Partial data inverse problems for the Hodge Laplacian

We prove uniqueness results for a Calderon type inverse problem for the Hodge Laplacian acting on graded forms on certain manifolds in three dimensions. In particular, we show that partial measurements of the relative-to-absolute or absolute-to-relative boundary value maps uniquely determine a zeroth order potential. The method is based on Carleman estimates for the Hodge Laplacian with relative or absolute boundary conditions, and on the construction of complex geometric optics solutions which reduce the Calderon type problem to a tensor tomography problem for 2-tensors. The arguments in this paper allow to establish partial data results for elliptic systems that generalize the scalar results due to Kenig-Sjostrand-Uhlmann.Comment: 54 pages, updated versio

Resolvent estimates for the magnetic Schr\"odinger operator in dimension n≥2n \geq 2

It is well known that the resolvent of the free Schr\"odinger operator on weighted $L^2$ spaces has norm decaying like $\lambda^{-\frac{1}{2}}$ at energy $\lambda$. There are several works proving analogous high-frequency estimates for magnetic Schr\"odinger operators, with large long or short range potentials, in dimensions $n \geq 3$. We prove that the same estimates remain valid in all dimensions $n \geq 2$.Comment: 21 page

A monolithic collapse origin for the thin/thick disc structure of ESO 243-49

ESO 243-49 is a high-mass (circular velocity $v_{\rm c}\approx200\,{\rm km\,s^{-1}}$) edge-on S0 galaxy in the Abell 2877 cluster at a distance of $\sim95\,{\rm Mpc}$. To elucidate the origin of its thick disc, we use MUSE science verification data to study its kinematics and stellar populations. The thick disc emits $\sim80\%$ of the light at heights in excess of $3.5^{\prime\prime}$ ($1.6\,{\rm kpc}$). The rotation velocities of its stars lag by $30-40\,{\rm km\,s^{-1}}$ compared to those in the thin disc, which is compatible with the asymmetric drift. The thick disc is found to be more metal-poor than the thin disc, but both discs have old ages. We suggest an internal origin for the thick disc stars in high-mass galaxies. We propose that the thick disc formed either ${\rm a)}$ first in a turbulent phase with a high star formation rate and that a thin disc formed shortly afterwards, or ${\rm b)}$ because of the dynamical heating of a thin pre-existing component. Either way, the star formation in ESO 243-49 was quenched just a few Gyrs after the galaxy was born and the formation of a thin and a thick disc must have occurred before the galaxy stopped forming stars. The formation of the discs was so fast that it could be described as a monolithic collapse where several generations of stars formed in a rapid succession.Comment: Accepted for publication in A&A. The reduced data-cube as well as the data necessary to build the kinematic and stellar population maps are available at https://etsin.avointiede.fi/dataset/urn-nbn-fi-csc-kata2016092414291163237

Statistics of the structure components in S0s: implications for bar induced secular evolution

The fractions and dimension of bars, rings and lenses are studied in the Near-IR S0 galaxy Survey (NIRS0S). We find evidence that multiple lenses in some barred S0s are related to bar resonances in a similar manner as the inner and outer rings, for which the outer/inner length ratio 2. Inner lenses in the non-barred galaxies normalized to galaxy diameter are clearly smaller than those in the barred systems. Interestingly, these small lenses in the non-barred galaxies have similar sizes as barlenses (lens-like structures embedded in a bar), and therefore might actually be barlenses in former barred galaxies, in which the outer, more elongated bar component, has been destroyed. We also find that fully developed inner lenses are on average a factor 1.3 larger than bars, whereas inner rings have similar sizes as bars. The fraction of inner lenses is found to be constant in all family classes (A, AB, B). Nuclear bars appear most frequently among the weakly barred (AB) galaxies, which is consistent with the theoretical models by Maciejewski & Athanassoula (2008). Similar sized bars as the nuclear bars were detected in seven 'non-barred' S0s. Galaxy luminosity does not uniquely define the sizes of bars or bar-related structures, neither is there any upper limit in galaxy luminosity for bar formation. Although all the family classes cover the same range of galaxy luminosity, the non-barred (A) galaxies are on average 0.6 mag brighter than the strongly barred (B) systems. Overall, our results are consistent with the idea that bars play an important role in the formation of the structure components of galaxies. The fact that multiple lenses are common in S0s, and that at least the inner lenses can have very old stellar populations, implies that the last destructive merger, or major gas accretion event, must have taken place at a fairly high redshift.Comment: 36 pages (include 13 figures, 11 tables). Accepted to MNRAS 2013 Jan 2

THE USE OF MOTION ANALYSIS AS A COACHING AID TO IMPROVE THE INDIVIDUAL TECHNIQUE IN SPRINT HURDLES

Biomechanical data are oflen presented as a group average, which may not always help individual athletes to improve their own performance. The purpose of this study was to analyse techniques in sprint hurdles within the athlete and find critical individual aspects, which influence performance. The hurdle clearance of three athletes (eight trials each) were videotaped with four video camera recorders and analysed three-dimensionally. There were several statistically significant correlations between the critical overall horizontal velocity and other variables, especially for one athlete. Such trends in individual performance presented ideas to coaches, athletes and also to researchers, regarding what happened in less successful runs and which technical points were worth individual attention in training

Frequency-dependent current correlation functions from scattering theory

We present a general formalism based on scattering theory to calculate quantum correlation functions involving several time-dependent current operators. A key ingredient is the causality of the scattering matrix, which allows one to deal with arbitrary correlation functions. The formalism proves useful, e.g., in view of recent developments in full counting statistics of charge transfer, where detecting schemes have been proposed for measurement of frequency dependent spectra of higher moments. Some of these schemes are different from the well-known fictitious spin detector and therefore generally involve calculation of non-Keldysh-contour-ordered correlation functions. As an illustration of the approach we consider various third order correlation functions of current, including the usual third cumulant of current statistics. We investigate the frequency dependence of these correlation functions explicitly in the case of energy-independent scattering. The results can easily be generalized to the calculation of arbitrary nth order correlation functions, or to include the effect of interactions.Peer reviewe