Mutual Consistency Research Articles

Free volume theories for penetrant diffusion in polymers

AbstractFree volume theories for the concentration dependence of organic penetrant diffusion coefficients in rubbery amorphous polymers have been correlated and extended with emphasis given to similarities and mathematical equivalence for small volume fractions of penetrant. The nature of the empirical parameter used in VASENIN's theory has been further clarified by considering the kinetic and thermodynamic aspects of the plasticization effect. Using similar assumptions to those originally used for rubbery polymers, VASENIN's theory is extended to treat solvent diffusion in glassy and semi‐crystalline polymers. A procedure has been developed to extend the applicability of FUJITA's theory over a wider range of polymer‐solvent composition. The general effects of plasticization leading to increase in penetrant diffusion coefficients and decrease in polymeric glass transition temperatures are considered as resulting from the same functional increase in fractional free volume of a mixture with increasing solvent content. It is suggested that the two phenomena should be quantitatively compared for mutual consistency rather than attempting to develop a fully rigorous treatment for either. In this way diffusion data can be predicted from measurements of glass temperature depression or vice versa.

Measurements of Gaseous Diffusion Coefficients

Diffusion coefficients for He-Ne, He-Ar, and 3He-4He systems have been measured as a function of temperature using a two-bulb method. The theory of the method has been developed to account for the removal of samples of nonnegligible volume for concentration analysis. The temperature range for the experimental values of the diffusion coefficients for 3He-4He has been extended to 900°K. The results of this investigation agree well with values in the literature and exhibit good mutual consistency with other transport properties. Theoretical diffusion coefficients also show reasonable agreement with the present results.

On the UniversalV-ACurrent-Current Interaction withCPViolation

A general universal V-A current-current interaction with CP violation proposed by com­ plete analogy with the ordinary weak interaction is analyzed. We propose a test of checking mutual consistency of the various components involved in the interaction; the test consists of the requirements that both the magnitude of the parity violating nuclear potential and that of the LIS=2 transition do not affect those obtained from the ordinary weak interaction. It is shown that there is still but a little possibility for this kind of interaction to satisfy our re­ quirements and that the CP violating phase difference in the amplitude of K-'~2n decay is at most 10-3 in magnitude which results in 'J+-=='Joo· A discussion is given for comparison with other similar proposals.

Analysis of Optical- and Inelastic-Electron-Scattering Data III Reflectance Data for Beryllium, Germanium, Antimony, and Bismuth

A procedure is described for simultaneously fitting reflectance data obtained for various photon energies and angles of incidence using a simple physical model for ε(ω), the complex frequency-dependent dielectric constant. The mutual consistency of the model and of the experimental data is tested, within the accuracy of each measurement. As an example of the technique, reflectance data in the vacuum ultraviolet obtained by Toots, Fowler, and Marton for Be, Ge, Sb, and Bi have been satisfactorily fitted. The model parameters have been used to derive the optical constants n and k (in satisfactory agreement with conventional determinations) and can be readily related to other relevant experimental results or theoretical calculations of ε(ω) if these are available.

The Incidence Of The Type Of Modelling On TheEvaluation Of Ductility Factors For RC BeamsAnd Columns

Reliability of the estimate of plastic deformation capacity of RC members depends on the accuracy degree of adopted analytical procedures. In particular, such accuracy degree is connected not only to the absolute approximation level of each adopted model, but also on mutual consistency of assumptions relating to the whole modelling process. The aim of the work is to assess effects due to combined adoption of models characterized by different approximation levels on the evaluation of ductility factors of RC elements. Obtained results show that an unsuitable combination of models may lead to a faulty interpretation of the investigated physical phenomenon.

Mutual consistency of the gaseous transport properties of helium-3 and helium-4 at low temperatures

Mutual consistency of the gaseous transport properties of helium-3 and helium-4 at low temperatures

Vertex functions in the dispersion theory of current algebras

Vertex functions are investigated in the dispersion theory of current algebras. The cases considered constitute a particularly simple opportunity to study the mutual consistency of the various assumptions usually used. It is demonstrated that the assumption of unsubtracted dispersion relations for integrals over matrix elements of current commutators leads to contradictions, when applied to all invariants in the kinematic decomposition of the tensors. These difficulties can be avoided only if one accepts operators of isospin one in Schwinger terms. The same contradictions are found, if in the infinitemomentum approach one admits commutators of current time and space components. The equivalence of the two approaches depends on the validity of superconvergence relations for the asymptotic behaviour of some form factors.

