12,618 research outputs found
Well-Posedness And Accuracy Of The Ensemble Kalman Filter In Discrete And Continuous Time
The ensemble Kalman filter (EnKF) is a method for combining a dynamical model
with data in a sequential fashion. Despite its widespread use, there has been
little analysis of its theoretical properties. Many of the algorithmic
innovations associated with the filter, which are required to make a useable
algorithm in practice, are derived in an ad hoc fashion. The aim of this paper
is to initiate the development of a systematic analysis of the EnKF, in
particular to do so in the small ensemble size limit. The perspective is to
view the method as a state estimator, and not as an algorithm which
approximates the true filtering distribution. The perturbed observation version
of the algorithm is studied, without and with variance inflation. Without
variance inflation well-posedness of the filter is established; with variance
inflation accuracy of the filter, with resepct to the true signal underlying
the data, is established. The algorithm is considered in discrete time, and
also for a continuous time limit arising when observations are frequent and
subject to large noise. The underlying dynamical model, and assumptions about
it, is sufficiently general to include the Lorenz '63 and '96 models, together
with the incompressible Navier-Stokes equation on a two-dimensional torus. The
analysis is limited to the case of complete observation of the signal with
additive white noise. Numerical results are presented for the Navier-Stokes
equation on a two-dimensional torus for both complete and partial observations
of the signal with additive white noise
Oil Pollution in the Coastal Waters off Port Dickson, Straits of Malacca
The petroleum hydrocarbon dist1ibution in the Port Dichson coastal waters was studied over a period of three years
from 1986 to 1989. Generally, there was no significant difference (P > 0.05) of hydrocarbon levels in water among
the sampling stations on each of the sampling dates. However a pronounced fluctuation was found at different
samping dates. Similarly, a pronounced fluctuation of hydrocarbon content in the sediment with different sampling
dates was also detected. The mean hydrocarbon level in the water ranged between 14.69ppb and 150.28 ppb, ESSO
'Tapis A crude oil equivalent (or between 0.77 ppb and 7.87 ppb, chrysene equivalent), while for the sediment it
ranged between 21. 73 mg/kg and 74.50 mg/kgdry sediment, Esso Tapis A crude oil equivalent (or between 1.12
mg/hgand 3. 90 mg/kgdry sediment, chrysene equivalent). The oil pollution level in the PortDickson coastal waters
was comparable or higher than that found in the Exclusive Economic Zone watels off Pahang and Sabah, but was
lower than that detected in the Terengganu and Sanl1uak waters. The saUTce of hydrocarbon pollution in the POTt
Dichsm~ coastal waters was probably from the open sea and the nearby harbour and oil refineries rather than from
land TUn of
Entangled quantum tunneling of two-component Bose-Einstein condensates
We examine the quantum tunneling process in Bose condensates of two
interacting species trapped in a double well configuration. We discover the
condition under which particles of different species can tunnel as pairs
through the potential barrier between two wells in opposition directions. This
novel form of tunneling is due to the interspecies interaction that eliminates
the self- trapping effect. The correlated motion of tunneling atoms leads to
the generation of quantum entanglement between two macroscopically coherent
systems.Comment: 4 pages, 3 figure
Quantum Dot in 2D Topological Insulator: The Two-channel Kondo Fixed Point
In this work, a quantum dot couples to two helical edge states of a 2D
topological insulator through weak tunnelings is studied. We show that if the
electron interactions on the edge states are repulsive, with Luttinger liquid
parameter , the system flows to a stable two-channel fixed point at
low temperatures. This is in contrast to the case of a quantum dot couples to
two Luttinger liquid leads. In the latter case, a strong electron-electron
repulsion is needed, with , to reach the two-channel fixed point. This
two-channel fixed point is described by a boundary Sine-Gordon Hamiltonian with
a dependent boundary term. The impurity entropy at zero temperature is
shown to be . The impurity specific heat is when , and when . We
also show that the linear conductance across the two helical edges has
non-trivial temperature dependence as a result of the renormalization group
flow.Comment: 4+\epsilon page
Atomic layer deposition of ZnS nanotubes
We report on growth of high-aspect-ratio () zinc sulfide
nanotubes with variable, precisely tunable, wall thicknesses and tube diameters
into highly ordered pores of anodic alumina templates by atomic layer
deposition (ALD) at temperatures as low as 75 C. Various
characterization techniques are employed to gain information on the
composition, morphology, and crystal structure of the synthesized samples.
Besides practical applications, the ALD-grown tubes could be envisaged as model
systems for the study of a certain class of size-dependent quantum and
classical phenomena.Comment: 1 LaTeX source file, 8 eps figures, and the manuscript in PDF forma
Dynamics of spin-2 Bose condensate driven by external magnetic fields
Dynamic response of the F=2 spinor Bose-Einstein condensate (BEC) under the
influence of external magnetic fields is studied. A general formula is given
for the oscillation period to describe population transfer from the initial
polar state to other spin states. We show that when the frequency and the
reduced amplitude of the longitudinal magnetic field are related in a specific
manner, the population of the initial spin-0 state will be dynamically
localized during time evolution. The effects of external noise and nonlinear
spin exchange interaction on the dynamics of the spinor BEC are studied. We
show that while the external noise may eventually destroy the Rabi oscillations
and dynamic spin localization, these coherent phenomena are robust against the
nonlinear atomic interaction.Comment: 16 pages, 7 figures. accepted by Phys. Rev.
Double Phase Transitions in Magnetized Spinor Bose-Einstein Condensation
It is investigated theoretically that magnetized Bose-Einstein condensation
(BEC) with the internal (spin) degrees of freedom exhibits a rich variety of
phase transitions, depending on the sign of the interaction in the spin
channel. In the antiferromagnetic interaction case there exist always double
BEC transitions from single component BEC to multiple component BEC. In the
ferromagnetic case BEC becomes always unstable at a lower temperature, leading
to a phase separation. The detailed phase diagram for the temperature vs the
polarization, the spatial spin structure, the distribution of non-condensates
and the excitation spectrum are examined for the harmonically trapped systems.Comment: 6 pages, 7 figures. Submitted to J. Phys. Soc. Jp
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
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