Mass fluctuation kinetics: analysis and computation of equilibria and local dynamics

The mass fluctuation kinetics (MFK) model is a set of coupled ordinary differential equations approximating the time evolution of means and covariances of species concentrations in chemical reaction networks. It generalises classical mass action kinetics (MAK), in which fluctuations around the mean are ignored. MFK may be used to approximate stochasticity in system trajectories when stochastic simulation methods are prohibitively expensive computationally. This study presents a set of tools to aid in the analysis of systems within the MFK framework. A closed-form expression for the MFK Jacobian matrix is derived. This expression facilitates the computation of MFK equilibria and the characterisation of the dynamics of small deviations from the equilibria (i.e. local dynamics). Software developed in MATLAB to analyse systems within the MFK framework is also presented. The authors outline a homotopy continuation method that employs the Jacobian for bifurcation analysis, that is, to generate a locus of steady-state Jacobian eigenvalues corresponding to changing a chosen MFK parameter such as system volume or a rate constant. This method is applied to study the effect of small-volume stochasticity on local dynamics at equilibria in a pair of example systems, namely the formation and dissociation of an enzyme-substrate complex and a genetic oscillator. For both systems, this study reveals volume regimes where MFK provides a quantitatively and/or qualitatively correct description of system behaviour, and regimes where the MFK approximation is inaccurate. Moreover, our analysis provides evidence that decreasing volume from the MAK regime (infinite volume) has a destabilising effect on system dynamics

HST Observations of the Double-Peaked Emission Lines in the Seyfert Galaxy Markarian 78: Mass Outflows from a Single AGN

Previous ground based observations of the Seyfert 2 galaxy Mrk 78 revealed a double set of emission lines, similar to those seen in several AGN from recent surveys. Are the double lines due to two AGN with different radial velocities in the same galaxy, or are they due to mass outflows from a single AGN?We present a study of the outflowing ionized gas in the resolved narrow-line region (NLR) of Mrk 78 using observations from Space Telescope Imaging Spectrograph (STIS) and Faint Object Camera (FOC) aboard the Hubble Space Telescope(HST) as part of an ongoing project to determine the kinematics and geometries of active galactic nuclei (AGN) outflows. From the spectroscopic information, we deter- mined the fundamental geometry of the outflow via our kinematics modeling program by recreating radial velocities to fit those seen in four different STIS slit positions. We determined that the double emission lines seen in ground-based spectra are due to an asymmetric distribution of outflowing gas in the NLR. By successfully fitting a model for a single AGN to Mrk 78, we show that it is possible to explain double emission lines with radial velocity offsets seen in AGN similar to Mrk 78 without requiring dual supermassive black holes.Comment: 22 pages, 7 figures (2 color), accepted for publication in The Astrophysical Journa

Thin Animals

Lattice animals provide a discretized model for the theta transition displayed by branched polymers in solvent. Exact graph enumeration studies have given some indications that the phase diagram of such lattice animals may contain two collapsed phases as well as an extended phase. This has not been confirmed by studies using other means. We use the exact correspondence between the q --> 1 limit of an extended Potts model and lattice animals to investigate the phase diagram of lattice animals on phi-cubed random graphs of arbitrary topology (``thin'' random graphs). We find that only a two phase structure exists -- there is no sign of a second collapsed phase. The random graph model is solved in the thermodynamic limit by saddle point methods. We observe that the ratio of these saddle point equations give precisely the fixed points of the recursion relations that appear in the solution of the model on the Bethe lattice by Henkel and Seno. This explains the equality of non-universal quantities such as the critical lines for the Bethe lattice and random graph ensembles.Comment: Latex, 10 pages plus 6 ps/eps figure

A Potts/Ising Correspondence on Thin Graphs

We note that it is possible to construct a bond vertex model that displays q-state Potts criticality on an ensemble of phi3 random graphs of arbitrary topology, which we denote as ``thin'' random graphs in contrast to the fat graphs of the planar diagram expansion. Since the four vertex model in question also serves to describe the critical behaviour of the Ising model in field, the formulation reveals an isomorphism between the Potts and Ising models on thin random graphs. On planar graphs a similar correspondence is present only for q=1, the value associated with percolation.Comment: 6 pages, 5 figure

Prediction and Performance of Deep Excavations for Courthouse Station, Boston

Construction of the Silverline Courthouse Station in South Boston involved 18-m-deep excavations at a site underlain by more than 24 m of normally and lightly overconsolidated Boston blue clay (BBC). The excavations were supported by 27-m-deep floating diaphragm wall panels and five levels of preloaded cross-lot bracing. This paper compares the measured performance of the excavation support system with the Class A finite-element (FE) predictions prepared during the original design phase and with the results of Class C analyses using information obtained during construction. The numerical analyses used data from a special test program of laboratory and in situ tests at a nearby site. The analyses represent coupled consolidation within the soil mass and the anisotropic stress-strain-strength properties of BBC using the MIT-E3 soil model. The Class A analyses generally overestimate the lateral wall deflections and underestimate the measured strut loads, as preloading was not included in the original FE model. However, they provide remarkably consistent predictions of the measured soil deformations, including settlements, lateral spreading, and subgrade basal heave. The Class C analyses refine the stratigraphic section, in situ pore pressures, construction time frame, and strut preloads using the data available at the time of construction but make nominal changes in soil properties. With these limited changes, the Class C model is able to achieve excellent agreement with the measured data

