Chaos in a spatially-developing plane mixing layer

A spatially-developing plane mixing layer was analyzed for chaotic behavior. A direct numerical simulation of the Navier-Stokes equations in a 2-D domain infinite in y and having inflow-outflow boundary conditions in x was used for data. Spectra, correlation dimension and the largest Lyapunov exponent were computed as functions of downstream distance x. When forced at a single (fundamental) frequency with maximum amplitude, the flow is periodic at the inflow but becomes aperiodic with increasing x. The aperiodic behavior is caused by the presence of a noisy subharmonic caused by the feedback between the necessarily nonphysical inflow and outflow boundary conditions. In order to overshadow this noise the flow was also studied with the same fundamental forcing and added random forcing of amplitude upsilon prime sub R/delta U = 0.01 at the inlet. Results were qualitatively the same in both cases: for small x, spectral peaks were sharp and dimension was nearly 1, but as x increased a narrowband spectral peak grew, spectra decayed exponentially at high frequencies and dimension increased to greater than 3. Based on these results, the flow appears to exhibit deterministic chaos. However, at no location was the largest Lyapunov exponent found to be significantly greater than zero

The Faint End of the Quasar Luminosity Function at z ~ 4: Implications for Ionization of the Intergalactic Medium and Cosmic Downsizing

We present an updated determination of the z ~ 4 QSO luminosity function (QLF), improving the quality of the determination of the faint end of the QLF presented by Glikman et al. (2010). We have observed an additional 43 candidates from our survey sample, yielding one additional QSO at z = 4.23 and increasing the completeness of our spectroscopic follow-up to 48% for candidates brighter than R = 24 over our survey area of 3.76 deg^2. We study the effect of using K-corrections to compute the rest-frame absolute magnitude at 1450 Å compared with measuring M_(1450) directly from the object spectra. We find a luminosity-dependent bias: template-based K-corrections overestimate the luminosity of low-luminosity QSOs, likely due to their reliance on templates derived from higher luminosity QSOs. Combining our sample with bright quasars from the Sloan Digital Sky Survey and using spectrum-based M 1450 for all the quasars, we fit a double power law to the binned QLF. Our best fit has a bright-end slope, α = 3.3 ± 0.2, and faint-end slope, β = 1.6^(+0.8)_(–0.6). Our new data revise the faint-end slope of the QLF down to flatter values similar to those measured at z ~ 3. The break luminosity, though poorly constrained, is at M* = –24.1^(+0.7)_(–1.9), approximately 1-1.5 mag fainter than at z ~ 3. This QLF implies that QSOs account for about half the radiation needed to ionize the intergalactic medium at these redshifts

Meeting the communication support needs of children and young people with intellectual disabilities in the Bolivian Andes

Services available for people with disabilities in Bolivia tend to be fragmented and costly. Children and adults with intellectual disabilities are more likely to have a related communication disability and are thus both literally and metaphorically excluded from having a voice. The following research aimed to explore the experiences of accessing services by people with communication disabilities in Bolivia through semi-structured interviews and one focus group carried out with family members, professionals, service providers, educators and policymakers. It aimed to establish the nature of current services in Bolivia where knowledge, information and resources are scarce. Findings indicated the need to consider an alternative to a medical model approach through a focus on empowering other stakeholders to participate more fully in meeting communication support needs. Conclusions plot ideas for future service delivery and emphasize the central power of sharing practical and expert knowledge