Balanced Truncation Model Reduction of a Nonlinear Cable-Mass PDE System with Interior Damping

We consider model order reduction of a nonlinear cable-mass system modeled by a 1D wave equation with interior damping and dynamic boundary conditions. The system is driven by a time dependent forcing input to a linear mass-spring system at one boundary. The goal of the model reduction is to produce a low order model that produces an accurate approximation to the displacement and velocity of the mass in the nonlinear mass-spring system at the opposite boundary. We first prove that the linearized and nonlinear unforced systems are well-posed and exponentially stable under certain conditions on the damping parameters, and then consider a balanced truncation method to generate the reduced order model (ROM) of the nonlinear input-output system. Little is known about model reduction of nonlinear input-output systems, and so we present detailed numerical experiments concerning the performance of the nonlinear ROM. We find that the ROM is accurate for many different combinations of model parameters

SB9: The Ninth Catalogue of Spectroscopic Binary Orbits

The Ninth Catalogue of Spectroscopic Binary Orbits (http://sb9.astro.ulb.ac.be) continues the series of compilations of spectroscopic orbits carried out over the past 35 years by Batten and collaborators. As of 2004 May 1st, the new Catalogue holds orbits for 2,386 systems. Some essential differences between this catalogue and its predecessors are outlined and three straightforward applications are presented: (1) Completeness assessment: period distribution of SB1s and SB2s; (2) Shortest periods across the H-R diagram; (3) Period-eccentricity relation.Comment: Accepte for publication in A&A, 6 pages, 6 figure

Novel Ground-State Crystals with Controlled Vacancy Concentrations: From Kagom\'{e} to Honeycomb to Stripes

We introduce a one-parameter family, $0 \leq H \leq 1$, of pair potential functions with a single relative energy minimum that stabilize a range of vacancy-riddled crystals as ground states. The "quintic potential" is a short-ranged, nonnegative pair potential with a single local minimum of height $H$ at unit distance and vanishes cubically at a distance of \rt. We have developed this potential to produce ground states with the symmetry of the triangular lattice while favoring the presence of vacancies. After an exhaustive search using various optimization and simulation methods, we believe that we have determined the ground states for all pressures, densities, and $0 \leq H \leq 1$. For specific areas below 3\rt/2, the ground states of the "quintic potential" include high-density and low-density triangular lattices, kagom\'{e} and honeycomb crystals, and stripes. We find that these ground states are mechanically stable but are difficult to self-assemble in computer simulations without defects. For specific areas above 3\rt/2, these systems have a ground-state phase diagram that corresponds to hard disks with radius \rt. For the special case of H=0, a broad range of ground states is available. Analysis of this case suggests that among many ground states, a high-density triangular lattice, low-density triangular lattice, and striped phases have the highest entropy for certain densities. The simplicity of this potential makes it an attractive candidate for experimental realization with application to the development of novel colloidal crystals or photonic materials.Comment: 25 pages, 11 figure

The visual orbits of the spectroscopic binaries HD 6118 and HD 27483 from the Palomar Testbed Interferometer

We present optical interferometric observations of two double-lined spectroscopic binaries, HD 6118 and HD 27483, taken with the Palomar Testbed Interferometer (PTI) in the K band. HD 6118 is one of the most eccentric spectroscopic binaries and HD 27483 a spectroscopic binary in the Hyades open cluster. The data collected with PTI in 2001-2002 allow us to determine astrometric orbits and when combined with the radial velocity measurements derive all physical parameters of the systems. The masses of the components are 2.65 +/- 0.27 M_Sun and 2.36 +/- 0.24 M_Sun for HD 6118 and 1.38 +/- 0.13 M_Sun and 1.39 +/- 0.13 M_Sun for HD 27483. The apparent semi-major axis of HD 27483 is only 1.2 mas making it the closest binary successfully observed with an optical interferometer.Comment: submitted to Ap

Planetary systems around close binary stars: the case of the very dusty, Sun-like, spectroscopic binary BD+20 307

