Implications of a Fully Nonlocal Implementation of the Dispersive Optical Model

A fully nonlocal treatment for the dispersive optical model (DOM) is implemented for both the real and imaginary part of the self-energy inspired by ab initio theoretical calculations of this quantity. By means of the dispersion relation between the real and imaginary part of the optical potential a link between the energy domain of nuclear reactions and nuclear structure is established. The relevant scattering data for neutrons and protons on $^{40}$Ca are described with the same quality as was accomplished with previous local versions of the DOM. The solution of the Dyson equation at positive and negative energies is generated with a complete treatment of the nonlocality of the potentials. The resulting propagator has been utilized to explain and predict relevant quantities of the ground-state of the $^{40}$Ca nucleus. In particular the charge density, spectral strength and particle number can, for the first time, be accurately described. Moreover, due to the introduction of nonlocality in the imaginary part of the self-energy it is also possible to describe high-momentum protons and the contribution of the two-body interaction to the ground-state energy. The calculation of the spectral density at positive energies allows for the determination of the spectral strength of mostly occupied single-particle orbits in the continuum. Consistency of the resulting depletion numbers with the corresponding occupation numbers is studied and compared to ab initio calculations for these quantities. Starting from the $^{40}$Ca self-energy, an extension to the $^{48}$Ca nucleus is implemented focusing on the $N-Z$ dependence of the nucleon self-energy. Neutron scattering data can be described with even better quality than previous local DOM calculations. The scattering properties for protons are of similar excellent quality as for previous local results. From the solution of the Dyson equation for neutrons it is possible to calculate the neutron distribution of this nucleus allowing for the determination of the neutron skin which is relevant for the physics of neutron stars. The resulting value is larger than most calculations previously reported including an ab initio one. An argument supporting a large neutron skin is provided by analyzing proton elastic scattering data on both $^{40}$Ca and $^{48}$Ca

Computer Modeling of Close-to-Ground Tornado Wind-Fields for Different Tornado Widths

Tornadoes induce different wind forces on buildings than straight-line (SL) winds. The tangential velocity (Vθ) of tornados is the main parameter that causes damage to the buildings. In-field tornado measurements cannot evaluate the tornado’s Vθ at less than 20m above ground level (AGL). The laboratory tornado simulators suggest that the Swirl ratio (S) and the radius (ro) are the most influential factors affecting Vθ. However, due to scaling problems, laboratory simulators cannot report the Vθ for elevations less than 10m AGL. Well refined computational fluid dynamics (CFD) models can evaluate the Vθ at less than 10m AGL. However, the CFD models are limited to tornado radius ro=1.0km whereas observation of actual tornados by National Weather Service (NWS) shows that significant tornados in USA have width in the range of 0.7km to 2.3km. Thus, effect of ro on the Vθ is not investigated. Therefore, the aim of this study is to investigate the maximum Vθ (Vθ,max) for different tornado radii at elevations above and below 10m AGL. Simulation results show that by increasing the ro, the S parameter producing the Vθ,max will increase accordingly. In addition, results show that by increasing ro, the Vθ,max gradually reduces with respect to reference radial velocity Vr∞. In this respect, for 0.7km≤ ro ≤2.3km the Vθ,max is in the range of 6.5Vr∞ to 3.0Vr∞. Moreover, by increasing ro, the elevation of occurrence (zmax) of the Vθ,max will increase; However for all tornado radii, the zmax is always between 21m to 64m AGL. In addition, simulations show that for ro≤1.6km the radial Vθ profiles above 10m of the ground resemble the Rankine Combined Vortex Model (RCVM) flows, whereas at less than 10m of the ground the profile has two peaks for S greater than the touchdown S. Similarly, for ro≥1.8km the radial Vθ profiles below and above z=10m have two peaks for the S greater than the touchdown S

Optimal Allocation of Resources in Reliability Growth

Reliability growth testing seeks to identify and remove failure modes in order to improve system reliability. This dissertation centers around the resource allocation across the components of a multi-component system to maximize system reliability. We summarize this dissertation’s contributions to optimal resource allocation in reliability growth. Chapter 2 seeks to deploy limited testing resources across the components of a series-parallel system in effort to maximize system reliability under the assumption that each component’s reliability exhibits growth according to an AMSAA model with known parameters. An optimization model for this problem is developed and then extended to consider the allocation of testing resources in a series-parallel system with consideration for the possibility of testing at different levels (system, subsystem, and component). We contribute a class of exact algorithms that decomposes the problem based upon the series-parallel structure. We prove the algorithm is finite, compare it with heuristic approaches on a set of test instances, and provide detailed analyses of numerical examples. In Chapter 3, we extend model in Chapter 2 to solve a robust optimization version of this problem in which AMSAA parameters are uncertain but assumed to lie within a budget-restricted uncertainty set. We model the problem of robust allocation of testing resources to maximize system reliability for both series and series-parallel systems, and we develop and analyze exact solution approaches for this problem based on a cutting plane algorithm. Computational results demonstrate the value of the robust optimization approach as compared to deterministic alternatives. In the last chapter, we develop a new model that merges testing components and installing redundancies within an integrated optimization model that maximizes system reliability. Specifically, our model considers a series-parallel system in which the system reliability can be improved by both testing components and installing redundant components. We contribute an exact algorithm that decomposes the problem into smaller integer linear programs. We prove that this algorithm is finite and apply it to a set of instances. Experiments demonstrate that the integrated approach generates greater reliabilities than applying test planning and redundancy allocation models iteratively, and moreover, it yields significant savings in computational time