Derivation of Amplitude Equations by Renormalization Group Method

A proper formulation in the perturbative renormalization group method is presented to deduce amplitude equations. The formulation makes it possible not only avoiding a serious difficulty in the previous reduction to amplitude equations by eliminating all of the secular terms but also consistent derivation of higher-order correction to amplitude equations.Comment: 6 page, revte

On the Lack of Type I X-ray Bursts in Black Hole X-ray Binaries: Evidence for the Event Horizon?

Type I X-ray bursts are very common in neutron star X-ray binaries, but no Type I burst has been seen in the dozen or so binaries in which the accreting compact star is too massive to be a neutron star and therefore is identified as a black hole candidate. We have carried out a global linear stability analysis of the accumulating fuel on the surface of a compact star to identify the conditions under which thermonuclear bursts are triggered. Our analysis, which improves on previous calculations, reproduces the gross observational trends of bursts in neutron star systems. It further shows that, if black hole candidates have surfaces, they would very likely exhibit instabilities similar to those that lead to Type I bursts on neutron stars. The lack of bursts in black hole candidates is thus significant, and indicates that these objects have event horizons. We discuss possible caveats to this conclusion.Comment: 11 pages, 1 figure, to appear in 1 August 2002 edition of Astrophysical Journal Letters, significant changes to the methods, results unchange

X-ray Dust Scattering at Small Angles: The Complete Halo around GX13+1

The exquisite angular resolution available with Chandra should allow precision measurements of faint diffuse emission surrounding bright sources, such as the X-ray scattering halos created by interstellar dust. However, the ACIS CCDs suffer from pileup when observing bright sources, and this creates difficulties when trying to extract the scattered halo near the source. The initial study of the X-ray halo around GX13+1 using only the ACIS-I detector done by Smith, Edgar & Shafer (2002) suffered from a lack of sensitivity within 50'' of the source, limiting what conclusions could be drawn. To address this problem, observations of GX13+1 were obtained with the Chandra HRC-I and simultaneously with the RXTE PCA. Combined with the existing ACIS-I data, this allowed measurements of the X-ray halo between 2-1000''. After considering a range of dust models, each assumed to be smoothly distributed with or without a dense cloud along the line of sight, the results show that there is no evidence in this data for a dense cloud near the source, as suggested by Xiang et al. (2005). Finally, although no model leads to formally acceptable results, the Weingartner & Draine (2001) and nearly all of the composite grain models from Zubko, Dwek & Arendt (2004) give poor fits.Comment: 8 pages, 6 figures, accepted for publication in Ap

Spanning the Auditory System: Subcortical and Cortical Auditory Processing of Speech Sounds in Autistic and Typically Developing Children

Autistic individuals often report atypical sensory processing, particularly in the auditory domain. However, the neural mechanisms that produce such symptoms are poorly understood. The Speech Auditory Brainstem Response (speech-ABR) and the Mismatch Negativity (MMN) are neurophysiological measures that capture different levels of auditory processing, such that the speech-ABR reflects processing at the subcortical level and the MMN measures cortical processing. The present study integrated both techniques in a multimethod approach, which spans both subcortical and cortical processing of speech sounds in a group of autistic children (n = 11) matched on chronological age and non-verbal IQ to their typically developing (TD) peers (n = 11). Results suggest that both groups are similar in their speed of speech processing, as measured via the interpeak V-O latency of the speech-ABR and the MMN latency. Additionally, while the subcortical auditory processing did not predict cortical auditory processing, an interesting pattern of preliminary group differences emerged. These findings, which require replication in a larger sample, suggest that there may be important nuances in auditory processing among autistic youth that are enriched by employing a multimethod design and highlight the importance of a developmental framework in research with individuals with neurodevelopmental disabilities

Nonlinear Modulation of Travelling Rolls in Magnetoconvection

Modulational dynamics of oscillatory travelling rolls in magnetoconvection is studied near the onset of a Hopf bifurcation. Using weakly nonlinear analysis, we derive an envelope equation of oscillatory travelling rolls in the plane perpendicular to an ambient vertical magnetic field.The envelope equation is the Davey-Stewartson (DS) equation with complex coefficients, from which we obtain criteria for the modulational (Benjamin-Feir) instability of oscillatory travelling rolls.Comment: 8 pages,late