scholarly journals Flat surfaces in hyperbolic 3-space whose hyperbolic Gauss maps are bounded

2014 ◽  
Vol 30 (1) ◽  
pp. 309-316 ◽  
Author(s):  
Francisco Martín ◽  
Masaaki Umehara ◽  
Kotaro Yamada
Keyword(s):  
Flat Surfaces ◽  
Gauss Maps

scholarly journals Function-theoretic Properties for the Gauss Maps of Various Classes of Surfaces

2015 ◽  
Vol 67 (6) ◽  
pp. 1411-1434 ◽  
Author(s):  
Yu Kawakami
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Space Forms ◽  
Flat Surfaces ◽  
Immersed Surfaces ◽  
Gauss Maps ◽  
Improper Affine Spheres ◽  
Euclidean Three Space ◽  
Three Space ◽  
Three Dimensional Space

AbstractWe elucidate the geometric background of function-theoretic properties for the Gauss maps of several classes of immersed surfaces in three-dimensional space forms, for example, minimal surfaces in Euclidean three-space, improper affine spheres in the affine three-space, and constant mean curvature one surfaces and flat surfaces in hyperbolic three-space. To achieve this purpose, we prove an optimal curvature bound for a specified conformal metric on an open Riemann surface and give some applications. We also provide unicity theorems for the Gauss maps of these classes of surfaces.

GAUSSIAN CURVATURE AND UNICITY PROBLEM OF GAUSS MAPS OF VARIOUS CLASSES OF SURFACES

2019 ◽  
Vol 240 ◽  
pp. 275-297
Author(s):  
PHAM HOANG HA
Keyword(s):  
Gaussian Curvature ◽  
Riemann Surfaces ◽  
Constant Mean Curvature ◽  
Holomorphic Maps ◽  
Flat Surfaces ◽  
Gauss Maps ◽  
Improper Affine Spheres ◽  
Space Constant ◽  
Euclidean Three Space ◽  
Three Space

In this article, we establish a new estimate for the Gaussian curvature of open Riemann surfaces in Euclidean three-space with a specified conformal metric regarding the uniqueness of the holomorphic maps of these surfaces. As its applications, we give new proofs on the unicity problems for the Gauss maps of various classes of surfaces, in particular, minimal surfaces in Euclidean three-space, constant mean curvature one surfaces in the hyperbolic three-space, maximal surfaces in the Lorentz–Minkowski three-space, improper affine spheres in the affine three-space and flat surfaces in the hyperbolic three-space.

HREM observation of dislocations near room temperature fractures in silicon

1988 ◽  
Vol 46 ◽  
pp. 892-893
Author(s):  
M. H. Rhee ◽  
W. A. Coghlan
Keyword(s):  
Cross Section ◽  
Room Temperature ◽  
Single Crystal Silicon ◽  
Dislocation Nucleation ◽  
Back Side ◽  
Ion Milling ◽  
Crystal Silicon ◽  
Flat Surfaces ◽  
Induced Fractures ◽  
Vicker’S Microhardness

Silicon is believed to be an almost perfectly brittle material with cleavage occurring on {111} planes. In such a material at room temperature cleavage is expected to occur prior to any dislocation nucleation. This behavior suggests that cleavage fracture may be used to produce usable flat surfaces. Attempts to show this have failed. Such fractures produced in semiconductor silicon tend to occur on planes of variable orientation resulting in surfaces with a poor surface finish. In order to learn more about the mechanisms involved in fracture of silicon we began a HREM study of hardness indent induced fractures in thin samples of oxidized silicon.Samples of single crystal silicon were oxidized in air for 100 hours at 1000°C. Two pieces of this material were glued together and 500 μm thick cross-section samples were cut from the combined piece. The cross-section samples were indented using a Vicker's microhardness tester to produce cracks. The cracks in the samples were preserved by thinning from the back side using a combination of mechanical grinding and ion milling.

A TEM study of electron tunneling in biological macromolecules

1987 ◽  
Vol 45 ◽  
pp. 140-141
Author(s):  
J. A. Panitz
Keyword(s):  
Stark Effect ◽  
Electron Tunneling ◽  
Imaging Modality ◽  
Tunneling Current ◽  
Biological Species ◽  
Scanning Tunneling ◽  
Biological Macromolecules ◽  
Flat Surfaces ◽  
Virus Particles ◽  
Stm Images

Tunneling is a ubiquitous phenomenon. Alpha particle disintegration, the Stark effect, superconductivity in thin films, field-emission, and field-ionization are examples of electron tunneling phenomena. In the scanning tunneling microscope (STM) electron tunneling is used as an imaging modality. STM images of flat surfaces show structure at the atomic level. However, STM images of large biological species deposited onto flat surfaces are disappointing. For example, unstained virus particles imaged in the STM do not resemble their TEM counterparts.It is not clear how an STM image of a biological species is formed. Most biological species are large compared to the nominal electrode separation of ∼ 1nm that is required for electron tunneling. To form an image of a biological species, the tunneling electrodes must be separated by a distance that would normally be too large for a tunneling current to be observed.