Spatial variations of ionospheric height at middle latitudes

A method is developed for the determination of mean ionospheric height from an analysis of radio signals from a beacon satellite. Simultaneous measurements of Faraday rotation and Doppler dispersion are combined, and their mutual consistency is coupled with the height dependence of the earth's magnetic field to calculate mean ionospheric height along the locus of satellite directions from the observing station. The method is applied to a number of satellite passes involving both normal and unusual ionospheric conditions, and profiles of height are developed over a working range of about 5° of latitude. Spatial variations of height of up to 50 km within this range are found.

Algebra of Currents and Low-EnergyKπInteraction

Using the Fubini-Furlan-Adler-Weisberger technique, sum rules have been written down for strangeness-changing and strangeness-preserving axial-vector coupling constants. Coupled together, these sum rules provide information on the low-energy interactions of strongly interacting particles. In particular the $K\ensuremath{\pi}$ system is studied and a case made for the existence of an $S$-wave resonance near threshold in the $I=\frac{1}{2}$ channel. An evaluation of the $\mathrm{KN}\ensuremath{\Lambda}$ and $\mathrm{KN}\ensuremath{\Sigma}$ coupling constants required by the mutual consistency of the sum rules is also presented.

PROTON MAGNETIC RESONANCE IN PARAMAGNETIC AND ANTIFERROMAGNETIC CoCl2∙6H2O

The transition temperature TN of CoCl2∙6H2O was measured as a function of applied field and crystal orientation using the proton resonance lines, since they are very sensitive functions of temperature near TN. TN was found to be a complicated function of the applied field and crystal orientation, which cannot be described by the molecular field approximation. The transition is gradual rather than sudden and coexistence of the NMR spectra associated with the paramagnetic and antiferromagnetic phases was observed over a temperature region of about 10−2 °K. Short-range order effects were observed near TN in the form of anomalous broadening of the magnetic resonance lines. The magnetic susceptibility in zero field was measured along the preferred axis of antiferromagnetic alignment. This, together with specific heat data from published literature, was used to show a mutual consistency between thermodynamic variables and the dependence of TN on H in low fields as obtained by NMR. The treatment follows that of Buckingham and Fairbank for the λ transition in liquid helium. The sublattice magnetization in the antiferromagnetic phase was measured as a function of temperature. It was found to depend logarithmically on (TN – T), for all values of applied field.

Ammonia Masers

Operating characteristics of ammonia masers on the 3,2 line of N14H 3 and on the 3,3 line of N15 H 3 are described. Experimental and theoretical results on the stability, resettability and mutual consistency of ammonia masers are discussed. A method of manual tuning of the cavity by the magnetic perturbation of about 2 oersteds on the 3,2 line of N14H 3 ensures a resettability of the frequency within a few parts in 1011. A system of automatic cavity tuning for a pair of masers has been accomplished which allows higher accuracy. Various types of frequency shifts and fluctuations are considered and methods of reducing them are discussed. Numerical evaluations of the stability and reproducibility of the ammonia maser are compared with the hydrogen maser.

