Fourier analysis of 2-point Hermite interpolatory subdivision schemes

Two subdivision schemes with Hermite data on Z are studied. These schemes use 2 or 7 parameters respectively depending on whether Hermite data involve only first derivatives or include second derivatives. For a large region in the parameters space, the schemes are C1 or C2 convergent or at least are convergent on the space of Schwartz distributions. The Fourier transform of any interpolating function can be computed through products of matrices of order 2 or 3. The Fourier transform is related to a specific system of functional equations whose analytic solution is unique except for a multiplicative constant. The main arguments for these results come from Paley-Wiener-Schwartz theorem on the characterization of the Fourier transforms of distributions with compact support and a theorem of Artzrouni about convergent products of matrices

The FEBEX benchmark test: case definition and comparison of modelling approaches

The FEBEX (Full-scale Engineered Barriers Experiment in Crystalline Host Rock) ‘‘in situ’’ test was installed at the Grimsel Test Site underground laboratory (Switzerland) and is a near-to-real scale simulation of the Spanish reference concept of deep geological storage in crystalline host rock. A modelling exercise, aimed at predicting field behaviour, was divided in three parts. In Part A, predictions for both the total water inflow to the tunnel as well as the water pressure changes induced by the boring of the tunnel were required. In Part B, predictions for local field variables, such as temperature, relative humidity, stresses and displacements at selected points in the bentonite barrier, and global variables, such as the total input power to the heaters were required. In Part C, predictions for temperature, stresses, water pressures and displacements in selected points of the host rock were required. Ten Modelling Teams from Europe, North America and Japan were involved in the analysis of the test. Differences among approaches may be found in the constitutive models used, in the simplifications made to the balance equations and in the geometric symmetries considered. Several aspects are addressed in the paper: the basic THM physical phenomena which dominate the test response are discussed, a comparison of different modelling results with actual measurements is presented and a discussion is given to explain the performance of the various predictions.Peer Reviewe

Sarilumab in patients admitted to hospital with severe or critical COVID-19: a randomised, double-blind, placebo-controlled, phase 3 trial

Background: Elevated proinflammatory cytokines are associated with greater COVID-19 severity. We aimed to assess safety and efficacy of sarilumab, an interleukin-6 receptor inhibitor, in patients with severe (requiring supplemental oxygen by nasal cannula or face mask) or critical (requiring greater supplemental oxygen, mechanical ventilation, or extracorporeal support) COVID-19. Methods: We did a 60-day, randomised, double-blind, placebo-controlled, multinational phase 3 trial at 45 hospitals in Argentina, Brazil, Canada, Chile, France, Germany, Israel, Italy, Japan, Russia, and Spain. We included adults (≥18 years) admitted to hospital with laboratory-confirmed SARS-CoV-2 infection and pneumonia, who required oxygen supplementation or intensive care. Patients were randomly assigned (2:2:1 with permuted blocks of five) to receive intravenous sarilumab 400 mg, sarilumab 200 mg, or placebo. Patients, care providers, outcome assessors, and investigators remained masked to assigned intervention throughout the course of the study. The primary endpoint was time to clinical improvement of two or more points (seven point scale ranging from 1 [death] to 7 [discharged from hospital]) in the modified intention-to-treat population. The key secondary endpoint was proportion of patients alive at day 29. Safety outcomes included adverse events and laboratory assessments. This study is registered with ClinicalTrials.gov, NCT04327388; EudraCT, 2020-001162-12; and WHO, U1111-1249-6021. Findings: Between March 28 and July 3, 2020, of 431 patients who were screened, 420 patients were randomly assigned and 416 received placebo (n=84 [20%]), sarilumab 200 mg (n=159 [38%]), or sarilumab 400 mg (n=173 [42%]). At day 29, no significant differences were seen in median time to an improvement of two or more points between placebo (12·0 days [95% CI 9·0 to 15·0]) and sarilumab 200 mg (10·0 days [9·0 to 12·0]; hazard ratio [HR] 1·03 [95% CI 0·75 to 1·40]; log-rank p=0·96) or sarilumab 400 mg (10·0 days [9·0 to 13·0]; HR 1·14 [95% CI 0·84 to 1·54]; log-rank p=0·34), or in proportions of patients alive (77 [92%] of 84 patients in the placebo group; 143 [90%] of 159 patients in the sarilumab 200 mg group; difference −1·7 [−9·3 to 5·8]; p=0·63 vs placebo; and 159 [92%] of 173 patients in the sarilumab 400 mg group; difference 0·2 [−6·9 to 7·4]; p=0·85 vs placebo). At day 29, there were numerical, non-significant survival differences between sarilumab 400 mg (88%) and placebo (79%; difference +8·9% [95% CI −7·7 to 25·5]; p=0·25) for patients who had critical disease. No unexpected safety signals were seen. The rates of treatment-emergent adverse events were 65% (55 of 84) in the placebo group, 65% (103 of 159) in the sarilumab 200 mg group, and 70% (121 of 173) in the sarilumab 400 mg group, and of those leading to death 11% (nine of 84) were in the placebo group, 11% (17 of 159) were in the sarilumab 200 mg group, and 10% (18 of 173) were in the sarilumab 400 mg group. Interpretation: This trial did not show efficacy of sarilumab in patients admitted to hospital with COVID-19 and receiving supplemental oxygen. Adequately powered trials of targeted immunomodulatory therapies assessing survival as a primary endpoint are suggested in patients with critical COVID-19. Funding: Sanofi and Regeneron Pharmaceuticals

