The difficulty of measuring the local dark matter density

The analysis of the vertical velocity dispersion of disc stars is the most direct astronomical means of estimating the local dark matter density, $\rho_{DM}$. Current estimates based on the mid-plane dynamic density use a local baryonic correction that ignores the non-local effects of spiral structure and significantly underestimates the amount of dynamically relevant gas; the additional gas plus the remaining uncertainties make it practically impossible to measure $\rho_{DM}$ from mid-plane kinematics alone. The sampling of inhomogeneous tracer populations with different scale-heights and scale-lengths results in a systematic increase in the observed dispersion gradients and changes in the nominal density distributions that, if not properly considered, can be misinterpreted as a sign of more dark matter. If the disc gravity is modelled using an infinite disc, the local variation in the vertical gravity due to the globally exponential disc components results in an underestimation of the baryonic contribution by as much as ~40% Given only the assumptions of stationarity, an axially and vertically symmetric disc, doubly exponential tracer and mass-component density profiles, a phenomenologically justified model for the cross-dispersion component $\sigma_{Rz}$, and a realistic model for $g_z$, it is possible to solve the full vertical Jeans equation analytically for the vertical dispersion $\sigma_{z}(z)$ and hence test the robustness of previous attempts at measuring $\rho_{DM}$. When the model parameters are estimated from SEGUE G dwarf star data, it is still not possible to explain the difference in behaviour seen in the simple thick- and thin-disc datasets reported by Buedenbender et al.. Rather than being a fundamental problem with the kinematical model, this effect appears to be a further sign of the difficulty of defining and handling kinematically homogeneous tracer populations.Comment: 11 pages, 3 figures, Astron. & Ap., in pres

The quest for companions to post-common envelope binaries IV: The 2:1 mean-motion resonance of the planets orbiting NN Serpentis

We present 69 new mid-eclipse times of the young post-common envelope binary (PCEB) NN Ser, which was previously suggested to possess two circumbinary planets. We have interpreted the observed eclipse-time variations in terms of the light-travel time effect caused by two planets, exhaustively covering the multi-dimensional parameter space by fits in the two binary and ten orbital parameters. We supplemented the fits by stability calculations for all models with an acceptable chi-square. An island of secularly stable 2:1 resonant solutions exists, which coincides with the global chi-square minimum. Our best-fit stable solution yields current orbital periods P_o = 15.47 yr and P_i = 7.65 yr and eccentricities e_o = 0.14 and e_i = 0.22 for the outer (o) and inner (i) planets, respectively. The companions qualify as giant planets, with masses of 7.0 M_Jup and 1.7 M_Jup for the case of orbits coplanar with that of the binary. The two-planet model that starts from the present system parameters has a lifetime greater than 10^8 yr, which significantly exceeds the age of NN Ser of 10^6 yr as a PCEB. The resonance is characterized by libration of the resonant variable Theta_1 and circulation of omega_i-omega_o, the difference between the arguments of periapse of the two planets. No stable non-resonant solutions were found, and the possibility of a 5:2 resonance suggested previously by us is now excluded at the 99.3% confidence level.Comment: 8 pages, 8 figure

Investigation of Weibull statistics in fracture analysis of cast aluminum

The fracture strengths of two large batches of A357-T6 cast aluminum coupon specimens were compared by using two-parameter Weibull analysis. The minimum number of these specimens necessary to find the fracture strength of the material was determined. The applicability of three-parameter Weibull analysis was also investigated. A design methodology based on the combination of elementary stress analysis and Weibull statistical analysis is advanced and applied to the design of a spherical pressure vessel shell. The results from this design methodology are compared with results from the applicable ASME pressure vessel code

Comparison of Weibull strength parameters from flexure and spin tests of brittle materials

Fracture data from five series of four point bend tests of beam and spin tests of flat annular disks were reanalyzed. Silicon nitride and graphite were the test materials. The experimental fracture strengths of the disks were compared with the predicted strengths based on both volume flaw and surface flaw analyses of four point bend data. Volume flaw analysis resulted in a better correlation between disks and beams in three of the five test series than did surface flaw analysis. The Weibull (moduli) and characteristic gage strengths for the disks and beams were also compared. Differences in the experimental Weibull slopes were not statistically significant. It was shown that results from the beam tests can predict the fracture strength of rotating disks

Beyond Bidimensionality: Parameterized Subexponential Algorithms on Directed Graphs

We develop two different methods to achieve subexponential time parameterized algorithms for problems on sparse directed graphs. We exemplify our approaches with two well studied problems. For the first problem, {\sc $k$-Leaf Out-Branching}, which is to find an oriented spanning tree with at least $k$ leaves, we obtain an algorithm solving the problem in time $2^{O(\sqrt{k} \log k)} n+ n^{O(1)}$ on directed graphs whose underlying undirected graph excludes some fixed graph $H$ as a minor. For the special case when the input directed graph is planar, the running time can be improved to $2^{O(\sqrt{k})}n + n^{O(1)}$. The second example is a generalization of the {\sc Directed Hamiltonian Path} problem, namely {\sc $k$-Internal Out-Branching}, which is to find an oriented spanning tree with at least $k$ internal vertices. We obtain an algorithm solving the problem in time $2^{O(\sqrt{k} \log k)} + n^{O(1)}$ on directed graphs whose underlying undirected graph excludes some fixed apex graph $H$ as a minor. Finally, we observe that for any $\epsilon>0$, the {\sc $k$-Directed Path} problem is solvable in time $O((1+\epsilon)^k n^{f(\epsilon)})$, where $f$ is some function of \ve. Our methods are based on non-trivial combinations of obstruction theorems for undirected graphs, kernelization, problem specific combinatorial structures and a layering technique similar to the one employed by Baker to obtain PTAS for planar graphs

Progressive failure mechanisms in jointed rock: insight from 3D DEM modelling

Instabilities occurring in rock masses are generally related to the presence of preexisting discontinuities and the destabilization process often related to the complex interaction between the discontinuities and the rock matrix through the progressive breakage of rock bridges. A 3D model for fractured rock is presented here. The model uses a discrete representation of the intact medium over which discontinuity planes can be overlaid to represent predefined DFNs representative of pre-existing geological structures. These structures, or joints, can then be simulated using a modified contact logic where interactions are setup depending on the orientations and mechanical properties of the joint surfaces. Uniaxial compression tests on a pre-flawed sample are simulated in order to emphasize the relevance of the model in reproducing the so-called “wing crack” extensions usually observed around penny shaped cracks. The model capabilities in terms of crack propagation and coalescence are then discussed on the basis of simulations performed at the scale of a jointed rock slope, with an emphasis on its capability to reproduce one of the key mechanisms usually involved in the development of progressive failure surfaces, the so-called step-path failure mode