Calculus on surfaces with general closest point functions

The Closest Point Method for solving partial differential equations (PDEs) posed on surfaces was recently introduced by Ruuth and Merriman [J. Comput. Phys. 2008] and successfully applied to a variety of surface PDEs. In this paper we study the theoretical foundations of this method. The main idea is that surface differentials of a surface function can be replaced with Cartesian differentials of its closest point extension, i.e., its composition with a closest point function. We introduce a general class of these closest point functions (a subset of differentiable retractions), show that these are exactly the functions necessary to satisfy the above idea, and give a geometric characterization this class. Finally, we construct some closest point functions and demonstrate their effectiveness numerically on surface PDEs

Benchmark of FEM, Waveguide and FDTD Algorithms for Rigorous Mask Simulation

An extremely fast time-harmonic finite element solver developed for the transmission analysis of photonic crystals was applied to mask simulation problems. The applicability was proven by examining a set of typical problems and by a benchmarking against two established methods (FDTD and a differential method) and an analytical example. The new finite element approach was up to 100 times faster than the competing approaches for moderate target accuracies, and it was the only method which allowed to reach high target accuracies.Comment: 12 pages, 8 figures (see original publication for images with a better resolution

Rigorous Simulation of 3D Masks

We perform 3D lithography simulations by using a finite-element solver. To proof applicability to real 3D problems we investigate DUV light propagation through a structure of size 9 microns times 4 microns times 65 nm. On this relatively large computational domain we perform rigorous computations (No Hopkins) taking into account a grid of 11 times 21 source points with two polarization directions each. We obtain well converged results with an accuracy of the diffraction orders of about one percent. The results compare well to experimental aerial imaging results. We further investigate the convergence of 3D solutions towards quasi-exact results obtained with different methods.Comment: 8 pages, 5 figures (see original publication for images with a better resolution

The Secret ‘After Life’ of Foraminifera: Big Things Out of Small

Calcareous and siliceous microorganisms are common components of mudrocks, and can be important in terms of stratigraphy and environmental interpretation. In addition, such microorganisms can have a significant ‘after life’, through post-mortem alteration, and represent a potential source of additional information about the diagenetic and deformation history of the rock unit. Some examples of the latter are illustrated in this study from foraminifera within a Cretaceous black shale of Colombia. This includes foraminifera tests acting as understudied repositories of authigenic calcite cement, and of elements such as Ba, Zn, Fe and S through the formation of baryte, sphalerite and iron sulphides (pyrite, marcasite). Such repositories, within the body chambers of foraminiferal tests, can provide important windows into the diagenetic processes within mudstones. If calcite cement is not recognised or separated from biogenic calcite, the depositional calcite budget can be easily overestimated, skewing the application of mudrock classification schemes, and affecting environmental interpretation including that of productivity. The elements Ba, Zn and Fe (often in ratio with Al) are commonly utilised as geochemical proxies of environmental parameters (productivity, bottom water redox conditions, etc.). Therefore, the presence of significant amounts of baryte, sphalerite and pyrite-marcasite (within foraminifera) should be noted and their origins (source and timing) investigated based on their spatial relationships before making environmental deductions based on geochemical analysis alone. Additionally, commonly observed marginal shell damage of many of the observed foraminifera is reported. We interpret this damage, for the first time, as an indicator of lateral dissolution, brought about by horizontal foreshortening during orogenesis. This is also supported by the occurrence of microscale anastomosing horizontal to inclined baryte-filled fractures within the mudstone matrix

Synthetic tumor-associated glycopeptide antigens.

Glycopeptides with TN antigen (GalNAc)Ser/Thr and T-antigen structures (beta Gall-3GalNAc)Ser/Thr, described as tumor-associated antigens, were synthesized and coupled to bovine serum albumin. Alternatively, synthetic methods for the construction of beta-anomeric analogues of the TN and T-antigen glycopeptides were developed, aiming at antigenic structures having a varied stereochemistry of the linkage between the carbohydrate and the peptide moiety. As a further type of potential tumor-associated antigen, fucosyl-chitobiose asparagine glycopeptides were synthesized, deprotected, and coupled to bovine serum albumin. The chemical methods developed now make the complex sensitive glycoprotein partial structures accessible in analytically pure form and in preparative amounts

The effect of extraction techniques on calcium concentrations and isotope ratios of marine pore water

Comparing two different techniques applied for the extraction of marine pore water samples from sediments, the well-established whole round (WR) method and the more recent Rhizon method, in terms of their effects on stable calcium isotope ratios in extracted pore waters, we recognize a systematic offset between the two sampling methods. Higher δ44/40Ca values are associated with lower Ca concentrations for the Rhizon sampling technique and lower δ44/40Ca values are associated with higher Ca concentrations for the corresponding WR-derived pore water samples. Models involving Rayleigh fractionation and mixing calculation suggest that the observed offset is most likely caused by a combined process of CaCO3 precipitation and ion exchange taking place during Rhizon sampling-induced CO2 degassing. Changing pressure, extraction time or extraction yield during WR pressing does not lead to a variation in δ44/40Ca, indicating that no Ca isotope fractionation takes place during the sampling of pore water. On the basis of analytical and modelling results, WR samples appear to provide δ44/40Ca values that are more representative of the ‘true’ pore water isotopic composition. While the difference between the sampling techniques is close to the present-day analytical precision of Ca isotope analysis, it may become more relevant with increasing analytical precision in the future

Technical note: Uncovering the influence of methodological variations on the extractability of iron-bound organic carbon

Association of organic carbon (OC) with reactive iron (FeR) represents an important mechanism by which OC is protected against remineralisation in soils and marine sediments. Recent studies indicate that the molecular structure of organic compounds and/or the identity of associated FeR phases exert a control on the ability of an OC–FeR complex to be extracted by the citrate–bicarbonate–dithionite (CBD) method. However, many variations of the CBD extraction are used, and these are often uncalibrated to each other, rendering comparisons of OC–FeR values extracted via the different methods impossible. Here, we created synthetic ferrihydrite samples coprecipitated with simple organic structures and subjected these to modifications of the most common CBD method. We altered some of the method parameters (reagent concentration, time of the extraction and sample preparation methods) and measured FeR recovery to determine which (if any) modifications affected the release of FeR from the synthetic sample. We provide an assessment of the reducing capacity of Na dithionite in the CBD method (the amount of Fe reduced by a fixed amount of dithionite) and find that the concentration of dithionite deployed can limit OC–FeR extractability for sediments with a high FeR content. Additionally, we show that extending the length of any CBD extraction offers no benefit in removing FeR. Moreover, we demonstrate that for synthetic OC–FeR samples dominated by ferrihydrite, freeze-drying samples can significantly reduce OC–FeR extractability; this appears to be less of an issue for natural marine sediments where natural ageing mechanisms may mimic the freeze-drying process for more stable Fe phases. While our study is not an all-inclusive method comparison and is not aimed at delivering the “perfect” extraction setup, our findings provide a collected summary of critical factors which influence the efficiency of the CBD extraction for OC–FeR. As such, we provide a platform from which OC–FeR values obtained under different methods can be interpreted and future studies of sediment carbon cycling can build upon