Higher-Order Beta Matching with Solutions in Long Beta-Eta Normal Form

Higher-order matching is a special case of unification of simply-typed lambda-terms: in a matching equation, one of the two sides contains no unification variables. Loader has recently shown that higher-order matching up to beta equivalence is undecidable, but decidability of higher-order matching up to beta-eta equivalence is a long-standing open problem. We show that higher-order matching up to beta-eta equivalence is decidable if and only if a restricted form of higher-order matching up to beta equivalence is decidable: the restriction is that solutions must be in long beta-eta normal form

A computational study of thrust augmenting ejectors based on a viscous-inviscid approach

A viscous-inviscid interaction technique is advocated as both an efficient and accurate means of predicting the performance of two-dimensional thrust augmenting ejectors. The flow field is subdivided into a viscous region that contains the turbulent jet and an inviscid region that contains the ambient fluid drawn into the device. The inviscid region is computed with a higher-order panel method, while an integral method is used for the description of the viscous part. The strong viscous-inviscid interaction present within the ejector is simulated in an iterative process where the two regions influence each other en route to a converged solution. The model is applied to a variety of parametric and optimization studies involving ejectors having either one or two primary jets. The effects of nozzle placement, inlet and diffuser shape, free stream speed, and ejector length are investigated. The inlet shape for single jet ejectors is optimized for various free stream speeds and Reynolds numbers. Optimal nozzle tilt and location are identified for various dual-ejector configurations

A zonal computational procedure adapted to the optimization of two-dimensional thrust augmentor inlets

A viscous-inviscid interaction methodology based on a zonal description of the flowfield is developed as a mean of predicting the performance of two-dimensional thrust augmenting ejectors. An inviscid zone comprising the irrotational flow about the device is patched together with a viscous zone containing the turbulent mixing flow. The inviscid region is computed by a higher order panel method, while an integral method is used for the description of the viscous part. A non-linear, constrained optimization study is undertaken for the design of the inlet region. In this study, the viscous-inviscid analysis is complemented with a boundary layer calculation to account for flow separation from the walls of the inlet region. The thrust-based Reynolds number as well as the free stream velocity are shown to be important parameters in the design of a thrust augmentor inlet

Plastic Dissipation Energy in Mixed-Mode Fatigue Crack Growth on Ductile Bimaterial Interfaces

A new theory of fatigue crack growth in ductile solids has recently been proposed based on the total plastic energy dissipation per cycle ahead of the crack. This and previous energy-based approaches in the literature suggest that the total plastic dissipation per cycle can be closely correlated with fatigue crack growth rates under Mode I loading. The goal of the current study is to extend the dissipated energy approach to steady-state crack growth under mixed-mode loading conditions, with application to cyclic delamination of ductile interfaces in layered materials. The total plastic dissipation per cycle is obtained by 2-D elastic-plastic finite element analysis of a stationary crack in a general mixed-mode specimen geometry under constant amplitude loading. Both elastic-perfectly plastic and bi-linear kinematic hardening constitutive behaviors are considered, and numerical results for a dimensionless plastic dissipation per cycle are presented over the full range of relevant mechanical properties and mixed-mode loading conditions. In addition, numerical results are presented for the case of fatigue crack growth along a bonded interface between materials with identical elastic, yet dissimilar plastic properties, including mismatches in both kinematic hardening modulus and yield strength. Finally, the approach is generalized to include mismatches in both elastic and plastic properties, and results for the dimensionless plastic dissipation per cycle are reported over the complete design space of bimaterial interfaces. The results of this thesis are of interest in soldering, welding, coating, electronic packaging, and a variety of layered manufacturing applications, where mismatches in both elastic and plastic properties can exist between the deposited material and the substrate

Boundary Homogenization and Capture Time Distributions of Semipermeable Membranes with Periodic Patterns of Reactive Sites

We consider the capture dynamics of a particle undergoing a random walk in a half- space bounded by a plane with a periodic pattern of absorbing pores. In particular, we numerically measure and asymptotically characterize the distribution of capture times. Numerically we develop a kinetic Monte Carlo (KMC) method that exploits exact solutions to create an efficient particle- based simulation of the capture time that deals with the infinite half-space exactly and has a run time that is independent of how far from the pores one begins. Past researchers have proposed homogenizing the surface boundary conditions, replacing the reflecting (Neumann) and absorbing (Dirichlet) boundary conditions with a mixed (Robin) boundary condition. We extend previous work to asymptotically determine the leakage parameter for the mixed boundary condition for arbitrary periodic pore configurations in the dilute fraction limit. In this asymptotic limit, we pose and solve an optimization problem for the Bravais lattice which maximizes the capture rate of the absorbing pores, finding the hexagonal lattice to be the global maximum

Spring separation of spacecraft

IBM 7090 digital computer program for solving equations of motion for spacecraft separating from final rocket stage or another spacecraft by means of precision helical compression spring

Low-Energy Theorems from Holography

In the context of gauge/gravity duality, we verify two types of gauge theory low-energy theorems, the dilation Ward identities and the decoupling of heavy flavor. First, we provide an analytic proof of non-trivial dilation Ward identities for a theory holographically dual to a background with gluon condensate (the self-dual Liu--Tseytlin background). In this way an important class of low-energy theorems for correlators of different operators with the trace of the energy-momentum tensor is established, which so far has been studied in field theory only. Another low-energy relationship, the so-called decoupling theorem, is numerically shown to hold universally in three holographic models involving both the quark and the gluon condensate. We show this by comparing the ratio of the quark and gluon condensates in three different examples of gravity backgrounds with non-trivial dilaton flow. As a by-product of our study, we also obtain gauge field condensate contributions to meson transport coefficients.Comment: 32 pages, 4 figures, two references added, typos remove