An Examination of Costs and Per-Pupil Revenues in Special Education With Simulations Designed to Enhance the Equity of Louisiana\u27s Special Education Financing Program.

The primary issues this study addressed were special education costs and equity of special education per-pupil revenues among Louisiana\u27s sixty-six school districts. Actual data from 1980 to 1992 were examined and four special education finance models were developed which addressed these issues. Average annual rates of increase in mean per-pupil revenues for regular education and special education were examined to determine the increase in cost of special education versus regular education. Findings indicated special education per-pupil revenues increased at four times the rate of regular education per-pupil revenues for the period examined. Special education per-pupil revenues were examined to determine whether or not per-pupil revenue disparities increased or decreased. The Range (R), Standard Deviation (SD), Coefficient of Variation (CV), Federal Range Ratio (FRR), and McLoone Index (MI), indicated increased disparity in special education per-pupil revenues from 1980 to 1992. These measures also indicated the largest increases in per-pupil revenue disparity occurred from 1990 to 1992. During this period Louisiana utilized a placeholder formula until a new formula could be developed. Four special education finance models were developed which used pupil weighting schemes and addressed equity issues in regard to special education costs, per-pupil revenues, and amount of per-pupil revenue for mild and severe disabilities. Findings in regard to equity were mixed according to the perspective of the measure used. All measures with the exception of the McLoone Index indicated one weight not linked to local effort to be the most equitable model. The McLoone Index indicated two weights decreased per-pupil revenue disparity in the lower half of the distribution. Relationships between district fiscal capacity, special education enrollments, and special education per-pupil revenues were examined. Two alternative definitions of district fiscal capacity were used. When district fiscal capacity was defined using per-capita income, relationships were noted among all variables in 1992. When district fiscal capacity was defined using the Representative Tax System Index which Louisiana now uses, relationships between these variables no longer existed. Finally, enrollments of five mild disabilities were examined. Large enrollment increases in all disabilities were noted with the exception of Speech Impaired. Findings indicated lack of clarity in the definition of disabilities coupled with many different interpretations of these definitions contributed to considerable variability in enrollments across districts

Letting Down the Team? Evidence of Social Effects of Team Incentives

This paper estimates social effects of incentivizing people in teams. In two field experiments featuring exogenous team formation and opportunities for repeated social interactions, we find large team effects that operate through social channels. The team compensation system induced agents to choose effort as if they valued a marginal dollar of compensation for their teammate from two-thirds as much (in one study) to twice as much as they valued a dollar of their own compensation (in the other study). We conclude that social effects of monetary team incentives exist and can induce effort at lower cost than through direct individual payment.

η\eta Carinae's Dusty Homunculus Nebula from Near-Infrared to Submillimeter Wavelengths: Mass, Composition, and Evidence for Fading Opacity

Infrared observations of the dusty, massive Homunculus Nebula around the luminous blue variable $\eta$ Carinae are crucial to characterize the mass-loss history and help constrain the mechanisms leading to the Great Eruption. We present the 2.4 - 670 $\mu$m spectral energy distribution, constructed from legacy ISO observations and new spectroscopy obtained with the {\em{Herschel Space Observatory}}. Using radiative transfer modeling, we find that the two best-fit dust models yield compositions which are consistent with CNO-processed material, with iron, pyroxene and other metal-rich silicates, corundum, and magnesium-iron sulfide in common. Spherical corundum grains are supported by the good match to a narrow 20.2 $\mu$m feature. Our preferred model contains nitrides AlN and Si$_3$N$_4$ in low abundances. Dust masses range from 0.25 to 0.44 $M_\odot$ but $M_{\rm{tot}} \ge$ 45 $M_\odot$ in both cases due to an expected high Fe gas-to-dust ratio. The bulk of dust is within a 5$"$ $\times$ 7$"$ central region. An additional compact feature is detected at 390 $\mu$m. We obtain $L_{\rm{IR}}$ = 2.96 $\times$ 10$^6$ $L_\odot$, a 25\% decline from an average of mid-IR photometric levels observed in 1971-1977. This indicates a reduction in circumstellar extinction in conjunction with an increase in visual brightness, allowing 25-40\% of optical and UV radiation to escape from the central source. We also present an analysis of $^{12}$CO and $^{13}$CO $J = 5-4$ through $9-8$ lines, showing that the abundances are consistent with expectations for CNO-processed material. The [$^{12}$C~{\sc{ii}}] line is detected in absorption, which we suspect originates in foreground material at very low excitation temperatures.Comment: Accepted in Ap

Droplet and cluster formation in freely falling granular streams

Particle beams are important tools for probing atomic and molecular interactions. Here we demonstrate that particle beams also offer a unique opportunity to investigate interactions in macroscopic systems, such as granular media. Motivated by recent experiments on streams of grains that exhibit liquid-like breakup into droplets, we use molecular dynamics simulations to investigate the evolution of a dense stream of macroscopic spheres accelerating out of an opening at the bottom of a reservoir. We show how nanoscale details associated with energy dissipation during collisions modify the stream's macroscopic behavior. We find that inelastic collisions collimate the stream, while the presence of short-range attractive interactions drives structure formation. Parameterizing the collision dynamics by the coefficient of restitution (i.e., the ratio of relative velocities before and after impact) and the strength of the cohesive interaction, we map out a spectrum of behaviors that ranges from gas-like jets in which all grains drift apart to liquid-like streams that break into large droplets containing hundreds of grains. We also find a new, intermediate regime in which small aggregates form by capture from the gas phase, similar to what can be observed in molecular beams. Our results show that nearly all aspects of stream behavior are closely related to the velocity gradient associated with vertical free fall. Led by this observation, we propose a simple energy balance model to explain the droplet formation process. The qualitative as well as many quantitative features of the simulations and the model compare well with available experimental data and provide a first quantitative measure of the role of attractions in freely cooling granular streams

Wave-number Selection by Target Patterns and Side Walls in Rayleigh-Benard Convection

We present experimental results for Rayleigh-Benard convection patterns in a cylindrical container with static side-wall forcing induced by a heater. This forcing stabilized a pattern of concentric rolls (a target pattern) with the central roll (the umbilicus) at the center of the cell after a jump from the conduction to the convection state. A quasi-static increase of the control parameter (epsilon) beyond 0.8 caused the umbilicus of the pattern to move off center. As observed by others, a further quasi-static increase of epsilon up to 15.6 caused a sequence of transitions. Each transition began with the displacement of the umbilicus and then proceeded with the loss of one convection roll at the umbilicus and the return of the umbilicus to a location near the center of the cell. Alternatively, with decreasing epsilon new rolls formed at the umbilicus but large umbilicus displacements did not occur. In addition to quantitative measurements of the umbilicus displacement, we determined and analyzed the entire wave-director field of each image. The wave numbers varied in the axial direction, with minima at the umbilicus and at the cell wall and a maximum at a radial position close to 2/3 Gamma. The wave numbers at the maximum showed hysteretic jumps at the transitions, but on average agreed well with the theoretical predictions for the wave numbers selected in the far field of an infinitely extended target pattern.Comment: ReVTeX, 11 pages, 16 eps figures include