Relaxation rate, diffusion approximation and Fick's law for inelastic scattering Boltzmann models

We consider the linear dissipative Boltzmann equation describing inelastic interactions of particles with a fixed background. For the simplified model of Maxwell molecules first, we give a complete spectral analysis, and deduce from it the optimal rate of exponential convergence to equilibrium. Moreover we show the convergence to the heat equation in the diffusive limit and compute explicitely the diffusivity. Then for the physical model of hard spheres we use a suitable entropy functional for which we prove explicit inequality between the relative entropy and the production of entropy to get exponential convergence to equilibrium with explicit rate. The proof is based on inequalities between the entropy production functional for hard spheres and Maxwell molecules. Mathematical proof of the convergence to some heat equation in the diffusive limit is also given. From the last two points we deduce the first explicit estimates on the diffusive coefficient in the Fick's law for (inelastic hard-spheres) dissipative gases.Comment: 25 page

Compensating for pneumatic distortion in pressure sensing devices

A technique of compensating for pneumatic distortion in pressure sensing devices was developed and verified. This compensation allows conventional pressure sensing technology to obtain improved unsteady pressure measurements. Pressure distortion caused by frictional attenuation and pneumatic resonance within the sensing system makes obtaining unsteady pressure measurements by conventional sensors difficult. Most distortion occurs within the pneumatic tubing which transmits pressure impulses from the aircraft's surface to the measurement transducer. To avoid pneumatic distortion, experiment designers mount the pressure sensor at the surface of the aircraft, (called in-situ mounting). In-situ transducers cannot always fit in the available space and sometimes pneumatic tubing must be run from the aircraft's surface to the pressure transducer. A technique to measure unsteady pressure data using conventional pressure sensing technology was developed. A pneumatic distortion model is reduced to a low-order, state-variable model retaining most of the dynamic characteristics of the full model. The reduced-order model is coupled with results from minimum variance estimation theory to develop an algorithm to compensate for the effects of pneumatic distortion. Both postflight and real-time algorithms are developed and evaluated using simulated and flight data

An imaging vector magnetograph for the next solar maximum

Researchers describe the conceptual design of a new imaging vector magnetograph currently being constructed at the University of Hawaii. The instrument combines a modest solar telescope with a rotating quarter-wave plate, an acousto-optical tunable prefilter as a blocker for a servo-controlled Fabry-Perot etalon, CCD cameras, and on-line digital image processing. Its high spatial resolution (1/2 arcsec pixel size) over a large field of view (5 by 5 arcmin) will be sufficient to significantly measure, for the first time, the magnetic energy dissipated in major solar flares. Its millisecond tunability and wide spectral range (5000 to 7000 A) enable nearly simultaneous vector magnetic field measurements in the gas-pressure-dominated photosphere and magnetically-dominated chromosphere, as well as effective co-alignment with Solar-A's X ray images. Researchers expect to have the instrument in operation at Mees Solar Observatory (Haleakala) in early 1991. They have chosen to use tunable filters as wavelength-selection elements in order to emphasize the spatial relationships between magnetic field elements, and to permit construction of a compact, efficient instrument. This means that spectral information must be obtained from sequences of images, which can cause line profile distortions due to effects of atmospheric seeing