On the Faceting of Polar Ceramic Surfaces: Microscopy and Holography Studies of MGO(111) Surfaces

1996 ◽  
Vol 54 ◽  
pp. 366-367
Author(s):  
M. Gajdardziska-Josifovska ◽  
B. G. Frost ◽  
E. Völkl ◽  
L. F. Allard
Keyword(s):  
Electron Microscopy ◽  
High Vacuum ◽  
Ultra High Vacuum ◽  
Electron Holography ◽  
Flat Surfaces ◽  
Transmission Electron ◽  
Excess Surface ◽  
Polar Surfaces ◽  
Salt Structure ◽  
Crystallographic Planes

Polar surfaces are those crystallographic faces of ionically bonded solids which, when bulk terminated, have excess surface charge and a non-zero dipole moment perpendicular to the surface. In the case of crystals with a rock salt structure, {111} faces are the exemplary polar surfaces. It is commonly believed that such polar surfaces facet into neutral crystallographic planes to minimize their surface energy. This assumption is based on the seminal work of Henrich which has shown faceting of the MgO(111) surface into {100} planes giving rise to three sided pyramids that have been observed by scanning electron microscopy. These surfaces had been prepared by mechanical polishing and phosphoric acid etching, followed by Ar+ sputtering and 1400 K annealing in ultra-high vacuum (UHV). More recent reflection electron microscopy studies of MgO(111) surfaces, annealed in the presence of oxygen at higher temperatures, have revealed relatively flat surfaces stabilized by an oxygen rich reconstruction. In this work we employ a combination of optical microscopy, transmission electron microscopy, and electron holography to further study the issue of surface faceting.

Design of a Spectroscopic Low-Energy Emission Microscope

1990 ◽  
Vol 48 (1) ◽  
pp. 358-359
Author(s):  
Lee H. Veneklasen
Keyword(s):  
Parallel Imaging ◽  
Objective Lens ◽  
Energy Window ◽  
Flat Surfaces ◽  
Beam Voltage ◽  
New Instrument ◽  
Real Time Image ◽  
Image Planes ◽  
Backscatter Diffraction ◽  
Time Image

This paper discusses some of the unique aspects of a spectroscopic emission microscope now being tested in Clausthal. The instrument is designed for the direct parallel imaging of both elastic and inelastic electrons from flat surfaces. Elastic contrast modes of the familiar LEEM include large and small angle LEED, mirror microscopy, backscatter diffraction contrast (for imaging of surface structure), and phase contrast (for imaging of step dynamics)(1). Inelastic modes include topology sensitive secondary, and work function sensitive photoemission. Most important, the new instrument will also allow analytical imaging using characteristic Auger or soft X-ray emissions. The basic instrument has been described by Bauer and Telieps (2). This configuration has been redesigned to include an airlock, and a LaB6 gun, triple condensor lens, magnetic objective lens, a double focussing separator field, an imaging energy analyzer, and a real time image processor.Fig. 1 shows the new configuration. The basic beam voltage supply Vo = 20 KV, upon which separate supplies for the gun Vg, specimen Vs, lens electrode Vf, and analyzer bias Vb float. The incident energy at the sample can be varied from Vs = 0-1 KV for elastic imaging, or from Vg + Vs = (3 + Vs) KV for inelastic imaging. The image energy window Vs±V/2 may be varied without readjusting either the illumation, or imaging/analyzer optics. The diagram shows conjugate diffraction and image planes. The apertures defining incoming Humiliation and outgoing image angles are placed below the separator magnet to allow for their independent optimization. The instrument can illuminate and image 0.5-100 μm fields at 0-1 keV emission energies with an energy window down to 0.2 eV.

