Elastic symmetries of defective crystals

I construct discrete and continuous crystal structures that are compatible with a given choice of dislocation density tensor, and (following Mal’cev) provide a canonical form for these discrete structures. The symmetries of the discrete structures extend uniquely to symmetries of corresponding continuous structures—I calculate these symmetries explicitly for a particular choice of dislocation density tensor and deduce corresponding constraints on energy functions which model defective crystals

Group elastic symmetries common to continuum and discrete defective crystals

The Lie group structure of crystals which have uniform continuous distributions of dislocations allows one to construct associated discrete structures—these are discrete subgroups of the corresponding Lie group, just as the perfect lattices of crystallography are discrete subgroups of R 3 , with addition as group operation. We consider whether or not the symmetries of these discrete subgroups extend to symmetries of (particular) ambient Lie groups. It turns out that those symmetries which correspond to automorphisms of the discrete structures do extend to (continuous) symmetries of the ambient Lie group (just as the symmetries of a perfect lattice may be embedded in ‘homogeneous elastic’ deformations). Other types of symmetry must be regarded as ‘inelastic’. We show, following Kamber and Tondeur, that the corresponding continuous automorphisms preserve the Cartan torsion, and we characterize the discrete automorphisms by a commutativity condition, (6.14), that relates (via the matrix exponential) to the dislocation density tensor. This shows that periodicity properties of corresponding energy densities are determined by the dislocation density

Geometrical structure of two-dimensional crystals with non-constant dislocation density

We outline mathematical methods which seem to be necessary in order to discuss crystal structures with non-constant dislocation density tensor(ddt) in some generality. It is known that, if the ddt is constant (in space), then material points can be identified with elements of a certain Lie group, with group operation determined in terms of the ddt - the dimension of the Lie group equals that of the ambient space in which the body resides, in that case. When the ddt is non-constant, there is also a relevant Lie group (given technical assumptions), but the dimension of the group is strictly greater than that of the ambient space. The group acts on the set of material points, and there is a non-trivial isotropy group associated with the group action. We introduce and discuss the requisite mathematical apparatus in the context of Davini's model of defective crystals, and focus on a particular case where the ddt is such that a three dimensional Lie group acts on a two dimensional crystal state - this allows us to construct corresponding discrete structures too

Rotational symmetries of crystals with defects

I use the theory of Lie groups/algebras to discuss the symmetries of crystals with uniform distributions of defects

Solar neutrino detection in a large volume double-phase liquid argon experiment

Precision measurements of solar neutrinos emitted by specific nuclear reaction chains in the Sun are of great interest for developing an improved understanding of star formation and evolution. Given the expected neutrino fluxes and known detection reactions, such measurements require detectors capable of collecting neutrino-electron scattering data in exposures on the order of 1 ktonne yr, with good energy resolution and extremely low background. Two-phase liquid argon time projection chambers (LAr TPCs) are under development for direct Dark Matter WIMP searches, which possess very large sensitive mass, high scintillation light yield, good energy resolution, and good spatial resolution in all three cartesian directions. While enabling Dark Matter searches with sensitivity extending to the "neutrino floor" (given by the rate of nuclear recoil events from solar neutrino coherent scattering), such detectors could also enable precision measurements of solar neutrino fluxes using the neutrino-electron elastic scattering events. Modeling results are presented for the cosmogenic and radiogenic backgrounds affecting solar neutrino detection in a 300 tonne (100 tonne fiducial) LAr TPC operating at LNGS depth (3,800 meters of water equivalent). The results show that such a detector could measure the CNO neutrino rate with ~15% precision, and significantly improve the precision of the 7Be and pep neutrino rates compared to the currently available results from the Borexino organic liquid scintillator detector.Comment: 21 pages, 7 figures, 6 table

The structure of uniform discrete defective crystals

In the continuum context, a uniform crystal has dislocation density tensor constant in space. A simple iteration procedure generates an infinite set of points which is associated with uniform defective crystals. When certain necessary conditions are satisfied, there is a minimum (non-zero) separation of points in this set, so the set is discrete. We describe the structure of such sets explicitly, and show in particular that any such set is either a simple lattice or a 4-lattice

Atmospheric response to cold wintertime Tibetan Plateau conditions over eastern Asia in climate models

