Quadratic BSDEs with convex generators and unbounded terminal conditions

In a previous work, we proved an existence result for BSDEs with quadratic generators with respect to the variable z and with unbounded terminal conditions. However, no uniqueness result was stated in that work. The main goal of this paper is to fill this gap. In order to obtain a comparison theorem for this kind of BSDEs, we assume that the generator is convex with respect to the variable z. Under this assumption of convexity, we are also able to prove a stability result in the spirit of the a priori estimates stated in the article of N. El Karoui, S. Peng and M.-C. Quenez. With these tools in hands, we can derive the nonlinear Feynman--Kac formula in this context

Hamilton Jacobi Bellman equations in infinite dimensions with quadratic and superquadratic Hamiltonian

We consider Hamilton Jacobi Bellman equations in an inifinite dimensional Hilbert space, with quadratic (respectively superquadratic) hamiltonian and with continuous (respectively lipschitz continuous) final conditions. This allows to study stochastic optimal control problems for suitable controlled Ornstein Uhlenbeck process with unbounded control processes

Adaptive importance sampling with forward-backward stochastic differential equations

We describe an adaptive importance sampling algorithm for rare events that is based on a dual stochastic control formulation of a path sampling problem. Specifically, we focus on path functionals that have the form of cumulate generating functions, which appear relevant in the context of, e.g.~molecular dynamics, and we discuss the construction of an optimal (i.e. minimum variance) change of measure by solving a stochastic control problem. We show that the associated semi-linear dynamic programming equations admit an equivalent formulation as a system of uncoupled forward-backward stochastic differential equations that can be solved efficiently by a least squares Monte Carlo algorithm. We illustrate the approach with a suitable numerical example and discuss the extension of the algorithm to high-dimensional systems

Lois de Comportement à chaud avec Recristallisation Dynamique. Application au cas des Alliages à Base de Fer Pur

Un modèle de lois est proposé pour décrire le comportement mécanique à chaud en présence de la recristallisation dynamique. L'approche a été formulée à partir des relations θ-ε où θ représente le taux de consolidation à température et à vitesse de déformation constantes. Les relations proposées ont été validées à partir de données expérimentales obtenues par compression à chaud d'aciers faiblement alliés. Ce modèle permet de prévoir la déformation critique qui caractérise le début d'activation du processus de recristallisation dynamique.A constitutive relationship for predicting the flow stress with dynamic recrystallization were proposed. The approach is based on a phenomenological formalism of the law θ-ε where θ correspond to the work-hardening rate at constant strain rate and temperature. The equations proposed were justified by the experimental data collected by hot compression test of low-alloy steels. The model can be used to estimate the critical strain for the onset of dynamic recrystallization

Recristallisation des Fils de Tungstène Induite par la Diffusion du Nickel

Différents recuits effectués sur des fils de tungstène nickelés ont permis de déterminer une température de recuit critique (1000°C) au dessus de laquelle on observe un phénomène de recristallisation qui suit l'avance du front de diffusion intergranulaire du nickel dans la structure fibreuse du fil de tungstène. Des essais mécaniques ont montré le caractère fragilisant de cette transformation microstructurale ainsi que l'effet du dopage (potassium) sur les fils de tungstène. Cette recristallisation s'apparente au phénomène connu sous le terme de D.I.G.M. (Diffusion Induced Grain boundary Migration) mais notre système semble être un cas particulier qui nécessite de définir d'autres hypothèses concernant les forces motrices et les mécanismes mis en jeu au cours de ce phénomène de recristallisation.Various annealing on nickel coated tungsten wires have been performed and have determined a critical annealing temperature of 1000°C. Above this temperature a phenomenon of recrystallization is produced by an intergranular diffusion of nickel in the fibrous microstructure of the tungsten. Tensile tests have shown the brittle feature of this microstructural transformation and also the effect of the doping with potassium on tungsten wires. This recrystallisation is related to a phenomenon calied D.I.G.M. (Diffusion Induced Grain boundary Migration) but our system seems to be a particular case because it needs to find another hypothesis with respect to the driving forces and mechanisms to explain this phenomenon of recrystallization

Influence of Sulphur and Phophorus on the Hot Deformation of Fe-Cr 13% High Purity Steel

A series of Fe-Cr13%-C high purity steels containing increasing volume fractions of Sulphur (30, 60 and 100ppm) and Phosphorus (30, 60 and 100ppm) were prepared in order to study their hot deformation properties by tensile tests at various strain rates (10-1s-1 to 10-4s-1) and at temperatures from 700°C to 1100°C. It is observed that the hot ductility is lowered at 1000°C with the addition of sulphur. However, this decrease is relatively small (about 30% for l00ppm of sulphur) and quite similar for all additions of sulphur. When phosphorus is added, the embrittlement is along the whole deformed specimen. The usual criteria of ductility by parameter Z do not seem to be sufficient to describe this embrittlement

Influence of Trace Elements on Hot Ductility of an Ultra High Purity Invar Alloy

Like steels, austenitic INVAR alloys Fe-Ni 36 % show a large ductility trough between 500°C and 1100°C. To understand hot brittleness mechanisms and especially trace element effects, synthetic alloys were prepared using ultra-high purity iron and nickel doped with selected amounts of carbon, sulphur, boron, aluminium, and nitrogen. Four kinds of synthetic alloys were studied to establish the intrinsic influence of sulphur, the combined effects of sulphur and precipitates such AlN or BN, and the effect of boron in the presence of sulphur, on ductility and fracture mechanisms. We propose several mechanisms to explain the loss and the recovery of ductility for each of the studied alloys, and then define the field of temperatures where these mechanisms control ductility