A Comparison of Sensitivity Metrics for Two-Stage Ignition Behavior in Rapid Compression Machines

A rapid compression machine (RCM) multi-zone model is used to simulate the ignition of primary reference fuel (PRF) mixtures that exhibit two-stage ignition behavior. Sensitivity coefficients for each reaction in the PRF mechanism are calculated from four different metrics: (1) first-stage energy release, (2) first-stage pressure rise, (3) first-stage ignition delay time, and (4) total ignition delay time. The sensitivity coefficients are used to provide four unique rankings, and the rankings are compared using Spearman’s rank correlation coefficient. Special emphasis is given to comparing the rankings based on first-stage energy release and total ignition delay time. The level of agreement between these two rankings is shown to depend on the reaction conditions. Simulation cases with high peak heat release rates during the first stage of ignition tend to exhibit disagreement in the rankings, indicating that new kinetic information can be obtained by studying first stage energy release in addition to total ignition delay time. Simulations show that the high peak heat release rates are associated with energy release across a broad range of temperatures (range can be in excess of 100 K even for lean conditions). This distribution leads to a discrepancy between sensitivity coefficients calculated for the total ignition delay time and the first-stage energy release. Sensitivity coefficients for the total ignition delay time are characterized by reactivity at the highest temperatures in the RCM, while sensitivity coefficients for the first-stage energy release are characterized by reactivity across the full range of temperatures in the RCM

Long path and cycle decompositions of even hypercubes

We consider edge decompositions of the $n$-dimensional hypercube $Q_n$ into isomorphic copies of a given graph $H$. While a number of results are known about decomposing $Q_n$ into graphs from various classes, the simplest cases of paths and cycles of a given length are far from being understood. A conjecture of Erde asserts that if $n$ is even, $\ell < 2^n$ and $\ell$ divides the number of edges of $Q_n$, then the path of length $\ell$ decomposes $Q_n$. Tapadia et al.\ proved that any path of length $2^mn$, where $2^m<n$, satisfying these conditions decomposes $Q_n$. Here, we make progress toward resolving Erde's conjecture by showing that cycles of certain lengths up to $2^{n+1}/n$ decompose $Q_n$. As a consequence, we show that $Q_n$ can be decomposed into copies of any path of length at most $2^{n}/n$ dividing the number of edges of $Q_n$, thereby settling Erde's conjecture up to a linear factor

Chaos and Turbulent Nucleosynthesis Prior to a Supernova Explosion

Three-dimensional (3D), time dependent numerical simulations, of flow of matter in stars, now have sufficient resolution to be fully turbulent. The late stages of the evolution of massive stars, leading up to core collapse to a neutron star (or black hole), and often to supernova explosion and nucleosynthesis, are strongly convective because of vigorous neutrino cooling and nuclear heating. Unlike models based on current stellar evolutionary practice, these simulations show a chaotic dynamics characteristic of highly turbulent flow. Theoretical analysis of this flow, both in the Reynolds-averaged Navier-Stokes (RANS) framework and by simple dynamic models, show an encouraging consistency with the numerical results. It may now be possible to develop physically realistic and robust procedures for convection and mixing which (unlike 3D numerical simulation) may be applied throughout the long life times of stars. In addition, a new picture of the presupernova stages is emerging which is more dynamic and interesting (i.e., predictive of new and newly observed phenomena) than our previous one.Comment: 11 pages, 2 figures, Submitted to AIP Advances: Stardust, added figures and modest rewritin

Quality of Life, Firm Productivity, and the Value of Amenities across Canadian Cities

This paper presents the first hedonic general-equilibrium estimates of quality-of-life and firm productivity differences across Canadian cities, using data on local wages and housing costs. These estimates account for the unobservability of land rents and geographic differences in federal and provincial tax burdens. Quality of life estimates are generally higher in Canada’s larger cities: Victoria, Vancouver are the nicest overall, particularly for Anglophones, while Montreal and Ottawa are the nicest for Francophones. These estimates are positively correlated with estimates in the popular literature and may be explained by differences in climate. Toronto is Canada’s most productive city; Vancouver, the overall most valued city.quality of life, firm productivity, cost-of-living, firm productivity, compensating wage differentials

Toward a consistent use of overshooting parametrizations in 1D stellar evolution codes

Several parametrizations for overshooting in 1D stellar evolution calculations coexist in the literature. These parametrizations are used somewhat arbitrarily in stellar evolution codes, based on what works best for a given problem, or even for historical reasons related to the development of each code. We bring attention to the fact that these different parametrizations correspond to different physical regimes of overshooting, depending whether the effects of radiation are dominant, marginal, or negligible. Our analysis is based on previously published theoretical results, as well as multidimensional hydrodynamical simulations of stellar convection where the interaction between the convective region and a stably-stratified region is observed. Although the underlying hydrodynamical processes are the same, the outcome of the overshooting process is profoundly affected by radiative effects. Using a simple picture of the scales involved in the overshooting process, we show how three regimes are obtained, depending on the importance of radiative effects. These three regimes correspond to the different behaviors observed in hydrodynamical simulations so far, and to the three types of parametrizations used in 1D codes. We suggest that the existing parametrizations for overshooting should coexist in 1D stellar evolution codes, and should be applied consistently at convective boundaries depending on the local physical conditions.Comment: 5 pages, 2 figures, to appear in A&A as a regular paper. Last version: language editing + typos in Eq. (6) & (9) correcte