The principle of equivalence and projective structure in space-times

This paper discusses the extent to which one can determine the space-time metric from a knowledge of a certain subset of the (unparametrised) geodesics of its Levi-Civita connection, that is, from the experimental evidence of the equivalence principle. It is shown that, if the space-time concerned is known to be vacuum, then the Levi-Civita connection is uniquely determined and its associated metric is uniquely determined up to a choice of units of measurement, by the specification of these geodesics. It is further demonstrated that if two space-times share the same unparametrised geodesics and only one is assumed vacuum then their Levi-Civita connections are again equal (and so the other metric is also a vacuum metric) and the first result above is recovered.Comment: 23 pages, submitted to Classical and Quantum Gravit

Characterizing Ground Motions That Collapse Steel Special Moment-Resisting Frames or Make Them Unrepairable

This work applies 64,765 simulated seismic ground motions to four models each of 6- or 20-story, steel special moment-resisting frame buildings. We consider two vector intensity measures and categorize the building response as “collapsed,” “unrepairable,” or “repairable.” We then propose regression models to predict the building responses from the intensity measures. The best models for “collapse” or “unrepairable” use peak ground displacement and velocity as intensity measures, and the best models predicting peak interstory drift ratio, given that the frame model is “repairable,” use spectral acceleration and epsilon (ϵ) as intensity measures. The more flexible frame is always more likely than the stiffer frame to “collapse” or be “unrepairable.” A frame with fracture-prone welds is substantially more susceptible to “collapse” or “unrepairable” damage than the equivalent frame with sound welds. The 20-story frames with fracture-prone welds are more vulnerable to P-delta instability and have a much higher probability of collapse than do any of the 6-story frames

Diurnal cycle of tropical deep convection examined using high space and time resolution satellite data

September 1997.Includes bibliographical references.Infrared (IR) and visible (VIS) satellite data from GMS-4 with 5-km spatial and 1-hr temporal resolution was used to examine the diurnal cycle of deep convection over a sector of the tropical west Pacific warm pool (WP) bounded by 140°-180°E, 0°-20°N. Data were analyzed for 45 days of summer from 22 June 1994 - 5 August 1994 (JJA) and for 65 days of winter between 28 November 1994 – 31 January 1995 (NDJ). The synoptic backdrop for JJA was characterized by the monsoon trough, oriented northwest to southeast through the WP. Convection was largely focused along the trough. During NDJ, convection was concentrated within 5° latitude of the intertropical convergence zone (ITCZ) which was oriented east to west near the equator. December 1994 was characterized by an active phase of the intraseasonal oscillation (ISO) while January 1995 coincided with an inactive phase. Deep convective cloud was identified in IR imagery using brightness temperature (TBB) threshold techniques. Cloud forms associated with deep convection showed two distinct diurnal modes representing deep convection (TBB ≤ -60°C) and stratiform cirrus (-52°C ≤ TBB ≤ -23°C). Clouds with TBB warmer than -60°C and colder than -53°C comprised a mixed deep convection and cirrus anvil regime from the satellite's perspective with a diurnal cycle reflecting both modes of variability. The diurnal variation of cloud in these regimes was consistent for all time periods and for two tropical storms which occurred in the WP during December 1994. Based on these results and on previous studies, a -65°C cloud-top TBB threshold was chosen to isolate pixels containing active, deep convection. Spectral analysis of time series constructed from hourly cold cloud (≤ -65°C) pixel counts revealed a powerful diurnal cycle of deep convection significant at the 95% confidence level during JJA and NDJ. Composited hourly statistics of fractional areal cloud cover documented a 0500-0600 LST maximum with a 1500-1900 LST minimum of convection for both seasons. The ratio of maximum to minimum areal cold cloud coverage was greater than 2: I. A significant bi-diurnal cycle was evident in both JJA and January 1995. The bi-diurnal peak was strongest in the near-equatorial region during JJA. No semi-diurnal (spectral) peak occurred during either season. This suggests that semi-diurnal atmospheric tides do not strongly influence convection in the WP. Three objective analysis techniques were developed to analyze the relation of tropical cloud cluster structure to the daily spatial and temporal variation of deep convection. The first technique identified cold cloud intervals, called line clusters, in each image. These line clusters represented a characteristic horizontal dimension for cloud clusters of various sizes. Results showed that the diurnal cycle of convective rainfall with an early morning maximum was disproportionately dominated by the largest ~ 10% of clusters for each time period. While the number of large clusters increased only slightly throughout nocturnal hours, the area of cold cloud associated with these systems expanded dramatically. An algorithm called threshold initiation showed that all scales of organized, intensifying deep convection existed at all times of day and night. In addition, the early morning peak was composed primarily of building convection. Conditional recurrence probabilities of line clusters were computed at 24 and 48 hour intervals. Results for JJA and December 1994 revealed that when early morning convection occurred at any location, the same region contained convection the next morning nearly half the time. Convection was less likely at the 48 hour point. These results do not support diurnal theories based on sea surface heating, afternoon initiation of convection and nocturnal evolution of mesoscale convective systems. Findings indicate that the diurnal cycle of deep convective cloud is driven by the internal variation of large clusters. Clusters that exist into or form during the night, grow spatially larger and more intense. Some results support direct radiative forcing of clouds and large scale clear region radiative destabalization as possible contributors to diurnal convective variability. However, all findings are consistent with the work of Gray and colleagues that emphasizes the role of day-night variations in net tropospheric cooling in clear and longwave cooling in cloudy versus clear regions as an explanation of the observed daily variation of tropical convective rainfall.Research supported under the Center for Geosciences, Phase II at CIRA/CSU by DoD grant no. DAAH04-94-G-0420

