Local structure of intercomponent energy transfer in homogeneous turbulent shear flow

Intercomponent energy transfer by pressure-strain-rate was investigated for homogeneous turbulent shear flow. The rapid and slow parts of turbulent pressure (decomposed according to the influence of the mean deformation rate) are found to be uncorrelated; this finding provides strong justification for current modeling procedure in which the pressure-strain-rate term is split into the corresponding parts. Issues pertinent to scales involved in the intercomponent energy transfer are addressed in comparison with those for the Reynolds-stress and vorticity fields. A physical picture of the energy transfer process is described from a detailed study of instantaneous events of high transfer regions. It was found that the most significant intercomponent energy transfer events are highly localized in space and are imbedded within a region of concentrated vorticity

Pressure-strain-rate events in homogeneous turbulent shear flow

A detailed study of the intercomponent energy transfer processes by the pressure-strain-rate in homogeneous turbulent shear flow is presented. Probability density functions (pdf's) and contour plots of the rapid and slow pressure-strain-rate show that the energy transfer processes are extremely peaky, with high-magnitude events dominating low-magnitude fluctuations, as reflected by very high flatness factors of the pressure-strain-rate. A concept of the energy transfer class was applied to investigate details of the direction as well as magnitude of the energy transfer processes. In incompressible flow, six disjoint energy transfer classes exist. Examination of contours in instantaneous fields, pdf's and weighted pdf's of the pressure-strain-rate indicates that in the low magnitude regions all six classes play an important role, but in the high magnitude regions four classes of transfer processes, dominate. The contribution to the average slow pressure-strain-rate from the high magnitude fluctuations is only 50 percent or less. The relative significance of high and low magnitude transfer events is discussed

Sets Characterized by Missing Sums and Differences in Dilating Polytopes

A sum-dominant set is a finite set $A$ of integers such that $|A+A| > |A-A|$. As a typical pair of elements contributes one sum and two differences, we expect sum-dominant sets to be rare in some sense. In 2006, however, Martin and O'Bryant showed that the proportion of sum-dominant subsets of $\{0,\dots,n\}$ is bounded below by a positive constant as $n\to\infty$. Hegarty then extended their work and showed that for any prescribed $s,d\in\mathbb{N}_0$, the proportion $\rho^{s,d}_n$ of subsets of $\{0,\dots,n\}$ that are missing exactly $s$ sums in $\{0,\dots,2n\}$ and exactly $2d$ differences in $\{-n,\dots,n\}$ also remains positive in the limit. We consider the following question: are such sets, characterized by their sums and differences, similarly ubiquitous in higher dimensional spaces? We generalize the integers in a growing interval to the lattice points in a dilating polytope. Specifically, let $P$ be a polytope in $\mathbb{R}^D$ with vertices in $\mathbb{Z}^D$, and let $\rho_n^{s,d}$ now denote the proportion of subsets of $L(nP)$ that are missing exactly $s$ sums in $L(nP)+L(nP)$ and exactly $2d$ differences in $L(nP)-L(nP)$. As it turns out, the geometry of $P$ has a significant effect on the limiting behavior of $\rho_n^{s,d}$. We define a geometric characteristic of polytopes called local point symmetry, and show that $\rho_n^{s,d}$ is bounded below by a positive constant as $n\to\infty$ if and only if $P$ is locally point symmetric. We further show that the proportion of subsets in $L(nP)$ that are missing exactly $s$ sums and at least $2d$ differences remains positive in the limit, independent of the geometry of $P$. A direct corollary of these results is that if $P$ is additionally point symmetric, the proportion of sum-dominant subsets of $L(nP)$ also remains positive in the limit.Comment: Version 1.1, 23 pages, 7 pages, fixed some typo

A New Cost-Benefit and Rate of Return Analysis for the Perry Preschool Program: A Summary

This paper summarizes our recent work on the rate of return and cost-benefit ratio of an influential early childhood program.early childhood, rate of return, cost-benefit analysis

Analyzing Social Experiments as Implemented: A Reexamination of the Evidence from the HighScope Perry Preschool Program

Social experiments are powerful sources of information about the effectiveness of interventions. In practice, initial randomization plans are almost always compromised. Multiple hypotheses are frequently tested. "Significant" effects are often reported with p-values that do not account for preliminary screening from a large candidate pool of possible effects. This paper develops tools for analyzing data from experiments as they are actually implemented. We apply these tools to analyze the influential HighScope Perry Preschool Program. The Perry program was a social experiment that provided preschool education and home visits to disadvantaged children during their preschool years. It was evaluated by the method of random assignment. Both treatments and controls have been followed from age 3 through age 40. Previous analyses of the Perry data assume that the planned randomization protocol was implemented. In fact, as in many social experiments, the intended randomization protocol was compromised. Accounting for compromised randomization, multiple-hypothesis testing, and small sample sizes, we find statistically significant and economically important program effects for both males and females. We also examine the representativeness of the Perry study.social experiment, compromised randomization, early childhood intervention, multiple-hypothesis testing

