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    Representativeness of the Natura 2000 network for preserving plant biodiversity in the European Union

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    International audienceThe Natura 2000 (N2K) network of protected areas is one of the main tools for area‐based conservation in the European Union (EU), yet its role in preserving plant biodiversity requires better understanding. We examined data kept in the European Vegetation Archive from over 1.2 million vegetation plots and obtained over 14.2 million plant species occurrences. To test the N2K network's representativeness of plant species gamma diversity, we compared the number and percentage of native and conservation priority species in‐ and outside the N2K network throughout the EU and for individual countries, biogeographical regions, and combinations thereof. We then determined whether N2K sites hosted more species than sites outside the network with the species–area relationship. Overall, almost 90% of the native vascular plant species occurred at least once in the N2K network. Yet, significant variation exists across countries and biogeographical regions—from 0% of species in the Boreal region of Lithuania, to 98% in the Alpine region of Croatia—indicating that local N2K sites are not equally representative of the regional gamma diversity. Nonetheless, the N2K network contains more species than land outside the network when area is taken into account. The planned expansion of the N2K network, as mandated by the European Biodiversity Strategy for 2030, should prioritize areas with currently underrepresented elements of the EU vascular flora.Representatividad de la red Natura 2000 para la conservación de la diversidad vegetal en la Unión Europea Resumen La red Natura 2000 (N2K) de áreas protegidas es una de las principales herramientas para la conservación basada en áreas de la Unión Europea (UE), pero su papel en la preservación de la biodiversidad vegetal requiere una mejor comprensión. Analizamos los datos conservados en el Archivo Europeo de Vegetación de más de 1.2 millones de parcelas de vegetación y obtuvimos más de 14.2 millones de ocurrencias de especies vegetales. Para comprobar la representatividad de la red N2K en cuanto a la diversidad gamma de especies vegetales, comparamos el número y el porcentaje de especies autóctonas y prioritarias para la conservación dentro y fuera de la red N2K en toda la UE y para cada país, región biogeográfica y combinaciones de ambas. A continuación, determinamos si los sitios N2K albergaban más especies que los sitios fuera de la red con la relación especie‐área. En general, casi el 90% de las especies de plantas vasculares autóctonas aparecieron al menos una vez en la red N2K. Sin embargo, existen variaciones significativas entre países y regiones biogeográficas, desde el 0% de las especies en la región boreal de Lituania hasta el 98% en la región alpina de Croacia, lo que indica que los sitios locales de la red N2K no representan de igual manera la diversidad gamma regional. No obstante, la red N2K contiene más especies que las zonas fuera de la red si se tiene en cuenta la superficie. La ampliación prevista de la red N2K, según lo dispuesto en la Estrategia Europea de Biodiversidad para 2030, debería dar prioridad a las zonas con elementos actualmente infrarrepresentados de la flora vascular de la UE

    Gurson revisited and multiscale-multimechanisms modeling

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    International audienceDuctile fracture of metallic alloys is mainly attributed to initiation, growth and coalescence of micrometric voids. In 1977, Gurson's kinematic limit analysis of the hollow sphere provided an analytical upper bound of the yield surface in the case of fully plastic flow: Gurson's famous porous plasticity model. But in the case of flow with a conical rigid section, Gurson only fitted an empirical equation to his "data points". In 2004, the numerical limit analysis methods developed by Pastor et al. pointed out the existence of a corner of the yield surface on the hydrostatic axis that is not obtained with the empirical equation. The two parameters of Rousselier's thermodynamically-derived model provide a good fit to Gurson's data points in both cases of fully plastic flow and flow with rigid section, simultaneously. It is of utmost importance for ductile fracture modeling as void coalescence involves a transition from fully plastic flow to flow with rigid section. This model yield surface shows a corner with the right slope -3∕2 corresponding to void coalescence and strain localization in a band normal to the main loading direction. In shear-dominated loadings, rotation and flattening of micrometric voids is also observed. It is usually modeled either with uncoupled failure criteria or with porous plasticity. In the first approach, criteria depending on the third invariant of the stress tensor: the Lode variable, have been developed. In porous plasticity, a second porosity was added to the yield criterion by Gologanu, Madou, Leblond and Morin (1993, 1994, 2012). In this work, the two approaches are combined with a very simple equation for the second porosity evolution depending on the Lode variable. The novelty lies in applying void nucleation, growth, rotation and flattening models also to the secondary nanometric voids that are observed inside the grains and in microscopic shear bands. At this latter scale, a modified Lode variable is used depending on the resolved shear and normal stresses of each slip system. Multiscale modeling is thus required. The dissipative Coulomb-Rousselier-Luo (2014) failure model at the slip system scale is also considered for ductile fracture without voids observed in aluminum alloys. The use of reduced texture polycrystalline models is a good compromise between macroscopic plasticity and crystal plasticity finite element method. Finite element calculations of a notched specimen are performed to illustrate the effects of the various damage models