Mechanical effects induced by shock waves generated by high energy laser pulses

Specimens made of low alloy and non alloyed medium carbon steels were subjected to high energy laser pulses. Direct ablation and confined plasma procedures were both investigated. An optimum impulse momentum transfer to the material is attained with a pulse duration of 30 ns and a power density of 10 GW .cm$^2$. Fatigue testing shows that the fatigue strengths of the selected materials are significantly increased. This can be related to the fact that laser shock processing generates an appropriate residual compressive stress field in a sufficiently thick layer and does not alter the initial surface roughness. In addition, the use of cumulative laser impacts and of dual treatment combining thermal and mechanical effects of the laser beam have been investigated and shown to result in an enhanced fatigue strength.Des échantillons d'acier éventuellement faiblement allié sont irradiés par un ou plusieurs pulses laser ayant une intensité comprise entre 1 et 100 GW/cm$^2$ et une durée d'émission laser de 3 ou 30 ns, les deux configurations d'ablation directe ou de plasma confiné étant utilisées. Les contraintes résiduelles résultant du passage de l'onde de choc sont analysées à l'aide de la technique de diffraction de rayons X. D'après cette étude, il apparaît clairement que les valeurs d'intensité et de durée d'émission laser les plus appropriées sont respectivement 10 GW/cm$^2$ et 30 ns. Ces valeurs correspondent à l'optimum de transfert d'impulsion. De plus, l'influence du nombre d'impacts laser utilisés est discuté et un essai de fatigue montre que ce traitement mécanique de surface augmente de manière significative la limite d'endurance du matériau étudié

Non-uniform interpolatory curve subdivision with edge parameters built upon compactly supported fundamental splines

In this paper we present a family of Non-Uniform Local Interpolatory (NULI) subdivision schemes, derived from compactly supported cardinal splines with non-uniform knots (NULICS). For this spline family, the knot partition is defined by a sequence of break points and by one additional knot, arbitrarily placed along each knot-interval. The resulting refinement algorithms are linear and turn out to contain a set of edge parameters that, when fixed to a value in the range [0,1], allow us to move each auxiliary knot to any position between the break points to simulate the behavior of the NULICS interpolants. Among all the members of this new family of schemes, we will then especially analyze the NULI 4-point refinement. This subdivision scheme has all the fundamental features of the quadratic cardinal spline basis it is originated from, namely compact support, C 1 smoothness, second order polynomials reproduction and approximation order 3. In addition the NULI 4-point subdivision algorithm has the possibility of setting consecutive edge parameters to simulate triple knots - that are not achievable when using the corresponding spline basis - thus allowing for limit curves with crease vertices, without using an ad hoc mask. Numerical examples and comparisons with other methods will be given to the aim of illustrating the performance of the NULI 4-point scheme in the case of highly non-uniform initial data