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

Effects of systematic errors on the mixing ratios of trace gases obtained from occulation spectra

The influence of systematic errors in the parameters of the models describing the geometry and the atmosphere on the profiles of trace gases retrieved from simulated solar occultation spectra, collected at satellite altitudes, is investigated. Because of smearing effects and other uncertainties, it may be preferable to calibrate the spectra internally by measuring absorption lines of an atmospheric gas such as CO2 whose vertical distribution is assumed rather than to relay on externally supplied information

Investigation of effects of background water on upwelled reflectance spectra and techniques for analysis of dilute primary-treated sewage sludge

In an effort to improve understanding of the effects of variations in background water on reflectance spectra, laboratory tests were conducted with various concentrations of sewage sludge diluted with several types of background water. The results from these tests indicate that reflectance spectra for sewage-sludge mixtures are dependent upon the reflectance of the background water. Both the ratio of sewage-sludge reflectance to background-water reflectance and the ratio of the difference in reflectance to background-water reflectance show spectral variations for different turbid background waters. The difference in reflectance is the only parameter considered

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

Plasma density measurements using chirped pulse broad-band Raman amplification

Stimulated Raman backscattering is used as a non-destructive method to determine the density of plasma media at localized positions in space and time. By colliding two counter-propagating, ultra-short laser pulses with a spectral bandwidth larger than twice the plasma frequency, amplification occurs at the Stokes wavelengths, which results in regions of gain and loss separated by twice the plasma frequency, from which the plasma density can be deduced. By varying the relative delay between the laser pulses, and therefore the position and timing of the interaction, the spatio-temporal distribution of the plasma density can be mapped out

Stochastic background from extra-galactic double neutron stars

We present Monte Carlo simulations of the extra galactic population of inspiralling double neutron stars, and estimate its contribution to the astrophysical gravitational wave background, in the frequency range of ground based interferometers, corresponding to the last thousand seconds before the last stable orbit when more than 96 percent of the signal is released. We show that sources at redshift z>0.5 contribute to a truly continuous background which may be detected by correlating third generation interferometers.Comment: 13 pages, 7 figures - proceeding of a talk given at the 11th GWDAW, to appear in CQ

Chirped pulse Raman amplification in plasma

Raman amplification in plasma has been proposed to be a promising method of amplifying short radiation pulses. Here, we investigate chirped pulse Raman amplification (CPRA) where the pump pulse is chirped and leads to spatiotemporal distributed gain, which exhibits superradiant scaling in the linear regime, usually associated with the nonlinear pump depletion and Compton amplification regimes. CPRA has the potential to serve as a high-efficiency high-fidelity amplifier/compressor stage

Statistical theory of the continuous double auction

Most modern financial markets use a continuous double auction mechanism to store and match orders and facilitate trading. In this paper we develop a microscopic dynamical statistical model for the continuous double auction under the assumption of IID random order flow, and analyze it using simulation, dimensional analysis, and theoretical tools based on mean field approximations. The model makes testable predictions for basic properties of markets, such as price volatility, the depth of stored supply and demand vs. price, the bid-ask spread, the price impact function, and the time and probability of filling orders. These predictions are based on properties of order flow and the limit order book, such as share volume of market and limit orders, cancellations, typical order size, and tick size. Because these quantities can all be measured directly there are no free parameters. We show that the order size, which can be cast as a nondimensional granularity parameter, is in most cases a more significant determinant of market behavior than tick size. We also provide an explanation for the observed highly concave nature of the price impact function. On a broader level, this work suggests how stochastic models based on zero-intelligence agents may be useful to probe the structure of market institutions. Like the model of perfect rationality, a stochastic-zero intelligence model can be used to make strong predictions based on a compact set of assumptions, even if these assumptions are not fully believable.Comment: 36 pages, 40 figures, RevTex4, submitted to Quantitative Financ