Combinatorial models of rigidity and renormalization

We first introduce the percolation problems associated with the graph theoretical concepts of $(k,l)$-sparsity, and make contact with the physical concepts of ordinary and rigidity percolation. We then devise a renormalization transformation for $(k,l)$-percolation problems, and investigate its domain of validity. In particular, we show that it allows an exact solution of $(k,l)$-percolation problems on hierarchical graphs, for $k\leq l<2k$. We introduce and solve by renormalization such a model, which has the interesting feature of showing both ordinary percolation and rigidity percolation phase transitions, depending on the values of the parameters.Comment: 22 pages, 6 figure

Fibre optic sensors for high speed hypervelocity impact studies and low velocity drop tests

The initial aim of this project was to develop a non-contact fibre optic based displacement sensor to operate in the harsh environment of a 'Light Gas Gun' (LGG), which can 'fire' small particles at velocities ranging from 1-8.4 km/s. The LGG is used extensively for research in aerospace to analyze the effects of high speed impacts on materials. Ideally the measurement should be made close to the centre of the impact to minimise corruption of the data from edge effects and survive the impact. A further requirement is that it should operate at a stand-off distance of ~ 8cm. For these reasons we chose to develop a pseudo con-focal intensity sensor, which demonstrated resolution comparable with conventional PVDF sensors combined with high survivability and low cost. A second sensor was developed based on 'Fibre Bragg Gratings' (FBG) which although requiring contact with the target the low weight and very small contact area had minimal effect on the dynamics of the target. The FBG was mounted either on the surface of the target or tangentially between a fixed location. The output signals from the FBG were interrogated in time by a new method. Measurements were made on composite and aluminium plates in the LGG and on low speed drop tests. The particle momentum for the drop tests was chosen to be similar to that of the particles used in the LGG

Stochastic B-series analysis of iterated Taylor methods

For stochastic implicit Taylor methods that use an iterative scheme to compute their numerical solution, stochastic B--series and corresponding growth functions are constructed. From these, convergence results based on the order of the underlying Taylor method, the choice of the iteration method, the predictor and the number of iterations, for It\^o and Stratonovich SDEs, and for weak as well as strong convergence are derived. As special case, also the application of Taylor methods to ODEs is considered. The theory is supported by numerical experiments

High angular resolution mm- and submm-observations of dense molecular gas in M82

Researchers observed CO(7-6), CO(3-2), HCN(3-2) and HCO+(3-2) line emission toward the starburst nucleus of M82 and have obtained an upper limit to H13CN(3-2). These are the first observations of the CO(7-6), HCN(3-2) and HCO+(3-2) lines in any extragalactic source. Researchers took the CO(7-6) spectrum in January 1988 at the Infrared Telescope Facility (IRTF) with the Max Planck Institute for Extraterrestrial Physics/Univ. of California, Berkeley 800 GHz Heterodyne Receiver. In March 1989 researchers used the Institute for Radio Astronomy in the Millimeter range (IRAM) 30 m telescope to observe the CO(3-2) line with the new MPE 350 GHz Superconductor Insulator Superconductor (SIS) receiver and the HCN(3-2) and HCO+(3-2) lines with the (IRAM) 230 GHz SIS receiver (beam 12" FWHM, Blundell et al. 1988). The observational parameters are summarized

Predicting seawater intrusion in coastal groundwater boreholes using self-potential data

Many coastal groundwater abstraction wells are under threat from seawater intrusion: this is exacerbated in summer by low water tables and increased abstraction. Existing hydrochemistry or geophysical techniques often fail to predict the timing of intrusion events. We investigate whether the presence and transport of seawater can influence self-potentials (SPs) measured within groundwater boreholes, with the aim of using SP monitoring to provide early warning of saline intrusion. SP data collection: SP data were collected from a coastal groundwater borehole and an inland borehole (> 60 km from the coast) in the Seaford Chalk of southern England. The SP gradient in the inland borehole was approximately 0.05 mV/m, while that in the coastal borehole varied from 0.16-0.26 mV/m throughout the monitoring period. Spectral analysis showed that semi-diurnal fluctuations in the SP gradient were several orders of magnitude higher at the coast than inland, indicating a strong influence from oceanic tides. A characteristic decrease in the gradient, or precursor, was observed in the coastal borehole several days prior to seawater intrusion. Modelling results: Hydrodynamic transport and geoelectric modelling suggest that observed pressure changes (associated with the streaming potential) are insufficient to explain either the magnitude of the coastal SP gradient or the semi-diurnal SP fluctuations. By contrast, a model of the exclusion-diffusion potential closely matches these observations and produces a precursor similar to that observed in the field. Sensitivity analysis suggests that both a sharp saline front and spatial variations in the exclusion efficiency arising from aquifer heterogeneities are necessary to explain the SP gradient observed in the coastal borehole. The presence of the precursor in the model depends also on the presence and depth of fractures near the base of the borehole. Conclusions: Our results indicate that SP monitoring, combined with hydrodynamic transport and geoelectric modelling, holds considerable promise as an early warning device for seawater intrusion. We now aim to refine our understanding of the technique by applying it to a range of aquifer types

