New Fe II energy levels from stellar spectra

The spectra of B-type and early A-type stars show numerous unidentified lines in the whole optical range, especially in the 5100 - 5400 A interval. Because Fe II transitions to high energy levels should be observed in this region, we used semiempirical predicted wavelengths and gf-values of Fe II to identify unknown lines. Semiempirical line data for Fe II computed by Kurucz are used to synthesize the spectrum of the slow-rotating, Fe-overabundant CP star HR 6000. We determined a total of 109 new 4f levels for Fe II with energies ranging from 122324 cm^-1 to 128110 cm^-1. They belong to the Fe II subconfigurations 3d^6(^3P)4f (10 levels), 3d^6(^3H)4f (36 levels), 3d^6(^3F)4f (37 levels), and 3d^6(^3G)4f (26 levels). We also found 14 even levels from 4d (3 levels), 5d (7 levels), and 6d (4 levels) configurations. The new levels have allowed us to identify more than 50% of the previously unidentified lines of HR 6000 in the wavelength region 3800-8000 A. Tables listing the new energy levels are given in the paper; tables listing the spectral lines with loggf>/=-1.5 that are transitions to the 4f energy levels are given in the Online Material. These new levels produce 18000 lines throughout the spectrum from the ultraviolet to the infrared.Comment: Paper accepted by A&A for publicatio

A study of the apsidal angle and a proof of monotonicity in the logarithmic potential case

This paper concerns the behaviour of the apsidal angle for orbits of central force system with homogenous potential of degree $-2\leq \alpha\leq 1$ and logarithmic potential. We derive a formula for the apsidal angle as a fixed-end points integral and we study the derivative of the apsidal angle with respect to the angular momentum $\ell$. The monotonicity of the apsidal angle as function of $\ell$ is discussed and it is proved in the logarithmic potential case.Comment: 24 pages, 1 figur

Oscillating waves and optimal smoothing effect for one-dimensional nonlinear scalar conservation laws

Lions, Perthame, Tadmor conjectured in 1994 an optimal smoothing effect for entropy solutions of nonlinear scalar conservations laws . In this short paper we will restrict our attention to the simpler one-dimensional case. First, supercritical geometric optics lead to sequences of $C^\infty$ solutions uniformly bounded in the Sobolev space conjectured. Second we give continuous solutions which belong exactly to the suitable Sobolev space. In order to do so we give two new definitions of nonlinear flux and we introduce fractional $BV$ spaces

Existence and instability of steady states for a triangular cross-diffusion system: a computer-assisted proof

In this paper, we present and apply a computer-assisted method to study steady states of a triangular cross-diffusion system. Our approach consist in an a posteriori validation procedure, that is based on using a fxed point argument around a numerically computed solution, in the spirit of the Newton-Kantorovich theorem. It allows us to prove the existence of various non homogeneous steady states for different parameter values. In some situations, we get as many as 13 coexisting steady states. We also apply the a posteriori validation procedure to study the linear stability of the obtained steady states, proving that many of them are in fact unstable

Rigorous numerics for NLS: bound states, spectra, and controllability

In this paper it is demonstrated how rigorous numerics may be applied to the one-dimensional nonlinear Schr\"odinger equation (NLS); specifically, to determining bound--state solutions and establishing certain spectral properties of the linearization. Since the results are rigorous, they can be used to complete a recent analytical proof [6] of the local exact controllability of NLS.Comment: 30 pages, 2 figure

A refined analysis of the remarkable Bp star HR 6000

UVES spectra of the very young (~10^7 years) peculiar B-type star HR 6000 were analyzed in the near-UV and visual spectral regions (3050-9460 A) with the aim to extend to other spectral ranges the study made previously in the UV using IUE spectra. Stellar parameters Teff=12850K, logg=4.10, and xi=0km/s, as determined from H_beta, H_gamma, H_delta Balmer profiles and from the Fe I, Fe II ionization equilibrium, were used to compute an individual abundances ATLAS12 model. We identified spectral peculiarities and obtained final stellar abundances by comparing observed and computed equivalent widths and line profiles. The adopted model fails to reproduce the (b-y) and c color indices. The spectral analysis has revealed: the presence of emission lines for Mn II, Cr II, and Fe II; isotopic anomalies for Hg, Ca; the presence of interstellar lines of Na I at lambda lambda 3302.3, 3302.9, 5890, 5896 A, and of K I at 7665, 7699 A; the presence of a huge quantity of unidentified lines, which we presume to be mostly due to Fe II transitions owing to the large Fe overabundance amounting to [+0.7]. The main chemical peculiarities are an extreme overabundance of Xe, followed by those of Hg, P, Y, Mn, Fe, Be, and Ti. The most underabundant element is Si, followed by C, N, Al, S, Mg, V, Sr, Co, Cl, Sc, and Ni. The silicon underabundance [-2.9] is the lowest value for Si ever observed in any HgMn star. The observed lines of He I can not be reproduced by a single value of the He abundance, but they require values ranging from [-0.8] to [-1.6]. Furthermore, when the observed and computed wings of He I lines are fitted, the observed line cores are much weaker than the computed ones. From the present analysis we infer the presence of vertical abundance stratification for He, Mn, and possibly also P.Comment: 14 pages, 8 figures, 6 tables, accepted for publication in A&