Asymptotic stability, concentration, and oscillation in harmonic map heat-flow, Landau-Lifshitz, and Schroedinger maps on R^2

We consider the Landau-Lifshitz equations of ferromagnetism (including the harmonic map heat-flow and Schroedinger flow as special cases) for degree m equivariant maps from R^2 to S^2. If m \geq 3, we prove that near-minimal energy solutions converge to a harmonic map as t goes to infinity (asymptotic stability), extending previous work down to degree m = 3. Due to slow spatial decay of the harmonic map components, a new approach is needed for m=3, involving (among other tools) a "normal form" for the parameter dynamics, and the 2D radial double-endpoint Strichartz estimate for Schroedinger operators with sufficiently repulsive potentials (which may be of some independent interest). When m=2 this asymptotic stability may fail: in the case of heat-flow with a further symmetry restriction, we show that more exotic asymptotics are possible, including infinite-time concentration (blow-up), and even "eternal oscillation".Comment: 34 page

Closure between measured and modelled particle hygroscopic growth during TORCH2 implies ammonium nitrate artefact in the HTDMA measurements

International audienceMeasurements of aerosol properties were made in aged polluted and clean background air masses encountered at the North Norfolk (UK) coastline during the second field campaign of the Tropospheric ORganic CHemistry project (TORCH2) in May 2004. Hygroscopic growth factor (GF) measurements were performed at 90% relative humidity (RH) for D0=27?217 nm particles using a Hygroscopicity Tandem Differential Mobility Analyser (HTDMA), while the aerosol composition was simultaneously measured with an Aerodyne aerosol mass spectrometer (Q-AMS). During the clean background events the aerosol was characterised by little size dependence of properties with generally large GFs and inorganic sulphate being the dominant compound. In aged polluted air masses the particles were dominated by inorganic sulphate and nitrate at larger sizes, whereas organics were the largest fraction in smaller particles, thus explaining the trend of smaller GFs at smaller sizes. Organics do contribute to the hygroscopic growth, particularly at small sizes, but generally the dominant contribution to growth at 90% RH comes from inorganic salts. The ZSR mixing rule was used to predict GFs based on the chemical composition, theoretical GFs of pure inorganic salts and a "bulk" GF of ~1.20 for the organics. Good quantitative closure with HTDMA measurements as a function of both particle size and time was achieved in the absence of nitrate. However, GFs were clearly overpredicted at times when a significant fraction of nitrate was present. After careful considerations we attribute the overprediction to substantial evaporation losses of ammonium nitrate in the HTDMA instrument. If true, this implies that the ZSR predictions based on composition might be more representative of the actual "bulk" behaviour of undisturbed ambient particles than the HTDMA measurements. The simplified model approach using the ZSR rule and a constant organic growth factor made high size and time resolution possible, which has proven to be essential for a valid closure study. The ZSR mixing rule appears to be sufficiently accurate, as the GF predictions are more sensitive to the exact GFs of the inorganic compounds than to the growth factor of the moderately hygroscopic organics. Therefore a more detailed analysis and modelling of the organic fraction at the expense of time and size resolution is not worth the effort for an aged aerosol and discrepancies in either direction might even be cancelled out by averaging

Closure study between chemical composition and hygroscopic growth of aerosol particles during TORCH2

International audienceMeasurements of aerosol properties were made in aged polluted and clean background air masses encountered at the North Norfolk (UK) coastline as part of the TORCH2 field campaign in May 2004. Hygroscopic growth factors (GF) at 90% relative humidity (RH) for D0=27?217 nm particles and size-resolved chemical composition were simultaneously measured using a Hygroscopicity Tandem Differential Mobility Analyser (HTDMA) and an Aerodyne aerosol mass spectrometer (Q-AMS), respectively. Both hygroscopic properties and chemical composition showed pronounced variability in time and with particles size. With this data set we could demonstrate that the Zdanovskii-Stokes-Robinson (ZSR) mixing rule combined with chemical composition data from the AMS makes accurate quantitative predictions of the mean GF of mixed atmospheric aerosol particles possible. In doing so it is crucial that chemical composition data are acquired with high resolution in both particle size and time, at least matching the actual variability of particle properties. The closure results indicate an ensemble GF of the organic fraction of ~1.20±0.10 at 90% water activity. Thus the organics contribute somewhat to hygroscopic growth, particularly at small sizes, however the inorganic salts still dominate. Furthermore it has been found that most likely substantial evaporation losses of NH4NO3 occurred within the HTDMA instrument, exacerbated by a long residence time of ~1 min. Such an artefact is in agreement with our laboratory experiments and literature data for pure NH4NO3, both showing similar evaporation losses within HTDMAs with residence times of ~1 min. Short residence times and low temperatures are hence recommended for HTDMAs in order to minimise such evaporation artefacts

A spinorial energy functional: critical points and gradient flow

On the universal bundle of unit spinors we study a natural energy functional whose critical points, if dim M \geq 3, are precisely the pairs (g, {\phi}) consisting of a Ricci-flat Riemannian metric g together with a parallel g-spinor {\phi}. We investigate the basic properties of this functional and study its negative gradient flow, the so-called spinor flow. In particular, we prove short-time existence and uniqueness for this flow.Comment: Small changes, final versio

Employing culturally responsive pedagogy to foster literacy learning in schools

 In recent years it has become increasingly obvious that, to enable students in schools from an increasingly diverse range of cultural backgrounds to acquire literacy to a standard that will support them to achieve academically, it is important to adopt pedagogy that is responsive to, and respectful of, them as culturally situated. What largely has been omitted from the literature, however, is discussion of a relevant model of learning to underpin this approach. For this reason this paper adopts a socio-cultural lens (Vygotsky, 1978) through which to view such pedagogy and refers to a number of seminal texts to justify of its relevance. Use of this lens is seen as having a particular rationale. It forces a focus on the agency of the teacher as a mediator of learning who needs to acknowledge the learner’s cultural situatedness (Kozulin, 2003) if school literacy learning for all students is to be as successful as it might be. It also focuses attention on the predominant value systems and social practices that characterize the school settings in which students’ literacy learning is acquired. The paper discusses implications for policy and practice at whole-school, classroom and individual student levels of culturally-responsive pedagogy that is based on a socio-cultural model of learning. In doing so it draws on illustrations from the work of a number of researchers, including that of the author

Investigating Off-shell Stability of Anti-de Sitter Space in String Theory

We propose an investigation of stability of vacua in string theory by studying their stability with respect to a (suitable) world-sheet renormalization group (RG) flow. We prove geometric stability of (Euclidean) anti-de Sitter (AdS) space (i.e., $\mathbf{H}^n$) with respect to the simplest RG flow in closed string theory, the Ricci flow. AdS space is not a fixed point of Ricci flow. We therefore choose an appropriate flow for which it is a fixed point, prove a linear stability result for AdS space with respect to this flow, and then show this implies its geometric stability with respect to Ricci flow. The techniques used can be generalized to RG flows involving other fields. We also discuss tools from the mathematics of geometric flows that can be used to study stability of string vacua.Comment: 29 pages, references added in this version to appear in Classical and Quantum Gravit

Phenoloxidase activity acts as a mosquito innate immune response against infection with semliki forest virus

Several components of the mosquito immune system including the RNA interference (RNAi), JAK/STAT, Toll and IMD pathways have previously been implicated in controlling arbovirus infections. In contrast, the role of the phenoloxidase (PO) cascade in mosquito antiviral immunity is unknown. Here we show that conditioned medium from the Aedes albopictus-derived U4.4 cell line contains a functional PO cascade, which is activated by the bacterium Escherichia coli and the arbovirus Semliki Forest virus (SFV) (Togaviridae; Alphavirus). Production of recombinant SFV expressing the PO cascade inhibitor Egf1.0 blocked PO activity in U4.4 cell- conditioned medium, which resulted in enhanced spread of SFV. Infection of adult female Aedes aegypti by feeding mosquitoes a bloodmeal containing Egf1.0-expressing SFV increased virus replication and mosquito mortality. Collectively, these results suggest the PO cascade of mosquitoes plays an important role in immune defence against arboviruses