This paper presents a methodology for the allocation of natural gas. The model consists of several objective functions, a set of linear constraints, and a set of nonlinear constraints. The objective functions represent allocation in various categories and can be optimized sequentially. The linear constraints represent the conservation of flow equations for the pipeline network and various accounting relationships. The nonlinear constraints represent the momentum balance necessary for each pipe segment, compressor, or valve. The nonlinear constraints are linearized in a method similar to the method of approximate programming (MAP). A matrix generator is used to create the necessary files for the program execution. We have solved example problems with over 250 linear constraints, 240 nonlinear constraints, and 800 structural columns.

We report on the results of a recent study on the deposition of [100] textured MgO films on fused quartz substrates by using the metalorganic chemical vapor deposition technique. Magnesium β-diketonate was used as the metal source and the growth rate of the film was about 0.4 μm/h at 740 °C in a horizontal warm wall reactor. X-ray diffraction experiments provided evidence that the MgO films on fused quartz were fully textured with [100] orientation perpendicular to the substrate surface. The films had a very smooth surface morphology and optical transparency with an index of refraction of 1.71.

In aperture counters, particles in fluid suspension flow through a small orifice or aperture, causing a change in the electrical resistance of the aperture. This change is sensed by an external electronic circuit and translated into a voltage pulse, the signal height of which is proportional to the volume of the particle in the aperture. These signal pulses are collated into a spectrum of pulse heights by a multichannel pulse-height analyzer. The channel number (voltage increment) spectrum is proportional to the volume distribution of the particles sensed. A problem is that pulse height not only depends on cell volume, but also on the orientation and shape of the particle sensed and the current density along the path taken by the particle through the aperture. Uneven current density exists, primarily at the aperture entrance and exit, close to the wall. Orientation and shape of particles are altered near the wall by the unbalanced shear forces there. Toward the center of the aperture, the shear forces act so as not to induce continuous change in the orientation of the particles sensed. Thus introduction into the pulse-height spectrum of pulses that do not show a good proportionality to volume is primarily caused by particles that are traveling near the aperture wall. Residence time in the aperture for a particle traveling near the wall will be longer than that for a particle traveling down the center of the aperture, because of the smaller fluid velocity near the wall. Duration of the signal pulse created by a particle traveling near the wall will be correspondingly greater. We discuss an electronic filter to remove from the pulse-height spectrum those pulses that appear to result from particles traveling near the wall and the effect of the filter on the measured signal height and hence the volume distribution of erythrocytes. Use of this technique to characterize erythrocytes by volume distribution is described.