An embedding technique for the solution of reaction-fiffusion equations on algebraic surfaces with isolated singularities

In this paper we construct a parametrization-free embedding technique for numerically evolving reaction-diffusion PDEs defined on algebraic curves that possess an isolated singularity. In our approach, we first desingularize the curve by appealing to techniques from algebraic geometry.\ud We create a family of smooth curves in higher dimensional space that correspond to the original curve by projection. Following this, we pose the analogous reaction-diffusion PDE on each member of this family and show that the solutions (their projection onto the original domain) approximate the solution of the original problem. Finally, we compute these approximants numerically by applying the Closest Point Method which is an embedding technique for solving PDEs on smooth surfaces of arbitrary dimension or codimension, and is thus suitable for our situation. In addition, we discuss the potential to generalize the techniques presented for higher-dimensional surfaces with multiple singularities

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

Classical ratchet effects in heterostructures with a lateral periodic potential

We study terahertz radiation induced ratchet currents in low dimensional semiconductor structures with a superimposed one-dimensional lateral periodic potential. The periodic potential is produced by etching a grating into the sample surface or depositing metal stripes periodically on the sample top. Microscopically, the photocurrent generation is based on the combined action of the lateral periodic potential, verified by transport measurements, and the in-plane modulated pumping caused by the lateral superlattice. We show that a substantial part of the total current is caused by the polarization-independent Seebeck ratchet effect. In addition, polarization-dependent photocurrents occur, which we interpret in terms of their underlying microscopical mechanisms. As a result, the class of ratchet systems needs to be extended by linear and circular ratchets, sensitive to linear and circular polarizations of the driving electro-magnetic force.Comment: 11 pages, 9 figures, 2 column

Association between the A-2518G polymorphism in the monocyte chemoattractant protein-1 gene and insulin resistance and Type 2 diabetes mellitus

Aims/hypothesis: The molecular mechanisms of obesity-related insulin resistance are incompletely understood. Macrophages accumulate in adipose tissue of obese individuals. In obesity, monocyte chemoattractant protein-1 (MCP-1), a key chemokine in the process of macrophage accumulation, is overexpressed in adipose tissue. MCP-1 is an insulin-responsive gene that continues to respond to exogenous insulin in insulin-resistant adipocytes and mice. MCP-1 decreases insulin-stimulated glucose uptake into adipocytes. The A-2518G polymorphism in the distal regulatory region of MCP-1 may regulate gene expression. The aim of this study was to investigate the impact of this gene polymorphism on insulin resistance. Methods: We genotyped the Ludwigshafen Risk and Cardiovascular Health (LURIC) cohort (n=3307). Insulin resistance, estimated by homeostasis model assessment, and Type 2 diabetes were diagnosed in 803 and 635 patients respectively. Results: Univariate analysis revealed that plasma MCP-1 levels were significantly and positively correlated with WHR (p=0.011), insulin resistance (p=0.0097) and diabetes (p<0.0001). Presence of the MCP-1 G-2518 allele was associated with decreased plasma MCP-1 (p=0.017), a decreased prevalence of insulin resistance (odds ratio [OR]=0.82, 95% CI: 0.70-0.97, p=0.021) and a decreased prevalence of diabetes (OR=0.80, 95% CI: 0.67-0.96, p=0.014). In multivariate analysis, the G allele retained statistical significance as a negative predictor of insulin resistance (OR=0.78, 95% CI: 0.65-0.93, p=0.0060) and diabetes (OR=0.80, 95% CI: 0.66-0.96, p=0.018). Conclusions/interpretation: In a large cohort of Caucasians, the MCP-1 G-2518 gene variant was significantly and negatively correlated with plasma MCP-1 levels and the prevalence of insulin resistance and Type 2 diabetes. These results add to recent evidence supporting a role for MCP-1 in pathologies associated with hyperinsulinaemi

Enantiomerically Pure Tetravalent Neptunium Amidinates: Synthesis and Characterization

The synthesis of a tetravalent neptunium amidinate [NpCl((S )‐PEBA)$_{3}$] (1 ) ((S )‐PEBA=(S ,S )‐N ,N′‐bis‐(1‐phenylethyl)‐benzamidinate) is reported. This complex represents the first structurally characterized enantiopure transuranic compound. Reactivity studies with halide/pseudohalides yielding [NpX((S )‐PEBA)$_{3}$] (X=F (2 ), Br (3 ), N3 (4 )) have shown that the chirality‐at‐metal is preserved for all compounds in the solid state. Furthermore, they represent an unprecedented example of a structurally characterized metal–organic Np complex featuring a Np−Br (3 ) bond. In addition, 4 is the only reported tetravalent transuranic azide. All compounds were additionally characterized in solution using para‐magnetic NMR spectroscopy showing an expected C$_{3}$‐symmetry at low temperatures

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

Insights into the Electronic Structure of a U(IV) Amido and U(V) Imido Complex

Reaction of the N-heterocylic carbene ligand $^{i}$PrIm (L$^{1}$) and lithium bis(trimethylsilyl)amide (TMSA) as a base with UCl$_{4}$ resulted in U(IV) and U(V) complexes. Uranium\u27s +V oxidation state in (HL$^{1}$)$_{2}$[U(V)(TMSI)Cl$_{5}$] (TMSI=trimethylsilylimido) (2) was confirmed by HERFD-XANES measurements. Solid state characterization by SC-XRD and geometry optimisation of [U(IV)(L$^{1}$)$_{2}$(TMSA)Cl$_{3}$] (1) indicated a silylamido ligand mediated inverse trans influence (ITI). The ITI was examined regarding different metal oxidation states and was compared to transition metal analogues by theoretical calculations