A note on the index of closed minimal hypersurfaces of flat tori

Generalizing earlier work by Ros in ambient dimension three, we prove an affine lower bound for the Morse index of closed minimal hypersurfaces inside a flat torus in terms of their first Betti number (with purely dimensional coefficients)

Modelo para o Cálculo de Tensões Biaxial e Triaxial em Materiais Ortotrópicos: Análise da Coerência das Equações para um Filme Fino Transversalmente Isotrópio de Ouro

Neste trabalho um modelo analítico com base na teoria da elasticidade proposto para mensurar as tensões residuais em materiais ortotrópicosn foi descrito e aplicado para avaliar o coeficiente de Poisson em filmes finos de ouro. Os matérias metálicos geralmente possuem anisotropia e textura cristalográfica, o que gera problemas para se analisar as tensões via difração de raios X, uma vez que, as curvas de ε vs sen² Ψ tornam-se não lineares. Aplicando as simetrias referentes a ortotropia do material no tensor elasticidade, obtêve-se as relações tensão deformação para materiais ortotrópicos, as equações para as deformações foram encontradas em função do estado de tensões principais triaxial e biaxial para o caso onde as deformações são calculadas via XRD. Uma nova equação foi proposta para o coeficiente de Poisson fora do plano para o caso de filmes finos transversalmente isotrópicos. Um estudo de caso foi realizado aplicando-se as equações à dados experimentais obtidos na literatura para um filme fino de ouro com textura de fibra {111}, assim o valor do coeficiente de Poisson fora do plano pôde ser calculado de duas formas. A primeira foi realizada ajustando os dados experimentais pelo método dos mínimos quadrados. Na segunda o coeficiente de Poisson foi calculado como um valor médio de uma superfície que foi construida para o coeficiente de Poisson for a do plano como função de sen² Ψ e ε

Simulações atomísticas e previsão de espectros de RMN em materiais carbonosos.

Neste trabalho, os parâmetros espectrais de RMN de 13C foram calculados para materiais carbonosos ordenados e desordenados através de simulações computacionais. A blindagem magnética em RMN de 13C foi calculada em uma monocamada de grafeno usando a teoria do funcional da densidade (DFT) e o método GIPAW (gauge including projector augmented plane wave). Após realizar os testes de convergência envolvendo a variação do número de pontos k e do tamanho da supercélula, os cálculos foram então estendidos a sistemas contendo mais de uma folha de grafeno, incluindo a bicamada de grafeno e o grafite hexagonal. Com respeito aos materiais carbonosos desordenados, os deslocamentos químicos de RMN de 13C correspondendo a diferentes sítios em modelos atomísticos de carbonos amorfos hidrogenados também foram calculados para diferentes quantidades de H através do emprego dinâmica molecular e métodos de primeiros princípios. Os modelos foram validados através das funções de distribuição de pares e as frações de átomos de carbono sp3 e sp2 foram determinadas através da análise das ligações do átomo de carbono nas estruturas. Especificamente, os resultados obtidos permitiram distinguir os deslocamentos químicos associados com diversos tipos de sítios de carbono, com diferentes estados de hibridização e ligados ou não com átomos de hidrogênios. Os resultados dos cálculos mostraram bom acordo com espectros experimentais de RMN de 13 de diferentes tipos de materiais carbonosos, evidenciando o poder de cálculos DFT na previsão de parâmetros de RMN em materiais baseados no grafeno e para identificar características estruturais locais de materiais carbonosos desordenados

Compactness analysis for free boundary minimal hypersurfaces

We investigate compactness phenomena involving free boundary minimal hypersurfaces in Riemannian manifolds of dimension less than eight. We provide natural geometric conditions that ensure strong one-sheeted graphical subsequential convergence, discuss the limit behaviour when multi-sheeted convergence happens and derive various consequences in terms of finiteness and topological control

Compactness of the Space of Minimal Hypersurfaces with Bounded Volume and p-th Jacobi Eigenvalue

Given a closed Riemannian manifold of dimension less than eight, we prove a compactness result for the space of closed, embedded minimal hypersurfaces satisfying a volume bound and a uniform lower bound on the first eigenvalue of the stability operator. When the latter assumption is replaced by a uniform lower bound on the p-th Jacobi eigenvalue for p≥2 one gains strong convergence to a smooth limit submanifold away from at most p−1 points

Bubbling analysis and geometric convergence results for free boundary minimal surfaces

We investigate the limit behaviour of sequences of free boundary minimal hypersurfaces with bounded index and volume, by presenting a detailed blow-up analysis near the points where curvature concentration occurs. Thereby, we derive a general quantization identity for the total curvature functional, valid in ambient dimension less than eight and applicable to possibly improper limit hypersurfaces. In dimension three, this identity can be combined with the Gauss-Bonnet theorem to provide a constraint relating the topology of the free boundary minimal surfaces in a converging sequence, of their limit, and of the bubbles or half-bubbles that occur as blow-up models. We present various geometric applications of these tools, including a description of the behaviour of index one free boundary minimal surfaces inside a 3-manifold of non-negative scalar curvature and strictly mean convex boundary. In particular, in the case of compact, simply connected, strictly mean convex domains in $\mathbb{R}^3$ unconditional convergence occurs for all topological types except the disk and the annulus, and in those cases the possible degenerations are classified

