Some finite solvable groups with non-trivial lattice endomorphisms

The main purpose of this paper is to exhibit a doubly-infinite family of examples which are extensions of a p-group by a p′-group, with the action satisfying some conditions of Zappa (1951), arising from his study of dual-standard (meet-distributive) subgroups. The examples show that Zappa's conditions do not bound the nilpotency class (or even the derived length) of the p-group. The key to this work is found in closely related conditions of Hartley (published here for the first time). The examples use some exceptional relationships between primes

Storyline description of Southern Hemisphere midlatitude circulation and precipitation response to greenhouse gas forcing

As evidence of climate change strengthens, knowledge of its regional implications becomes an urgent need for decision making. Current understanding of regional precipitation changes is substantially limited by our understanding of the atmospheric circulation response to climate change, which to a high degree remains uncertain. This uncertainty is reflected in the wide spread in atmospheric circulation changes projected in multimodel ensembles, which cannot be directly interpreted in a probabilistic sense. The uncertainty can instead be represented by studying a discrete set of physically plausible storylines of atmospheric circulation changes. By mining CMIP5 model output, here we take this broader perspective and develop storylines for Southern Hemisphere (SH) midlatitude circulation changes, conditioned on the degree of global-mean warming, based on the climate responses of two remote drivers: the enhanced warming of the tropical upper troposphere and the strengthening of the stratospheric polar vortex. For the three continental domains in the SH, we analyse the precipitation changes under each storyline. To allow comparison with previous studies, we also link both circulation and precipitation changes with those of the Southern Annular Mode. Our results show that the response to tropical warming leads to a strengthening of the midlatitude westerly winds, whilst the response to a delayed breakdown (for DJF) or strengthening (for JJA) of the stratospheric vortex leads to a poleward shift of the westerly winds and the storm tracks. However, the circulation response is not zonally symmetric and the regional precipitation storylines for South America, South Africa, South Australia and New Zealand exhibit quite specific dependencies on the two remote drivers, which are not well represented by changes in the Southern Annular Mode

Storylines of atmospheric circulation change for European regional climate impact assessment

There is increasing interest to understand the regional impacts of different global warming targets. However, several regional climate impacts depend on the atmospheric circulation, whose response to climate change remains substantially uncertain and not interpretable in a probabilistic sense in multi–model ensemble projections. To account for these uncertainties, a novel approach where regional climate change is analysed as a function of carbon emissions conditional on plausible storylines of atmospheric circulation change is here presented and applied to the CMIP5 models future projections. The different storylines are determined based on the response in three remote drivers of regional circulation: the tropical and polar amplification of global warming, and the stratospheric vortex strength. As an illustration of this approach, it is shown that the severity of the projected wintertime Mediterranean precipitation decline and Central European windiness increase strongly depends on the storyline of circulation change. For a given magnitude of global warming, the highest impact storyline for these aspects of European climate is found for a high tropical amplification and a strengthening of the vortex. The difference in the precipitation and wind responses between the storylines is substantial and equivalent to the contribution from several degrees of global warming. Improving the understanding of the remote driver responses is thus needed to better bound the projected regional impacts in the European sector. The value of these storylines to represent the uncertainty in regional climate projections and to inform the selection of CMIP5 models in regional climate impact studies is discussed

Multimodel evidence for an atmospheric circulation response to Arctic sea ice loss in the CMIP5 future projections

Previous single model experiments have found that Arctic sea–ice loss can influence the atmospheric circulation. To evaluate this process in a multi–model ensemble, a novel methodology is here presented and applied to infer the influence of Arctic sea–ice loss in the CMIP5 future projections. Sea–ice influence is estimated by comparing the circulation response in the RCP8.5 scenario against the circulation response to sea surface warming and CO2 increase inferred from the AMIPFuture and AMIP4xCO2 experiments, where sea ice is unperturbed. Multi–model evidence of the impact of sea–ice loss on mid–latitude atmospheric circulation is identified in late winter (January–March), when the sea–ice related surface heat flux perturbation is largest. Sea–ice loss acts to suppress the projected poleward shift of the North Atlantic jet, to increase surface pressure in Northern Siberia and to lower it in North America. These features are consistent with previous single–model studies and the present results indicate they are robust to model formulation

