A numerical investigation of self-sustained cavity flow oscillations

Two-dimensional (2-D) cavity flow physics and oscillation control were investigated through solutions of the Reynolds-Averaged Navier-Stokes equations coupled with a two-equation k-? turbulence model. Effects of the leading edge modifications including compression ramps, expansion surfaces and mass injection on supersonic cavity flow oscillation were investigated. Different flow mechanisms were observed at Mach 1.5 and 2.5. The study proposed a different explanation of the flow control mechanism when mass injection was used. An optimal mass injection rate was identified. A further improvement on the 2-D model was made by considering the effect of the turbulent viscous sub-layer using the Integration-to-the-wall boundary condition. The results confirmed that the shear layer instability reduced gradually from Mach 1.5 to 3.5. An improvement in SPL prediction was achieved. Dominant modes were also correctly predicted.The capability of the model was extended for the investigation of the 3-D compressible unsteady turbulent flow physics. It was validated against a hypersonic symmetric corner flow. The turbulent effect was modelled by a two-equation k-? turbulence model. A laminar cavity flow oscillation at Mach 1.5 was predicted. The result showed a self-sustained pressure oscillation. The predicted pressure oscillation was dominated by the second mode and its frequency was 5702H z which was close to the measured value of 5900H z. The SPL discrepancies with the measurements were within 2.3dB. A secondary symmetric flow pattern inside the cavity displayed a 3-D effect and showed the effect of the side wall within a spanwise distance of 2D. Further simulation of the turbulent cavity flow at Mach 1.5 showed a weak pressure oscillation, which indicated the RANS is sensitive to the choice of turbulence model. However, the surface flow pattern and surface pressure distribution were consistent with the measurements. The strongest surface pressure oscillation was observed near the rear corner on the centre plane. A secondary symmetric flow pattern also existed. A spanwise wave was found in the cavity. At the trailing plate, a flow separation was formed in the laminar boundary layer but was not observed in the turbulent boundary layer

Continuous-time Markov decision processes under the risk-sensitive average cost criterion

This paper studies continuous-time Markov decision processes under the risk-sensitive average cost criterion. The state space is a finite set, the action space is a Borel space, the cost and transition rates are bounded, and the risk-sensitivity coefficient can take arbitrary positive real numbers. Under the mild conditions, we develop a new approach to establish the existence of a solution to the risk-sensitive average cost optimality equation and obtain the existence of an optimal deterministic stationary policy.Comment: 14 page

Revealing the formation of stellar-mass black hole binaries: The need for deci-Hertz gravitational wave observatories

The formation of compact stellar-mass binaries is a difficult, but interesting problem in astrophysics. There are two main formation channels: In the field via binary star evolution, or in dense stellar systems via dynamical interactions. The Laser Interferometer Gravitational-Wave Observatory (LIGO) has detected black hole binaries (BHBs) via their gravitational radiation. These detections provide us with information about the physical parameters of the system. It has been claimed that when the Laser Interferometer Space Antenna (LISA) is operating, the joint observation of these binaries with LIGO will allow us to derive the channels that lead to their formation. However, we show that for BHBs in dense stellar systems dynamical interactions could lead to high eccentricities such that a fraction of the relativistic mergers are not audible to LISA. A non-detection by LISA puts a lower limit of about $0.005$ on the eccentricity of a BHB entering the LIGO band. On the other hand, a deci-Hertz observatory, like DECIGO or Tian Qin, would significantly enhance the chances of a joint detection, and shed light on the formation channels of these binaries.Comment: Submitte

The fragmenting past of the disk at the Galactic Center : The culprit for the missing red giants

