Stability of planar flames as gasdynamic discontinuities

The stability of a steadily propagating planar premixed flame has been the subject of numerous studies since Darrieus and Landau showed that in their model flames are unstable to perturbations of any wavelength. Moreover, the instability was shown to persist even for very small wavelengths, i.e. there was no high-wavenumber cutoff of the instability. In addition to the Darrieus-Landau instability, which results from thermal expansion, analysis of the diffusional thermal model indicates that premixed flames may exhibit cellular and pulsating instabilities as a consequence of preferential diffusion. However, no previous theory captured all the instabilities including a high-wavenumber cutoff for each. In Class, Matkowsky & Klimenko (2003) a unified theory is proposed which, in appropriate limits and under appropriate assumptions, recovers all the relevant previous theories. It also includes additional new terms, not present in previous theories. In the present paper we consider the stability of a uniformly propagating planar flame as a solution of the unified model. The results are then compared to those based on the models of Darrieus-Landau, Sivashinsky and Matalon-Matkowsky. In particular, it is shown that the unified model is the only model to capture the Darrieus-Landau, cellular and pulsating instabilities including a high-wavenumber cutoff for each.

Alterations of neocortical pyramidal cell phenotype in the Ts65Dn mouse model of Down syndrome: Effects of environmental enrichment

Mental retardation in individuals with Down syndrome (DS) is thought to result from anomalous development and function of the brain; however, the underlying neuropathological processes have yet to be determined. Early implementation of special care programs result in limited, and temporary, cognitive improvements in DS individuals. In the present study, we investigated the possible neural correlates of these limited improvements. More specifically, we studied cortical pyramidal cells in the frontal cortex of Ts65Dn mice, a partial trisomy of murine chromosome 16 (MMU16) model characterized by cognitive deficits, hyperactivity, behavioral disruption and reduced attention levels similar to those observed in DS, and their control littermates. Animals were raised either in a standard or in an enriched environment. Environmental enrichment had a marked effect on pyramidal cell structure in control animals. Pyramidal cells in environmentally enriched control animals were significantly more branched and more spinous than non-enriched controls. However, environmental enrichment had little effect on pyramidal cell structure in Ts65Dn mice. As each dendritic spine receives at least one excitatory input, differences in the number of spines found in the dendritic arbors of pyramidal cells in the two groups reflect differences in the number of excitatory inputs they receive and, consequently, complexity in cortical circuitry. The present results suggest that behavioral deficits demonstrated in the Ts65Dn model could be attributed to abnormal circuit development.