Half-Integer Point Defects in the Q-Tensor Theory of Nematic Liquid Crystals

We investigate prototypical profiles of point defects in two dimensional liquid crystals within the framework of Landau-de Gennes theory. Using boundary conditions characteristic of defects of index $k/2$, we find a critical point of the Landau-de Gennes energy that is characterised by a system of ordinary differential equations. In the deep nematic regime, $b^2$ small, we prove that this critical point is the unique global minimiser of the Landau-de Gennes energy. We investigate in greater detail the regime of vanishing elastic constant $L \to 0$, where we obtain three explicit point defect profiles, including the global minimiser.Comment: 15 pages, 16 figure

Dimension reduction for the micromagnetic energy functional on curved thin films

Micromagnetic con gurations of the vortex and onion type have beenwidely studied in the context of planar structures. Recently a signi cant interest to micromagnetic curved thin lms has appeared. In particular, thin spherical shells are currently of great interest due to their capability to support skyrmion solutions which can be stabilized by curvature e ects only, in contrast to the planar case where the intrinsic Dzyaloshinsky-Moriya interaction is required.The aimof the paper is to performa $\Gamma$-development analysis of the micromagnetic energy functional, when the shell is generated, like in the case of a sphere, by a bounded and convex smooth surface

Dimension reduction for the micromagnetic energy functional on curved thin films

Micromagnetic con gurations of the vortex and onion type have beenwidely studied in the context of planar structures. Recently a signi cant interest to micromagnetic curved thin lms has appeared. In particular, thin spherical shells are currently of great interest due to their capability to support skyrmion solutions which can be stabilized by curvature e ects only, in contrast to the planar case where the intrinsic Dzyaloshinsky-Moriya interaction is required.The aimof the paper is to performa $\Gamma$-development analysis of the micromagnetic energy functional, when the shell is generated, like in the case of a sphere, by a bounded and convex smooth surface

A note on boundedness of operators in Grand Grand Morrey spaces

In this note we introduce grand grand Morrey spaces, in the spirit of the grand Lebesgue spaces. We prove a kind of \textit{reduction lemma} which is applicable to a variety of operators to reduce their boundedness in grand grand Morrey spaces to the corresponding boundedness in Morrey spaces. As a result of this application, we obtain the boundedness of the Hardy-Littlewood maximal operator and Calder\'on-Zygmund operators in the framework of grand grand Morrey spaces.Comment: 8 page

Landau-de Gennes Corrections to the Oseen-Frank Theory of Nematic Liquid Crystals

We study the asymptotic behavior of the minimisers of the Landau-de Gennes model for nematic liquid crystals in a two-dimensional domain in the regime of small elastic constant. At leading order in the elasticity constant, the minimum-energy configurations can be described by the simpler Oseen-Frank theory. Using a refined notion of Γ-development we recover Landau-de Gennes corrections to the Oseen-Frank energy. We provide an explicit characterisation of minimizing Q-tensors at this order in terms of optimal Oseen-Frank directors and observe the emerging biaxiality. We apply our results to distinguish between optimal configurations in the class of conformal director fields of fixed topological degree saturating the lower bound for the Oseen-Frank energy

Reduced energies for thin ferromagnetic films with perpendicular anisotropy

We derive four reduced two-dimensional models that describe, at different spatial scales, the micromagnetics of ultrathin ferromagnetic materials of finite spatial extent featuring perpendicular magnetic anisotropy and interfacial Dzyaloshinskii-Moriya interaction. Starting with a microscopic model that regularizes the stray field near the material's lateral edges, we carry out an asymptotic analysis of the energy by means of $\Gamma$-convergence. Depending on the scaling assumptions on the size of the material domain vs. the strength of dipolar interaction, we obtain a hierarchy of the limit energies that exhibit progressively stronger stray field effects of the material edges. These limit energies feature, respectively, a renormalization of the out-of-plane anisotropy, an additional local boundary penalty term forcing out-of-plane alignment of the magnetization at the edge, a pinned magnetization at the edge, and, finally, a pinned magnetization and an additional field-like term that blows up at the edge, as the sample's lateral size is increased. The pinning of the magnetization at the edge restores the topological protection and enables the existence of magnetic skyrmions in bounded samples.Comment: 29 pages, 1 figur

Experimental determination of the permeability of engineering textiles: Benchmark II

