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Détection de contact de haut degré et modèle mixte de tige pour la simulation numérique prédictive d'assemblées de fibres emmêlées
No full textThis thesis focuses on the study of elastic fibre assemblies through numerical simulations. Generally, the focus is put on the quality of the geometry of the structures rather than the produced forces. Indeed, while the state of the art offers impressive visual simulations of fibre assemblies, especially in the computer graphic community, the study of the forces at play, in contact for example, remains sparse, even at the experimental level, where the research focuses mostly on isotropic granular medium rather than fibrous medium. The study of the forces is however important in many domains, haptic feedback or sound generation to name a few. The objective of this thesis is therefore to provide robust and predictive fibres assemblies simulation tools both in terms of geometry and forces.We start with an overview of the state of the art in elastic fibre modelling and the combination with frictional contact. This introduction concludes by underlining the issues caused by a low order contact detection method – that is a method relying on segments primitive – on the forces computed during a simulation.This motivates a first numerical contribution, the development of high order contact detection methods – that is methods relying on C2 curves primitives – in two and three dimensions, adapted to high order rod model. We show their comparative efficiency to low order methods. A second factor then proves limiting, the cubic complexity to update the dynamic of the rod. The second numerical contribution is a new development, more general, robust and optimised in two dimensions of a curvature based discretisation of a rod model. This is called a mixed model because it uses both position and curvature as degrees of freedom. For the generalisation to the third dimension, we present a general method, based on the results in the two dimension case as well as the specific issues that arise with the extra dimension. While some ways to address the issues are proposed, the global model remains a work in progress.In a second time, we present different contributions in the domain of physics. We start by calibrating and validating the simulator on simple experiments, which underline the effect of friction in a controlled manner. This allows to study tangled fibre assemblies ranging from a dozen to thousands of elements in contact. We study the absorption and dissipation properties of a meta material with random structure in two dimensions. We show that despite the lack of a regular structure, it is possible to control the dissipative properties of the material as a function of the properties of its constitutive elements. We conclude with an application in three dimensions, the combing of curly hair. Despite being a preliminary study, it illustrates the contributions brought in by this work.Cette thèse porte sur la modélisation numérique d’assemblées de fibres élastiques. En général, l’accent est mis sur la qualité de la géométrie des structures plutôt que celle des forces produites. En effet, si l’état de l’art offre des résultats impressionnants pour la simulation visuelle d’assemblées de fibres, particulièrement dans le domaine de l’informatique graphique, il y a peu d’études des forces en jeu, notamment des forces de contact, même au niveau expérimental, où la recherche s’est concentrée sur les milieux granulaires isotropes plutôt que sur les milieux fibreux. Pourtant, l’étude des forces est importante dans plusieurs domaines, le retour haptique, ou la génération de son pour en citer quelques uns. L’objectif de cette thèse est donc de fournir des outils robustes et prédictifs pour la simulation de milieux fibreux en géométrie et en forces.Nous commençons par un tour de l’état de l’art sur la modélisation de tiges élastiques et de leur combinaison avec du contact frottant. Cette introduction se conclut par la mise en avant des problèmes causés par une méthode de détection de contact de bas degré – c’est-à-dire utilisant des primitives en lignes brisées – sur les forces calculées durant la simulation.Cela motive une première contribution numérique, la mise au point de méthodes de détection de contact de haut degré – c’est-à-dire utilisant pour primitives des courbes C 2 – en deux et trois dimensions, adaptées à des modèles de tiges de haut degré. Nous montrons leur efficacité en temps comparable à des méthodes de bas degré. Un second facteur se révèle ensuite limitant, la complexité cubique de mise à jour du modèle de tige utilisé. La seconde contribution numérique est donc la mise au point d’un modèle de tige plus général, robuste et optimisé en deux dimensions dont la discrétisation se fait en courbure. Nous l’appelons un modèle mixte car il utilise des degrés de liberté en position et en courbure. Pour la généralisation à la troisième dimension, nous présentons la méthode générale fondée sur les résultats obtenus en deux dimensions, ainsi que les problèmes spécifiques que cette dimension supplémentaire soulèvent. Si des propositions pour résoudre ces problèmes sont faites, le résultat d’ensemble reste un projet en cours.Ensuite nous proposons différentes contributions dans le domaine de la physique. Nous commençons par calibrer et valider le simulateur sur des expériences simples qui mettent en jeu les effets du frottement de façon contrôlée. Nous nous concentrons enfin sur l’étude d’assemblées de fibres emmêlées allant de la dizaine aux milliers d’éléments en contact. Nous étudions les propriétés d’absorption et de dissipation d’un méta matériau à structure aléatoire en deux dimensions, qui montre que malgré l’absence de régularité dans la structure, il est possible de contrôler l’écrasement et la dissipation du matériau en fonction des caractéristiques de ses éléments constitutifs. Nous ouvrons enfin sur une application en trois dimensions avec le peignage de cheveux bouclées. Bien que préliminaire, cette étude permet de souligner les apports des contributions numériques de ce travail
