Analysis of fully discrete, quasi non-conforming approximations of evolution equations and applications

In this paper we consider fully discrete approximations of abstract evolution equations, by means of a quasi non-conforming spatial approximation and finite differences in time (Rothe-Galerkin method). The main result is the convergence of the discrete solutions to a weak solution of the continuous problem. Hence, the result can be interpreted either as a justification of the numerical method, or as an alternative way of constructing weak solutions. We set the problem in the very general and abstract setting of pseudo-monotone operators, which allows for a unified treatment of several evolution problems. The examples -- which fit into our setting and which motivated our research -- are problems describing the motion of incompressible fluids, since the quasi non-conforming approximation allows to handle problems with prescribed divergence. Our abstract results for pseudo-monotone operators allow to show convergence just by verifying a few natural assumptions on the operator time-by-time and on the discretization spaces. Hence, applications and extensions to several other evolution problems can be easily performed. The results of some numerical periments are reported in the final section

Geochemical and isotopic evidence bearing on the origin of large, igneous-textured inclusions in ordinary chondrites

Geochemical and isotopic data for large, igneous-textured inclusions in ordinary chondrites suggest that the inclusions formed by the melting of diverse precursors, and that various inclusions had different origins. Some inclusions were metasomatized (chemically altered) and metamorphosed, and many appear to have degassed argon in late shock events. The inclusions can be subdivided into two chemical groups, Na-rich (Na/Al>0.35 at.) and Na-poor (≤0.35), which may have originated in different ways. The major-and trace-element abundances of Na-rich inclusions are best explained by these inclusions having formed by the shock-melting of ordinary chondrites, often accompanied by loss of FeNi-metal and sulfide and by preferential melting and accumulation of an albitic feldspar component. In contrast, there is no evidence that shock-melting was involved in the formation of Na-poor inclusions, which have compositions that were largely controlled by vapor-fractionation processes. It is suggested that the precursors to Na-poor inclusions consisted of mixtures of vapor-fractionated materials in a system of condensed phases that chemically resembled CI-chondrites, except for being depleted in volatile-lithophile elements and in metal and sulfide. Sodium-poor inclusions can be subdivided into two types, Trend A and Trend B, which differ in their trace-element characteristics, in the nature of their compositional variations, and in their inferred precursors. Trend A Na-poor inclusions are enriched in refractory elements, and could have formed by the melting of mixtures containing a chondritic (CI-like) component and a refractory (Al-rich, CAI-like) component. Trend B Na-poor inclusions are enriched in elements of intermediate volatility (Si) and appear to have formed from precursors that lost both a refractory (Mg-rich, olivine-rich) and a volatile component. The precursors to these inclusions could have been produced by the removal of an olivine-rich condensate during fractional condensation, or by the condensation of Si-rich gases during fractional vaporization

Petrology and oxygen isotopic composition of large igneous inclusions in ordinary chondrites: Early solar system igneous processes and oxygen reservoirs

Large (>3.5 mm and up to 4 cm across) igneous inclusions poor in metal and sulfide are a minor but not uncommon component in ordinary chondrites, and have implications for the nature of physiochemical and melting processes in the early solar system. We obtained petrographic-chemical data for forty-two large igneous inclusions in ordinary chondrites of various groups (H, L, LL) and petrographic types (3-6) and oxygen isotope data for a subset of twelve of these inclusions and their host chondrites. Different inclusions formed both before and after the thermal metamorphism experienced by their host chondrites. The bulk chemical compositions of the inclusions vary broadly around whole-rock chondrite composition, comprise four main chemical types and some other variants, and show little evidence of having formed as igneous differentiates. Oxygen isotope compositions overlap ordinary chondrite compositions and are related to inclusion chemical type. Most prevalent in type 3 and 4 chondrites are inclusions, often droplets, of the vapor-fractionated (Vfr) chemical type, either enriched in refractory lithophile elements, or depleted in volatile lithophile elements, or both. These inclusions have low Δ17O (∼0.1-0.6‰) and high δ18O (∼4-8‰) values and formed in reservoirs with Δ17O lower than their hosts, primarily as evaporative melts and mixtures that probably experienced kinetic isotopic fractionation. Another chemical type (Unfr+K) has unfractionated abundances of lithophile elements except for being strongly enriched in K, a signature also found in some impact melts from melt rocks and melt breccias. These inclusions formed by impact melting of chondritic material and accompanying K enrichment. Inclusions with unfractionated (Unfr) lithophile element abundances are present in type 3-6 chondrites and are prevalent in type 5 and 6. Some are spatially associated with coarse metal-sulfide nodules in the chondrites and likely formed by in situ impact melting. Others were melted prior to thermal metamorphism and were chemically but not isotopically homogenized during metamorphism; they are xenoliths that formed in oxygen reservoirs different than the hosts in which they were metamorphosed. The latter inclusions provide evidence for nebular or collisional mixing of primitive materials prior to thermal metamorphism of asteroid bodies, including transport of H-like source materials to the L body, LL-like source materials to the L body, and low-Δ17O materials to the LL body. Feldspar-rich (FldR) inclusions have compositions similar to melt pockets and could have formed by disequilibrium melting and concentration of feldspar during an impact event to form large droplets or large masses. Overall, the results of this study point to important and varied roles for both “planetary” impact melting and “nebular” evaporative melting processes to form different large igneous inclusions in ordinary chondrites. Chondrules may have formed by processes similar to those inferred for large inclusions, but there are important differences in the populations of these objects

