A variational problem on Stiefel manifolds

In their paper on discrete analogues of some classical systems such as the rigid body and the geodesic flow on an ellipsoid, Moser and Veselov introduced their analysis in the general context of flows on Stiefel manifolds. We consider here a general class of continuous time, quadratic cost, optimal control problems on Stiefel manifolds, which in the extreme dimensions again yield these classical physical geodesic flows. We have already shown that this optimal control setting gives a new symmetric representation of the rigid body flow and in this paper we extend this representation to the geodesic flow on the ellipsoid and the more general Stiefel manifold case. The metric we choose on the Stiefel manifolds is the same as that used in the symmetric representation of the rigid body flow and that used by Moser and Veselov. In the extreme cases of the ellipsoid and the rigid body, the geodesic flows are known to be integrable. We obtain the extremal flows using both variational and optimal control approaches and elucidate the structure of the flows on general Stiefel manifolds.Comment: 30 page

Low temperature magneto-morphological characterisation of coronene and the resolution of previously observed unexplained phenomena

The polyaromatic hydrocarbon coronene has been the molecule of choice for understanding the physical properties of graphene for over a decade. The modelling of the latter by the former was considered to be valid, as since it was first synthesised in 1932, the physical behaviour of coronene has been determined extremely accurately. We recently discovered however, an unforeseen polymorph of coronene, which exists as an enantiotrope with the previously observed crystal structure. Using low-temperature magnetisation and crystallographic measurements, we show here for the first time that the electronic and magnetic properties of coronene depend directly on the temperature at which it is observed, with hysteretic behaviour exhibited between 300 K and 100 K. Furthermore we determine that this behaviour is a direct result of the appearance and disappearance of the newly-discovered polymorph during thermal cycling. Our results not only highlight the need for theoretical models of graphene to take into account this anomalous behaviour at low temperatures, but also explain puzzling experimental observations of coronene dating back over 40 years

The impact of ENSO on Southern African rainfall in CMIP5 ocean atmosphere coupled climate models

We study the ability of 24 ocean atmosphere global coupled models from the Coupled Model Intercomparison Project 5 (CMIP5) to reproduce the teleconnections between El Niño Southern Oscillation (ENSO) and Southern African rainfall in austral summer using historical forced simulations, with a focus on the atmospheric dynamic associated with El Niño. Overestimations of summer rainfall occur over Southern Africa in all CMIP5 models. Abnormal westward extensions of ENSO patterns are a common feature of all CMIP5 models, while the warming of the Indian Ocean that happens during El Niño is not correctly reproduced. This could impact the teleconnection between ENSO and Southern African rainfall which is represented with mixed success in CMIP5 models. Large-scale anomalies of suppressed deep-convection over the tropical maritime continent and enhanced convection from the central to eastern Pacific are correctly simulated. However, regional biases occur above Africa and the Indian Ocean, particularly in the position of the deep convection anomalies associated with El Niño, which can lead to the wrong sign in rainfall anomalies in the northwest part of South Africa. From the near-surface to mid-troposphere, CMIP5 models underestimate the observed anomalous pattern of pressure occurring over Southern Africa that leads to dry conditions during El Niño years

SARS-CoV-2 infects the human kidney and drives fibrosis in kidney organoids

Kidney failure is frequently observed during and after COVID-19, but it remains elusive whether this is a direct effect of the virus. Here, we report that SARS-CoV-2 directly infects kidney cells and is associated with increased tubule-interstitial kidney fibrosis in patient autopsy samples. To study direct effects of the virus on the kidney independent of systemic effects of COVID-19, we infected human-induced pluripotent stem-cell-derived kidney organoids with SARS-CoV-2. Single-cell RNA sequencing indicated injury and dedifferentiation of infected cells with activation of profibrotic signaling pathways. Importantly, SARS-CoV-2 infection also led to increased collagen 1 protein expression in organoids. A SARS-CoV-2 protease inhibitor was able to ameliorate the infection of kidney cells by SARS-CoV-2. Our results suggest that SARS-CoV-2 can directly infect kidney cells and induce cell injury with subsequent fibrosis. These data could explain both acute kidney injury in COVID-19 patients and the development of chronic kidney disease in long COVID