Logarithm Of Resistivity Research Articles

D.C. Resistance Moisture Meters for Wood

SYNOPSIS Regression equations are given for the relationship between logarithm of resistance measured with pin electrodes and reciprocal of absolute temperature for Pinus pinaster and P. radiata. The most important finding of the present work was that the relationship between log R and 1/T at lower moisture contents was curvilinear and not linear as found by most other workers. The curvilinear relationship at higher moisture contents was also confirmed by the present results. Regression equations expressing the functional relationship between log R and moisture content at various temperatures are also given for the two species as well as a set of pooled regression equations which permit the design of a temperature compensated moisture meter for P. pinaster and P. radiata.

Hydraulic Resistance of Artificial Strip Roughness

An experimental study of two-dimensional flow over non-uniform roughness is reported in which artificial strip roughness was employed. The roughness elements were square in cross section and placed at different relative spacings. A six-fold classification system is suggested based upon the ideas of Morris and Adachi. Resistance data from other investigators is also considered, and the variation of resistance coefficient with Reynolds number, relative spacing, and relative depth examined. The general resistance parameter, X, first introduced by Sayre and Albertson is found to be particularly helpful in synthesizing the various sets of resistance data. Logarithmic resistance equations involving X are validated over a wide range of roughness wavelength to height ratio. The relationship between roughness height and Nikuradse's equivalent sand roughness size is also examined.

Disappearance of the kondo effect of Ce impurities in (La, Th) based alloys

We present an experimental study of the resistivity at low temperature of (La, Th) based alloys with Ce impurities. We observe a logarithmic behaviour of the resistivity vs temperature at low concentration of Th. When we increase the concentration of Th, the magnetic resistivity is no longer logarithmic but linear with T, and at still higher concentrations of Th, the anomaly in the resistivity disappears. Moreover, the curve of the slope of the logarithmic resistivity vs the concentration of Th goes through a maximum for 20% Th before vanishing for 50% Th.

Low temperature magneto-resistance, logarithmic resistivity rise and anisotropic superconductivity in TaS 2(pyridine) [formula omitted

The superconducting intercalation complex TaS 2(pyridine) 1 2 has received considerable attention as a prototype of two dimensional superconductivity. In this material we have detected a substantial, anisotropic magneto-resistance 11 K° above the superconducting transition and an anisotropic logarithmic resistivity rise below 20°K. The resistively measured superconducting transition temperature is also anisotropic. T c is the lowest when the current is perpendicular to the layers.

Statistical Properties of Missouri River Bed Forms

A logarithmic resistance relationship for flow near rough boundaries was formulated which relates bed form dimensions to flow resistance in large alluvial channels with dune beds. Bed profile data, obtained from a reach of the Missouri River at Omaha, NE, were analyzed statistically to obtain characteristic bed form dimensions. Different statistical techniques were explored and the zero-crossing distances and amplitudes analysis is shown to be the one best suited for this investigation. Estimates of bed form dimensions obtained form the preceding analyses together with frequency distributions of bed elevations, wave lengths, amplitudes and heights of the dune bed forms are presented. A plot of the bed form friction factor versus a modified relative roughness parameter incorporating statistical estimates of bed form dimensions is presented and is shown to be roughly consistent with the Karman-Prandtl logarithmic law.

Formulation of Mathematical Watershed-Flow Model

In a macroscopic hydrodynamic approach, a set of one-dimensional spatially varied unsteady flow equations, that include terms for lateral mass flux, lateral momentum flux, overpressure head due to raindrop impact, and boundary shear, are derived from the equation of continuity and the Navier-Stokes equations for the three-dimensional flow of viscous incompressible fluid in cooperation with the kinematic and dynamic boundary conditions on the water and ground surfaces of a watershed. The Darcy-Weisbach equation is employed to evaluate the friction slope, and the laminar uniform flow equation for the Darcy-Weisbach friction coefficient coupled with the Karman-Prandtl logarithmic resistance equation for turbulent flow is used to simulate, as a first approximation, the unknown function of the Darcy-Weisbach friction coefficient for watershed surface flow. The proposed mathematical model for watershed surface flow consists of a set of quasilinear partial differential flow equations of hyperbolic type with the appropriately prescribed initial and boundary conditions.