In this second international permeability benchmark, the in-plane permeability values of a carbon fabric were studied by twelve research groups worldwide. One participant also investigated the deformation of the tested carbon fabric. The aim of this work was to obtain comparable results in order to make a step toward standardization of permeability measurements. Unidirectional injections were thus conducted to determine the unsaturated in-plane permeability tensor of the fabric. Procedures used by participants were specified in the guidelines defined for this benchmark. Participants were asked to use the same values for parameters such as fiber volume fraction, injection pressure and fluid viscosity to minimize sources of scatter. The comparison of the results from each participant was encouraging. The scatter between data obtained while respecting the guidelines was below 25%. However, a higher dispersion was observed when some parameters differed from the recommendations of this exercise.The authors are grateful to J.M. Beraud from Hexcel Fabrics for his support that made possible this exercise. The contributions of J.B. Alms, N.C. Correia, S. Advani, E. Ruiz and P.C.T. Goncalves to the preparation of the guidelines document and templates are acknowledged by the participants of this benchmark.Vernet, N.; Ruiz, E.; Advani, S.; Alms, JB.; Aubert, M.; Barburski, M.; Barari, B.... (2014). Experimental determination of the permeability of engineering textiles: Benchmark II. Composites Part A: Applied Science and Manufacturing. 61:172-184. doi:10.1016/j.compositesa.2014.02.010S1721846

Identification of hemodynamically stable patients with acute pulmonary embolism at high risk for death: external validation of different models

Background: The optimal strategy for identification of hemodynamically stable patients with acute pulmonary embolism (PE) at risk for death and clinical deterioration remains undefined. Objectives: We aimed to assess the performances of currently available models/scores for identifying hemodynamically stable patients with acute, symptomatic PE at risk of death and clinical deterioration. Methods: This was a prospective multicenter cohort study including patients with acute PE (NCT03631810). Primary study outcome was in-hospital death within 30 days or clinical deterioration. Other outcomes were in-hospital death, death, and PE-related death, all at 30 days. We calculated positive and negative predictive values, c-statistics of European Society of Cardiology (ESC)-2014, ESC-2019, Pulmonary Embolism Thrombolysis (PEITHO), Bova, Thrombo-embolism lactate outcome study (TELOS), fatty acid binding protein, syncope and tachicardia (FAST), and National Early Warning Scale 2 (NEWS2) for the study outcomes. Results: In 5036 hemodynamically stable patients with acute PE, positive predictive values for the evaluated models/scores were all below 10%, except for TELOS and NEWS2; negative predictive values were above 98% for all the models/scores, except for FAST and NEWS2. ESC-2014 and TELOS had good performances for in-hospital death or clinical deterioration (c-statistic of 0.700 and 0.722, respectively), in-hospital death (c-statistic of 0.713 and 0.723, respectively), and PE-related death (c-statistic of 0.712 and 0.777, respectively); PEITHO, Bova, and NEWS2 also had good performances for PE-related death (c-statistic of 0.738, 0.741, and 0.742, respectively). Conclusion: In hemodynamically stable patients with acute PE, the accuracy for identification of hemodynamically stable patients at risk for death and clinical deterioration varies across the available models/scores; TELOS seems to have the best performance. These data can inform management studies and clinical practice

Analysis of shared common genetic risk between amyotrophic lateral sclerosis and epilepsy

Because hyper-excitability has been shown to be a shared pathophysiological mechanism, we used the latest and largest genome-wide studies in amyotrophic lateral sclerosis (n = 36,052) and epilepsy (n = 38,349) to determine genetic overlap between these conditions. First, we showed no significant genetic correlation, also when binned on minor allele frequency. Second, we confirmed the absence of polygenic overlap using genomic risk score analysis. Finally, we did not identify pleiotropic variants in meta-analyses of the 2 diseases. Our findings indicate that amyotrophic lateral sclerosis and epilepsy do not share common genetic risk, showing that hyper-excitability in both disorders has distinct origins

DMTs and Covid-19 severity in MS: a pooled analysis from Italy and France

We evaluated the effect of DMTs on Covid-19 severity in patients with MS, with a pooled-analysis of two large cohorts from Italy and France. The association of baseline characteristics and DMTs with Covid-19 severity was assessed by multivariate ordinal-logistic models and pooled by a fixed-effect meta-analysis. 1066 patients with MS from Italy and 721 from France were included. In the multivariate model, anti-CD20 therapies were significantly associated (OR = 2.05, 95%CI = 1.39–3.02, p < 0.001) with Covid-19 severity, whereas interferon indicated a decreased risk (OR = 0.42, 95%CI = 0.18–0.99, p = 0.047). This pooled-analysis confirms an increased risk of severe Covid-19 in patients on anti-CD20 therapies and supports the protective role of interferon