The Diffuse Nature of Stromgren Spheres

In this Letter, we argue that the standard analytical derivations of properties of HII regions, such as the speed, shape and asymptotic position of ionisation fronts require a more precise treatment. These derivations use the on the spot approximation, which in effect ignores the diffuse component of the radiation field. We show that, in fact, HII regions are diffusion dominated. This has as a result that the morphology of inhomogeneous HII regions will be drastically different, because shadowing effects have a less profound impact on the apparent shape. Moreover, it will have influence on the propagation speed of ionisation fronts. We quantify our claims by analytically deriving the internal radiation structure of HII regions, taking diffusion fully into account for several different cosmologically relevant density distributions.Comment: 4 pages, 2 figures, accepted for publication in A&A Letter

Approximations in Fusion and Breakup reactions induced by Radioactive Beams

Some commonly used approximations for complete fusion and breakup transmission coefficients in collisions of weakly bound projectiles at near barrier energies are assessed. We show that they strongly depend on the adopted classical trajectory and can be significantly improved with proper treatment of the incident and emergent currents in the WKB approximation.Comment: 15 pages, 7 figure

Improved WKB approximation for quantum tunneling: Application to heavy ion fusion

In this paper we revisit the one-dimensional tunneling problem. We consider Kemble's approximation for the transmission coefficient. We show how this approximation can be extended to above-barrier energies by performing the analytical continuation of the radial coordinate to the complex plane. We investigate the validity of this approximation by comparing their predictions for the cross section and for the barrier distribution with the corresponding quantum mechanical results. We find that the extended Kemble's approximation reproduces the results of quantum mechanics with great accuracy.Comment: 8 pages, 6 figures, in press, in European. Phys. Journal A (2017

Sharp reverse Hölder inequality for Cp weights and applications

We prove an appropriate sharp quantitative reverse Hölder inequality for the $C_p$ class of weights fromwhich we obtain as a limiting case the sharp reverse Hölder inequality for the $A_\infty$ class of weights (Hytönen in Anal PDE 6:777–818, 2013; Hytönen in J Funct Anal 12:3883–3899, 2012). We use this result to provide a quantitative weighted norm inequality between Calderón–Zygmund operators and theHardy–Littlewood maximal function, precisely $$|| T f ||_{ L^p(w)} \leq C_{T,n,p,q} [w]_{C_q} (1 + \log^+[w]_{C_q} ) ||Mf ||_{ L^p(w)} ,$$ for $w ∈ C_q$ and $q > p > 1$, quantifying Sawyer’s theorem (StudMath 75(3):753–763, 1983).Basque Government IT1247-1

Approximate transmission coefficients in heavy ion fusion

In this paper we revisit the one-dimensional tunnelling problem. We consider different approximations for the transmission through the Coulomb barrier in heavy ion collisions at near-barrier energies. First, we discuss approximations of the barrier shape by functional forms where the transmission coefficient is known analytically. Then, we consider Kemble's approximation for the transmission coefficient. We show how this approximation can be extended to above-barrier energies by performing the analytical continuation of the radial coordinate to the complex plane. We investigate the validity of the different approximations considered in this paper by comparing their predictions for transmission coefficients and cross sections of three heavy ion systems with the corresponding quantum mechanical results.Comment: 12 pages, 6 figure

Geometric Harmonic Analysis

This thesis is the compilation of the results obtained during my PhD, which started in January 2018 and is being completed in the end of 2021. The main matter is divided into  ve chapters, Chapters 2 6. Each of these chapters has its own introductory part, some longer some shorter. This chapter is intended to be an introduction to the whole thesis. Without going into technical details, in this Chapter we will not only motivate the results and the content of the dissertation, but we also explain how and why these results came to be studied. We also introduce the main notation and some preliminary concepts that will be used throughout the dissertation

Modeling Nonaxisymmetric Bow Shocks: Solution Method and Exact Analytic Solutions

A new solution method is presented for steady-state, momentum-conserving, non-axisymmetric bow shocks and colliding winds in the thin-shell limit. This is a generalization of previous formulations to include a density gradient in the pre-shock ambient medium, as well as anisotropy in the pre-shock wind. For cases where the wind is unaccelerated, the formalism yields exact, analytic solutions. Solutions are presented for two bow shock cases: (1) that due to a star moving supersonically with respect to an ambient medium with a density gradient perpendicular to the stellar velocity, and (2) that due to a star with a misaligned, axisymmetric wind moving in a uniform medium. It is also shown under quite general circumstances that the total rate of energy thermalization in the bow shock is independent of the details of the wind asymmetry, including the orientation of the non-axisymmetric driving wind, provided the wind is non-accelerating and point-symmetric. A typical feature of the solutions is that the region near the standoff point is tilted, so that the star does not lie along the bisector of a parabolic fit to the standoff region. The principal use of this work is to infer the origin of bow shock asymmetries, whether due to the wind or ambient medium, or both.Comment: 26 pages and 6 figures accepted to ap

The asymmetric profile of the H76 alpha line emission from MWC349

MWC349 is an emission-line star found by Merrill, Humason and Burwell (1932). Braes, Habing and Schoenmaker (1972) discovered that it is a strong radio source. The radio emission originates in a massive ionized wind that is expanding with a velocity of about 50 km s(-1). Its continuum spectrum fits well a nu(0.6) power law from the cm wavelengths to the far-IR. Radio recombination line emission from the envelope of MWC349 was first detected by Altenhoff, Strittmatter and Wendker (1981). We have obtained good signal-to-noise ratio, Very Large Array observations of the H76 alpha radio recombination line from the ionized wind of MWC349. Our data reveal that the profile is markedly asymmetric, with a steep rise on the blue side. This asymmetry could be due to non-LTE effects in the formation and transfer of the line or to intrinsic asymmetries in the envelope. Our analysis suggests that most probably the peculiar profile is caused by a non-LTE enhancement of the line emission from the side of the envelope nearer to the observer. This asymmetry has the opposite sense than that observed in optical and IR recombination lines, where a different effect (absorption of the stellar continuum by the gas in the wind between the star and the observer) is known to be dominant, leading to the classic P Cygni profile. We propose that the profiles of the radio recombination lines from ionized stellar winds will have this characteristic shape, while optical and IR recombination lines are characterized by P Cygni-like profiles. Unfortunately, at present the detection of radio recombination lines from ionized stellar winds is only feasible for MWC349 and a few other objects