Analysis and simulations for a phase‐field fracture model at finite strains based on modified invariants

Phase‐field models have already been proven to predict complex fracture patterns for brittle fracture at small strains. In this paper we discuss a model for phase‐field fracture at finite deformations in more detail. Among the identification of crack location and projection of crack growth the numerical stability is one of the main challenges in solid mechanics. Here we present a phase‐field model at finite strains, which takes into account the anisotropy of damage by applying an anisotropic split of the modified invariants of the right Cauchy‐Green strain tensor. We introduce a suitable weak notion of solution that also allows for a spatial and temporal discretization of the model. In this framework we study the existence of solutions and we show that the time‐discrete solutions converge in a weak sense to a solution of the time‐continuous formulation of the model. Numerical examples in two and three space dimensions illustrate the range of validity of the analytical results

SPIDER: Probing the Early Universe with a Suborbital Polarimeter

We evaluate the ability of SPIDER, a balloon-borne polarimeter, to detect a divergence-free polarization pattern ("B-modes") in the Cosmic Microwave Background (CMB). In the inflationary scenario, the amplitude of this signal is proportional to that of the primordial scalar perturbations through the tensor-to-scalar ratio r. We show that the expected level of systematic error in the SPIDER instrument is significantly below the amplitude of an interesting cosmological signal with r=0.03. We present a scanning strategy that enables us to minimize uncertainty in the reconstruction of the Stokes parameters used to characterize the CMB, while accessing a relatively wide range of angular scales. Evaluating the amplitude of the polarized Galactic emission in the SPIDER field, we conclude that the polarized emission from interstellar dust is as bright or brighter than the cosmological signal at all SPIDER frequencies (90 GHz, 150 GHz, and 280 GHz), a situation similar to that found in the "Southern Hole." We show that two ~20-day flights of the SPIDER instrument can constrain the amplitude of the B-mode signal to r<0.03 (99% CL) even when foreground contamination is taken into account. In the absence of foregrounds, the same limit can be reached after one 20-day flight.Comment: 29 pages, 8 figures, 4 tables; v2: matches published version, flight schedule updated, two typos fixed in Table 2, references and minor clarifications added, results unchange

The Gaia-ESO Public Spectroscopic Survey: Motivation, implementation, GIRAFFE data processing, analysis, and final data products

Context. The Gaia-ESO Public Spectroscopic Survey is an ambitious project designed to obtain astrophysical parameters and elemental abundances for 100 000 stars, including large representative samples of the stellar populations in the Galaxy, and a well-defined sample of 60 (plus 20 archive) open clusters. We provide internally consistent results calibrated on benchmark stars and star clusters, extending across a very wide range of abundances and ages. This provides a legacy data set of intrinsic value, and equally a large wide-ranging dataset that is of value for the homogenisation of other and future stellar surveys and Gaia's astrophysical parameters. Aims. This article provides an overview of the survey methodology, the scientific aims, and the implementation, including a description of the data processing for the GIRAFFE spectra. A companion paper introduces the survey results. Methods. Gaia-ESO aspires to quantify both random and systematic contributions to measurement uncertainties. Thus, all available spectroscopic analysis techniques are utilised, each spectrum being analysed by up to several different analysis pipelines, with considerable effort being made to homogenise and calibrate the resulting parameters. We describe here the sequence of activities up to delivery of processed data products to the ESO Science Archive Facility for open use. Results. The Gaia-ESO Survey obtained 202 000 spectra of 115 000 stars using 340 allocated VLT nights between December 2011 and January 2018 from GIRAFFE and UVES. Conclusions. The full consistently reduced final data set of spectra was released through the ESO Science Archive Facility in late 2020, with the full astrophysical parameters sets following in 2022. A companion article reviews the survey implementation, scientific highlights, the open cluster survey, and data products

The Gaia-ESO Public Spectroscopic Survey: Implementation, data products, open cluster survey, science, and legacy

Context. In the last 15 years different ground-based spectroscopic surveys have been started (and completed) with the general aim of delivering stellar parameters and elemental abundances for large samples of Galactic stars, complementing Gaia astrometry. Among those surveys, the Gaia-ESO Public Spectroscopic Survey, the only one performed on a 8m class telescope, was designed to target 100 000 stars using FLAMES on the ESO VLT (both Giraffe and UVES spectrographs), covering all the Milky Way populations, with a special focus on open star clusters. Aims. This article provides an overview of the survey implementation (observations, data quality, analysis and its success, data products, and releases), of the open cluster survey, of the science results and potential, and of the survey legacy. A companion article reviews the overall survey motivation, strategy, Giraffe pipeline data reduction, organisation, and workflow. Methods. We made use of the information recorded and archived in the observing blocks; during the observing runs; in a number of relevant documents; in the spectra and master catalogue of spectra; in the parameters delivered by the analysis nodes and the working groups; in the final catalogue; and in the science papers. Based on these sources, we critically analyse and discuss the output and products of the Survey, including science highlights. We also determined the average metallicities of the open clusters observed as science targets and of a sample of clusters whose spectra were retrieved from the ESO archive. Results. The Gaia-ESO Survey has determined homogeneous good-quality radial velocities and stellar parameters for a large fraction of its more than 110 000 unique target stars. Elemental abundances were derived for up to 31 elements for targets observed with UVES. Lithium abundances are delivered for about 1/3 of the sample. The analysis and homogenisation strategies have proven to be successful; several science topics have been addressed by the Gaia-ESO consortium and the community, with many highlight results achieved. Conclusions. The final catalogue will be released through the ESO archive in the first half of 2022, including the complete set of advanced data products. In addition to these results, the Gaia-ESO Survey will leave a very important legacy, for several aspects and for many years to come