Live and Dead Nodes

In this paper, we explore the consequences of a distinction between `live' and `dead' network nodes; `live' nodes are able to acquire new links whereas `dead' nodes are static. We develop an analytically soluble growing network model incorporating this distinction and show that it can provide a quantitative description of the empirical network composed of citations and references (in- and out-links) between papers (nodes) in the SPIRES database of scientific papers in high energy physics. We also demonstrate that the death mechanism alone can result in power law degree distributions for the resulting network.Comment: 12 pages, 3 figures. To be published in Computational and Mathematical Organization Theor

Matter wave solitons at finite temperatures

We consider the dynamics of a dark soliton in an elongated harmonically trapped Bose-Einstein condensate. A central question concerns the behavior at finite temperatures, where dissipation arises due to the presence of a thermal cloud. We study this problem using coupled Gross-Pitaevskii and $N$-body simulations, which include the mean field coupling between the condensate and thermal cloud. We find that the soliton decays relatively quickly even at very low temperatures, with the decay rate increasing with rising temperature.Comment: 6 pages, 2 figures, submitted to the Proceedings of QFS '0

The shell-forming proteome of Lottia gigantea reveals both deep conservations and lineage-specific novelties

19 pagesInternational audienceProteins that are occluded within the molluscan shell, the so-called shell matrix proteins (SMPs), are an assemblage of biomolecules attractive to study for several reasons. They increase the fracture resistance of the shell by several orders of magnitude, determine the polymorph of CaCO(3) deposited, and regulate crystal nucleation, growth initiation and termination. In addition, they are thought to control the shell microstructures. Understanding how these proteins have evolved is also likely to provide deep insight into events that supported the diversification and expansion of metazoan life during the Cambrian radiation 543 million years ago. Here, we present an analysis of SMPs isolated form the CaCO(3) shell of the limpet Lottia gigantea, a gastropod that constructs an aragonitic cross-lamellar shell. We identified 39 SMPs by combining proteomic analysis with genomic and transcriptomic database interrogations. Among these proteins are various low-complexity domain-containing proteins, enzymes such as peroxidases, carbonic anhydrases and chitinases, acidic calcium-binding proteins and protease inhibitors. This list is likely to contain the most abundant SMPs of the shell matrix. It reveals the presence of both highly conserved and lineage-specific biomineralizing proteins. This mosaic evolutionary pattern suggests that there may be an ancestral molluscan SMP set upon which different conchiferan lineages have elaborated to produce the diversity of shell microstructures we observe nowadays. DATABASE: Novel protein sequences reported in this article have been deposited in Swiss-Prot database under accession nos. B3A0P1-B3A0S4

The Emission of Electromagnetic Radiation from Charges Accelerated by Gravitational Waves and its Astrophysical Implications

We provide calculations and theoretical arguments supporting the emission of electromagnetic radiation from charged particles accelerated by gravitational waves (GWs). These waves have significant indirect evidence to support their existence, yet they interact weakly with ordinary matter. We show that the induced oscillations of charged particles interacting with a GW, which lead to the emission of electromagnetic radiation, will also result in wave attenuation. These ideas are supported by a small body of literature, as well as additional arguments for particle acceleration based on GW memory effects. We derive order of magnitude power calculations for various initial charge distributions accelerated by GWs. The resulting power emission is extremely small for all but very strong GWs interacting with large quantities of charge. If the results here are confirmed and supplemented, significant consequences such as attenuation of early universe GWs could result. Additionally, this effect could extend GW detection techniques into the electromagnetic regime. These explorations are worthy of study to determine the presence of such radiation, as it is extremely important to refine our theoretical framework in an era of active GW astrophysics.Comment: Appears in Gravitational Wave Astrophysics, Editor C.F. Sopuerta, Astrophysics and Space Science Proceedings, Volume 40. ISBN 978-3-319-10487-4. Springer International Publishing Switzerland, 2015, p. 30