NO sub X Deposited in the Stratosphere by the Space Shuttle Solid Rocket Motors

The possible effects of the interaction of the plumes from the two solid rocket motors (SRM) from the space shuttles and mixing of the rocket exhaust products and ambient air in the base recirculation region on the total nitrous oxide deposition rate in the stratosphere were investigated. It was shown that these phenomena will not influence the total NOx deposition rate. It was also shown that uncertainties in the particle size of Al2O3, size distributions and particle/gas drag and heat transfer coefficients will not have a significant effect on the predicted NOx deposition rate. The final results show that the total mass flow of NOx leaving the plume at 30 km altitude is 4000 g./sec with a possible error factor of 3. For a vehicle velocity of 1140 meter/sec this yields an NOx deposition rate of about 3.5 g./meter. The corresponding HCl deposition rate at this altitude is about a factor of 500 greater than this value

Algorithms for 3D rigidity analysis and a first order percolation transition

A fast computer algorithm, the pebble game, has been used successfully to study rigidity percolation on 2D elastic networks, as well as on a special class of 3D networks, the bond-bending networks. Application of the pebble game approach to general 3D networks has been hindered by the fact that the underlying mathematical theory is, strictly speaking, invalid in this case. We construct an approximate pebble game algorithm for general 3D networks, as well as a slower but exact algorithm, the relaxation algorithm, that we use for testing the new pebble game. Based on the results of these tests and additional considerations, we argue that in the particular case of randomly diluted central-force networks on BCC and FCC lattices, the pebble game is essentially exact. Using the pebble game, we observe an extremely sharp jump in the largest rigid cluster size in bond-diluted central-force networks in 3D, with the percolating cluster appearing and taking up most of the network after a single bond addition. This strongly suggests a first order rigidity percolation transition, which is in contrast to the second order transitions found previously for the 2D central-force and 3D bond-bending networks. While a first order rigidity transition has been observed for Bethe lattices and networks with ``chemical order'', this is the first time it has been seen for a regular randomly diluted network. In the case of site dilution, the transition is also first order for BCC, but results for FCC suggest a second order transition. Even in bond-diluted lattices, while the transition appears massively first order in the order parameter (the percolating cluster size), it is continuous in the elastic moduli. This, and the apparent non-universality, make this phase transition highly unusual.Comment: 28 pages, 19 figure

Are cascading flows stable?

The stability of flows cascading down slopes as dense inclined plumes is examined, with particular reference to flows observed in Lake Geneva during winter periods of severe cooling. A previous conjecture by Turner that the flow may be in a state of marginal stability is confirmed: the observed mean velocity and density profiles are unstable to Kelvin-Helmholtz instability, but only marginally so; the growth rates of the most unstable small disturbances to the cascading flow in Lake Geneva are small, with e-folding periods of about 2 h. A reduction in the maximum velocity by about 20% is required to stabilize the flow. The possibility that stationary hydraulic jumps may occur in the observed flow is also considered. Several plausible flow states downstream of transitions are examined, allowing for mixing and density changes to occur, ranging from one that preserves the shape of the density and velocity profiles to one in which, as a consequence of mixing, the velocity and density become uniform in depth within the cascading flow. Neither of these extreme states is found to conserve the fluxes of volume, mass and momentum through a transition in which the energy flux does not increase, and to be unique or ‘stable' in the sense that no further transition is possible to a similar flow state without more entrainment. Stable transitions to intermediate downstream flows that conserve flow properties and reduce energy flux are, however, found, although the smallest value of the flow parameter, Fr≡ Umax2/gΔ h (where Umax is the maximum flow speed, g is the acceleration due to gravity, Δ is a fractional density difference within the flow and h is the flow thickness) at which transitions may occur is only slightly less than that of the cascading flow in Lake Geneva. In this sense, the observed flow is marginally unstable to a finite-amplitude transition or hydraulic jump. Velocity and density profiles of possible flows downstream of a transition are found. The amplitudes of possible transitions and the flux of water entrained from the ambient overlying water mass are limited to narrow range

