An Unsplit Monte-Carlo scheme for the resolution of the linear Boltzmann equation coupled to (stiff) Bateman equations

In this paper, we are interested in the resolution of the time-dependent problem of particle transport in a media whose composition evolves with time due to interactions, the only constraint being the use of Monte-Carlo (MC) scheme for the transport phase. A common resolution strategy consists in a splitting between the MC/transport phase and the time discretization scheme/matter evolution phase. After going over and illustrating the main drawbacks of split schemes in a simplified configuration (monokinet-ic/monocomposition problem), we progressively build a new Unsplit MC (UMC) scheme improving the accuracy of the solutions, avoiding numerical instabilities, and less sensitive to time discretization. The new scheme needs two key ingredients: an Unsplit MC solver and a specific change of variable implying an on the fly resolution of a system of ODEs for each MC particle in order to describe along their flight path the time evolution of the matter

Les fonctions de l’écrit intime dans la constitution du héros : Jackson Teller, volonté intime et destin tragique

Bien qu’ultra-violente et basée sur le quotidien de bikers hors-la-loi, la série Sons of Anarchy (FX, 2008-2014) multiplie les références littéraires (William Shakespeare, Edgar Rice Burroughs, Stephen King), mythologique (Œdipe, Prométhée) et bibliques. Oscillant entre l’allusion légère et l’appropriation perspicace, ces mentions troublent les limites entre un espace culturel fictif et un espace culturel réel et sont pour le créateur Kurt Sutter l’occasion de questionner le travail même de l’écriture. Mieux, grâce à la figure du diariste, qui unit par-delà la mort un père et son fils – tous deux rédigeant des carnets intimes –, Sons of Anarchy établit la lecture et l’écriture comme ressources efficientes de son fonctionnement scénaristique. Mais plus encore que des procédés narratifs, ces actes instillent à la série une distance propice autant à l’affirmation d’une volonté intime dans un parcours initiatique – celui suivi par Jax Teller, successivement jeune homme dérouté, prince flamboyant et roi sanguinaire – qu’à l’émergence d’une force tragique – celle entrelaçant ses inconciliables conditions de fils, d’époux, de père et de chef de bande. C’est en cela que les écrits intimes dépassent l’écueil de leur caractère fragmentaire et privé pour devenir de véritables moteurs pour la constitution psychologique et ontologique du héros, grâce à plusieurs fonctions majeures (dialogique, introspective, programmatique et narrative).Despite its ultraviolence and the fact that it is based on the everyday life of outlaws bikers, the TV show Sons of Anarchy (FX, 2008-2014) cites numerous references to literature (William Shakespeare, Edgar Rice Burroughs, Stephen King), mythology (Œdipus, Prometheus) and the Bible. Whether simple hints or insightful appropriations, these mentions blur the limits between a fictional cultural space and a real one in addition to become the opportunity for the creator Kurt Sutter to question the work of writing itself. Moreover, thanks to the diarists, a dead father and his living son, both intimate writers, Sons of Anarchy considers the acts of reading and writing as efficient means for its plot. But, these actions are more than ordinary narrative devices : they instil into the show a relevant gap that leads to assert an intimate will during the initiatory journey of Jax Teller – successively a confuse young man, a brilliant prince and a murderous king – and to rise a tragic might – the same that ties his irreconcilable conditions of son, husband, father and leader. This is how the diaries and the intimate writings fill in their discontinuity and secrecy to help the hero psychological and ontological personality, thanks to their main functions (dialogical, introspective, programmatic and narrative)

Accelerating hypersonic reentry simulations using deep learning-based hybridization (with guarantees)

In this paper, we are interested in the acceleration of numerical simulations. We focus on a hypersonic planetary reentry problem whose simulation involves coupling fluid dynamics and chemical reactions. Simulating chemical reactions takes most of the computational time but, on the other hand, cannot be avoided to obtain accurate predictions. We face a trade-off between cost-efficiency and accuracy: the simulation code has to be sufficiently efficient to be used in an operational context but accurate enough to predict the phenomenon faithfully. To tackle this trade-off, we design a hybrid simulation code coupling a traditional fluid dynamic solver with a neural network approximating the chemical reactions. We rely on their power in terms of accuracy and dimension reduction when applied in a big data context and on their efficiency stemming from their matrix-vector structure to achieve important acceleration factors ($\times 10$ to $\times 18.6$). This paper aims to explain how we design such cost-effective hybrid simulation codes in practice. Above all, we describe methodologies to ensure accuracy guarantees, allowing us to go beyond traditional surrogate modeling and to use these codes as references.Comment: Under revie

Optoelectronic mixer with a photoconductive switch for 1550 nm wavelengths

We demonstrate an optoelectronic mixer based on an ultrafast InGaAs photoconductive switch and its use in an innovative heterodyne detection system for Radio over Fibre transmission. The advantage of the proposed switch is its relatively flat response curve in a wide frequency range up to 67 GHz. Two mixing schemes are presented through I-Q modulated data-stream down-conversion. The data can modulate either the electrical signal or the optical signal. In case the electrical signal is modulated, a mode-locked semiconductor laser diode is used as an optical local oscillator at the self-oscillating frequency of 24.5 GHz. The InP based quantum-dash mode-locked laser emitting in the 1570 nm wavelength range is stabilized by a feedback loop and shows a low phase noise in order to increase the mixing performances of the detection apparatus. In a second experiment, the photoconductive switch is combined with a continuous wave laser to demonstrate the feasibility of down converting an optically provided data-stream with an electrical local oscillator

A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws

In this article we consider one-dimensional random systems of hyperbolic conservation laws. We first establish existence and uniqueness of random entropy admissible solutions for initial value problems of conservation laws which involve random initial data and random flux functions. Based on these results we present an a posteriori error analysis for a numerical approximation of the random entropy admissible solution. For the stochastic discretization, we consider a non-intrusive approach, the Stochastic Collocation method. The spatio-temporal discretization relies on the Runge--Kutta Discontinuous Galerkin method. We derive the a posteriori estimator using continuous reconstructions of the discrete solution. Combined with the relative entropy stability framework this yields computable error bounds for the entire space-stochastic discretization error. The estimator admits a splitting into a stochastic and a deterministic (space-time) part, allowing for a novel residual-based space-stochastic adaptive mesh refinement algorithm. We conclude with various numerical examples investigating the scaling properties of the residuals and illustrating the efficiency of the proposed adaptive algorithm

Uncertainty quantification for kinetic models in socio-economic and life sciences

Kinetic equations play a major rule in modeling large systems of interacting particles. Recently the legacy of classical kinetic theory found novel applications in socio-economic and life sciences, where processes characterized by large groups of agents exhibit spontaneous emergence of social structures. Well-known examples are the formation of clusters in opinion dynamics, the appearance of inequalities in wealth distributions, flocking and milling behaviors in swarming models, synchronization phenomena in biological systems and lane formation in pedestrian traffic. The construction of kinetic models describing the above processes, however, has to face the difficulty of the lack of fundamental principles since physical forces are replaced by empirical social forces. These empirical forces are typically constructed with the aim to reproduce qualitatively the observed system behaviors, like the emergence of social structures, and are at best known in terms of statistical information of the modeling parameters. For this reason the presence of random inputs characterizing the parameters uncertainty should be considered as an essential feature in the modeling process. In this survey we introduce several examples of such kinetic models, that are mathematically described by nonlinear Vlasov and Fokker--Planck equations, and present different numerical approaches for uncertainty quantification which preserve the main features of the kinetic solution.Comment: To appear in "Uncertainty Quantification for Hyperbolic and Kinetic Equations