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

Response to erlotinib in a patient with lung adenocarcinoma harbouring the EML4-ALK translocation: A case report.

Lung cancer is the leading cause of cancer-associated mortality worldwide, and the mainstay of treatment remains to be personalised therapy. Tyrosine kinase inhibitors of the epidermal growth factor receptor (EGFR-TKIs) have been reported to exert a significant impact in the treatment of non-small cell lung cancer (NSCLC), particularly in patients harbouring mutations in the EGFR gene. The echinoderm microtubule-associated protein-like 4-anaplastic lymphoma kinase (EML4-ALK) gene translocation has been described in a subset of patients with NSCLC and possesses potent oncogenic activity. This translocation represents one of the most novel molecular targets in the treatment of NSCLC. Patients who harbour the EML4-ALK rearrangement possess lung tumours that lack EGFR or K-ras mutations. The present study reports the case of a patient possessing the EML4-ALK rearrangement that was initially treated with erlotinib and achieved a lasting clinical response. To the best of our knowledge, the current study is the first report of a clinical response to EGFR-TKI in a patient with lung adenocarcinoma harbouring the EML4-ALK fusion gene, but no EGFR mutations. However, as the disease progressed, the ALK gene status of the tumour was investigated, and based upon a positive result, the patient was treated with crizotinib and achieved a complete response. In conclusion, the present study suggests that the EML4-ALK rearrangement is not always associated with resistance to EGFR-TKIs. Further studies are required to clarify the biological features of these tumours and to investigate the mechanisms underlying the primary resistance to EGFR-TKIs when the EML4-ALK rearrangement is present

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

Discrete structures in continuum descriptions of defective crystals

I discuss various mathematical constructions that combine together to provide a natural setting for discrete and continuum geometric models of defective crystals. In particular I provide a quite general list of `plastic strain variables', which quantifies inelastic behaviour, and exhibit rigorous connections between discrete and continuous mathematical structures associated with crystalline materials that have a correspond-ingly general constitutive specification

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

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

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

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

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