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

Evaporation of a Kerr black hole by emission of scalar and higher spin particles

We study the evolution of an evaporating rotating black hole, described by the Kerr metric, which is emitting either solely massless scalar particles or a mixture of massless scalar and nonzero spin particles. Allowing the hole to radiate scalar particles increases the mass loss rate and decreases the angular momentum loss rate relative to a black hole which is radiating nonzero spin particles. The presence of scalar radiation can cause the evaporating hole to asymptotically approach a state which is described by a nonzero value of $a_* \equiv a / M$. This is contrary to the conventional view of black hole evaporation, wherein all black holes spin down more rapidly than they lose mass. A hole emitting solely scalar radiation will approach a final asymptotic state described by $a_* \simeq 0.555$. A black hole that is emitting scalar particles and a canonical set of nonzero spin particles (3 species of neutrinos, a single photon species, and a single graviton species) will asymptotically approach a nonzero value of $a_*$ only if there are at least 32 massless scalar fields. We also calculate the lifetime of a primordial black hole that formed with a value of the rotation parameter $a_{*}$, the minimum initial mass of a primordial black hole that is seen today with a rotation parameter $a_{*}$, and the entropy of a black hole that is emitting scalar or higher spin particles.Comment: 22 pages, 13 figures, RevTeX format; added clearer descriptions for variables, added journal referenc

Pooled Analysis of Individually Fed Finishing Trials

A pooled analysis of 21 finishing trials (2002–2016; 1530 animals) with cattle individually fed in Calan gate barns was conducted. Mixed model regression analysis following random coefficient methodology was used to evaluate relationships between performance variables and carcass characteristics. Gain had a greater effect on efficiency (R2 = 0.72) compared to intake (R2 = 0.02). The relationship between gain and efficiency was cubic, while intake had a quadratic relationship. The cubic response of gain relative to efficiency was continually increasing with relatively slight curves in the line heavily influenced by points that lay on the ends of the data. Efficiency also had cubic relationships with fat thickness and marbling of carcasses; however, the regressions had low R2 values of 0.01. There was a significant relationship between efficiency and fat thickness and marbling, but the variation around the trend line was high. Efficiency alone is a poor predictor of fat thickness and marbling

Electrochemical methods in pesticides control

The state of the art of voltammetric and amperometric methods used in the study and determination of pesticides in crops, food, phytopharmaceutical products, and environmental samples is reviewed. The main structural groups of pesticides, i.e., triazines, organophosphates, organochlorides, nitrocompounds, carbamates, thiocarbamates, sulfonylureas, and bipyridinium compounds are considered with some degradation products. The advantages, drawbacks, and trends in the development of voltammetric and amperometric methods for study and determination of pesticides in these samples are discussed

Electrochemical oxidation of propanil and related N-substituted amides

The electrochemical behaviour of propanil and related N-substituted amides (acetanilide and N,N-diphenylacetamide) was studied by cyclic and square wave voltammetry using a glassy carbon electrode. Propanil has been found to have chemical stability under the established analytical conditions and showed an oxidation peak at +1.27 V versus Ag/AgCl at pH 7.5. N,N-diphenylacetamide has a higher oxidation potential than the other compounds of +1.49 V versus Ag/AgCl. Acetanilide oxidation occurred at a potential similar to that of propanil, +1.24 V versus Ag/AgCl. These results are in agreement with the substitution pattern of the nitrogen atom of the amide. A degradation product of propanil, 3,4-dichloroaniline (DCA), was also studied, and showed an oxidation peak at +0.66 V versus Ag/AgCl. A simple and specific quantitative electroanalytical method is described for the analysis of propanil in commercial products that contain propanil as the active ingredient, used in the treatment of rice crops in Portugal.http://www.sciencedirect.com/science/article/B6TF4-430G3H9-5/1/43d591ce02cac4cb03b04dbedd1ac99

Electrochemical oxidation of propanil and related N-substituted amides

The electrochemical behaviour of propanil and related N-substituted amides (acetanilide and N,N-diphenylacetamide) was studied by cyclic and square wave voltammetry using a glassy carbon electrode. Propanil has been found to have chemical stability under the established analytical conditions and showed an oxidation peak at +1.27 V versus Ag/AgCl at pH 7.5. N,N-diphenylacetamide has a higher oxidation potential than the other compounds of +1.49 V versus Ag/AgCl. Acetanilide oxidation occurred at a potential similar to that of propanil, +1.24 V versus Ag/AgCl. These results are in agreement with the substitution pattern of the nitrogen atom of the amide. A degradation product of propanil, 3,4-dichloroaniline (DCA), was also studied, and showed an oxidation peak at +0.66 V versus Ag/AgCl. A simple and specific quantitative electroanalytical method is described for the analysis of propanil in commercial products that contain propanil as the active ingredient, used in the treatment of rice crops in Portugal.http://www.sciencedirect.com/science/article/B6TF4-430G3H9-5/1/43d591ce02cac4cb03b04dbedd1ac99

A Multi-Wavelength, Multi-Epoch Study of the Soft X-Ray Transient Prototype, V616 Mon (A0620-00)

We have obtained optical and infrared photometry of the soft x-ray transient prototype V616 Mon (A0620-00). From this photometry, we find a spectral type of K4 for the secondary star in the system, which is consistent with spectroscopic observations. We present J-, H-, and K-band light curves modeled with WD98 and ELC. Combining detailed, independently run models for ellipsoidal variations due to a spotted, non-spherical secondary star, and the observed ultraviolet to infrared spectral energy distribution of the system, we show that the most likely value for the orbital inclination is 40.75 +/- 3 deg. This inclination angle implies a primary black hole mass of 11.0 +/- 1.9 solar masses.Comment: 29 pages (preprint format), including 7 figures and 4 tables, accepted for publication in the Nov 2001 issue of A

Laser-induced ultrafast electron emission from a field emission tip

We show that a field emission tip electron source that is triggered with a femtosecond laser pulse can generate electron pulses shorter than the laser pulse duration (100&#; fs). The emission process is sensitive to a power law of the laser intensity, which supports an emission mechanism based on multiphoton absorption followed by over-the-barrier emission. Observed continuous transitions between power laws of different orders are indicative of field emission processes. We show that the source can also be operated so that thermionic emission processes become significant. Understanding these different emission processes is relevant for the production of sub-cycle electron pulses