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

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

Computational models for the viscous/inviscid analysis of jet aircraft exhaust plumes

Computational models which analyze viscous/inviscid flow processes in jet aircraft exhaust plumes are discussed. These models are component parts of an NASA-LaRC method for the prediction of nozzle afterbody drag. Inviscid/shock processes are analyzed by the SCIPAC code which is a compact version of a generalized shock capturing, inviscid plume code (SCIPPY). The SCIPAC code analyzes underexpanded jet exhaust gas mixtures with a self-contained thermodynamic package for hydrocarbon exhaust products and air. A detailed and automated treatment of the embedded subsonic zones behind Mach discs is provided in this analysis. Mixing processes along the plume interface are analyzed by two upgraded versions of an overlaid, turbulent mixing code (BOAT) developed previously for calculating nearfield jet entrainment. The BOATAC program is a frozen chemistry version of BOAT containing the aircraft thermodynamic package as SCIPAC; BOATAB is an afterburning version with a self-contained aircraft (hydrocarbon/air) finite-rate chemistry package. The coupling of viscous and inviscid flow processes is achieved by an overlaid procedure with interactive effects accounted for by a displacement thickness type correction to the inviscid plume interface

Model metadata report for a 3D model of Cirencester-Cricklade

This report publishes the metadata of a 3d modelling study by a BUFI student which subsequently was then formalised by British Geological Survey (BGS) modelling staff. As the model was created by a visiting student no accurate metadata was maintained during the project set-up period. This document aims to publish all known metadata and indicates where uncertainty of source arises. The model was given to BGS after the initial student completion phase to allow the in-house modelling team to bring the model into line with BGS best practice. The model was developed under the 3d Models for Teaching team, part of the Geological Modelling Systems program at BGS. 3D geological models have great potential as a resource for universities when teaching foundation geological concepts as it allows the student to visualise and interrogate UK geology. They are especially useful when dealing with the conversion of 2D field, map and GIS outputs into three dimensional geological units, which is a common problem for all students of geology. Today’s earth science students use a variety of skills and processes during their learning experience including the application of schema’s, spatial thinking, image construction, detecting patterns, memorising figures, mental manipulation and interpretation, making predictions and deducing the orientation of themselves and the rocks. 3D geological models can reinforce spatial thinking strategies and encourage students to think about processes and properties, in turn helping the student to recognise pre-learnt geological principles in the field and to convert what they see at the surface into a picture of what is going on at depth

Self-organization with equilibration: a model for the intermediate phase in rigidity percolation

Recent experimental results for covalent glasses suggest the existence of an intermediate phase attributed to the self-organization of the glass network resulting from the tendency to minimize its internal stress. However, the exact nature of this experimentally measured phase remains unclear. We modify a previously proposed model of self-organization by generating a uniform sampling of stress-free networks. In our model, studied on a diluted triangular lattice, an unusual intermediate phase appears, in which both rigid and floppy networks have a chance to occur, a result also observed in a related model on a Bethe lattice by Barre et al. [Phys. Rev. Lett. 94, 208701 (2005)]. Our results for the bond-configurational entropy of self-organized networks, which turns out to be only about 2% lower than that of random networks, suggest that a self-organized intermediate phase could be common in systems near the rigidity percolation threshold.Comment: 9 pages, 6 figure

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

Fascicles and the interfascicular matrix show decreased fatigue life with ageing in energy storing tendons

Tendon is composed of rope-like fascicles bound together by interfascicular matrix (IFM). The IFM is critical for the function of energy storing tendons, facilitating sliding between fascicles to allow these tendons to cyclically stretch and recoil. This capacity is required to a lesser degree in positional tendons. We have previously demonstrated that both fascicles and IFM in energy storing tendons have superior fatigue resistance compared with positional tendons, but the effect of ageing on the fatigue properties of these different tendon subunits has not been determined. Energy storing tendons become more injury-prone with ageing, indicating reduced fatigue resistance, hence we tested the hypothesis that the decline in fatigue life with ageing in energy storing tendons would be more pronounced in the IFM than in fascicles. We further hypothesised that tendon subunit fatigue resistance would not alter with ageing in positional tendons. Fascicles and IFM from young and old energy storing and positional tendons were subjected to cyclic fatigue testing until failure, and mechanical properties were calculated. The results show that both IFM and fascicles from the SDFT exhibit a similar magnitude of reduced fatigue life with ageing. By contrast, the fatigue life of positional tendon subunits was unaffected by ageing. The age-related decline in fatigue life of tendon subunits in energy storing tendons is likely to contribute to the increased risk of injury in aged tendons. Full understanding of the mechanisms resulting in this reduced fatigue life will aid in the development of treatments and interventions to prevent age-related tendinopathy

Variation of the glass transition temperature with rigidity and chemical composition

The effects of flexibility and chemical composition in the variation of the glass transition temperature are obtained by using the Lindemann criteria, that relates melting temperature with atomic vibrations. Using this criteria and that floppy modes at low frequencies enhance in a considerable way the average cuadratic displacement, we show that the consequence is a modified glass transition temperature. This approach allows to obtain in a simple way the empirically modified Gibbs-DiMarzio law, which has been widely used in chalcogenide glasses to fit the changes in the glass transition temperature with the chemical composition . The method predicts that the constant that appears in the law depends upon the ratio of two characteristic frequencies (or temperatures). Then, the constant for the Se-Ge-As glass is estimated by using the experimental density of vibrational states, and the result shows a very good agreement with the experimental fit from glass transition temperature variation