3,187 research outputs found
Guiding chemical pulses through geometry: Y-junctions
We study computationally and experimentally the propagation of chemical
pulses in complex geometries.The reaction of interest, CO oxidation, takes
place on single crystal Pt(110) surfaces that are microlithographically
patterned; they are also addressable through a focused laser beam, manipulated
through galvanometer mirrors, capable of locally altering the crystal
temperature and thus affecting pulse propagation. We focus on sudden changes in
the domain shape (corners in a Y-junction geometry) that can affect the pulse
dynamics; we also show how brief, localized temperature perturbations can be
used to control reactive pulse propagation.The computational results are
corroborated through experimental studies in which the pulses are visualized
using Reflection Anisotropy Microscopy.Comment: submitted to Phys. Rev.
Hydrodynamics and two-dimensional dark lump solitons for polariton superfluids
We study a two-dimensional incoherently pumped exciton-polariton condensate described by an open-dissipative Gross-Pitaevskii equation for the polariton dynamics coupled to a rate equation for the exciton density. Adopting a hydrodynamic approach, we use multiscale expansion methods to derive several models appearing in the context of shallow water waves with viscosity. In particular, we derive a Boussinesq/Benney-Luke–type equation and its far-field expansion in terms of Kadomtsev-Petviashvili-I (KP-I) equations for right- and left-going waves. From the KP-I model, we predict the existence of vorticity-free, weakly (algebraically) localized two-dimensional dark-lump solitons. We find that, in the presence of dissipation, dark lumps exhibit a lifetime three times larger than that of planar dark solitons. Direct numerical simulations show that dark lumps do exist, and their dissipative dynamics is well captured by our analytical approximation. It is also shown that lumplike and vortexlike structures can spontaneously be formed as a result of the transverse “snaking” instability of dark soliton stripes.Europe Union project AEI/FEDER: MAT2016-79866-
Dynamic and Energetic Stabilization of Persistent Currents in Bose-Einstein Condensates
We study conditions under which vortices in a highly oblate harmonically
trapped Bose-Einstein condensate (BEC) can be stabilized due to pinning by a
blue-detuned Gaussian laser beam, with particular emphasis on the potentially
destabilizing effects of laser beam positioning within the BEC. Our approach
involves theoretical and numerical exploration of dynamically and energetically
stable pinning of vortices with winding number up to , in correspondence
with experimental observations. Stable pinning is quantified theoretically via
Bogoliubov-de Gennes excitation spectrum computations and confirmed via direct
numerical simulations for a range of conditions similar to those of
experimental observations. The theoretical and numerical results indicate that
the pinned winding number, or equivalently the winding number of the superfluid
current about the laser beam, decays as a laser beam of fixed intensity moves
away from the BEC center. Our theoretical analysis helps explain previous
experimental observations, and helps define limits of stable vortex pinning for
future experiments involving vortex manipulation by laser beams.Comment: 8 pages 5 figure
Controlling the transverse instability of dark solitons and nucleation of vortices by a potential barrier
We study possibilities to suppress the transverse modulational instability
(MI) of dark-soliton stripes in two-dimensional (2D) Bose-Einstein condensates
(BECs) and self-defocusing bulk optical waveguides by means of quasi-1D
structures. Adding an external repulsive barrier potential (which can be
induced in BEC by a laser sheet, or by an embedded plate in optics), we
demonstrate that it is possible to reduce the MI wavenumber band, and even
render the dark-soliton stripe completely stable. Using this method, we
demonstrate the control of the number of vortex pairs nucleated by each spatial
period of the modulational perturbation. By means of the perturbation theory,
we predict the number of the nucleated vortices per unit length. The analytical
results are corroborated by the numerical computation of eigenmodes of small
perturbations, as well as by direct simulations of the underlying
Gross-Pitaevskii/nonlinear Schr\"{o}dinger equation.Comment: 10 pages, 7 figures. To appear on Phys. Rev. A, 201
Bayesian estimation of species divergence times using correlated quantitative characters
Discrete morphological data have been widely used to study species evolution, but the use of quantitative (or continuous) morphological characters is less common. Here, we implement a Bayesian method to estimate species divergence times using quantitative characters. Quantitative character evolution is modelled using Brownian diffusion with character correlation and character variation within populations. Through simulations, we demonstrate that ignoring the population variation (or population “noise”) and the correlation among characters leads to biased estimates of divergence times and rate, especially if the correlation and population noise are high. We apply our new method to the analysis of quantitative characters (cranium landmarks) and molecular data from carnivoran mammals. Our results show that time estimates are affected by whether the correlations and population noise are accounted for or ignored in the analysis. The estimates are also affected by the type of data analysed, with analyses of morphological characters only, molecular data only, or a combination of both; showing noticeable differences among the time estimates. Rate variation of morphological characters among the carnivoran species appears to be very high, with Bayesian model selection indicating that the independent-rates model fits the morphological data better than the autocorrelated-rates model. We suggest that using morphological continuous characters, together with molecular data, can bring a new perspective to the study of species evolution. Our new model is implemented in the MCMCtree computer program for Bayesian inference of divergence times
A Nonlinear Adiabatic Theorem for Coherent States
We consider the propagation of wave packets for a one-dimensional nonlinear
Schrodinger equation with a matrix-valued potential, in the semi-classical
limit. For an initial coherent state polarized along some eigenvector, we prove
that the nonlinear evolution preserves the separation of modes, in a scaling
such that nonlinear effects are critical (the envelope equation is nonlinear).
The proof relies on a fine geometric analysis of the role of spectral
projectors, which is compatible with the treatment of nonlinearities. We also
prove a nonlinear superposition principle for these adiabatic wave packets.Comment: 21 pages, no figur
Impact of anisotropy on vortex clusters and their dynamics
We investigate the effects of anisotropy on the stability and dynamics of
vortex cluster states which arise in Bose-Einstein condensates. Sufficiently
strong anisotropies are shown to stabilize states with arbitrary numbers of
vortices that are highly unstable in the isotropic limit. Conversely,
anisotropy can be used to destabilize states which are stable in the isotropic
limit. Near the linear limit, we identify the bifurcations of vortex states
including their emergence from linear eigenstates, while in the strongly
nonlinear limit, a particle-like description of the dynamics of the vortices in
the anisotropic trap is developed. Both are in very good agreement with
numerical results. Collective modes of stabilized many vortex cluster states
are demonstrated.Comment: 6 pages, 6 figure
Statics, Dynamics and Manipulations of Bright Matter-Wave Solitons in Optical Lattices
Motivated by recent experimental achievement in the work with Bose-Einstein
condensates (BECs), we consider bright matter-wave solitons, in the presence of
a parabolic magnetic trap and a spatially periodic optical lattice (OL), in the
attractive BEC. We examine pinned states of the soliton and their stability by
means of perturbation theory. The analytical predictions are found to be in
good agreement with numerical simulations. We then explore possibilities to use
a time-modulated OL as a means of stopping and trapping a moving soliton, and
of transferring an initially stationary soliton to a prescribed position by a
moving OL. We also study the emission of radiation from the soliton moving
across the combined magnetic trap and OL. We find that the soliton moves freely
(without radiation) across a weak lattice, but suffers strong loss for stronger
OLs.Comment: 7 pages, 5 figs, Phys Rev A in Press (2005
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