Analysis of the 3DVAR Filter for the Partially Observed Lorenz '63 Model

The problem of effectively combining data with a mathematical model constitutes a major challenge in applied mathematics. It is particular challenging for high-dimensional dynamical systems where data is received sequentially in time and the objective is to estimate the system state in an on-line fashion; this situation arises, for example, in weather forecasting. The sequential particle filter is then impractical and ad hoc filters, which employ some form of Gaussian approximation, are widely used. Prototypical of these ad hoc filters is the 3DVAR method. The goal of this paper is to analyze the 3DVAR method, using the Lorenz '63 model to exemplify the key ideas. The situation where the data is partial and noisy is studied, and both discrete time and continuous time data streams are considered. The theory demonstrates how the widely used technique of variance inflation acts to stabilize the filter, and hence leads to asymptotic accuracy

Liquid bridging of cylindrical colloids in near-critical solvents

Within mean field theory, we investigate the bridging transition between a pair of parallel cylindrical colloids immersed in a binary liquid mixture as a solvent which is close to its critical consolute point $T_c$. We determine the universal scaling functions of the effective potential and of the force between the colloids. For a solvent which is at the critical concentration and close to $T_c$, we find that the critical Casimir force is the dominant interaction at close separations. This agrees very well with the corresponding Derjaguin approximation for the effective interaction between the two cylinders, while capillary forces originating from the extension of the liquid bridge turn out to be more important at large separations. In addition, we are able to infer from the wetting characteristics of the individual colloids the first-order transition of the liquid bridge connecting two colloidal particles to the ruptured state. While specific to cylindrical colloids, the results presented here provide also an outline for identifying critical Casimir forces acting on bridged colloidal particles as such, and for analyzing the bridging transition between them.Comment: 23 pages, 12 figure

Relative abundance and size composition of subtidal abalone, Haliotis spp., sea urchin, Strongylocentrotus spp., and abundance of sea stars off Fitzgerald marine reserve, September 1993

Data were collected at twenty-six dive stations at seven discrete latitudes along Fitzgerald Marine Reserve (FMR). Dive stations were targeted at three stratified depth zones: shallow (6.1 m), medium (10.7 m), and deep (16.8 m) in six of the seven locations. Two types of line transects, emergent and invasive, were completed by separate dive teams at each dive station. The area surveyed totalled 1,510 m2 for emergent and 560 m2 for invasive transects. Reef habitat dominated all depth zones, with moveable boulder and cobble increasing at medium and shallow depths. Encrusting coraline and surface algae dominated (49%), followed by turf (37%), sub-canopy (11.2%), and rare canopy (0.2%). Canopy was found only at shallow depths. Turf and sub-canopy decreased with depth. Only two species of abalone, red, Haliotis rufescens, and flat, H. walallensis, were found. Flat abalone were extremely rare with only two found on invasive transects (0.004 abalone m-2). Red abalone densities were low at both emergent (0.02 abalone m-2, s.e.=O.Ol) and invasive (0.07 abalone m-2, s.e.=0.03 ) transects. Red abalone concentrations differed significantly by depth and location. No abalone were found at deep depths and only one sport-legal (178 mm shell length) abalone was found at medium depth. One commercial legal (198 mm shell length) abalone was found on the entire survey. Most sport-legal abalone were located in cryptic habitat in shallow invasive transects (38%), compared to 7% on emergent transects. The only evidence of recruitment was found on invasive transects where three young-of-the-year (<=31 mm shell length) red abalone were found. Evidence from our survey and other sources suggests that sport and commercial fisheries are not sustainable off the San Mateo coast. Red urchin, Stongylocentrotus franciscanus, were more abundant than purple urchin, S. purpuratus, or red abalone. Red urchin densities were lower in emergent (1.08 urchin m-2,s.e.=0.04) than invasive (1.52, s.e.=0.06 m-2) transects. Densities of red urchin at deep stations in areas of lower algal abundance and potentially greater commercial fishing pressure were about one-half the densities at medium and shallow depths. ANOVA showed significant differences by depth and location. Mean Test Diameter (MTD) increased from deep to medium to shallow depths, while juvenile (<=50 mm) MTD showed an inverse relationship with depth. Shallow-depth invasive transects revealed a missing mode of 83 mm red urchin. This size mode was not found in emergent transects, probably due to cryptic habitat. Purple urchin were found at low densities at all three depth strata. Purple urchin densities were comparable in emergent (0.11 urchin m-2, s.e.=0.02 ) and invasive (0.09 urchin m-2,s.e.=0.03) transects. ANOVA showed densities varied significantly by location but not depth. 'Juvenile' purple urchin abundance showed an inverse relation to juvenile red urchin, increasing from deep to shallow depths. Purple urchin MTD of 84 mm (s.d.=23) was larger than reported for intertidal areas off FMR. Sea stars were found in high abundance off FMR. Bat stars, Asterina minata, had the highest densities (0.79 sea stars m-2, s.e.=0.03) followed by Pisaster sp. (0.47 sea stars m-2,s.e.=0.03 ), and sunflower stars, Pycnopodia helianthoides, (0.11 sea stars m-2, s.e.=0.04). Pisaster sp. was the only group of sea stars where differences in density were significant by depth or location. (30pp.

