Shear-induced pressure changes and seepage phenomena in a deforming porous layer-I

We present a model for flow and seepage in a deforming, shear-dilatant sensitive porous layer that enables estimates of the excess pore fluid pressures and flow rates in both the melt and solid phase to be captured simultaneously as a function of stress rate. Calculations are relevant to crystallizing magma in the solidosity range 0.5–0.8 (50–20 per cent melt), corresponding to a dense region within the solidification front of a crystallizing magma chamber. Composition is expressed only through the viscosity of the fluid phase, making the model generally applicable to a wide range of magma types. A natural scaling emerges that allows results to be presented in non-dimensional form. We show that all length-scales can be expressed as fractions of the layer height H, timescales as fractions of H2(nβ'θ+ 1)/(θk) and pressures as fractions of . Taking as an example the permeability k in the mush of the order of magnitude 1015 m2 Pa1 s1, a layer thickness of tens of metres and a mush strength (θ) in the range 108–1012 Pa, an estimate of the consolidation time for near-incompressible fluids is of the order of 105–109 s. Using mush permeability as a proxy, we show that the greatest maximum excess pore pressures develop consistently in rhyolitic (high-viscosity) magmas at high rates of shear ( , implying that during deformation, the mechanical behaviour of basaltic and rhyolitic magmas will differ. Transport parameters of the granular framework including tortuosity and the ratio of grain size to layer thickness (a/H) will also exert a strong effect on the mechanical behaviour of the layer at a given rate of strain. For dilatant materials under shear, flow of melt into the granular layer is implied. Reduction in excess pore pressure sucks melt into the solidification front at a velocity proportional to the strain rate. For tectonic rates (generally 1014 s1), melt upwelling (or downwelling, if the layer is on the floor of the chamber) is of the order of cm yr1. At higher rates of loading comparable with emplacement of some magmatic intrusions (1010 s1), melt velocities may exceed effects due to instabilities resulting from local changes in density and composition. Such a flow carries particulates with it, and we speculate that these may become trapped in the granular layer depending on their sizes. If on further solidification the segregated grain size distribution of the particulates is frozen in the granular layer, structure formation including layering and grading may result. Finally, as the process settles down to a steady state, the pressure does not continue to decrease. We find no evidence for critical rheological thresholds, and the process is stable until so much shear has been applied that the granular medium fails, but there is no hydraulic failure

Topologies and Laplacian spectra of a deterministic uniform recursive tree

The uniform recursive tree (URT) is one of the most important models and has been successfully applied to many fields. Here we study exactly the topological characteristics and spectral properties of the Laplacian matrix of a deterministic uniform recursive tree, which is a deterministic version of URT. Firstly, from the perspective of complex networks, we determine the main structural characteristics of the deterministic tree. The obtained vigorous results show that the network has an exponential degree distribution, small average path length, power-law distribution of node betweenness, and positive degree-degree correlations. Then we determine the complete Laplacian spectra (eigenvalues) and their corresponding eigenvectors of the considered graph. Interestingly, all the Laplacian eigenvalues are distinct.Comment: 7 pages, 1 figures, definitive version accepted for publication in EPJ