Since 1996 we have known that the Galactic Center (GC) displays a core-like distribution of red giant branch (RGB) stars starting at ~ 10", which poses a theoretical problem, because the GC should have formed a segregated cusp of old stars. This issue has been addressed invoking stellar collisions, massive black hole binaries, and infalling star clusters, which can explain it to some extent. Another observational fact, key to the work presented here, is the presence of a stellar disk at the GC. We postulate that the reason for the missing stars in the RGB is closely intertwined with the disk formation, which initially was gaseous and went through a fragmentation phase to form the stars. Using simple analytical estimates, we prove that during fragmentation the disk developed regions with densities much higher than a homogeneous gaseous disk, i.e. "clumps", which were optically thick, and hence contracted slowly. Stars in the GC interacted with them and in the case of RGB stars, the clumps were dense enough to totally remove their outer envelopes after a relatively low number of impacts. Giant stars in the horizontal branch (HB), however, have much denser envelopes. Hence, the fragmentation phase of the disk must have had a lower impact in their distribution, because it was more difficult to remove their envelopes. We predict that future deeper observations of the GC should reveal less depletion of HB stars and that the released dense cores of RGB stars will still be populating the GC.Comment: 5 pages, no figures, accepted for publication ApJ Lett

A rapid evolving region in the Galactic Center: Why S-stars thermalize and more massive stars are missing

The existence of "S-stars" within a distance of 1" from SgrA$^*$ contradicts our understanding of star formation, due to the forbiddingly violent environment. A suggested possibility is that they form far and have been brought in by some fast dynamical process, since they are young. Nonetheless, all conjectured mechanisms either fail to reproduce their eccentricities --without violating their young age-- or cannot explain the problem of "inverse mass segregation": The fact that lighter stars (the S-stars) are closer to SgrA$^*$ and more massive ones, Wolf-Rayet (WR) and O-stars, are farther out. In this Letter we propose that the responsible for both, the distribution of the eccentricities and the paucity of massive stars, is the Kozai-Lidov-{\em like} resonance induced by a sub-parsec disk recently discovered in the Galactic center. Considering that the disk probably extended to smaller radius in the past, we show that in as short as (a few) $10^6$ years, the stars populating the innermost 1" region would redistribute in angular-momentum space and recover the observed "super-thermal" distribution. Meanwhile, WR and O-stars in the same region intermittently attain ample eccentricities that will lead to their tidal disruptions by the central massive black hole. Our results provide new evidences that SgrA$^*$ was powered several millions years ago by an accretion disk as well as by tidal stellar disruptions.Comment: 5 pages, two figures, accepted for publication ApJ Lett

Enhanced off-center stellar tidal disruptions by supermassive black holes in merging galaxies

Off-center stellar tidal disruption flares have been suggested to be a powerful probe of recoiling supermassive black holes (SMBHs) out of galactic centers due to anisotropic gravitational wave radiations. However, off-center tidal flares can also be produced by SMBHs in merging galaxies. In this paper, we computed the tidal flare rates by dual SMBHs in two merging galaxies before the SMBHs become self-gravitationally bounded. We employ an analytical model to calculate the tidal loss-cone feeding rates for both SMBHs, taking into account two-body relaxation of stars, tidal perturbations by the companion galaxy, and chaotic stellar orbits in triaxial gravitational potential. We show that for typical SMBHs with mass 10^7 M_\sun, the loss-cone feeding rates are enhanced by mergers up to \Gamma ~ 10^{-2} yr^{-1}, about two order of magnitude higher than those by single SMBHs in isolated galaxies and about four orders of magnitude higher than those by recoiling SMBHs. The enhancements are mainly due to tidal perturbations by the companion galaxy. We suggest that off-center tidal flares are overwhelmed by those from merging galaxies, making the identification of recoiling SMBHs challenging. Based on the calculated rates, we estimate the relative contributions of tidal flare events by single, binary, and dual SMBH systems during cosmic time. Our calculations show that the off-center tidal disruption flares by un-bound SMBHs in merging galaxies contribute a fraction comparable to that by single SMBHs in isolated galaxies. We conclude that off-center tidal disruptions are powerful tracers of the merging history of galaxies and SMBHs.Comment: 17 pages, 8 figures; Typos are corrected to match the published version in Ap