Ergodicity of a stress release point process seismic model with aftershocks

We prove ergodicity of a point process earthquake model combining the classical stress release model for primary shocks with the Hawkes model for aftershocks.Comment: 20 page

Mechanical damping of wood as related to species classification: a preliminary survey

International audienceSome morphological and biochemical taxonomic markers are also affecting factors of dynamic mechanical properties of wood. Thus, could these properties reflect the classification/phylogeny of taxa? This work is a first insight into this question. It relied on the gathering (through experimental campaigns and exhaustive literature review) of a large database on the viscoelastic (i.e. including damping) vibrational properties of 445 woody species. relationship between damping was confirmed at a wide interspecific scale, but described no more than 40% of not in a way that could be easily related to the phylogenetic tree. Damping was a bit more -Papilionoideae and, to a lesser extent, Lauraceae, Cupressaceae and Moraceae) damping than average, independently While for some other families no clear characteristics could be observed at least with the present number of represented species. In the future, increasing the amount of data and compiling anatomical and chemical markers / affecting factors will allow further analysis at sub-family levels, and a better understanding of this wide topic

Anisotropy of wood vibrational properties: dependence on grain angle and review of literature data

International audienceThe anisotropy of vibrational properties influences the acoustic behaviour of wooden pieces and their dependence on grain angle (GA). As most pieces of wood include some GA, either for technological reasons or due to grain deviations inside trunks, predicting its repercussions would be useful. This paper aims at evaluating the variability in the anisotropy of wood vibrational properties and analysing resulting trends as a function of orientation. GA dependence is described by a model based on transformation formulas applied to complex compliances, and literature data on anisotropic vibrational properties are reviewed. Ranges of variability, as well as representative sets of viscoelastic anisotropic parameters, are defined for mean hardwoods and softwoods and for contrasted wood types. GA-dependence calculations are in close agreement with published experimental results and allow comparing the sensitivity of different woods to GA. Calculated trends in damping coefficient (tanδ) and in specific modulus of elasticity (E′/ρ) allow reconstructing the general tanδ-E′/ρ statistical relationships previously reported. Trends for woods with different mechanical parameters merge into a single curve if anisotropic ratios (both elastic and of damping) are correlated between them, and with axial properties, as is indicated by the collected data. On the other hand, varying damping coefficient independently results in parallel curves, which coincide with observations on chemically modified woods, either "artificially", or by natural extractives

Projections, Pseudo-Stopping Times and the Immersion Property

Given two filtrations $\mathbb F \subset \mathbb G$, we study under which conditions the $\mathbb F$-optional projection and the $\mathbb F$-dual optional projection coincide for the class of $\mathbb G$-optional processes with integrable variation. It turns out that this property is equivalent to the immersion property for $\mathbb F$ and $\mathbb G$, that is every $\mathbb F$-local martingale is a $\mathbb G$-local martingale, which, equivalently, may be characterised using the class of $\mathbb F$-pseudo-stopping times. We also show that every $\mathbb G$-stopping time can be decomposed into the minimum of two barrier hitting times

An insensitivity property of Lundberg's estimate for delayed claims

This short note shows that the Lundberg's exponential upperbound in the ruin problem of non-life insurance with compound Poisson claims is also valid for the Poisson shot noise delayed claims model, and that the optimal exponent depends only on the distribution of the total claim per accident, not on the time it takes to honor the claim. This result holds under Cramer's condition

Changes in viscoelastic vibrational properties between compression and normal wood : roles of microfibril angle and of lignin

International audienceThis study aims at better understanding the respective influences of specific gravity (γ), microfibril angle (MFA), and cell-wall matrix polymers on viscoelastic vibrational properties of wood in axial direction. The wide variations of properties between normal wood (NW) and compression wood (CW) are in focus. Three young bent trees (Picea abies, Pinus sylvestris and Pinus pinaster) that recovered verticality were sampled. Several observed differences between NW and CW were highly significant in terms of anatomical, physical (γ, shrinkage, CIELab colorimetry), mechanical (compressive strength), and vibrational properties. Specific dynamic modulus of elasticity (E'/γ) decreases with increasing MFA, and Young's modulus (E') can be satisfactorily explained by γ and MFA. Apparently, the type of the cell wall polymer matrix is not influential in this regard. The damping coefficient (tanδ) does not depend solely on MFA of NW and CW. The tanδ - E'/γ relationship evidences that, at equivalent E'/γ, the tanδ of CW is approx. 34% lower than that of NW. This observation is ascribed to the more condensed nature of CW lignins, and this is discussed in the context of previous findings in other hygrothermal and time/frequency domains. It is proposed that the lignin structure and the amount and type of extractives, which are both different in various species, are partly responsible for taxonomy-related damping characteristics