Modified Green's Functions for Shallow Water Acoustic Wave Propagation

This article presents an assessment of alternative forms of the Green’s function for boundary element simulations of acoustic wave propagation in shallow water. It is assumed that the problem is two-dimensional, the source of acoustic disturbance is time-harmonic, the velocity of sound is constant and the medium in the absence of perturbations is quiescent. Efficient implementations of the boundary element method for underwater acoustics should employ Green's functions which directly satisfy the boundary conditions on the free surface and the horizontal parts of the bottom boundary. In the present work, these Green's functions are constructed by using different techniques, namely the method of images, eigenfunction expansions and the Ewald’s method

X-ray Properties of Radio-Selected Dual Active Galactic Nuclei

Merger simulations predict that tidally induced gas inflows can trigger kpc-scale dual active galactic nuclei (dAGN) in heavily obscured environments. Previously with the Very Large Array, we have confirmed four dAGN with redshifts between $0.04 < z < 0.22$ and projected separations between 4.3 and 9.2 kpc in the SDSS Stripe 82 field. Here, we present $Chandra$ X-ray observations that spatially resolve these dAGN and compare their multi-wavelength properties to those of single AGN from the literature. We detect X-ray emission from six of the individual merger components and obtain upper limits for the remaining two. Combined with previous radio and optical observations, we find that our dAGN have properties similar to nearby low-luminosity AGN, and they agree well with the black hole fundamental plane relation. There are three AGN-dominated X-ray sources, whose X-ray hardness-ratio derived column densities show that two are unobscured and one is obscured. The low obscured fraction suggests these dAGN are no more obscured than single AGN, in contrast to the predictions from simulations. These three sources show an apparent X-ray deficit compared to their mid-infrared continuum and optical [OIII] line luminosities, suggesting higher levels of obscuration, in tension with the hardness-ratio derived column densities. Enhanced mid-infrared and [OIII] luminosities from star formation may explain this deficit. There is ambiguity in the level of obscuration for the remaining five components since their hardness ratios may be affected by non-nuclear X-ray emissions, or are undetected altogether. They require further observations to be fully characterized.Comment: 11 pages, 5 figures, Accepted for publication in the Astrophysical Journa

Multi-focal laser surgery: cutting enhancement by hydrodynamic interactions between cavitation bubbles

Transparent biological tissues can be precisely dissected with ultrafast lasers using optical breakdown in the tight focal zone. Typically, tissues are cut by sequential application of pulses, each of which produces a single cavitation bubble. We investigate the hydrodynamic interactions between simultaneous cavitation bubbles originating from multiple laser foci. Simultaneous expansion and collapse of cavitation bubbles can enhance the cutting efficiency by increasing the resulting deformations in tissue, and the associated rupture zone. An analytical model of the flow induced by the bubbles is presented and experimentally verified. The threshold strain of the material rupture is measured in a model tissue. Using the computational model and the experimental value of the threshold strain one can compute the shape of the rupture zone in tissue resulting from application of multiple bubbles. With the threshold strain of 0.7 two simultaneous bubbles produce a continuous cut when applied at the distance 1.35 times greater than that required in sequential approach. Simultaneous focusing of the laser in multiple spots along the line of intended cut can extend this ratio to 1.7. Counter-propagating jets forming during collapse of two bubbles in materials with low viscosity can further extend the cutting zone - up to a factor of 1.54.Comment: 16 pages, 8 figures. Paper is accepted for publication in Physical Review

Numerical solution of the two-dimensional Helmholtz equation with variable coefficients by the radial integration boundary integral and integro-differential equation methods

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2012 Taylor & Francis.This paper presents new formulations of the boundary–domain integral equation (BDIE) and the boundary–domain integro-differential equation (BDIDE) methods for the numerical solution of the two-dimensional Helmholtz equation with variable coefficients. When the material parameters are variable (with constant or variable wave number), a parametrix is adopted to reduce the Helmholtz equation to a BDIE or BDIDE. However, when material parameters are constant (with variable wave number), the standard fundamental solution for the Laplace equation is used in the formulation. The radial integration method is then employed to convert the domain integrals arising in both BDIE and BDIDE methods into equivalent boundary integrals. The resulting formulations lead to pure boundary integral and integro-differential equations with no domain integrals. Numerical examples are presented for several simple problems, for which exact solutions are available, to demonstrate the efficiency of the proposed methods