Tensor product representation of Kothe-Bochner spaces and their dual spaces

We provide a tensor product representation of Kothe-Bochner function spaces of vector valued integrable functions. As an application, we show that the dual space of a Kothe-Bochner function space can be understood as a space of operators satisfying a certain extension property. We apply our results in order to give an alternate representation of the dual of the Bochner spaces of p-integrable functions and to analyze some properties of the natural norms that are defined on the associated tensor products.First and third authors are supported by grant MTM201453009-P of the Ministerio de Economia y Competitividad (Spain). Second and fourth authors are supported by grant MTM2012-36740-C02-02 of the Ministerio de Economia y Competitividad (Spain).Calabuig, JM.; Jiménez Fernández, E.; Juan Blanco, MA.; Sánchez Pérez, EA. (2016). Tensor product representation of Kothe-Bochner spaces and their dual spaces. Positivity. 20(1):155-169. https://doi.org/10.1007/s11117-015-0347-3S155169201Bochner, S.: Integration von Funktionen, deren Werte die Elemente eines Vectorraumes sind. Fundamenta Mathematicae 20, 262–276 (1933)Calabuig, J.M., Delgado, O., Juan, M.A., Sánchez, E.A.: Pérez, On the Banach lattice structure of $$L^1_w$$ L w 1 of a vector measure on a $$\delta$$ δ -ring. Collect. Math. 65, 6567–85 (2014)Calabuig, J.M., Delgado, O., Sánchez Pérez, E.A.: Factorizing operators on Banach function spaces through spaces of multiplication operators. J. Math. Anal. Appl. 364(1), 88–103 (2010)Calabuig, J.M., Gregori, P., Sánchez, E.A.: Pérez, Radon-Nikodým derivatives for vector measures belonging to Köthe function spaces. J. Math. Anal. Appl. 348, 469–479 (2008)Cerdà, J., Hudzik, H., Mastyło, M.: Geometric properties of Köthe-Bochner spaces. Math. Proc. Cambridge Philos. Soc. 120(3), 521–533 (1996)Chakraborty, N.D., Basu, S.: Spaces of p-tensor integrable functions and related Banach space properties. Real Anal. Exchange 34, 87–104 (2008)Chakraborty, N.D., Basu, S.: Integration of vector-valued functions with respect to vector measures defined on $$\delta$$ δ -rings. Ill. J. Math. 55(2), 495–508 (2011)Defant, A., Floret, K.: Tensor norms and operator ideals. North-Holland, Amsterdam (1993)Delgado, O., Juan, M.A.: Representation of Banach lattices as $$L^{1}_{w}$$ L w 1 spaces of a vector measure defined on a $$\delta -$$ δ - ring. Bull. Belgian Math. Soc. 19, 239–256 (2012)Diestel, J., Uhl, J.J.: Vector measures. Am. Math. Soc, Providence (1977)Dobrakov, I.: On integration in Banach spaces, VII. Czechoslovak Math. J. 38, 434–449 (1988)García-Raffi, L.M., Jefferies, B.: An application of bilinear integration to quantum scattering. J. Math. Anal. Appl. 415, 394–421 (2014)Gregori Huerta, P.: Espacios de medidas vectoriales. Thesis, Universidad de Valencia, ISBN:8437060591 (2005)Jefferies, B., Okada, S.: Bilinear integration in tensor products. Rocky Mt. J. Math. 28, 517–545 (1998)Lewis, D.R.: On integrability and summability in vector spaces. Ill. J. Math. 16, 294–307 (1972)Lin, P.-K.: Köthe-Bochner function spaces. Birkhauser, Boston (2004)Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces II. Springer, Berlin (1979)Okada, S., Ricker, W.J., Sánchez Pérez, E.A.: Optimal Domains and integral extensions of operators acting in function spaces. Operator Theory Advances and Applications, vol. 180. Birkhäuser, Basel (2008)Pallu de La Barriére, R.: Integration of vector functions with respect to vector measures. Studia Univ. Babes-Bolyai Math. 43, 55–93 (1998)Rodríguez, J.: On integration of vector functions with respect to vector measures. Czechoslovak Math. J. 56, 805–825 (2006

SN 2010jl: Optical to Hard X-ray Observations Reveal an Explosion Embedded In a Ten Solar Mass Cocoon

