On the origins of approximations for stochastic chemical kinetics

This paper considers the derivation of approximations for stochastic chemical kinetics governed by the discrete master equation. Here, the concepts of (1) partitioning on the basis of fast and slow reactions as opposed to fast and slow species and (2) conditional probability densities are used to derive approximate, partitioned master equations, which are Markovian in nature, from the original master equation. Under different conditions dictated by relaxation time arguments, such approximations give rise to both the equilibrium and hybrid (deterministic or Langevin equations coupled with discrete stochastic simulation) approximations previously reported. In addition, the derivation points out several weaknesses in previous justifications of both the hybrid and equilibrium systems and demonstrates the connection between the original and approximate master equations. Two simple examples illustrate situations in which these two approximate methods are applicable and demonstrate the two methods' efficiencies

Stochastic simulation of catalytic surface reactions in the fast diffusion limit

The master equation of a lattice gas reaction tracks the probability of visiting all spatial configurations. The large number of unique spatial configurations on a lattice renders master equation simulations infeasible for even small lattices. In this work, a reduced master equation is derived for the probability distribution of the coverages in the infinite diffusion limit. This derivation justifies the widely used assumption that the adlayer is in equilibrium for the current coverages and temperature when all reactants are highly mobile. Given the reduced master equation, two novel and efficient simulation methods of lattice gas reactions in the infinite diffusion limit are derived. The first method involves solving the reduced master equation directly for small lattices, which is intractable in configuration space. The second method involves reducing the master equation further in the large lattice limit to a set of differential equations that tracks only the species coverages. Solution of the reduced master equation and differential equations requires information that can be obtained through short, diffusion-only kinetic Monte Carlo simulation runs at each coverage. These simulations need to be run only once because the data can be stored and used for simulations with any set of kinetic parameters, gas-phase concentrations, and initial conditions. An idealized CO oxidation reaction mechanism with strong lateral interactions is used as an example system for demonstrating the reduced master equation and deterministic simulation techniques

Two classes of quasi-steady-state model reductions for stochastic kinetics

The quasi-steady-state approximation (QSSA) is a model reduction technique used to remove highly reactive species from deterministic models of reaction mechanisms. In many reaction networks the highly reactive intermediates (QSSA species) have populations small enough to require a stochastic representation. In this work we apply singular perturbation analysis to remove the QSSA species from the chemical master equation for two classes of problems. The first class occurs in reaction networks where all the species have small populations and the QSSA species sample zero the majority of the time. The perturbation analysis provides a reduced master equation in which the highly reactive species can sample only zero, and are effectively removed from the model. The reduced master equation can be sampled with the Gillespie algorithm. This first stochastic QSSA reduction is applied to several example reaction mechanisms (including Michaelis-Menten kinetics) [Biochem. Z. 49, 333 (1913)]. A general framework for applying the first QSSA reduction technique to new reaction mechanisms is derived. The second class of QSSA model reductions is derived for reaction networks where non-QSSA species have large populations and QSSA species numbers are small and stochastic. We derive this second QSSA reduction from a combination of singular perturbation analysis and the Omega expansion. In some cases the reduced mechanisms and reaction rates from these two stochastic QSSA models and the classical deterministic QSSA reduction are equivalent; however, this is not usually the case

The stochastic quasi-steady-state assumption: Reducing the model but not the noise

Highly reactive species at small copy numbers play an important role in many biological reaction networks. We have described previously how these species can be removed from reaction networks using stochastic quasi-steady-state singular perturbation analysis (sQSPA). In this paper we apply sQSPA to three published biological models: the pap operon regulation, a biochemical oscillator, and an intracellular viral infection. These examples demonstrate three different potential benefits of sQSPA. First, rare state probabilities can be accurately estimated from simulation. Second, the method typically results in fewer and better scaled parameters that can be more readily estimated from experiments. Finally, the simulation time can be significantly reduced without sacrificing the accuracy of the solution

Near-Infrared Observations of Powerful High-Redshift Radio Galaxies: 4C 40.36 and 4C 39.37

