A General-applications Direct Global Matrix Algorithm for Rapid Seismo-acoustic Wavefield Computations

A new matrix method for rapid wave propagation modeling in generalized stratified media, which has recently been applied to numerical simulations in diverse areas of underwater acoustics, solid earth seismology, and nondestructive ultrasonic scattering is explained and illustrated. A portion of recent efforts jointly undertaken at NATOSACLANT and NORDA Numerical Modeling groups in developing, implementing, and testing a new fast general-applications wave propagation algorithm, SAFARI, formulated at SACLANT is summarized. The present general-applications SAFARI program uses a Direct Global Matrix Approach to multilayer Green's function calculation. A rapid and unconditionally stable solution is readily obtained via simple Gaussian ellimination on the resulting sparsely banded block system, precisely analogous to that arising in the Finite Element Method. The resulting gains in accuracy and computational speed allow consideration of much larger multilayered air/ocean/Earth/engineering material media models, for many more source-receiver configurations than previously possible. The validity and versatility of the SAFARI-DGM method is demonstrated by reviewing three practical examples of engineering interest, drawn from ocean acoustics, engineering seismology and ultrasonic scattering

Numerical Techniques for Scattering from Submerged Objects

To represent the final results in terms of matrices, one expands all appropriate physical quantities in terms of partial wave basis states. This includes expansions for the incident and scattered fields and the surface quantities. The method then utilizes the Huygen-Poincare integral representation for both the exterior and interior solutions, leading to the required matrix equations. One thus deals with matrix equations, the complexity of which depends on the nature of the problem. It is shown that in general a transition matrix T can be obtained relating the incident field A with the scattered field f having the form T = PQ(-1), where f = TA. The structure of Q can be quite complicated and can itself be composed of other matrix inversions such as arise from layered objects. Recent improvements in this method appropriate for a variety of physical problems are focused on, and on their implementation. Results are outlined from scattering simulations for very elongated submerged objects and resonance scattering from elastic solids and shells. The final improvement concerns eigenfunction expansions of surface terms, arising from solution of the interior problem, obtained via a preconditioning technique. This effectively reduces the problem to that of obtaining eigenvalues of a Hermitian operator. This formalism is reviewed for scattering from targets that are rigid, sound-soft, acoustic, elastic solids, elastic shells, and elastic layered objects. Two sets of the more interesting results are presented. The first concerns scattering from elongated objects, and the second to thin elastic spheroids

The Angular Diameter and Fundamental Parameters of Sirius A

The Sydney University Stellar Interferometer (SUSI) has been used to make a new determination of the angular diameter of Sirius A. The observations were made at an effective wavelength of 694.1 nm and the new value for the limb-darkened angular diameter is 6.048 +/- 0.040mas (+/-0.66%). This new result is compared with previous measurements and is found to be in excellent agreement with a conventionally calibrated measurement made with the European Southern Observatory's Very Large Telescope Interferometer (VLTI) at 2.176 microns (but not with a second globally calibrated VLTI measurement). A weighted mean of the SUSI and first VLTI results gives the limb-darkened angular diameter of Sirius A as 6.041 +/- 0.017mas (+/-0.28%). Combination with the Hipparcos parallax gives the radius equal to 1.713 +/- 0.009R_sun. The bolometric flux has been determined from published photometry and spectrophotometry and, combined with the angular diameter, yields the emergent flux at the stellar surface equal to (5.32+/- 0.14)x10^8 Wm^-2 and the effective temperature equal to 9845 +/- 64 K. The luminosity is 24.7 +/- 0.7 L_sun.Comment: Accepted for publication in PAS

A low cost scheme for high precision dual-wavelength laser metrology

A novel method capable of delivering relative optical path length metrology with nanometer precision is demonstrated. Unlike conventional dual-wavelength metrology which employs heterodyne detection, the method developed in this work utilizes direct detection of interference fringes of two He-Ne lasers as well as a less precise stepper motor open-loop position control system to perform its measurement. Although the method may be applicable to a variety of circumstances, the specific application where this metrology is essential is in an astrometric optical long baseline stellar interferometer dedicated to precise measurement of stellar positions. In our example application of this metrology to a narrow-angle astrometric interferometer, measurement of nanometer precision could be achieved without frequency-stabilized lasers although the use of such lasers would extend the range of optical path length the metrology can accurately measure. Implementation of the method requires very little additional optics or electronics, thus minimizing cost and effort of implementation. Furthermore, the optical path traversed by the metrology lasers is identical with that of the starlight or science beams, even down to using the same photodetectors, thereby minimizing the non-common-path between metrology and science channels.Comment: 17 pages, 4 figures, accepted for publication in Applied Optic

