Radiative Transfer Effect on Ultraviolet Pumping of the 21cm Line in the High Redshift Universe

During the epoch of reionization the 21cm signal is sensitive to the scattering rate of the ultraviolet photons, redshifting across the Lyman_alpha resonance. Here we calculate the photon scattering rate profile for a single ultraviolet source. After taking into account previously neglected natural broadening of the resonance line, we find that photons approach the resonance frequency and experience most scatterings at a significantly smaller distance from the source than naively expected r=(dnu/nu_0)(c/H), where dnu=nu-nu_0 is the initial frequency offset, and the discrepancy increases as the initial frequency offset decreases. As a consequence, the scattering rate P(r) drops much faster with increasing distance than the previously assumed 1/r^2 profile. Near the source (r<1Mpc comoving), the scattering rate of photons that redshift into the Ly_alpha resonance converges to P(r) \propto r^{-7/3}. The scattering rate of Ly_alpha photons produced by splitting of photons that redshift into a higher resonance (Ly_gamma, Ly_delta, etc.) is only weakly affected by the radiative transfer, while the sum of scattering rates of Ly_alpha photons produced from all higher resonances also converges to P(r) \propto r^{-7/3} near the source. At 15<z<35, on scales of ~0.01-20Mpc/h (comoving), the total scattering rate of Ly_alpha photons from all Lyman resonances is found to be higher by a factor of ~1+0.3[(1+z)/20]^{2/3} than obtained without full radiative transfer. Consequently, during the early stage of reionization, the differential brightness of 21cm signal against the cosmic microwave background is also boosted by a similar factor.Comment: 7 pages, 4 figures, submitted to Ap

Stability of Model Predictive Control with Soft Constraints

We derive stability conditions for Model Predictive Control (MPC) with hard constraints on the inputs and "soft" constraints on the outputs for an infinitely long output horizon. We show that with state feedback MPC is globally asymptotically stabilizing if and only if all the eigenvalues of the open loop system are in the closed unit disk. With output feedback the eigenvalues must be strictly inside the unit circle. The on-line optimization problem defining MPC can be posed as a finite dimensional quadratic program even though the output constraints are specified over an infinite horizon

Flame Retardancy of Polystyrene Nanocomposites Based on an Oligomeric Organically-Modified Clay Containing Phosphate

Novel modified clays, which may enable the formation of flame retarded polystyrene nanocomposites by melt or solution blending, have been prepared using an ammonium salt which contains an oligomeric material consisting of vinylbenzyl chloride, styrene and vinyl phosphate reacting with dimethylhexadecylamine. These nanocomposites have been characterized by X-ray diffraction, transmission electron microscopy, thermogravimetric analysis, cone calorimetry and the evaluation of mechanical properties. Melt blending is an effective, economical way to produce intercalated nanocomposites with greatly reduced peak heat release rate and a decreased total heat release; the polymer does not all undergo thermal degradation

Nanocomposites Based on Poly (ε-Caprolactone) (PCL)/Clay Hybrid: Polystyrene, High Impact Polystyrene, ABS, Polypropylene and Polyethylene

Nanocomposites of polystyrene, high impact polystyrene, acrylonitrile–butadiene–styrene terploymer, polypropylene and polyethylene have been prepared using an organically-modified clay that contains polycaprolactone—PCL-modified clay. Depending upon the mode of preparation of the PCL-modified clay, all three types of nanocomposites, immiscible, intercalated and exfoliated, may be produced. The materials have been characterized by X-ray diffraction, transmission electron microscopy, cone calorimetry, thermogravimetric analysis, and the evaluation of mechanical properties