Geometry of Control-Affine Systems

Motivated by control-affine systems in optimal control theory, we introduce the notion of a point-affine distribution on a manifold X - i.e., an affine distribution F together with a distinguished vector field contained in F. We compute local invariants for point-affine distributions of constant type when dim(X)=n, rank(F)=n-1, and when dim(X)=3, rank(F)=1. Unlike linear distributions, which are characterized by integer-valued invariants - namely, the rank and growth vector - when dim(X)<=4, we find local invariants depending on arbitrary functions even for rank 1 point-affine distributions on manifolds of dimension 2

Geometry of Optimal Control for Control-Affine Systems

Motivated by the ubiquity of control-affine systems in optimal control theory, we investigate the geometry of point-affine control systems with metric structures in dimensions two and three. We compute local isometric invariants for point-affine distributions of constant type with metric structures for systems with 2 states and 1 control and systems with 3 states and 1 control, and use Pontryagin's maximum principle to find geodesic trajectories for homogeneous examples. Even in these low dimensions, the behavior of these systems is surprisingly rich and varied

Quantized Roentgen Effect in Bose-Einstein Condensates

A classical dielectric moving in a charged capacitor can create a magnetic field (Roentgen effect). A quantum dielectric, however, will not produce a magnetization, except at vortices. The magnetic field outside the quantum dielectric appears as the field of quantized monopoles

Sandstone Pore Aspect Ratio Spectra from Direct Observations and Velocity Inversion

Measurements of pore shapes from Scanning Electron Microscope (SEM) images for three sandstone samples (the Navajo Sandstone, the Weber Sandstone, and the Kayenta Sandstone) are compared to the aspect ratio spectra obtained from inverting laboratory velocity versus pressure data using the method of Cheng and Toksoz (1979). The results indicate that the inversion method is in very good agreement with the observations at high aspect ratios ( ex > 0.0 1). At low aspect ratios the agreement is very good for the clean Navajo Sandstone sample, but poor for the Weber and Kayenta samples which contain clay. The Navajo sample is composed chiefly of quartz with significant pressure dissolution apparent along grain contacts resulting in smooth, flat cracks between grains. The Weber and Kayenta samples have rougher crack surfaces as well as tapered pore edges, indicating that asperities ,and non-elliptical pore shapes may result in an over estimation of low aspect ratio cracks by velocity inversion. The presence of degraded feldspars may also play a role.Phillips Petroleum Fellowshi

Determining Shear Wave Velocities in Soft Marine Sediments

The inversion technique presented in this volume (Cheng, 1987) that simultaneously inverts full waveform acoustic logs for shear wave velocity (V[subscript 3]) and compressional wave attenuation (Q[subscript p]) was applied to selected full waveform acoustic logs taken in soft sediments from Deep Sea Drilling Project Site 613. Besides V[subscript 3] and Q[subscript p], the sensitivity of the inversion to perturbations in the fixed parameters, P-wave velocity (V[subscript p]), fluid velocity (V[[subscript f]), borehole diameter, bulk density (P[subscript b]), and borehole fluid attenuation (Q[subscript f]), were tested. Our study shows that the inversion technique is most sensitive to the estimate of V[subscript p] because the inversion is based on the P leaky mode energy portion of the spectrum. The Poisson's ratio, however, which primarily controls the amplitude of the waveforms, is rather stable with different estimates in V[subscript p]. The inversion technique is less sensitive to small perturbations in borehole diameter, P[subscript b], V[subscript f], and Q[subscript f] The shear wave velocities inferred from these inversions correlate well with the attendant velocity logs run at Site 613 and the diagenetic changes identified by shipboard stratigraphers. For example, there is an increase in both V[subscript p] and V[subscript 3] at the diagenetic boundary between siliceous nannofossil oozes and porcellanite. This boundary is responsible for a sharp seismic reflector in a USGS. seismic line run nearby. Over the depth interval that we analyzed, from 390.0 to 582.0 meters below sea floor, we determined shear wave velocities ranging from 0.74 to 1.06 km/sec corresponding to compressional wave velocities from 1.70 to 2.20 km/sec.Massachusetts Institute of Technology. Full Waveform Acoustic Logging ConsortiumNational Science Foundation (U.S.) (Grant OCE84-08761)Chevron (Fellowship

