Multidimensional computer simulation of Stirling cycle engines

This report summarizes the activities performed under NASA-Grant NAG3-1097 during 1991. During that period, work centered on the following tasks: (1) to investigate more effective solvers for ALGAE; (2) to modify the plotting package for ALGAE; and (3) to validate ALGAE by simulating oscillating flow problems similar to those studied by Kurzweg and Ibrahim

Managing Option Fragility

We analyze and explore option fragility, the notion that option incentives are fragile due to their non-linear payoff structure. Option incentives become weaker as options fall underwater, leading to pressures to reprice options or restore incentives through additional grants of equity-based pay. We build a detailed data set on executives' portfolios of stock and options and find that executive options are frequently underwater, even when average stock returns have been high. For example, at the height of the bull market in 1999, approximately one-third of all executive options were underwater. We find that, in contrast to the incentives provided by stock, the incentives provided by options are quite sensitive to stock price changes, especially on the downside. Overall, we find that the incentives created by all executive holdings have an elasticity with respect to stock price decreases of about 0.7, and this elasticity is larger for high-option executives and for executives with high percentages of options already underwater. The dominant mechanism through which companies manage option fragility is larger option grants following stock price declines; on average, these larger grants restore approximately 40% of the stock-price-induced incentive declines. Option repricings are far less prevalent, despite the attention they have garnered. Interestingly, we find that for positive stock returns, higher returns lead to larger option grants, which raise incentives further. Thus, option grants are largest when companies do very poorly or very well. Executive exercising behavior also affects option fragility. Since executives are much less likely to exercise options following stock price decreases, the natural declines in incentives due to exercises are attenuated on the downside, leading executives to 'manage their own incentives' in a way that augments company management of option fragility.

Momentum transfer dependence of the proton's electric and magnetic polarizabilities

The Q^2-dependence of the sum of the electric and magnetic polarizabilities of the proton is calculated over the range 0 \leq Q^2 \leq 6 GeV^2 using the generalized Baldin sum rule. Employing a parametrization of the F_1 structure function valid down to Q^2 = 0.06 GeV^2, the polarizabilities at the real photon point are found by extrapolating the results of finite Q^2 to Q^2 = 0 GeV^2. We determine the evolution over four-momentum transfer to be consistent with the Baldin sum rule using photoproduction data, obtaining \alpha + \beta = 13.7 \pm 0.7 \times 10^{-4}\, \text{fm}^3.Comment: 4 pages, 3 figure

On the nonlinear interaction of Gortler vortices and Tollmien-Schlichting waves in curved channel flows at finite Reynolds numbers

The flow in a two-dimensional curved channel driven by an azimuthal pressure gradient can become linearly unstable due to axisymmetric perturbations and/or nonaxisymmetric perturbations depending on the curvature of the channel and the Reynolds number. For a particular small value of curvature, the critical neighborhood of this curvature value and critical Reynolds number, nonlinear interactions occur between these perturbations. The Stuart-Watson approach is used to derive two coupled Landau equations for the amplitudes of these perturbations. The stability of the various possible states of these perturbations is shown through bifurcation diagrams. Emphasis is given to those cases which have relevance to external flows

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

Baryon resonances and hadronic interactions in a finite volume

In a finite volume, resonances and multi-hadron states are identified by discrete energy levels. When comparing the results of lattice QCD calculations to scattering experiments, it is important to have a way of associating the energy spectrum of the finite-volume lattice with the asymptotic behaviour of the S-matrix. A new technique for comparing energy eigenvalues with scattering phase shifts is introduced, which involves the construction of an exactly solvable matrix Hamiltonian model. The model framework is applied to the case of $\Delta\rightarrow N\pi$ decay, but is easily generalized to include multi-channel scattering. Extracting resonance parameters involves matching the energy spectrum of the model to that of a lattice QCD calculation. The resulting fit parameters are then used to generate phase shifts. Using a sample set of pseudodata, it is found that the extraction of the resonance position is stable with respect to volume for a variety of regularization schemes, and compares favorably with the well-known Luescher method. The model-dependence of the result is briefly investigated.Comment: 7 pages, 3 figures. Talk presented at the 30th International Symposium on Lattice Field Theory (Lattice 2012), June 24-29, 2012, Cairns, Australi

Quark-hadron duality constraints on \gamma Z box corrections to parity-violating elastic scattering

We examine the interference \gamma Z box corrections to parity-violating elastic electron--proton scattering in the light of the recent observation of quark-hadron duality in parity-violating deep-inelastic scattering from the deuteron, and the approximate isospin independence of duality in the electromagnetic nucleon structure functions down to Q^2 \approx 1 GeV^2. Assuming that a similar behavior also holds for the \gamma Z proton structure functions, we find that duality constrains the \gamma Z box correction to the proton's weak charge to be \Re e\, \square_{\gamma Z}^V = (5.4 \pm 0.4) \times 10^{-3} at the kinematics of the Q_{\text{weak}} experiment. Within the same model we also provide estimates of the \gamma Z corrections for future parity-violating experiments, such as MOLLER at Jefferson Lab and MESA at Mainz.Comment: 10 pages, 3 figures. Final version to be published in Phys. Lett.

A Polyhedral Intersection Theorem for Capacitated Spanning Trees

In a two-capacitated spanning tree of a complete graph with a distinguished root vertex v, every component of the induced subgraph on V\{v} has at most two vertices. We give a complete,non-redundant characterization of the polytope defined by the convex hull of the incidence vectors of two-capacitated spanning trees. This polytope is the intersection of the spanning tree polytope on the given graph and the matching polytope on the subgraph induced by removing the root node and its incident edges. This result is one of very few known cases in which the intersection of two integer polyhedra yields another integer polyhedron. We also give a complete polyhedral characterization of a related polytope, the 2-capacitated forest polytope

Adolescent smoking networks: The effects of influence and selection on future smoking

Submitted in fulfillment of KU faculty's Open Access Policy.Peer influence and peer selection have both been linked to the smoking behavior of adolescents. The present investigation uses social network analysis methodology to explore the simultaneous effects of both processes on adolescent smoking and smoking susceptibility over two time periods. Results suggest the effects of friendship selection in 6th grade on smoking behavior in 7th grade were primarily direct. Selecting smokers as friends in 6th grade predicted both smoking and smoking susceptibility in 7th grade, and selecting susceptibles predicted future friendship selection and peer influence. Influence processes were indirectly related to smoking. Smokers' influence in 6th grade predicts the selection of smokers as friends in 7th grade. Smokers' influence also demonstrated a protective effect when ties were not reciprocated