Variational principles of anisotropic elasticity have been applied to aggregates of randomly oriented pure-phase polycrystals having hexagonal symmetry and trigonal symmetry. The bounds of the effective elastic moduli obtained in this way show a considerable improvement over the bounds obtained by means of the Voigt and Reuss assumptions. The Hill average is found to be in most cases a good approximation when compared to the bounds found from the variational method. The new bounds reduce in their limits to the Voigt and Reuss values.
Many in vitro experiments on the biological effects of extremely low frequency (ELF) electromagnetic fields utilize a uniform external magnetic flux density (B) to expose biological materials. A significant number of researchers do not measure or estimate the resulting electric field strength (E) or current density (J) in the sample medium. The magnitude and spatial distribution of the induced E field are highly dependent on the sample geometry and its relative orientation with respect to the magnetic field. We have studied the E fields induced in several of the most frequently used laboratory culture dishes and flasks under various exposure conditions. Measurements and calculations of the E field distributions in the aqueous sample volume in the containers were performed, and a set of simple, quantitative tables was developed. These tables allow a biological researcher to determine, in a straightforward fashion, the magnitudes and distributions of the electric fields that are induced in the aqueous sample when it is subjected to a uniform, sinusoidal magnetic field of known strength and frequency. In addition, we present a novel exposure technique based on a standard organ culture dish containing two circular, concentric annular rings. Exposure of the organ culture dish to a uniform magnetic field induces different average electric fields in the liquid medium in the inner and outer rings. Results of experiments with this system, which were reported in a separate paper, have shown the dominant role of the magnetically induced E field in producing specific biological effects on cells, in vitro. These results emphasize the need to report data about the induced E field in ELF in-vitro studies, involving magnetic field exposures. Our data tables on E and J in standard containers provide simple means to enable determination of these parameters.
Measurements of ultrasonic propagation of longitudinal and shear waves over a wide frequency and temperature range were made in an homologous series of associated liquids, butanediol 1,3, 2-methyl pentanediol 2,4 and hexanetriol 1,2,6. In each case, the absorption data demonstrated the presence of shear and structural or volume viscosities which are of the same order of magnitude and have the same temperature dependence. In order to account for the shear and compressional data, it was necessary to assume that a distribution of relaxation times excited. It was found that a different distribution was necessary for the compressional data than that used in accounting for the shear relaxation data. Comparison of the average relaxation time of structural and shear processes in the associated liquids shows that they are very close in value departing by a maximum of a factor of 4. In addition, it was found that the shear modulus was about 20 to 30% of the high-frequency compressional modulus. The ratio of shear compressional modulus in these liquids was very close to the values found in typical solids, even though the magnitudes of the moduli of the liquids was about a factor of 10 smaller than found in typical solids. The temperature dependence of the shear modulus and the relaxation part of the compressional modulus was found to be the same. The moduli linearly increase with decreasing temperature in a manner which is not accounted for by the Eyring-Hirai theory. It was found that the Tobolsky-Leaderman Ferry reduction formula, which is based on the assumption that the moduli are proportional to temperature, does not hold for these liquids and probably not for any high frequency visco-elastic data not associated with an ``entropy'' modulus. The data in the associated liquids were reduced by using the proper temperature dependence of the moduli. In considering the data of high frequencies, the absorption could not be accounted for by the same distribution which was used to fit the velocity data. At frequencies well above the dispersion region it was found that an attenuation set was independent of frequency. This appears to be characteristic of these liquids at very high frequencies and viscosities. At this time, there seems to be no acceptable mechanism to explain this type of loss. The latter authors have suggested that the hysteresis effect is not related to the viscous flow mechanism causing absorption at the lower frequencies and viscosities.
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