[1] The finite element method (FEM) combined with unstructured meshes forms an elegant and versatile approach capable of dealing with the complexities of problems in Earth science. Practical applications often require high-resolution models that necessitate advanced computational strategies. We therefore developed ''Million a Minute'' (MILAMIN), an efficient MATLAB implementation of FEM that is capable of setting up, solving, and postprocessing two-dimensional problems with one million unknowns in one minute on a modern desktop computer. MILAMIN allows the user to achieve numerical resolutions that are necessary to resolve the heterogeneous nature of geological materials. In this paper we provide the technical knowledge required to develop such models without the need to buy a commercial FEM package, programming compiler-language code, or hiring a computer specialist. It has been our special aim that all the components of MILAMIN perform efficiently individually and as a package. While some of the components rely on readily available routines, we develop others from scratch and make sure that all of them work together efficiently. One of the main technical focuses of this paper is the optimization of the global matrix computations. The performance bottlenecks of the standard FEM algorithm are analyzed. An alternative approach is developed that sustains high performance for any system size. Applied optimizations eliminate Basic Linear Algebra Subprograms (BLAS) drawbacks when multiplying small matrices, reduce operation count and memory requirements when dealing with symmetric matrices, and increase data transfer efficiency by maximizing cache reuse. Applying loop interchange allows us to use BLAS on large matrices. In order to avoid unnecessary data transfers between RAM and CPU cache we introduce loop blocking. The optimization techniques are useful in many areas as demonstrated with our MILAMIN applications for thermal and incompressible flow (Stokes) problems. We use these to provide performance comparisons to other open source as well as commercial packages and find that MILAMIN is among the best performing solutions, in terms of both speed and memory usage. The corresponding MATLAB source code for the entire MILAMIN, including input generation, FEM solver, and postprocessing, is available from the authors (http://www.milamin.org) and can be downloaded as auxiliary material.

We study segregation of the subducted oceanic crust (OC) at the core-mantle boundary and its ability to accumulate and form large thermochemical piles (such as the seismically observed Large Low Shear Velocity Provinces (LLSVPs)). Our high-resolution numerical simulations of thermochemical mantle convection suggest that the longevity of LLSVPs for up to three billion years, and possibly longer, can be ensured by a balance in the rate of segregation of high-density OC material to the core-mantle boundary (CMB) and the rate of its entrainment away from the CMB by mantle upwellings. For a range of parameters tested in this study, a large-scale compositional anomaly forms at the CMB, similar in shape and size to the LLSVPs. Neutrally buoyant thermochemical piles formed by mechanical stirring-where thermally induced negative density anomaly is balanced by the presence of a fraction of dense anomalous material-best resemble the geometry of LLSVPs. Such neutrally buoyant piles tend to emerge and survive for at least 3 Gyr in simulations with quite different parameters. We conclude that for a plausible range of values of density anomaly of OC material in the lower mantle-it is likely that it segregates to the CMB, gets mechanically mixed with the ambient material, and forms neutrally buoyant large-scale compositional anomalies similar in shape to the LLSVPs.

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BackgroundThe COVID-19 crisis forced hospitals in the UK dramatically to reduce outpatient activity. To provide continuity of care and to assist patients reluctant or unable to leave their homes, video consultations were rapidly implemented across routine and emergency ophthalmology services.ObjectiveTo describe the deployment and scaling to a large volume of teleophthalmology using a video consultation platform ‘Attend Anywhere’ in Moorfields Eye Hospital’s accident and emergency (A&E) department (London, UK).MethodPatient satisfaction, waiting time, consultation duration, outcome and management were audited following the launch of the new virtual A&E service.ResultsIn the 12 days following the service launch, 331 patients were seen by video consultation. 78.6% of patients (n=260) were determined not to need hospital A&E review and were managed with advice (n=126), remote prescription (n=57), general practitioner referral (n=27), direct referral to hospital subspecialty services (n=26) or diversion to a local eye unit (n=24). Mean patient satisfaction was 4.9 of 5.0 (n=62). The mean consultation duration was 12 min (range 5–31 min) and the wait time was 6 min (range 0–37 min).ConclusionVideo consultations showed greater than expected usefulness in the remote management of eye disease and supported a substantial reduction in the number of people visiting the hospital.

[1] We present a combined shape and mechanical anisotropy evolution model for a two-phase inclusion-bearing rock subject to large deformation. A single elliptical inclusion embedded in a homogeneous but anisotropic matrix is used to represent a simplified shape evolution enforced on all inclusions. The mechanical anisotropy develops due to the alignment of elongated inclusions. The effective anisotropy is quantified using the differential effective medium (DEM) approach. The model can be run for any deformation path and an arbitrary viscosity ratio between the inclusion and host phase. We focus on the case of simple shear and weak inclusions. The shape evolution of the representative inclusion is largely insensitive to the anisotropy development and to parameter variations in the studied range. An initial hardening stage is observed up to a shear strain of g = 1 irrespective of the inclusion fraction. The hardening is followed by a softening stage related to the developing anisotropy and its progressive rotation toward the shear direction. The traction needed to maintain a constant shear rate exhibits a fivefold drop at g = 5 in the limiting case of an inviscid inclusion. Numerical simulations show that our analytical model provides a good approximation to the actual evolution of a two-phase inclusion-host composite. However, the inclusions develop complex sigmoidal shapes resulting in the formation of an S-C fabric. We attribute the observed drop in the effective normal viscosity to this structural development. We study the localization potential in a rock column bearing varying fraction of inclusions. In the inviscid inclusion case, a strain jump from g = 3 to g = 100 is observed for a change of the inclusion fraction from 20% to 33%.

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We present an improved approach for the preparation of highly selective and homogeneous molecular cavities in molecularly imprinted polymers (MIPs) via the combination of surface imprinting and semi-covalent imprinting. Toward that, first, a colloidal crystal mold was prepared via the Langmuir–Blodgett (LB) technique. Then, human chorionic gonadotropin (hCG) template protein was immobilized on the colloidal crystal mold. Later, hCG derivatization with electroactive functional monomers via amide chemistry was performed. In a final step, optimized potentiostatic polymerization of 2,3′-bithiophene enabled depositing an MIP film as the macroporous structure. This synergistic strategy resulted in the formation of molecularly imprinted cavities exclusively on the internal surface of the macropores, which were accessible after dissolution of silica molds. The recognition of hCG by the macroporous MIP film was transduced with the help of electric transducers, namely, extended-gate field-effect transistors (EG-FET) and capacitive impedimetry (CI). These readout strategies offered the ability to create chemosensors for the label-free determination of the hCG hormone. Other than the simple confirmation of pregnancy, hCG assay is a common tool for the diagnosis and follow-up of ectopic pregnancy or trophoblast tumors. Concentration measurements with these EG-FET and CI-based devices allowed real-time measurements of hCG in the range of 0.8–50  and 0.17–2.0 fM, respectively, in 10 mM carbonate buffer (pH = 10). Moreover, the selectivity of chemosensors with respect to protein interferences was very high.