Analytical reliability calculation of linear dynamical systems in higher dimensions

The recent application of reliability analysis to controller synthesis has created the need for a computationally efficient method for the estimation of the first excursion probabilities for linear dynamical systems in higher dimensions. Simulation methods cannot provide an adequate solution to this specific application, which involves numerical optimization of the system reliability with respect to the controller parameters, because the total computational time needed is still prohibitive. Instead, an analytical approach is presented in this paper. The problem reduces to the calculation of the conditional upcrossing rate at each surface of the failure boundary. The correlation between upcrossings of the failure surface for the different failure events may be addressed by the introduction of a multi-dimensional integral. An efficient algorithm is adopted for the numerical calculation of this integral. Also, the problem of approximation of the conditional upcrossing rate is discussed. For the latter there is no known theoretical solution. Three of the semi-empirical corrections that have been proposed previously for scalar processes are compared and it is shown that the correction should be based on the bandwidth characteristics of the system. Finally, examples that verify the validity of the analytical approximations for systems in higher dimensions are discussed

Common Bulkhead Joint Development and Evaluation Final Report

Optimized composite welded joint design for Saturn booster common bulkhea

Alignment microscope for rotating laser scanner

Microscopic assembly for alignment of rotary laser focuses on small film area along scan line at oblique angle. Suitable choice of angle and location of optical components project laser beam line as X coordinate reticle. Coordination with horizontal recticle line included microscope facilitates Y coordinate position indexing

Red-giant stars in eccentric binaries

The unparalleled photometric data obtained by NASA’s Kepler Space Telescope has led to improved understanding of red-giant stars and binary stars. We discuss the characterization of known eccentric system, containing a solar-like oscillating red-giant primary component. We also report several new binary systems that are candidates for hosting an oscillating companion. A powerful approach to study binary stars is to combine asteroseimic techniques with light curve fitting. Seismology allows us to deduce the properties of red giants. In addition, by modeling the ellipsoidal modulations we can constrain the parameters of the binary system. An valuable independent source are ground-bases, high-resolution spectrographs

Accounting for Seismic Risk in Financial Analysis of Property Investment

A methodology is presented for making property investment decisions using loss analysis and the principles of decision analysis. It proposes that the investor choose among competing investment alternatives on the basis of the certainty equivalent of their net asset value which depends on the uncertain discounted future net income, uncertain discounted future earthquake losses, initial equity and the investor’s risk tolerance. The earthquake losses are modelled using a seismic vulnerability function, the site seismic hazard function, and an assumption that strong shaking at a site follows a Poisson process. A building-specific vulnerability approach, called assembly-based vulnerability, or ABV, is used. ABV involves a simulation approach that includes dynamic structural analyses and damage analyses using fragility functions and probability distributions on unit repair costs and downtimes for all vulnerable structural and nonstructural components in a building. The methodology is demonstrated using some results from a seven-storey reinforced-concrete hotel in Los Angeles

Simulations of the Galaxy Cluster CIZA J2242.8+5301 I: Thermal Model and Shock Properties

The giant radio relic in CIZA J2242.8+5301 is likely evidence of a Mpc sized shock in a massive merging galaxy cluster. However, the exact shock properties are still not clearly determined. In particular, the Mach number derived from the integrated radio spectrum exceeds the Mach number derived from the X-ray temperature jump by a factor of two. We present here a numerical study, aiming for a model that is consistent with the majority of observations of this galaxy cluster. We first show that in the northern shock upstream X-ray temperature and radio data are consistent with each other. We then derive progenitor masses for the system using standard density profiles, X-ray properties and the assumption of hydrostatic equilibrium. We find a class of models that is roughly consistent with weak lensing data, radio data and some of the X-ray data. Assuming a cool-core versus non-cool-core merger, we find a fiducial model with a total mass of $1.6 \times 10^{15}\,M_\odot$, a mass ratio of 1.76 and a Mach number that is consistent with estimates from the radio spectrum. We are not able to match X-ray derived Mach numbers, because even low mass models over-predict the X-ray derived shock speeds. We argue that deep X-ray observations of CIZA J2242.8+5301 will be able to test our model and potentially reconcile X-ray and radio derived Mach numbers in relics.Comment: 19 pages, 19 figure

Surface energetics and structure of the Ge wetting layer on Si(100)

Ge deposited on Si(100) initially forms heteroepitaxial layers, which grow to a critical thickness of ~3 MLs before the appearance of three-dimensional strain relieving structures. Experimental observations reveal that the surface structure of this Ge wetting layer is a dimer vacancy line (DVL) superstructure of the unstrained Ge(100) dimer reconstruction. In the following, the results of first-principles calculations of the thickness dependence of the wetting layer surface excess energy for the c(4×2) and 4×6 DVL surface reconstructions are reported. These results predict a wetting layer critical thickness of ~3 MLs, which is largely unaffected by the presence of dimer vacancy lines. The 4×6 DVL reconstruction is found to be thermodynamically stable with respect to the c(4×2) structure for wetting layers at least 2 ML thick. A strong correlation between the fraction of total surface induced deformation present in the substrate and the thickness dependence of wetting layer surface energy is also shown

Hybrid Atom--Photon Quantum Gate in a Superconducting Microwave Resonator

We propose a novel hybrid quantum gate between an atom and a microwave photon in a superconducting coplanar waveguide cavity by exploiting the strong resonant microwave coupling between adjacent Rydberg states. Using experimentally achievable parameters gate fidelities $> 0.99$ are possible on sub-$\mu$s timescales for waveguide temperatures below 40 mK. This provides a mechanism for generating entanglement between two disparate quantum systems and represents an important step in the creation of a hybrid quantum interface applicable for both quantum simulation and quantum information processing.Comment: 4 pages, 4 figure