4,709 research outputs found
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 -dimensional hypercube into
isomorphic copies of a given graph . While a number of results are known
about decomposing 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 is even, and divides the number
of edges of , then the path of length decomposes . Tapadia et
al.\ proved that any path of length , where , satisfying these
conditions decomposes . Here, we make progress toward resolving Erde's
conjecture by showing that cycles of certain lengths up to
decompose . As a consequence, we show that can be decomposed into
copies of any path of length at most dividing the number of edges of
, 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
Getting the practical teaching element right: A guide for literacy, numeracy and ESOL teacher educators
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
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