We present near-infrared imaging and spectroscopic observations of two FR II high-redshift radio galaxies (HzRGs), 4C 40.36 (z=2.3) and 4C 39.37 (z=3.2), obtained with the Hubble, Keck, and Hale Telescopes. High resolution images were taken with filters both in and out of strong emission lines, and together with the spectroscopic data, the properties of the line and continuum emissions were carefully analyzed. Our analysis of 4C 40.36 and 4C 39.37 shows that strong emission lines (e.g., [O III] 5007 A and H alpha+[N II]) contribute to the broad-band fluxes much more significantly than previously estimated (80% vs. 20-40%), and that when the continuum sources are imaged through line-free filters, they show an extremely compact morphology with a high surface brightness. If we use the R^1/4-law parametrization, their effective radii (r(e)) are only 2-3 kpc while their restframe B-band surface brightnesses at r(e) are I(B) ~ 18 mag/arcsec^2. Compared with z ~ 1 3CR radio galaxies, the former is x3-5 smaller, while the latter is 1-1.5 mag brighter than what is predicted from the I(B)-r(e) correlation. Although exponential profiles produce equally good fits for 4C 40.36 and 4C 39.37, this clearly indicates that with respect to the z~1 3CR radio galaxies, the light distribution of these two HzRGs is much more centrally concentrated. Spectroscopically, 4C 40.36 shows a flat (fnu=const) continuum while 4C 39.37 shows a spectrum as red as that of a local giant elliptical galaxy. Although this difference may be explained in terms of a varying degree of star formation, the similarities of their surface brightness profiles and the submillimeter detection of 4C 39.37 might suggest that the intrinsic spectra is equally blue (young stars or an AGN), and that the difference is the amount of reddening.Comment: 30 pages, 6 tables, 10 figures; Accepted for publication in Astronomical Journa

Predictive Control for Alleviation of Gust Loads on Very Flexible Aircraft

In this work the dynamics of very flexible aircraft are described by a set of non-linear, multi-disciplinary equations of motion. Primary structural components are represented by a geometrically-exact composite beam model which captures the large dynamic deformations of the aircraft and the interaction between rigid-body and elastic degrees-of-freedom. In addition, an implementation of the unsteady vortex-lattice method capable of handling arbitrary kinematics is used to capture the unsteady, three-dimensional flow-eld around the aircraft as it deforms. Linearization of this coupled nonlinear description, which can in general be about a nonlinear reference state, is performed to yield relatively high-order linear time-invariant state-space models. Subsequent reduction of these models using standard balanced truncation results in low-order models suitable for the synthesis of online, optimization-based control schemes that incorporate actuator constraints. Predictive controllers are synthesized using these reduced-order models and applied to nonlinear simulations of the plant dynamics where they are shown to be superior to equivalent optimal linear controllers (LQR) for problems in which constraints are active

The Optical - Infrared Colors of CORALS QSOs: Searching for Dust Reddening Associated With High Redshift Damped Lyman Alpha Systems

The presence of dust in quasar absorbers, such as damped Lyman alpha (DLA) systems, may cause the background QSO to appear reddened. We investigate the extent of this potential reddening by comparing the optical-to-infrared (IR) colors of QSOs with and without intervening absorbers. Our QSO sample is based on the Complete Optical and Radio Absorption Line System (CORALS) survey of Ellison et al (2001). We have obtained near-simultaneous B and K band magnitudes for subset of the CORALS sample and supplemented our observations with further measurements published in the literature. To account for redshift-related color changes, the B-K colors are normalized using the Sloan Digital Sky Survey (SDSS) QSO composite. The mean normalized B-K color of the DLA sub-sample is +0.12, whereas the mean for the no-DLA sample is -0.10; both distributions have RMS scatters ~0.5. Neither a student's T-test nor a KS test indicate that there is any significant difference between the two color distributions. Based on simulations which redden the colors of QSOs with intervening DLAs, we determine a reddening limit which corresponds to E(B-V) < 0.04 (SMC-like extinction) at 99% confidence (3 sigma), assuming that E(B-V) is the same for all DLAs. Finally, we do not find any general correlation between absorber properties (such as [Fe/Zn] or neutral hydrogen column density) and B-K color. One of these two QSOs shows evidence for strong associated absorption from X-ray observations, an alternative explanation for its very red color. We conclude that the presence of intervening galaxies causes a minimal reddening of the background QSO.Comment: Accepted for publication in A