Some supernovae (SNe) may be powered by the interaction of the SN ejecta with a large amount of circumstellar matter (CSM). However, quantitative estimates of the CSM mass around such SNe are missing when the CSM material is optically thick. Specifically, current estimators are sensitive to uncertainties regarding the CSM density profile and the ejecta velocity. Here we outline a method to measure the mass of the optically thick CSM around such SNe. We present new visible-light and X-ray observations of SN 2010jl (PTF 10aaxf), including the first detection of an SN in the hard X-ray band using NuSTAR. The total radiated luminosity of SN 2010jl is extreme—at least 9 × 1050 erg. By modeling the visible-light data, we robustly show that the mass of the circumstellar material within ~1016 cm of the progenitor of SN 2010jl was in excess of 10 M☉. This mass was likely ejected tens of years prior to the SN explosion. Our modeling suggests that the shock velocity during shock breakout was ~6000 km s–1, decelerating to ~2600 km s–1 about 2 yr after maximum light. Furthermore, our late-time NuSTAR and XMM spectra of the SN presumably provide the first direct measurement of SN shock velocity 2 yr after the SN maximum light—measured to be in the range of 2000-4500 km s–1 if the ions and electrons are in equilibrium, and ≳2000 km s–1 if they are not in equilibrium. This measurement is in agreement with the shock velocity predicted by our modeling of the visible-light data. Our observations also show that the average radial density distribution of the CSM roughly follows an r–2 law. A possible explanation for the ≳10 M☉ of CSM and the wind-like profile is that they are the result of multiple pulsational pair instability events prior to the SN explosion, separated from each other by years

Caenorhabditis briggsae Recombinant Inbred Line Genotypes Reveal Inter-Strain Incompatibility and the Evolution of Recombination

The nematode Caenorhabditis briggsae is an emerging model organism that allows evolutionary comparisons with C. elegans and exploration of its own unique biological attributes. To produce a high-resolution C. briggsae recombination map, recombinant inbred lines were generated from reciprocal crosses between two strains and genotyped at over 1,000 loci. A second set of recombinant inbred lines involving a third strain was also genotyped at lower resolution. The resulting recombination maps exhibit discrete domains of high and low recombination, as in C. elegans, indicating these are a general feature of Caenorhabditis species. The proportion of a chromosome's physical size occupied by the central, low-recombination domain is highly correlated between species. However, the C. briggsae intra-species comparison reveals striking variation in the distribution of recombination between domains. Hybrid lines made with the more divergent pair of strains also exhibit pervasive marker transmission ratio distortion, evidence of selection acting on hybrid genotypes. The strongest effect, on chromosome III, is explained by a developmental delay phenotype exhibited by some hybrid F2 animals. In addition, on chromosomes IV and V, cross direction-specific biases towards one parental genotype suggest the existence of cytonuclear epistatic interactions. These interactions are discussed in relation to surprising mitochondrial genome polymorphism in C. briggsae, evidence that the two strains diverged in allopatry, the potential for local adaptation, and the evolution of Dobzhansky-Muller incompatibilities. The genetic and genomic resources resulting from this work will support future efforts to understand inter-strain divergence as well as facilitate studies of gene function, natural variation, and the evolution of recombination in Caenorhabditis nematodes

Electrical characterization of Ca1-xErxF2+x luminescent thin films

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Electrical characterization of Ca1-xErxF2+x luminescent thin films

no abstrac

Correlation between the Indium Tin Oxide morphology and the performances of polymer light-emitting diodes

This paper reports on performance enhancement of polymer light-emitting diodes (PLEDs) based on poly(2,5-bis(3′,7′-dimethyl-octyloxy)1,4-phenylene-vinylene) (BDMO-PPV) after Indium Tin Oxide (ITO) pre-treatment. Diluted aqua regia surface treatments of ITO substrates were investigated before PLEDs manufacturing. The correlation between ITO surface morphology and the properties of devices were discussed. The residual roughness, the global ITO thickness and developed anodic active area were found extremely dependent on treatment time. The performances of the ITO/BDMO-PPV/Ca/Al diodes were improved. With long treatments, the roughness was dramatically increased and poor PLEDs performances were achieved. The incorporation of a conducting polymer layer, poly(3,4-ethylene dioxythiophene) doped with polystyrene sulfonate, between the ITO layer and the emissive polymer, was also studied. With this buffer layer, no effect of the acidic treatment was observed on luminance–voltage characteristics and low turn-on voltage devices were made