Convergence of Multilevel Stationary Gaussian Convolution

In this paper we give a short note showing convergence rates for multilevel periodic approximation of smooth functions by multilevel Gaussian convolution. We will use the Gaussian scaling in the convolution at the finest level as a proxy for degrees of freedom $d$ in the model. We will show that, for functions in the native space of the Gaussian, convergence is of the order $d^{-\frac{\ln(d)}{\ln(2)}}$. This paper provides a baseline for what should be expected in discrete convolution, which will be the subject of a follow up paper

Convergence of Multilevel Stationary Gaussian Quasi-Interpolation

In this paper we present a new multilevel quasi-interpolation algorithm for smooth periodic functions using scaled Gaussians as basis functions. Recent research in this area has focussed upon implementations using basis function with finite smoothness. In this paper we deliver a first error estimates for the multilevel algorithm using analytic basis functions. The estimate has two parts, one involving the convergence of a low degree polynomial truncation term and one involving the control of the remainder of the truncation as the algorithm proceeds. Thus, numerically one observes a convergent scheme. Numerical results suggest that the scheme converges much faster than the theory shows

The effect of phase-correlated returns and spatial smoothing on the accuracy of radar refractivity retrievals

Radar refractivity retrievals have the potential to accurately capture near-surface humidity fields from the phase change of ground clutter returns. In practice, phase changes are very noisy and the required smoothing will diminish large radial phase change gradients, leading to severe underestimates of large refractivity changes (ΔN). To mitigate this, the mean refractivity change over the field (ΔNfield) must be subtracted prior to smoothing. However, both observations and simulations indicate that highly correlated returns (e.g., when single targets straddle neighboring gates) result in underestimates of ΔNfield when pulse-pair processing is used. This may contribute to reported differences of up to 30 N units between surface observations and retrievals. This effect can be avoided if ΔNfield is estimated using a linear least squares fit to azimuthally averaged phase changes. Nevertheless, subsequent smoothing of the phase changes will still tend to diminish the all-important spatial perturbations in retrieved refractivity relative to ΔNfield; an iterative estimation approach may be required. The uncertainty in the target location within the range gate leads to additional phase noise proportional to ΔN, pulse length, and radar frequency. The use of short pulse lengths is recommended, not only to reduce this noise but to increase both the maximum detectable refractivity change and the number of suitable targets. Retrievals of refractivity fields must allow for large ΔN relative to an earlier reference field. This should be achievable for short pulses at S band, but phase noise due to target motion may prevent this at C band, while at X band even the retrieval of ΔN over shorter periods may at times be impossible

Flake Density, Roll Diameter, and Flake Moisture All Influence Starch Availability of Steam-Flaked Corn

Steam-flaked corn is commonly fed in feedlot finishing diets because steam-flaking improves starch availability and nutrient utilization, thus improving the overall feeding value of corn. In most operations which utilize steam-flaked corn, grain is processed to a pre-determined flake density by setting the rolls to a specific separation distance and using tension to hold rolls together. Flaked grain is most often produced to a bulk density between 24 and 32 lb/bu, with a common recommendation of 27 lb/bu for corn; however, flake density among steam-flakers within a single mill and among feedlots can vary greatly. Flaking to a similar density using 2 flakers does not ensure similar starch availability. The degree of starch gelatinization or starch availability of steam-flaked corn can be estimated using analytical procedures such as enzymatic hydrolysis, gas production, and steam-flaked corn gelatinization methods. Routinely evaluating starch availability is used as a quality control method to standardize the steam-flaking process to ensure within-day and day-to-day manufacturing consistency. The concentration of readily available starch in steam-flaked corn is indicative of the rate of starch fermentation in the rumen. When starch is too readily available and is fermented at an excessively rapid rate, acid can accumulate in the rumen, reducing ruminal pH, and ultimately resulting in increased prevalence of digestive disturbances. Factors that contribute to variation between feedlot operations with respect to steamflaked corn quality include type and dimensions of flaking equipment, grain type, grain variety and moisture content, roll wear, and steam-flaking procedures. Sampling and handling procedures contribute to precision of results; therefore, sampling procedures need special attention, and consistency must be evaluated when attempting to determine starch availability of steam-flaked corn. The objective of this study was to evaluate starch availability of steam-flaked corn comparing roll dimensions and steam-flaked corn flake densities among flaking systems and feedyards and to provide information on the equipment utilized, steam-flaked corn flaking procedures, and to define current manufacturing practices of steam-flaking in commercial feedlot operations

Polarimetric radar observations and interpretation of co-cross-polar correlation coefficients