2D Color-Intensity Representation of Ultrasonic Thickness Gauge Measurements

2020 ◽  
pp. 1192-1198
Author(s):  
M.S. Mohammad ◽  
Tibebe Tesfaye ◽  
Kim Ki-Seong
Keyword(s):  
Cost Effective ◽  
The Other ◽  
Thickness Gauge ◽  
Color Intensity ◽  
Digital Readout ◽  
Flat Surfaces ◽  
Video Cameras ◽  
Wide Range ◽  
Cost Effective Alternative ◽  
Ultrasonic Thickness

Ultrasonic thickness gauges are easy to operate and reliable, and can be used to measure a wide range of thicknesses and inspect all engineering materials. Supplementing the simple ultrasonic thickness gauges that present results in either a digital readout or as an A-scan with systems that enable correlating the measured values to their positions on the inspected surface to produce a two-dimensional (2D) thickness representation can extend their benefits and provide a cost-effective alternative to expensive advanced C-scan machines. In previous work, the authors introduced a system for the positioning and mapping of the values measured by the ultrasonic thickness gauges and flaw detectors (Tesfaye et al. 2019). The system is an alternative to the systems that use mechanical scanners, encoders, and sophisticated UT machines. It used a camera to record the probe’s movement and a projected laser grid obtained by a laser pattern generator to locate the probe on the inspected surface. In this paper, a novel system is proposed to be applied to flat surfaces, in addition to overcoming the other limitations posed due to the use of the laser projection. The proposed system uses two video cameras, one to monitor the probe’s movement on the inspected surface and the other to capture the corresponding digital readout of the thickness gauge. The acquired images of the probe’s position and thickness gauge readout are processed to plot the measured data in a 2D color-coded map. The system is meant to be simpler and more effective than the previous development.

Mathematical Model of Flat Surface Machining Inaccuracies due to Elastic Strains of Technological System

2018 ◽  
pp. 1-14 ◽  
Author(s):  
I. I. Kravchenko
Keyword(s):  
Mathematical Model ◽  
Vector Field ◽  
Model Development ◽  
Technological System ◽  
Mutual Arrangement ◽  
Real Surface ◽  
Main Bearing ◽  
Flat Surfaces ◽  
Internal Surfaces ◽  
Elastic Strains

The paper considers the mathematical model development technique to build a vector field of the shape deviations when machining flat surfaces of shell parts on multi-operational machines under conditions of anisotropic rigidity in technological system (TS). The technological system has an anisotropic rigidity, as its elastic strains do not obey the accepted concepts, i.e. the rigidity towards the coordinate axes of the machine is the same, and they occur only towards the external force. The record shows that the diagrams of elastic strains of machine units are substantially different from the circumference. The issues to ensure the specified accuracy require that there should be mathematical models describing kinematic models and physical processes of mechanical machining under conditions of the specific TS. There are such models for external and internal surfaces of rotation [2,3], which are successfully implemented in practice. Flat surfaces (FS) of shell parts (SP) are both assembly and processing datum surfaces. Therefore, on them special stipulations are made regarding deviations of shape and mutual arrangement. The axes of the main bearing holes are coordinated with respect to them. The joints that ensure leak tightness and distributed load on the product part are closed on these surfaces. The paper deals with the analytical construction of the vector field F, which describes with appropriate approximation the real surface obtained as a result of modeling the process of machining flat surfaces (MFS) through face milling under conditions of anisotropic properties.

Quasi-Barrierless Submolecular Motion in Mechanically Interlocked Carbon Nanotubes

2020 ◽  
Author(s):  
Julia Villalva ◽  
Belén Nieto-Ortega ◽  
Manuel Melle-Franco ◽  
Emilio Pérez
Keyword(s):  
Density Functional ◽  
Close Contact ◽  
Tight Binding ◽  
Energetic Cost ◽  
Molecular Fragments ◽  
Activation Barriers ◽  
Flat Surfaces ◽  
Different Types ◽  
Atomically Flat ◽  
Derivatives Of

The motion of molecular fragments in close contact with atomically flat surfaces is still not fully understood. Does a more favourable interaction imply a larger barrier towards motion even if there are no obvious minima? Here, we use mechanically interlocked rotaxane-type derivatives of SWNTs (MINTs) featuring four different types of macrocycles with significantly different affinities for the SWNT thread as models to study this problem. Using molecular dynamics, we find that there is no direct correlation between the interaction energy of the macrocycle with the SWNT and its ability to move along or around it. Density functional tight-binding calculations reveal small (<2.5 Kcal·mol-1) activation barriers, the height of which correlates with the commensurability of the aromatic moieties in the macrocycle with the SWNT. Our results show that macrocycles in MINTs rotate and translate freely around and along SWNTs at room temperature, with an energetic cost lower than the rotation around the C−C bond in ethane.<br>

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