Transport in Transitory Dynamical Systems

We introduce the concept of a "transitory" dynamical system---one whose time-dependence is confined to a compact interval---and show how to quantify transport between two-dimensional Lagrangian coherent structures for the Hamiltonian case. This requires knowing only the "action" of relevant heteroclinic orbits at the intersection of invariant manifolds of "forward" and "backward" hyperbolic orbits. These manifolds can be easily computed by leveraging the autonomous nature of the vector fields on either side of the time-dependent transition. As illustrative examples we consider a two-dimensional fluid flow in a rotating double-gyre configuration and a simple one-and-a-half degree of freedom model of a resonant particle accelerator. We compare our results to those obtained using finite-time Lyapunov exponents and to adiabatic theory, discussing the benefits and limitations of each method.Comment: Updated and corrected version. LaTeX, 29 pages, 21 figure

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

Engineering of β-glycosidases from hyperthermophilic Archaea

Hyperthermophilic Archaea are microorganisms that grow optimally above 80°C. To be able to live at these temperature extremes their cell components display extreme resistance towards thermal degradation. This characteristic is an attractive feature for use of their enzymes in industrial processes. Examples of thermozymes with potential applications in food and pharmaceutical industry are b -Glycosidases, enzymes that specifically hydrolize b -linked glycosidic bonds, which are present in for instance cellulose or the milk sugar lactose. .Using the b -glucosidase CelB from Pyrococcus furiosus as a model enzyme, molecular determinants of substrate recognition and catalysis in b -glycosidases have been studied by rational design and directed evolution approaches. A 3D model of CelB was established, and its active site was compared to that of a related enzyme with a distinct specificity, the 6-phospho-b -galactosidase LacG of Lactococcus lactis. The substrate specificity of CelB was adjusted by engineering a phosphate-binding site, which resulted in a significant improvement in the hydrolysis of 6-phospho-b-glycosides. In a second study, the active sites of b -glucosidase CelB was compared to that of a b -mannosidase BglB from Pyrococcus horikoshii , and the substrate affinities and activities of the two enzymes could be swapped by exchange of unique residues in their active sites.The b -glucosidase CelB of P. furiosus was also compared to that of the related b -glycosidase LacS of the hyperthermophile Sulfolobus solfataricus. While the enzymes are very similar regarding catalytic mechanism and substrate specificity, they have not been stabilized to withstand high temperatures in the same way. While CelB is relatively sensitive to detergents, LacS is readily inactivated in the presence of salts. This strongly suggests that CelB is mainly stabilized by hydrophobic interactions, while ion-pair interactions contribute most to the stability of LacS.In one of the first laboratory evolution studies on proteins from a hyperthermophile, CelB has been optimized for low-temperature catalysis. In several CelB mutants this was accomplished with retention of wild-type stability. Increased activity at low temperatures seemed to result from mutations that increase protein flexibility. In a second directed evolution study, the genes coding for CelB and LacS were shuffled to functional b -glycosidase hybrids. The hybrids of this DNA shuffling experiment were screened for thermostability and hydrolysis of lactose at 70 °C. Several thermostable high-performance mutants were isolated and characterized. The hybrids consisted of an N-terminal LacS stretch, followed by a CelB core. This resulted in a hybrid active site structure, which could explain the altered catalytic properties.Finally, site-directed CelB mutants from the previous mentioned studies have been tested for their ability to catalyze oligosaccharide synthesis. Indeed, several variants showed increased yields in galacto-oligosaccharide synthesis with lactose as a substrate, compared to wild-type CelB.The studies described in the thesis are illustrative for the differences in protein engineering by rational design versus by directed evolution. While rational design can give an initial change in activity or substrate specificity, directed evolution is more likely to be successful for fine-tuning of enzyme properties. </font

XMM-Newton X-ray spectroscopy of the high-mass X-ray binary 4U1700-37 at low flux

We present results of a monitoring campaign of the high-mass X-ray binary system 4U 1700-37/HD 153919, carried out with XMM-Newton in February 2001. The system was observed at four orbital phase intervals, covering 37% of one 3.41-day orbit. The lightcurve includes strong flares, commonly observed in this source. We focus on three epochs in which the data are not affected by photon pile up: the eclipse, the eclipse egress and a low-flux interval in the lightcurve around orbital phase phi ~0.25. The high-energy part of the continuum is modelled as a direct plus a scattered component, each represented by a power law with identical photon index (alpha ~1.4), but with different absorption columns. We show that during the low-flux interval the continuum is strongly reduced, probably due to a reduction of the accretion rate onto the compact object. A soft excess is detected in all spectra, consistent with either another continuum component originating in the outskirts of the system or a blend of emission lines. Many fluorescence emission lines from near-neutral species and discrete recombination lines from He- and H-like species are detected during eclipse and egress. The detection of recombination lines during eclipse indicates the presence of an extended ionised region surrounding the compact object. The observed increase in strength of some emission lines corresponding to higher values of the ionisation parameter xi further substantiates this conclusion.Comment: 15 pages, 7 figures, accepted for publication in Astronomy and Astrophysic

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

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