Sur la biogenèse de la pyrimidine de la thiamine

Climatological mean monthly distributions of pH in the total H+ scale, total CO2 concentration (TCO2), and the degree of CaCO3 saturation for the global surface ocean waters (excluding coastal areas) are calculated using a data set for pCO2, alkalinity and nutrient concentrations in surface waters (depths < 50 m), which is built upon the GLODAP, CARINA and LDEO databases. The mutual consistency among these measured parameters is demonstrated using the inorganic carbon chemistry model with the dissociation constants for carbonic acid by Lueker et al. (2000) and for boric acid by Dickson (1990). Linear potential alkalinity-salinity relationships are established for 24 regions of the global ocean. The mean monthly distributions of pH and carbon chemistry parameters for the reference year 2005 are computed using the climatological mean monthly pCO2 data adjusted to a reference year 2005 and the alkalinity estimated from the potential alkalinity-salinity relationships. The equatorial zone (4°N-4°S) of the Pacific is excluded from the analysis because of the large interannual changes associated with ENSO events. The pH thus calculated ranges from 7.9 to 8.2. Lower values are located in the upwelling regions in the tropical Pacific and in the Arabian and Bering Seas; higher values are found in the subpolar and polar waters during the spring-summer months of intense photosynthetic production. The vast areas of subtropical oceans have seasonally varying pH values ranging from 8.05 during warmer months to 8.15 during colder months. The warm tropical and subtropical waters are supersaturated by a factor of as much as 4.2 with respect to aragonite and 6.3 for calcite, whereas the cold subpolar and polar waters are supersaturated by 1.2 for aragonite and 2.0 for calcite because of the lower pH values resulting from greater TCO2 concentrations. In the western Arctic Ocean, aragonite undersaturation is observed. The time-series data from the Bermuda (BATS), Hawaii (HOT), Canary (ESTOC) and the Drake Passage show that pH has been declining at a mean rate of about -0.02 pH per decade, and that pCO2 has been increasing at about 19 μatm per decade tracking the atmospheric pCO2 increase rate. This suggests that the ocean acidification is caused primarily by the uptake of atmospheric CO2. The relative importance of the four environmental drivers (temperature, salinity, alkalinity and total CO2 concentration) controlling the seasonal variability of carbonate chemistry at these sites is quantitatively assessed. The ocean carbon chemistry is governed sensitively by the TA/TCO2 ratio, and the rate of change in TA is equally important for the future ocean environment as is the TCO2 in ocean waters increases in the future.

Relativity and Electromagnetism: An Epistemological Appraisal

This paper follows up the analysis of relativity theory begun by Margenau and Mould, by including electromagnetic theory which in their treatment was tacitly accepted. It is shown that the experiments on which Margenau and Mould rely to establish the special theory of relativity actually confirm the mutual consistency of the Maxwell-Lorentz electromagnetic theory and the special relativity theory, but throw no light on the validity of the two theories taken jointly. It is further shown that a modification of the rules of correspondence between the mathematical structure of the theories and immediate experience would bring the theories into agreement with an alternative relativity theory based on the Galilean instead of the Lorentz transformation. An experiment is suggested by which the need for such modification can be tested. A proof is then given that the rules of correspondence between the concepts of the special relativity theory (and therefore of current electromagnetic theory) and experience are not self-consistent, so that some modification of current ideas is essential. It is suggested that a generalisation of Maxwell's theory, in terms of Faraday's “ray vibrations” instead of Lorentz's static ether, might provide a satisfactory basis for a relativistic electromagnetic theory.

Histochemical methods for calcium.

An account is given of an investigation of histochemical methods for calcium using standard test tissues (McGee-Russell, 1957) known to contain calcium salts, as test objects upon which to assess the success, reproducibility, and mutual consistency of methods. The methods for the revelation of calcium in the literature fall into two groups: metal substitution techniques, and dye-lake reactions. Published methods have been tested and many have been found of little use for cytological investigations. A set of six metal substitution techniques, including a new copper dithioxamide method, has been established as giving useful results. The empirical basis of the staining reactions for calcium with dyestuffs has been investigated, and sensitive and specific techniques using anthraquinone derivatives are outlined. The significance of pH in dye-lake reactions is emphasized, and it is pointed out that previous results with anthraquinone dyestuffs have been achieved by an empirical adjustment of pH in the staining solution. The necessity of making a distinction between the formation of a dye-lake precipitate as a true histochemical positive, and staining effects which may occur upon tissue components in the neighborhood of calcium deposits, through the interaction of the dye, the dye-lake, the calcium salt, and the matrix, is stressed. An oxazin dyestuff, gallamine blue, recently introduced for the staining of calcium deposits, was found to be inconsistent in its results, and capable of giving misleading information. Its general use is not recommended. The possibility of studying calcium deposits by means of the presence of contaminating metals is considered. The reagent sodium rhodizonate was found to give very fine localization of known calcium deposits in a number of tissues.

