Analysis of the accuracy and convergence of equation-free projection to a slow manifold

In [C.W. Gear, T.J. Kaper, I.G. Kevrekidis, and A. Zagaris, Projecting to a Slow Manifold: Singularly Perturbed Systems and Legacy Codes, SIAM J. Appl. Dyn. Syst. 4 (2005) 711-732], we developed a class of iterative algorithms within the context of equation-free methods to approximate low-dimensional, attracting, slow manifolds in systems of differential equations with multiple time scales. For user-specified values of a finite number of the observables, the m-th member of the class of algorithms (m = 0, 1, ...) finds iteratively an approximation of the appropriate zero of the (m+1)-st time derivative of the remaining variables and uses this root to approximate the location of the point on the slow manifold corresponding to these values of the observables. This article is the first of two articles in which the accuracy and convergence of the iterative algorithms are analyzed. Here, we work directly with explicit fast--slow systems, in which there is an explicit small parameter, epsilon, measuring the separation of time scales. We show that, for each m = 0, 1, ..., the fixed point of the iterative algorithm approximates the slow manifold up to and including terms of O(epsilon^m). Moreover, for each m, we identify explicitly the conditions under which the m-th iterative algorithm converges to this fixed point. Finally, we show that when the iteration is unstable (or converges slowly) it may be stabilized (or its convergence may be accelerated) by application of the Recursive Projection Method. Alternatively, the Newton-Krylov Generalized Minimal Residual Method may be used. In the subsequent article, we will consider the accuracy and convergence of the iterative algorithms for a broader class of systems-in which there need not be an explicit small parameter-to which the algorithms also apply

Modeling Ultraviolet Wind Line Variability in Massive Hot Stars

We model the detailed time-evolution of Discrete Absorption Components (DACs) observed in P Cygni profiles of the Si IV lam1400 resonance doublet lines of the fast-rotating supergiant HD 64760 (B0.5 Ib). We adopt the common assumption that the DACs are caused by Co-rotating Interaction Regions (CIRs) in the stellar wind. We perform 3D radiative transfer calculations with hydrodynamic models of the stellar wind that incorporate these large-scale density- and velocity-structures. We develop the 3D transfer code Wind3D to investigate the physical properties of CIRs with detailed fits to the DAC shape and morphology. The CIRs are caused by irregularities on the stellar surface that change the radiative force in the stellar wind. In our hydrodynamic model we approximate these irregularities by circular symmetric spots on the stellar surface. We use the Zeus3D code to model the stellar wind and the CIRs, limited to the equatorial plane. We constrain the properties of large-scale wind structures with detailed fits to DACs observed in HD 64760. A model with two spots of unequal brightness and size on opposite sides of the equator, with opening angles of 20 +/- 5 degr and 30 +/- 5 degr diameter, and that are 20 +/- 5 % and 8 +/- 5 % brighter than the stellar surface, respectively, provides the best fit to the observed DACs. The recurrence time of the DACs compared to the estimated rotational period corresponds to spot velocities that are 5 times slower than the rotational velocity. The mass-loss rate of the structured wind model for HD 64760 does not exceed the rate of the spherically symmetric smooth wind model by more than 1 %. The fact that DACs are observed in a large number of hot stars constrains the clumping that can be present in their winds, as substantial amounts of clumping would tend to destroy the CIRs.Comment: 58 pages, 16 figures, 1 animation. Accepted for publication in The Astrophysical Journal, Main Journal. More information and animations are available at http://alobel.freeshell.org/hotstars.htm

Staphylococcus aureus-Fibronectin Interactions with and without Fibronectin-Binding Proteins and Their Role in Adhesion and Desorption

Adhesion and residence-time-dependent desorption of two Staphylococcus aureus strains with and without fibronectin (Fn) binding proteins (FnBPs) on Fn-coated glass were compared under flow conditions. To obtain a better understanding of the role of Fn-FnBP binding, the adsorption enthalpies of Fn with staphylococcal cell surfaces were determined using isothermal titration calorimetry (ITC). Interaction forces between staphylococci and Fn coatings were measured using atomic force microscopy (AFM). The strain with FnBPs adhered faster and initially stronger to an Fn coating than the strain without FnBPs, and its Fn adsorption enthalpies were higher. The initial desorption was high for both strains but decreased substantially within 2 s. These time scales of staphylococcal bond ageing were confirmed by AFM adhesion force measurement. After exposure of either Fn coating or staphylococcal cell surfaces to bovine serum albumin (BSA), the adhesion of both strains to Fn coatings was reduced, suggesting that BSA suppresses not only nonspecific but also specific Fn-FnBP interactions. Adhesion forces and adsorption enthalpies were only slightly affected by BSA adsorption. This implies that under the mild contact conditions of convective diffusion in a flow chamber, adsorbed BSA prevents specific interactions but does allow forced Fn-FnBP binding during AFM or stirring in ITC. The bond strength energies calculated from retraction force-distance curves from AFM were orders of magnitude higher than those calculated from desorption data, confirming that a penetrating Fn-coated AFM tip probes multiple adhesins in the outermost cell surface that remain hidden during mild landing of an organism on an Fn-coated substratum, like that during convective diffusional flow