The optically-powerful quasar E1821+643 is associated with a 300-kpc scale FRI radio structure

We present a deep image of the optically-powerful quasar E1821+643 at 18cm made with the Very Large Array (VLA). This image reveals radio emission, over 280 kpc in extent, elongated way beyond the quasar's host galaxy. Its radio structure has decreasing surface brightness with increasing distance from the bright core, characteristic of FRI sources (Fanaroff & Riley 1974). Its radio luminosity at 5GHz falls in the classification for `radio-quiet' quasars (it is only 10^23.9 W/Hz/sr; see e.g. Kellermann et al 1994). Its radio luminosity at 151MHz (which is 10^25.3 W/Hz/sr) is at the transition luminosity observed to separate FRIs and FRIIs. Hitherto, no optically-powerful quasar had been found to have a conventional FRI radio structure. For searches at low-frequency this is unsurprising given current sensitivity and plausible radio spectral indices for radio-quiet quasars. We demonstrate the inevitability of the extent of any FRqI radio structures being seriously under-estimated by existing targetted follow-up observations of other optically-selected quasars, which are typically short exposures of z > 0.3 objects, and discuss the implications for the purported radio bimodality in quasars. The nature of the inner arcsec-scale jet in E1821+643, together with its large-scale radio structure, suggest that the jet-axis in this quasar is precessing (cf. Galactic jet sources such as SS433). A possible explanation for this is that its central engine is a binary whose black holes have yet to coalesce. The ubiquity of precession in `radio-quiet' quasars, perhaps as a means of reducing the observable radio luminosity expected in highly-accreting systems, remains to be established.Comment: Accepted by ApJ Letters; higher quality versions of figures available at http://www-astro.physics.ox.ac.uk/~km

Using Laguerre functions to improve the tuning and performance of predictive functional control

This paper proposes a novel modification to the predictive functional control (PFC) algorithm to facilitate significant improvements in the tuning efficacy. The core concept is the use of an alternative parameterisation of the degrees of freedom in the PFC law. Building on recent insights into the potential of Laguerre functions in traditional MPC (Rossiter et al., 2010; Wang, 2009), the paper develops an appropriate framework for PFC and then demonstrates that these functions can be exploited to allow easier and more effective tuning in PFC as well as facilitating strong constraint handling properties. The proposed design approach and the associated tuning methodology are developed and their efficacy is demonstrated with a number of numerical examples

What Powers the Compact Radio Emission in Nearby Elliptical and S0 Galaxies?

Many nearby early-type (elliptical and S0) galaxies contain weak (milli-Jansky level) nuclear radio sources on scales a few hundred parsecs or less. The origin of the radio emission, however, has remained unclear, especially in volume-limited samples that select intrinsically less luminous galaxies. Both active galactic nuclei and nuclear star formation have been suggested as possible mechanisms for producing the radio emission. This paper utilizes optical spectroscopic information to address this issue. A substantial fraction of the early-type galaxies surveyed with the Very Large Array by Wrobel & Heeschen (1991) exhibits detectable optical emission lines in their nuclei down to very sensitive limits. Comparison of the observed radio continuum power with that expected from the thermal gas traced by the optical emission lines implies that the bulk of the radio emission is nonthermal. Both the incidence and the strength of optical line emission correlate with the radio power. At a fixed line luminosity, ellipticals have stronger radio cores than S0s. The relation between radio power and line emission observed in this sample is consistent with the low-luminosity extension of similar relations seen in classical radio galaxies and luminous Seyfert nuclei. A plausible interpretation of this result is that the weak nuclear sources in nearby early-type galaxies are the low-luminosity counterparts of more powerful AGNs. The spectroscopic evidence supports this picture. Most of the emission-line objects are optically classified as Seyfert nuclei or low-ionization nuclear emission-line regions (LINERs), the majority of which are likely to be accretion-powered sources.Comment: LaTex, 16 pages including embedded figures. Accepted for publication in the Astrophysical Journa