Numerical integration of nonlinear differential equations by use of rational approximation Final report, 15 Jan. 1965 - 14 Jul. 1967

Numerical integration of nonlinear differential equations by use of rational approximatio

Evolution and nucleosynthesis of helium-rich asymptotic giant branch models

There is now strong evidence that some stars have been born with He mass fractions as high as $Y \approx 0.40$ (e.g., in $\omega$ Centauri). However, the advanced evolution, chemical yields, and final fates of He-rich stars are largely unexplored. We investigate the consequences of He-enhancement on the evolution and nucleosynthesis of intermediate-mass asymptotic giant branch (AGB) models of 3, 4, 5, and 6 M$_\odot$ with a metallicity of $Z = 0.0006$ ([Fe/H] $\approx -1.4$). We compare models with He-enhanced compositions ($Y=0.30, 0.35, 0.40$) to those with primordial He ($Y=0.24$). We find that the minimum initial mass for C burning and super-AGB stars with CO(Ne) or ONe cores decreases from above our highest mass of 6 M$_\odot$ to $\sim$ 4-5 M$_\odot$ with $Y=0.40$. We also model the production of trans-Fe elements via the slow neutron-capture process (s-process). He-enhancement substantially reduces the third dredge-up efficiency and the stellar yields of s-process elements (e.g., 90% less Ba for 6 M$_\odot$, $Y=0.40$). An exception occurs for 3 M$_\odot$, where the near-doubling in the number of thermal pulses with $Y=0.40$ leads to $\sim$ 50% higher yields of Ba-peak elements and Pb if the $^{13}$C neutron source is included. However, the thinner intershell and increased temperatures at the base of the convective envelope with $Y=0.40$ probably inhibit the $^{13}$C neutron source at this mass. Future chemical evolution models with our yields might explain the evolution of s-process elements among He-rich stars in $\omega$ Centauri.Comment: 21 pages, 16 figures, accepted for publication by MNRAS. Stellar yields included as online data table

Liquid recirculation in microfluidic channels by the interplay of capillary and centrifugal forces

We demonstrate a technique to recirculate liquids in a microfluidic device, maintaining a thin fluid layer such that typical diffusion times for analytes to reach the device surface are < 1 min. Fluids can be recirculated at least 1000 times across the same surface region, with no change other than slight evaporation, by alternating the predominance of centrifugal and capillary forces. Mounted on a rotational platform, the device consists of two hydrophilic layers separated by a thin pressure-sensitive adhesive (PSA) layer that defines the microfluidic structure. We demonstrate rapid, effective fluid mixing with this device

Perspectives on Online Education: A Snapshot of State Regulatory Framework Development in Elementary and Secondary Online Education

With the advent and growth of elementary and secondary online education in the United States, teaching and learning has undergone radical change with heretofore unimagined alternatives to traditional brick-and-mortar classrooms