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In this brief note we explore the space of genus one and elliptic fibrations within CY manifolds, their organizing principles, and how they relate to the set of all CY manifolds. We provide examples of genus one fibered manifolds that exhibit different Hodge numbers -- and physically lead to different gauge groups - than their Jacobian fibrations. We suggest a physical mechanism for understanding this difference in twisted circle reductions of 6-dimensional compactifications of F-theory. 

Granular flows occur in a wide range of situations of practical interest to industry, in our natural environment and in our everyday lives. This paper focuses on granular flow in the so-called inertial regime, when the rheology is independent of the very large particle stiffness. Such flows have been modelled with the $\unicode[STIX]{x1D707}(I),\unicode[STIX]{x1D6F7}(I)$ -rheology, which postulates that the bulk friction coefficient $\unicode[STIX]{x1D707}$ (i.e. the ratio of the shear stress to the pressure) and the solids volume fraction $\unicode[STIX]{x1D719}$ are functions of the inertial number $I$ only. Although the $\unicode[STIX]{x1D707}(I),\unicode[STIX]{x1D6F7}(I)$ -rheology has been validated in steady state against both experiments and discrete particle simulations in several different geometries, it has recently been shown that this theory is mathematically ill-posed in time-dependent problems. As a direct result, computations using this rheology may blow up exponentially, with a growth rate that tends to infinity as the discretization length tends to zero, as explicitly demonstrated in this paper for the first time. Such catastrophic instability due to ill-posedness is a common issue when developing new mathematical models and implies that either some important physics is missing or the model has not been properly formulated. In this paper an alternative to the $\unicode[STIX]{x1D707}(I),\unicode[STIX]{x1D6F7}(I)$ -rheology that does not suffer from such defects is proposed. In the framework of compressible $I$ -dependent rheology (CIDR), new constitutive laws for the inertial regime are introduced; these match the well-established $\unicode[STIX]{x1D707}(I)$ and $\unicode[STIX]{x1D6F7}(I)$ relations in the steady-state limit and at the same time are well-posed for all deformations and all packing densities. Time-dependent numerical solutions of the resultant equations are performed to demonstrate that the new inertial CIDR model leads to numerical convergence towards physically realistic solutions that are supported by discrete element method simulations. 

Abstract The global network of gravitational-wave observatories now includes five detectors, namely LIGO Hanford, LIGO Livingston, Virgo, KAGRA, and GEO 600. These detectors collected data during their third observing run, O3, composed of three phases: O3a starting in 2019 April and lasting six months, O3b starting in 2019 November and lasting five months, and O3GK starting in 2020 April and lasting two weeks. In this paper we describe these data and various other science products that can be freely accessed through the Gravitational Wave Open Science Center at https://gwosc.org . The main data set, consisting of the gravitational-wave strain time series that contains the astrophysical signals, is released together with supporting data useful for their analysis and documentation, tutorials, as well as analysis software packages. 

An expanded sedimentary section provides an opportunity to elucidate conditions in the nascent Chicxulub crater during the hours to millennia after the Cretaceous‐Paleogene (K‐Pg) boundary impact. The sediments were deposited by tsunami followed by seiche waves as energy in the crater declined, culminating in a thin hemipelagic marlstone unit that contains atmospheric fallout. Seiche deposits are predominantly composed of calcite formed by decarbonation of the target limestone during impact followed by carbonation in the water column. Temperatures recorded by clumped isotopes of these carbonates are in excess of 70°C, with heat likely derived from the central impact melt pool. Yet, despite the turbidity and heat, waters within the nascent crater basin soon became a viable habitat for a remarkably diverse cross section of the food chain. The earliest seiche layers deposited with days or weeks of the impact contain earliest Danian nannoplankton and dinocyst survivors. The hemipelagic marlstone representing the subsequent years to a few millennia contains a nearly monogeneric calcareous dinoflagellate resting cyst assemblage suggesting deteriorating environmental conditions, with one interpretation involving low light levels in the impact aftermath. At the same horizon, microbial fossils indicate a thriving bacterial community and unique phosphatic fossils including appendages of pelagic crustaceans, coprolites and bacteria‐tunneled fish bone, suggesting that this rapid recovery of the base of the food chain may have supported the survival of larger, higher trophic‐level organisms. The extraordinarily diverse fossil assemblage indicates that the crater was a unique habitat in the immediate impact aftermath, possibly as a result of heat and nutrients supplied by hydrothermal activity.