Maxwell Type Research Articles

Note on a surprising result in field-mechanics

Some years ago the au thor has invest igated the classical equations of mot ion of a charged part icle which result if Mawxell 's equations are modified in a certain way (i). The t e rm (( field mechanics >) was used for these equations of motion. According to recent discussions wi th Mr. DESTOUCI-IES, Paris, and Mr. F. CAP, Innsb ruck (5) it m a y be of interest to know tha t the existence of absorptionless orbits is a general feature of field mechanics. I am s ta t ing the results here as m a t h e m a t i c a l facts wi thout intending, for the momen t , to draw any physical conclusions. J u s t like in Born 's theory (3) we have considered modified field equations ~)f Maxwell type, distinguishing between the field s trengths (~, !8) ~ (]~) and ( ~ ) ~ ( F ) . The ma in difference to Born ' s theory consists in the relat ion be tween the two field tensors, which is in our case a linear one:

Mechanical Properties of Long Chain Molecule Liquids at Ultrasonic Frequencies

Measurements have been made of the mechanical properties of long chain molecule liquids of the polyisobutylene type by means of shear and longitudinal waves in the ultrasonic frequency range. The shear waves show that these liquids behave as Maxwell relaxing liquids. The viscosity measurements in the range around 14 kilocycles check the viscosities measured by falling ball measurements within the experimental error. As the temperature decreases or the frequency increases, the reaction of the liquid shows that a shear elasticity of the Maxwell type comes into play with a shear elastic constant of from 5\ifmmode\times\else\texttimes\fi{}${10}^{6}$ dynes/${\mathrm{cm}}^{2}$ to 5\ifmmode\times\else\texttimes\fi{}${10}^{7}$. This elasticity increases with decreasing temperature and increases with chain length, and represents an intermediate type to the "frozen" type of elasticity or the "kinetic theory" type in that it has the high compliance of the "kinetic theory" type but the temperature variation of the "frozen" type of elasticity. It is suggested that this type of elasticity may be due to a composite motion of the chains, including hindered rotation within chains, as well as interaction of segments between chains. At very high frequencies this composite motion disappears and the shear stiffness becomes very high.Above about 30 kilocycles for these liquids, some shear viscosity is relaxed by the shear elasticity. Measurements with longitudinal ultrasonic waves show, however, a dispersion of velocity and an associated attenuation curve. From very low frequencies to very high frequencies the velocity increases by about 25 percent, while the attenuation has the high value of 0.7 neper per wave-length at a frequency for which the velocity is a mean between the two extremes. These measurements show that a relaxation occurs in either the shear elasticity, $\ensuremath{\mu}$, or the Lame constant, $\ensuremath{\lambda}$. Current investigations show this to be in the shear constant, $\ensuremath{\mu}$. However, the measured attenuation frequency curve is broader than that of a single relaxation frequency and moreover indicates that the attenuation reaches a constant value per wave-length at high frequencies. A simple explanation of this is that the rearrangement compliance has a hysteresis component. Calculations of the velocity and attenuation on this basis agree very well with the measured curves.