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

High speed quantum gates with cavity quantum electrodynamics

Cavity quantum electrodynamic schemes for quantum gates are amongst the earliest quantum computing proposals. Despite continued progress, and the dramatic recent demonstration of photon blockade, there are still issues with optimal coupling and gate operation involving high-quality cavities. Here we show dynamic control techniques that allow scalable cavity-QED based quantum gates, that use the full bandwidth of the cavities. When applied to quantum gates, these techniques allow an order of magnitude increase in operating speed, and two orders of magnitude reduction in cavity Q, over passive cavity-QED architectures. Our methods exploit Stark shift based Q-switching, and are ideally suited to solid-state integrated optical approaches to quantum computing.Comment: 4 pages, 3 figures, minor revision

The LuckyCam Survey for Very Low Mass Binaries II: 13 new M4.5-M6.0 Binaries

We present results from a high-angular-resolution survey of 78 very low mass (VLM) binary systems with 6.0 = 0.15 arcsec/yr. 21 VLM binaries were detected, 13 of them new discoveries. The new binary systems range in separation between 0.18 arcsec and 1.3 arcsec. The distance-corrected binary fraction is 13.5% (+6.5%/-4%), in agreement with previous results. 9 of the new binary systems have orbital radii > 10 AU, including a new wide VLM binary with 27 AU projected orbital separation. One of the new systems forms two components of a 2300 AU separation triple system. We find that the orbital radius distribution of the binaries with V-K < 6.5 in this survey appears to be different from that of redder (lower-mass) objects, suggesting a possible rapid change in the orbital radius distribution at around the M5 spectral type. The target sample was also selected to investigate X-ray activity among VLM binaries. There is no detectable correlation between excess X-Ray emission and the frequency and binary properties of the VLM systems.Comment: 11 pages, 8 figures. Submitted to MNRA

A mid-infrared survey of the inner 2 × 1.5 degrees of the Galaxy with Spitzer/IRAC

We present a survey of Spitzer Space Telescope/IRAC observations of the central 2 × 1.5 degrees (265 × 200 pc) of the Galaxy at 3-8 μm. These data represent the highest spatial resolution and sensitivity large-scale map made to date of the Galactic Center (GC) at mid-infrared wavelengths. The IRAC data provide a census of the optically obscured stellar sources as well as a detailed map of the highly filamentary structure in the interstellar medium. The diffuse emission is dominated by PAH emission from small grains in star-forming regions. Dark clouds displaying a large variety of sizes and morphologies are imaged, many of which remain opaque at IRAC wavelengths. Using a multiwavelength comparison, we determine which objects are likely to be in the foreground and which are located at the GC. We find no counterparts at IRAC wavelengths to the unique system of linear, nonthermal radio filaments present at the GC

The mid-infrared colors of the interstellar medium and extended sources at the Galactic center

A mid-infrared (3.6–8 μm) survey of the Galactic center has been carried out with the IRAC instrument on the Spitzer Space Telescope. This survey covers the central 2º x 1.4º (~280 x 200 pc) of the Galaxy. At 3.6 and 4.5 μm the emission is dominated by stellar sources, the fainter ones merging into an unresolved background. At 5.8 and 8 μm the stellar sources are fainter, and large-scale diffuse emission from the ISM of the Galaxy's central molecular zone becomes prominent. The survey reveals that the 8-to-5.8 μm color of the ISM emission is highly uniform across the surveyed region. This uniform color is consistent with a flat extinction law and emission from polycyclic aromatic hydrocarbons (PAHs). Models indicate that this broadband color should not be expected to change if the incident radiation field heating the dust and PAHs is ~10^4 times that of the solar neighborhood. Other regions of very red emission indicate cases where thick dust clouds obscure deeply embedded objects or very early stages of star formation

Mean field ground state of a spin-1 condensate in a magnetic field

We revisit the topic of the mean field ground state of a spin-1 atomic condensate inside a uniform magnetic field ($B$) under the constraints that both the total number of atoms ($N$) and the magnetization ($\cal M$) are conserved. In the presence of an internal state (spin component) independent trap, we also investigate the dependence of the so-called single spatial mode approximation (SMA) on the magnitude of the magnetic field and ${\cal M}$. Our result indicate that the quadratic Zeeman effect is an important factor in balancing the mean field energy from elastic atom-atom collisions that are known to conserve both $N$ and $\cal M$.Comment: 13 pages, 9 figures, to be published in New J. Phys. (http://www.njp.org/

Spin correlation and Discrete symmetry in Spinor Bose-Einstein Condensates

We study spin correlations in Bose-Einstein condensates of spin 1 bosons with scatterings dominated by a total spin equal 2 channel. We show the low energy spin dynamics in the system can be mapped into an $o(n)$ nonlinear sigma model(NL$\sigma$M). $n=3$ at the zero magnetic field limit and $n=2$ in the presence of weak magnetic fields. In an ordered phase, the ground state has a hidden $Z_2$ symmetry and is degenerate under the group $[U(1)\times S^{n-1}]/Z_2$. We explore consequences of the hidden symmetry and propose some measurements to probe it.Comment: 4 pages; published version in Phys. Rev. Lett. vol 87, 080401-1(2001

Characterization of unwanted noise in realistic cavities

The problem of the description of absorption and scattering losses in high-Q cavities is studied. The considerations are based on quantum noise theories, hence the unwanted noise associated with scattering and absorption is taken into account by introduction of additional damping and noise terms in the quantum Langevin equations and input--output relations. Completeness conditions for the description of the cavity models obtained in this way are studied and corresponding replacement schemes are discussed.Comment: Contribution to XI International Conference on Quantum Optics, Minsk, Belarus, 26-31 May, 200

X-ray Observations of Stellar Clusters Near the Galactic Center

We report the first detection of X-ray emission from the Quintuplet star cluster and compare its X-ray emission to that of the Arches star cluster. Four point sources are significantly detected near the core of the Quintuplet cluster with a total, absorption-corrected luminosity of ~1\times10^{33} ergs s^{-1}. Diffuse, thermal emission is also detected near the core of the Quintuplet cluster with an absorption-corrected luminosity of ~1\times10^{34} ergs s^{-1}. We analyze the diffuse and point-like emission from the Arches and Quintuplet and discuss the possibility that they are host to cluster wind outflows. We also present the results of our search for X-ray emission from candidate star clusters in the Galactic center (GC) region. We use extinction estimated by near-IR colors and X-ray spectral fits, as well as other IR properties, to determine if the candidate clusters are new, GC star clusters. We find that three of the six candidate clusters found toward the GC are likely foreground clusters, two of the candidate clusters are not detected in the X-ray data, but have near-IR extinctions consistent with a GC location, and one of the candidate clusters has X-ray and near-IR extinctions consistent with being in the GC. The X-ray and IR emission from the candidate clusters is compared to the known, massive, GC star clusters.Comment: Accepted to ApJ. 30 pages, 7 figure