Numerical solution of the two-dimensional Helmholtz equation with variable coefficients by the radial integration boundary integral and integro-differential equation methods

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2012 Taylor & Francis.This paper presents new formulations of the boundary–domain integral equation (BDIE) and the boundary–domain integro-differential equation (BDIDE) methods for the numerical solution of the two-dimensional Helmholtz equation with variable coefficients. When the material parameters are variable (with constant or variable wave number), a parametrix is adopted to reduce the Helmholtz equation to a BDIE or BDIDE. However, when material parameters are constant (with variable wave number), the standard fundamental solution for the Laplace equation is used in the formulation. The radial integration method is then employed to convert the domain integrals arising in both BDIE and BDIDE methods into equivalent boundary integrals. The resulting formulations lead to pure boundary integral and integro-differential equations with no domain integrals. Numerical examples are presented for several simple problems, for which exact solutions are available, to demonstrate the efficiency of the proposed methods

Sub-Relativistic Radio Jets and Parsec-Scale Absorption in Two Seyfert Galaxies

The Very Long Baseline Array has been used at 15 GHz to image the milliarcsecond structure of the Seyfert galaxies Mrk 231 and Mrk 348 at two epochs separated by about 1.7 yr. Both galaxies contain parsec-scale double radio sources whose components have brightness temperatures of 10^9-10^{11} K, implying that they are generated by synchrotron emission. The nuclear components are identified by their strong variability between epochs, indicating that the double sources represent apparently one-sided jets. Relative component speeds are measured to be ~0.1c at separations of 1.1 pc or less (for H_0 = 65 km/s/Mpc), implying that parsec-scale Seyfert jets are intrinsically different from those in most powerful radio galaxies and quasars. The lack of observed counterjets is most likely due to free-free absorption by torus gas, with an ionized density n_e > 2 X 10^5 cm^{-3} at T~8000 K, or n_e > 10^7 cm^{-3} at T~10^{6.6} K, in the inner parsec of each galaxy. The lower density is consistent with values found from X-ray absorption measurements, while the higher temperature and density are consistent with direct radio imaging of the NGC 1068 torus by Gallimore et al.Comment: 12 pages, 2 postscript figures, LaTeX file in AASTeX format, accepted by ApJ Letter

A Kiloparsec-Scale Binary Active Galactic Nucleus Confirmed by the Expanded Very Large Array

We report the confirmation of a kpc-scale binary active galactic nucleus (AGN) with high-resolution radio images from the Expanded Very Large Array (EVLA). SDSS J150243.1+111557 is a double-peaked [O III] AGN at z = 0.39 selected from the Sloan Digital Sky Survey. Our previous near-infrared adaptive optics imaging reveals two nuclei separated by 1.4" (7.4 kpc), and our optical integral-field spectroscopy suggests that they are a type-1--type-2 AGN pair. However, these data alone cannot rule out the single AGN scenario where the narrow emission-line region associated with the secondary is photoionized by the broad-line AGN in the primary. Our new EVLA images at 1.4, 5.0, and 8.5 GHz show two steep-spectrum compact radio sources spatially coincident with the optical nuclei. The radio power of the type-2 AGN is an order-of-magnitude in excess of star-forming galaxies with similar extinction-corrected [O II] 3727 luminosities, indicating that the radio emission is powered by accretion. Therefore, SDSS J150243.1+111557 is one of the few confirmed kpc-scale binary AGN systems. Spectral-energy-distribution modeling shows that SDSS J150243.1+111557 is a merger of two ~10^{11} M_sun galaxies. With both black hole masses around 10^8 Msun, the AGNs are accreting at ~10 times below the Eddington limit.Comment: ApJL accepted. 6 pages, 3 figures, 1 tabl

VLA Polarimetry of VLBI Core–Jet Sources

Radio imaging of VLBI core-jet sources can be used to examine the case for continuity of jet-like features between parsec and circumgalactic scales. Futhermore, polarimetry of such sources allows investigation of the dominant magnetic field topologies as a function of linear offset from the central engine. Examination of these continuity and field topology issues is essential for an understanding of how energy is channeled from the nuclear regions to the circumgalactic environment