Optimisation de formes distributionnellement robuste à des changements de distributions
No full textThis article aims to introduce the paradigm of distributional robustness from the field of convex optimization to tackle optimal design problems under uncertainty. We consider realistic situations where the physical model, and thereby the cost function of the design to be minimized depend on uncertain parameters. The probability distribution of the latter is itself known imperfectly, through a nominal law, reconstructed from a few observed samples. The distributionally robust optimal design problem is an intricate bilevel program which consists in minimizing the worst value of a statistical quantity of the cost function (typically, its expectation) when the law of the uncertain parameters belongs to a certain "ambiguity set". We address three classes of such problems: firstly, this ambiguity set is made of the probability laws whose Wasserstein distance to the nominal law is less than a given threshold; secondly, the ambiguity set is based on the first-and second-order moments of the actual and nominal probability laws. Eventually, a statistical quantity of the cost other than its expectation is made robust with respect to the law of the parameters, namely its conditional value at risk. Using techniques from convex duality, we derive tractable, single-level reformulations of these problems, framed over augmented sets of variables. Our methods are essentially agnostic of the optimal design framework; they are described in a unifying abstract framework, before being applied to multiple situations in density-based topology optimization and in geometric shape optimization. Several numerical examples are discussed in two and three space dimensions to appraise the features of the proposed techniques
Model guided development of astaxanthin production in microalgae biofilms
No full textInternational audienceBiofilm systems present a promising approach for microalgae production by reducing water and energy costs while improving productivity and operational efficiency. However, this technology is still in its infancy, particularly for high-value compounds production. To confirm its potential at large scale, mathematical models are required to better understand biofilm behavior under varying environmental conditions and to predict productivity. In this study, a dynamic model was developed to estimate astaxanthin production by Haematococcus lacustris biofilms on a rotating system. It incorporates well-established dynamics, accounting for nitrogen limitation and photoacclimation, while introducing a novel hypothesis correlating astaxanthin dynamics with those of chlorophyll. The model predicts key biofilm traits, including biomass density, intracellular nitrogen, and pigment quotas, demonstrating its ability to simulate changes in light and nitrogen conditions and assess their impact on biofilm physiology. Furthermore, the possibility of dynamically altering the life cycle of H. lacustris within a biofilm was demonstrated both experimentally and mathematically, enabling reversible transitions between green and red stages. This reversion facilitates continuous astaxanthin production through repeated harvest and regrowth cycles. This was assessed through the development of an optimization strategy that maximized astaxanthin productivity by adjusting light intensity over time and determining the optimal harvest frequency. The model provides a valuable framework for optimizing astaxanthin production in microalgal biofilms, enabling the development of continuous production systems and supporting the scale-up of biofilm technolog
Energy Replenishment Strategies for Robot Swarms
No full textInternational audienceThe utility of swarms of robots would greatly increase if they could operate over extended periods of time. Here,we consider two strategies for swarms of robots to replenish their energy while performing work in a remote location. Inthe first, each robot commutes to work and replenishes at its base. In the second, some robots perform work, whereas others commute to provide them with energy. We present results from extensive physics-based simulations. The first strategy performs 92.8% of the work at only 12.6% lower energy efficiency than an optimal strategy. The second strategy is beneficial for low charging rates or if the robots providing energy are permitted increased amounts of storage. We provide proof-of-concept validation using the CapBot swarm robot platform
Eagle: Vulnerability and Congestion Aware Software Update Synthesis in Softwarized Networks with a 5G Network Case Study
No full textInternational audienceEffective scheduling of software updates is a significant challenge in network operations and management, particularly when considering specific performance and security requirements. This paper focuses on the synthesis of such software updates in the context of emerging virtualized and softwarized networks, such as 5G network infrastructures, with the objective of ensuring vulnerability avoidance and congestion freedom at any time during the updates. We formalize the update synthesis problem and propose an algorithmic solution, called Eagle, that exploits formal methods and mixed integer linear programming, to achieve optimal solutions. We then complement it with a greedy algorithm to support faster computation. We exemplify our framework considering an implementation of a 5G architecture, as the one described in the ETSI 5123 standard, and which relies on kubernetes. Finally, we evaluate our approach through a large range of realistic ISP topologies from the Topology Zoo dataset, and we also perform extensive experiments on our kubernetes cluster, where we execute the software update sequences generated by our tool. This allows us to discuss the scalability of our approach along with its practical applicability
Mathematical modeling of photoplethysmography: model assessment and validation