Central Asian orography (namely the Tibetan and Mongolian plateaux) sets important features of the winter climate over eastern Asia and the Pacific. By deflecting the mid-latitude jet polewards it contributes to the formation of the Siberian high and, on the lee side, to the advection of dry cold continental air over the eastern Asian coast and the Pacific Ocean, where atmospheric instability and cyclogenesis thrive. While the mechanic forcing by the orography is assessed in a number of modelling studies, it is still not clear how near-surface temperature over the two most prominent orographic barriers of the central Asian continent – the Tibetan and Mongolian plateaux – influences the winter climate. The problem is particularly relevant in view of a well-known cold bias in state-of-the-art climate models in proximity to the Tibetan Plateau, likely related to the modelling of land processes and land–atmosphere interaction over complex orography. Here we take advantage of the large spread in near-surface temperature over the central Asian plateaux within the Coupled Model Intercomparison Project Phase 6 (CMIP6) to study how colder-than-average Asian plateau temperatures impact the atmospheric circulation. Based on composites of the CMIP6 models' climatologies showing the coldest Tibetan Plateau conditions, we find that such negative temperature anomalies appear to amplify the atmospheric response to orography, with an intensification of the eastern Asian winter monsoon and of the equatorward flank of the Pacific jet. The results of the CMIP6 composite analysis are supported by experiments run with an intermediate-complexity atmospheric model, forced by a similar pattern of cold surface temperatures over the central Asian plateaux. Within this setting, the relative influence of the Tibetan and the Mongolian Plateau surface conditions is analysed. Based on the results reported in this work we project that advances in the modelling of the land energy budget over the elevated regions of central Asia could improve the simulation of the climate in the Asian–Pacific sector climate, together with the reliability of climate projections and the performance of shorter-term forecasts.</p

Existence theorems in the geometrically non-linear 6-parametric theory of elastic plates

In this paper we show the existence of global minimizers for the geometrically exact, non-linear equations of elastic plates, in the framework of the general 6-parametric shell theory. A characteristic feature of this model for shells is the appearance of two independent kinematic fields: the translation vector field and the rotation tensor field (representing in total 6 independent scalar kinematic variables). For isotropic plates, we prove the existence theorem by applying the direct methods of the calculus of variations. Then, we generalize our existence result to the case of anisotropic plates. We also present a detailed comparison with a previously established Cosserat plate model.Comment: 19 pages, 1 figur

Euro-Atlantic weather regimes in the PRIMAVERA coupled climate simulations: impact of resolution and mean state biases on model performance

Recently, much attention has been devoted to better understand the internal modes of variability of the climate system. This is particularly important in mid-latitude regions like the North-Atlantic, which is characterized by a large natural variability and is intrinsically difficult to predict. A suitable framework for studying the modes of variability of the atmospheric circulation is to look for recurrent patterns, commonly referred to as Weather Regimes. Each regime is characterized by a specific large-scale atmospheric circulation pattern, thus influencing regional weather and extremes over Europe. The focus of the present paper is the study of the Euro-Atlantic wintertime Weather Regimes in the climate models participating to the PRIMAVERA project. We analyse here the set of coupled historical simulations (hist-1950), which have been performed both at standard and increased resolution, following the HighresMIP protocol. The models’ performance in reproducing the observed Weather Regimes is assessed in terms of different metrics, focussing on systematic biases and on the impact of resolution. We also analyse the connection of the Weather Regimes with the Jet Stream latitude and blocking frequency over the North-Atlantic sector. We find that—for most models—the regime patterns are better represented in the higher resolution version, for all regimes but the NAO-. On the other side, no clear impact of resolution is seen on the regime frequency of occurrence and persistence. Also, for most models, the regimes tend to be more tightly clustered in the increased resolution simulations, more closely resembling the observed ones. However, the horizontal resolution is not the only factor determining the model performance, and we find some evidence that biases in the SSTs and mean geopotential field might also play a role

Coupled climate response to Atlantic Multidecadal Variability in a multi-model multi-resolution ensemble

North Atlantic sea surface temperatures (SSTs) underwent pronounced multidecadal variability during the twentieth and early twenty-first century. We examine the impacts of this Atlantic Multidecadal Variability (AMV), also referred to as the Atlantic Multidecadal Oscillation (AMO), on climate in an ensemble of five coupled climate models at both low and high spatial resolution. We use a SST nudging scheme specified by the Coupled Model Intercomparision Project’s Decadal Climate Prediction Project Component C (CMIP6 DCPP-C) to impose a persistent positive/negative phase of the AMV in the North Atlantic in coupled model simulations; SSTs are free to evolve outside this region. The large-scale seasonal mean response to the positive AMV involves widespread warming over Eurasia and the Americas, with a pattern of cooling over the Pacific Ocean similar to the Pacific Decadal Oscillation (PDO), together with a northward displacement of the inter-tropical convergence zone (ITCZ). The accompanying changes in global atmospheric circulation lead to widespread changes in precipitation. We use Analysis of Variance (ANOVA) to demonstrate that this large-scale climate response is accompanied by significant differences between models in how they respond to the common AMV forcing, particularly in the tropics. These differences may arise from variations in North Atlantic air-sea heat fluxes between models despite a common North Atlantic SST forcing pattern. We cannot detect a widespread effect of increased model horizontal resolution in this climate response, with the exception of the ITCZ, which shifts further northwards in the positive phase of the AMV in the higher resolution configuratio