Supremum estimates for degenerate, quasilinear stochastic partial differential equations

We prove a priori estimates in L∞ for a class of quasilinear stochastic partial differential equations. The estimates are obtained independently of the ellipticity constant ε and thus imply analogous estimates for degenerate quasilinear stochastic partial differential equations, such as the stochastic porous medium equation

Random attractors for degenerate stochastic partial differential equations

We prove the existence of random attractors for a large class of degenerate stochastic partial differential equations (SPDE) perturbed by joint additive Wiener noise and real, linear multiplicative Brownian noise, assuming only the standard assumptions of the variational approach to SPDE with compact embeddings in the associated Gelfand triple. This allows spatially much rougher noise than in known results. The approach is based on a construction of strictly stationary solutions to related strongly monotone SPDE. Applications include stochastic generalized porous media equations, stochastic generalized degenerate p-Laplace equations and stochastic reaction diffusion equations. For perturbed, degenerate p-Laplace equations we prove that the deterministic, infinite dimensional attractor collapses to a single random point if enough noise is added.Comment: 34 pages; The final publication is available at http://link.springer.com/article/10.1007%2Fs10884-013-9294-

Ergodicity for Stochastic Porous Media Equations with Multiplicative Noise

The long time behavior of solutions to stochastic porous media equations with nonlinear multiplicative noise on bounded domains with Dirichlet boundary data is studied. Based on weighted $L^{1}$-estimates, the existence and uniqueness of invariant measures with optimal bounds on the rate of mixing are proved. Along the way, the existence and uniqueness of entropy solutions are shown

Non-negative Martingale Solutions to the Stochastic Thin-Film Equation with Nonlinear Gradient Noise

We prove the existence of non-negative martingale solutions to a class of stochastic degenerate-parabolic fourth-order PDEs arising in surface-tension driven thin-film flow influenced by thermal noise. The construction applies to a range of mobilites including the cubic one which occurs under the assumption of a no-slip condition at the liquid-solid interface. Since their introduction more than 15 years ago, by Davidovitch, Moro, and Stone and by Grün, Mecke, and Rauscher, the existence of solutions to stochastic thin-film equations for cubic mobilities has been an open problem, even in the case of sufficiently regular noise. Our proof of global-in-time solutions relies on a careful combination of entropy and energy estimates in conjunction with a tailor-made approximation procedure to control the formation of shocks caused by the nonlinear stochastic scalar conservation law structure of the noise

From teaching physics to teaching children : beginning teachers learning from pupils

This paper discusses the development of beginning physics teachers' pedagogical content knowledge (PCK) in the context of teaching basic electricity during a one-year Professional Graduate Diploma in Education course (PGDE) and beyond. This longitudinal study used repeated semi-structured interviews over a period of four-and-a-half years. The interview schedule followed a line of development through the secondary school electrical syllabus in Scotland. Fifteen student teachers were interviewed during the PGDE year. Six of them were followed up at the end of the Induction Year (their first year as a newly qualified teacher), and again two-and-a-half years later. Thematic analysis of the interviews showed that before the beginning teachers had taught any classes, their initial focus was on how to transform their own subject matter knowledge (SMK) about electricity into forms that were accessible to pupils. As the beginning teachers gained experience working with classes, they gave vivid descriptions of interacting with particular pupils when teaching electricity which showed the development of their pedagogical knowledge. This played a significant role in the teachers' change of focus from teaching physics to teaching children as they transformed their SMK into forms that were accessible to pupils and developed their general pedagogical knowledge

Deoxy-sphingolipids, oxidative stress, and vitamin C correlate with qualitative and quantitative patterns of small fiber dysfunction and degeneration

Defined by dysfunction or degeneration of Aδ and C fibers, small fiber neuropathies (SFNs) entail a relevant health burden. In 50% of cases, the underlying cause cannot be identified or treated. In 100 individuals (70% female individuals; mean age: 44.8 years) with an idiopathic, skin biopsy-confirmed SFN, we characterized the symptomatic spectrum and measured markers of oxidative stress (vitamin C, selenium, and glutathione) and inflammation (transforming growth factor beta, tumor necrosis factor alpha), as well as neurotoxic 1-deoxy-sphingolipids. Neuropathic pain was the most abundant symptom (95%) and cause of daily life impairment (72%). Despite the common use of pain killers (64%), the painDETECT questionnaire revealed scores above 13 points in 80% of patients. In the quantitative sensory testing (QST), a dysfunction of Aδ fibers was observed in 70% and of C fibers in 44%, affecting the face, hands, or feet. Despite normal nerve conduction studies, QST revealed Aβ fiber involvement in 46% of patients' test areas. Despite absence of diabetes mellitus or mutations in SPTLC1 or SPTLC2 , plasma 1-deoxy-sphingolipids were significantly higher in the sensory loss patient cluster when compared with those in patients with thermal hyperalgesia ( P 25 kg/m 2 ), or hyperlipidemia showed significantly lower L-serine (arterial hypertension: P < 0.01) and higher 1-deoxy-sphingolipid levels (arterial hypertension: P < 0.001, overweight: P < 0.001, hyperlipidemia: P < 0.01). Lower vitamin C levels correlated with functional Aβ involvement ( P < 0.05). Reduced glutathione was lower in patients with Aδ dysfunction ( P < 0.05). Idiopathic SFNs are heterogeneous. As a new pathomechanism, plasma 1-deoxy-sphingolipids might link the metabolic syndrome with small fiber degeneration

Rinistachya hilleri gen. et sp. nov.(Sphenophyllales), from the upper Devonian of South Africa

A rich and diverse plant assemblage has been excavated from latest Devonian (Famennian) black shales of the Witpoort Formation (Witteberg Group) at Waterloo Farm, close to the city of Grahamstown (South Africa). Several specimens of a new sphenopsid have been collected. The description of this as a new taxon, here named Rinistachya hilleri, gen. et sp. nov., provides an important addition to the scarce early record of the group. Rinistachya hilleri presents a novel architecture that include apparently plesiomorphic characters, reminiscent of the organisation of the Iridopteridales (including the production of two types of laterals at one node, the location of fertile parts in loose whorls on lateral branches and an organisation of the fertile parts in which they branch several times before bearing distally elongate sporangia). Other characters unambiguously nest Rinistachya within the Sphenopsida (including presence of planate and slightly webbed ultimate appendages and lateral strobili made of successive whorls of fertile leaves with fertile parts located at their axil). This provides strong support for a close relationship between Sphenopsida and Iridopteridales. Rinistachya furthermore represents the first record of a Devonian sphenopsid from Gondwana and extends the known distribution of the Sphenopsida from the tropics to very high palaeolatitudes. It is a new sphenopsid with a peculiar organisation. The new taxon allows better characterization of the initial evolutionary radiation at the base of the group