Hole curvature

Glossary 1079. Dogleg Severity (Hole Curvature) Calculations 1083. Deflection Tool Orientation 1085. Three-Dimensional Deflecting Model 1088. 

Based on work done by A. Lubinski, J. E. Hansford and R. W. Nicholson (API RP 7G, Section 6), gives the formula for the maximum permissible hole curvature in order to avoid fatigue damage to drill pipe. 

Calculate the maximum permissible hole curvature for data as below ... 

Hole curvature Refers to changes in inclination and direction of the borehole. 

In certain sense ELFbe can be seen as a modified version of the approach of Luken and Culberson (cf. Sect. 2.3). Both approaches refer to the Fermi hole curvature and both need a reference system, chosen to be the uniform electron gas. However, there are two major differences between the approaches. Although the Fermi hole mobility function of Luken and Culberson is governed by the Fermi hole curvature, in their model the sensitivity of the Fermi hole shape to the change of the position of the reference electron is analyzed, whereas Becke and Edgecombe ask for the probability density to find an electron with respect to examined reference position (with simple words, in case of ELFbe the reference electron is not meant to move). Moreover, Luken and Culberson chose the subtraction for the comparison with the uniform electron gas, whereas Becke and Edgecombe preferred the division. 

Soon after the appearance of the ELF, some interesting interpretations and remarks were given by Dobson [41]. He stated that the kernel of the ELF formula (cf. Eqs. (10) and (11)) is valid for states with zero Schrodinger current density, which explicitly means that time dependency would change the formula. Additionally, Dobson connected the Fermi hole curvature with the kinetic energy of the relative motion of same-spin electron pairs. 

In another interpretation Dobson pointed out that the Fermi hole curvature is related to the conditional number of same-spin electrons within a small sphere of radius R around the reference electron. This number of other same-spin electrons is given by the integral of conditional pair density within the sphere. The integral can be determined from the Taylor expansion of the pair density around the reference position. In this way the particle numbers enter the scene, replacing the probability... 

As the 2-particle control functimi can serve, for instance, the same-spin electron pair density, />f"(ri,r2) normalized to the total number of spin electron pairs NaiNg— l)/2. The integral of the same-spin pair density over each micro-cell volume yields the number of same-spin pairs in the micro-cell. As will be shown later, the number of pairs U,- can be approximated by the integral of the pair density Laplacian (in which case 5c = 8/3 and tc(r,) is the Fermi hole curvature). The number of micro-cells with Uf" restricted to the value coo could be determined if the number of pairs formed between the micro-cells would be known as well. 

The negative electron and light hole masses Hsted for HgTe are a consequence of its being a semimetal rather than semiconductor. The curvatures of these two bands are inverted with respect to the convention defined for semiconductors. 

Concerning the nature and structure of such amyloid peptide or protein channels, oligomers with annular morphologies have in fact been observed by EM for a-synuclein (Lashuel et al., 2002) and equine lysozyme (Malisauskas et al., 2003) even in the absence of any lipids or membranes. Channel-like structures have also been reconstituted in liposomes and observed by SFM for A/ i 4o, A/ j 42, human amylin, a-synuclein, ABri, ADan, and serum amyloid A (Fig. 5A Lin et al., 2001 Quist et al., 2005). Doughnut-shaped structures with a diameter of 10-12 nm and a central hole size of 1-2 nm (Fig. 5B) were imaged on top of lipid membranes (Quist et al., 2005). However, the radius of curvature of the SFM tips meant that it is not possible to say whether the pores were really traversing the lipid bilayer. 

The method of caustics has also been used to study the formation of cracks and crazes formed by exposure of PMMA to solvents (259). ISO 4599 (260) has been developed to better control the application of stress using a jig having the curve of the arc of a circle for shaping the specimen and maintaining a set curvature during exposure to the agent. After a predetermined time the specimen is tested for tensile or flexural properties and compared to preexposure test values. ISO 4600 (261) uses the technique of impressing an oversized ball or pin into a hole drilled in the specimen to apply a strain. 

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