The band spectrum of the periodic airy-schrodinger operator on the real line

We introduce the periodic Airy-Schr\"odinger operator and we study its band spectrum. This is an example of an explicitly solvable model with a periodic potential which is not differentiable at its minima and maxima. We define a semiclassical regime in which the results are stated for a fixed value of the semiclassical parameter and are thus estimates instead of asymptotic results. We prove that there exists a sequence of explicit constants, which are zeroes of classical functions, giving upper bounds of the semiclassical parameter for which the spectral bands are in the semiclassical regime. We completely determine the behaviour of the edges of the first spectral band with respect to the semiclassical parameter. Then, we investigate the spectral bands and gaps situated in the range of the potential. We prove precise estimates on the widths of these spectral bands and these spectral gaps and we determine an upper bound on the integrated spectral density in this range. Finally, in the semiclassical regime, we get estimates of the edges of every spectral bands and thus of the widths of every spectral bands and spectral gaps

SAFT-γ force field for the simulation of molecular fluids: 4. A single-site coarse-grained model of water applicable over a wide temperature range

In this work, we develop coarse-grained (CG) force fields for water, where the effective CG intermolecular interactions between particles are estimated from an accurate description of the macroscopic experimental vapour-liquid equilibria data by means of a molecular-based equation of state. The statistical associating fluid theory for Mie (generalised Lennard-Jones) potentials of variable range (SAFT-VR Mie) is used to parameterise spherically symmetrical (isotropic) force fields for water. The resulting SAFT-γ CG models are based on the Mie (8-6) form with size and energy parameters that are temperature dependent; the latter dependence is a consequence of the angle averaging of the directional polar interactions present in water. At the simplest level of CG where a water molecule is represented as a single bead, it is well known that an isotropic potential cannot be used to accurately reproduce all of the thermodynamic properties of water simultaneously. In order to address this deficiency, we propose two CG potential models of water based on a faithful description of different target properties over a wide range of temperatures: our CGW1-vle model is parameterised to match the saturated-liquid density and vapour pressure; our other CGW1-ift model is parameterised to match the saturated-liquid density and vapour-liquid interfacial tension. A higher level of CG corresponding to two water molecules per CG bead is also considered: the corresponding CGW2-bio model is developed to reproduce the saturated-liquid density and vapour-liquid interfacial tension in the physiological temperature range, and is particularly suitable for the large-scale simulation of bio-molecular systems. A critical comparison of the phase equilibrium and transport properties of the proposed force fields is made with the more traditional atomistic models

A geometric optics method for high-frequency electromagnetic fields computations near fold caustics—Part II. The energy

AbstractWe present the computation of the amplitudes needed to evaluate the energy deposited by the laser wave in a plasma when a fold caustic forms. We first recall the Eulerian method designed in Benamou et al. (J. Comput. Appl. Math. 156 (2003) 93) to compute the caustic location and the phases associated to the two ray branches on its illuminated side. We then turn to the computation of the amplitudes needed to evaluate the energy. We use the classical geometrical form of the amplitudes to avoid the blow up problem at the caustic. As our proposed method is Eulerian we have to consider transport equations for these geometrical quantities where the advection field depends on the ray flow. The associated vector field structurally vanishes like the square root of the distance to the caustic when approaching the caustic. This introduces an additional difficulty as traditional finite difference scheme do not retain their accuracy for such advection fields. We propose a new scheme which remains of order 1 at the caustic and present a partial theoretical analysis as well as a numerical validation. We also test the capability of our Eulerian geometrical algorithm to produce numerical solution of the Helmholtz equation and attempt to check their frequency asymptotic accuracy

Direction of light propagation to order G^2 in static, spherically symmetric spacetimes: a new derivation

A procedure avoiding any integration of the null geodesic equations is used to derive the direction of light propagation in a three-parameter family of static, spherically symmetric spacetimes within the post-post-Minkowskian approximation. Quasi-Cartesian isotropic coordinates adapted to the symmetries of spacetime are systematically used. It is found that the expression of the angle formed by two light rays as measured by a static observer staying at a given point is remarkably simple in these coordinates. The attention is mainly focused on the null geodesic paths that we call the "quasi-Minkowskian light rays". The vector-like functions characterizing the direction of propagation of such light rays at their points of emission and reception are firstly obtained in the generic case where these points are both located at a finite distance from the centre of symmetry. The direction of propagation of the quasi-Minkowskian light rays emitted at infinity is then straightforwardly deduced. An intrinsic definition of the gravitational deflection angle relative to a static observer located at a finite distance is proposed for these rays. The expression inferred from this definition extends the formula currently used in VLBI astrometry up to the second order in the gravitational constant G.Comment: 19 pages; revised introduction; added references for introduction; corrected typos; published in Class. Quantum Gra

Radioscience simulations in General Relativity and in alternative theories of gravity

In this communication, we focus on the possibility to test GR with radioscience experiments. We present a new software that in a first step simulates the Range/Doppler signals directly from the space time metric (thus in GR and in alternative theories of gravity). In a second step, a least-squares fit of the involved parameters is performed in GR. This software allows one to get the order of magnitude and the signature of the modifications induced by an alternative theory of gravity on radioscience signals. As examples, we present some simulations for the Cassini mission in Post-Einsteinian gravity and with the MOND External Field Effect.Comment: 4 pages; Proceedings of "Les Rencontres de Moriond 2011 - Gravitation session

Open-Angle Glaucoma and Paraoptic Cyst: First Description of a Series of 11 Patients

