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Third-order sectorially A-stable alternating implicit Runge-Kutta schemes
No full textInternational audienceWe design pairs of six-stage, third-order, alternating implicit Runge--Kutta (RK) schemes that can be used to integrate in time two stiff operators by an operator-splitting technique. We also design for each pair a companion explicit RK scheme to be used for a third, nonstiff operator in an implicit-explicit (IMEX) fashion. The main application we have in mind is (non)linear parabolic problems, where the two stiff operators represent diffusion processes (for instance, in two spatial directions) and the nonstiff operator represents (non)linear transport. We identify necessary conditions for linear sectorial A(\alpha)-stability by considering a scalar ODE with two (complex) eigenvalues lying in some fixed cone of the half-complex plane with nonpositive real part. We show numerically that it is possible to achieve A(0)-stability when combining two operators with negative eigenvalues, irrespective of their relative magnitude. Finally, we show by numerical examples including two-dimensional nonlinear transport problems discretized in space using finite elements that the proposed schemes behave well
Fairness by design in shared-energy allocation problems
No full textInternational audienceThis paper studies how to aggregate prosumers (or large consumers) and their collective decisions in electricity markets, with a focus on fairness. Fairness is essential for prosumers to participate in aggregation schemes. Some prosumers may not be able to access the energy market directly, even though it would be beneficial for them. Therefore, new companies offer to aggregate them and promise to treat them fairly. This leads to a fair resource allocation problem. We propose to use acceptability constraints to guarantee that each prosumer gains from the aggregation. Moreover, we aim to distribute the costs and benefits fairly, taking into account the multi-period and uncertain nature of the problem. Rather than using financial mechanisms to adjust for fairness issues, we focus on various objectives and constraints, within decision problems, that achieve fairness by design. We start from a simple single-period and deterministic model, and then generalize it to a dynamic and stochastic setting using, e.g., stochastic dominance constraints
Efficiency and equity in a socially-embedded economy
No full textInternational audienceA model that only focuses on economic relations, and in which efficiency and equity are defined in terms of resource allocation may miss an important part of the picture. We propose a canonical extension of the standard general equilibrium model that embeds economic activities in a larger game of social interactions. Such a model combines general equilibrium effects with social multiplier effects and considerably enriches the analysis of efficiency and equity. Efficiency involves coordination between economic and social interactions, may depend on social norms, and may strongly interact with the distribution of resources. Equity can be defined in a comprehensive, socioeconomic way, and a decomposition into an economic and a social component is possible
Gaussian framework and optimal projection of weather fields for prediction of extreme events
No full text40 pages, 11 figures, 6 tablesInternational audienceExtreme events are the major weather related hazard for humanity. It is then of crucial importance to have a good understanding of their statistics and to be able to forecast them. However, lack of sufficient data makes their study particularly challenging. In this work we provide a simple framework to study extreme events that tackles the lack of data issue by using the whole dataset available, rather than focusing on the extremes in the dataset. To do so, we make the assumption that the set of predictors and the observable used to define the extreme event follow a jointly Gaussian distribution. This naturally gives the notion of an optimal projection of the predictors for forecasting the event. We take as a case study extreme heatwaves over France, and we test our method on an 8000-year-long intermediate complexity climate model time series and on the ERA5 reanalysis dataset. For a-posteriori statistics, we observe and motivate the fact that composite maps of very extreme events look similar to less extreme ones. For prediction, we show that our method is competitive with off-the-shelf neural networks on the long dataset and outperforms them on reanalysis. The optimal projection pattern, which makes our forecast intrinsically interpretable, highlights the importance of soil moisture deficit and quasi-stationary Rossby waves as precursors to extreme heatwaves
A Godunov-type scheme and a relaxation scheme for second-order turbulence-moment models
No full textInternational audienceA Godunov-type scheme and a relaxation scheme are presented to approximate discrete solutions of the convective subsystem arising from a second-order turbulence model in the incompressible framework. An analytical representation is proposed for the case of the occurrence of a laminar zone. Numerical tests of the two schemes and a comparison with the Rusanov scheme complete the paper
Information campaigns and ecolabels by environmental NGOs: Effective strategies to eliminate environmentally harmful components?
No full textInternational audienceEnvironmental nongovernmental organizations (NGOs) are increasingly using strategies to encourage firms to eliminate product components (e.g., palm oil) that are harmful to the environment (e.g., rainforests) or to replace them with NGO‐certified sustainable components. Under what conditions do NGOs' information and ecolabeling strategies succeed in eliminating certain harmful components when these components contribute to the intrinsic quality of a product? The paper addresses these questions using a model of two‐dimensional vertical product differentiation in a market with consumers either informed or uninformed about the environmental quality of products and two firms that initially offer a product with the harmful component and a harmful component‐free product. We show that the information campaign plays a crucial and effective role in improving environmental quality, although the optimal share of informed consumers for the NGO is large but not always 100%. Ecolabeling cannot replace the information campaign. It is only a complementary tool to an intensive information campaign. Used together, they can succeed in triggering the substitution of the certified sustainable component for the harmful one
Numerical homogenization of fibrous composites within the framework of 3d elasticity: reducing the number of unknowns for the case of very high aspect ratio fibers
No full textWe propose here to extend the equivalent inclusion method developed in [6] for homogenization of fibrous composites, this time within the framework of 3d linear elasticity. The method previously developed within the framework of conductivity was shown to be accurate and efficient. In the case of linear elasticity, the dimension spaces are higher, but the method can be extended without increasing hugely the cost. The main idea is to find the form of the polarization field in the fibers, and to accurately compute the interactions between cylinders. The method again permits a huge reduction of number of unknowns, comparing to the traditional full field methods such as finite element method and fast Fourier transform based method. The order of magnitude of the reduction of unknowns can be around 10,000 . We here implement the method in periodic boundary conditions in order to compute homogenized stiffnesses of microstructures containing cylinders whose aspect ratio goes from 40 to 400
The heterogeneous impact of the EU-Canada agreement with causal machine learning
No full textThis paper introduces a causal machine learning approach to investigate the impact of the EU-Canada Comprehensive Economic Trade Agreement (CETA). We propose a matrix completion algorithm on French customs data to obtain multidimensional counterfactuals at the firm, product and destination levels. We find a small but significant positive impact on average at the product-level intensive margin. On the other hand, the extensive margin shows product churning due to the treaty beyond regular entry-exit dynamics: one product in eight that was not previously exported substitutes almost as many that are no longer exported. When we delve into the heterogeneity, we find that the effects of the treaty are higher for products at a comparative advantage. Focusing on multiproduct firms, we find that they adjust their portfolio in Canada by reallocating towards their first and most exported product due to increasing local market competition after trade liberalization. Finally, multidimensional counterfactuals allow us to evaluate the general equilibrium effect of the CETA. Specifically, we observe trade diversion, as exports to other destinations are re-directed to Canada
Hoping for the best while preparing for the worst in the face of uncertainty: a new type of incomplete preferences
No full textWe propose and axiomatize a new model of incomplete preferences under uncertainty, which we call hope-and-prepare preferences. Act f is considered more desirable than act g when, and only when, both an optimistic evaluation, computed as the welfare level attained in a best-case scenario, and a pessimistic one, computed as the welfare level attained in a worst-case scenario, rank f above g. Our comparison criterion involves multiple priors, as best and worst cases are determined among sets of probability distributions, and is, generically, less conservative than Bewley preferences and twofold multi-prior preferences, the two ambiguity models that are closest to ours
