Search results for " Geometry"
showing 10 items of 2294 documents
Extensions and corona decompositions of low-dimensional intrinsic Lipschitz graphs in Heisenberg groups
2020
This note concerns low-dimensional intrinsic Lipschitz graphs, in the sense of Franchi, Serapioni, and Serra Cassano, in the Heisenberg group $\mathbb{H}^n$, $n\in \mathbb{N}$. For $1\leq k\leq n$, we show that every intrinsic $L$-Lipschitz graph over a subset of a $k$-dimensional horizontal subgroup $\mathbb{V}$ of $\mathbb{H}^n$ can be extended to an intrinsic $L'$-Lipschitz graph over the entire subgroup $\mathbb{V}$, where $L'$ depends only on $L$, $k$, and $n$. We further prove that $1$-dimensional intrinsic $1$-Lipschitz graphs in $\mathbb{H}^n$, $n\in \mathbb{N}$, admit corona decompositions by intrinsic Lipschitz graphs with smaller Lipschitz constants. This complements results that…
L∞-variational problems associated to measurable Finsler structures
2016
Abstract We study L ∞ -variational problems associated to measurable Finsler structures in Euclidean spaces. We obtain existence and uniqueness results for the absolute minimizers.
p −1-Linear Maps in Algebra and Geometry
2012
At least since Habousch’s proof of Kempf’s vanishing theorem, Frobenius splitting techniques have played a crucial role in geometric representation theory and algebraic geometry over a field of positive characteristic. In this article we survey some recent developments which grew out of the confluence of Frobenius splitting techniques and tight closure theory and which provide a framework for higher dimension geometry in positive characteristic. We focus on local properties, i.e. singularities, test ideals, and local cohomology on the one hand and global geometric applicatioms to vanishing theorems and lifting of sections on the other.
Vertical versus horizontal Sobolev spaces
2020
Let $\alpha \geq 0$, $1 < p < \infty$, and let $\mathbb{H}^{n}$ be the Heisenberg group. Folland in 1975 showed that if $f \colon \mathbb{H}^{n} \to \mathbb{R}$ is a function in the horizontal Sobolev space $S^{p}_{2\alpha}(\mathbb{H}^{n})$, then $\varphi f$ belongs to the Euclidean Sobolev space $S^{p}_{\alpha}(\mathbb{R}^{2n + 1})$ for any test function $\varphi$. In short, $S^{p}_{2\alpha}(\mathbb{H}^{n}) \subset S^{p}_{\alpha,\mathrm{loc}}(\mathbb{R}^{2n + 1})$. We show that the localisation can be omitted if one only cares for Sobolev regularity in the vertical direction: the horizontal Sobolev space $S_{2\alpha}^{p}(\mathbb{H}^{n})$ is continuously contained in the vertical Sobolev sp…
Laser Ultrasonics Inspection for Defect Evaluation on Train Wheel
2019
Abstract Passengers’ safety and in-service life of wheelset axles play an important role in railway vehicles. For this reason, periodic inspections are necessary. Among non-destructive techniques, ultrasonic ones are widely applied in this field. The main disadvantage of conventional ultrasonic techniques is that the overall inspection of wheels requires the train to be put out-of-service and disassembly each part, which is time-consuming and expensive. In this paper, a non-conventional non-contact laser ultrasonic inspection for train wheels is proposed. The proposed method uses a laser interferometer to receive the ultrasonic wave without contact. The receiving system allows choosing the …
Theoretical insights on the importance of anchoring vs molecular geometry in magnetic molecules acting as junctions
2019
The anchoring of the molecule to an electrode is known to be a key factor in single-molecule spintronics experiments. Likewise, a relaxation down to the most stable geometry is a critical step in theoretical simulations of transport through single-molecule junctions. Herein we present a set of calculations designed to analyze and compare the effect of different anchoring points and the effect of perturbations in the molecular geometry and interelectrode distance. As model system we chose the [V($\alpha$-C$_3$S$_5$)$_3$]$^{2-}$ complex connecting two Au(111) electrodes in a slightly compressed geometry. In our calculations, the attachment happens through an S-Au bond, a common anchoring stra…
3D modeling of growth ridge and edge facet formation in 〈100〉 floating zone silicon crystal growth process
2019
Abstract A 3D quasi-stationary model for crystal ridge formation in FZ crystal growth systems for silicon is presented. Heat transfer equations for the melt and crystal are solved, and an anisotropic crystal growth model together with a free surface shape solver is used to model the facet growth and ridge formation. The simulation results for 4″ and 5″ crystals are presented and compared to experimental ridge shape data.
Effect of process parameters and crystal orientation on 3D anisotropic stress during CZ and FZ growth of silicon
2017
Abstract Simulations of 3D anisotropic stress are carried out in and oriented Si crystals grown by FZ and CZ processes for different diameters, growth rates and process stages. Temperature dependent elastic constants and thermal expansion coefficients are used in the FE simulations. The von Mises stress at the triple point line is ~5–11% higher in crystals compared to crystals. The process parameters have a larger effect on the von Mises stress than the crystal orientation. Generally, the crystal has a higher azimuthal variation of stress along the triple point line (~8%) than the crystal (~2%). The presence of a crystal ridge increases the stress beside the ridge and decreases it on the ri…
Correlation between surface engineering and deformation response of some natural polymer fibrous systems
2018
Surfaces of bamboo derived cellulosic fibrous systems have been modified by air-plasma treatment. Their deformational response was studied to establish the relationship between their three-dimensional profile and permanent deformation as a measure of their comfort properties since the fibrous system made of natural polymer comes into contact with the skin. The composite should have a permanent deformation close to zero, in order to be, in terms of dimensions, as stable as possible. By analyzing the area of 1 cm2 using a Universal Surface Tester (UST), different 3D surface diagrams and surface roughness values were obtained. This type of surface investigation provides relevant information a…
Review of the PEA Method for Space Charge Measurements on HVDC Cables and Mini-Cables
2019
This review takes into account articles and standards published in recent years concerning the application of the Pulsed Electro Acoustic (PEA) method for space charge measurement on High Voltage Direct Current (HVDC) cables and mini-cables. Since the 80s, the PEA method has been implemented for space charge measurements on flat specimens in order to investigate space charge phenomena and to evaluate the ageing of dielectrics. In recent years, this technique has been adapted to cylindrical geometry. Several studies and experiments have been carried out on the use of the PEA method for full size cables and HVDC cable models. The experiments have been conducted using different arrangements of…