A finite element method for nonlinear elliptic problems

We present a Galerkin method with piecewise polynomial continuous elements for fully nonlinear elliptic equations. A key tool is the discretization proposed in Lakkis and Pryer, 2011, allowing us to work directly on the strong form of a linear PDE. An added benefit to making use of this discretization method is that a recovered (finite element) Hessian is a byproduct of the solution process. We build on the linear method and ultimately construct two different methodologies for the solution of second order fully nonlinear PDEs. Benchmark numerical results illustrate the convergence properties of the scheme for some test problems as well as the Monge–Amp`ere equation and the Pucci equation.

A finite element method for second order nonvariational elliptic problems

We propose a numerical method to approximate the solution of second order elliptic problems in nonvariational form. The method is of Galerkin type using conforming finite elements and applied directly to the nonvariational (nondivergence) form of a second order linear elliptic problem. The key tools are an appropriate concept of “finite element Hessian” and a Schur complement approach to solving the resulting linear algebra problem. The method is illustrated with computational experiments on three linear and one quasi-linear PDE, all in nonvariational form.

A finite element-spherical harmonics model for radiative transfer in inhomogeneous clouds. Part II. some applications

EVENT has been used to examine the effects of 3D cloud structure, distribution, and inhomogeneity on the scattering of visible solar radiation and the resulting 3D radiation field. Large eddy simulation and aircraft measurements are used to create realistic cloud fields which are continuous or broken with smooth or uneven tops. The values, patterns and variance in the resulting downwelling and upwelling radiation from incident visible solar radiation at different angles are then examined and compared to measurements. The results from EVENT confirm that 3D cloud structure is important in determining the visible radiation field, and that these results are strongly influenced by the solar zenith angle. The results match those from other models using visible solar radiation, and are supported by aircraft measurements of visible radiation, providing confidence in the new model.

Antipathogenic activity of probiotics against Salmonella Typhimurium and Clostridium difficile in anaerobic batch culture systems: is it due to synergies in probiotic mixtures or the specificity of single strains?

Probiotics are currently being investigated for prevention of infections caused by enteric pathogens. The aim of this in vitro study was to evaluate the influence of three single probiotics: Lactobacillus casei NCIMB 30185 (PXN 37), Lactobacillus acidophilus NCIMB 30184 (PXN 35), Bifidobacterium breve NCIMB 30180 (PXN 25) and a probiotic mixture containing the above strains plus twelve other strains belonging to the Lactobacillus, Bifidobacterium, Lactococcus, Streptococcus and Bacillus genera on the survival of Salmonella Typhimurium and Clostridium difficile using pH-controlled anaerobic batch cultures containing mixed fecal bacteria. Changes in relevant bacterial groups and effects of probiotic addition on survival of the two pathogens were assessed over 24 h. Quantitative analysis of bacterial populations revealed that there was a significant increase in lactobacilli and/or bifidobacteria numbers, depending on probiotic addition, compared with the control (no added probiotic). There was also a significant reduction in S. Typhimurium and C. difficile numbers in the presence of certain probiotics compared with controls. Of the probiotic treatments, two single strains namely L. casei NCIMB 30185 (PXN 37), and B. breve NCIMB 30180 (PXN 25) were the most potent in reducing the numbers of S. Typhimurium and C. difficile. In addition, the supplementation with probiotics into the systems influenced some fermentations parameters. Acetate was found in the largest concentrations in all vessels and lactate and formate were generally detected in higher amounts in vessels with probiotic addition compared to controls.

The effect of (mis-specified) GARCH filters on the finite sample distribution of the BDS test

This paper considers the effect of using a GARCH filter on the properties of the BDS test statistic as well as a number of other issues relating to the application of the test. It is found that, for certain values of the user-adjustable parameters, the finite sample distribution of the test is far-removed from asymptotic normality. In particular, when data generated from some completely different model class are filtered through a GARCH model, the frequency of rejection of iid falls, often substantially. The implication of this result is that it might be inappropriate to use non-rejection of iid of the standardised residuals of a GARCH model as evidence that the GARCH model ‘fits’ the data.

Finite sample weighting of recursive forecast errors

This paper proposes and tests a new framework for weighting recursive out-of-sample prediction errors according to their corresponding levels of in-sample estimation uncertainty. In essence, we show how to use the maximum possible amount of information from the sample in the evaluation of the prediction accuracy, by commencing the forecasts at the earliest opportunity and weighting the prediction errors. Via a Monte Carlo study, we demonstrate that the proposed framework selects the correct model from a set of candidate models considerably more often than the existing standard approach when only a small sample is available. We also show that the proposed weighting approaches result in tests of equal predictive accuracy that have much better sizes than the standard approach. An application to an exchange rate dataset highlights relevant differences in the results of tests of predictive accuracy based on the standard approach versus the framework proposed in this paper.

