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Target controllability for a minimum time problem in a trait-structured chemostat model
No full textIn this paper, we consider a minimum time control problem governed by a trait-structured chemostat model including mutation and one limiting substrate. Our first main result proves the well-posedness of the control-to-state mapping. We subsequently analyze the class of {\it{auxostat-type controls}}, feedback laws designed to regulate substrate concentration, and prove that the corresponding solutions converge to a stationary state of the system. These convergence results are used to show the reachability of a target set corresponding to the selection of a population with a low weighted averaged half-saturation constant. Finally, we show the existence of an optimal control for the minimum time problem associated with reaching the target set. These theoretical findings are completed by numerical simulations
Conjecture de Kakeya et algèbres de von Neumann de réseaux de rang supérieur
No full textIf the non-commutative L p space of SLn(Z) has the completely bounded approximation property for some non-trivial value of p, then some form of the Kakeya conjecture holds in dimension d, for all d ≤ n+12 . The proof relies on a spherical analogue of the following question in Euclidean harmonic analysis, that we raise and investigate: does a radially symmetric Fourier multiplier that is bounded on Lp(R d ) for some p ̸ = 2 necessarily have a continuous symbol? We leave the question open, but we prove that the primitive of such function is smooth in the sense of Zygmund, give some necessary conditions for Lp-boundedness in terms of Besov spaces and Littlewood-Paley decomposition for the symbol, and observe that a negative answer implies some form of the Kakeya conjecture in dimension d. We then provide spherical forms of these results, which, when combined with a refinement of Lafforgue's rank 0 reduction, leads to the claimed result.</div
Automatic Physically-Based Sim2Real for Tactile Images through Differentiable Path-Tracing Rendering
No full textInternational audienceHigh-fidelity simulation of vision-based tactile sensors is essential for developing data-driven robotic manipulation algorithms. However, a significant sim-to-real gap persists due to the difficulty in modeling complex optical effects, such as refraction through protective glass layers, and in accurately estimating physical parameters like sensor pose and lighting. To bridge this gap, we introduce a novel, fully differentiable pipeline for visual tactile simulation. Leveraging a differentiable path tracer, our method optimizes critical parameters—including camera pose, lighting conditions, and object texture—directly from just three real images. This approach achieves highly realistic simulations with physically accurate light transport and glass refraction. We validate our method through a comprehensive benchmark against real-world data, demonstrating state-of-the-art sim-to-real accuracy. We also enable novel applications, such as mesh reconstruction from a single tactile image via inverse rendering. To overcome the computational cost of path tracing, we further use a image-to-image translation model. This model uses high-fidelity simulated data alongside Normalized Object Coordinate Space (NOCS) maps as input, preserving crucial deformation information while enabling rapid inference
Critical assessment of the reliability and provenance of global plastic pollution flow statistics
No full textInternational audienc
On the parameterized complexity of the Maker-Breaker domination game
No full textSince its introduction as a Maker-Breaker positional game by Duchêne et al. in 2020, the Maker-Breaker domination game has become one of the most studied positional games on vertices. In this game, two players, Dominator and Staller, alternately claim an unclaimed vertex of a given graph G. If at some point the set of vertices claimed by Dominator is a dominating set, she wins; otherwise, i.e. if Staller manages to isolate a vertex by claiming all its closed neighborhood, Staller wins. Given a graph G and a first player, Dominator or Staller must have a winning strategy. We are interested in the computational complexity of determining which player has such a strategy. This problem is known to be PSPACE-complete on bipartite graphs of bounded degree and split graphs; polynomial on cographs, outerplanar graphs, and block graphs; and in NP for interval graphs. In this paper, we consider the parameterized complexity of this game. We start by considering as a parameter the number of moves of both players. We prove that for the general framework of Maker-Breaker positional games in hypergraphs, determining whether Breaker can claim a transversal of the hypergraph in k moves is W[2]-complete, in contrast to the problem of determining whether Maker can claim all the vertices of a hyperedge in k moves, which is known to be W[1]-complete since 2017. These two hardness results are then applied to the Maker-Breaker domination game, proving that it is W[2]-complete to decide if Dominator can dominate the graph in k moves and W[1]-complete to decide if Staller can isolate a vertex in k moves. Next, we provide FPT algorithms for the Maker-Breaker domination game parameterized by the neighborhood diversity, the modular width, the P4-fewness, the distance to cluster, and the feedback edge number
Competing effects of charge-carrier and impurity scattering limiting phonon heat conduction in heavily-doped silicon
No full textWith respect to undoped semiconductors, thermal transport by phonons is limited by two additional mechanisms when doping increases: charge-carrier and impurity scattering. Previous works provided contradicting conclusions on the dominant doping-induced scattering mechanism in silicon. In this work, we clarify the competing roles of impurity and charge-carrier scatterings of phonons in the reduction of the lattice thermal conductivity in n-and p-doped silicon, by comparing experimental results obtained with the 3ω method and predictive DFT-based calculations for a large set of doping concentrations and a wide temperature range. The analysis allows delimiting the doping and temperature ranges where (i) extrinsic scattering surpasses intrinsic (phonon-phonon and phonon-isotope) one and (ii) one of the two doping-induced mechanisms plays the dominant role. We observe that the experimental setup impacts both the thermal conductivity value and the critical doping concentration at which the thermal conductivity is reduced by half
Influence of the starting powder and ball milling on microstructure and mechanical properties of Al0.3CoCrFeNi high entropy alloy, obtained by spark plasma sintering
No full textInternational audienceThis work investigates the effect of ball milling on the microstructure and mechanical properties of Al0.3CoCrFeNi high entropy alloy (HEA), starting from two different powders: pre-alloyed powders obtained by gas atomization and a pure elemental mixture. The powders were densified using spark plasma sintering (SPS). For the atomized powders, ball milling leads to the formation of a heterogeneous core–shell structure that remains after sintering, with grain sizes ranging from 1 to 10 μm in the cores and less than 1 μm in the shells. Slight air contamination during the milling stage promoted the formation of nanometric AlN at grain boundaries within the shells, which inhibited grain coarsening during SPS. Additionally, Al₂O₃ precipitates formed at prior particle boundaries (PPBs). Grain size after sintering is refined from 13 μm to 3.3 μm (without and with 28 h milling of atomized powder), resulting in an increase in hardness (from 182 to 280 HV₂), yield strength (from 370 to 615 MPa), and ultimate tensile strength (from 653 to 770 MPa), accompanied by a loss in ductility (from 54 % to 18 %). However, below 28 h of milling, the strengthening is not as high as would be expected from the Hall-Petch effect. PPBs have been identified as crack initiation sites, leading to lower-than-expected tensile properties. This negative effect of PPBs can be decreased by increasing powder particle size through prolonged milling, thereby reducing PPBs density. In contrast, mechanical activation of elemental powder mixture leads to the formation of an ultrafine-grained microstructure with dispersed nanometric B2 and Al₂O₃ phases. This elaboration route allows a higher mechanical strength (1175 MPa) and hardness (512 HV2), but significantly lower ductility (2 %). The random distribution of minor secondary phases does not lead to PPB-related failure. This study demonstrated the strong influence of starting powders on the milling-induced microstructure, phase formation, and the resulting strengthening mechanisms governing the mechanical behavior of Al0.3CoCrFeNi HEAs
A Cahn--Hilliard--Willmore phase field model for non-oriented interfaces
No full textInternational audienceWe investigate a new phase field model for representing non-oriented interfaces, approximating their area and simulating their area-minimizing flow. Our contribution is related to the approach proposed in arXiv:2105.09627 that involves ad hoc neural networks. We show here that, instead of neural networks, similar results can be obtained using a more standard variational approach that combines a Cahn-Hilliard-type functional involving an appropriate non-smooth potential and a Willmore-type stabilization energy. We show some properties of this phase field model in dimension and, for radially symmetric functions, in arbitrary dimension. We propose a simple numerical scheme to approximate its -gradient flow. We illustrate numerically that the new flow approximates fairly well the mean curvature flow of codimension or interfaces in dimensions and