Search results for "symmetry"

Tendencies in ABO3 Perovskite and SrF2, BaF2 and CaF2 Bulk and Surface F-Center Ab Initio Computations at High Symmetry Cubic Structure

2021

This research was partly funded by the Latvian Council of Science project No. LZP‐ 2020/2‐0009 (for R. Eglitis), as well as the ERAF Project No. 1.1.1.1/18/A/073. We express our gratitude for the financial support from Latvian–Ukraine cooperation Project No. Latvia–Ukraine LV‐ UA/2021/5. The Institute of Solid State Physics, University of Latvia (Latvia), as the Centre of Excellence has received funding from the European Unions Horizon 2020 Framework Pro‐ gramme H2020‐WIDESPREAD01‐2016‐2017‐Teaming Phase2 under Grant Agreement No. 739508, project CAMART2.

Optical Symmetry of Ferroelectric Liquid Crystal Cells

1990

We observe an exact optical symmetry in Surface Stabilized Ferroelectric Liquid Crystal (SSFLC) cells in polarized transmission optical microscopy and spectroscopy. A theoretical argument based on the intrinsic time reversibility of Maxwell's equations and energy conservation is developed to explain this symmetry. The results support the model of Clark and Rieker for zig-zag wall structure and illustrate the necessity of including the orientational binding of the director at the chevron interface.

Blending Planes and Canal Surfaces Using Dupin Cyclides

2011

We develop two different new algorithms of G1-blending between planes and canal surfaces using Dupin cyclides. It is a generalization of existing algorithms that blend revolution surfaces and planes using a plane called construction plane. Spatial constraints were necessary to do that. Our work consist in building three spheres to determine the Dupin cyclide of the blending. The first algorithm is based on one of the definitions of Dupin cyclides taking into account three spheres of the same family enveloping the cyclide. The second one uses only geometric properties of Dupin cyclide. The blending is fixed by a circle of curvature onto the canal surface. Thanks to this one, we can determine…

Determination of the object surface function by structured light: application to the study of spinal deformities.

1999

The projection of structured light is a technique frequently used to determine the surface shape of an object. In this paper, a new procedure is described that efficiently resolves the correspondence between the knots of the projected grid and those obtained on the object when the projection is made. The method is based on the use of three images of the projected grid. In two of them the grid is projected over a flat surface placed, respectively, before and behind the object; both images are used for calibration. In the third image the grid is projected over the object. It is not reliant on accurate determination of the camera and projector pair relative to the grid and object. Once the met…

Shell structure in large nonspherical metal clusters.

1992

Electronic shell structure of icosahedral and cuboctahedral sodium clusters with 300 to 1500 atoms has been studied using a potential-well approximation for the effective one-electron potential. The results show that icosahedral clusters yield the same shell structure as spherical clusters up to the cluster size of about 500 atoms and that similarities persist until the cluster has about 1000 atoms. The shell structure of a cuboctahedral geometry begins to deviate from that of a sphere when the cluster size is about 100. A study on quadrupole deformations of large clusters shows that surface fluctuations in liquid clusters cannot destroy the shell structure even in the largest clusters.

Symmetry of minimizers with a level surface parallel to the boundary

2015

We consider the functional $$I_\Omega(v) = \int_\Omega [f(|Dv|) - v] dx,$$ where $\Omega$ is a bounded domain and $f$ is a convex function. Under general assumptions on $f$, G. Crasta [Cr1] has shown that if $I_\Omega$ admits a minimizer in $W_0^{1,1}(\Omega)$ depending only on the distance from the boundary of $\Omega$, then $\Omega$ must be a ball. With some restrictions on $f$, we prove that spherical symmetry can be obtained only by assuming that the minimizer has one level surface parallel to the boundary (i.e. it has only a level surface in common with the distance). We then discuss how these results extend to more general settings, in particular to functionals that are not differenti…

Deformation of sulfur hexafluoride and floppiness of trifluoromethyl sulfur pentafluoride

2006

International audience; With recent advances in space exploration and atmospheric chemistry there is an increased need for more spectroscopic tools to allow the of study complex species. One such tool is the theory of frame transformation of coupled rotor systems. In this article, the theory of frame transformation along with the concept of rotational energy surface is used to study the symmetry that occurs in trifluoromethyl sulfur pentafluoride due to the internal rotation of the CF3 radical and, more generally, to the extent of floppiness of SF5CF3. Other lower symmetries when a CF4 molecule is stuck on the various symmetry axes of an SF6 molecule are also discussed.

Symmetry of minimizers with a level surface parallel to the boundary

2011

Stability results for solutions of elliptic equations with a level surface parallel to the boundary

2013

Electronic structure trends of Möbius graphene nanoribbons from minimal-cell simulations

2014

Investigating topological effects in materials requires often the modeling of material systems as a whole. Such modeling restricts system sizes, and makes it hard to extract systematic trends. Here, we investigate the effect of M\"obius topology in the electronic structures of armchair graphene nanoribbons. Using density-functional tight-binding method and minimum-cell simulations through revised periodic boundary conditions, we extract electronic trends merely by changing cells' symmetry operations and respective quantum number samplings. It turns out that for a minimum cell calculation, once geometric and magnetic contributions are ignored, the effect of the global topology is unexpectedl…