The effect of temperature and inorganic phosphorus supply on growth and acid phosphatase production in arctic and temperate strains of ectomycorrhizal Hebeloma spp. in axenic culture

Acid phosphatase production by 12 Hebeloma strains was usually derepressed when inorganic phosphorus in the growth medium was limited, but appeared to be constitutive in some strains. At low temperatures (≤ 12°) arctic strains produced more extracellular and wall-bound acid phosphatase, yet grew more slowly than the temperate strains. We suggest that low growth rates in arctic strains may be a physiological response to cold whereby resources are diverted into carbohydrate accumulation for cryoprotection. At near freezing temperatures, increased extracellular phosphatase production may compensate for a loss of enzyme activity at low temperature and serve to hydrolyse organic phosphorus in frozen soil over winter.

Rawls and Rousseau: 'amour-propre' and the strains of commitment

In this paper I try to illuminate the Rawlsian architectonic through an interpretation of what Rawls’ Lectures on the History of Political Philosophy say about Rousseau. I argue that Rawls’ emphasis there when discussing Rousseau on interpreting amour-propre so as to make it compatible with a life in at least some societies draws attention to, and helps explicate, an analogous feature of his own work, the strains of commitment broadly conceived. Both are centrally connected with protecting a sense of self which is vital for one’s own agency. This allows us to appreciate better than much of the literature presently does the requirement for Rawls that justice and the good are congruent, that a society of justice does not disfigure citizens’ ability to live out lives relatively unmarked by relations of domination. Some comments on G. A. Cohen’s critiques of Rawls are made.

Noether-type discrete conserved quantities arising from a finite element approximation of a variational problem

In this work, we prove a weak Noether-type Theorem for a class of variational problems that admit broken extremals. We use this result to prove discrete Noether-type conservation laws for a conforming finite element discretisation of a model elliptic problem. In addition, we study how well the finite element scheme satisfies the continuous conservation laws arising from the application of Noether’s first theorem (1918). We summarise extensive numerical tests, illustrating the conservation of the discrete Noether law using the p-Laplacian as an example and derive a geometric-based adaptive algorithm where an appropriate Noether quantity is the goal functional.

Rossby wave propagation on potential vorticity fronts with finite width

The horizontal gradient of potential vorticity (PV) across the tropopause typically declines with lead time in global numerical weather forecasts and tends towards a steady value dependent on model resolution. This paper examines how spreading the tropopause PV contrast over a broader frontal zone affects the propagation of Rossby waves. The approach taken is to analyse Rossby waves on a PV front of finite width in a simple single-layer model. The dispersion relation for linear Rossby waves on a PV front of infinitesimal width is well known; here an approximate correction is derived for the case of a finite width front, valid in the limit that the front is narrow compared to the zonal wavelength. Broadening the front causes a decrease in both the jet speed and the ability of waves to propagate upstream. The contribution of these changes to Rossby wave phase speeds cancel at leading order. At second order the decrease in jet speed dominates, meaning phase speeds are slower on broader PV fronts. This asymptotic phase speed result is shown to hold for a wide class of single-layer dynamics with a varying range of PV inversion operators. The phase speed dependence on frontal width is verified by numerical simulations and also shown to be robust at finite wave amplitude, and estimates are made for the error in Rossby wave propagation speeds due to the PV gradient error present in numerical weather forecast models.

Clonal Relationship among Atypical Enteropathogenic Escherichia coli Strains Isolated from Different Animal Species and Humans

Forty-nine typical and atypical enteropathogenic Escherichia coli (EPEC) strains belonging to different serotypes and isolated from humans, pets (cats and dogs), farm animals (bovines, sheep, and rabbits), and wild animals (monkeys) were investigated for virulence markers and clonal similarity by pulsed-field gel electrophoresis (PFGE) and multilocus sequence typing (MLST). The virulence markers analyzed revealed that atypical EPEC strains isolated from animals have the potential to cause diarrhea in humans. A close clonal relationship between human and animal isolates was found by MLST and PFGE. These results indicate that these animals act as atypical EPEC reservoirs and may represent sources of infection for humans. Since humans also act as a reservoir of atypical EPEC strains, the cycle of mutual infection of atypical EPEC between animals and humans, mainly pets and their owners, cannot be ruled out since the transmission dynamics between the reservoirs are not yet clearly understood.