Some useful techniques for pointwise and local error estimates of the quantities of interest in the finite element approximation

In this paper we review some existing techniques to obtain pointwise and local a posteriori error estimates for the quantities of interest in finite element approximations by using duality arguments. We also present a new approach to obtain computable error bounds for the recovered pointwise quantities. The new method is extended to include the practically important case of non-homogeneous Dirichlet data. Existing methods require purely Neumann data, or the Dirichlet data to be homogeneous. The new techniques are developed here to provide computable error bounds on the genuine pointwise quantities and allow the use of non-homogeneous Dirichlet data. The strength and weakness of each technique will be analysed and compared. The numerical experiments to justify our analysis will be presented

High flow conditions mediate damaging impacts of sub-lethal thermal stress on corals' endosymbiotic algae

The effects of thermal anomalies on tropical coral endosymbiosis can be mediated by a range of environmental factors, which in turn ultimately influence coral health and survival. One such factor is the water flow conditions over coral reefs and corals. Although the physiological benefits of living under high water flow are well known, there remains a lack of conclusive experimental evidence characterizing how flow mitigates thermal stress responses in corals. Here we use in situ measurements of flow in a variety of reef habitats to constrain the importance of flow speeds on the endosymbiosis of an important reef building species under different thermal regimes. Under high flow speeds (0.15 m s−1) and thermal stress, coral endosymbionts retained photosynthetic function and recovery capacity for longer compared to low flow conditions (0.03 m s−1). We hypothesize that this may be due to increased rates of mass transfer of key metabolites under higher flow, putatively allowing corals to maintain photosynthetic efficiency for longer. We also identified a positive interactive effect between high flow and a pre-stress, sub-lethal pulse in temperature. While higher flow may delay the onset of photosynthetic stress, it does not appear to confer long-term protection; sustained exposure to thermal stress (eDHW accumulation equivalent to 4.9°C weeks) eventually overwhelmed the coral meta-organism as evidenced by eventual declines in photo-physiological function and endosymbiont densities. Investigating flow patterns at the scale of metres within the context of these physiological impacts can reveal interesting avenues for coral reef management. This study increases our understanding of the effects of water flow on coral reef health in an era of climate change and highlights the potential to learn from existing beneficial bio-physical interactions for the effective preservation of coral reefs into the future

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

Estimation of productivity in pine and oak forests in northern Portugal using Biome-BGC

Studies about the productivity of forest ecosystems help to quantify sequestered carbon and provide data that are used in forest management. Forests in northern Portugal are an important economic resource, but their productivity in scenarios of future climate change is not yetwell understood. The objectives of this study were to evaluate and compare simulated net primary production (NPP) andNPPbased onmeasured data of twotree species located in the Vila Real district forests, pine (Pinus pinaster Aiton) and oak (Quercus pyrenaica Willd.) and assess their simulatedNPPin diverse climate conditions, including future climate scenariosandincreasing atmospheric CO2 concentrations. An ecosystem process model, Biome-BGC, which simulates carbon, nitrogen and water cycles of forest ecosystems close to equilibrium conditions, was used to examine the importance of site and ecophysiological factors on the productivity of these forests. Climate change scenarios and increased CO2 concentrations were tested to explore potential responses of the studied species. The model provided good estimates of NPP. There was a strong correlation between the simulated and measured NPP values in the pine (15) and oak (15) stands. The NPP of these forests are predicted to increase in the future with a CO2 increase whereas in a climate with higher temperature and lower soil moisture, the NPP will decrease. These results confirm that precipitation is a very important climate variable to growth and productivity in the Mediterranean forest ecosystems. This study also demonstrated the ability of Biome-BGC to accurately simulate forest ecosystems behaviour and encourages the application of model simulations in Portugalinfo:eu-repo/semantics/publishedVersio

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]

A methodology for the capture and analysis of hybrid data: a case study of program debugging

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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