The fractional Bessel equation in H\"older spaces

Motivated by the Poisson equation for the fractional Laplacian on the whole space with radial right hand side, we study global H\"older and Schauder estimates for a fractional Bessel equation. Our methods stand on the so-called semigroup language. Indeed, by using the solution to the Bessel heat equation we derive pointwise formulas for the fractional operators. Appropriate H\"older spaces, which can be seen as Campanato-type spaces, are characterized through Bessel harmonic extensions and fractional Carleson measures. From here the regularity estimates for the fractional Bessel equations follow. In particular, we obtain regularity estimates for radial solutions to the fractional Laplacian.Comment: 36 pages. To appear in Journal of Approximation Theor

Damped and sub-damped Lyman-α absorbers in z > 4 QSOs

We present the results of a survey of damped (DLA, log N(H I) > 20.3) and sub-damped Lyman-α systems (19.5 2.55 along the lines-of-sight to 77 quasars with emission redshifts in the range 4 19.5 were detected of which 40 systems are damped Lyman-α systems for an absorption length of ΔX = 378. About half of the lines of sight of this homogeneous survey have never been investigated for DLAs. We study the evolution with redshift of the cosmological density of the neutral gas and find, consistent with previous studies at similar resolution, that Ω_(DLA,HI) decreases at z > 3.5. The overall cosmological evolution of Ω_(HI) shows a peak around this redshift. The H I column density distribution for log N(H I) ≥ 20.3 is fitted, consistent with previous surveys, with a single power-law of index α ~ −1.8 ± 0.25. This power-law overpredicts data at the high-end and a second, much steeper, power-law (or a gamma function) is needed. There is a flattening of the function at lower H I column densities with an index of α ~ −1.4 for the column density range log N(H I) = 19.5−21. The fraction of H I mass in sub-DLAs is of the order of 30%. The H I column density distribution does not evolve strongly from z ~ 2.5 to z ~ 4.5

High Resolution Ionization of Ultracold Neutral Plasmas

Collective effects, such as waves and instabilities, are integral to our understanding of most plasma phenomena. We have been able to study these in ultracold neutral plasmas by shaping the initial density distribution through spatial modulation of the ionizing laser intensity. We describe a relay imaging system for the photoionization beam that allows us to create higher resolution features and its application to extend the observation of ion acoustic waves to shorter wavelengths. We also describe the formation of sculpted density profiles to create fast expansion of plasma into vacuum and streaming plasmas

Inducing energy gaps in graphene monolayer and bilayer

In this paper we propose a mechanism for the induction of energy gaps in the spectrum of graphene and its bilayer, when both these materials are covered with water and ammonia molecules. The energy gaps obtained are within the range 20-30 meV, values compatible to those found in experimental studies of graphene bilayer. We further show that the binding energies are large enough for the adsorption of the molecules to be maintained even at room temperature