Effects of Fault Dip and Slip Rake Angles on Near-Source Ground Motions: Why Rupture Directivity Was Minimal in the 1999 Chi-Chi, Taiwan, Earthquake

We study how the fault dip and slip rake angles affect near-source ground velocities and displacements as faulting transitions from strike-slip motion on a vertical fault to thrust motion on a shallow-dipping fault. Ground motions are computed for five fault geometries with different combinations of fault dip and rake angles and common values for the fault area and the average slip. The nature of the shear-wave directivity is the key factor in determining the size and distribution of the peak velocities and displacements. Strong shear-wave directivity requires that (1) the observer is located in the direction of rupture propagation and (2) the rupture propagates parallel to the direction of the fault slip vector. We show that predominantly along-strike rupture of a thrust fault (geometry similar in the Chi-Chi earthquake) minimizes the area subjected to large-amplitude velocity pulses associated with rupture directivity, because the rupture propagates perpendicular to the slip vector; that is, the rupture propagates in the direction of a node in the shear-wave radiation pattern. In our simulations with a shallow hypocenter, the maximum peak-to-peak horizontal velocities exceed 1.5 m/sec over an area of only 200 km^2 for the 30°-dipping fault (geometry similar to the Chi-Chi earthquake), whereas for the 60°- and 75°-dipping faults this velocity is exceeded over an area of 2700 km^2. These simulations indicate that the area subjected to large-amplitude long-period ground motions would be larger for events of the same size as Chi-Chi that have different styles of faulting or a deeper hypocenter

Dynamic Earthquake Ruptures in the Presence of Lithostatic Normal Stresses: Implications for Friction Models and Heat Production

We simulate dynamic ruptures on a strike-slip fault in homogeneous and layered half-spaces and on a thrust fault in a layered half-space. With traditional friction models, sliding friction exceeds 50% of the fault normal compressive stress, and unless the pore pressures approach the lithostatic stress, the rupture characteristics depend strongly on the depth, and sliding generates large amounts of heat. Under application of reasonable stress distributions with depth, variation of the effective coefficient of friction with the square root of the shear modulus and the inverse of the depth creates distributions of stress drop and fracture energy that produce realistic rupture behavior. This ad hoc friction model results in (1) low-sliding friction at all depths and (2) fracture energy that is relatively independent of depth. Additionally, friction models with rate-weakening behavior (which form pulselike ruptures) appear to generate heterogeneity in the distributions of final slip and shear stress more effectively than those without such behavior (which form cracklike ruptures). For surface rupture on a thrust fault, the simple slip-weakening friction model, which lacks rate-weakening behavior, accentuates the dynamic interactions between the seismic waves and the rupture and leads to excessively large ground motions on the hanging wall. Waveforms below the center of the fault (which are associated with waves radiated to teleseismic distances) indicate that source inversions of thrust events may slightly underestimate the slip at shallow depths

Ultra Wide Band Millimeter Wave Holographic 3-D Imaging of Concealed Targets on Mannequins

Ultra wide band (chirp frequency) millimeter wave “3-D” holography is a unique technique for imaging concealed targets on human subjects with extremely high lateral and depth resolution. Recent “3-D” holographic images of full size mannequins with concealed weapons illustrate the efficacy of this technique for airport security

Antinuclear antibodies (ANA) in chronic hepatitis C virus infection: correlates of positivity and clinical relevance.