A method of interpolating magnetic data under conditions of mutual consistency

Because of the discreteness of the data obtained in magnetic surveys, it is necessary to interpolate between measured points before charts can be drawn. Rigorous relations connecting surface variations of different elements are herein introduced into the interpolation formulas, so that the resulting charts are mutually consistent. Related elements are continued by a power series in which the unknown coefficients are computed under the conditions for consistency.

Note on the adjustment of isomagnetic charts to mutual consistency

Precise aeromagnetic measurements of total magnetic intensity permit the construction of isomagnetic charts which are mutually consistent in the horizontal and vertical components of the geomagnetic fields. Equations incorporating this new result are provided.

Dielectric Dispersion in Materials Having a Distribution of Relaxation Times

On the basis of considerable experimental evidence, a particular form for the dielectric loss factor, ε″, is assumed to hold for many materials exhibiting a distribution of relaxation times. The dielectric constant, ε′, corresponding to the assumed form of ε″ is then computed by means of the Kronig-Kramers relations and tabulated as a function of log frequency and of the distribution function half-width parameter, α. Using these results, experimental ε′ and ε″ curves can be easily tested for mutual consistency and can be fitted individually. In conclusion, a brief discussion of other methods of dealing with the many-relaxation-time dispersion problem is given.

On the mutual consistency of magnetic charts

Introduction— This paper is the result of a study to find and apply a method of improving the accuracy of world isomagnetic and isoporic charts using only the data provided in the original construction, the final results to be in accord with the requirements of electromagnetic theory. It contains, mainly, an appraisal of the curl‐test for mutual consistency of magnetic charts which was proposed and used by Chapman [see 1 of “References” at end of paper].This statement of the problem does not presume that the cartographer did not make the best use (by reference to the criteria he actually employed) of the data at his disposal, but rather that certain conditions provided by theory were ignored. Consider, for example, the world‐charts for horizontal intensity (H) and declination (D) [or north intensity (X) and east intensity (Y)]. Each is drawn separately, the contours of the one being sketched without reference to the other, and the curves then are smoothed visually. The observations upon which the charts are based are poorly distributed, of varying reliability, and no trustworthy observations at all obtain for some significantly large areas. The main function of the test for consistency and scheme of adjustment is to assist in improving chart‐values in the poorly surveyed regions.

The mutual consistency of successive monthly means of declination, Huancayo Magnetic Observatory

In reducing the declination‐records for 1942 of the Huancayo Magnetic Observatory of the Department of Terrestrial Magnetism, Carnegie Institution of Washington, the changes in base‐line values appeared to be somewhat larger than usual. Thus the adopted base‐line during January 1 to 10, 1942, was 6° 33′.0 east and the observed values of declination required a regular progression of changes to May 15, when for the next succeeding 20 days the adopted base‐line was 6° 33′.9. Hence the excellence of adopted base‐lines was tested by plotting the monthly means. Vestine, in his article “Reduction of magnetic observations to epoch” [Terr. Mag., 47, 97–113 (1942)], has pointed out that “the geomagnetic east component of the departures is small in all latitudes.”

Notes on Isomagnetic Charts: VIII—The Mutual Consistency of the Declination and Horizontal‐Intensity Isoporic Charts

Summary—The rate of change of the vertical component of the earth‐air electric current‐density i is expressed in terms of the surface‐gradients of the rates of change of the horizontal magnetic elements X and Y or D and H: the formulas enable (di/dt) to be calculated from the distribution of the isomagnetic and isoporic lines for these elements. It is shown that if the directions and spacing of the isoporic lines are seriously uncertain, (di/dt) should be found, from the magnetic charts, to have a value of order five milliamperes per km2 per year; this is confirmed by calculations based on the Admiralty charts for 1922, the Fisk isoporic charts for the same epoch, and the Swedish magnetic surveys of epochs 1929.5 and 1936.5. The actual value of (di/dt) is inferred, from atmospheric‐electric observations, to be at most 10−4, so that these much larger calculated values of (di/dt) indicate errors in the isoporic charts.