5,279 research outputs found
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
Sharp reverse Hölder inequality for Cp weights and applications
We prove an appropriate sharp quantitative reverse Hölder inequality for the class of
weights fromwhich we obtain as a limiting case the sharp reverse Hölder inequality for
the 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
for and , quantifying Sawyer’s theorem (StudMath 75(3):753–763,
1983).Basque Government IT1247-1
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
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
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
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
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