We examined correlates of antinuclear antibody (ANA) positivity (ANA+) in individuals with chronic hepatitis C virus (HCV) infection and the effect of positivity on clinical outcome of HCV. Pretreatment sera from 645 patients from three centres in Sweden (n = 225), the UK (n = 207) and Italy (n = 213) were evaluated by indirect immunofluorescence on Hep-2 cells for ANA pattern and titre by a single laboratory. Liver biopsies were all scored by one pathologist. A total of 258 patients were subsequently treated with interferon monotherapy. There was a significant difference in the prevalence of ANA (1:40) by geographic location: Lund 4.4%, London 8.7%, Padova 10.3% [odds ratio (OR) = 0.66; 95% CI: 0.46-0.94; P = 0.023]. Duration of HCV infection, age at infection, current age, route of infection, viral genotype, alcohol consumption, fibrosis stage and inflammatory score were not correlated with ANA+ or ANA pattern. Female gender was correlated with ANA+ and this association persisted in multivariable analyses (OR = 3.0; P = 0.002). Increased plasma cells were observed in the liver biopsies of ANA-positive individuals compared with ANA-negative individuals, while a trend towards decreased lymphoid aggregates was observed [hazard ratio (HR) = 9.0, P = 0.037; HR = 0.291, P = 0.118, respectively]. No correlations were observed between ANA positivity and nonresponse to therapy (OR = 1.4; P = 0.513), although ANA+ was correlated with faster rates of liver fibrosis, this was not statistically significant (OR = 1.8; P = 0.1452). Low titre ANA+ should not be a contraindication for interferon treatment. Our observation of increased plasma cells in ANA+ biopsies might suggest B-cell polyclonal activity with a secondary clinical manifestation of increased serum immunoglobulins

Metal Speciation. Effects on Aquatic Toxicity

Most Water Quality Criteria for Metals Are Presently based on Total Metal Concentrations. However, for a Series of Algal Bioassays in Which Zinc and Various Chelators Were Added, Toxicity Was Not Related to Total Metal but Was Related to the Predicted Free Metal Concentration. © 1980, American Chemical Society. All Rights Reserved

Coherent states on spheres

We describe a family of coherent states and an associated resolution of the identity for a quantum particle whose classical configuration space is the d-dimensional sphere S^d. The coherent states are labeled by points in the associated phase space T*(S^d). These coherent states are NOT of Perelomov type but rather are constructed as the eigenvectors of suitably defined annihilation operators. We describe as well the Segal-Bargmann representation for the system, the associated unitary Segal-Bargmann transform, and a natural inversion formula. Although many of these results are in principle special cases of the results of B. Hall and M. Stenzel, we give here a substantially different description based on ideas of T. Thiemann and of K. Kowalski and J. Rembielinski. All of these results can be generalized to a system whose configuration space is an arbitrary compact symmetric space. We focus on the sphere case in order to be able to carry out the calculations in a self-contained and explicit way.Comment: Revised version. Submitted to J. Mathematical Physic

Slow roll inflation in the presence of a dark energy coupling

In models of coupled dark energy, in which a dark energy scalar field couples to other matter components, it is natural to expect a coupling to the inflaton as well. We explore the consequences of such a coupling in the context of single-field slow-roll inflation. Assuming an exponential potential for the quintessence field we show that the coupling to the inflaton causes the quintessence field to be attracted toward the minimum of the effective potential. If the coupling is large enough, the field is heavy and is located at the minimum. We show how this affects the expansion rate and the slow-roll of the inflaton field, and therefore the primordial perturbations generated during inflation. We further show that the coupling has an important impact on the processes of reheating and preheating