Crystallization of random trigonometric polynomials

We give a precise measure of the rate at which repeated differentiation of a random trigonometric polynomial causes the roots of the function to approach equal spacing. This can be viewed as a toy model of crystallization in one dimension. In particular we determine the asymptotics of the distribution of the roots around the crystalline configuration and find that the distribution is not Gaussian.Comment: 10 pages, 3 figure

Particle phase function measurements by a new Fiber Array Nephelometer: FAN 1

A fiber array polar nephelometer of advanced design, the FAN I is capable of in-situ phase function measurements of scattered light from man-made or natural atmospheric particles. The scattered light is measured at 100 different angles throughout 360 degrees, thus providing a potential measurement of the asymmetry of irregularly shaped particles. Phase functions can be measured at 10 to 100 Hz rates and the range of measurable single particle sizes is from 5 micron m to as large as 8mm. For particles smaller than 5 micro m the ensemble average can be measured. The FAN I is microprocessor controlled and the data may be stored on floppy disk or printed out in tabular and/or graphical form. The optical head may be separated from the computer system for operation in field or adverse conditions. Examples of laboratory measured scattering phase functions obtained with the FAN I for spherical particles is given to illustrate its measurement capabilities

On-orbit structural dynamic performance of a 15-meter microwave radiometer antenna

The on-orbit structural dynamic performance of a microwave radiometer antenna for Earth science applications is addressed. The radiometer is one of the Earth-observing instruments aboard a proposed geostationary platform as part of the Mission to the Planet Earth. A sequential approach is presented for assessing the ability of an antenna structure to retain its geometric shape subject to a representative onboard disturbance. This approach includes establishing the structural requirements of the antenna, developing the structural and disturbance models, performing modal and forced response analyses, and evaluating the resulting distortions in terms of the antenna's ability to meet stringent structural performance requirements. Two antenna configurations are discussed: free-flying and platform-mounted. These configurations are analyzed for a representative disturbance function which simulates rotation of the subreflector in order to perform a raster-type scan of the Earth disk. Results show that the scanning maneuver modeled would not induce antenna structural errors outside the specified limits

Measurement of spray combustion processes

A free jet configuration was chosen for measuring noncombusting spray fields and hydrocarbon-air spray flames in an effort to develop computational models of the dynamic interaction between droplets and the gas phase and to verify and refine numerical models of the entire spray combustion process. The development of a spray combustion facility is described including techniques for laser measurements in spray combustion environments and methods for data acquisition, processing, displaying, and interpretation

System impacts of solar dynamic and growth power systems on space station

Concepts for the 1990's space station envision an initial operational capability with electrical power output requirements of approximately 75 kW and growth power requirements in the range of 300 kW over a period of a few years. Photovoltaic and solar dynamic power generation techniques are contenders for supplying this power to the space station. A study was performed to identify growth power subsystem impacts on other space station subsystems. Subsystem interactions that might suggest early design changes for the space station were emphasized. Quantitative analyses of the effects of power subsystem mass and projected area on space station controllability and reboost requirements were conducted for a range of growth station configurations. Impacts on space station structural dynamics as a function of power subsystem growth were also considered

Autocorrelation of Random Matrix Polynomials

We calculate the autocorrelation functions (or shifted moments) of the characteristic polynomials of matrices drawn uniformly with respect to Haar measure from the groups U(N), O(2N) and USp(2N). In each case the result can be expressed in three equivalent forms: as a determinant sum (and hence in terms of symmetric polynomials), as a combinatorial sum, and as a multiple contour integral. These formulae are analogous to those previously obtained for the Gaussian ensembles of Random Matrix Theory, but in this case are identities for any size of matrix, rather than large-matrix asymptotic approximations. They also mirror exactly autocorrelation formulae conjectured to hold for L-functions in a companion paper. This then provides further evidence in support of the connection between Random Matrix Theory and the theory of L-functions

Random polynomials, random matrices, and LL-functions

We show that the Circular Orthogonal Ensemble of random matrices arises naturally from a family of random polynomials. This sheds light on the appearance of random matrix statistics in the zeros of the Riemann zeta-function.Comment: Added background material. Final version. To appear in Nonlinearit