Limit Theorems For Quantum Walks Associated with Hadamard Matrices

We study a one-parameter family of discrete-time quantum walk models on the line and in the xy-plane associated with the Hadamard walk. Weak convergence in the long-time limit of all moments of the walker's pseudo-velocity on the line and in the xy-plane is proved. Symmetrization on the line and in the xy-plane is theoretically investigated, leading to the resolution of the Konno-Namiki-Soshi conjecture in the special case of symmetrization of the unbiased Hadamard walk on the line . A necessary condition for the existence of a phenomenon known as localization is given

The impact of uncertainty in satellite data on the assessment of flood inundation models

The performance of flood inundation models is often assessed using satellite observed data; however these data have inherent uncertainty. In this study we assess the impact of this uncertainty when calibrating a flood inundation model (LISFLOOD-FP) for a flood event in December 2006 on the River Dee, North Wales, UK. The flood extent is delineated from an ERS-2 SAR image of the event using an active contour model (snake), and water levels at the flood margin calculated through intersection of the shoreline vector with LiDAR topographic data. Gauged water levels are used to create a reference water surface slope for comparison with the satellite-derived water levels. Residuals between the satellite observed data points and those from the reference line are spatially clustered into groups of similar values. We show that model calibration achieved using pattern matching of observed and predicted flood extent is negatively influenced by this spatial dependency in the data. By contrast, model calibration using water elevations produces realistic calibrated optimum friction parameters even when spatial dependency is present. To test the impact of removing spatial dependency a new method of evaluating flood inundation model performance is developed by using multiple random subsamples of the water surface elevation data points. By testing for spatial dependency using Moran’s I, multiple subsamples of water elevations that have no significant spatial dependency are selected. The model is then calibrated against these data and the results averaged. This gives a near identical result to calibration using spatially dependent data, but has the advantage of being a statistically robust assessment of model performance in which we can have more confidence. Moreover, by using the variations found in the subsamples of the observed data it is possible to assess the effects of observational uncertainty on the assessment of flooding risk

Timelike and Spacelike Matter Inheritance Vectors in Specific Forms of Energy-Momentum Tensor

This paper is devoted to the investigation of the consequences of timelike and spacelike matter inheritance vectors in specific forms of energy-momentum tensor, i.e., for string cosmology (string cloud and string fluid) and perfect fluid. Necessary and sufficient conditions are developed for a spacetime with string cosmology and perfect fluid to admit a timelike matter inheritance vector, parallel to $u^a$ and spacelike matter inheritance vector, parallel to $x^a$. We compare the outcome with the conditions of conformal Killing vectors. This comparison provides us the conditions for the existence of matter inheritance vector when it is also a conformal Killing vector. Finally, we discuss these results for the existence of matter inheritance vector in the special cases of the above mentioned spacetimes.Comment: 27 pages, accepted for publication in Int. J. of Mod. Phys.

Development of technology for modeling of a 1/8-scale dynamic model of the shuttle Solid Rocket Booster (SRB)

A NASTRAN analysis of the solid rocket booster (SRB) substructure of the space shuttle 1/8-scale structural dynamics model. The NASTRAN finite element modeling capability was first used to formulate a model of a cylinder 10 in. radius by a 200 in. length to investigate the accuracy and adequacy of the proposed grid point spacing. Results were compared with a shell analysis and demonstrated relatively accurate results for NASTRAN for the lower modes, which were of primary interest. A finite element model of the full SRB was then formed using CQUAD2 plate elements containing membrane and bending stiffness and CBAR offset bar elements to represent the longerons and frames. Three layers of three-dimensional CHEXAI elements were used to model the propellant. This model, consisting of 4000 degrees of freedom (DOF) initially, was reduced to 176 DOF using Guyan reduction. The model was then submitted for complex Eigenvalue analysis. After experiencing considerable difficulty with attempts to run the complete model, it was split into two substructres. These were run separately and combined into a single 116 degree of freedom A set which was successfully run. Results are reported

Development of technology for fluid-structure interaction modelling of a 1/8-scale dynamic model of the shuttle External Tank (ET). Volume 2: Supporting data appendixes A through C

For abstract, see N75-21359

Neotectonics and Paleoseismicity of a Major Junction Between Two Strands of the Awatere Fault, South Island, New Zealand

