Stryker Osteonics: Prosthetic Knee Joint

We examine, within a simple bearing model of a knee joint that only consideres pure sliding, the effect of the presence of a small vertical hole in the load area on the fluid film properties. The calculations indicate that fluid is entrapped in such a hole, which, for constant load, causes a smaller minimal film separation of the two surfaces. This will lower the horizontal friction, but may also bring about surface contact in high load situations

The complexity of the classification of Riemann surfaces and complex manifolds

In answer to a question by Becker, Rubel, and Henson, we show that countable subsets of ℂ can be used as complete invariants for Riemann surfaces considered up to conformal equivalence, and that this equivalence relation is itself Borel in a natural Borel structure on the space of all such surfaces. We further proceed to precisely calculate the classification difficulty of this equivalence relation in terms of the modern theory of Borel equivalence relations. On the other hand we show that the analog of Becker, Rubel, and Henson's question has a negative solution in (complex) dimension n ≥ 2

The Gravitational Lensing in the QSO 1208+10 from the Proximity Effect in its Lyman alpha Forest

The quasar Q1208+1011 (z_{em}=3.8) is the second highest redshift double quasar ever detected. Several indications point toward it being a gravitational lensed system, although a definitive proof is still lacking. We present new evidence of its lensed nature based on the weakness of the ``proximity effect'' measured in the high resolution Lyman absorption spectrum of the QSO. A luminosity amplification as large as 22 has been derived from this analysis. Indications on the redshift of the lensing galaxy can be obtained from the analysis of the intervening heavy element absorption systems discovered in the QSO high resolution spectrum. On statistical and dynamical grounds a MgII system present at z=1.13 appears as the most likely candidate for the lensing galaxy. We compare the observed parameters with a simple isothermal model for the lens to derive the properties of the lensing galaxy. The resulting magnification factor is smaller, although marginally consistent with that derived by the analysis of the proximity effect.Comment: 11 pages, 2 Postscript figures, ApJ in pres

VarIabiLity seLection of AstrophysIcal sources iN PTF (VILLAIN) I. Structure function fits to 71 million objects

Context. Lightcurve variability is well-suited for characterising objects in surveys with high cadence and long baseline. This is especially relevant in view of the large datasets to be produced by the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST). Aims. We aim to determine variability parameters for objects in the Palomar Transient Factory (PTF) and explore differences between quasars (QSOs), stars and galaxies. We will relate variability and colour information in preparation for future surveys. Methods. We fit joint likelihoods to structure functions (SFs) of 71 million PTF lightcurves with a Markov Chain Monte Carlo method. For each object, we assume a power law SF and extract two parameters: the amplitude on timescales of one year, $A$, and a power law index, $\gamma$. With these parameters and colours in the optical (Pan-STARRS1) and mid infrared (WISE), we identify regions of parameter space dominated by different types of spectroscopically confirmed objects from SDSS. Candidate QSOs, stars and galaxies are selected to show their parameter distributions. Results. QSOs have high amplitude variations in the $R$ band, and the strongest timescale dependence of variability. Galaxies have a broader range of amplitudes and low timescale dependency. With variability and colours, we achieve a photometric selection purity of 99.3 % for QSOs. Even though hard cuts in monochromatic variability alone are not as effective as seven-band magnitude cuts, variability is useful in characterising object sub-classes. Through variability, we also find QSOs that were erroneously classified as stars in the SDSS. We discuss perspectives and computational solutions in view of the upcoming LSST.Comment: Accepted by A&A on 11/04/2023, 16 pages, 14 figure

A "kilonova" associated with short-duration gamma-ray burst 130603B

Short-duration gamma-ray bursts (SGRBs) are intense flashes of cosmic gamma-rays, lasting less than ~2 s, whose origin is one of the great unsolved questions of astrophysics today. While the favoured hypothesis for their production, a relativistic jet created by the merger of two compact stellar objects (specifically, two neutron stars, NS-NS, or a neutron star and a black hole, NS-BH), is supported by indirect evidence such as their host galaxy properties, unambiguous confirmation of the model is still lacking. Mergers of this kind are also expected to create significant quantities of neutron-rich radioactive species, whose decay should result in a faint transient in the days following the burst, a so-called "kilonova". Indeed, it is speculated that this mechanism may be the predominant source of stable r-process elements in the Universe. Recent calculations suggest much of the kilonova energy should appear in the near-infrared (nIR) due to the high optical opacity created by these heavy r-process elements. Here we report strong evidence for such an event accompanying SGRB 130603B. If this simplest interpretation of the data is correct, it provides (i) support for the compact object merger hypothesis of SGRBs, (ii) confirmation that such mergers are likely sites of significant r-process production and (iii) quite possibly an alternative, un-beamed electromagnetic signature of the most promising sources for direct detection of gravitational waves.Comment: preprint of paper appearing in Nature (3 Aug 2013

Comparison of the Effective Interaction to Various Orders in Different Mass Regions

The convergence of the perturbation expansion for the effective interaction to be used in shell-model calculations is investigated as function of the mass number $A$, from $A=4$ to $A=208$. As the mass number increases, there are more intermediate states to sum over in each higher-order diagram which contributes to the effective interaction. Together with the fact that the energy denominators in each diagram are smaller for larger mass numbers, these two effects could largely enhance higher-order contributions to the effective interaction, thereby deteriorating the order-by-order convergence of the effective interaction. This effect is counterbalanced by the short range of the nucleon-nucleon interaction, which implies that its matrix elements are weaker for valence single-particle states in ``large'' nuclei with large mass number as compared to those in light nuclei. These effects are examined by comparing various mean values of the matrix elements. It turns out that the contributions from higher-order terms remain fairly stable as the mass number increases from $A=4$ to $A=208$. The implications for nuclear structure calculations are discussed.Comment: Revtex, 20 pages, 1 figure not include

Lens magnification by CL0024+1654 in the U and R band

[ABRIDGED] We estimate the total mass distribution of the galaxy cluster CL0024+1654 from the measured source depletion due to lens magnification in the R band. Within a radius of 0.54Mpc/h, a total projected mass of (8.1+/-3.2)*10^14 M_sol/h (EdS) is measured, which corresponds to a mass- to-light ratio of M/L(B)=470+/-180. We compute the luminosity function of CL0024+1654 in order to estimate contamination of the background source counts from cluster galaxies. Three different magnification-based reconstruction methods are employed using both local and non-local techniques. We have modified the standard single power-law slope number count theory to incorporate a break and applied this to our observations. Fitting analytical magnification profiles of different cluster models to the observed number counts, we find that the cluster is best described either by a NFW model with scale radius r_s=334+/-191 kpc/h and normalisation kappa_s=0.23+/-0.08 or a power-law profile with slope xi=0.61+/-0.11, central surface mass density kappa_0=1.52+/-0.20 and assuming a core radius of r_core=35 kpc/h. The NFW model predicts that the cumulative projected mass contained within a radius R scales as M(<R)=2.9*10^14*(R/1')^[1.3-0.5lg (R/1')] M_sol/h. Finally, we have exploited the fact that flux magnification effectively enables us to probe deeper than the physical limiting magnitude of our observations in searching for a change of slope in the U band number counts. We rule out both a total flattening of the counts with a break up to U_AB<=26.6 and a change of slope, reported by some studies, from dlog N/dm=0.4->0.15 up to U_AB<=26.4 with 95% confidence.Comment: 19 pages, 12 figures, submitted to A&A. New version includes more robust U band break analysis and contamination estimates, plus new plot