Includes bibliographical references (page 354).Preliminary analysis of all components of the polarimetric radar covariance matrix for precipitation measured with the NCAR S-band dual-polarization Doppler radar (S-Pol) and the Colorado State University-University of Chicago-Illinois State Water Survey (CSU-CHILL) radars is presented. Radar reflectivity at horizontal polarization Zh, differential reflectivity ZDR, linear depolarization ratio LDR, specific differential phase KDP, crosscorrelation coefficient | ρhv | , and two co-cross-polar correlation coefficients, ρxh and ρxv, have been measured and examined for two rain events: the 14 August 1998 case in Florida and the 8 August 1998 case in Colorado. Examination of the coefficients ρxh and ρxv is the major focus of the study. It is shown that hydrometeors with different types of orientation can be better delineated if the coefficients ρxv and ρxv are used. Rough estimates of the raindrop mean canting angles and the rms width of the canting angle distribution are obtained from the co-cross-polar correlation coefficients in combination with other polarimetric variables. Analysis of the two cases indicates that the raindrop net canting angles averaged over the propagation paths near the ground in typical convective cells do not exceed 2.5°. Nonetheless, the mean canting angles in individual radar resolution volumes in rain can be noticeably higher. Although the net canting angle for individual convective cells can deviate by a few degrees from zero, the average over a long propagation path along several cells is close to zero, likely because canting angles in different cells vary in sign. The rms width of the canting angle distribution in rain is estimated to vary mainly between 5° and 15° with the median value slightly below 10°

On the Dynamics of the Deployment of Renewable Energy Production Capacities

This chapter falls within the context of modeling the deployment of renewable en-ergy production capacities in the scope of the energy transition. This problem is addressed from an energy point of view, i.e. the deployment of technologies is seen as an energy investment under the constraint that an initial budget of non-renewable energy is provided. Using the Energy Return on Energy Investment (ERoEI) characteristics of technologies, we propose MODERN, a discrete-time formalization of the deployment of renewable energy production capacities. Be-sides showing the influence of the ERoEI parameter, the model also underlines the potential benefits of designing control strategies for optimizing the deployment of production capacities, and the necessity to increase energy efficiency.Peer reviewe

Seepage forces, important factors in the formation of horizontal hydraulic fractures and bedding-parallel fibrous veins ('beef' and 'cone-in-cone')

International audienceBedding-parallel fibrous veins ('beef' and 'cone-in-cone') are common to a number of sedimentary basins, especially those containing black shale. The type locality is SW England. The commonest mineral in the fibres is calcite. The fibres indicate vertical opening, against the force of gravity. In the past, this has been attributed to fluid overpressure. However, a simple analysis, based on Von Terzaghi's concepts, leads to the conclusion that, for the fractures to be horizontal, either the rock must be anisotropic, or it must be subject to horizontal compression. By means of a more complete analysis, supported by physical models, we show that horizontal fractures are to be expected, even if the rock is isotropic and there are no tectonic stresses. Upward fluid flow, in response to an overpressure gradient, imparts seepage forces to all elements of the solid framework. The seepage forces counteract the weight of the rock, and even surpass it, generating a tensile effective stress. The process may lead, either to tensile hydraulic fracturing, or to dilatant shear failure. We suggest that these two failure modes, and the availability of suitable solutes, explain the frequent occurrence of 'beef' and 'cone-in-cone' respectively

Stochastic electrotransport selectively enhances the transport of highly electromobile molecules

Nondestructive chemical processing of porous samples such as fixed biological tissues typically relies on molecular diffusion. Diffusion into a porous structure is a slow process that significantly delays completion of chemical processing. Here, we present a novel electrokinetic method termed stochastic electrotransport for rapid nondestructive processing of porous samples. This method uses a rotational electric field to selectively disperse highly electromobile molecules throughout a porous sample without displacing the low-electromobility molecules that constitute the sample. Using computational models, we show that stochastic electrotransport can rapidly disperse electromobile molecules in a porous medium. We apply this method to completely clear mouse organs within 1–3 days and to stain them with nuclear dyes, proteins, and antibodies within 1 day. Our results demonstrate the potential of stochastic electrotransport to process large and dense tissue samples that were previously infeasible in time when relying on diffusion.Simons Foundation. Postdoctoral FellowshipLife Sciences Research FoundationBurroughs Wellcome Fund (Career Awards at the Scientific Interface)Searle Scholars ProgramMichael J. Fox Foundation for Parkinson's ResearchUnited States. Defense Advanced Research Projects AgencyJPB FoundationNational Institutes of Health (U.S.)National Institutes of Health (U.S.) (Grant 1-U01-NS090473-01

Readings in the UK energy security

Over the last few decades, the debate about 'Peak Oil' became increasingly common and frustrating to governments, oil companies and individuals. Also in the last decade or so, some unusual events took places, which have raised the concern about the future of energy resources.i These events lead policy makers to consider what is known today as 'Energy Security'. The UK is one of these countries that fears the unknown future should petroleum resources worldwide become scarce or vanish. After the dwindling of the North Sea production, the UK found itself on the brink of losing its energy self-sufficiency (Macalister, 2010). This paper sets the following questions: has the UK’s oil and gas production peaked yet? If so, does the UK have a serious energy security problem? and if so, how this problem may be solved and what are the possible short, medium and long-term solutions for such a concern? In answering these questions, the paper discusses the concerns and challenges to the UK energy security and brings about the Government plans for tackling these concerns. It is found that the UK does not experience an energy security problem on the short to medium-term, but it may suffer energy insecurity on the longer-term