We obtain exact exterior and matching interior stationary axially symmehic solutions of the Einstein-Maxwell field equations. for rigidly rotating charged dust with vanishing Lorentz force. The solutions generate two sources, an infinitely long cylinder of charged dust rigidly rotating about its axis, and a surface layer with surface 4-cunent located on a singular hypersurface perpendicular to the axis of the cylinder at the origin of the coordinate system. The surface layer extends from the interior of the cylinder to the exterior, but the physical components of its surface sms-energy tensor and surface 4-cunenc vanish at infinite radial distances on the hypersurhce, in any direetion away from the origin The mass and charge densities of the cylinder, also vanish at infinite distances away from either side ofthe hypersurface The solutions are physically significant, because both sources of spacetime represent physically reasonable matter with well defined matter, elecuomagnetic and surface stressenergy tensors. whose physical components vanish at spatial infinity. The junction conditions on the hypersurface separating the exterior from the interior spacetime, and the more complicated set of junction conditions on the singular hypersurface. are satisfied. An analysis by means of the physical components of the Riemann CurfaNre tensor, shows that there a x no sinphities on the rotation axis and that spacetime is asymptotically Rat everywhere at sparial infinity.
A theoretical analysis and the results of the experimental verification of the adsorption-desorption process for ethanol dehydration are presented. This adsorption-desorption process is applied in industrial installations for the production of dehydrated ethanol as a fuel additive.In the present work, the experiments were performed using a small-scale experimental setup. The sequence of operations consisted of adsorption, vacuum desorption and purge. The adsorption column, filled with zeolite 3A pellets, was fed with a vapour-phase ethanol/water mixture containing 25 mol% water. The water vapour content at the column outlet was determined using gas chromatography. During the vacuum desorption step, the upper outlet of the column was connected to a vacuum pump. During the purge step, the lower outlet of the column was connected to a vessel containing pure ethanol while the upper outlet was connected to the vacuum pump.The process simulation results using the developed model have been compared with the experimental results in order to verify accuracy of the model. The agreement between the experimental and theoretical results demonstrated that the mathematical model adequately described the process.
A stationary axially symmetric exterior electrovacuum solution of the Einstein-Maxwell field equations was obtained. An interior solution for rotating charged dust with vanishing Lorentz force was also obtained. The two spacetimes are separated by a boundary which is a surface layer with surface stress-energy tensor and surface electric 4-current. The layer is the spherical surface bounding the charged matter. It was further shown, that all the exterior physical quantities vanished at the asymptotic spatial infinity where spacetime was shown to be flat. There are two different sets of junction conditions: the electromagnetic junction conditions, which were expressed in the traditional 3-dimensional form of classical electromagnetic theory; and the considerably more complicated gravitational junction conditions. It was shown that both—the electromagnetic and gravitational junction conditions—were satisfied. The mass, charge and angular momentum were determined from the metric. Exact analytical formulae for the dipole moment and gyromagnetic ratio were also derived. The conditions, under which the latter formulae gave Blackett’s empirical result for rotating stars, were investigated
We obtain two alternative forms of the dispersion relation for electron Bernstein waves in a relativistic plasma, propagating at right angles to the equilibrium magnetic field. We show that its low-temperature limit leads to the well known classical result. The dispersion relations obtained could be important if electron Bernstein waves are to be used in the heating of a plasma to relativistic energies.
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