Complex determinantal processes and H1 noise

For the plane, sphere, and hyperbolic plane we consider the canonical invariant determinantal point processes with intensity rho dnu, where nu is the corresponding invariant measure. We show that as rho converges to infinity, after centering, these processes converge to invariant H1 noise. More precisely, for all functions f in the interesection of H1(nu) and L1(nu) the distribution of sum f(z) - rho/pi integral f dnu converges to Gaussian with mean 0 and variance given by ||f||_H1^2 / (4 pi).Comment: 22 pages, 1 figur

Asteroseismic surface gravity for evolved stars

Context: Asteroseismic surface gravity values can be of importance in determining spectroscopic stellar parameters. The independent log(g) value from asteroseismology can be used as a fixed value in the spectroscopic analysis to reduce uncertainties due to the fact that log(g) and effective temperature can not be determined independently from spectra. Since 2012, a combined analysis of seismically and spectroscopically derived stellar properties is ongoing for a large survey with SDSS/APOGEE and Kepler. Therefore, knowledge of any potential biases and uncertainties in asteroseismic log(g) values is now becoming important. Aims: The seismic parameter needed to derive log(g) is the frequency of maximum oscillation power (nu_max). Here, we investigate the influence of nu_max derived with different methods on the derived log(g) values. The large frequency separation between modes of the same degree and consecutive radial orders (Dnu) is often used as an additional constraint for the determination of log(g). Additionally, we checked the influence of small corrections applied to Dnu on the derived values of log(g). Methods We use methods extensively described in the literature to determine nu_max and Dnu together with seismic scaling relations and grid-based modeling to derive log(g). Results: We find that different approaches to derive oscillation parameters give results for log(g) with small, but different, biases for red-clump and red-giant-branch stars. These biases are well within the quoted uncertainties of ~0.01 dex (cgs). Corrections suggested in the literature to the Dnu scaling relation have no significant effect on log(g). However somewhat unexpectedly, method specific solar reference values induce biases of the order of the uncertainties, which is not the case when canonical solar reference values are used.Comment: 8 pages, 5 figures, accepted for publication by A&

Steep anomalous dispersion in coherently prepared Rb vapor

Steep dispersion of opposite signs in driven degenerate two-level atomic transitions have been predicted and observed on the D2 line of 87Rb in an optically thin vapor cell. The intensity dependence of the anomalous dispersion has been studied. The maximum observed value of anomalous dispersion [dn/dnu ~= -6x10^{-11}Hz^{-1}] corresponds to anegative group velocity V_g ~= -c/23000.Comment: 4 pages, 4 figure

Mitigating the mass dependence in the Δν\Delta\nu scaling relation of red-giant stars

The masses and radii of solar-like oscillators can be estimated through the asteroseismic scaling relations. These relations provide a direct link between observables, i.e. effective temperature and characteristics of the oscillation spectra, and stellar properties, i.e. mean density and surface gravity (thus mass and radius). These scaling relations are commonly used to characterize large samples of stars. Usually, the Sun is used as a reference from which the structure is scaled. However, for stars that do not have a similar structure as the Sun, using the Sun as a reference introduces systematic errors as large as 10\% in mass and 5\% in radius. Several alternatives for the reference of the scaling relation involving the large frequency separation (typical frequency difference between modes of the same degree and consecutive radial order) have been suggested in the literature. In a previous paper, we presented a reference function with a dependence on both effective temperature and metallicity. The accuracy of predicted masses and radii improved considerably when using reference values calculated from our reference function. However, the residuals indicated that stars on the red-giant branch possess a mass dependence that was not accounted for. Here, we present a reference function for the scaling relation involving the large frequency separation that includes the mass dependence. This new reference function improves the derived masses and radii significantly by removing the systematic differences and mitigates the trend with $\nu_{\rm max}$ (frequency of maximum oscillation power) that exists when using the solar value as a reference.Comment: 12 pages, 7 figures, accepted for publication in MNRA

Boundary regularity for elliptic systems under a natural growth condition

We consider weak solutions $u \in u_0 + W^{1,2}_0(\Omega,R^N) \cap L^{\infty}(\Omega,R^N)$ of second order nonlinear elliptic systems of the type $- div a (\cdot, u, Du) = b(\cdot,u,Du)$ in $\Omega$ with an inhomogeneity satisfying a natural growth condition. In dimensions $n \in \{2,3,4\}$ we show that $\mathcal{H}^{n-1}$-almost every boundary point is a regular point for $Du$, provided that the boundary data and the coefficients are sufficiently smooth.Comment: revised version, accepted for publication in Ann. Mat. Pura App

Spectral measures of small index principal graphs

The principal graph $X$ of a subfactor with finite Jones index is one of the important algebraic invariants of the subfactor. If $\Delta$ is the adjacency matrix of $X$ we consider the equation $\Delta=U+U^{-1}$. When $X$ has square norm $\leq 4$ the spectral measure of $U$ can be averaged by using the map $u\to u^{-1}$, and we get a probability measure $\epsilon$ on the unit circle which does not depend on $U$. We find explicit formulae for this measure $\epsilon$ for the principal graphs of subfactors with index $\le 4$, the (extended) Coxeter-Dynkin graphs of type $A$, $D$ and $E$. The moment generating function of $\epsilon$ is closely related to Jones' $\Theta$-series.Comment: 23 page

Homogenization of oscillating boundaries and applications to thin films

We prove a homogenization result for integral functionals in domains with oscillating boundaries, showing that the limit is defined on a degenerate Sobolev space. We apply this result to the description of the asymptotic behaviour of thin films with fast-oscillating profile, proving that they can be described by first applying the homogenization result above and subsequently a dimension-reduction technique.Comment: 31 pages, 7 figure