scholarly journals On characterization of horizontal biharmonic curves in H^2 × R

2020 ◽  
Vol 15 (2) ◽  
pp. 35-41
Author(s):  
Talat Körpinar ◽  
Essin Turhan
Keyword(s):  
Curvature And Torsion ◽  
Biharmonic Curves

In this paper, we study biharmonic curves in H2 × R. We show that all of them are helices. By using the curvature and torsion of the curves, we give some characterizations of horizontal biharmonic curves in H2 × R.

scholarly journals CHARACTERIZATION OF SPACELIKE BIHARMONIC CURVES WITH TIMELIKE BINORMAL ACCORDING TO FLAT METRIC IN LORENTZIAN HEISENBERG GROUP Heis³ - doi: 10.5269/bspm.v30i2.14706

2011 ◽  
Vol 30 (2) ◽  
pp. 101-107
Author(s):  
Talat Körpınar ◽  
Essin Turhan
Keyword(s):  
Heisenberg Group ◽  
Parametric Representation ◽  
Flat Metric ◽  
Curvature And Torsion ◽  
Biharmonic Curves

In this paper, we study spacelike biharmonic curves with timelike binormal according to flat metric in the Lorentzian Heisenberg group Heis³. We characterize spacelike biharmonic curves with timelike binormal in terms of their curvature and torsion. Additionally, we determine the parametric representation of the spacelike biharmonic curves with timelike binormal according to flat metric from this characterization.

On Characterization of Time-Like Horizontal Biharmonic Curves in the Lorentzian Heisenberg Group Heis3

2010 ◽  
Vol 65 (8-9) ◽  
pp. 641-648 ◽  
Author(s):  
Essin Turhan ◽  
Talat Körpinar
Keyword(s):  
Heisenberg Group ◽  
Curvature And Torsion ◽  
Biharmonic Curves

In this paper, we study energy of time-like horizontal biharmonic curves in the Lorentzian Heisenberg group Heis3. We characterize the biharmonic curves in terms of their curvature and torsion. We prove that all of the biharmonic curves are helices. Finally, we study the mechanics of biharmonic curves and provide conditions for energy of horizontal biharmonic curves

scholarly journals Tubular Surfaces Around Timelike Biharmonic Curves in Lorentzian Heisenberg Group Heis3

2012 ◽  
Vol 20 (1) ◽  
pp. 431-446 ◽  
Author(s):  
Talat Körpinar ◽  
Essin Turhan
Keyword(s):  
Heisenberg Group ◽  
New Method ◽  
Tubular Surface ◽  
Curvature And Torsion ◽  
Tubular Surfaces ◽  
Biharmonic Curves

Abstract In this paper, we describe a new method for constructing a tubular surface surrounding a timelike biharmonic curve in the Lorentzian Heisenberg group Heis3. Firstly, we characterize timelike biharmonic curves in terms of their curvature and torsion. Also, by using timelike biharmonic curves, we give explicit parametrizations of tubular surfaces in the Lorentzian Heisenberg group Heis3.

scholarly journals Characterization of Rectifying and Sphere Curves in ℝ3

2017 ◽  
Vol 14 (2) ◽  
Author(s):  
Julie Logan ◽  
Yun Myung Oh
Keyword(s):  
Tangent Vector ◽  
Normal Vector ◽  
Extra Condition ◽  
Space Curves ◽  
3D Space ◽  
Nonzero Curvature ◽  
Unit Speed ◽  
Curvature And Torsion ◽  
Rectifying Curve

Studies of curves in 3D-space have been developed by many geometers and it is known that any regular curve in 3D space is completely determined by its curvature and torsion, up to position. Many results have been found to characterize various types of space curves in terms of conditions on the ratio of torsion to curvature. Under an extra condition on the constant curvature, Y. L. Seo and Y. M. Oh found the series solution when the ratio of torsion to curvature is a linear function. Furthermore, this solution is known to be a rectifying curve by B. Y. Chen’s work. This project, uses a different approach to characterize these rectifying curves. This paper investigates two problems. The first problem relates to figuring out what we can say about a unit speed curve with nonzero curvature if every rectifying plane of the curve passes through a fixed point in ℝ3. Secondly, some formulas of curvature and torsion for sphere curves are identified. KEYWORDS: Space Curve; Rectifying Curve; Curvature; Torsion; Rectifying Plane; Tangent Vector; Normal Vector; Binormal Vector

Geometrical characterization of canted coil springs

2006 ◽  
Vol 220 (12) ◽  
pp. 1831-1841
Author(s):  
J M Soler ◽  
R H Rangel
Keyword(s):  
Computer Aided Design ◽  
Mechanical Response ◽  
Three Dimensional ◽  
Helical Spring ◽  
Element Analysis ◽  
Geometrical Characterization ◽  
Three Dimensional Models ◽  
Curvature And Torsion ◽  
Aided Design

This article presents a geometrical description of canted coil springs as a particular type of space curve. The influence of the canted angle on the geometrical curvature and torsion is investigated in order to characterize the three-dimensional geometry of the springs. Geometrical descriptions of helical spring rings generated by joining together the two ends of a rectilinear-axis spring as well as several types of spring rings, obtained from rectilinear-axis canted coil springs, are proposed. To create such ring geometries, conservation of length of wire is assumed and approximate relations are derived in order to simplify computations. These geometrical descriptions are then applied to generate appropriate three-dimensional models. Such models can be further imported to computer-aided design and finite-element analysis programmes in order to estimate the mechanical response of such springs.

