Estimating eddy diffusivities from noisy Lagrangian observations

The problem of estimating the eddy diffusivity from Lagrangian observations in the presence of measurement error is studied in this paper. We consider a class of incompressible velocity fields for which is can be rigorously proved that the small scale dynamics can be parameterised in terms of an eddy diffusivity tensor. We show, by means of analysis and numerical experiments, that subsampling of the data is necessary for the accurate estimation of the eddy diffusivity. The optimal sampling rate depends on the detailed properties of the velocity field. Furthermore, we show that averaging over the data only marginally reduces the bias of the estimator due to the multiscale structure of the problem, but that it does significantly reduce the effect of observation error

An Evaluation of the Effect of Discharging a High Quality Effluent into a Small Ozark Mountain Stream

Recently the newly constructed Fayetteville wastewater treatment plant went on line and directed a portion of its discharge to a point in the Mud Creek drainage basin that had previously not received any effluent. Prior to the discharge, a background study had been performed to establish the water quality in the basin. The background data, when compared to the data collected by this study, allowed any alteration of the stream water quality to be evaluated. Also the modeling procedure used to set the effluent limits for the treatment plant was analyzed. All stream data were compared to the limits set forth for surface water quality by the Department of Pollution Control and Ecology. The new discharge had some effect on the receiving stream, however, the stream still meets Arkansas water quality standards for all parameters

A Constrained Approach to Multiscale Stochastic Simulation of\ud Chemically Reacting Systems

Stochastic simulation of coupled chemical reactions is often computationally intensive, especially if a chemical system contains reactions occurring on different time scales. In this paper we introduce a multiscale methodology suitable to address this problem. It is based on the Conditional Stochastic Simulation Algorithm (CSSA) which samples from the conditional distribution of the suitably defined fast variables, given values for the slow variables. In the Constrained Multiscale Algorithm (CMA) a single realization of the CSSA is then used for each value of the slow variable to approximate the effective drift and diffusion terms, in a similar manner to the constrained mean-force computations in other applications such as molecular dynamics. We then show how using the ensuing Stochastic Differential Equation (SDE) approximation, we can in turn approximate average switching times in stochastic chemical systems

Use of active control technology to improve ride qualities of large transport aircraft

Analyses, construction and flight testing of two systems: Beta-vane and Modal Suppression Augmentation System (MSAS), which were developed to suppress gust induced lateral accelerations of large aircraft, are described. The 747 transport was used as the test vehicle. The purpose of the Beta-vane system is to reduce acceleration levels at the dutch roll frequency whereas the function of the MSAS system is to reduce accelerations due to flexible body motions caused by turbulence. Data from flight test, with both systems engaged shows a 50 to 70 percent reduction in lateral aft body acceleration levels. Furthermore, it is suggested that present day techniques used for developing dynamic equations of motion in the flexible mode region are limited

MCMC methods for functions modifying old algorithms to make\ud them faster

Many problems arising in applications result in the need\ud to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes. Standard MCMC algorithms typically become arbitrarily slow under the mesh refinement dictated by nonparametric description of the unknown function. We describe an approach to modifying a whole range of MCMC methods which ensures that their speed of convergence is robust under mesh refinement. In the applications of interest the data is often sparse and the prior specification is an essential part of the overall modeling strategy. The algorithmic approach that we describe is applicable whenever the desired probability measure has density with respect to a Gaussian process or Gaussian random field prior, and to some useful non-Gaussian priors constructed through random truncation. Applications are shown in density estimation, data assimilation in fluid mechanics, subsurface geophysics and image registration. The key design principle is to formulate the MCMC method for functions. This leads to algorithms which can be implemented via minor modification of existing algorithms, yet which show enormous speed-up on a wide range of applied problems

16S rRNA gene sequencing of mock microbial populations- impact of DNA extraction method, primer choice and sequencing platform

peer-reviewedBackground Next-generation sequencing platforms have revolutionised our ability to investigate the microbiota composition of complex environments, frequently through 16S rRNA gene sequencing of the bacterial component of the community. Numerous factors, including DNA extraction method, primer sequences and sequencing platform employed, can affect the accuracy of the results achieved. The aim of this study was to determine the impact of these three factors on 16S rRNA gene sequencing results, using mock communities and mock community DNA. Results The use of different primer sequences (V4-V5, V1-V2 and V1-V2 degenerate primers) resulted in differences in the genera and species detected. The V4-V5 primers gave the most comparable results across platforms. The three Ion PGM primer sets detected more of the 20 mock community species than the equivalent MiSeq primer sets. Data generated from DNA extracted using the 2 extraction methods were very similar. Conclusions Microbiota compositional data differed depending on the primers and sequencing platform that were used. The results demonstrate the risks in comparing data generated using different sequencing approaches and highlight the merits of choosing a standardised approach for sequencing in situations where a comparison across multiple sequencing runs is required.This publication has emanated from research supported in part by a research grant from Science Foundation Ireland (SFI) under Grant Numbers SFI/12/RC/2273 and 11/PI/1137 and by FP7 funded CFMATTERS (Cystic Fibrosis Microbiome-determined Antibiotic Therapy Trial in Exacerbations: Results Stratified, Grant Agreement no. 603038)

The Redshift Distribution of FIRST Radio Sources at 1 mJy

We present spectra for a sample of radio sources from the FIRST survey, and use them to define the form of the redshift distribution of radio sources at mJy levels.We targeted 365 sources and obtained 46 redshifts (13 per cent of the sample). We find that our sample is complete in redshift measurement to R $\sim 18.6$, corresponding to $z\sim 0.2$. Early-type galaxies represent the largest subset (45 per cent) of the sample and have redshifts 0.15\la z \la 0.5 ; late-type galaxies make up 15 per cent of the sample and have redshifts 0.05\la z \la 0.2; starbursting galaxies are a small fraction ($\sim 6$ per cent), and are very nearby (z\la 0.05). Some 9 per cent of the population have Seyfert1/quasar-type spectra, all at z\ga 0.8, and there are 4 per cent are Seyfert2 type galaxies at intermediate redshifts ($z\sim 0.2$). Using our measurements and data from the Phoenix survey, we obtain an estimate for $N(z)$ at $S_{1.4 \rm {GHz}}\ge 1$ mJy and compare this with model predictions. At variance with previous conclusions, we find that the population of starbursting objects makes up \la 5 per cent of the radio population at S $\sim 1$ mJy.Comment: 20 pages, sumbitted to MNRA

Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics

In Holm (Holm 2015 Proc. R. Soc. A 471, 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow