On stability of discretizations of the Helmholtz equation (extended version)

We review the stability properties of several discretizations of the Helmholtz equation at large wavenumbers. For a model problem in a polygon, a complete $k$-explicit stability (including $k$-explicit stability of the continuous problem) and convergence theory for high order finite element methods is developed. In particular, quasi-optimality is shown for a fixed number of degrees of freedom per wavelength if the mesh size $h$ and the approximation order $p$ are selected such that $kh/p$ is sufficiently small and $p = O(\log k)$, and, additionally, appropriate mesh refinement is used near the vertices. We also review the stability properties of two classes of numerical schemes that use piecewise solutions of the homogeneous Helmholtz equation, namely, Least Squares methods and Discontinuous Galerkin (DG) methods. The latter includes the Ultra Weak Variational Formulation

Relativistic Approach to Superfluidity in Nuclear Matter

Pairing correlations in symmetric nuclear matter are studied within a relativistic mean-field approximation based on a field theory of nucleons coupled to neutral ($\sigma$ and $\omega$) and to charged ($\varrho$) mesons. The Hartree-Fock and the pairing fields are calculated in a self-consistent way. The energy gap is the result of a strong cancellation between the scalar and vector components of the pairing field. We find that the pair amplitude vanishes beyond a certain value of momentum of the paired nucleons. This fact determines an effective cutoff in the gap equation. The value of this cutoff gives an energy gap in agreement with the estimates of non relativistic calculations.Comment: 21 pages, REVTEX, 8 ps-figures, to appear in Phys.Rev.C. e-mail: [email protected]

Towards an Efficient Finite Element Method for the Integral Fractional Laplacian on Polygonal Domains

We explore the connection between fractional order partial differential equations in two or more spatial dimensions with boundary integral operators to develop techniques that enable one to efficiently tackle the integral fractional Laplacian. In particular, we develop techniques for the treatment of the dense stiffness matrix including the computation of the entries, the efficient assembly and storage of a sparse approximation and the efficient solution of the resulting equations. The main idea consists of generalising proven techniques for the treatment of boundary integral equations to general fractional orders. Importantly, the approximation does not make any strong assumptions on the shape of the underlying domain and does not rely on any special structure of the matrix that could be exploited by fast transforms. We demonstrate the flexibility and performance of this approach in a couple of two-dimensional numerical examples

Morphological Criteria for Comparing Effects of X-Rays and Neon Ions on Mouse Small Intestine

Several techniques have been used to assess changes in different parts of mouse small intestine three days after a single dose of either 16.5 Gy X-rays or 11 Gy neon beam. The doses were chosen to be approximately equivalent in terms of their effect on the number of microcolonies present. In qualitative terms, villous damage was seen after both types of radiation exposure: collared crypts, similar to those seen in biopsies taken from patients suffering from coeliac disease, were conspicuous after neon irradiation. In semi quantitative terms the doses used, although estimated from previous work to give biologically equivalent damage, produced a greater drop in microcolony numbers after X-irradiation, This makes all the more important the fact that significantly greater changes were seen after neon irradiation - a greater drop was seen in the number of villous profiles and the number of goblet cells per villus. There was also greater breakdown in the integrity of the villous basement membrane. Different responses after the two types of irradiation are therefore seen in the cryptal and villous compartment. Progress is being made towards identifying and quantitating radiation induced changes in different populations of cells or tissues in the small intestine

Endogenous fantasy and learning in digital games.

Many people believe that educational games are effective because they motivate children to actively engage in a learning activity as part of playing the game. However, seminal work by Malone (1981), exploring the motivational aspects of digital games, concluded that the educational effectiveness of a digital game depends on the way in which learning content is integrated into the fantasy context of the game. In particular, he claimed that content which is intrinsically related to the fantasy will produce better learning than that which is merely extrinsically related. However, this distinction between intrinsic and extrinsic (or endogenous and exogenous) fantasy is a concept that has developed a confused standing over the following years. This paper will address this confusion by providing a review and critique of the empirical and theoretical foundations of endogenous fantasy, and its relevance to creating educational digital games. Substantial concerns are raised about the empirical basis of this work and a theoretical critique of endogenous fantasy is offered, concluding that endogenous fantasy is a misnomer, in so far as the "integral and continuing relationship" of fantasy cannot be justified as a critical means of improving the effectiveness of educational digital games. An alternative perspective on the intrinsic integration of learning content is described, incorporating game mechanics, flow and representations

Pairing in low-density Fermi gases

We consider pairing in a dilute system of Fermions with a short-range interaction. While the theory is ill-defined for a contact interaction, the BCS equations can be solved in the leading order of low-energy effective field theory. The integrals are evaluated with the dimensional regularization technique, giving analytic formulas relating the pairing gap, the density, and the energy density to the two-particle scattering length.Comment: 12 pages, 2 EPS-figures, uses psfig.sty, eq.(9) correcte

Interactive effects of elevated CO2, warming, and drought on photosynthesis of Deschampsia flexuosa in a temperate heath ecosystem

Global change factors affect plant carbon uptake in concert. In order to investigate the response directions and potential interactive effects, and to understand the underlying mechanisms, multifactor experiments are needed. The focus of this study was on the photosynthetic response to elevated CO2 [CO2; free air CO2 enrichment (FACE)], drought (D; water-excluding curtains), and night-time warming (T; infrared-reflective curtains) in a temperate heath. A/Ci curves were measured, allowing analysis of light-saturated net photosynthesis (Pn), light- and CO2-saturated net photosynthesis (Pmax), stomatal conductance (gs), the maximal rate of Rubisco carboxylation (Vcmax), and the maximal rate of ribulose bisphosphate (RuBP) regeneration (Jmax) along with leaf δ13C, and carbon and nitrogen concentration on a monthly basis in the grass Deschampsia flexuosa. Seasonal drought reduced Pn via gs, but severe (experimental) drought decreased Pn via a reduction in photosynthetic capacity (Pmax, Jmax, and Vcmax). The effects were completely reversed by rewetting and stimulated Pn via photosynthetic capacity stimulation. Warming increased early and late season Pn via higher Pmax and Jmax. Elevated CO2 did not decrease gs, but stimulated Pn via increased Ci. The T×CO2 synergistically increased plant carbon uptake via photosynthetic capacity up-regulation in early season and by better access to water after rewetting. The effects of the combination of drought and elevated CO2 depended on soil water availability, with additive effects when the soil water content was low and D×CO2 synergistic stimulation of Pn after rewetting. The photosynthetic responses appeared to be highly influenced by growth pattern. The grass has opportunistic water consumption, and a biphasic growth pattern allowing for leaf dieback at low soil water availability followed by rapid re-growth of active leaves when rewetted and possibly a large resource allocation capability mediated by the rhizome. This growth characteristic allowed for the photosynthetic capacity up-regulations that mediated the T×CO2 and D×CO2 synergistic effects on photosynthesis. These are clearly advantageous characteristics when exposed to climate changes. In conclusion, after 1 year of experimentation, the limitations by low soil water availability and stimulation in early and late season by warming clearly structure and interact with the photosynthetic response to elevated CO2 in this grassland species

Size and emotion or depth and emotion? Evidence, using Matryoshka (Russian) dolls, of children using physical depth as a proxy for emotional charge

Background: The size and emotion effect is the tendency for children to draw people and other objects with a positive emotional charge larger than those with a negative or neutral charge. Here we explored the novel idea that drawing size might be acting as a proxy for depth (proximity).Methods: Forty-two children (aged 3-11 years) chose, from 2 sets of Matryoshka (Russian) dolls, a doll to represent a person with positive, negative or neutral charge, which they placed in front of themselves on a sheet of A3 paper. Results: We found that the children used proximity and doll size, to indicate emotional charge. Conclusions: These findings are consistent with the notion that in drawings, children are using size as a proxy for physical closeness (proximity), as they attempt with varying success to put positive charged items closer to, or negative and neutral charge items further away from, themselves

Avulsion cycles and their stratigraphic signature on an experimental backwater‐controlled delta

River deltas grow in large part through repeated cycles of lobe construction and channel avulsion. Understanding avulsion cycles is important for coastal restoration and ecology, land management, and flood hazard mitigation. Emerging theories suggest that river avulsions on lowland deltas are controlled by backwater hydrodynamics; however, our knowledge of backwater-controlled avulsion cycles is limited. Here, we present results from an experimental delta that evolved under persistent backwater hydrodynamics achieved through variable flood discharges, shallow bed-slopes, and subcritical flows. The experimental avulsion cycles consisted of an initial phase of avulsion setup, an avulsion trigger, selection of a new flow path, and abandonment of the parent channel. Avulsions were triggered during the largest floods (78% of avulsions) after the channel was filled by a fraction (0.3 ± 0.13) of its characteristic flow depth at the avulsion site, which occurred in the upstream part of the backwater zone. The new flow path following avulsion was consistently one of the shortest paths to the shoreline, and channel abandonment occurred through temporal decline in water flow and sediment delivery to the parent channel. Experimental synthetic stratigraphy indicates that the bed thicknesses were maximum at the avulsion sites, consistent with our morphologic measurements of avulsion setup and the idea that there is a record of avulsion locations and thresholds in sedimentary rocks. Finally, we discuss the implications of our findings within the context of sustainable management of deltas, their stratigraphic record, and predicting avulsions on deltas