consisting of interdependent spatially
embedded networks modeled as lattice networks. Surprisingly, we find that in
lattice systems, in contrast to non-embedded systems, there is no CD and
\textit{any} small fraction of interdependent nodes leads to an abrupt
collapse. We show that this extreme vulnerability of very weakly coupled
lattices is a consequence of the critical exponent describing the percolation
transition of a single lattice. Our results are important for understanding the
vulnerabilities and for designing robust interdependent spatial embedded
networks.Comment: 13 pages, 5 figure
The Goldbeter-Koshland switch in the first-order region and its response to dynamic disorder
In their classical work (Proc. Natl. Acad. Sci. USA, 1981, 78:6840-6844),
Goldbeter and Koshland mathematically analyzed a reversible covalent
modification system which is highly sensitive to the concentration of
effectors. Its signal-response curve appears sigmoidal, constituting a
biochemical switch. However, the switch behavior only emerges in the
"zero-order region", i.e. when the signal molecule concentration is much lower
than that of the substrate it modifies. In this work we showed that the
switching behavior can also occur under comparable concentrations of signals
and substrates, provided that the signal molecules catalyze the modification
reaction in cooperation. We also studied the effect of dynamic disorders on the
proposed biochemical switch, in which the enzymatic reaction rates, instead of
constant, appear as stochastic functions of time. We showed that the system is
robust to dynamic disorder at bulk concentration. But if the dynamic disorder
is quasi-static, large fluctuations of the switch response behavior may be
observed at low concentrations. Such fluctuation is relevant to many biological
functions. It can be reduced by either increasing the conformation
interconversion rate of the protein, or correlating the enzymatic reaction
rates in the network.Comment: 23 pages, 4 figures, accepted by PLOS ON
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