The role of Barents-Kara sea ice loss in projected polar vortex changes

The Northern Hemisphere stratospheric polar vortex (SPV) plays a key role for mid-latitude weather and climate. However, in what way the SPV will respond to global warming is not clear, with climate models disagreeing on the sign and magnitude of projected SPV strength change. Here we address the potential role of Barents and Kara (BK) sea ice loss in this. We provide evidence for a non-linear response of the SPV to global mean temperature change, coincident with the time the BK Seas become ice-free. Using a causal network approach, we demonstrate that climate models show some partial support for the previously proposed link between low BK sea ice in autumn and a weakened winter SPV, but that this effect is plausibly very small relative to internal variability. Yet, given the expected dramatic decrease of sea ice in the future, even a small causal effect can explain all of the projected ensemble-mean SPV weakening, approximately one-half of the ensemble spread at the middle of the 21st century, and one-third of the spread at the end of the century. Finally, we note that most models have unrealistic amounts of BK sea ice, meaning that their SPV response to ice loss is unrealistic. Bias-adjusting for this effect leads to pronounced differences in SPV response of individual models at both ends of the spectrum, but has no strong consequences for the overall ensemble mean and spread. Overall, our results indicate the importance of exploring all plausible implications of a changing Arctic for regional climate risk assessments

Failure analysis of thin metal foils

The mechanical response and the failure mode of thin metal foils under tensile load has been analyzed supplementing the usual test records with full-field measurements performed by three-dimensional digital image correlation (3D DIC) techniques. The experiments have been simulated by finite element models formulated within a non-linear continuum framework. The study presented in this contribution concerns symmetrically pre-cracked aluminum samples. The wrinkling of the specimens during the test and the possible and alternative failure mechanisms are evidenced and discussed

Time-evolving sea surface warming patterns modulate the climate change response of subtropical precipitation over land

Greenhouse gas (GHG) emissions affect precipitation worldwide. The response is commonly described by two timescales linked to different processes: a rapid adjustment to radiative forcing, followed by a slower response to surface warming. However, additional timescales exist in the surface warming response, tied to the time evolution of the sea surface temperature (SST) response. Here we show that in climate model projections the rapid adjustment and surface mean warming are insufficient to explain the time evolution of the hydro-climate response in three key Mediterranean-like areas, namely California, Chile and the Mediterranean. The time evolution of those responses critically depends on distinct shifts in the regional atmospheric circulation associated with the existence of distinct fast and slow SST warming patterns. As a result, Mediterranean and Chilean drying are in quasi-equilibrium with GHG concentrations, meaning that the drying will not continue after GHG concentrations are stabilised, whereas California wetting will largely emerge only after GHG concentrations are stabilised. The rapid adjustment contributes to a reduction in precipitation but has a limited impact on the balance between precipitation and evaporation. In these Mediterranean-like regions, future hydro-climate related impacts will be substantially modulated by the time evolution of the pattern of SST warming that is realised in the real world

The dependence of wintertime Mediterranean precipitation on the atmospheric circulation response to climate change

Climate models indicate a future wintertime precipitation reduction in the Mediterranean region but there is large uncertainty in the amplitude of the projected change. We analyse CMIP5 climate model output to quantify the role of atmospheric circulation in the Mediterranean precipitation change. It is found that a simple circulation index, i.e. the 850 hPa zonal wind (U850) in North Africa, well describes the year to year fluctuations in the area-averaged Mediterranean precipitation, with positive (i.e. westerly) U850 anomalies in North Africa being associated with positive precipitation anomalies. Under climate change, U850 in North Africa and the Mediterranean precipitation are both projected to decrease consistently with the relationship found in the inter-annual variability. This enables us to estimate that about 85% of the CMIP5 mean precipitation response and 80% of the variance in the inter-model spread are related to changes in the atmospheric circulation. In contrast, there is no significant correlation between the mean precipitation response and the global-mean surface warming across the models. It follows that the uncertainty in cold-season Mediterranean precipitation projection will not be narrowed unless the uncertainty in the atmospheric circulation response is reduced

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