First constraint on cosmological variation of the proton-to-electron mass ratio from two independent telescopes

A high signal-to-noise spectrum covering the largest number of hydrogen lines (90 H2 lines and 6 HD lines) in a high redshift object was analyzed from an observation along the sight-line to the bright quasar source J2123$-$005 with the UVES spectrograph on the ESO Very Large Telescope (Paranal, Chile). This delivers a constraint on a possible variation of the proton-to-electron mass ratio of Dmu/mu = (8.5 \pm 3.6_{stat} \pm 2.2_{syst}) x 10^{-6} at redshift z=2.059$, which agrees well with a recently published result on the same system observed at the Keck telescope yielding Dmu/mu = (5.6 \pm 5.5_{stat} \pm 2.9_{syst}) x 10^{-6}. Both analyses used the same robust absorption line fitting procedures with detailed consideration of systematic errors.Comment: Accepte

Testing Hydrodynamic Models of LMC X-4 with UV and X-ray Spectra

We compare the predictions of hydrodynamic models of the LMC X-4 X-ray binary system with observations of UV P Cygni lines with the GHRS and STIS spectrographs on the Hubble Space Telescope. The hydrodynamic model determines density and velocity fields of the stellar wind, wind-compressed disk, accretion stream, Keplerian accretion disk, and accretion disk wind. We use a Monte Carlo code to determine the UV P Cygni line profiles by simulating the radiative transfer of UV photons that originate on the star and are scattered in the wind. The qualitative orbital variation predicted is similar to that observed, although the model fails to reproduce the strong orbital asymmetry (the observed absorption is strongest for phi>0.5). The model predicts a mid-eclipse X-ray spectrum, due almost entirely to Compton scattering, with a factor 4 less flux than observed with ASCA. We discuss how the model may need to be altered to explain the spectral variability of the system.Comment: 11 figures, accepted by Ap

High-mass X-ray binaries and OB-runaway stars

High-mass X-ray binaries (HMXBs) represent an important phase in the evolution of massive binary systems. HMXBs provide unique diagnostics to test massive-star evolution, to probe the physics of radiation-driven winds, to study the process of mass accretion, and to measure fundamental parameters of compact objects. As a consequence of the supernova explosion that produced the neutron star (or black hole) in these systems, HMXBs have high space velocities and thus are runaways. Alternatively, OB-runaway stars can be ejected from a cluster through dynamical interactions. Observations obtained with the Hipparcos satellite indicate that both scenarios are at work. Only for a minority of the OB runaways (and HMXBs) a wind bow shock has been detected. This might be explained by the varying local conditions of the interstellar medium.Comment: 15 pages, latex (sty file included) with 5 embedded figures (one in jpg format), to appear in Proc. "Influence of binaries on stellar population studies", Eds. Vanbeveren, Van Rensberge

The N Enrichment and Supernova Ejection of the Runaway Microquasar LS 5039

We present an investigation of new optical and ultraviolet spectra of the mass donor star in the massive X-ray binary LS 5039. The optical band spectral line strengths indicate that the atmosphere is N-rich and C-poor, and we classify the stellar spectrum as type ON6.5 V((f)). The N-strong and C-weak pattern is also found in the stellar wind P Cygni lines of N V 1240 and C IV 1550. We suggest that the N-enrichment may result from internal mixing if the O-star was born as a rapid rotator, or the O-star may have accreted N-rich gas prior to a common-envelope interaction with the progenitor of the supernova. We re-evaluated the orbital elements to find an orbital period of P=4.4267 +/- 0.0010 d. We compared the spectral line profiles with new non-LTE, line-blanketed model spectra, from which we derive an effective temperature T_eff = 37.5 +/- 1.7 kK, gravity log g = 4.0 +/- 0.1, and projected rotational velocity V sin i = 140 +/- 8 km/s. We fit the UV, optical, and IR flux distribution using a model spectrum and extinction law with parameters E(B-V)= 1.28 +/- 0.02 and R= 3.18 +/- 0.07. We confirm the co-variability of the observed X-ray flux and stellar wind mass loss rate derived from the H-alpha profile, which supports the wind accretion scenario for the X-ray production in LS 5039. Wind accretion models indicate that the compact companion has a mass M_X/M_sun = 1.4 +/- 0.4, consistent with its identification as a neutron star. The observed eccentricity and runaway velocity of the binary can only be reconciled if the neutron star received a modest kick velocity due to a slight asymmetry in the supernova explosion (during which >5 solar masses was ejected).Comment: 38 pages, 9 figures; 2004, ApJ, 600, Jan. 10 issue, in press Discussion revised thanks to comments from P. Podsiadlowsk