Use Of Scaling Factors Research Articles

An interlaboratory study to test instrument performance of hydrogen dual-inlet isotope-ratio mass spectrometers.

An interlaboratory comparison of forty isotope-ratio mass spectrometers of different ages from several vendors has been performed to test 2H/1H performance with hydrogen gases of three different isotopic compositions. The isotope-ratio results (unsufficiently corrected for H3+ contribution to the m/z = 3 collector, uncorrected for valve leakage in the change-over valves, etc.) expressed relative to one of these three gases covered a wide range of values: -630% to -790% for the second gas and -368% to -462% for the third gas. After normalizing the isotopic abundances of these test gases (linearly adjusting the delta values so that the gases with the lowest and highest 2H content were identical for all laboratories), the standard deviation of the 40 measurements of the intermediate gas was a remarkably low 0.85%. It is concluded that the use of scaling factors is mandatory for providing accurate internationally comparable isotope-abundance values. Linear scaling for the isotope-ratio scales of gaseous hydrogen mass spectrometers is completely adequate.

Ab initio and density functional calculations of mean-square amplitudes of vibration for benzene and cubane

Mean-square amplitudes of vibration were calculated using ab initio and density functional methods for benzene and cubane. Both 6-31G ∗ and 6-311G ∗∗ basis sets were employed. It was found that significant improvements were achieved when electron correlation was introduced, even if only at the local density functional level. The mean-square amplitudes calculated were not effected by the basis set used for benzene and slightly improved for the highly strained cubane molecule when the larger basis set was used. An attempt was also made to improve the calculated mean-square amplitudes by making use of scale factors found in the literature, which were developed to improve the calculated frequencies. It was found that only the SCF mean-square amplitudes were significantly improved.

The Use of Scale Factors in Map Analysis An Elementary Approach

Throughout human history there has been a close connection between mathematics and cartography to the benefit of both disciplines. Yet most undergraduate students in both areas are unaware of it. In this paper, itself a cooperative effort between a cartographer and a mathematician, we hope to show that mathematical ideas available to many first-year college students can be used to analyze properties of some commonly used map projections. Specifically, our principal mathematical tool is the Calculus of functions of a single variable. After giving a proof, using only high-school algebra and trigonometry, that there can be no fixed-scale flat map of the earth, we demonstrate how the Calculus can be used to compute the scale factors along meridians and parallels for selected cylindrical and azimuthal projections. Conditions that these scale factors should satisfy for a projection to be either conformal or equal-area are then discussed, and canonical examples of each type are exhibited. Finally, we use scale factors to analyze how each projection distorts areas and angles, and discuss how the classic tool known as Tissot's indicatrix applies to this setting.

On the Use of Scaling Factors to Improve Interspecies Extrapolation of Acute Toxicity in Birds

In avian toxicology, it is customary to extrapolate between species on the basis of acute toxicity measurements expressed in mg/kg body weight. Recently, it has been suggested that extrapolations should be on the basis of weight raised to the 0.6–0.7 power because there is good empirical evidence that, for mammals, this produces the best agreement between species. We used an avian LD50database to derive empirically the appropriate scaling factor for birds. With a subset of 37 pesticides of varying structures but heavily weighted to cholinesterase inhibitors, we found that the appropriate scaling factor in birds is usually higher than 1 and can be as high as 1.55. Extrapolations on the basis of weight alone or, worse, the use of inappropriate mammalian scaling factors could lead to serious underprotection of small-bodied bird species modeled in the course of risk assessment procedures.

Studies on Important Radionuclides for the Safety of a Radioactive Waste Disposal Site: Correlation Between Easily Measurable Gamma Emitters and Long-Lived Radionuclides

To comply with the regulations laid down by the French safety authorities for a national surface disposal site, one must obtain a good evaluation of the activity of the long-lived nuclides in each individual package. Because this cannot be done on a routine basis by direct nondestructive measurements, experiments are being conducted in France to calculate the activity of long-lived nuclides from the measured activity of “key” nuclides (60Co and 137Cs). This is achieved through the use of scaling factors and correlation functions that are calculated from the analysis of a limited number of representative waste samples. The first results obtained for some typical French pressurized water reactor radioactive wastes, including ion-exchange resins, evaporator concentrates, and filter cartridges, are presented. Significant correlations are observed for the 63Ni/60Co and 94Nb/60Co nuclide pairs, while I4C does not seem to correlate with 60Co. A good correlation between 137Cs and 90Sr is established for resins, while in the case of filters, only a tendency to correlation appears. This evaluation work is only at a preliminary stage, and much improvement of the results presented here is expected from research programs being carried out in this field by Electricité de France, Commissariat a l’Energie Atomique, and the French National Agency for Radioactive Waste Management in cooperation with the Commission of the European Communities.

Stochastic approach of soil water flow through the use of scaling factors: Measurement and simulation

The method of scaling, which is extensively used in hydraulics and fluid mechanics, has not been widely developed in soil physics, most probably due to the fact that vigorous assumptions are rarely met in nature. It will, however, be shown that heterogeneity from location to location within a field or at the scale of a watershed may be approximated with the use of a scaling coefficient for each site.

A corresponding-states examination of the equations of state of liquid argon, krypton, and xenon

Recent experimental PVT results for liquid argon, krypton and xenon have been used to examine how closely these three liquids conform to a single reduced equation of state. Reduced molar volumes have been compared at rounded values of T/ T c and P/ P c, over virtually the entire liquid range, using two different sets of reducing parameters: (1) two empirically determined, dimensionless scale factors related to the characteristic energy and length parameters ε and σ of the intermolecular field; and (2) the critical constants T c, P c, V c. The use of scale factors requires no a priori knowledge of the values of any characteristic constants. With the scale factors adjusted to obtain the best agreement, the reduced volumes of all three liquids agree on average to within one or two parts per thousand, which is comparable with the accuracy of the experimental data. A comparison based on literature values of the critical constants leads to differences in reduced volume as large as two per cent; however, by allowing all nine critical constants to “float” to get the best agreement, the average difference is again reduced to one or two parts per thousand, and the optimum values of the two sets of reducing parameters are seen to be equivalent. Although the values of the critical constants which give the best agreement between the reduced volumes fall within the expected error bounds of experimental values, one cannot assert that they are superior to the experimental values, owing to uncertainty concerning the extent of real departures from corresponding states. Evidence of the existence of small, systematic, real departures from corresponding states is presented, and possible causes of these departures are briefly discussed.

Elastic Surface Wave Guidance by (Δv/v) Effect Guidance Structures

The possibility of utilizing guided surface acoustic waves in signal processing devices has generated interest in basic investigations of guidance mechanisms and structures for surface acoustic waves. Surface wave propagation, investigated in detail thus far in guidance structures, has unfortunately proven sufficiently dispersive to rule out many practical device applications. Reported here are theoretical investigations of the basic physical phenomena of a (Δv/v) guidance structure which is substantially nondispersive. Acoustic guidance in the (Δv/v) structure is assumed to be due principally to the velocity reduction Δv of a thin conducting strip on a piezoelectric substrate. With this assumption, major features of (Δv/v) guidance can be predicted theoretically from an isotropic nonpiezoelectric model which incorporates the velocity difference Δv. Numerical results are presented for quartz and lithium niobate. In addition, a generalized description for guided waves is developed which is approximately independent of the (Δv/v) velocity ratio. Thus, with the use of scaling factors, the normalized data are applicable to materials with a range of (Δv/v) ratios. Simply put, our principal conclusion is that for many common piezoelectrics, strong guidance and low dispersion are theoretically predicted. Basic experimental investigations thus appear warranted.