Age at symptom onset and death and disease duration in genetic frontotemporal dementia : an international retrospective cohort study

Background: Frontotemporal dementia is a heterogenous neurodegenerative disorder, with about a third of cases being genetic. Most of this genetic component is accounted for by mutations in GRN, MAPT, and C9orf72. In this study, we aimed to complement previous phenotypic studies by doing an international study of age at symptom onset, age at death, and disease duration in individuals with mutations in GRN, MAPT, and C9orf72. Methods: In this international, retrospective cohort study, we collected data on age at symptom onset, age at death, and disease duration for patients with pathogenic mutations in the GRN and MAPT genes and pathological expansions in the C9orf72 gene through the Frontotemporal Dementia Prevention Initiative and from published papers. We used mixed effects models to explore differences in age at onset, age at death, and disease duration between genetic groups and individual mutations. We also assessed correlations between the age at onset and at death of each individual and the age at onset and at death of their parents and the mean age at onset and at death of their family members. Lastly, we used mixed effects models to investigate the extent to which variability in age at onset and at death could be accounted for by family membership and the specific mutation carried. Findings: Data were available from 3403 individuals from 1492 families: 1433 with C9orf72 expansions (755 families), 1179 with GRN mutations (483 families, 130 different mutations), and 791 with MAPT mutations (254 families, 67 different mutations). Mean age at symptom onset and at death was 49\ub75 years (SD 10\ub70; onset) and 58\ub75 years (11\ub73; death) in the MAPT group, 58\ub72 years (9\ub78; onset) and 65\ub73 years (10\ub79; death) in the C9orf72 group, and 61\ub73 years (8\ub78; onset) and 68\ub78 years (9\ub77; death) in the GRN group. Mean disease duration was 6\ub74 years (SD 4\ub79) in the C9orf72 group, 7\ub71 years (3\ub79) in the GRN group, and 9\ub73 years (6\ub74) in the MAPT group. Individual age at onset and at death was significantly correlated with both parental age at onset and at death and with mean family age at onset and at death in all three groups, with a stronger correlation observed in the MAPT group (r=0\ub745 between individual and parental age at onset, r=0\ub763 between individual and mean family age at onset, r=0\ub758 between individual and parental age at death, and r=0\ub769 between individual and mean family age at death) than in either the C9orf72 group (r=0\ub732 individual and parental age at onset, r=0\ub736 individual and mean family age at onset, r=0\ub738 individual and parental age at death, and r=0\ub740 individual and mean family age at death) or the GRN group (r=0\ub722 individual and parental age at onset, r=0\ub718 individual and mean family age at onset, r=0\ub722 individual and parental age at death, and r=0\ub732 individual and mean family age at death). Modelling showed that the variability in age at onset and at death in the MAPT group was explained partly by the specific mutation (48%, 95% CI 35\u201362, for age at onset; 61%, 47\u201373, for age at death), and even more by family membership (66%, 56\u201375, for age at onset; 74%, 65\u201382, for age at death). In the GRN group, only 2% (0\u201310) of the variability of age at onset and 9% (3\u201321) of that of age of death was explained by the specific mutation, whereas 14% (9\u201322) of the variability of age at onset and 20% (12\u201330) of that of age at death was explained by family membership. In the C9orf72 group, family membership explained 17% (11\u201326) of the variability of age at onset and 19% (12\u201329) of that of age at death. Interpretation: Our study showed that age at symptom onset and at death of people with genetic frontotemporal dementia is influenced by genetic group and, particularly for MAPT mutations, by the specific mutation carried and by family membership. Although estimation of age at onset will be an important factor in future pre-symptomatic therapeutic trials for all three genetic groups, our study suggests that data from other members of the family will be particularly helpful only for individuals with MAPT mutations. Further work in identifying both genetic and environmental factors that modify phenotype in all groups will be important to improve such estimates. Funding: UK Medical Research Council, National Institute for Health Research, and Alzheimer's Society