5,841 research outputs found
Chaotic diffusion of particles with finite mass in oscillating convection flows
Deterministic diffusion in temporally oscillating convection is studied for
particles with finite mass. The particles are assumed to obey a simple
dissipative dynamical system and the particle diffusion is induced by the
strange attractor. The diffusion constants are numerically calculated for
convection models with free and rigid boundary conditions.Comment: 5 figure
Gap solitons in Bragg gratings with a harmonic superlattice
Solitons are studied in a model of a fiber Bragg grating (BG) whose local
reflectivity is subjected to periodic modulation. The superlattice opens an
infinite number of new bandgaps in the model's spectrum. Averaging and
numerical continuation methods show that each gap gives rise to gap solitons
(GSs), including asymmetric and double-humped ones, which are not present
without the superlattice.Computation of stability eigenvalues and direct
simulation reveal the existence of completely stable families of fundamental
GSs filling the new gaps - also at negative frequencies, where the ordinary GSs
are unstable. Moving stable GSs with positive and negative effective mass are
found too.Comment: 7 pages, 3 figures, submitted to EP
Localized matter-waves patterns with attractive interaction in rotating potentials
We consider a two-dimensional (2D) model of a rotating attractive
Bose-Einstein condensate (BEC), trapped in an external potential. First, an
harmonic potential with the critical strength is considered, which generates
quasi-solitons at the lowest Landau level (LLL). We describe a family of the
LLL quasi-solitons using both numerical method and a variational approximation
(VA), which are in good agreement with each other. We demonstrate that kicking
the LLL mode or applying a ramp potential sets it in the Larmor (cyclotron)
motion, that can also be accurately modeled by the VA.Comment: 13 pages, 11 figure
Nondegenerate Super-Anti-de Sitter Algebra and a Superstring Action
We construct an Anti-de Sitter(AdS) algebra in a nondegenerate superspace.
Based on this algebra we construct a covariant kappa-symmetric superstring
action, and we examine its dynamics: Although this action reduces to the usual
Green-Schwarz superstring action in flat limit, the auxiliary fermionic
coordinates of the nondegenerate superspace becomes dynamical in the AdS
background.Comment: Latex, 12 pages, explanations added, version to be published in Phys.
Rev.
Fluctuation Dissipation Relation for a Langevin Model with Multiplicative Noise
A random multiplicative process with additive noise is described by a
Langevin equation. We show that the fluctuation-dissipation relation is
satisfied in the Langevin model, if the noise strength is not so strong.Comment: 11 pages, 6 figures, other comment
Disordered Regimes of the one-dimensional complex Ginzburg-Landau equation
I review recent work on the ``phase diagram'' of the one-dimensional complex
Ginzburg-Landau equation for system sizes at which chaos is extensive.
Particular attention is paid to a detailed description of the spatiotemporally
disordered regimes encountered. The nature of the transition lines separating
these phases is discussed, and preliminary results are presented which aim at
evaluating the phase diagram in the infinite-size, infinite-time, thermodynamic
limit.Comment: 14 pages, LaTeX, 9 figures available by anonymous ftp to
amoco.saclay.cea.fr in directory pub/chate, or by requesting them to
[email protected]
Characterization of ellipses as uniformly dense sets with respect to a family of convex bodies
Let K \subset R^N be a convex body containing the origin. A measurable set G
\subset R^N with positive Lebesgue measure is said to be uniformly K-dense if,
for any fixed r > 0, the measure of G \cap (x + rK) is constant when x varies
on the boundary of G (here, x + rK denotes a translation of a dilation of K).
We first prove that G must always be strictly convex and at least C1,1-regular;
also, if K is centrally symmetric, K must be strictly convex, C1,1-regular and
such that K = G - G up to homotheties; this implies in turn that G must be
C2,1- regular. Then for N = 2, we prove that G is uniformly K-dense if and only
if K and G are homothetic to the same ellipse. This result was already proven
by Amar, Berrone and Gianni in [3]. However, our proof removes their regularity
assumptions on K and G and, more importantly, it is susceptible to be
generalized to higher dimension since, by the use of Minkowski's inequality and
an affine inequality, avoids the delicate computations of the higher-order
terms in the Taylor expansion near r = 0 for the measure of G\cap(x+rK) (needed
in [3])
Stochastic synchronization in globally coupled phase oscillators
Cooperative effects of periodic force and noise in globally Cooperative
effects of periodic force and noise in globally coupled systems are studied
using a nonlinear diffusion equation for the number density. The amplitude of
the order parameter oscillation is enhanced in an intermediate range of noise
strength for a globally coupled bistable system, and the order parameter
oscillation is entrained to the external periodic force in an intermediate
range of noise strength. These enhancement phenomena of the response of the
order parameter in the deterministic equations are interpreted as stochastic
resonance and stochastic synchronization in globally coupled systems.Comment: 5 figure
Cascade Failure in a Phase Model of Power Grids
We propose a phase model to study cascade failure in power grids composed of
generators and loads. If the power demand is below a critical value, the model
system of power grids maintains the standard frequency by feedback control. On
the other hand, if the power demand exceeds the critical value, an electric
failure occurs via step out (loss of synchronization) or voltage collapse. The
two failures are incorporated as two removal rules of generator nodes and load
nodes. We perform direct numerical simulation of the phase model on a
scale-free network and compare the results with a mean-field approximation.Comment: 7 pages, 2 figure
Quantum switches and quantum memories for matter-wave lattice solitons
We study the possibility of implementing a quantum switch and a quantum
memory for matter wave lattice solitons by making them interact with
"effective" potentials (barrier/well) corresponding to defects of the optical
lattice. In the case of interaction with an "effective" potential barrier, the
bright lattice soliton experiences an abrupt transition from complete
transmission to complete reflection (quantum switch) for a critical height of
the barrier. The trapping of the soliton in an "effective" potential well and
its release on demand, without loses, shows the feasibility of using the system
as a quantum memory. The inclusion of defects as a way of controlling the
interactions between two solitons is also reported
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