Semidirect computations for transonic flow

A semidirect method, driven by a Poisson solver, was developed for inviscid transonic flow computations. It is an extension of a recently introduced algorithm for solving subsonic rotational flows. Shocks are captured by implementing a form of artificial compressibility. Nonisentropic cases are computed using a shock tracking procedure coupled with the Rankine-Hugoniot relationships. Results are presented for both subsonic and transonic flows. For the test geometry, an unstaggered cascade of 20 percent thick circular arc airfoils at zero angle of attack, shocks are crisply resolved in supercritical situations and the algorithm converges rapidly. In addition, the convergence rate appears to be nearly independent of the entropy and vorticity production at the shock

Supersonic unstalled flutter

Flutter analyses were developed to predict the onset of supersonic unstalled flutter of a cascade of two-dimensional airfoils. The first of these analyzes the onset of supersonic flutter at low levels of aerodynamic loading (i.e., backpressure), while the second examines the occurrence of supersonic flutter at moderate levels of aerodynamic loading. Both of these analyses are based on the linearized unsteady inviscid equations of gas dynamics to model the flow field surrounding the cascade. These analyses are utilized in a parametric study to show the effects of cascade geometry, inlet Mach number, and backpressure on the onset of single and multi degree of freedom unstalled supersonic flutter. Several of the results are correlated against experimental qualitative observation to validate the models

Improved Approximation Algorithms for Stochastic Matching

In this paper we consider the Stochastic Matching problem, which is motivated by applications in kidney exchange and online dating. We are given an undirected graph in which every edge is assigned a probability of existence and a positive profit, and each node is assigned a positive integer called timeout. We know whether an edge exists or not only after probing it. On this random graph we are executing a process, which one-by-one probes the edges and gradually constructs a matching. The process is constrained in two ways: once an edge is taken it cannot be removed from the matching, and the timeout of node $v$ upper-bounds the number of edges incident to $v$ that can be probed. The goal is to maximize the expected profit of the constructed matching. For this problem Bansal et al. (Algorithmica 2012) provided a $3$-approximation algorithm for bipartite graphs, and a $4$-approximation for general graphs. In this work we improve the approximation factors to $2.845$ and $3.709$, respectively. We also consider an online version of the bipartite case, where one side of the partition arrives node by node, and each time a node $b$ arrives we have to decide which edges incident to $b$ we want to probe, and in which order. Here we present a $4.07$-approximation, improving on the $7.92$-approximation of Bansal et al. The main technical ingredient in our result is a novel way of probing edges according to a random but non-uniform permutation. Patching this method with an algorithm that works best for large probability edges (plus some additional ideas) leads to our improved approximation factors

The Penn State - Toru\'n Centre for Astronomy Planet Search stars IV. Dwarfs and the complete sample

Our knowledge of the intrinsic parameters of exoplanets is as precise as our determinations of their stellar hosts parameters. In the case of radial velocity searches for planets, stellar masses appear to be crucial. But before estimating stellar masses properly, detailed spectroscopic analysis is essential. With this paper we conclude a general spectroscopic description of the Pennsylvania-Torun Planet Search (PTPS) sample of stars. We aim at a detailed description of basic parameters of stars representing the complete PTPS sample. We present atmospheric and physical parameters for dwarf stars observed within the PTPS along with updated physical parameters for the remaining stars from this sample after the first Gaia data release. We used high resolution (R=60 000) and high signal-to-noise-ratio (S/N=150-250) spectra from the Hobby-Eberly Telescope and its High Resolution Spectrograph. Stellar atmospheric parameters were determined through a strictly spectroscopic local thermodynamic equilibrium analysis (LTE) of the equivalent widths of FeI and FeII lines. Stellar masses, ages, and luminosities were estimated through a Bayesian analysis of theoretical isochrones. We present $T_{eff}$, log$g$ , [Fe/H], micrturbulence velocities, absolute radial velocities, and rotational velocities for 156 stars from the dwarf sample of PTPS. For most of these stars these are the first determinations. We refine the definition of PTPS subsamples of stars (giants, subgiants, and dwarfs) and update the luminosity classes for all PTPS stars. Using available Gaia and Hipparcos parallaxes, we redetermine the stellar parameters (masses, radii, luminosities, and ages) for 451 PTPS stars. The complete PTPS sample of 885 stars is composed of 132 dwarfs, 238 subgiants, and 515 giants, of which the vast majority are of roughly solar mass.Comment: 11 pages, 10 figures, Accepted for publication in Astronomy & Astrophysic