The Rate of Return to the High/Scope Perry Preschool Program

This paper estimates the rate of return to the High/Scope Perry Preschool Program, an early intervention program targeted toward disadvantaged African-American youth. Estimates of the rate of return to the Perry program are widely cited to support the claim of substantial economic benefits from preschool education programs. Previous studies of the rate of return to this program ignore the compromises that occurred in the randomization protocol. They do not report standard errors. The rates of return estimated in this paper account for these factors. We conduct an extensive analysis of sensitivity to alternative plausible assumptions. Estimated social rates of return generally fall between 7-10 percent, with most estimates substantially lower than those previously reported in the literature. However, returns are generally statistically significantly different from zero for both males and females and are above the historical return on equity. Estimated benefit-to-cost ratios support this conclusion.early childhood intervention programs, compromised randomization, Perry Preschool Program, standard errors, cost-benefit analysis, rate of return, deadweight costs

Analyzing Social Experiments as Implemented: A Reexamination of the Evidence From the HighScope Perry Preschool Program

Social experiments are powerful sources of information about the effectiveness of interventions. In practice, initial randomization plans are almost always compromised. Multiple hypotheses are frequently tested. "Signicant" effects are often reported with p-values that do not account for preliminary screening from a large candidate pool of possible effects. This paper develops tools for analyzing data from experiments as they are actually implemented. We apply these tools to analyze the influential HighScope Perry Preschool Program. The Perry program was a social experiment that provided preschool education and home visits to disadvantaged children during their preschool years. It was evaluated by the method of random assignment. Both treatments and controls have been followed from age 3 through age 40. Previous analyses of the Perry data assume that the planned randomization protocol was implemented. In fact, as in many social experiments, the intended randomization protocol was compromised. Accounting for compromised randomization, multiple-hypothesis testing, and small sample sizes, we find statistically significant and economically important program effects for both males and females. We also examine the representativeness of the Perry study.early childhood intervention; compromised randomization; social experiment; multiple-hypothesis testing

The Rate of Return to the High/Scope Perry Preschool Program

This paper estimates the rate of return to the High/Scope Perry Preschool Program, an early intervention program targeted toward disadvantaged African-American youth. Estimates of the rate of return to the Perry program are widely cited to support the claim of substantial economic benefits from preschool education programs. Previous studies of the rate of return to this program ignore the compromises that occurred in the randomization protocol. They do not report standard errors. The rates of return estimated in this paper account for these factors. We conduct an extensive analysis of sensitivity to alternative plausible assumptions. Estimated social rates of return generally fall between 7–10 percent, with most estimates substantially lower than those previously reported in the literature. However, returns are generally statistically significantly different from zero for both males and females and are above the historical return on equity. Estimated benefit-to-cost ratios support this conclusion.rate of return, cost-benefit analysis, standard errors, Perry Preschool Program, compromised randomization, early childhood intervention programs, deadweight costs

Enhanced Energy Dissipation in Stepped Chutes. (Discussion)

The contribution is a timely reminder that most research on stepped chute hydraulics has been narrowly limited to flat identical horizontal steps in straight prismatic rectangular channels (Chanson 2001). For completeness, the writer wishes to provide relevant information on early stepped spillways and related works. He also adds some pertinent comment

Reconciliation of Waiting Time Statistics of Solar Flares Observed in Hard X-Rays

We study the waiting time distributions of solar flares observed in hard X-rays with ISEE-3/ICE, HXRBS/SMM, WATCH/GRANAT, BATSE/CGRO, and RHESSI. Although discordant results and interpretations have been published earlier, based on relatively small ranges ($< 2$ decades) of waiting times, we find that all observed distributions, spanning over 6 decades of waiting times ($\Delta t \approx 10^{-3}- 10^3$ hrs), can be reconciled with a single distribution function, $N(\Delta t) \propto \lambda_0 (1 + \lambda_0 \Delta t)^{-2}$, which has a powerlaw slope of $p \approx 2.0$ at large waiting times ($\Delta t \approx 1-1000$ hrs) and flattens out at short waiting times \Delta t \lapprox \Delta t_0 = 1/\lambda_0. We find a consistent breakpoint at $\Delta t_0 = 1/\lambda_0 = 0.80\pm0.14$ hours from the WATCH, HXRBS, BATSE, and RHESSI data. The distribution of waiting times is invariant for sampling with different flux thresholds, while the mean waiting time scales reciprocically with the number of detected events, $\Delta t_0 \propto 1/n_{det}$. This waiting time distribution can be modeled with a nonstationary Poisson process with a flare rate $\lambda=1/\Delta t$ that varies as $f(\lambda) \propto \lambda^{-1} \exp{-(\lambda/\lambda_0)}$. This flare rate distribution represents a highly intermittent flaring productivity in short clusters with high flare rates, separated by quiescent intervals with very low flare rates.Comment: Preprint also available at http://www.lmsal.com/~aschwand/eprints/2010_wait.pd