Condition number analysis and preconditioning of the finite cell method

The (Isogeometric) Finite Cell Method - in which a domain is immersed in a structured background mesh - suffers from conditioning problems when cells with small volume fractions occur. In this contribution, we establish a rigorous scaling relation between the condition number of (I)FCM system matrices and the smallest cell volume fraction. Ill-conditioning stems either from basis functions being small on cells with small volume fractions, or from basis functions being nearly linearly dependent on such cells. Based on these two sources of ill-conditioning, an algebraic preconditioning technique is developed, which is referred to as Symmetric Incomplete Permuted Inverse Cholesky (SIPIC). A detailed numerical investigation of the effectivity of the SIPIC preconditioner in improving (I)FCM condition numbers and in improving the convergence speed and accuracy of iterative solvers is presented for the Poisson problem and for two- and three-dimensional problems in linear elasticity, in which Nitche's method is applied in either the normal or tangential direction. The accuracy of the preconditioned iterative solver enables mesh convergence studies of the finite cell method

Discontinuities without discontinuity: The Weakly-enforced Slip Method

Tectonic faults are commonly modelled as Volterra or Somigliana dislocations in an elastic medium. Various solution methods exist for this problem. However, the methods used in practice are often limiting, motivated by reasons of computational efficiency rather than geophysical accuracy. A typical geophysical application involves inverse problems for which many different fault configurations need to be examined, each adding to the computational load. In practice, this precludes conventional finite-element methods, which suffer a large computational overhead on account of geometric changes. This paper presents a new non-conforming finite-element method based on weak imposition of the displacement discontinuity. The weak imposition of the discontinuity enables the application of approximation spaces that are independent of the dislocation geometry, thus enabling optimal reuse of computational components. Such reuse of computational components renders finite-element modeling a viable option for inverse problems in geophysical applications. A detailed analysis of the approximation properties of the new formulation is provided. The analysis is supported by numerical experiments in 2D and 3D.Comment: Submitted for publication in CMAM

Inverting elastic dislocations using the Weakly-enforced Slip Method

Earthquakes cause lasting changes in static equilibrium, resulting in global deformation fields that can be observed. Consequently, deformation measurements such as those provided by satellite based InSAR monitoring can be used to infer an earthquake's faulting mechanism. This inverse problem requires a numerical forward model that is both accurate and fast, as typical inverse procedures require many evaluations. The Weakly-enforced Slip Method (WSM) was developed to meet these needs, but it was not before applied in an inverse problem setting. Consequently, it was unknown what effect particular properties of the WSM, notably its inherent continuity, have on the inversion process. Here we show that the WSM is able to accurately recover slip distributions in a Bayesian-inference setting, provided that data points in the vicinity of the fault are removed. In a representative scenario, an element size of 2 km was found to be sufficiently fine to generate a posterior probability distribution that is close to the theoretical optimum. For rupturing faults a masking zone of 20 km sufficed to avoid numerical disturbances that would otherwise be induced by the discretization error. These results demonstrate that the WSM is a viable forward method for earthquake inversion problems. While our synthesized scenario is basic for reasons of validation, our results are expected to generalize to the wider gamut of scenarios that finite element methods are able to capture. This has the potential to bring modeling flexibility to a field that if often forced to impose model restrictions in a concession to computability.Comment: The associated software implementation is openly available in zenodo at https://doi.org/10.5281/zenodo.507179

Connecting species’ geographical distributions to environmental variables: range maps versus observed points of occurrence

Connecting the geographical occurrence of a species with underlying environmental variables is fundamental for many analyses of life history evolution and for modeling species distributions for both basic and practical ends. However, raw distributional information comes principally in two forms: points of occurrence (specific geographical coordinates where a species has been observed), and expert-prepared range maps. Each form has potential short-comings: range maps tend to overestimate the true occurrence of a species, whereas occurrence points (because of their frequent non-random spatial distribution) tend to underestimate it. Whereas previous comparisons of the two forms have focused on how they may differ when estimating species richness, less attention has been paid to the extent to which the two forms actually differ in their representation of a species’ environmental associations. We assess such differences using the globally distributed avian order Galliformes (294 species). For each species we overlaid range maps obtained from IUCN and point-of-occurrence data obtained from GBIF on global maps of four climate variables and elevation. Over all species, the median difference in distribution centroids was 234 km, and median values of all five environmental variables were highly correlated, although there were a few species outliers for each variable. We also acquired species’ elevational distribution mid-points (mid-point between minimum and maximum elevational extent) from the literature; median elevations from point occurrences and ranges were consistently lower (median −420 m) than mid-points. We concluded that in most cases occurrence points were likely to produce better estimates of underlying environmental variables than range maps, although differences were often slight. We also concluded that elevational range mid-points were biased high, and that elevation distributions based on either points or range maps provided better estimates

