Search results for "Differential geometry"
showing 10 items of 462 documents
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…
Anisotropy and chemical composition of ultra-high energy cosmic rays using arrival directions measured by the Pierre Auger Observatory
2011
The Pierre Auger Collaboration has reported evidence for anisotropy in the distribution of arrival directions of the cosmic rays with energies $E>E_{th}=5.5\times 10^{19}$ eV. These show a correlation with the distribution of nearby extragalactic objects, including an apparent excess around the direction of Centaurus A. If the particles responsible for these excesses at $E>E_{th}$ are heavy nuclei with charge $Z$, the proton component of the sources should lead to excesses in the same regions at energies $E/Z$. We here report the lack of anisotropies in these directions at energies above $E_{th}/Z$ (for illustrative values of $Z=6,\ 13,\ 26$). If the anisotropies above $E_{th}$ are du…
On the arithmetic and geometry of binary Hamiltonian forms
2011
Given an indefinite binary quaternionic Hermitian form $f$ with coefficients in a maximal order of a definite quaternion algebra over $\mathbb Q$, we give a precise asymptotic equivalent to the number of nonequivalent representations, satisfying some congruence properties, of the rational integers with absolute value at most $s$ by $f$, as $s$ tends to $+\infty$. We compute the volumes of hyperbolic 5-manifolds constructed by quaternions using Eisenstein series. In the Appendix, V. Emery computes these volumes using Prasad's general formula. We use hyperbolic geometry in dimension 5 to describe the reduction theory of both definite and indefinite binary quaternionic Hermitian forms.
Abel transforms with low regularity with applications to X-ray tomography on spherically symmetric manifolds
2017
We study ray transforms on spherically symmetric manifolds with a piecewise $C^{1,1}$ metric. Assuming the Herglotz condition, the X-ray transform is injective on the space of $L^2$ functions on such manifolds. We also prove injectivity results for broken ray transforms (with and without periodicity) on such manifolds with a $C^{1,1}$ metric. To make these problems tractable in low regularity, we introduce and study a class of generalized Abel transforms and study their properties. This low regularity setting is relevant for geophysical applications.
Validity of the Colposcopic Criteria Inner Border Sign, Ridge Sign, and Rag Sign for Detection of High-Grade Cervical Intraepithelial Neoplasia
2013
OBJECTIVE: To evaluate the association of three patho-gnomonic criteria, inner border, ridge sign, and rag sign with high-grade cervical intraepithelial neoplasia (CIN) using video exoscopy. METHODS: Retrospective evaluation of video recordings of 335 patients, referred for diagnostic colposcopy, who underwent cervical biopsies, and, if indicated loop excisions, was performed. The most severe histologic diagnosis was recorded. Sensitivity, specificity, positive, negative predictive value, and likelihood ratios for highgrade CIN were calculated. RESULTS: In 285 patients (85%), a single colposcopy directed biopsy was taken; 50 patients (15%) underwent two biopsies. One hundred sixty-two patie…
Segre and the Foundations of Geometry: From Complex Projective Geometry to Dual Numbers
2016
In 1886 Corrado Segre wrote to Felix Klein about his intention to study ‘geometrie projective pure’, completing and developing the work of von Staudt. He would continue this research project throughout the whole of his scientific life. In 1889, following a suggestion of Segre, Mario Pieri published his translation of the Geometrie der Lage, and from 1889 to 1890 Segre published four important papers, “Un nuovo campo di ricerche geometriche”, in which he completely developed complex projective geometry, considering new mathematical objects such as antiprojectivities and studying the Hermitian forms from a geometrical point of view with the related ‘hyperalgebraic varieties’. Segre developed …
Zur Geometrie der Translationsstrukturen mit eigentlichen Dilatationen
1983
The module structure of Hochschild homology in some examples
2008
Abstract In this Note we give a simple proof of a conjecture by A. Caldararu stating the compatibility between the modified Hochschild–Kostant–Rosenberg isomorphism and the action of Hochschild cohomology on Hochschild homology in the case of Calabi–Yau manifolds and smooth projective curves. To cite this article: E. Macri` et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).
Local Berry curvature signatures in dichroic angle-resolved photoelectron spectroscopy from two-dimensional materials
2020
Orbital polarization and Berry curvature signatures are mapped out by circular dichroism in angle-resolved photoemission.