James Quirk

The role of unsteadiness in direct initiation of gaseous detonations

An analytical model is presented for the direct initiation of gaseous detonations by a blast wave. For stable or weakly unstable mixtures, numerical simulations of the spherical direct initiation event and local analysis of the one-dimensional unsteady reaction zone structure identify a competition between heat release, wave front curvature and unsteadiness. The primary failure mechanism is found to be unsteadiness in the induction zone arising from the deceleration of the wave front. The quasi-steady assumption is thus shown to be incorrect for direct initiation. The numerical simulations also suggest a non-uniqueness of critical energy in some cases, and the model developed here is an attempt to explain the lower critical energy only. A critical shock decay rate is determined in terms of the other fundamental dynamic parameters of the detonation wave, and hence this model is referred to as the critical decay rate (CDR) model. The local analysis is validated by integration of reaction-zone structure equations with real gas kinetics and prescribed unsteadiness. The CDR model is then applied to the global initiation problem to produce an analytical equation for the critical energy. Unlike previous phenomenological models of the critical energy, this equation is not dependent on other experimentally determined parameters and for evaluation requires only an appropriate reaction mechanism for the given gas mixture. For different fuel–oxidizer mixtures, it is found to give agreement with experimental data to within an order of magnitude.

Owner objectives and competitive balance.

A growing literature on leagues composed of owners maximizing winning percentage shows that particular league rules have different impacts compared with leagues composed of profit-maximizing owners. But the underlying question of how to distinguish between the two types of leagues has received no treatment. In this article, we show that the two types of leagues can be distinguished in the talent market. A league of winning-percentage-maximizing owners will have higher talent costs and greater demand for talent. But, and perhaps more important, the level of competitive balance between the two types of leagues is indeterminate. In addition, a new policy instrument is suggested, namely, nudging owners toward one or the other objective, depending upon the particular locations of the demand for talent if owners pursue profits or winning percentage.

A parallel adaptive grid algorithm for computational shock hydrodynamics

Abstract Adaptive Mesh Refinement (AMR) algorithms that dynamically match the local resolution of the computational grid to the numerical solution being sought have emerged as powerful tools for solving problems that contain disparate physical scales. In particular several workers have demonstrated the effectiveness of employing an adaptive, hierarchical block-structured grid system for time-accurate simulations of complex shock wave phenomena. Here we present an overview of one such block-structured AMR algorithm. Our formulation has progressed far beyond the development stage to become a reliable numerical tool for performing detailed investigations of complex flows. While our refinement machinery is not tied to a specific application and is intended for general use, in this paper we adopt detonation phenomena as a theme so as to provide a sense of purpose.

Rational Expectations and Pro Sports Leagues

We put a new set of shoes on that old workhorse, the competitive talent market (CTM) model in sports economics. There exist unique rational expectations equilibria for both national football league (NFL-type leagues) and major league baseball (MLB-type leagues) under the CTM model. A cursory statistical test fails to reject the empirical implications for the NFL-type league. The model also suggests empirical tests of whether or not talent demand (marginal revenues from talent), including induced effects, actually slopes down. But like all models, the competitive talent model should be applied in its context. It describes highly cooperative North American sports leagues that have a wealth of common information. But it may not do the same for other leagues if they lack this common information.

Optimal Competitive Balance in a Season Ticket League

Theory predicts that a planner maximizing the sum of fan and owner surpluses from a league dominated by season ticket sales may prefer more, less, or the same level of competitive balance produced by a league of profit-maximizing owners. The optimal level of balance depends on the relationship between marginal impacts of talent rearrangements in larger-revenue and smaller-revenue markets. Ultimately, then, judging whether an increase in balance enhances welfare rests on careful and thorough empirical investigation. Our reading of the literature and the policy debate shows that this careful work remains to be done.

Optimal Competitive Balance in Single-Game Ticket Sports Leagues

The authors extend the theory of optimal competitive balance to leagues where single-game ticket sales dominate revenues. Whether a planner that maximizes the sum of fan and owner surpluses prefers more balance or less in such a league depends on the relative magnitude of marginal consumers’ surpluses with respect to talent in larger and smaller revenue markets. This relationship is much more complex than previous cases in the literature. Ultimately, then, the determination of whether more balance is preferred to less in any particular sports league requires careful and thorough empirical investigation.

Choosing a government discount rate: An alternative approach

Abstract This paper examines the choice of a government discount rate, under the reasonable assumption that the level of government spending is determined in a “top down” fashion, by macroeconomic and political considerations, rather than in a “bottom up” fashion. It is shown that setting the discount rate at the maximal internal rate of return available from unfunded government projects leads to an efficient portfolio choice. Under current and foreseeable conditions, this implies a discount rate in the 10% or more real range, rather than the 2–4% real discount rate recommended by second-best theorists.

Analysis of steady compaction waves in polyurea aerogel

Submitted for the SHOCK17 Meeting of The American Physical Society Analysis of steady compaction waves in polyurea aerogel MATTHEW A. PRICE, TARIQ D. ASLAM, JAMES J. QUIRK, Los Alamos National Laboratory — Steady compaction waves in an inert porous material are investigated using a p − α model. In a steady traveling wave reference frame, the one-dimensional Euler equations are reduced to a set of ordinary differential equations. A Mie-Grüneisen equation of state (EOS) is used with parameters calibrated for polyurea aerogel (PUA). Analytic solutions for non-equilibrium compaction are developed which compliment numerical models and are able to predict the complete wave structure, including the compaction wave speed, zone length, and final compacted solid volume fraction. The dynamic compaction of PUA is studied for a range of piston velocities. Three regions of behavior are identified: supersonic, subsonic-complete, and subsonic-partial compaction. Below a critical piston velocity, a subsonic compaction wave is produced without a leading shock. At even lower piston velocities, there is partial compaction and a greater dependence on the dynamic compaction relation. Some features and limitations of the current model are discussed. Matthew A. Price Los Alamos National Laboratory Date submitted: 16 Feb 2017 Electronic form version 1.4