On the singular nature of the elastocapillary ridge

The functionality of soft interfaces is crucial to many applications in biology and surface science. Recent studies have used liquid drops to probe the surface mechanics of elastomeric networks. Experiments suggest an intricate surface elasticity, also known as the Shuttleworth effect, where surface tension is not constant but depends on substrate deformation. However, interpretations have remained controversial due to singular elastic deformations, induced exactly at the point where the droplet pulls the network. Here we reveal the nature of the elastocapillary singularity on a hyperelastic substrate with various constitutive relations for the interfacial energy. First, we finely resolve the vicinity of the singularity using goal-adaptive finite element simulations. This confirms the universal validity, also at large elastic deformations, of the previously disputed Neumann's law for the contact angles. Subsequently, we derive exact solutions of nonlinear elasticity that describe the singularity analytically. These solutions are in perfect agreement with numerics, and show that the stretch at the contact line, as previously measured experimentally, consistently points to a strong Shuttleworth effect. Finally, using Noether's theorem we provide a quantitative link between wetting hysteresis and Eshelby-like forces, and thereby offer a complete framework for soft wetting in the presence of the Shuttleworth effect.Comment: 17 Pages, 7 figure

Pulmonary Sarcoidosis

Background: A 34-year-old male teacher was referred to the hospital with a persisting dry cough and dyspnea on exercise since eight weeks. He had no fever, neither complaints of ear, nose or throat. There were no complaints during the night. He had been a smoker until four months before presentation (12 pack years). At work a student was diagnosed with pulmonary tuberculosis, but the Mantoux and Quantiferon tests were negative. Physical examination was normal, without fever, lymphadenopathy or auscultation abnormalities. Laboratory investigation revealed a C-reactive protein of 2 mg/L. Pulmonary function testing showed a slight restriction. Immunological bronchial alveolar lavage (BAL) was rich of cells, especially T-lymphocytes of the CD4 type. CD4+/CD8+ ratio of the BAL was raised to 4.2, compared to a ratio of 2.4 in blood. There were no eosinophils found in the BAL. Conventional chest radiographs were performed, and showed multiple areas of consolidation in the bilateral lung fields, predominantly on the right side

A SIMPLIFIED BUT EFFECTIVE METHOD FOR THE QUALITY CONTROL OF MEDICINAL PLANTS BY PLANAR CHROMATOGRAPHY

Three of the factors limiting the rational use of herbal medicine are uncertainty on effectivity, uncertainty on safety and variation in quality of the product. Because many herbal medicines have been used over centuries by indigenous peoples, the safety and effectivity is frequently not such a big concern. With more people collecting and distributing herbal medicine, the offered product is however, frequently not what the label indicates either through a genuine mistake, but also through fraud especially where expensive herbal medicine is concerned. Some wrong identifications have already led to serious side effects and deaths. Planar chromatography or thin layer chromatography [TLC] is widely used to verify the identity of plant extracts by determining the chemical fingerprint of the extracts. In a leading publication 17 different extractants, 41 solvent systems and 44 spray reagents have been used to verify the identity of important herbal preparations. We investigated whether a simplified system could not be developed to aid small laboratories in identifying different herbal medicines. We compared the efficacy of different extractants, identified and developed three TLC solvent systems that would separate compounds with low, medium and high polarity and then also investigated the use of several spray reagents. With acetone as extractant and benzene:ethanol:ammonia [9:1:0.1], chloroform:ethylacetate:formic acid [5:4:1] and ethylacetate:methanol:water [10:1.35:1] as TLC solvent system and vanillin-sulphuric acid as spray reagent the identity of 81 samples of more than 50 herbal preparations could be verified on the basis of the chromatograms. The same product from different suppliers usually gave similar chromatograms. More importantly in several cases it was clear that products with the same label were so different that a mistake must have occurred in the labelling. This method has found application in the quality control of the most important African medicinal plants in the recently published African Herbal Pharmacopoeia produced by the Association for African Medicinal Plant Standards (AAMPS)