Sentinel-3 Delay-Doppler altimetry over Antarctica

The launch of Sentinel-3A in February 2016 represented the beginning of a new long-term series of operational satellite radar altimeters, which will provide Delay-Doppler altimetry measurements over ice sheets for decades to come. Given the potential benefits that these satellites can offer to a range of glaciological applications, it is important to establish their capacity to monitor ice sheet elevation and elevation change. Here, we present the first analysis of Sentinel-3 Delay-Doppler altimetry over the Antarctic ice sheet, and assess the accuracy and precision of retrievals of ice sheet elevation across a range of topographic regimes. Over the low-slope regions of the ice sheet interior, we find that the instrument achieves both an accuracy and a precision of the order of 10 cm, with ∼98 % of the data validated being within 50 cm of co-located airborne measurements. Across the steeper and more complex topography of the ice sheet margin, the accuracy decreases, although analysis at two coastal sites with densely surveyed airborne campaigns shows that ∼60 %–85 % of validated data are still within 1 m of co-located airborne elevation measurements. We then explore the utility of the Sentinel-3A Delay-Doppler altimeter for mapping ice sheet elevation change. We show that with only 2 years of available data, it is possible to resolve known signals of ice dynamic imbalance and to detect evidence of subglacial lake drainage activity. Our analysis demonstrates a new, long-term source of measurements of ice sheet elevation and elevation change, and the early potential of this operational system for monitoring ice sheet imbalance for decades to come

Index estimates for free boundary minimal hypersurfaces

We show that the Morse index of a properly embedded free boundary minimal hypersurface in a strictly mean convex domain of the Euclidean space grows linearly with the dimension of its first relative homology group (which is at least as big as the number of its boundary components, minus one). In ambient dimension three, this implies a lower bound for the index of a free boundary minimal surface which is linear both with respect to the genus and the number of boundary components. Thereby, the compactness theorem by Fraser and Li implies a strong compactness theorem for the space of free boundary minimal surfaces with uniformly bounded Morse index inside a convex domain. Our estimates also imply that the examples constructed, in the unit ball, by Fraser–Schoen and Folha–Pacard–Zolotareva have arbitrarily large index. Extensions of our results to more general settings (including various classes of positively curved Riemannian manifolds and other convexity assumptions) are discussed

Effect of Systemic Hypertension With Versus Without Left Ventricular Hypertrophy on the Progression of Atrial Fibrillation (from the Euro Heart Survey).

Hypertension is a risk factor for both progression of atrial fibrillation (AF) and development of AF-related complications, that is major adverse cardiac and cerebrovascular events (MACCE). It is unknown whether left ventricular hypertrophy (LVH) as a consequence of hypertension is also a risk factor for both these end points. We aimed to assess this in low-risk AF patients, also assessing gender-related differences. We included 799 patients from the Euro Heart Survey with nonvalvular AF and a baseline echocardiogram. Patients with and without hypertension were included. End points after 1 year were occurrence of AF progression, that is paroxysmal AF becoming persistent and/or permanent AF, and MACCE. Echocardiographic LVH was present in 33% of 379 hypertensive patients. AF progression after 1 year occurred in 10.2% of 373 patients with rhythm follow-up. In hypertensive patients with LVH, AF progression occurred more frequently as compared with hypertensive patients without LVH (23.3% vs 8.8%, p = 0.011). In hypertensive AF patients, LVH was the most important multivariably adjusted determinant of AF progression on multivariable logistic regression (odds ratio 4.84, 95% confidence interval 1.70 to 13.78, p = 0.003). This effect was only seen in male patients (27.5% vs 5.8%, p = 0.002), while in female hypertensive patients, no differences were found in AF progression rates regarding the presence or absence of LVH (15.2% vs 15.0%, p = 0.999). No differences were seen in MACCE for hypertensive patients with and without LVH. In conclusion, in men with hypertension, LVH is associated with AF progression. This association seems to be absent in hypertensive women

Progression From Paroxysmal to Persistent Atrial Fibrillation. Clinical Correlates and Prognosis

Objectives: We investigated clinical correlates of atrial fibrillation (AF) progression and evaluated the prognosis of patients demonstrating AF progression in a large population. Background: Progression of paroxysmal AF to more sustained forms is frequently seen. However, not all patients will progress to persistent AF. Methods: We included 1,219 patients with paroxysmal AF who participated in the Euro Heart Survey on AF and had a known rhythm status at follow-up. Patients who experienced AF progression after 1 year of follow-up were identified. Results: Progression of AF occurred in 178 (15%) patients. Multivariate analysis showed that heart failure, age, previous transient ischemic attack or stroke, chronic obstructive pulmonary disease, and hypertension were the only independent predictors of AF progression. Using the regression coefficient as a benchmark, we calculated the HATCH score. Nearly 50% of the patients with a HATCH score >5 progressed to persistent AF compared with only 6% of the patients with a HATCH score of 0. During follow-up, patients with AF progression were more often admitted to the hospital and had more major adverse cardiovascular events. Conclusions: A substantial number of patients progress to sustained AF within 1 year. The clinical outcome of these patients regarding hospital admissions and major adverse cardiovascular events was worse compared with patients demonstrating no AF progression. Factors known to cause atrial structural remodeling (age and underlying heart disease) were independent predictors of AF progression. The HATCH score may help to identify patients who are likely to progress to sustained forms of AF in the near future. \ua9 2010 American College of Cardiology Foundation