Linear feedback control of transient energy growth and control performance limitations in subcritical plane Poiseuille flow

Suppression of the transient energy growth in subcritical plane Poiseuille flow via feedback control is addressed. It is assumed that the time derivative of any of the velocity components can be imposed at the walls as control input, and that full-state information is available. We show that it is impossible to design a linear state-feedback controller that leads to a closed-loop flow system without transient energy growth. In a subsequent step, full-state feedback controllers -- directly targeting the transient growth mechanism -- are designed, using a procedure based on a Linear Matrix Inequalities approach. The performance of such controllers is analyzed first in the linear case, where comparison to previously proposed linear-quadratic optimal controllers is made; further, transition thresholds are evaluated via Direct Numerical Simulations of the controlled three-dimensional Poiseuille flow against different initial conditions of physical interest, employing different velocity components as wall actuation. The present controllers are effective in increasing the transition thresholds in closed loop, with varying degree of performance depending on the initial condition and the actuation component employed

On rapid migration and accretion within disks around supermassive black holes

Galactic nuclei should contain a cluster of stars and compact objects in the vicinity of the central supermassive black hole due to stellar evolution, minor mergers and gravitational dynamical friction. By analogy with protoplanetary migration, nuclear cluster objects (NCOs) can migrate in the accretion disks that power active galactic nuclei by exchanging angular momentum with disk gas. Here we show that an individual NCO undergoing runaway outward migration comparable to Type III protoplanetary migration can generate an accretion rate corresponding to Seyfert AGN or quasar luminosities. Multiple migrating NCOs in an AGN disk can dominate traditional viscous disk accretion and at large disk radii, ensemble NCO migration and accretion could provide sufficient heating to prevent the gravitational instability from consuming disk gas in star formation. The magnitude and energy of the X-ray soft excess observed at ~0.1-1keV in Seyfert AGN could be explained by a small population of ~10^{2}-10^{3} accreting stellar mass black holes or a few ULXs. NCO migration and accretion in AGN disks are therefore extremely important mechanisms to add to realistic models of AGN disks.Comment: 6 pages, 2 figures, MNRAS Letters (accepted

On the rate of black hole binary mergers in galactic nuclei due to dynamical hardening

We assess the contribution of dynamical hardening by direct three-body scattering interactions to the rate of stellar-mass black hole binary (BHB) mergers in galactic nuclei. We derive an analytic model for the single-binary encounter rate in a nucleus with spherical and disk components hosting a super-massive black hole (SMBH). We determine the total number of encounters $N_{\rm GW}$ needed to harden a BHB to the point that inspiral due to gravitational wave emission occurs before the next three-body scattering event. This is done independently for both the spherical and disk components. Using a Monte Carlo approach, we refine our calculations for $N_{\rm GW}$ to include gravitational wave emission between scattering events. For astrophysically plausible models we find that typically $N_{\rm GW} \lesssim$ 10. We find two separate regimes for the efficient dynamical hardening of BHBs: (1) spherical star clusters with high central densities, low velocity dispersions and no significant Keplerian component; and (2) migration traps in disks around SMBHs lacking any significant spherical stellar component in the vicinity of the migration trap, which is expected due to effective orbital inclination reduction of any spherical population by the disk. We also find a weak correlation between the ratio of the second-order velocity moment to velocity dispersion in galactic nuclei and the rate of BHB mergers, where this ratio is a proxy for the ratio between the rotation- and dispersion-supported components. Because disks enforce planar interactions that are efficient in hardening BHBs, particularly in migration traps, they have high merger rates that can contribute significantly to the rate of BHB mergers detected by the advanced Laser Interferometer Gravitational-Wave Observatory.Comment: 13 pages, 9 figures, accepted for publication in MNRA

The Kinematics and Physical Conditions pf the Ionized Gas in Markarian 509. II. STIS Echelle Observations

We present observations of the UV absorption lines in the luminous Seyfert 1 galaxy Mrk 509, obtained with the medium resolution (lambda/Delta-lambda ~ 40,000) echelle gratings of the Space Telescope Imaging Spectrograph on the Hubble Space Telescope. The spectra reveal the presence of eight kinematic components of absorption in Ly-alpha, C IV, and N V, at radial velocities of -422, -328, -259, -62, -22, +34, +124, and +210 km s^-1 with respect to an emission-line redshift of z = 0.03440, seven of which were detected in an earlier Far Ultraviolet Spectrographic Explorer (FUSE) spectrum. The component at -22 km s^-1 also shows absorption by Si IV. The covering factor and velocity width of the Si IV lines were lower than those of the higher ionization lines for this component, which is evidence for two separate absorbers at this velocity. We have calculated photoionization models to match the UV column densities in each of these components. Using the predicted O VI column densities, we were able to match the O VI profiles observed in the FUSE spectrum. Based on our results, none of the UV absorbers can produce the X-ray absorption seen in simultaneous Chandra observations; therefore, there must be more highly ionized gas in the radial velocity ranges covered by the UV absorbers.Comment: 30 pages, three figures (Figure 1 is in color). Accepted for publication in the Astrophysical Journa

Instrumentation for Millimeter-wave Magnetoelectrodynamic Investigations of Low-Dimensional Conductors and Superconductors

We describe instrumentation for conducting high sensitivity millimeter-wave cavity perturbation measurements over a broad frequency range (40-200 GHz) and in the presence of strong magnetic fields (up to 33 tesla). A Millimeter-wave Vector Network Analyzer (MVNA) acts as a continuously tunable microwave source and phase sensitive detector (8-350 GHz), enabling simultaneous measurements of the complex cavity parameters (resonance frequency and Q-value) at a rapid repetition rate (approx. 10 kHz). We discuss the principal of operation of the MVNA and the construction of a probe for coupling the MVNA to various cylindrical resonator configurations which can easily be inserted into a high field magnet cryostat. We also present several experimental results which demonstrate the potential of the instrument for studies of low-dimensional conducting systems.Comment: 20 pages including fig

SDW and FISDW transition of (TMTSF)2_2ClO4_4 at high magnetic fields

The magnetic field dependence of the SDW transition in (TMTSF)$_2$ClO$_4$ for various anion cooling rates has been measured, with the field up to 27T parallel to the lowest conductivity direction $c^{\ast}$. For quenched (TMTSF)$_2$ClO$_4$, the SDW transition temperature $T_{\rm {SDW}}$ increases from 4.5K in zero field up to 8.4K at 27T. A quadratic behavior is observed below 18T, followed by a saturation behavior. These results are consistent with the prediction of the mean-field theory. From these behaviors, $T_{\rm {SDW}}$ is estimated as $T_{\rm {SDW_0}}$=13.5K for the perfect nesting case. This indicates that the SDW phase in quenched (TMTSF)$_2$ClO$_4$, where $T_{\rm {SDW}}$ is less than 6K, is strongly suppressed by the two-dimensionality of the system. In the intermediate cooled state in which the SDW phase does not appear in zero field, the transition temperature for the field-induced SDW shows a quadratic behavior above 12T and there is no saturation behavior even at 27T, in contrast to the FISDW phase in the relaxed state. This behavior can probably be attributed to the difference of the dimerized gap due to anion ordering.Comment: 4pages,5figures(EPS), accepted for publication in PR