Quenched‐in Electrical Resistivity of Dilute Binary Alloys

AbstractThe quenched‐in electrical resistivity of dilute binary alloys has been calculated, assuming that the alloy system contains single vacancies, di‐vacancies, single solutes (impurities), di‐solutes, and solute—vacancy pairs in an otherwise perfect matrix. Some numerical computations have been made for dilute binary alloys of Au. By assuming that the electrical resistance of a point defect in the paired or associated state is less than that of the unpaired or single state, it is shown that the solutes do have a significant effect on the quenched‐in electrical resistivity if the perturbation introduced into the alloy by the solutes is large. For instance, the change of the binding energy or the concentration of solute‐vacancy pairs will change the slope of the curves in the logarithmic resistivity vs. reciprocal temperature plot and the contribution due to di‐solutes will give rise to a non‐linearity of the curves at lower quenching temperatures. The results are discussed in the light of experimental observations.

Electron tunneling in carbon blacks

Volume and electrical resistance of a series of representative carbon blacks have been determined over a pressure range of 10–8000 p.s.i. The relation between logarithm of resistance and cube root of specific volume is linear for all blacks over the entire range investigated. The lines for furnace blacks intersect by extrapolation in a single point, corresponding to an open packing at the resistance of solid carbon, independent of the presence of particle chains. These results are incompatible with a through-going path concept of electrical conductance. It is shown that field emission and electron tunneling through gaps may account quantitatively for the observed phenomena.

A Method of Analyzing Electrical Logs Recorded on a Logarithmic Scale

Abstract A minimum of three resistivity measurements are necessary to estimate the influence of invasion and thereby assure an adequate determination of Rt. This requirement is fulfilled by the Dual Induction-Laterolog, the first modern logging tool to combine three focused resistivity devices. The three resistivity curves are recorded simultaneously on a logarithmic resistivity scale. Proportional dividers can be used to obtain ratios and products of the resistivity measurements by treating the logarithmic scale in a manner similar to the principle of the slide rule. This leads to a very quick, easy and mechanical method of determining Di, Rt, Rxo. and estimates of Sw. These values are obtained as plots directly on the log, thus providing a permanent record that is an integral part of the log itself. The method significantly reduces interpretation time by eliminating the necessities of making calculations and reading scales. Also, the accuracy of the log is more nearly maintained, particularly since interpolation is mechanical rather than interpretive. Thin-bed corrections and borehole-enlargement corrections are also greatly simplified. It is believed that the use of the proportional divider techniques with logarithmic resistivity scales will significantly improve the otherwise time-consuming task of log analysis. Introduction To determine true formation resistivity has always been a fundamental problem in quantitative log analysis. Modern induction logs have simplified this problem for cases of moderate invasion so that a value adequately close to R is often recorded directly. However, the problem remains that one cannot be sure that the recorded resistivity is adequately close to Rt, and too often the analyst fails to recognize when it is not. The Dual Induction-Laterolog is an important step forward in obtaining adequate values of Rt for invaded formations. This logging sonde includes three focused resistivity devices:a Laterolog (LLs) which has a comparatively shallow depth of investigation (resistivity designated RLLs);an induction log (ILm) which has a moderate depth of investigation (resistivity designated RILm); andan induction log (ILd) which has a depth of investigation about twice as large as ILm (resistivity designated RILd). Resistivities from these three devices are recorded simultaneously on a logarithmic scale. In effect, the Dual Induction-Laterolog provides three "equations", each containing the three variables Di, Rxo and Rt. This assumes a simple frontal invasion pattern; that is, a permeable formation with a homogeneous invaded zone of resistivity Rxo extending to a diameter Di, beyond which lies a homogeneous zone of true formation resistivity Rt. A simultaneous solution of the three "equations" to obtain Di, Rxo and R is shown as Fig 1. A fullscale reproduction of Fig. 1 is shown in the Appendix. The purpose of the paper is to introduce a simple, quick and accurate method of mechanically determining Di, Rxo, and Rt, and of estimating water saturation. With this method, the time-consuming necessities of mathematical manipulation and the reading and interpolation of numerical values are essentially eliminated. A systematic procedure of log analysis develops from this method. The proposed method utilizes the logarithmic resistivity scale from which ratios of resistivity values can be extracted in a manner similar to the principle of the slide rule. That is, the distance between two resistivity curves represents the logarithm of the ratio of the two resistivities, inasmuch as the logarithm of a ratio is expressed by subtracting the logarithm of the denominator from the logarithm of the numerator. This distance can be extracted with a pair of proportional dividers. Similarly, the proportional dividers can be used to enter this ratio into the logarithmic scale of an interpretation chart. With this idea as a beginning, the technique can be expanded into a systematic method of determining Di, Rxo, Rt and Rxo/Rt. Continuous plots of Rt and Rxo/Rt can be quickly made on the log. Estimates of water saturation Sw can be made directly from the Rxo/Rt plot and, in this manner, possible oil-bearing zones can be isolated. With the Rt plot and a porosity log, the value of Sw can be verified. JPT P. 844^

