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

In vitro anti-plasmodial activity of Dicoma anomala subsp. gerrardii (Asteraceae): identification of its main active constituent, structure-activity relationship studies and gene expression profiling

<p>Abstract</p> <p>Background</p> <p>Anti-malarial drug resistance threatens to undermine efforts to eliminate this deadly disease. The resulting omnipresent requirement for drugs with novel modes of action prompted a national consortium initiative to discover new anti-plasmodial agents from South African medicinal plants. One of the plants selected for investigation was <it>Dicoma anomala </it>subsp. <it>gerrardii</it>, based on its ethnomedicinal profile.</p> <p>Methods</p> <p>Standard phytochemical analysis techniques, including solvent-solvent extraction, thin-layer- and column chromatography, were used to isolate the main active constituent of <it>Dicoma anomala </it>subsp. <it>gerrardii</it>. The crystallized pure compound was identified using nuclear magnetic resonance spectroscopy, mass spectrometry and X-ray crystallography. The compound was tested <it>in vitro </it>on <it>Plasmodium falciparum </it>cultures using the parasite lactate dehydrogenase (pLDH) assay and was found to have anti-malarial activity. To determine the functional groups responsible for the activity, a small collection of synthetic analogues was generated - the aim being to vary features proposed as likely to be related to the anti-malarial activity and to quantify the effect of the modifications <it>in vitro </it>using the pLDH assay. The effects of the pure compound on the <it>P. falciparum </it>transcriptome were subsequently investigated by treating ring-stage parasites (alongside untreated controls), followed by oligonucleotide microarray- and data analysis.</p> <p>Results</p> <p>The main active constituent was identified as dehydrobrachylaenolide, a eudesmanolide-type sesquiterpene lactone. The compound demonstrated an <it>in vitro </it>IC₅₀of 1.865 μM against a chloroquine-sensitive strain (D10) of <it>P. falciparum</it>. Synthetic analogues of the compound confirmed an absolute requirement that the α-methylene lactone be present in the eudesmanolide before significant anti-malarial activity was observed. This feature is absent in the artemisinins and suggests a different mode of action. Microarray data analysis identified 572 unique genes that were differentially expressed as a result of the treatment and gene ontology analysis identified various biological processes and molecular functions that were significantly affected. Comparison of the dehydrobrachylaenolide treatment transcriptional dataset with a published artesunate (also a sesquiterpene lactone) dataset revealed little overlap. These results strengthen the notion that the isolated compound and the artemisinins have differentiated modes of action.</p> <p>Conclusions</p> <p>The novel mode of action of dehydrobrachylaenolide, detected during these studies, will play an ongoing role in advancing anti-plasmodial drug discovery efforts.</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

Diffuse-interface two-phase flow models with different densities: a new quasi-incompressible form and a linear energy-stable method

While various phase-field models have recently appeared for two-phase fluids with different densities, only some are known to be thermodynamically consistent, and practical stable schemes for their numerical simulation are lacking. In this paper, we derive a new form of thermodynamically-consistent quasi-incompressible diffuse-interface Navier–Stokes–Cahn–Hilliard model for a two-phase flow of incompressible fluids with different densities. The derivation is based on mixture theory by invoking the second law of thermodynamics and Coleman–Noll procedure. We also demonstrate that our model and some of the existing models are equivalent and we provide a unification between them. In addition, we develop a linear and energy-stable time-integration scheme for the derived model. Such a linearly-implicit scheme is nontrivial, because it has to suitably deal with all nonlinear terms, in particular those involving the density. Our proposed scheme is the first linear method for quasi-incompressible two-phase flows with non-solenoidal velocity that satisfies discrete energy dissipation independent of the time-step size, provided that the mixture density remains positive. The scheme also preserves mass. Numerical experiments verify the suitability of the scheme for two-phase flow applications with high density ratios using large time steps by considering the coalescence and breakup dynamics of droplets including pinching due to gravity

A Constructive Framework for the Preventive Signalling Maintenance Crew Scheduling Problem in the Danish Railway system

In this paper we consider the problem of planning preventive maintenance of railway signals in Denmark. This case is particularly interesting, as the entire railway signalling system is currently being upgraded to the new European Railway Traffic Management System (ERTMS) standard. This upgrade has significant implications for signal maintenance scheduling in the system. We formulate the problem as a multidepot vehicle routing and scheduling problem with time windows and synchronisation constraints, in a multiday time schedule. The requirement that some tasks require the simultaneous presence of more than one engineer means that task synchronisation must be considered. A multi-stage constructive framework is proposed, which first distributes maintenance tasks using a clustering formulation. Following this, a Constraint Programming (CP) based approach is used to generate feasible monthly plans for large instances of practical interest. Experimental results indicate that the proposed framework can generate feasible solutions and schedule a monthly plan of up to 1000 tasks for eight crew members, in a reasonable amount of computational tim

Untargeted Metabolomics Reveals a Lack Of Synergy between Nifurtimox and Eflornithine against Trypanosoma brucei

A non-targeted metabolomics-based approach is presented that enables the study of pathways in response to drug action with the aim of defining the mode of action of trypanocides. Eflornithine, a polyamine pathway inhibitor, and nifurtimox, whose mode of action involves its metabolic activation, are currently used in combination as first line treatment against stage 2, CNS-involved, human African trypanosomiasis (HAT). Drug action was assessed using an LC-MS based non-targeted metabolomics approach. Eflornithine revealed the expected changes to the polyamine pathway as well as several unexpected changes that point to pathways and metabolites not previously described in bloodstream form trypanosomes, including a lack of arginase activity and N-acetylated ornithine and putrescine. Nifurtimox was shown to be converted to a trinitrile metabolite indicative of metabolic activation, as well as inducing changes in levels of metabolites involved in carbohydrate and nucleotide metabolism. However, eflornithine and nifurtimox failed to synergise anti-trypanosomal activity in vitro, and the metabolomic changes associated with the combination are the sum of those found in each monotherapy with no indication of additional effects. The study reveals how untargeted metabolomics can yield rapid information on drug targets that could be adapted to any pharmacological situation