The X-ray Properties of the Most-Luminous Quasars from the Sloan Digital Sky Survey

Utilizing 21 new Chandra observations as well as archival Chandra, ROSAT, and XMM-Newton data, we study the X-ray properties of a representative sample of 59 of the most optically luminous quasars in the Universe (M_i~~-29.3 to -30.2) spanning a redshift range of z~~1.5-4.5. Our full sample consists of 32 quasars from the Sloan Digital Sky Survey (SDSS) Data Release 3 (DR3) quasar catalog, two additional objects in the DR3 area that were missed by the SDSS selection criteria, and 25 comparably luminous quasars at z>~4. This is the largest X-ray study of such luminous quasars to date. By jointly fitting the X-ray spectra of our sample quasars, excluding radio-loud and broad absorption line (BAL) objects, we find a mean X-ray power-law photon index of Gamma=1.92^{+0.09}_{-0.08} and constrain any neutral intrinsic absorbing material to have a mean column density of N_H<~2x10^{21} cm^{-2}. We find, consistent with other studies, that Gamma does not change with redshift, and we constrain the amount of allowed Gamma evolution for the most-luminous quasars. Our sample, excluding radio-loud and BAL quasars, has a mean X-ray-to-optical spectral slope of a_ox=-1.80+/-0.02, as well as no significant evolution of a_ox with redshift. We also comment upon the X-ray properties of a number of notable quasars, including an X-ray weak quasar with several strong narrow absorption-line systems, a mildly radio-loud BAL quasar, and a well-studied gravitationally lensed quasar.Comment: 18 pages (emulateapj), 11 figures. Accepted for publication in The Astrophysical Journa

The Isomorphism Relation Between Tree-Automatic Structures

An $\omega$-tree-automatic structure is a relational structure whose domain and relations are accepted by Muller or Rabin tree automata. We investigate in this paper the isomorphism problem for $\omega$-tree-automatic structures. We prove first that the isomorphism relation for $\omega$-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups, nilpotent groups of class n >1) is not determined by the axiomatic system ZFC. Then we prove that the isomorphism problem for $\omega$-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups, nilpotent groups of class n >1) is neither a $\Sigma_2^1$-set nor a $\Pi_2^1$-set

Role of unstable periodic orbits in phase transitions of coupled map lattices

The thermodynamic formalism for dynamical systems with many degrees of freedom is extended to deal with time averages and fluctuations of some macroscopic quantity along typical orbits, and applied to coupled map lattices exhibiting phase transitions. Thereby, it turns out that a seed of phase transition is embedded as an anomalous distribution of unstable periodic orbits, which appears as a so-called q-phase transition in the spatio-temporal configuration space. This intimate relation between phase transitions and q-phase transitions leads to one natural way of defining transitions and their order in extended chaotic systems. Furthermore, a basis is obtained on which we can treat locally introduced control parameters as macroscopic ``temperature'' in some cases involved with phase transitions.Comment: 13 pages, 9 figures; further explanation and 2 figures are added (minor revision

Continued-fraction expansion of eigenvalues of generalized evolution operators in terms of periodic orbits

A new expansion scheme to evaluate the eigenvalues of the generalized evolution operator (Frobenius-Perron operator) $H_{q}$ relevant to the fluctuation spectrum and poles of the order-$q$ power spectrum is proposed. The ``partition function'' is computed in terms of unstable periodic orbits and then used in a finite pole approximation of the continued fraction expansion for the evolution operator. A solvable example is presented and the approximate and exact results are compared; good agreement is found.Comment: CYCLER Paper 93mar00

Time--delay autosynchronization of the spatio-temporal dynamics in resonant tunneling diodes

The double barrier resonant tunneling diode exhibits complex spatio-temporal patterns including low-dimensional chaos when operated in an active external circuit. We demonstrate how autosynchronization by time--delayed feedback control can be used to select and stabilize specific current density patterns in a noninvasive way. We compare the efficiency of different control schemes involving feedback in either local spatial or global degrees of freedom. The numerically obtained Floquet exponents are explained by analytical results from linear stability analysis.Comment: 10 pages, 16 figure

Controlling chaos in spatially extended beam-plasma system by the continuous delayed feedback

In present paper we discuss the control of complex spatio-temporal dynamics in a {spatially extended} non-linear system (fluid model of Pierce diode) based on the concepts of controlling chaos in the systems with few degrees of freedom. A presented method is connected with stabilization of unstable homogeneous equilibrium state and the unstable spatio-temporal periodical states analogous to unstable periodic orbits of chaotic dynamics of the systems with few degrees of freedom. We show that this method is effective and allows to achieve desired regular dynamics chosen from a number of possible in the considered system.Comment: 12 pages, 12 figure

Time-delayed feedback control in astrodynamics

In this paper we present time-delayed feedback control (TDFC) for the purpose of autonomously driving trajectories of nonlinear systems into periodic orbits. As the generation of periodic orbits is a major component of many problems in astodynamics we propose this method as a useful tool in such applications. To motivate the use of this method we apply it to a number of well known problems in the astrodynamics literature. Firstly, TDFC is applied to control in the chaotic attitude motion of an asymmetric satellite in an elliptical orbit. Secondly, we apply TDFC to the problem of maintaining a spacecraft in a periodic orbit about a body with large ellipticity (such as an asteroid) and finally, we apply TDFC to eliminate the drift between two satellites in low Earth orbits to ensure their relative motion is bounded

Discovery of a stellar companion to the nearby solar-analogue HD 104304

Sun-like stars are promising candidates to host exoplanets and are often included in exoplanet surveys by radial velocity (RV) and direct imaging. In this paper we report on the detection of a stellar companion to the nearby solar-analogue star HD 104304, which previously was considered to host a planetary mass or brown dwarf companion. We searched for close stellar and substellar companions around extrasolar planet host stars with high angular resolution imaging to characterize planet formation environments. The detection of the stellar companion was achieved by high angular resolution measurements, using the "Lucky Imaging" technique at the ESO NTT 3.5m with the AstraLux Sur instrument. We combined the results with VLT/NACO archive data, where the companion could also be detected. The results were compared to precise RV measurements of HD 104304, obtained at the Lick and Keck observatories from 2001-2010. We confirmed common proper motion of the binary system. A spectral type of M4V of the companion and a mass of 0.21 M_Sun was derived. Due to comparison of the data with RV measurements of the unconfirmed planet candidate listed in the Extrasolar Planets Encyclopaedia, we suggest that the discovered companion is the origin of the RV trend and that the inclination of the orbit of approximately 35 degrees explains the relatively small RV signal.Comment: 4 pages, 4 PNG figures, use aa.cls, accepted for publication in Astronomy & Astrophysic

Brownian motion with dry friction: Fokker-Planck approach

We solve a Langevin equation, first studied by de Gennes, in which there is a solid-solid or dry friction force acting on a Brownian particle in addition to the viscous friction usually considered in the study of Brownian motion. We obtain both the time-dependent propagator of this equation and the velocity correlation function by solving the associated time-dependent Fokker-Planck equation. Exact results are found for the case where only dry friction acts on the particle. For the case where both dry and viscous friction forces are present, series representations of the propagator and correlation function are obtained in terms of parabolic cylinder functions. Similar series representations are also obtained for the case where an external constant force is added to the Langevin equation.Comment: 18 pages, 13 figures (in color