No full textPhotoplethysmography (PPG) is a well-known technique employed to assess optically perfused bio-tissue volume changes. A PPG apparatus consists of a light emitter and a receptor. The analysis of the received light is used to infer properties of the illuminated tissues. This paper aims at presenting a novel distributed mathematical model for PPG signals, which combines a poroelastic model of tissue perfusion with a diffusion model for light absorption and scattering. We assume that the tissues undergo small deformations, allowing for a linear poroelastic description of perfusion. Since many PPG devices are applied to the fingertips (due to the rich vascularization in that area) we model the system specifically on the finger, with arterial blood pulse pressure serving as the primary perfusion driver. The numerical discretization of the governing equations is carried out using the finite element method. After calibration of the model, 216k simulations are performed with varying parameters (quasi-Monte Carlo approach). The aggregated results for two key biomarkers, AC/DC PPG amplitude ratio and pulse pressure, are compared against experimental PPG and pulse pressure measurements obtained from 20 volunteers. Within the prescribed parameter ranges, numerical simulations successfully reproduce the AC/DC PPG amplitude biomarker in both the red and infrared wavelengths, with a few outliers observed for the green. Furthermore, in the vicinity of the combined red and infrared measured biomarkers, there are simulated biomarkers whose corresponding pulse pressures closely match the mapped-to-finger measured pulse pressure, with a difference of less than 1 mmHg. This work demonstrates the relevance of the proposed mathematical model for simulating PPG signals and highlights its potential for estimating tissue perfusion parameters, such as arterial pulse pressure
D 4.2-1 Use Case Prototypes
No full textThis report is a deliverable for the ANR SCALER project. It reports on the initial experimentation on deploying and using two of the target microservice benchmarks, namely TeaStore and towards5GS
Modélisation numérique de métasurfaces modulées temporellement avec une méthode de type Galerkin discontinu
No full textInternational audienceThe overarching goal of this work is to propose and develop a novel numerical methodology for the design of time-modulated metasurfaces. Here, we present a first step in this direction with the introduction of a Discontinuous Galerkin (DG) method for the solution of time-domain Maxwell's equations for time-varying materials.L'objectif général de ce travail est de proposer et de développer une nouvelle méthodologie numérique pour la conception de métasurfaces modulées temporellement. Nous présentons ici une première étape vers ce but avec l'introduction d'une méthode Galerkin discontinue (DG) pour la résolution des équations de Maxwell dans le domaine temporel pour les matériaux variables dans le temps
What to Expect when Using DECT NR+
No full textInternational audienceDECT NR+ is the new kid on the block in wireless technologies: it re-purposes the 1.9 GHz Digital Enhanced Cordless Telecommunications (DECT) standard for IoT-type applications. How does DECT NR+ perform in practice and where should we be using it? The ambition of this article is to provide answers to those questions. We start by an overview of the fundamental principles of the physical layer. We then survey the DECT NR+ products on the market today. Using the nRF91 series from Nordic Semiconductor, we conduct a comprehensive set of hands-on power consumption and communication range measurements. Our results place DECT NR+ in a gap in-between existing technologies. Its range is comparable to long range standards such as IEEE 802.15.4g under certain parameter choices: 200 m in an urban setting, 6 km in the most favorable line-of-sight conditions. For higher order Modulation and Coding Schemes, range drops and is rather comparable to Wi-Fi. The nRF9161 draws significant power (at 3.7 V, 220 mA transmitting at +19 dBm, 45 mA receiving), approximately 10× higher than BLE radios. This is likely primarily due to earlystage design inefficiencies and the inherent complexity of the DECT NR+ physical layer, limiting its adoption in batterypowered applications. We conclude that DECT NR+ is particularly appropriate for applications that require a dynamic tradeoff between communication range and data rate, but are not cost-sensitive
Toward unified biomarkers for focal epilepsy
No full textAccurately localizing the epileptogenic network (EpiNet) remains a major barrier to effective epilepsy treatment, largely due to limited mechanistic understanding. The EpiNet is a patientspecific brain network shaped by complex, overlapping pathology. While combining biomarkers can improve localization, it also generates high-dimensional feature data that increases the risk of overfitting and reduces interpretability. We hypothesized that the core epileptogenic dynamics could be captured in a low-dimensional latent space derived from empirical data, without the need to record seizures. From interictal stereo-EEG (SEEG) recordings in 64 patients (29 females), we extracted 260 neuronal features and reduced them to 10 latent components using singular value decomposition. A classifier trained on these 10 components was then simplified into a probabilistic EpiNet model requiring only two components as input. Individual position in this two-dimensional latent space correlated with previously reported classification accuracy (r 2 =0.5), supporting its functional relevance. In three independent patients, the probabilistic model captured time-varying epileptogenic dynamics during sleep-SEEG recordings, corroborated clinical assessments, and achieved peak classification accuracies of 0.63, 0.85, and 0.94. These predictions were independently validated by tensor component analysis. Together, these results provide evidence for a robust low-dimensional representation of epileptogenicity across brain states and pathological substrates. This approach simplifies interpretation, facilitates integration of additional biomarkers, and enables large-scale cohort analyses, establishing a proof of concept for a unified framework for epilepsy biomarkers