Formal deformations and their categorical general fibre

We study the general fibre of a formal deformation over the formal disk of a projective variety from the view point of abelian and derived categories. The abelian category of coherent sheaves of the general fibre is constructed directly from the formal deformation and is shown to be linear over the field of Laurent series. The various candidates for the derived category of the general fibre are compared. If the variety is a surface with trivial canonical bundle, we show that the derived category of the general fibre is again a linear triangulated category with a Serre functor given by the square of the shift functor

The 3-fold vertex via stable pairs

The theory of stable pairs in the derived category yields an enumerative geometry of curves in 3-folds. We evaluate the equivariant vertex for stable pairs on toric 3-folds in terms of weighted box counting. In the toric Calabi-Yau case, the result simplifies to a new form of pure box counting. The conjectural equivalence with the DT vertex predicts remarkable identities. The equivariant vertex governs primary insertions in the theory of stable pairs for toric varieties. We consider also the descendent vertex and conjecture the complete rationality of the descendent theory for stable pairs.Comment: Typos fixed. 40 pages, 8 figure

Numerical prediction of ship resistance and squat in confined waters

Accurate prediction of hydrodynamic forces opposing a ship displacement in restricted waterways is necessary in order to improve energy efficiency of inland transport. When a ship moves in restricted waterways, a significant increase in ship squat (combination of sinkage and trim) and resistance occurs compared to a movement in open waters. In this paper, a 3D numerical model based on fluid-structure coupling is presented and used to investigate the effect of limited water depth and channel width on ship resistance and squat

Food photographs in nutritional surveillance: errors in portion size estimation using drawings of bread and photographs of margarine and beverages consumption

Food photographs are widely used as instruments to estimate portion sizes of consumed foods. Several food atlases are available, all developed to be used in a specific context and for a given study population. Frequently, food photographs are adopted for use in other studies with a different context or another study population. In the present study, errors in portion size estimation of bread, margarine on bread and beverages by two-dimensional models used in the context of a Belgian food consumption survey are investigated. A sample of 111 men and women (age 45–65 years) were invited for breakfast; two test groups were created. One group was asked to estimate portion sizes of consumed foods using photographs 1–2 d after consumption, and a second group was asked the same after 4 d. Also, real-time assessment of portion sizes using photographs was performed. At the group level, large overestimation of margarine, acceptable underestimation of bread and only small estimation errors for beverages were found. Women tended to have smaller estimation errors for bread and margarine compared with men, while the opposite was found for beverages. Surprisingly, no major difference in estimation error was found after 4 d compared with 1–2 d. Individual estimation errors were large for all foods. The results from the present study suggest that the use of food photographs for portion size estimation of bread and beverages is acceptable for use in nutrition surveys. For photographs of margarine on bread, further validation using smaller amounts corresponding to actual consumption is recommended

A new spatially and temporally variable sigma parameter in degree-day melt modelling of the Greenland Ice Sheet 1870–2013

The degree-day based method of calculating ice-/snow-melt across the Greenland Ice Sheet (GrIS) commonly includes the temperature parameter sigma (σ) accounting for temperature variability on short (sub-monthly down to hourly) timescales, in order to capture melt in months where the mean temperature is below 0 °C. Sigma is typically assumed to be constant in space and time, with values ranging from ~ 2.5 to 5.5 °C. It is unclear in many cases how these values were derived and little sensitivity analysis or validation has been conducted. Here we determine spatially and temporally varying monthly values of σ for the unique, extended 1870–2013 timescale based on downscaled, corrected European Centre for Medium-Range Weather Forecasts (ECMWF) Interim (ERA-I) and Twentieth Century Reanalysis (20CR) meteorological reanalysis 2 m air temperatures on a 5 km × 5 km polar stereographic grid for the GrIS. The resulting monthly σ values reveal a distinct seasonal cycle. The mean summer σ value for the study period is ~ 3.2 °C, around 1 °C lower than the value of 4.2 °C commonly used in the literature. Sigma values for individual summers range from 1.7 to 5.9 °C. Since the summer months dominate the melt calculation, use of the new variable σ parameter would lead to a smaller melt area and a more positive surface mass balance for the GrIS. Validation of our new variable σ dataset shows good agreement with standard deviations calculated from automatic weather station observations across the ice sheet. Trend analysis shows large areas of the ice sheet exhibit statistically significant increasing temperature variability from 1870–2013 in all seasons, with notable exceptions around Summit in spring, and Summit and South Dome in winter. More recently, since 1990, σ has been decreasing, significantly so in the north-west during July. These interannual σ trends reflect climate change and variability processes operating across the ice sheet, several mechanisms of which are briefly discussed

