Application of a multi-level grid method to transonic flow calculations

A multi-level grid method was studied as a possible means of accelerating convergence in relaxation calculations for transonic flows. The method employs a hierarchy of grids, ranging from very coarse to fine. The coarser grids are used to diminish the magnitude of the smooth part of the residuals. The method was applied to the solution of the transonic small disturbance equation for the velocity potential in conservation form. Nonlifting transonic flow past a parabolic arc airfoil is studied with meshes of both constant and variable step size

The multigrid method: Fast relaxation

A multi-level grid method was studied as a possible means of accelerating convergence in relaxation calculations for transonic flows. The method employs a hierarchy of grids, ranging from very coarse (e.g. 4 x 2 mesh cells) to fine (e.g. 64 x 32); the coarser grids are used to diminish the magnitude of the smooth part of the residuals, hopefully with far less total work than would be required with optimal iterations on the finest grid. To date the method was applied quite successfully to the solution of the transonic small-disturbance equation for the velocity potential in conservation form. Nonlifting transonic flow past a parabolic arc airfoil is the example studied, with meshes of both constant and variable step size

X-ray absorption in the strong FeII narrow-line Seyfert 1 galaxy Mrk 507

We present results from spectral analysis of ASCA data on the NLS1 Mrk 507. This galaxy was found to have an exceptionally flat ROSAT spectrum among the NLS1s. The ASCA spectrum however shows a clear absorption feature in the energy band below 2 keV, which partly accounts for the flat spectrum observed with the ROSAT PSPC. The absorption is mainly due to cold gas with a column density of (2-3)E21 cm-2. A reanalysis of the PSPC data indicates that the absorber is slightly ionized, covers only part of the central source, or there is extra soft thermal emission from an extended region. There is also evidence that the X-ray absorption is complex; an edge feature marginally detected at 0.84 keV suggests the presence of an additional high ionization absorber which imposes a strong OVIII edge on the spectrum. After correction for the absorption, the photon index of the intrinsic continuum, 1.8, obtained from the ASCA data is quite similar to that of ordinary Seyfert 1 galaxies. Mrk 507 still has one of the flattest continuum slopes among NLS1, but is no longer exceptional. The strong optical FeII emission remains unusual in the light of the correlation between FeII strengths and steepness of soft X-ray slope.Comment: 6 pages, 3 Postscript figures, to be published in MNRA

A longer XMM-Newton look at I Zwicky 1: Distinct modes of X-ray spectral variability

The short-term spectral variability of the narrow-line Seyfert 1 galaxy I Zwicky 1 (I Zw 1) as observed in an 85 ks XMM-Newton observation is discussed in detail. I Zw 1 shows distinct modes of variability prior to and after a flux dip in the broad-band light curve. Before the dip the variability can be described as arising from changes in shape and normalisation of the spectral components. Only changes in normalisation are manifested after the dip. The change in the mode of behaviour occurs on dynamically short timescales in I Zw 1. The data suggest that the accretion-disc corona in I Zw 1 could have two components that are co-existing. The first, a uniform, physically diffuse plasma responsible for the "typical'' long-term (e.g. years) behaviour; and a second compact, centrally located component causing the rapid flux and spectral changes. This compact component could be the base of a short or aborted jet as sometimes proposed for radio-quiet active galaxies. Modelling of the average and time-resolved rms spectra demonstrate that a blurred Compton-reflection model can describe the spectral variability if we allow for pivoting of the continuum component prior to the dip.Comment: 8 pages, 9 figures. Accepted by MNRA

On the X-ray Properties of OH Megamaser Sources: Chandra Snapshot Observations

We present Chandra snapshot observations for a sample of 7 sources selected from the Arecibo OH megamaser (OHM) survey at z~0.13-0.22 and with far-infrared luminosities in excess of 10^{11} L_sun. In contrast with the known H2O megamasers, which are mostly associated with powerful Active Galactic Nuclei (AGN), the situation is far less clear for OHMs, which have been poorly studied in the X-ray band thus far. All of the observed sources are X-ray weak, with only one OHM, IRAS FSC 03521+0028 (z=0.15), being detected by Chandra (with 5 counts). The results from this pilot program indicate that the X-ray emission, with luminosities of less than ~10^{42} erg/s, is consistent with that from star formation (as also suggested in some cases by the optical spectra) and low-luminosity AGN emission. If an AGN is present, its contribution to the broad-band emission of OHM galaxies is likely modest. Under reasonable assumptions about the intrinsic X-ray spectral shape, the observed count distribution from stacking analysis suggests absorption of ~10^{22} cm^{-2}.Comment: 8 pages, 3 figures, accepted for publication in MNRA

The Effective Potential in Non-Conformal Gauge Theories

By using the renormalization group (RG) equation it has proved possible to sum logarithmic corrections to quantities that arise due to quantum effects in field theories. In particular, the effective potential V in the Standard Model in the limit that there are no massive parameters in the classical action (the "conformal limit") has been subject to this analysis, as has the effective potential in a scalar theory with a quartic self coupling and in massless scalar electrodynamics. Having multiple coupling constants and/or mass parameters in the initial action complicates this analysis, as then several mass scales arise. We show how to address this problem by considering the effective potential in scalar electrodynamics when the scalar field has a tree level mass term. In addition to summing logarithmic corrections by using the RG equation, we also consider the consequences of the condition V'(v)=0 where v is the vacuum expectation value of the scalar. If V is expanded in powers of the logarithms that arise, then it proves possible to show that either v is zero or that V is independent of the scalar. (That is, either there is no spontaneous symmetry breaking or the vacuum expectation value is not determined by minimizing V as V is "flat".

Quantum statistical correlations in thermal field theories: boundary effective theory

We show that the one-loop effective action at finite temperature for a scalar field with quartic interaction has the same renormalized expression as at zero temperature if written in terms of a certain classical field $\phi_c$, and if we trade free propagators at zero temperature for their finite-temperature counterparts. The result follows if we write the partition function as an integral over field eigenstates (boundary fields) of the density matrix element in the functional Schr\"{o}dinger field-representation, and perform a semiclassical expansion in two steps: first, we integrate around the saddle-point for fixed boundary fields, which is the classical field $\phi_c$, a functional of the boundary fields; then, we perform a saddle-point integration over the boundary fields, whose correlations characterize the thermal properties of the system. This procedure provides a dimensionally-reduced effective theory for the thermal system. We calculate the two-point correlation as an example.Comment: 13 pages, 1 figur