Data Assimilation: A Mathematical Introduction

These notes provide a systematic mathematical treatment of the subject of data assimilation

Two Wide Planetary-mass Companions to Solar-type Stars in Upper Scorpius

At wide separations, planetary-mass and brown dwarf companions to solar-type stars occupy a curious region of parameter space not obviously linked to binary star formation or solar system scale planet formation. These companions provide insight into the extreme case of companion formation (either binary or planetary), and due to their relative ease of observation when compared to close companions, they offer a useful template for our expectations of more typical planets. We present the results from an adaptive optics imaging survey for wide (~50–500 AU) companions to solar-type stars in Upper Scorpius. We report one new discovery of a ~14 M_J companion around GSC 06214−00210and confirm that the candidate planetary-mass companion 1RXS J160929.1−210524 detected by Lafrenière et al. is in fact comoving with its primary star. In our survey, these two detections correspond to ~4% of solar-type stars having companions in the 6–20 M_J mass and ~200–500 AU separation range. This figure is higher than would be expected if brown dwarfs and planetary-mass companions were drawn from an extrapolation of the binary mass function. Finally, we discuss implications for the formation of these objects

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

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

Field Induced Magnetic Ordering and Single-ion Anisotropy in the Quasi-1D Haldane Chain Compound SrNi2V2O8: A Single Crystal investigation

Field-induced magnetic ordering in the Haldane chain compound SrNi$_{2}$V$_{2}$O$_{8}$ and effect of anisotropy have been investigated using single crystals. Static susceptibility, inelastic neutron scattering, high-field magnetization, and low temperature heat-capacity studies confirm a non-magnetic spin-singlet ground state and a gap between the singlet ground state and triplet excited states. The intra-chain exchange interaction is estimated to be $J \sim 8.9{\pm}$0.1 meV. Splitting of the dispersions into two modes with minimum energies 1.57 and 2.58 meV confirms the existence of single-ion anisotropy $D(S^z){^2}$. The value of {\it D} is estimated to be $-0.51{\pm}0.01$ meV and the easy axis is found to be along the crystallographic {\it c}-axis. Field-induced magnetic ordering has been found with two critical fields [$\mu_0H_c^{\perp c} = 12.0{\pm}$0.2 T and $\mu_0H_c^{\parallel c} = 20.8{\pm}$0.5 T at 4.2 K]. Field-induced three-dimensional magnetic ordering above the critical fields is evident from the heat-capacity, susceptibility, and high-field magnetization study. The Phase diagram in the {\it H-T} plane has been obtained from the high-field magnetization. The observed results are discussed in the light of theoretical predictions as well as earlier experimental reports on Haldane chain compounds

Climatic versus biotic constraints on carbon and water fluxes in seasonally drought-affected ponderosa pine ecosystems

We investigated the relative importance of climatic versus biotic controls on gross primary production (GPP) and water vapor fluxes in seasonally drought-affected ponderosa pine forests. The study was conducted in young (YS), mature (MS), and old stands (OS) over 4 years at the AmeriFlux Metolius sites. Model simulations showed that interannual variation of GPP did not follow the same trends as precipitation, and effects of climatic variation were smallest at the OS (50%), and intermediate at the YS (<20%). In the young, developing stand, interannual variation in leaf area has larger effects on fluxes than climate, although leaf area is a function of climate in that climate can interact with age-related shifts in carbon allocation and affect whole-tree hydraulic conductance. Older forests, with well-established root systems, appear to be better buffered from effects of seasonal drought and interannual climatic variation. Interannual variation of net ecosystem exchange (NEE) was also lowest at the OS, where NEE is controlled more by interannual variation of ecosystem respiration, 70% of which is from soil, than by the variation of GPP, whereas variation in GPP is the primary reason for interannual changes in NEE at the YS and MS. Across spatially heterogeneous landscapes with high frequency of younger stands resulting from natural and anthropogenic disturbances, interannual climatic variation and change in leaf area are likely to result in large interannual variation in GPP and NEE

Laser-only adaptive optics achieves significant image quality gains compared to seeing-limited observations over the entire sky

Adaptive optics laser guide star systems perform atmospheric correction of stellar wavefronts in two parts: stellar tip-tilt and high-spatial-order laser-correction. The requirement of a sufficiently bright guide star in the field-of-view to correct tip-tilt limits sky coverage. Here we show an improvement to effective seeing without the need for nearby bright stars, enabling full sky coverage by performing only laser-assisted wavefront correction. We used Robo-AO, the first robotic AO system, to comprehensively demonstrate this laser-only correction. We analyze observations from four years of efficient robotic operation covering 15,000 targets and 42,000 observations, each realizing different seeing conditions. Using an autoguider (or a post-processing software equivalent) and the laser to improve effective seeing independent of the brightness of a target, Robo-AO observations show a 39+/-19% improvement to effective FWHM, without any tip-tilt correction. We also demonstrate that 50% encircled-energy performance without tip-tilt correction remains comparable to diffraction-limited, standard Robo-AO performance. Faint-target science programs primarily limited by 50% encircled-energy (e.g. those employing integral field spectrographs placed behind the AO system) may see significant benefits to sky coverage from employing laser-only AO.Comment: Accepted for publication in The Astronomical Journal. 7 pages, 6 figure