A model for closing the inviscid form of the average-passage equation system

A mathematical model is proposed for closing or mathematically completing the system of equations which describes the time average flow field through the blade passages of multistage turbomachinery. These equations referred to as the average passage equation system govern a conceptual model which has proven useful in turbomachinery aerodynamic design and analysis. The closure model is developed so as to insure a consistency between these equations and the axisymmetric through flow equations. The closure model was incorporated into a computer code for use in simulating the flow field about a high speed counter rotating propeller and a high speed fan stage. Results from these simulations are presented

A numerical simulation of the inviscid flow through a counter-rotating propeller

The results of a numerical simulation of the time-averaged inviscid flow field through the blade rows of a multiblade row turboprop configuration are presented. The governing equations are outlined along with a discussion of the solution procedure and coding strategy. Numerical results obtained from a simulation of the flow field through a modern high-speed turboprop will be shown

Constant-Factor FPT Approximation for Capacitated k-Median

Capacitated k-median is one of the few outstanding optimization problems for which the existence of a polynomial time constant factor approximation algorithm remains an open problem. In a series of recent papers algorithms producing solutions violating either the number of facilities or the capacity by a multiplicative factor were obtained. However, to produce solutions without violations appears to be hard and potentially requires different algorithmic techniques. Notably, if parameterized by the number of facilities k, the problem is also W[2] hard, making the existence of an exact FPT algorithm unlikely. In this work we provide an FPT-time constant factor approximation algorithm preserving both cardinality and capacity of the facilities. The algorithm runs in time 2^O(k log k) n^O(1) and achieves an approximation ratio of 7+epsilon

Three red giants with substellar-mass companions

We present three giant stars from the ongoing Penn State-Toru\'n Planet Search with the Hobby-Eberly Telescope, which exhibit radial velocity variations that point to a presence of planetary --mass companions around them. BD+49 828 is a $M=1.52 \pm 0.22$ $M_{\odot}$ K0 giant with a $m sini$=$1.6^{+0.4}_{-0.2}$ $M_{J}$ minimum mass companion in $a=4.2^{+0.32}_{-0.2}$ AU ($2590^{+300}_{-180}$d), $e=0.35^{+0.24}_{-0.10}$ orbit. HD 95127, a log$L$/$L_{\odot}$=$2.28 \pm 0.38$, $R = 20\pm 9$ $R_{\odot}$, $M=1.20 \pm 0.22$ $M_{\odot}$ K0 giant has a $m sini$=$5.01^{+0.61}_{-0.44}$ $M_{J}$ minimum mass companion in $a=1.28^{+0.01}_{-0.01}$ AU ($482^{+5}_{-5}$d), $e=0.11^{+0.15}_{-0.06}$ orbit. Finally, HD 216536, is a $M=1.36 \pm 0.38$ $M_{\odot}$ K0 giant with a $m sin i=1.47^{+0.20}_{-0.12}$ $M_{J}$ minimum mass companion in $a=0.609^{+0.002}_{-0.002}$ AU ($148.6^{+0.7}_{-0.7}$d), $e=0.38^{+0.12}_{-0.10}$ orbit. Both, HD 95127 b and HD 216536 b in their compact orbits, are very close to the engulfment zone and hence prone to ingestion in the near future. BD+49 828 b is among the longest period planets detected with the radial velocity technique until now and it will remain unaffected by stellar evolution up to a very late stage of its host. We discuss general properties of planetary systems around evolved stars and planet survivability using existing data on exoplanets in more detail.Comment: 47 pages, 11 figures. Accepted by Ap