Evaluation And Prediction Of Shear Wave Velocities In Soft Marine Sediments

Shear wave velocities from full waveform acoustic logs were determined at DSDP Site 613 using the spectral ratio inversion method. Discrete shear wave velocities for a 350 meter interval at 0.5-2 meter depth increments were calculated. Shear wave velocities were not evaluated for the upper 130m of the log because of data recording problems. The sediments of Site 613 represent a progression from carbonaceous-siliceous oozes through partial lithification and cementation. A method for predicting shear wave velocities using Wood's equation, the bulk moduli of water and carbonate grains, the P-wave velocity and porosity from well logs will be described. The predictions of this method provided a theoretical maximum value for the shear wave velocity to compare with the inversion results. In general, the method works well for shear wave velocities greater than 800 m/s. The inverted data fall just below the predicted theoretical maximum value from Wood's equation and agree quite well with the trends. Below this velocity threshold, trends with depth and Poisson's ratio and the divergence of the inversion itself seem to indicate incorrect behavior.Massachusetts Institute of Technology. Full Waveform Acoustic Logging ConsortiumNational Science Foundation (U.S.) (Grant OCE84-08761)National Science Foundation (U.S.) (Grant OCE87-10226)National Science Foundation (U.S.) (Grant OCE87-20032

Interethnic differences in pancreatic cancer incidence and risk factors: The Multiethnic Cohort.

While disparity in pancreatic cancer incidence between blacks and whites has been observed, few studies have examined disparity in other ethnic minorities. We evaluated variations in pancreatic cancer incidence and assessed the extent to which known risk factors account for differences in pancreatic cancer risk among African Americans, Native Hawaiians, Japanese Americans, Latino Americans, and European Americans in the Multiethnic Cohort Study. Risk factor data were obtained from the baseline questionnaire. Cox regression was used to estimate the relative risks (RRs) and 95% confidence intervals (CIs) for pancreatic cancer associated with risk factors and ethnicity. During an average 16.9-year follow-up, 1,532 incident pancreatic cancer cases were identified among 184,559 at-risk participants. Family history of pancreatic cancer (RR 1.97, 95% CI 1.50-2.58), diabetes (RR 1.32, 95% CI 1.14-1.54), body mass index ≥30&nbsp;kg/m2 (RR 1.25, 95% CI 1.08-1.46), current smoking (&lt;20 pack-years RR 1.43, 95% CI 1.19-1.73; ≥20 pack-years RR 1.76, 95% CI 1.46-2.12), and red meat intake (RR 1.17, 95% CI 1.00-1.36) were associated with pancreatic cancer. After adjustment for these risk factors, Native Hawaiians (RR 1.60, 95% CI 1.30-1.98), Japanese Americans (RR 1.33, 95% CI 1.15-1.54), and African Americans (RR 1.20, 95% CI 1.01-1.42), but not Latino Americans (RR 0.90, 95% CI 0.76-1.07), had a higher risk of pancreatic cancer compared to European Americans. Interethnic differences in pancreatic cancer risk are not fully explained by differences in the distribution of known risk factors. The greater risks in Native Hawaiians and Japanese Americans are new findings and elucidating the causes of these high rates may improve our understanding and prevention of pancreatic cancer

Determination of Shear Wave Velocity and Attenuation From Waveforms in Low Velocity Formations

In boreholes where formation shear velocity is lower than borehole fluid velocity neither refracted shear waves nor pseudo-Rayleigh waves can propagate. When frequency response of the sonde does not extend to low frequencies (e.g. 2 kHz) Stoneley waves are not excited efficiently. In such cases refracted P, leaking modes (PL) and fluid waves become dominant phases on a full waveform acoustic log. The P wave velocity can be determined from the first arrivals. Then, using synthetic microseismograms and a waveform matching technique, formation shear wave velocity and attenuation can be determined. This method· is demonstrated using data from a well in the Baltimore Canyon Trough area of the Atlantic margin.Massachusetts Institute of Technology. Full Waveform Acoustic Logging Consortiu