Factors controlling the last interglacial climate as simulated by LOVECLIM1.3

The last interglacial (LIG), also identified to the Eemian in Europe, began at approximately 130 kyr BP and ended at about 115 kyr BP (before present). More and more proxy-based reconstructions of the LIG climate are becoming more available even though they remain sparse. The major climate forcings during the LIG are rather well known and therefore models can be tested against paleoclimatic data sets and then used to better understand the climate of the LIG. However, models are displaying a large range of responses, being sometimes contradictory between them or with the reconstructed data. Here we would like to investigate causes of these differences. We focus on a single climate model, LOVECLIM, and we perform transient simulations over the LIG, starting at 135 kyr BP and run until 115 kyr BP. With these simulations, we test the role of the surface boundary conditions (the time-evolution of the Northern Hemisphere (NH) ice sheets) on the simulated LIG climate and the importance of the parameter sets (internal to the model, such as the albedos of the ocean and sea ice), which affect the sensitivity of the model. The magnitude of the simulated climate variations through the LIG remains too low compared to reconstructions for climate variables such as surface air temperature. Moreover, in the North Atlantic, the large increase in summer sea surface temperature towards the peak of the interglacial occurs too early (at ∼128 kyr BP) compared to the reconstructions. This feature as well as the climate simulated during the optimum of the LIG, between 131 and 121 kyr BP, does not depend on changes in surface boundary conditions and parameter sets. The additional freshwater flux (FWF) from the melting NH ice sheets is responsible for a temporary abrupt weakening of the North Atlantic meridional overturning circulation, which causes a strong global cooling in annual mean. However, the changes in the configuration (extent and albedo) of the NH ice sheets during the LIG only slightly impact the simulated climate. Together, configuration of and FWF from the NH ice sheets greatly increase the magnitude of the temperature variations over continents as well as over the ocean at the beginning of the simulation and reduce the difference between the simulated climate and the reconstructions. Lastly, we show that the contribution from the parameter sets to the climate response is actually very modest

Improved convergence and stability properties in a three-dimensional higher-order ice sheet model

We present a finite difference implementation of a three-dimensional higher-order ice sheet model. In comparison to a conventional centred difference discretisation it enhances both numerical stability and convergence. In order to achieve these benefits the discretisation of the governing force balance equation makes extensive use of information on staggered grid points. Using the same iterative solver, a centred difference discretisation that operates exclusively on the regular grid serves as a reference. The reprise of the ISMIP-HOM experiments indicates that both discretisations are capable of reproducing the higher-order model inter-comparison results. This setup allows a direct comparison of the two numerical implementations also with respect to their convergence behaviour. First and foremost, the new finite difference scheme facilitates convergence by a factor of up to 7 and 2.6 in average. In addition to this decrease in computational costs, the accuracy for the resultant velocity field can be chosen higher in the novel finite difference implementation. Changing the discretisation also prevents build-up of local field irregularites that occasionally cause divergence of the solution for the reference discretisation. <br><br> The improved behaviour makes the new discretisation more reliable for extensive application to real ice geometries. Higher accuracy and robust numerics are crucial in time dependent applications since numerical oscillations in the velocity field of subsequent time steps are attenuated and divergence of the solution is prevented