19,425 research outputs found
Localized structures in Kagome lattices
We investigate the existence and stability of gap vortices and multi-pole gap
solitons in a Kagome lattice with a defocusing nonlinearity both in a discrete
case and in a continuum one with periodic external modulation. In particular,
predictions are made based on expansion around a simple and analytically
tractable anti-continuum (zero coupling) limit. These predictions are then
confirmed for a continuum model of an optically-induced Kagome lattice in a
photorefractive crystal obtained by a continuous transformation of a honeycomb
lattice
Evidence of a bond-nematic phase in LiCuVO4
Polarized and unpolarized neutron scattering experiments on the frustrated
ferromagnetic spin-1/2 chain LiCuVO4 show that the phase transition at HQ of 8
Tesla is driven by quadrupolar fluctuations and that dipolar correlations are
short-range with moments parallel to the applied magnetic field in the
high-field phase. Heat-capacity measurements evidence a phase transition into
this high-field phase, with an anomaly clearly different from that at low
magnetic fields. Our experimental data are consistent with a picture where the
ground state above HQ has a next-nearest neighbour bond-nematic order along the
chains with a fluid-like coherence between weakly coupled chains.Comment: 5 pages, 4 figures. To appear in Phys. Rev. Let
Model for resonant photon creation in a cavity with time dependent conductivity
In an electromagnetic cavity, photons can be created from the vacuum state by
changing the cavity's properties with time. Using a simple model based on a
massless scalar field, we analyze resonant photon creation induced by the
time-dependent conductivity of a thin semiconductor film contained in the
cavity. This time dependence may be achieved by irradiating periodically the
film with short laser pulses. This setup offers several experimental advantages
over the case of moving mirrors.Comment: 9 pages, 1 figure. Minor changes. Version to appear in Phys. Rev.
A 2MASS All-Sky View of the Sagittarius Dwarf Galaxy: IV. Modeling the Sagittarius Tidal Tails
M giants recovered from the Two Micron All-Sky Survey (2MASS) have recently
been used to map the position and velocity distributions of tidal debris from
the Sagittarius (Sgr) dwarf spheroidal galaxy entirely around the Galaxy. We
compare this data set to both test particle orbits and N-body simulations of
satellite destruction run within a variety of rigid Milky Way potentials and
find that the mass of the Milky Way within 50 kpc of its center should be
3.8-5.6 x 10^11 Msun in order for any Sgr orbit to simultaneously fit the
velocity gradient in the Sgr trailing debris and the apocenter of the Sgr
leading debris. Orbital pole precession of young debris and leading debris
velocities in regions corresponding to older debris provide contradictory
evidence in favor of oblate/prolate Galactic halo potentials respectively,
leading us to conclude that the orbit of Sgr has evolved over the past few Gyr.
Based upon the velocity dispersion and width along the trailing tidal stream
we estimate the current bound mass of Sgr to be M_Sgr = 2 - 5 x 10^8 Msun
independant of the form of the Galactic potential; this corresponds to a range
of mass to light ratios (M/L)_Sgr = 14 - 36 (M/L)_Sun for the Sgr core. Models
with masses in this range best fit the apocenter of leading Sgr tidal debris
when they orbit with a radial period of roughly 0.85 Gyr and have periGalactica
and apoGalactica of about 15 kpc and 60 kpc respectively. These distances will
scale with the assumed distance to the Sgr dwarf and the assumed depth of the
Galactic potential. The density distribution of debris along the orbit in these
models is consistent with the M giant observations, and debris at all orbital
phases where M giants are obviously present is younger (i.e. was lost more
recently from the satellite) than the typical age of a Sgr M giant star.Comment: 42 pages, 13 figures; Accepted for publication by ApJ (October 08,
2004; originally submitted May 10, 2004). Fixed typos and added references.
PDF file with high resolution figures may be downloaded from
http://www.astro.caltech.edu/~drlaw/Papers/Sgr_paper4.pd
Stability of Filters for the Navier-Stokes Equation
Data assimilation methodologies are designed to incorporate noisy
observations of a physical system into an underlying model in order to infer
the properties of the state of the system. Filters refer to a class of data
assimilation algorithms designed to update the estimation of the state in a
on-line fashion, as data is acquired sequentially. For linear problems subject
to Gaussian noise filtering can be performed exactly using the Kalman filter.
For nonlinear systems it can be approximated in a systematic way by particle
filters. However in high dimensions these particle filtering methods can break
down. Hence, for the large nonlinear systems arising in applications such as
weather forecasting, various ad hoc filters are used, mostly based on making
Gaussian approximations. The purpose of this work is to study the properties of
these ad hoc filters, working in the context of the 2D incompressible
Navier-Stokes equation. By working in this infinite dimensional setting we
provide an analysis which is useful for understanding high dimensional
filtering, and is robust to mesh-refinement. We describe theoretical results
showing that, in the small observational noise limit, the filters can be tuned
to accurately track the signal itself (filter stability), provided the system
is observed in a sufficiently large low dimensional space; roughly speaking
this space should be large enough to contain the unstable modes of the
linearized dynamics. Numerical results are given which illustrate the theory.
In a simplified scenario we also derive, and study numerically, a stochastic
PDE which determines filter stability in the limit of frequent observations,
subject to large observational noise. The positive results herein concerning
filter stability complement recent numerical studies which demonstrate that the
ad hoc filters perform poorly in reproducing statistical variation about the
true signal
Multiphoton entanglement through a Bell multiport beam splitter
Multiphoton entanglement is an important resource for linear optics quantum
computing. Here we show that a wide range of highly entangled multiphoton
states, including W-states, can be prepared by interfering single photons
inside a Bell multiport beam splitter and using postselection. A successful
state preparation is indicated by the collection of one photon per output port.
An advantage of the Bell multiport beam splitter is that it redirects the
photons without changing their inner degrees of freedom. The described setup
can therefore be used to generate polarisation, time-bin and frequency
multiphoton entanglement, even when using only a single photon source.Comment: 8 pages, 2 figures, carefully revised version, references adde
Development of a new machine system for the forming of micro-sheet-products
Most of the developed micro-forming machines were based on standalone concepts which do not support efficient integration to make them fully automated and integrated. At present, material feeding in micro-forming is not of sufficient precision and reliability for high throughput manufacturing applications. Precise feeding is necessary to ensure that micro-parts can be produced with sufficient accuracy, especially in multi-stage forming, while high-speed feeding is a must to meet the production-rate requirements. Therefore, design of a new high-precision and high-speed feeder for micro-forming is proposed. Several possible approaches are examined with a view to establishing feasible concepts. Based on the investigation, several concepts for thin sheet-metal feeding for micro-forming are generated, they being argued and assessed with applicable loads and forces analysis. These form a basis of designing a new feeder
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