Dust Scattering in Miras R Car and RR Sco resolved by optical interferometric polarimetry

We present optical interferometric polarimetry measurements of the Mira-like variables R Car and RR Sco, using the Sydney University Stellar Interferometer. By making visibility measurements in two perpendicular polarisations, the relatively low-surface brightness light scattered by atmospheric dust could be spatially separated from the bright Mira photospheric flux. This is the first reported successful use of long-baseline optical interferometric polarimetry. Observations were able to place constraints on the distribution of circumstellar material in R Car and RR Sco. The inner radius of dust formation for both stars was found to be less than 3 stellar radii: much closer than the expected innermost stable location for commonly-assumed astrophysical ``dirty silicate'' dust in these systems (silicate dust with a significant iron content). A model with the dust distributed over a shell which is geometrically thin compared to the stellar radius was preferred over an outflow. We propose dust components whose chemistry and opacity properties enable survival at these extreme inner radii.Comment: 8 pages, 4 figures, accepted for MNRA

\gamma^2 Velorum: Orbital Solution and Fundamental Parameter Determination with SUSI

The first complete orbital solution for the double-lined spectroscopic binary system \gamma^2 Velorum, obtained from measurements with the Sydney University Stellar Interferometer (SUSI), is presented. This system contains the closest example of a Wolf-Rayet star and the promise of full characterisation of the basic properties of this exotic high-mass system has subjected it to intense study as an archetype for its class. In combination with the latest radial-velocity results, our orbital solution produces a distance of 336^{+8}_{-7} pc, significantly more distant than the Hipparcos estimation (Schaerer et al. 1997; van der Hucht 1997). The ability to fully specify the orbital parameters has enabled us to significantly reduce uncertainties and our result is consistent with the VLTI observational point (Millour et al. 2006), but not with their derived distance. Our new distance, which is an order of magnitude more precise than prior work, demands critical reassessment of all distance-dependent fundamental parameters of this important system. In particular, membership of the Vela OB2 association has been reestablished, and the age and distance are also in good accord with the population of young stars reported by Pozzo et al. (2000). We determine the O-star primary component parameters to be M_V(O) = -5.63 \pm 0.10 mag, R(O) = 17 \pm 2 R_{\sun} and {\cal M}(O) = 28.5 \pm 1.1 M_{\sun}. These values are consistent with calibrations found in the literature if a luminosity class of II--III is adopted. The parameters of the Wolf-Rayet component are M_v(WR) = -4.33 \pm 0.17 mag and {\cal M}(WR) = 9.0 \pm 0.6 M_{\sun}.Comment: 3 figures, accepted for publication in MNRA

The radius and mass of the subgiant star bet Hyi from interferometry and asteroseismology

We have used the Sydney University Stellar Interferometer (SUSI) to measure the angular diameter of beta Hydri. This star is a nearby G2 subgiant whose mean density was recently measured with high precision using asteroseismology. We determine the radius and effective temperature of the star to be 1.814+/-0.017 R_sun (0.9%) and 5872+/-44 K (0.7%) respectively. By combining this value with the mean density, as estimated from asteroseismology, we make a direct estimate of the stellar mass. We find a value of 1.07+/-0.03 M_sun (2.8%), which agrees with published estimates based on fitting in the H-R diagram, but has much higher precision. These results place valuable constraints on theoretical models of beta Hyi and its oscillation frequencies.Comment: 3 figures, 3 tables, to appear in MNRAS Letter

Low-cost scheme for high-precision dual-wavelength laser metrology

A method capable of delivering relative optical path length metrology with nanometer precision is demonstrated. Unlike conventional dual-wavelength metrology, which employs heterodyne detection, the method developed in this work utilizes direct detection of interference fringes of two He-Ne lasers as well as a less precise stepper motor open-loop position control system to perform its measurement. Although the method may be applicable to a variety of circumstances, the specific application in which this metrology is essential is in an astrometric optical long baseline stellar interferometer dedicated to precise measurement of stellar positions. In our example application of this metrology to a narrow-angle astrometric interferometer, measurement of nanometer precision could be achieved without frequency-stabilized lasers, although the use of such lasers would extend the range of optical path length the metrology can accurately measure. Implementation of the method requires very little additional optics or electronics, thus minimizing the cost and effort of implementation. Furthermore, the optical path traversed by the metrology lasers is identical to that of the starlight or science beams, even down to using the same photodetectors, thereby minimizing the noncommon path between metrology and science channels.This research was supported under the Australian Research Council’s Discovery Project funding scheme. Y. K. was supported by the University of Sydney International Scholarship (USydIS)