The Caves and Karst of Rota Island, Commonwealth of the Northern Mariana Islands

Rota Island, the southernmost island in the Commonwealth of the Northern Mariana Islands in the western Pacific, has the types of caves previously documented on the other limestone mantled islands in the Mariana Arc that have been investigated for caves: Aguijan, Guam, Tinian and Saipan. Caves developed at the edge of the fresh-water lens by zones of enhanced carbonate dissolution produced by fresh-water/salt-water mixing are most common. Among these mixing zone caves, flank margin caves dominate. Flank margin caves were found singly and in extensive horizons representing significant sea-level still stands. However, another type of mixing zone cave was found on Rota in numbers not documented on neighboring islands. Mixing zone fracture caves, apparently formed as zones of enhanced dissolution, produced fresh-water discharging from the lens along fractures, migrated vertically as sea-level changed. Some mixing zone fracture caves on Rota are developed in clusters from two to four caves. The mixing zone caves of Rota reflect the interaction of eogenetic limestone, glacioeustasy, local tectonics and enhanced carbonate dissolution via mixing of disparate waters. The development of mixing zone caves on Rota is in agreement with the Carbonate Island Karst Model (CIKM). Rota has a few caves developed along the contact between limestone and the insoluble volcanic rock that makes up the core of the island. The most important of these is Water Cave, a large spring that is the source for most of the municipal water on Rota. Rota also two extensive zones of vertical fissures developed along bedrock fractures; Fissure City and As Mundo Fissure Zone. In addition, Rota has one cave apparently developed along a fault; Gagani Cave. Some of the caves documented on Rota are difficult to classify and warrant further investigation

An Overdetermined System for Improved Autocorrelation Based Spectral Moment Estimator Performance

Autocorrelation based spectral moment estimators are typically derived using the Fourier transform relationship between the power spectrum and the autocorrelation function along with using either an assumed form of the autocorrelation function, e.g., Gaussian, or a generic complex form and applying properties of the characteristic function. Passarelli has used a series expansion of the general complex autocorrelation function and has expressed the coefficients in terms of central moments of the power spectrum. A truncation of this series will produce a closed system of equations which can be solved for the central moments of interest. The autocorrelation function at various lags is estimated from samples of the random process under observation. These estimates themselves are random variables and exhibit a bias and variance that is a function of the number of samples used in the estimates and the operational signal-to-noise ratio. This contributes to a degradation in performance of the moment estimators. This dissertation investigates the use autocorrelation function estimates at higher order lags to reduce the bias and standard deviation in spectral moment estimates. In particular, Passarelli's series expansion is cast in terms of an overdetermined system to form a framework under which the application of additional autocorrelation function estimates at higher order lags can be defined and assessed. The solution of the overdetermined system is the least squares solution. Furthermore, an overdetermined system can be solved for any moment or moments of interest and is not tied to a particular form of the power spectrum or corresponding autocorrelation function. As an application of this approach, autocorrelation based variance estimators are defined by a truncation of Passarelli's series expansion and applied to simulated Doppler weather radar returns which are characterized by a Gaussian shaped power spectrum. The performance of the variance estimators determined from a closed system is shown to improve through the application of additional autocorrelation lags in an overdetermined system. This improvement is greater in the narrowband spectrum region where the information is spread over more lags of the autocorrelation function. The number of lags needed in the overdetermined system is a function of the spectral width, the number of terms in the series expansion, the number of samples used in estimating the autocorrelation function, and the signal-to-noise ratio. The overdetermined system provides a robustness to the chosen variance estimator by expanding the region of spectral widths and signal-to-noise ratios over which the estimator can perform as compared to the closed system

Adaptive clutter rejection filters for airborne Doppler weather radar applied to the detection of low altitude windshear

An optimum adaptive clutter rejection filter for use with airborne Doppler weather radar is presented. The radar system is being designed to operate at low-altitudes for the detection of windshear in an airport terminal area where ground clutter returns may mask the weather return. The coefficients of the adaptive clutter rejection filter are obtained using a complex form of a square root normalized recursive least squares lattice estimation algorithm which models the clutter return data as an autoregressive process. The normalized lattice structure implementation of the adaptive modeling process for determining the filter coefficients assures that the resulting coefficients will yield a stable filter and offers possible fixed point implementation. A 10th order FIR clutter rejection filter indexed by geographical location is designed through autoregressive modeling of simulated clutter data. Filtered data, containing simulated dry microburst and clutter return, are analyzed using pulse-pair estimation techniques. To measure the ability of the clutter rejection filters to remove the clutter, results are compared to pulse-pair estimates of windspeed within a simulated dry microburst without clutter. In the filter evaluation process, post-filtered pulse-pair width estimates and power levels are also used to measure the effectiveness of the filters. The results support the use of an adaptive clutter rejection filter for reducing the clutter induced bias in pulse-pair estimates of windspeed

On the uniqueness of solutions to the Gross-Pitaevskii hierarchy

We give a new proof of uniqueness of solutions to the Gross-Pitaevskii hierarchy, first established by Erdos, Schlein and Yau, in a different space, based on space-time estimates

Global well-posedness for KdV in Sobolev Spaces of negative index

The initial value problem for the Korteweg-deVries equation on the line is shown to be globally well-posed for rough data. In particular, we show global well-posedness for initial data in H^s({\mathbb{R}), -3/10<s.Comment: 5 pages. Electronic Journal of Differential equations (submitted