The onset of convection caused by buoyancy during transient heat conduction in deep fluids

The onset of convection in a thermal layer generated by transient heat conduction in deep fluid is examined. It is generally accepted that buoyancy driven convection predominates in deep fluids while surface tension driven convection can occur only in very thin layers of liquid. The occurrence of buoyancy convection can be predicted from conventional linear stability analysis for steady-state heat conduction. Its results are summarised in terms of critical Rayleigh numbers. The point of instability in transient heat conduction is, however, less well understood. Its onset in deep fluids is determined by the mode and rate of cooling. In this paper, the judicial application of transient heat conduction equations and a newly defined transient local Ra with the appropriate boundary conditions has allowed the tracking of the time and spatial development of local hydrodynamic equilibrium to the point of instability. The onset of convection can be predicted from the maximum transient Ra whose values are the same as those previously obtained by linear stability analysis for the same boundary conditions. The critical times and critical depths for stable diffusion in fluids (i.e. without convection) can thus be determined accurately. Agreement with observed values from the literature is very good. The mode and rate of heat conduction are confirmed to be the controlling factors in determining the time of onset of convection

Kinetic glass behavior in a diffusive model

Three properties of the Edwards-Anderson model with mobile bonds are investigated which are characteristic of kinetic glasses. First is two-time relaxation in aged systems, where a significant difference is observed between spin and bond autocorrelation functions. The spin subsystem does not show two-time behavior, and the relaxation is stretched exponential. The bond subsystem shows two-time behavior, with the first relaxation nearly exponential and the second similar to the spin one. Second is the two-temperature behavior, which can be tuned by bond dilution through the full range reported in the literature. Third is the rigid-to-floppy transition, identified as a function of bond dilution. Simple Glauber Monte Carlo evolution without extraneous constraints reproduces the behavior of classical kinetic simulations, with the bond (spin) degree of freedom corresponding to configurational (orientational) disorder.Comment: 4 pages, 3 figures, minimal corrections, to appear in Phys. Rev. B (RC

Evaluation and management implications of uncertainty in a multispecies size-structured model of population and community responses to fishing

1. Implementation of an ecosystem approach to fisheries requires advice on trade-offs among fished species and between fisheries yields and biodiversity or food web properties. However, the lack of explicit representation, analysis and consideration of uncertainty in most multispecies models has limited their application in analyses that could support management advice. 2. We assessed the consequences of parameter uncertainty by developing 78 125 multispecies size-structured fish community models, with all combinations of parameters drawn from ranges that spanned parameter values estimated from data and literature. This unfiltered ensemble was reduced to 188 plausible models, the filtered ensemble (FE), by screening outputs against fish abundance data and ecological principles such as requiring species' persistence. 3. Effects of parameter uncertainty on estimates of single-species management reference points for fishing mortality (FMSY, fishing mortality rate providing MSY, the maximum sustainable yield) and biomass (BMSY, biomass at MSY) were evaluated by calculating probability distributions of estimated reference points with the FE. There was a 50% probability that multispecies FMSY could be estimated to within ±25% of its actual value, and a 50% probability that BMSY could be estimated to within ±40% of its actual value. 4. Signal-to-noise ratio was assessed for four community indicators when mortality rates were reduced from current rates to FMSY. The slope of the community size spectrum showed the greatest signal-to-noise ratio, indicating that it would be the most responsive indicator to the change in fishing mortality F. Further, the power of an ongoing international monitoring survey to detect predicted responses of size spectrum slope was higher than for other size-based metrics. 5. Synthesis and applications: Application of the ensemble model approach allows explicit representation of parameter uncertainty and supports advice and management by (i) providing uncertainty intervals for management reference points, (ii) estimating working values of reference points that achieve a defined reduction in risk of not breaching the true reference point, (iii) estimating the responsiveness of population, community, food web and biodiversity indicators to changes in F, (iv) assessing the performance of indicators and monitoring programmes and (v) identifying priorities for data collection and changes to model structure to reduce uncertainty