Effective elastic properties of randomly distributed void models for porous materials

This is the post-print version of the final paper published in International Journal of Mechanical Sciences. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2010 Elsevier B.V.Many 2D analytical models are available for estimating the effective elastic properties of porous materials. Most of these models adopt circular voids of a uniform diameter in superlattice arrays, such as unit void or periodically positioned models. There are two principal issues in a realistic representation of porous materials: the random distribution of a statistically sufficiently large number of voids in the model, and the random distribution of the size and position of the voids. Numerical schemes such as the FEM or the BEM have also been presented to cater for regular patterned circular voids. However, due to the large number of elements needed to produce sufficient accuracy for the curved boundary of circular voids or modelling a statistically sufficient number of voids with a random distribution in both the void size and the position, no such model has yet been produced. Modelling based on an FEM approach using a simplified approximation for void geometry is proposed here for the calculation of the effective elastic properties of porous solids. A plane strain model of a square geometry is adopted for a 2D array of voids. This simplified square shape allows a large number of voids to be simulated with a random distribution for both void sizes and their locations. The problem of anisotropy, which arises from the square shape, is discussed. It is verified that along the two principal directions (parallel to the sides of the square voids), the elastic properties remain the same as those predicted by using a circular void geometry. This square-shaped approximation, with its reduced requirement for FE analysis, has the potential to be extended to 3-dimensional modelling for a realistic simulation of engineering materials.University of Aberdee

Exploring the parent population of beamed NLS1s: from the black hole to the jet

The aim of this work is to understand the nature of the parent population of beamed narrow-line Seyfert 1 galaxies (NLS1s), by studying the physical properties of three parent candidates samples: steep-spectrum radio-loud NLS1s, radio-quiet NLS1s and disk-hosted radio-galaxies. In particular, we focused on the black hole mass and Eddington ratio distribution and on the interactions between the jet and the narrow-line region.Comment: 6 pages, 2 figures, to appear in Proceedings of High Energy Phenomena in Relativistic Outflows (HEPRO) V, Workshop Series of the Argentinian Astronomical Societ

Stress-free states of continuum dislocation fields: Rotations, grain boundaries, and the Nye dislocation density tensor

We derive general relations between grain boundaries, rotational deformations, and stress-free states for the mesoscale continuum Nye dislocation density tensor. Dislocations generally are associated with long-range stress fields. We provide the general form for dislocation density fields whose stress fields vanish. We explain that a grain boundary (a dislocation wall satisfying Frank's formula) has vanishing stress in the continuum limit. We show that the general stress-free state can be written explicitly as a (perhaps continuous) superposition of flat Frank walls. We show that the stress-free states are also naturally interpreted as configurations generated by a general spatially-dependent rotational deformation. Finally, we propose a least-squares definition for the spatially-dependent rotation field of a general (stressful) dislocation density field.Comment: 9 pages, 3 figure

Two-year observations of the Jupiter polar regions by JIRAM on board Juno

We observed the evolution of Jupiter's polar cyclonic structures over two years between February 2017 and February 2019, using polar observations by the Jovian InfraRed Auroral Mapper, JIRAM, on the Juno mission. Images and spectra were collected by the instrument in the 5‐μm wavelength range. The images were used to monitor the development of the cyclonic and anticyclonic structures at latitudes higher than 80° both in the northern and the southern hemispheres. Spectroscopic measurements were then used to monitor the abundances of the minor atmospheric constituents water vapor, ammonia, phosphine and germane in the polar regions, where the atmospheric optical depth is less than 1. Finally, we performed a comparative analysis with oceanic cyclones on Earth in an attempt to explain the spectral characteristics of the cyclonic structures we observe in Jupiter's polar atmosphere

Efficient CSL Model Checking Using Stratification

For continuous-time Markov chains, the model-checking problem with respect to continuous-time stochastic logic (CSL) has been introduced and shown to be decidable by Aziz, Sanwal, Singhal and Brayton in 1996. Their proof can be turned into an approximation algorithm with worse than exponential complexity. In 2000, Baier, Haverkort, Hermanns and Katoen presented an efficient polynomial-time approximation algorithm for the sublogic in which only binary until is allowed. In this paper, we propose such an efficient polynomial-time approximation algorithm for full CSL. The key to our method is the notion of stratified CTMCs with respect to the CSL property to be checked. On a stratified CTMC, the probability to satisfy a CSL path formula can be approximated by a transient analysis in polynomial time (using uniformization). We present a measure-preserving, linear-time and -space transformation of any CTMC into an equivalent, stratified one. This makes the present work the centerpiece of a broadly applicable full CSL model checker. Recently, the decision algorithm by Aziz et al. was shown to work only for stratified CTMCs. As an additional contribution, our measure-preserving transformation can be used to ensure the decidability for general CTMCs.Comment: 18 pages, preprint for LMCS. An extended abstract appeared in ICALP 201

Variational approach to a class of nonlinear oscillators with several limit cycles

We study limit cycles of nonlinear oscillators described by the equation $\ddot x + \nu F(\dot x) + x =0$. Depending on the nonlinearity this equation may exhibit different number of limit cycles. We show that limit cycles correspond to relative extrema of a certain functional. Analytical results in the limits $\nu ->0$ and $\nu -> \infty$ are in agreement with previously known criteria. For intermediate $\nu$ numerical determination of the limit cycles can be obtained.Comment: 12 pages, 3 figure

Unveiling the parent population of beamed narrow-line Seyfert 1s

Narrow-line Seyfert 1 galaxies (NLS1s) are active galactic nuclei (AGN) recently identified as a new class of $\gamma$-ray sources. The high energy emission is explained by the presence of a relativistic jet observed at small angles, just like in the case of blazars. When the latter are observed at larger angles they appear as radio-galaxies, but an analogue parent population for beamed NLS1s has not yet been determined. In this work we analyze this problem by studying the physical properties of three different samples of parent sources candidates: steep-spectrum radio-loud NLS1s, radio-quiet NLS1s, and disk-hosted radio-galaxies, along with compact steep-spectrum sources. In our approach, we first derived black hole mass and Eddington ratio from the optical spectra, then we investigated the interaction between the jet and the narrow-line region from the [O III] $\lambda\lambda$4959,5007 lines. Finally, the radio luminosity function allowed us to compare their jet luminosity and hence determine the relations between the samples.Comment: 6 pages, no figures. Proceedings of the 28th Texas Symposium, Geneva, December 13-18, 201