International audienceWe report 11 patients who were referred to our institution for severe open-angle glaucoma who had a paraoptic cyst on MR imaging. All cysts were extraoptic and retrolaminar; most were deforming the adjacent optic nerve. Cysts had a high signal on T2 and FLAIR sequences, and a variable signal on T1 and variable echogenicity, suggesting different proteinaceous content. Arterial vascularization of the optic nerve was normal. Cyst volumes were inversely correlated with the severity of glaucoma on the same eye (P .01–.05, Spearman correlation coefficient). We hypothesized that such cysts may reflect a valve mechanism, which would allow preservation of the trans-lamina cribrosa pressure and thus could preserve visual function. The rarity of this association, together with the frequent mass effect of the cyst on the optic nerve, stresses the necessity of long-term follow-up in these patients

Open-Angle Glaucoma and Paraoptic Cyst: First Description of a Series of 11 Patients

International audienceWe report 11 patients who were referred to our institution for severe open-angle glaucoma who had a paraoptic cyst on MR imaging. All cysts were extraoptic and retrolaminar; most were deforming the adjacent optic nerve. Cysts had a high signal on T2 and FLAIR sequences, and a variable signal on T1 and variable echogenicity, suggesting different proteinaceous content. Arterial vascularization of the optic nerve was normal. Cyst volumes were inversely correlated with the severity of glaucoma on the same eye (P < .01-.05, Spearman correlation coefficient). We hypothesized that such cysts may reflect a valve mechanism, which would allow preservation of the translamina cribrosa pressure and thus could preserve visual function. The rarity of this association, together with the frequent mass effect of the cyst on the optic nerve, stresses the necessity of long-term follow-up in these patients

Genetic analysis of adaptation differences between highland and lowland tropical maize using molecular markers

Molecular-marker loci were used to investigate the adaptation differences between highland and lowland tropical maize. An F2 population from the cross of two inbred lines independently derived from highland and lowland maize germplasm was developed, and extracted F3:4 lines were phenotype in replicated field trials at four thermally diverse tropical testing sites, ranging from lowland to extreme highland (mean growing season temperature range 13.2–24.6°C). Traits closely related with adaptation, such as biomass and grain yield, yield components, days from sowing to male and female flowering, total leaf number, plant height and number of primary tassel branches (TBN), were analyzed. A large line ´ environment interaction was observed for most traits. The genetic basis of this interaction was reflected by significant, but systematic, changes from lowland to highland sites in the correlation between the trait value and genomic composition (designated by the proportion of marker alleles with the same origin). Joint analysis of quantitative trait loci (QTLs) over sites detected 5–8 QTLs for each trait (except disease scores, with data only from one site). With the exception of one QTL for TBN, none of these accounted for more than 15% of the total phenotypic variation. In total, detected QTLs accounted for 24–61% of the variation at each site on average. For yield, yield components and disease scores, alleles generally favored the site of origin. Highland-derived alleles had little effect at lowland sites, while lowland- derived alleles showed relatively broader adaptation. Gradual changes in the estimated QTL effects with increasing mean site temperature were observed, and paralleled the observed patterns of adaptation in high land and lowland germplasm. Several clusters of QTLs for different traits reflected the relative importance in the adaptation differences between the two germplasm types, and pleiotropy is suggested as the main cause for the clustering. Breeding for broad thermal adaptation should be possible by pooling genes showing adaptation to specific thermal regimes, though perhaps at the expense of reduced progress for adaptation to a specific site. Molecular marker-assisted selection would be an ideal tool for this task, since it could greatly reduce the linkage drag caused by the unintentional transfer of undesirable trait

A three-arm phase III randomised trial assessing, in patients with extensive-disease small-cell lung cancer, accelerated chemotherapy with support of haematological growth factor or oral antibiotics

The European Lung Cancer Working Party (ELCWP) designed a 3-arm phase III randomised trial to determine the role of accelerated chemotherapy in extensive-disease (ED) small-cell lung cancer (SCLC). Eligible patients were randomised between the 3 following arms: (A) Standard chemotherapy with 6 courses of EVI (epirubicin 60 mg m−2, vindesine 3 mg m−2, ifosfamide 5 g m−2; all drugs given on day 1 repeated every three weeks. (B) Accelerated chemotherapy with EVI administered every 2 weeks and GM-CSF support. (C) Accelerated chemotherapy with EVI and oral antibiotics (cotrimoxazole). Primary endpoint was survival. 233 eligible patients were randomised. Chemotherapy could be significantly accelerated in arm B with increased absolute dose-intensity. Best response rates, in the population of evaluable patients, were, respectively for arm A, B and C, 59%, 76% and 70%. The response rate was significantly higher in arm B in comparison to arm A (P = 0.04). There was, however, no survival difference with respective median duration and 2-year rate of 286 days and 5% for arm A, 264 days and 6% for arm B and 264 days and 6% for arm C. Severe thrombopenia occurred more frequently in arm B but without an increased rate of bleeding. Non-severe infections were more frequent in arm B and severe infections were less frequent in arm C. Our trial failed to demonstrate, in ED-SCLC, a survival benefit of chemotherapy acceleration by using GM-CSF support.   http://www.bjcancer.co

Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers

General relativistic deflection of light by mass, dipole, and quadrupole moments of gravitational field of a moving massive planet in the Solar system is derived. All terms of order 1 microarcsecond are taken into account, parametrized, and classified in accordance with their physical origin. We calculate the instantaneous patterns of the light-ray deflections caused by the monopole, the dipole and the quadrupole moments, and derive equations describing apparent motion of the deflected position of the star in the sky plane as the impact parameter of the light ray with respect to the planet changes due to its orbital motion. The present paper gives the physical interpretation of the observed light-ray deflections and discusses the observational capabilities of the near-future optical (SIM) and radio (SKA) interferometers for detecting the Doppler modulation of the radial deflection, and the dipolar and quadrupolar light-ray bendings by the Jupiter and the Saturn.Comment: 33 pages, 10 figures, accepted to Phys. Rev.