Search

We introduce the Newton--Sinkhorn and implied Newton algorithms which significantly speed up the Sinkhorn algorithm that [Guyon, The joint S&P 500/VIX smile calibration puzzle solved, Risk, April 2020] used to build the first arbitrage-free model exactly consistent with S&P 500 and VIX market data. Using a purely forward Markov functional model, we show how to build a continuous-time extension of the previous discrete-time model. We also compute model-free bounds on S&P 500 options that show the importance of taking VIX smile information into account. Extensive numerical tests are conducted.

International audience

International audience; Titanium aluminide (TiAl) alloys have attracted considerable attention due to their unique combination of properties such as high specific strength and stiffness, good creep properties and resistance against oxidation and corrosion, which make them suitable candidate materials for High Temperature (HT) applications [1]. TiAl alloys are brittle at Room Temperature (RT), i.e. below their brittle-to-ductile transition temperature which lies between 800°C and 1000°C [2]. Despite intense research, literature suffers from a lack of understanding of their elementary deformation mechanisms and the precise role of microstructures [2].The investigation presented here focuses on the study of RT deformation mechanisms at the mesoscopic scale. With an original combination of experiments, we investigate the evolution of deformation microstructures at RT in the γ phase of a dual-phase bulk TiAl alloy. Because of the RT brittleness of this material, plastic deformation is induced by nanoindentation. The evolution of the microstructures is characterized by accurate Electron Channeling Contrast Imaging (aECCI) before and after deformation [3]. aECCI is a non-destructive powerful method offering the ability to provide, inside a SEM, TEM-like diffraction contrast imaging of sub-surface defects (at a depth of about one hundred of nanometers) on centimetric bulk specimen [4]. Defects, such as dislocations, can be characterized by applying the TEM extinction criteria [5]. Accommodation of the deformation are reported and a scenario is proposed [3]. Références[1] – Y. Kim, D. Dimiduk, JOM 43, (1991).[2] – C. Zambaldi, Thèse, Aachen (2010).[3] – A. Guitton, H. Kriaa, E. Bouzy, J. Guyon, N. Maloufi, Materials 11, 2 (2018)[4] – H. Kriaa, A. Guitton, N. Maloufi, Scientific reports 7, (2017).[5] – H. Kriaa, A. Guitton, N. Maloufi, Materials 12 (2019)

International audience; Developing new materials and understanding how they deform is the main challenge of engineers in order to follow and predict the fast evolutions of our society. For instance, in a framework of energetic cost reductions, titanium aluminide (TiAl) alloys have attracted considerable attention due to their unique combination of properties such as high specific strength and stiffness, good creep properties and resistance against oxidation and corrosion, which make them suitable candidate materials for high temperature applications [1]. However, TiAl alloys are brittle at Room Temperature (RT), i.e. below their brittle-to-ductile transition temperature, which lies between 800°C and 1000°C [2]. Furthermore, their complex microstructures (multiphase, different types of microstructures, specific dislocation mechanisms…) with several impacts at different scales are puzzling the materials science community. Despite intense research, literature suffers from a lack of understanding of their elementary deformation mechanisms and the precise role of microstructures [2]. In order to address these questions, we report here, an original and an innovative approach bringing the necessary information, thus allowing linking the multiscale aspects of the mechanical behavior of TiAl alloys at RT. Particularly, we bring new breakthrough on the evolution of deformation microstructures at RT in the vicinity of interfaces in γ phase of a dual-phase bulk TiAl alloy. Plastic deformation is induced locally by µN-nanoindentation. The evolution of the microstructures is characterized comprehensively by accurate Electron Channeling Contrast Imaging (aECCI) before and after deformation [3]. aECCI is a non-destructive groundbreaking procedure offering the ability to provide, inside a SEM, TEM-like diffraction contrast imaging of sub-surface defects (at a depth of about one hundred of nanometers) on centimetric bulk specimen with still unsurpassed resolutions [4]. Defects, such as dislocations, can be characterized by applying the TEM extinction criteria [5]. All features help to explain the poor ductility of the TiAl-based alloys at RT. Accommodation of the deformation is reported and a scenario is proposed [3].References[1] – Y. Kim, D. Dimiduk, JOM 43, (1991).[2] – C. Zambaldi, Thèse, Aachen (2010).[3] – A. Guitton, H. Kriaa, E. Bouzy, J. Guyon, N. Maloufi, Materials 11, 2 (2018)[4] – H. Kriaa, A. Guitton, N. