Brushed finishes are widely used in architecture, large and small appliances, etc. ANISO aims to develop new digital and manufacturing technologies to produce customized and innovative anisotropic surface finishes. The aim is to go beyond unidirectional and circular surface finishes by allowing the designer to choose the brushing orientation for all surface positions. This freedom makes it possible to design customized and complex anisotropic appearances. Fabricating anisotropic appearances on 3D surfaces with arbitrary, spatially varying, high-definition orientations remains an open problem. We target glossy materials: metals (e.g., aluminum, silver, and gold), plastics (e.g., PETG and PLA), and glass. ANISO's key idea is to use manufacturing processes that directly produce anisotropic surface roughness: Fused Filament Fabrication (FFF) and surface brushing. We plan to develop an algorithm that generates orientable, space-filling trajectories to control the direction of anisotropy at each point. Open-source software will be developed to interactively design and visualize anisotropic appearances with spatially variable directions to democratize the manufacture of this type of appearance. ANISO will enable Industry 4.0 to customize surface finishes and make them unique. Customization will be achieved using a single material that does not require paint or chemicals, making recycling easier. In addition, the surface finish of injection molding could be impacted by ANISO, enabling Industry 4.0 to produce customized parts and unique visuals on a large scale.

One approach aiming at reducing the number of bugs is sound static program analysis. Static analyzers come with a variety of configurations, allowing users to choose different performance-precision trade-offs. The goal of this project is to develop techniques enabling resource-aware static analyses, that will automatically find the best configuration for the analysis in order to yield the most precise results while respecting a provided resource envelope (CPU time, peak memory usage). This project will improve the usability of static analyzers, simplify their use in industrial development cycles (where each cycle has different resource constraints), and develop a computing-within-limits approach to static analysis fitting to a post-Moore’s law era.

Developing and improving CO2 capture and storage (CCS) technologies are essential steps for meeting the global net zero emissions expected by 2050 (Paris agreement, adopted in 2015). The efficiency and safety of such new technologies could be hindered by the presence of fractures. Fracture are among of the primary risk of CO2 leakage. Their structures and connections play a critical role in the dynamics of governing subsurface processes. Numerical simulation is a key tool in order to perform physical process forecasting and risk assessment studies of these new technologies. Building trustworthy predictions require models that accurately describe the subsurface and the various processes over large space time scales. Such simulations are not easily tractable as their computational cost would be prohibitive with classical numerical methods based on quasi uniform meshes and uniform time steps. Therefore, we propose a novel approach based on space time adaptive numerical methods. For a given level of accuracy, STEERS will reduce the computational cost thanks to three main ingredients: 1/ a combined Hybrid High-Order / Discontinuous Galerkin (HHO/DG) method for the spatial discretization on agglomerated meshes; 2/ a posteriori error estimates steered space time mesh adaptivity algorithms; 3/ an implementation of the proposed space time algorithms in an open source parallel library. This library will be validated throughout the project on applications of increasing complexity: from linear problems (Darcy type) to non linear ones (multiphase flow), from small scale problem to large scale ones (up to thousands of fractures).

The aim of this project is to investigate how the inherent heterogeneity of a population of interacting particles affects its capacity for self-organization, via the mathematical analysis of models for interacting particles, and an application to fish collective motion. Despite increasing experimental evidence that a biological system’s heterogeneity impacts its collective behavior, to this day few mathematical models for interacting particles take into account their non-exchangeable nature. To shed light on the role of heterogeneity in the formation of collective patterns, we propose to study the asymptotic behavior of solutions to PDE models for self-organization in heterogeneous populations. To bridge this macroscopic description with microscopic models of interacting systems, we will also contribute to the development of a novel framework for large-population limits of non-exchangeable particle systems. Simultaneously, we will investigate the impact of inter-individual heterogeneity on phase transition between swimming patterns in a population of gregarious fish in a lab environment, in collaboration with a team of physicists.

In very recent years, the structural method has been introduced to build very high-order numerical schemes to solve partial differential equations (PDEs) on compact stencils. A particularity of this finite difference method is that it not only approximates the PDE solution with high order accuracy, but also its derivatives. It relies on defining two independent sets of discrete equations, the physical and the structural equations. The physical equations describe the physics of the problem, i.e. the underlying PDEs. As such, treating problems with specific constraints (for instance, ensuring that some vector field is divergence-free) becomes a matter of adding or modifying a physical equation. The structural equations are responsible for the order of the discretization, and thus their modification makes it possible to treat non-smooth solutions or improve the accuracy on continuous ones. The overarching goal of this project is to extend the structural method to the approximation of hyperbolic systems of balance laws, in at least two space dimensions. In such problems, continuous initial conditions can generate non-smooth solutions in finite time, and multiscale regime changes frequently occur. For instance, such PDEs are widely used in fluid mechanics or electromagnetism. Although the structural method is a general finite difference framework, it is particularly well-suited to such systems. Indeed, the separation between physics and discretization provides a natural setting to construct a scheme that can switch on or off physical and/or structural equations locally and on the fly, depending on the situation. SMEAGOL thus contains two sub-goals: the construction and the adaptation of the structural method.