The Yang Lee Edge Singularity on Feynman Diagrams

We investigate the Yang-Lee edge singularity on non-planar random graphs, which we consider as the Feynman Diagrams of various d=0 field theories, in order to determine the value of the edge exponent. We consider the hard dimer model on phi3 and phi4 random graphs to test the universality of the exponent with respect to coordination number, and the Ising model in an external field to test its temperature independence. The results here for generic (``thin'') random graphs provide an interesting counterpoint to the discussion by Staudacher of these models on planar random graphs.Comment: LaTeX, 6 pages + 3 figure

Interaction of Agulhas filaments with mesoscale turbulence: a case study

The inter-ocean leakage of heat and salt from the South Indian Ocean to the South Atlantic has important consequences for the global thermohaline circulation and in particular for the strength of overturning of the Atlantic Ocean as a whole. This leakage between these two subtropical gyres takes place south of Africa. The main mechanisms are the intermittent shedding of Agulhas rings from the retroflection of the Agulhas Current and the advection of Agulhas filaments from the border of the Agulhas Current, both of which move northwestward into the South Atlantic. The subsequent behaviour and mixing of Agulhas rings has been much studied over the past years, that of Agulhas filaments not at all. We report here on fortuitous hydrographic observations of the behaviour of an Agulhas filament that interacted with a number of mesoscale features shortly after formation. This suggests that Agulhas filaments may be involved in many other circulation elements and not only the Benguela upwelling front, as was surmised previously, and may mix out in a very site-specific region

Probing the Ionizing Continuum of Narrow-Line Seyfert 1 Galaxies. I.Observational Results

We present optical spectra and emission-line ratios of 12 Narrow-Line Seyfert 1 (NLS1) galaxies that we observed to study the ionizing EUV continuum. A common feature in the EUV continuum of active galactic nuclei is the big blue bump (BBB), generally associated with thermal accretion disk emission. While Galactic absorption prevents direct access to the EUV range, it can be mapped by measuring the strength of a variety of forbidden optical emission lines that respond to different EUV continuum regions. We find that narrow emission-line ratios involving [OII]3727, Hbeta, [OIII]5007, [OI]6300, Halpha,[NII]6583, and [SII]6716,6731 indicate no significant difference between NLS1s and Broad-Line Seyfert 1 (BLS1) galaxies, which suggests that the spectral energy distributions of their ionizing EUV - soft X-ray continua are similar. The relative strength of important forbidden high ionization lines like [NeV]3426 compared to HeII4686 and the relative strength of [FeX]6374 appear to show the same range as in BLS1 galaxies. However, a trend of weaker F([OI]6300)/F(Halpha) emission-line ratios is indicated for NLS1s compared to BLS1s. To recover the broad emission-line profiles we used Gaussian components. This approach indicates that the broad Hbeta profile can be well described with a broad component (FWHM = 3275 +- 800 km/s) and an intermediate broad component (FWHM = 1200 +- 300 km/s). The width of the broad component is in the typical range of normal BLS1s. The emission-line flux that is associated with the broad component in these NLS1s amounts to at least 60% of the total flux. Thus it dominates the total line flux, similar to BLS1 galaxies.Comment: 34 pages, 9 figures. accepted for publication in the Astrophys.Journa

The black hole in IC 1459 from HST observations of the ionized gas disk

The peculiar elliptical galaxy IC 1459 (M_V = -21.19, D = 16.5 Mpc) has a fast counterrotating stellar core, stellar shells and ripples, a blue nuclear point source and strong radio core emission. We present results of a detailed HST study of IC 1459, and in particular its central gas disk, aimed a constraining the central mass distribution. We obtained WFPC2 narrow-band imaging centered on the Halpha+[NII] emission lines to determine the flux distribution of the gas emission at small radii, and we obtained FOS spectra at six aperture positions along the major axis to sample the gas kinematics. We construct different dynamical models for the Halpha+[NII] and Hbeta kinematics that include a supermassive black hole, and in which the stellar mass distribution is constrained by the observed surface brightness distribution and ground-based stellar kinematics. All models are consistent with a black hole mass in the range Mbh=1-4 x 10^8 Msun, and models without a black hole are always ruled out at high confidence.Comment: 40 pages including 14 figures, Latex; submitted to A

Accurate Redshifts and Classifications for 110 Radio-Loud AGNs

We report accurate redshifts of 110 active galaxies (mostly radio-loud objects at z<0.4) observed in the course of a survey to find broad, double-peaked emission lines. These redshifts are measured from the narrow emission lines of these objects and are accurate to at least one part in 10^4 . For each object we determine a redshift from high- and low-ionization lines separately, as well as an average redshift from all the available lines. We find that in about 15% of cases, the low-ionization lines yield a slightly higher redshift than the high-ionization lines; the average redshift difference amounts to a velocity difference of approximately 80 km/s. In addition to the redshift measurements we also report revised redshifts for two objects as well as new classifications for three narrow-line objects.Comment: To appear in the Astrophysical Journal Supplement