On Characterization Canal Surfaces around Timelike Horizontal Biharmonic Curves in Lorentzian Heisenberg Group Heis3

2011 ◽  
Vol 66 (6-7) ◽  
pp. 441-449 ◽  
Author(s):  
Essin Turhan ◽  
Talat Körpinar
Keyword(s):  
Heisenberg Group ◽  
New Method ◽  
Canal Surface ◽  
Canal Surfaces ◽  
Curvature And Torsion ◽  
Biharmonic Curves

In this paper, we describe a new method for constructing a canal surface surrounding a timelike horizontal biharmonic curve in the Lorentzian Heisenberg group Heis3. Firstly, we characterize timelike biharmonic curves in terms of their curvature and torsion. Also, by using timelike horizontal biharmonic curves, we give explicit parametrizations of canal surfaces in the Lorentzian Heisenberg group Heis3

Morphological Characterization of Mycobacteriophage R1

1974 ◽  
Vol 32 ◽  
pp. 254-255
Author(s):  
B. L. Soloff ◽  
T. A. Rado
Keyword(s):  
Carbon Source ◽  
Stationary Phase ◽  
Growth Phase ◽  
Minimal Medium ◽  
Morphological Characterization ◽  
Logarithmic Growth Phase ◽  
Complete Lysis ◽  
Lysogenic Culture ◽  
Logarithmic Growth

Mycobacteriophage R1 was originally isolated from a lysogenic culture of M. butyricum. The virus was propagated on a leucine-requiring derivative of M. smegmatis, 607 leu−, isolated by nitrosoguanidine mutagenesis of typestrain ATCC 607. Growth was accomplished in a minimal medium containing glycerol and glucose as carbon source and enriched by the addition of 80 μg/ ml L-leucine. Bacteria in early logarithmic growth phase were infected with virus at a multiplicity of 5, and incubated with aeration for 8 hours. The partially lysed suspension was diluted 1:10 in growth medium and incubated for a further 8 hours. This permitted stationary phase cells to re-enter logarithmic growth and resulted in complete lysis of the culture.

AEM analysis of crystallization in Ti-based amorphous alloys

1983 ◽  
Vol 41 ◽  
pp. 270-271
Author(s):  
A.R. Pelton ◽  
A.F. Marshall ◽  
Y.S. Lee
Keyword(s):  
Magnetic Properties ◽  
Amorphous Alloys ◽  
Amorphous Materials ◽  
Isothermal Annealing ◽  
Amorphous Matrix ◽  
Nucleation And Growth ◽  
Current Interest ◽  
Amorphous Films ◽  
Electrical And Magnetic Properties

Amorphous materials are of current interest due to their desirable mechanical, electrical and magnetic properties. Furthermore, crystallizing amorphous alloys provides an avenue for discerning sequential and competitive phases thus allowing access to otherwise inaccessible crystalline structures. Previous studies have shown the benefits of using AEM to determine crystal structures and compositions of partially crystallized alloys. The present paper will discuss the AEM characterization of crystallized Cu-Ti and Ni-Ti amorphous films.Cu60Ti40: The amorphous alloy Cu60Ti40, when continuously heated, forms a simple intermediate, macrocrystalline phase which then transforms to the ordered, equilibrium Cu3Ti2 phase. However, contrary to what one would expect from kinetic considerations, isothermal annealing below the isochronal crystallization temperature results in direct nucleation and growth of Cu3Ti2 from the amorphous matrix.

Characterization of Coherent, Ordered Precipitates in Nickel-Base Alloys

1973 ◽  
Vol 31 ◽  
pp. 144-145
Author(s):  
B. H. Kear ◽  
J. M. Oblak
Keyword(s):  
Stable Phase ◽  
Nickel Base Superalloy ◽  
Alloy 718 ◽  
Commercial Alloy ◽  
Precipitate Morphology ◽  
Continuous Precipitation ◽  
Nickel Base ◽  
Base Superalloy ◽  
Strengthening Precipitate

A nickel-base superalloy is essentially a Ni/Cr solid solution hardened by additions of Al (Ti, Nb, etc.) to precipitate a coherent, ordered phase. In most commercial alloy systems, e.g. B-1900, IN-100 and Mar-M200, the stable precipitate is Ni3 (Al,Ti) γ′, with an LI2structure. In A lloy 901 the normal precipitate is metastable Nis Ti3 γ′ ; the stable phase is a hexagonal Do2 4 structure. In Alloy 718 the strengthening precipitate is metastable γ″, which has a body-centered tetragonal D022 structure.Precipitate MorphologyIn most systems the ordered γ′ phase forms by a continuous precipitation re-action, which gives rise to a uniform intragranular dispersion of precipitate particles. For zero γ/γ′ misfit, the γ′ precipitates assume a spheroidal.

The Use of Advanced Analytical Techniques for Characterization of the Chemical, Physical, and Crystallographic Nature of a Surface

1973 ◽  
Vol 31 ◽  
pp. 132-133 ◽  
Author(s):  
R. E. Herfert
Keyword(s):  
Surface Characterization ◽  
Analytical Techniques ◽  
X Ray Diffraction ◽  
Depth Of Penetration ◽  
X Ray ◽  
The Past ◽  
Transmission Electron ◽  
Scanning Electron

Studies of the nature of a surface, either metallic or nonmetallic, in the past, have been limited to the instrumentation available for these measurements. In the past, optical microscopy, replica transmission electron microscopy, electron or X-ray diffraction and optical or X-ray spectroscopy have provided the means of surface characterization. Actually, some of these techniques are not purely surface; the depth of penetration may be a few thousands of an inch. Within the last five years, instrumentation has been made available which now makes it practical for use to study the outer few 100A of layers and characterize it completely from a chemical, physical, and crystallographic standpoint. The scanning electron microscope (SEM) provides a means of viewing the surface of a material in situ to magnifications as high as 250,000X.

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