In northeastern South Island, New Zealand, obliquely-convergent relative motion between the Pacific and Australian plates is accommodated by slip across active dextral-oblique faults in the Marlborough fault system. The Awatere Fault is one of four principal active strike-slip faults within this plate boundary zone, and includes two sections (the eastern and Molesworth sections) that have different strikes and that join across a complex fault junction in the upper Awatere Valley. Detailed mapping of the fault traces and measurement of 97 geomorphic displacements along the Awatere Fault in the vicinity of the fault junction show that the eastern and Molesworth sections of the fault intersect one another at a low angle (10-15º), at the eastern end of an internally faulted, elongate, ~15 km long and up to 3 km wide fault wedge or sliver. The region between the fault sections is split by a series of discontinuous, en-echelon scarps that are oriented from ~10º to 20-30º clockwise from the principal fault sections. Based on other observations of discontinuities in strike-slip earthquake ruptures around the globe, this low-angle intersection geometry suggests that the junction between these fault sections may not act as a significant barrier to earthquake rupture propagation. This interpretation of the mechanical significance of the fault junction to earthquake ruptures is counter to previous suggestions, but is supported by new paleoseismic data from four paleoseismic trenches excavated on each side of the junction. In a new paleoseismic trench on the Molesworth section at Saxton River, 18 km to the west of the junction, up to ten surface-rupturing events in the past ~15 ka are recognised from 12 radiocarbon ages and 1 optically stimulated luminescence age. In two new trenches on the eastern section near to Upcot Saddle, 12 km northeast of the fault junction, five events took place in the past 5.5 ka, based on 21 radiocarbon ages. This chronology from Upcot Saddle is combined with data from two previous trenches located ~55 km to the northeast at Lake Jasper, to infer nine events on the eastern section since 8330-8610 cal. years B.P. These well-dated events on the eastern section are compared to those on the Molesworth section to the west of the fault junction. At 95% confidence, five events on both sections have occurred with statistical contemporaneity since ~6 ka B.P. These five events may have ruptured both the eastern and Molesworth sections simultaneously, in accordance with the interpretation that the fault section junction does not arrest rupture propagation. Alternatively, these events may have been separate earthquakes that occurred within the statistical resolution provided by radiocarbon dating. The most recent event to rupture the eastern section was the Mw ~7.5 1848 Marlborough earthquake. The coseismic slip distribution and maximum traceable length of this surface rupture are calculated from the magnitude and distribution of small, metre-scale geomorphic displacements attributable to this earthquake. These data suggest this event ruptured >100-110 km of the eastern section, with mean surface displacement of 5.3 ±1.6 m. Based on these parameters, the moment magnitude of this earthquake would be Mw 7.4-7.7. This magnitude estimate is indistinguishable from previous calculations that were based on attenuation of shaking intensity isoseismals that were assigned from contemporary historical accounts of that earthquake. On the basis of similar rupture lengths and coseismic displacements, it is inferred that the penultimate event had a similar moment magnitude to the 1848 earthquake. Horizontal displacement of a flight of 6 fluvial terraces at Saxton River by the Molesworth section of the Awatere Fault is constrained to have occurred at a nearconstant rate of 5.5 ±1.5 mm/a since ~15 ka B.P. These rates are based on two new optically stimulated luminescence ages for the highest terrace treads of 14.5 ±1.5 and 6.69 ±0.74 ka B.P. These rates are indistinguishable from recent strike-slip rate estimates for the eastern section of 5.6 ±1.1 and 6 ±2 mm/a. Comparing the magnitudes and ages of the terrace riser displacements at Saxton River to the timing of paleoearthquakes on the Molesworth section implies a mean per-event displacement of 4.4 ±0.2 m since ~15 ka. The new terrace ages also record two periods of aggradation that post-date the Last Glacial Maximum

The measurement errors in the Swift-UVOT and XMM-OM

The probability of photon measurement in some photon counting instrumentation, such as the Optical Monitor on the XMM-Newton satellite, and the UVOT on the Swift satellite, does not follow a Poisson distribution due to the detector characteristics, but a Binomial distribution. For a single-pixel approximation, an expression was derived for the incident countrate as a function of the measured count rate by Fordham, Moorhead and Galbraith (2000). We show that the measured countrate error is binomial, and extend their formalism to derive the error in the incident count rate. The error on the incident count rate at large count rates is larger than the Poisson-error of the incident count rate.Comment: 4 pages, 2 postscript figures, submitted to MNRA

Analytical and experimental investigation of a 1/8-scale dynamic model of the shuttle orbiter. Volume 3A: Supporting data

For abstract, see N75-15681

Analytical and experimental investigation of a 1/8-scale dynamic model of the shuttle orbiter. Volume 1: Summary report

A 1/8-scale structural dynamics model of the space shuttle orbiter was analyzed using the NASA Structural Analysis System (NASTRAN). Comparison of the calculated eigenvalues with preliminary test data for the unrestrained condition indicate that the analytical model was consistently stiffer, being about 20% higher in the first mode. The eigenvectors show reasonably good agreement with test data. A series of analytical and experimental investigations undertaken to resolve the discrepancy are described. Modifications in the NASTRAN model based upon these investigations resulted in close agreement for both eigenvalues and eigenvectors