Field star BD+20 307 is the dustiest known main sequence star, based on the fraction of its bolometric luminosity, 4%, that is emitted at infrared wavelengths. The particles that carry this large IR luminosity are unusually warm, comparable to the temperature of the zodiacal dust in the solar system, and their existence is likely to be a consequence of a fairly recent collision of large objects such as planets or planetary embryos. Thus, the age of BD+20 307 is potentially of interest in constraining the era of terrestrial planet formation. The present project was initiated with an attempt to derive this age using the Chandra X-ray Observatory to measure the X-ray flux of BD+20 307 in conjunction with extensive photometric and spectroscopic monitoring observations from Fairborn Observatory. However, the recent realization that BD+20 307 is a short period, double-line, spectroscopic binary whose components have very different lithium abundances, vitiates standard methods of age determination. We find the system to be metal-poor; this, combined with its measured lithium abundances, indicates that BD+20 307 may be several to many Gyr old. BD+20 307 affords astronomy a rare peek into a mature planetary system in orbit around a close binary star (because such systems are not amenable to study by the precision radial velocity technique).Comment: accepted for ApJ, December 10, 200

Multi-Line Geometry of Qubit-Qutrit and Higher-Order Pauli Operators

The commutation relations of the generalized Pauli operators of a qubit-qutrit system are discussed in the newly established graph-theoretic and finite-geometrical settings. The dual of the Pauli graph of this system is found to be isomorphic to the projective line over the product ring Z2xZ3. A "peculiar" feature in comparison with two-qubits is that two distinct points/operators can be joined by more than one line. The multi-line property is shown to be also present in the graphs/geometries characterizing two-qutrit and three-qubit Pauli operators' space and surmised to be exhibited by any other higher-level quantum system.Comment: 8 pages, 6 figures. International Journal of Theoretical Physics (2007) accept\'

SB9: The ninth catalogue of spectroscopic binary orbits

The Ninth Catalogue of Spectroscopic Binary Orbits (http://sb9.astro.ulb.ac.be) continues the series of compilations of spectroscopic orbits carried out over the past 35 years by Batten and collaborators. As of 2004 May 1st, the new Catalogue holds orbits for 2386 systems. Some essential differences between this catalogue and its predecessors are out-lined and three straightforward applications are presented: (1) completeness assessment: period distribution of SB1s and SB2s; (2) shortest periods across the H-R diagram; (3) period-eccentricity relation.Facultad de Ciencias Astronómicas y Geofísica

Testing Rotational Mixing Predictions with New Boron Abundances in Main Sequence B-type Stars

(Abridged) New boron abundances for seven main-sequence B-type stars are determined from HST STIS spectroscopy around the BIII 2066A line. Boron abundances provide a unique and critical test of stellar evolution models that include rotational mixing since boron is destroyed in the surface layers of stars through shallow mixing long before other elements are mixed from the stellar interior through deep mixing. Boron abundances range from 12+log(B/H) = 1.0 to 2.2. The boron abundances are compared to the published values of their stellar nitrogen abundances (all have 12+log(N/H) < 7.8, i.e., they do not show significant CNO-mixing) and to their host cluster ages (4 to 16 Myr) to investigate the predictions from models of massive star evolution with rotational mixing effects (Heger & Langer 2000). Only three stars (out of 34) deviate from the model predictions, including HD36591, HD205021, and HD30836. These three stars suggest that rotational mixing could be more efficient than currently modelled at the highest rotation rates.Comment: 10 figures, 7 tables; accepted for publication in the Astrophysical Journa

An Optical Study of BG Geminorum: An Ellipsoidal Binary with an Unseen Primar Star

We describe optical photometric and spectroscopic observations of the bright variable BG Geminorum. Optical photometry shows a pronounced ellipsoidal variation of the K0 I secondary, with amplitudes of ~0.5 mag at VRI and a period of 91.645 days. A deep primary eclipse is visible for wavelengths < 4400A; a shallower secondary eclipse is present at longer wavelengths. Eclipse timings and the radial velocity curve of the K0 secondary star indicate an interacting binary where a lobe-filling secondary, M_2 ~ 0.5 Msun, transfers material into a extended disk around a massive primary, M_1 ~ 4.5 Msun. The primary star is either an early B-type star or a black hole. If it did contain a black hole, BG Gem would be the longest period black hole binary known by a factor of 10, as well as the only eclipsing black hole binary system.Comment: 27 pages, includes 8 figures and 5 tables, accepted to A