SUGGESTIONS FOR BETTER ELECTRIC LOG COMBINATIONS AND IMPROVED INTERPRETATIONS

In modern electrical logging, several resistivity measuring devices are now available or are under development which cover a wide range of radial investigations. In order of increasing penetration, they include: a) The Proximity Log (a new tool for recording formation resistivity close to the wall of the hole). b) A new type of Laterolog having a shallow investigation and adapted for simultaneous recording with an Induction Log. c) An Induction Log appropriate for moderate invasion (e.g., the present 5FF40). d) A deep investigation Induction Log (e.g., the new 6FF40). All these devices have a high vertical resolution, and their readings are practically unaffected by the mud column. This paper deals essentially with the case of logging in fresh mud. A discussion is presented of the information which can be obtained on saturation, when combinations of respectively two, three, or four of the above listed devices are used. The general case where nothing is known about the depth of invasion is first considered: The combination of the Laterolog and deep investigation Induction Log, when compared with SP curve, permits visual recognition of most salt‐water‐bearing beds. With the addition of the Proximity Log, and medium investigation Induction Log, the effect of invasion can be estimated and the distinction of practically all water‐bearing and oil‐bearing beds is made possible. The possible presence of a low resistivity zone beyond the invaded zone can be detected and accounted for. The ratio [Formula: see text] can be determined, from which an estimation of saturation can be made. The value of [Formula: see text] can be furthermore derived, which gives another way of computing saturation if the formation factor can also be obtained, for example from the porosity given by a Sonic Log. In these combinations the 16 inch normal can be used instead of the Laterolog, when bed resistivities are not too high. In those regions where the depth of invasion is known from local experience, one or even two of the above devices can be omitted. The advantage of a logarithmic resistivity scale for a convenient and rapid visual interpretation of the logs is explained. Charts to be used in the above procedures are shown, and the discussion is illustrated with field examples.

Oscillator Strengths in the Far Ultraviolet. I. Nitric Oxide

Absolute integrated absorption intensities have been measured for the nitric oxide beta, gamma, delta, and epsilon bands in the range 1700 to 2300 A. From these data the electronic absorption oscillator strengths of the beta and gamma band systems have been calculated to be 0.00151±7% and 0.00240±5%, respectively. The experimental method involved the photometric detection of pressure broadened nitric oxide spectra. Also described is the construction of a logarithmic load resistance which allows the direct tracing of spectra in absorbance units.

On the Electrical Conductivity of Some Alkaline Earth Titanates

The compounds Mg2TiO4, MgTiO3, MgTi2O5, CaTiO3, SrTiO3, and BaTiO3 were prepared in crystalline form by reactions in the solid state. The rod-shaped samples were sintered in oxygen at 1450°C and reduced in hydrogen at temperatures from 560°C to 1400°C producing n type semiconductors. Resistivity values from 10−1 to 108Ω·cm at 25°C were obtained. Reductions of about 3 percent by weight could be given the most reduced magnesium titanates while the largest reduction obtainable in CaTiO3, SrTiO3, or BaTiO3 was less than 0.25 percent. The logarithm of resistivity was plotted versus reciprocal absolute temperature and showed a linear dependence in most cases over a wide range of temperature and resistivity. The curves for BaTiO3 changed the slope abruptly at approximately 115°C, probably attributable to the crystal structure change at the Curie temperature, about 120°C. The dependences of impurity activation energy and Fermi level on percent reduction were determined for the case of Mg2TiO4. The Biltz-Meyer rule, stating a linear relationship of impurity activation energy with resistivity at a reference temperature, was not obeyed over the large range of reductions obtained.