5,202 research outputs found
Domain-size control by global feedback in bistable systems
We study domain structures in bistable systems such as the Ginzburg-Landau
equation. The size of domains can be controlled by a global negative feedback.
The domain-size control is applied for a localized spiral pattern
Oscillatory phase transition and pulse propagation in noisy integrate-and-fire neurons
We study non-locally coupled noisy integrate-and-fire neurons with the
Fokker-Planck equation. A propagating pulse state and a wavy state appear as a
phase transition from an asynchronous state. We also find a solution in which
traveling pulses are emitted periodically from a pacemaker region.Comment: 9 pages, 4 figure
How to Track Protists in Three Dimensions
We present an apparatus optimized for tracking swimming microorganisms in the
size range 10-1000 microns, in three dimensions (3D), far from surfaces, and
with negligible background convective fluid motion. CCD cameras attached to two
long working distance microscopes synchronously image the sample from two
perpendicular directions, with narrowband dark-field or bright-field
illumination chosen to avoid triggering a phototactic response. The images from
the two cameras can be combined to yield 3D tracks of the organism. Using
additional, highly directional broad-spectrum illumination with millisecond
timing control the phototactic trajectories in 3D of organisms ranging from
Chlamydomonas to Volvox can be studied in detail. Surface-mediated hydrodynamic
interactions can also be investigated without convective interference. Minimal
modifications to the apparatus allow for studies of chemotaxis and other taxes.Comment: 8 pages, 7 figure
Collective synchronization in populations of globally coupled phase oscillators with drifting frequencies
We generalize the Kuramoto model for coupled phase oscillators by allowing
the frequencies to drift in time according to Ornstein-Uhlenbeck dynamics. Such
drifting frequencies were recently measured in cellular populations of
circadian oscillator and inspired our work. Linear stability analysis of the
Fokker-Planck equation for an infinite population is amenable to exact solution
and we show that the incoherent state is unstable passed a critical coupling
strength K_c(\ga, \sigf), where \ga is the inverse characteristic drifting
time and \sigf the asymptotic frequency dispersion. Expectedly agrees
with the noisy Kuramoto model in the large \ga (Schmolukowski) limit but
increases slower as \ga decreases. Asymptotic expansion of the solution for
\ga\to 0 shows that the noiseless Kuramoto model with Gaussian frequency
distribution is recovered in that limit. Thus varying a single parameter allows
to interpolate smoothly between two regimes: one dominated by the frequency
dispersion and the other by phase diffusion.Comment: 5 pages, 5 figures, accepted 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
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.
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
Resonant nonlinearity management for nonlinear-Schr\"{o}dinger solitons
We consider effects of a periodic modulation of the nonlinearity coefficient
on fundamental and higher-order solitons in the one-dimensional NLS equation,
which is an issue of direct interest to Bose-Einstein condensates in the
context of the Feshbach-resonance control, and fiber-optic telecommunications
as concerns periodic compensation of the nonlinearity. We find from
simulations, and explain by means of a straightforward analysis, that the
response of a fundamental soliton to the weak perturbation is resonant, if the
modulation frequency is close to the intrinsic frequency of the
soliton. For higher-order -solitons with and 3, the response to an
extremely weak perturbation is also resonant, if is close to the
corresponding intrinsic frequency. More importantly, a slightly stronger drive
splits the 2- or 3-soliton, respectively, into a set of two or three moving
fundamental solitons. The dependence of the threshold perturbation amplitude,
necessary for the splitting, on has a resonant character too.
Amplitudes and velocities of the emerging fundamental solitons are accurately
predicted, using exact and approximate conservation laws of the perturbed NLS
equation.Comment: 14 pages, 6 figure
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
The Auxiliary Field Method in Quantum Mechanical Four-Fermi Models -- A Study Toward Chiral Condensation in QED
A study for checking validity of the auxiliary field method (AFM) is made in
quantum mechanical four-fermi models which act as a prototype of models for
chiral symmetry breaking in Quantum Electrodynamics. It has been shown that
AFM, defined by an insertion of Gaussian identity to path integral formulas and
by the loop expansion, becomes more accurate when taking higher order terms
into account under the bosonic model with a quartic coupling in 0- and
1-dimensions as well as the model with a four-fermi interaction in 0-dimension.
The case is also confirmed in terms of two models with the four-fermi
interaction among species in 1-dimension (the quantum mechanical four-fermi
models): higher order corrections lead us toward the exact energy of the ground
state. It is found that the second model belongs to a WKB-exact class that has
no higher order corrections other than the lowest correction. Discussions are
also made for unreliability on the continuous time representation of path
integration and for a new model of QED as a suitable probe for chiral symmetry
breaking.Comment: 30 pages, 12 figure
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