Analysis-suitable adaptive T-mesh refinement with linear complexity

We present an efficient adaptive refinement procedure that preserves analysis-suitability of the T-mesh, this is, the linear independence of the T-spline blending functions. We prove analysis-suitability of the overlays and boundedness of their cardinalities, nestedness of the generated T-spline spaces, and linear computational complexity of the refinement procedure in terms of the number of marked and generated mesh elements.Comment: We now account for T-splines of arbitrary polynomial degree. We replaced the proof of Dual-Compatibility by a proof of Analysis-suitability, added a section where we address nestedness of the corresponding T-spline spaces, and removed the section on finite overlap the spline supports. 24 pages, 9 Figure

Mesh Refinement Strategies for the Adaptive Isogeometric Method

This thesis introduces four mesh refinement algorithms refine_hb, refine_thb, refine_ts2D and refine_tsnD for the Adaptive Isogeometric Method using multivariate Hierarchical B-splines, multivariate Truncated Hierarchical B-splines, bivariate T-splines, and multivariate T-splines, respectively. We address, for refine hb and refine_thb, boundedness of the overlap of basis functions, boundedness of mesh overlays and linear complexity in the sense of a uniform upper bound on the ratio of generated and marked elements. The existence of an upper bound on the overlap of basis functions implies that the system matrix of the linear equation system to solve is sparse, i.e., it has a uniformly bounded number of non-zero entries in each row and column. The upper bound on the number of elements in the coarsest common refinement (the overlay) of two meshes, as well as linear complexity are crucial ingredients for a later proof of rate-optimality of the method. For refine_ts2D and refine_tsnD, the overlap of basis functions is bounded a priori and did not need further investigation. We investigate the boundedness of mesh overlays, linear independence of the T-splines, nestedness of the T-spline spaces, and linear complexity as above. Nestedness of the spline spaces is crucial in the sense that it implies the so-called Galerkin orthogonality, which characterizes the approximate solution as a best-approximation of the exact solution with respect to a norm that depends on the problem. Altogether, this work paves the way for a proof of rate-optimality for the Adaptive Isogeometric Method with HB-splines, THB-splines, or T-splines in any space dimension. In order to justify the proposed methods and theoretical results in this thesis, numerical experiments underline their practical relevance, showing that they are not outperformed by currently prevalent refinement strategies. As an outlook to future work, we outline an approach for the handling of zero knot intervals and multiple lines in the interior of the domain, which are used in CAD applications for controlling the continuity of the spline functions, and we also sketch basic ideas for the local refinement of two-dimensional meshes that do not have tensor-product structure

Analysis‐Suitable T‐Splines of arbitrary degree and dimension

This paper defines analysis-suitable T-splines for arbitrary degree (including even and mixed degrees) and arbitrary dimension. We generalize the concept of anchor elements known from the two-dimensional setting, extend two existing concepts of analysis-suitability and justify their sufficiency for linear independence of the T-spline basis

Adaptive refinement for unstructured T-splines with linear complexity

We present an adaptive refinement algorithm for T-splines on unstructured 2D meshes. While for structured 2D meshes, one can refine elements alternatingly in horizontal and vertical direction, such an approach cannot be generalized directly to unstructured meshes, where no two unique global mesh directions can be assigned. To resolve this issue, we introduce the concept of direction indices, i.e., integers associated to each edge, which are inspired by theory on higher-dimensional structured T-splines. Together with refinement levels of edges, these indices essentially drive the refinement scheme. We combine these ideas with an edge subdivision routine that allows for I-nodes, yielding a very flexible refinement scheme that nicely distributes the T-nodes, preserving global linear independence, analysis-suitability (local linear independence) except in the vicinity of extraordinary nodes, sparsity of the system matrix, and shape regularity of the mesh elements. Further, we show that the refinement procedure has linear complexity in the sense of guaranteed upper bounds on a) the distance between marked and additionally refined elements, and on b) the ratio of the numbers of generated and marked mesh elements. © 2022 The Author(s

Synthesis and electrochemistry of remotely thioether‐functionalized disilenes

We report the synthesis of p-methylthio-functionalized disilenes with (oligo)phenylene-linkers of different sizes between the thiomethyl group and the Si=Si moiety. 29Si NMR and UV/vis data suggests that the linker-size affects the Si=Si moiety only moderately. Cyclic voltammetry reveals an increasing number of reduction events with the number of phenylene rings, which are therefore clearly associated to the oligo(phenylene) linking unit. The exchange current density of the oxidation and reduction reactions as determined by linear sweep voltammetry with a rotating disc electrode also shows significant differences between the prepared disilenes

Eastern Mediterranean Mobility in the Bronze and Early Iron Ages: Inferences from Ancient DNA of Pigs and Cattle

