Linearized potential solution for an airfoil in nonuniform parallel streams

A small perturbation potential flow theory is applied to the problem of determining the chordwise pressure distribution, lift and pitching moment of a thin airfoil in the middle of five parallel streams. This theory is then extended to the case of an undisturbed stream having a given smooth velocity profile. Two typical examples are considered and the results obtained are compared with available solutions of Euler's equations. The agreement between these two results is not quite satisfactory. Possible reasons for the differences are indicated

Studies on the interference of wings and propeller slipstreams

The small disturbance potential flow theory is applied to determine the lift of an airfoil in a nonuniform parallel stream. The given stream is replaced by an equivalent stream with a certain number of velocity discontinuities, and the influence of these discontinuities is obtained by the method of images. Next, this method is extended to the problem of an airfoil in a nonuniform stream of smooth velocity profile. This model allows perturbation velocity potential in a rotational undisturbed stream. A comparison of these results with numerical solutions of Euler equations indicates that, although approximate, the present method provides useful information about the interaction problem while avoiding the need to solve the Euler equations

A modified lifting line theory for wing-propeller interference

An inviscid incompressible model for the interaction of a wing with a single propeller slipstream is presented. The model allows the perturbation quantities to be potential even though the undisturbed flow is rotational. The governing equations for the spanwise lift distribution are derived and a simple method of solving these is indicated. Spanwise lift and induced drag distribution for two cases are computed

Effect of Out-Gassing on the Onset of Hypersonic Boundary Layer Transition

Prediction and control of the onset of transition and the associated variation in aerothermodynamic parameters in high-speed flows is key to optimize the performance and design of Thermal Protection Systems (TPS) of next-generation aerospace vehicles [1]. Boundary Layer Transition (BLT) characteristics can influence the surface heating budget determining the TPS thickness and consequently its weight penalty. Ablative heatshields are designed to alleviate the high heat flux at the surface through pyrolysis of their polymeric matrix and subsequent fiber ablation [2]. Pyrolysis leads to out-gassing and non-uniform ablation lead to surface roughness, both of which are known to influence the transition process. An ablator impacts BLT through three main routes: gas injecting into the boundary layer from the wall, changing the surface heat transfer due to wall-flow chemical reactions, and modifying surface roughness [3]. In preparation to Mars 2020 mission post-flight analysis, the predictive transition capability has been initiated toward hard-coupling porous material response analysis and aerothermal environment calculation

Extremal primes for elliptic curves without complex multiplication

Fix an elliptic curve E over Q. An extremal prime for E is a prime p of good reduction such that the number of rational points on E modulo p is maximal or minimal in relation to the Hasse bound. Assuming that all the symmetric power L-functions associated to E are automorphic and satisfy the Generalized Riemann Hypothesis, we give the first non-trivial upper bounds for the number of such primes when E is a curve without complex multiplication. In order to obtain this bound, we use explicit equidistribution for the Sato-Tate measure as in the work of Rouse and Thorner (arXiv:1305.5283) and refine certain intermediate estimates taking advantage of the fact that extremal primes have a very small Sato-Tate measure

The AGN and Gas Disk in the Low Surface Brightness Galaxy PGC045080

We present radio observations and optical spectroscopy of the giant low surface brightness (LSB) galaxy PGC 045080 (or 1300+0144). PGC 045080 is a moderately distant galaxy having a highly inclined optical disk and massive HI gas content. Radio continuum observations of the galaxy were carried out at 320 MHz, 610 MHz and 1.4 GHz. Continuum emission was detected and mapped in the galaxy. The emission appears extended over the inner disk at all three frequencies. At 1.4 GHz and 610 MHz it appears to have two distinct lobes. We also did optical spectroscopy of the galaxy nucleus; the spectrum did not show any strong emission lines associated with AGN activity but the presence of a weak AGN cannot be ruled out. Furthermore, comparison of the H$\alpha$ flux and radio continuum at 1.4 GHz suggests that a significant fraction of the emission is non-thermal in nature. Hence we conclude that a weak or hidden AGN may be present in PGC 045080. The extended radio emission represents lobes/jets from the AGN. These observations show that although LSB galaxies are metal poor and have very little star formation, their centers can host significant AGN activity. We also mapped the HI gas disk and velocity field in PGC 045080. The HI disk extends well beyond the optical disk and appears warped. In the HI intensity maps, the disk appears distinctly lopsided. The velocity field is disturbed on the lopsided side of the disk but is fairly uniform in the other half. We derived the HI rotation curve for the galaxy from the velocity field. The rotation curve has a flat rotation speed of ~ 190 km/s.Comment: Paper contains 14 figures and 4 tables. Figures 8, 10 (color) and 13 supplied separately. Accepted for publication in MNRA

Equidistribution of p alpha p theta with a Chebotarev condition and applications to

We establish a joint distribution result concerning the fractional part of $\alpha p^\theta$ for $\theta \in (0,1), \ \alpha>0$, where $p$ is a prime satisfying a Chebotarev condition in a fixed finite Galois extension over $\mathbb{Q}$. As an application, for a fixed non-CM elliptic curve $E/\mathbb{Q}$, an asymptotic formula is given for the number of primes at the extremes of the Sato-Tate measure modulo a large prime $\ell$. These are precisely the primes $p$ for which the Frobenius trace $a_p(E)$ satisfies the congruence $a_p(E)\equiv [2\sqrt{p}] \bmod \ell$. We assume a zero-free region hypothesis for Dedekind zeta functions of number fields