Shock compaction heating and collisional processes in the production of type 3 ordinary chondrites: Lessons from the (nearly) unique L3 chondrite melt breccia Northwest Africa 8709*

Northwest Africa (NWA) 8709 is a rare example of a type 3 ordinary chondrite melt breccia and provides critical information for the shock compaction histories of chondrites. An L3 protolith for NWA 8709 is inferred on the basis of oxygen isotope composition, elemental composition, diverse mineral chemistry, and overall texture. NWA 8709 is among the most strongly shocked type 3 chondrites known, and experienced complete melting of the matrix and partial melting of chondrules. Unmelted phases underwent FeO reduction and partial homogenization, with reduction possibly occurring by reaction of olivine and low‐Ca pyroxene with an S‐bearing gas that was produced by vaporization. Chondrules and metal grains became foliated by uniaxial compaction, and during compression, chondrules and fragments became attached to form larger clumps. This process, and possibly also melt incorporation into chondrules to cause “inflation,” may have contributed to anomalously large chondrule sizes in NWA 8709. The melt breccia character is attributed to strong shock affecting a porous precursor. Data‐model comparisons suggest that a precursor with 23% porosity that was impacted by a 3 km/s projectile could have produced the meteorite. The rarity of other type 3 ordinary chondrite melt breccias implies that the immediate precursors to such chondrites were lower in porosity than the NWA 8709 precursor, or experienced weaker shocks. Altogether, the data imply a predominantly “quiet” dynamical environment to form most type 3 ordinary chondrites, with compaction occurring in a series of relatively weak shock events

The Gene Ontology knowledgebase in 2023

The Gene Ontology (GO) knowledgebase (http://geneontology.org) is a comprehensive resource concerning the functions of genes and gene products (proteins and noncoding RNAs). GO annotations cover genes from organisms across the tree of life as well as viruses, though most gene function knowledge currently derives from experiments carried out in a relatively small number of model organisms. Here, we provide an updated overview of the GO knowledgebase, as well as the efforts of the broad, international consortium of scientists that develops, maintains, and updates the GO knowledgebase. The GO knowledgebase consists of three components: (1) the GO-a computational knowledge structure describing the functional characteristics of genes; (2) GO annotations-evidence-supported statements asserting that a specific gene product has a particular functional characteristic; and (3) GO Causal Activity Models (GO-CAMs)-mechanistic models of molecular "pathways" (GO biological processes) created by linking multiple GO annotations using defined relations. Each of these components is continually expanded, revised, and updated in response to newly published discoveries and receives extensive QA checks, reviews, and user feedback. For each of these components, we provide a description of the current contents, recent developments to keep the knowledgebase up to date with new discoveries, and guidance on how users can best make use of the data that we provide. We conclude with future directions for the project

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data

Fully discrete, quasi non-conforming approximation of evolution equations

In this paper we consider a fully discrete approximation of an abstract evolution equa- tion, by means of a quasi non-conforming space approximation and finite differences in time (Rothe- Galerkin method). The main result is the convergence of the discrete solutions to weak solutions of the continuous problem. Hence, the result can be interpreted either as a justification of the numerical method or as an alternative way of constructing weak solutions. We set the problem in the very general and abstract setting of pseudo-monotone operators, which allows for a unified treatment of several evolution problems. Nevertheless, the paradigmatic example –which fits into our setting and which originated our research– is represented by the p- Navier-Stokes equations, since the quasi non-conforming approximation allows to handle problems with prescribed divergence. Our abstract results for pseudo-monotone operators allow to show convergence just by verifying a few natural assumptions on the monotone operator (and its compact perturbation) time-by-time and on the discretization spaces. Hence, applications and extensions to several other evolution problems can be easily performed. The results of some numerical experiments are reported in the final section

On the existence of weak solutions for a family of unsteady rotational Smagorinsky models

In this paper we show that the rotational Smagorinsky model for turbulent flows, can be put, for a wide range of parameters in the setting of Bochner pseudo-monotone evolution equations. This allows to prove existence of weak solutions a) identifying a proper functional setting in weighted spaces and b) checking some easily verifiable assumptions, at fixed time. We also will discuss the critical role of the exponents present in the model (power of the distance function and power of the curl) for what concerns the application of the theory of pseudo-monotone operators