The Late Bronze of the Eastern Mediterranean (1550-1150 BCE) was a period of strong commercial relations and great prosperity, which ended in collapse and migration of groups to the Levant. Here we aim at studying the translocation of cattle and pigs during this period. We sequenced the first ancient mitochondrial and Y chromosome DNA of cattle from Greece and Israel and compared the results with morphometric analysis of the metacarpal in cattle. We also increased previous ancient pig DNA datasets from Israel and extracted the first mitochondrial DNA for samples from Greece. We found that pigs underwent a complex translocation history, with links between Anatolia with southeastern Europe in the Bronze Age, and movement from southeastern Europe to the Levant in the Iron I (ca. 1150-950 BCE). Our genetic data did not indicate movement of cattle between the Aegean region and the southern Levant. We detected the earliest evidence for crossbreeding between taurine and zebu cattle in the Iron IIA (ca. 900 BCE). In light of archaeological and historical evidence on Egyptian imperial domination in the region in the Late Bronze Age, we suggest that Egypt attempted to expand dry farming in the region in a period of severe droughts

Influence of adatom interactions on second layer nucleation

We develop a theory for the inclusion of adatom interactions in second layer nucleation occurring in epitaxial growth. The interactions considered are due to ring barriers between pairs of adatoms and binding energies of unstable clusters. The theory is based on a master equation, which describes the time development of microscopic states that are specified by cluster configurations on top of an island. The transition rates are derived by scaling arguments and tested against kinetic Monte-Carlo simulations. As an application we reanalyze experiments to determine the step edge barrier for Ag/Pt(111).Comment: 4 pages, 4 figure

Ferromagnetic MnSb2Te4: A p-type topological insulator with magnetic gap closing at high Curie temperatures of 45-50K

Resumen del trabajo presentado al APS March Meeting, celebrado de forma virtual del 13 al 19 de marzo de 2021Mn enables the formation of intrinsic magnetic topological insulatorsfor the quantum anomalous Hall effect with A1B2C4 stoichiometry, e. g., antiferromagnetic MnBi2Te4 with 25 K Néel temperature. Here, we showthat p-type MnSb2Te4, previously considered topologically trivial, is a ferromagnetic topological insulator with high Curie temperature of 45 to 50 K.It displays out-of-plane magnetic anisotropy, the nontrivial topology is robust in band structure calculations towards magnetic disorder, provides aDirac point of the topological surface state close to the Fermi level with out-of-plane spin polarization in spin-ARPES, and exhibits a magneticallyinduced band gap of 17 meV that closes at the Curie temperature as demonstrated by scanning tunneling spectroscopy. Moreover, it displays acritical exponent of magnetization β≈1, indicating the vicinity of a quantum critical point. We identify the influences of structural and magneticdisorder that render MnSb2Te4 the ideal system for tuning electric and magnetic properties of quantum anomalous Hall systems.Peer reviewe

Copeptin for risk stratification in non-traumatic headache in the emergency setting: a prospective multicenter observational cohort study

In the emergency setting, non-traumatic headache is a benign symptom in 80% of cases, but serious underlying conditions need to be ruled out. Copeptin improves risk stratification in several acute diseases. Herein, we investigated the value of copeptin to discriminate between serious secondary headache and benign headache forms in the emergency setting.; Patients presenting with acute non-traumatic headache were prospectively enrolled into an observational cohort study. Copeptin was measured upon presentation to the emergency department. Primary endpoint was serious secondary headache defined by a neurologic cause requiring immediate treatment of the underlying disease. Secondary endpoint was the combination of mortality and hospitalization within 3 months. Two board-certified neurologist blinded to copeptin levels verified the endpoints after a structured 3-month-telephone interview.; Of the 391 patients included, 75 (19%) had a serious secondary headache. Copeptin was associated with serious secondary headache (OR 2.03, 95%CI 1.52-2.70, p < 0.0001). Area under the curve (AUC) for copeptin to identify the primary endpoint was 0.70 (0.63-0.76). After adjusting for age > 50, focal-neurological abnormalities, and thunderclap onset of symptoms, copeptin remained an independent predictive factor for serious secondary headache (OR 1.74, 95%CI 1.26-2.39, p = 0.001). Moreover, copeptin improved the AUC of the multivariate logistic clinical model (p-LR-test < 0.001). Even though copeptin values were higher in patients reaching the secondary endpoint, this association was not significant in multivariate logistic regression.; Copeptin was independently associated with serious secondary headache as compared to benign headaches forms. Copeptin may be a promising novel blood biomarker that should be further validated to rule out serious secondary headache in the emergency department.; Study Registration on 08/02/2010 as NCT01174901 at clinicaltrials.gov