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Carleman-Based Reconstruction Algorithm on a wave Network
No full textInternational audienceIn the context of a network of vibrating strings, modelled by interconnected linear partial differential equations, we are interested in the reconstruction of a zeroth order term of each one-dimensional wave equation involved, using some appropriate external boundary measurements. More precisely, we are interested in an inverse problem set on a tree shaped network where each edge behaves according to the wave equation with potential, external nodes have Dirichlet boundary conditions and internal nodes follow the Kirchoff law. The main goal is the reconstruction of the potential everywhere on the network, from the Neumann boundary measurements at all but one external vertices. Leveraging from the Lipschitz stability of this inverse problem, we aim at providing an efficient reconstruction algorithm based on the use of a specific global Carleman estimate. The proof of the main tool and of the convergence of the algorithm are provided; along with a detailed description of the numerical illustrations given at the end of the article
On the approximation of separable non-convex optimization programs to an arbitrary numerical precision
No full textWe consider the problem of minimizing the sum of a series of univariate (possibly non-convex) functions on a polyhedral domain. We introduce an iterative method with optimality guarantees to approximate this problem to an arbitrary numerical tolerance. At every iteration, our method replaces the objective by a piecewise linear relaxation to compute a dual bound. Since the polyhedral domain in our method remains unchanged, a primal bound is computed by evaluating the cost function on the solution provided by the relaxation. If the difference between these two values is deemed as not satisfactory, the relaxation is locally tightened with an objective-driven refinement procedure, that computes an optimal domain partitioning and the process repeated. By keeping the scope of the update local, the computational burden is only slightly increased from iteration to iteration. The convergence of the method is assured under very mild assumptions, and no NLP nor MINLP solver/oracle is required to ever be invoked to do so. As a consequence, our method presents very nice scalability properties and is little sensitive to the desired tolerance. We provide a formal proof of the convergence of our method, and assess its efficiency in approximating the non-linear variants of five problems: the transportation problem, the uncapacitated facility location problem, the multicommodity flow problem, the multi-commodity network design problem, and the continuous knapsack problem. Our results indicate that the overall performance of our method is competitive to three state-of-the-art mixed-integer nonlinear solvers, often performing better. It also scales better than a naive variant of the method that avoids performing successive iterations in exchange of solving a much larger mixed-integer linear program
TCAD-Based Analysis on the Impact of AlN Interlayer in Normally-off AlGaN/GaN MISHEMTs with Buried p-Region
No full textInternational audienceWith the growing demand for more efficient power conversion and silicon reaching its theoretical limit, wide bandgap semiconductor devices are emerging as a potential solution. For instance, Gallium Nitride (GaN)-based high-electron-mobility transistors (HEMTs) are getting more attention, and several structures for the normally off operation have been proposed. Adding an AlN interlayer in conventional AlGaN/GaN normally on HEMT structures is known to enhance the current density. In this work, the effect of an AlN interlayer in the normally off AlGaN/GaN MISHEMT with a buried p-region was investigated using a TCAD simulation from Silvaco. The added AlN interlayer increases the two-dimensional electron gas density, requiring a higher p-doping concentration to achieve the same threshold voltage. The simulation results show that the overall effect is a reduction in the device’s current density and peak transconductance by 21.83% and 44.4%, respectively. Further analysis of the current profile shows that because of the buried p-region and at high gate voltages, the current flows near the AlGaN/GaN interface and along the insulator/AlGaN interface. Adding an AlN interface blocks the migration of channel electrons to the insulator/AlGaN interface, resulting in a lower current density
Numerical simulation of Lugiato-Lefever equation for Kerr combs generation in Fabry-Perot resonators
No full textLugiato-Lefever equation (LLE) is a nonlinear Schrödinger equation with damping, detuning and driving terms, introduced as a model for Kerr combs generation in ring-shape resonators and more recently, in the form of a variant, in Fabry-Perot (FP) resonators. The aim of this paper is to present some numerical methods that complement each other to solve the LLE in its general form both in the dynamic and in the steady state regimes. We also provide some mathematical properties of the LLE likely to help the understanding and interpretation of the numerical simulation results
On the integration of Dantzig-Wolfe and Fenchel decompositions via directional normalizations
No full textThe strengthening of linear relaxations and bounds of mixed integer linear programs has been an active research topic for decades. Enumeration-based methods for integer programming like linear programming-based branch-and-bound exploit strong dual bounds to fathom unpromising regions of the feasible space. In this paper, we consider the strengthening of linear programs via a composite of Dantzig-Wolfe and Fenchel decompositions. We provide geometric interpretations of these two classical methods. Motivated by these geometric interpretations, we introduce a novel approach for solving Fenchel sub-problems and introduce a novel decomposition combining Dantzig-Wolfe and Fenchel decompositions in an original manner. We carry out an extensive computational campaign assessing the performance of the novel decomposition on the unsplittable flow problem. Very promising results are obtained when the new approach is compared to classical decomposition methods