Reversal of Solvent Migration in Poroelastic Folds

Polymer networks and biological tissues are often swollen by a solvent such that their properties emerge from a coupling between swelling and elastic stress. This poroelastic coupling becomes particularly intricate in wetting, adhesion, and creasing, for which sharp folds appear that can even lead to phase separation. Here, we resolve the singular nature of poroelastic surface folds and determine the solvent distribution in the vicinity of the fold tip. Surprisingly, two opposite scenarios emerge depending on the angle of the fold. In obtuse folds such as creases, it is found that the solvent is completely expelled near the crease tip, according to a nontrivial spatial distribution. For wetting ridges with acute fold angles, the solvent migration is reversed as compared to creasing, and the degree of swelling is maximal at the fold tip. We discuss how our poroelastic fold analysis offers an explanation for phase separation, fracture, and contact angle hysteresis.</p

View From Outside the Viewing Sphere

The ‘viewing sphere’, as defined by Euclid and explored by Gibson as the ‘optic array’, is generally thought of as wrapped around the eye. Can an observer step out of it? With currently popular photographic techniques, the spectator is forced to, because the viewing sphere is presented as a pictorial object. Then the question is whether human observers are able to use such pictorial representations in an intuitive manner. Can the spectator ‘mentally step into the interior’ of the pictorial viewing sphere? We explore this issue in a short experiment. Perhaps unsurprisingly, because the eye cannot see itself, the short answer is no

BRAF Mutations as Predictive Biomarker for Response to Anti-EGFR Monoclonal Antibodies

Recently, the American Society of Clinical Oncology (ASCO) and the European Society for Medical Oncology (ESMO) recommended that patients with epidermal growth factor receptor (EGFR)-expressing metastatic colorectal cancer could be treated with anti-EGFR monoclonal antibodies (mAbs) cetuximab and panitumumab only in absence of Rat-Sarcoma (RAS) mutations. In addition to the previously established biomarker Kirsten rat sarcoma viral oncogene homolog (KRAS) exon 2, cumulative evidence also shows that patients whose tumors harbor KRAS exons 3 or 4 and neuroblastoma rat-sarcoma viral oncogene homolog (NRAS) exons 2, 3, and 4 mutations are found unlikely to benefit from anti-EGFR treatment.In line with the resistance of RAS mutated (mt) tumors, treatment response in BRAFmt tumors may also be altered given their important role in the EGFR signaling pathway. However, BRAF is not recommended as predictive biomarker yet because the evidence for the impact of BRAF mutations on treatment outcome is considered insufficient.This article summarizes the evidence for the impact of BRAF mutations on treatment outcome of anti-EGFR mAbs. Based on a review of literature, eight meta-analyses were included that consistently show that patients with BRAF mutations have a lack of treatment benefit of anti-EGFR mAbs. After discussing the quality and quantity of available evidence, we conclude that evidence is stronger than suggested by ESMO and ASCO. Additionally, we highlight that the quality of evidence for BRAF is even higher than for extended RAS as a biomarker. We therefore advise ESMO and ASCO to reconsider BRAF status as a predictive biomarker for response. The Oncologist 2017;22:1-9 IMPLICATIONS FOR PRACTICE: In metastatic colorectal cancer (mCRC), therapy with anti-epidermal growth factor receptor (EGFR) monoclonal antibodies cetuximab and panitumumab is indicated in absence of RAS mutations. Cumulative evidence shows that patients with BRAF mutations, who comprise 10% of the mCRC population, do not benefit from anti-EGFR-antibody treatment. Although guidelines state that evidence for BRAF as a predictive marker is insufficient, we highlight that the quality and quantity of evidence is higher than suggested. We therefore encourage the use of BRAF as a predictive marker in order to exclude patients from therapy for whom limited treatment benefit is expected