    A Poisson-Alekseev-Gröbner formula through Malliavin calculus for Poisson random integrals

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    In this paper, we establish an Alekseev--Gröbner formula for stochastic differential equations (SDEs) driven by a Poisson random measure, which express the global error between a functional of two processes solution of SDEs started at the same initial condition, in terms of the infinitesimal error (i.e, the difference between the SDEs coefficients). In particular, we consider the situation where the flow process is only assumed to be jointly stochastically continuous with respect to space and time. Our proof relies on a new approach for the definition of the Skorohod--Poisson integral to treat the anticipating term appearing in the formula, based on a definition of the Malliavin derivative on a class of smooth random variables, instead of the more standard polynomial chaos approach

    Residual stress determination in steel crash box

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    International audienceResidual stress determination in steel crash bo

    Linking absolute environmental sustainability assessments to the sustainability transition of local policies: a case study of the Metropolis of Lyon

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    International audienceLocal policies guiding sustainability transition uses targets. To be science-based, their definition can follow the principles of Absolute Environmental Sustainability Assessment. A way to define them is to use Planetary Boundaries (PB) translation methods, as they provide a systemic assessment of the environmental carrying capacities affected by a given territory. We reviewed 75 academic and non-academic publications that have carried out PB translations at the territorial level. Most of these publications aimed to guide local sustainability transitions. Yet, they did not systematically use absolute targets resting on environmental carrying capacities but rather privileged objectives originating from institutions. This may be because PB were not designed to be used operationally as local science-based targets, unlike Earth System Boundaries (ESB) framework, which aims to set operational science-based targets for local policies. There is a need to test the operationality of ESB indicators at local level. However, we have not yet identified any ESB translations in the review. In collaboration with the Metropolis of Lyon, we have tested a translation of 4 ESB indicators at the level of the metropolis of Lyon to assess impacts on climate change, biosphere functional integrity, water flows and nutrient cycles.It validates that ESB translations can set local science-based targets, some of which can be used as such, like the minimum ecosystem area to maintain functionality, or translated into pressures allocated to territories, such as the 1.5°C climate target. However, a limitation is that some of the indicators provided are not currently usable in a consumption-based analysis. We also tested that this ESB translation can enrich planning documents and local policies, especially those related to land use and climate change commitments. This analysis shows the potential and improvements needed for ESB translations to set operational, science-based targets for local policies

    Impact of time and spatial discretization on adjoint operators: Example of stationary and transient saturated flows

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    International audienceThis study compares the continuous (differentiate - then - discretize) and discrete (discretize - then - differentiate) adjoint derivation approaches in the context of adjoint-based automatic optimization. The objective is to study some of the pitfalls associated with spatial and temporal discretization of the adjoint state method, the accuracy of the resulting gradient estimate, and its impact on the convergence cost to reach the optimum solution. It is illustrated in the context of a classical and well documented saturated flow problem. We first present insights of the complete formulations and discretizations of the saturated transient and stationary flow equations, the continuous adjoint equations and their counterparts the discrete adjoint equations for the finite volume method, showing it on the example of Voronoi type mesh. The reference gradient to check both derivation and implementation is computed by finite difference approximation. The consistency between the continuous and discrete adjoint methods is found to depend on the discretization scheme used to solve the forward problem. The time discretization scheme used in the forward problem is preserved in the adjoint equations, and affects both the adjoint terminal condition and the gradient expressions. This is not apparent in the continuous approach. Reproductible numerical applications are provided through the PyRTID python code. The use of a variable time step affects the time derivative of the adjoint equations, and also impacts the analytical expression of the gradient with respect to the initial hydraulic head (initial state). The discretization of the adjoint sources is also critical when simulated values are interpolated both spatially and temporally to match observations. The derivations become more complex when observation errors are correlated and when the observation sampler is non-linear. Numerical experiments show that the use of an incorrect adjoint formulation can lead to incorrect gradients with shifts in both amplitude and localization. Investigation of agreement with the finite difference approximation shows that, if implemented correctly, the residuals between the adjoint state method and the finite difference gradients must be white noise following a zero-centered Gaussian distribution with a standard deviation several orders of magnitude smaller than the gradient values. Mesh refinement has no effect on the gradient accuracy. The main conclusion is that the discretize-then-differentiate approach is constrained on the discretized space contrary to the differentiate-then-discretize as the former integrates the discretization of the forward problem. The discretize-then-differentiate approach makes the derivation more explicit, particularly with respect to boundary conditions, and it is therefore advised regardless of the problem at hand

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