Singularly Perturbed Hybrid Systems for Analysis of Networks with Frequently Switching Graphs
No full textInternational audienceFor a class of hybrid systems, where jumps occur frequently, we analyze the stability of system trajectories in view of singularly perturbed dynamics. The specific model we consider comprises an interconnection of two hybrid subsystems, a timer which triggers the jumps, and some discrete variables to determine the index of the jump maps. The flow equations of these variables are singularly perturbed differential equations and, in particular, a smaller value of the singular perturbation parameter leads to an increase in the frequency of the jump instants. For the limiting value of this parameter, we consider a decomposition which comprises a quasi-steady-state system modeled by a differential equation without any jumps and a boundary-layer system described by purely discrete dynamics. Under appropriate assumptions on the quasi-steady-state system and the boundary-layer system, we derive results showing practical stability of a compact attractor when the jumps occur sufficiently often. As an application of our results, we discuss the control design problem in a network of second-order continuous-time coupled oscillators, where each agent communicates the information about its position to some of its neighbors at discrete times. Using the results developed in this article, we show that if the union of the communication graphs being used for information exchange between agents is connected, then the oscillators achieve practical consensus.</div
Active disturbance rejection control for four-wire inverters in standalone renewable resources-based microgrid -islanded microgrids ADRC-based control-
No full textInternational audienceThis paper presents an active disturbance rejection control (ADRC) approach for three-phase four-legs voltage source inverters (FL-VSIs) in a standalone renewable energy resources (RES)-based islanded microgrid. The key purpose of the proposed approach is to improve the control robustness against load-side disturbances, power supply parameters uncertainties, and faulty operating conditions. Indeed, a notable benefit of ADRC is its ability to operate effectively without the need for precise knowledge of disturbance characteristics or accurate modeling and FL-VSI parameters. As compared with conventional PI controllers, this advanced control strategy allows improving the voltage waveforms quality and conforming to existing power quality standards and metrics while using only output voltage sensors. Extensive simulations on Matlab/Simulink software have been conducted to assess the effectiveness of the proposed approach
50 Gbit/s Transmission at 850 nm with a Surface-Normal Electroabsorption Modulator
No full textInternational audienceWe demonstrate 50 Gbit/s modulation at 850 nm of an AlGaAs surface normal electro-absorption modulator with more than 15 dB extinction ratio and an electro-optical bandwidth of 33 GHz. Propagation over 2 km of standard SMF is demonstrated
Electrical Sensing of Molecular Spin State Switching in a Spin Crossover Complex Using an Organic Field‐Effect Transistor
No full textInternational audienceAn organic semiconductor – spin crossover polymer composite heterostructure is fabricated, and it is integrated into an organic field-effect transistor (OFET) with the aim to achieve electrical sensing of molecular spin state switching events. The OFETs display ≈50–70% increase in drain-source current intensity when going from the low spin (LS) to the high spin (HS) state. This phenomenon is reversible without apparent fatigue and the application of a gate voltage significantly enhances the sensing sensitivity. Capacitance measurements and finite element calculations allow identifying mechanical stress, induced by the spin state switching, at the origin of the transistor response. These results open up appealing perspectives for the integration of spin crossover molecules into technological applications, such as soft robotics
Porohyperelastic modeling of collagen-gel responses to periodic pressure actuation shows that embedded senescent fibroblasts induce tissue softening associated with fibrous-network reorganization
No full textInternational audienceThe poroelastic properties of tissues regulate molecular transport and mechanical signaling, yet their evolution during aging remains poorly understood. In particular, senescent fibroblasts accumulate in aged tissues, contributing to extracellular matrix (ECM) remodeling, but their impact on tissue mechanics and permeability is unclear. In this study, we developed a microfluidic-based in vitro model to assess the poroelastic properties of collagen gels embedded with senescent fibroblasts over time. Our approach integrates periodic pressure actuation with real-time pressure monitoring in a sealed air cavity, enabling the detection of fluid permeation and solid matrix deformations. We analyze our data using analytical and numerical models based on a porohyperelastic framework. This framework combines compressible Neo-Hookean elasticity with the Kozeny-Carman permeability relationship. We demonstrate that senescent fibroblasts induce a progressive softening of the ECM without altering its permeability. Immunostaining reveals that this softening correlates with structural reorganization of the collagen network, characterized by increased branching and network remodeling. Our findings provide insights into the biomechanical effects of senescent fibroblasts on ECM homeostasis. We further argue that our platform offers a unique solution to investigate ECM remodeling not only in aging but also fibrosis, cancer progression, or regenerative medicine strategies