Root system of singular perturbations of the harmonic oscillator type operators

We analyze perturbations of the harmonic oscillator type operators in a Hilbert space H, i.e. of the self-adjoint operator with simple positive eigenvalues μ k satisfying μ k+1 − μ k ≥ Δ > 0. Perturbations are considered in the sense of quadratic forms. Under a local subordination assumption, the eigenvalues of the perturbed operator become eventually simple and the root system contains a Riesz basis.

Fully Adaptive Newton--Galerkin Methods for Semilinear Elliptic Partial Differential Equations

In this paper we develop an adaptive procedure for the numerical solution of general, semilinear elliptic problems with possible singular perturbations. Our approach combines both prediction-type adaptive Newton methods and a linear adaptive finite element discretization (based on a robust a posteriori error analysis), thereby leading to a fully adaptive Newton–Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for various examples

How has climate responded to natural perturbations?

Wolff, E. W.; Harrison, S. P.; Knutti, R.; Sanchez-Goñi, M. F.; Wild, O.; Danlau, A.-L.; Masson-Delmotte, V.; Prentice, I. C.; Spahni, R.

Copper availability contributes to iron perturbations in human nonalcoholic fatty liver disease

BACKGROUND ; AIMS: Iron perturbations are frequently observed in nonalcoholic fatty liver disease (NAFLD). We aimed to investigate a potential association of copper status with disturbances of iron homeostasis in NAFLD. METHODS: We retrospectively studied 140 NAFLD patients and 25 control subjects. Biochemical and hepatic iron and copper parameters were analyzed. Hepatic expression of iron regulatory molecules was investigated in liver biopsy specimens by reverse-transcription polymerase chain reaction and Western blot analysis. RESULTS: NAFLD patients had lower hepatic copper concentrations than control subjects (21.9 +/- 9.8 vs 29.6 +/- 5.1 microg/g; P = .002). NAFLD patients with low serum and liver copper concentrations presented with higher serum ferritin levels (606.7 +/- 265.8 vs 224.2 +/- 176.0 mg/L; P < .001), increased prevalence of siderosis in liver biopsy specimens (36/46 vs 10/47 patients; P < .001), and with elevated hepatic iron concentrations (1184.4 +/- 842.7 vs 319.9 +/- 451.3 microg/g; P = .020). Lower serum concentrations of the copper-dependent ferroxidase ceruloplasmin (21.7 +/- 4.1 vs 30.4 +/- 6.4 mg/dL; P < .001) and decreased liver ferroportin (FP-1; P = .009) messenger RNA expression were found in these patients compared with NAFLD patients with high liver or serum copper concentrations. Accordingly, in rats, a reduced dietary copper intake was paralleled by a decreased hepatic FP-1 protein expression. CONCLUSIONS: A significant proportion of NAFLD patients should be considered copper deficient. Our results indicate that copper status is linked to iron homeostasis in NAFLD, suggesting that low copper bioavailability causes increased hepatic iron stores via decreased FP-1 expression and ceruloplasmin ferroxidase activity thus blocking liver iron export in copper-deficient subjects.

Essential spectrum of systems of singular differential equations

In this paper we develop a new method to determine the essential spectrum of coupled systems of singular differential equations. Applications to problems from magnetohydrodynamics and astrophysics are given.

Grain coarsening in contact metamorphic carbonates: effects of second-phase particles, fluid flow and thermal perturbations

Under contact metamorphic conditions, carbonate rocks in the direct vicinity of the Adamello pluton reflect a temperature-induced grain coarsening. Despite this large-scale trend, a considerable grain size scatter occurs on the outcrop-scale indicating local influence of second-order effects such as thermal perturbations, fluid flow and second-phase particles. Second-phase particles, whose sizes range from nano- to the micron-scale, induce the most pronounced data scatter resulting in grain sizes too small by up to a factor of 10, compared with theoretical grain growth in a pure system. Such values are restricted to relatively impure samples consisting of up to 10 vol.% micron-scale second-phase particles, or to samples containing a large number of nano-scale particles. The obtained data set suggests that the second phases induce a temperature-controlled reduction on calcite grain growth. The mean calcite grain size can therefore be expressed in the form D 1⁄4 C2 eQ*/RT(dp/fp)m*, where C2 is a constant, Q* is an activation energy, T the temperature and m* the exponent of the ratio dp/fp, i.e. of the average size of the second phases divided by their volume fraction. However, more data are needed to obtain reliable values for C2 and Q*. Besides variations in the average grain size, the presence of second-phase particles generates crystal size distribution (CSD) shapes characterized by lognormal distributions, which differ from the Gaussian-type distributions of the pure samples. In contrast, fluid-enhanced grain growth does not change the shape of the CSDs, but due to enhanced transport properties, the average grain sizes increase by a factor of 2 and the variance of the distribution increases. Stable d18O and d13C isotope ratios in fluid-affected zones only deviate slightly from the host rock values, suggesting low fluid/rock ratios. Grain growth modelling indicates that the fluid-induced grain size variations can develop within several ka. As inferred from a combination of thermal and grain growth modelling, dykes with widths of up to 1 m have only a restricted influence on grain size deviations smaller than a factor of 1.1.To summarize, considerable grain size variations of up to one order of magnitude can locally result from second-order effects. Such effects require special attention when comparing experimentally derived grain growth kinetics with field studies.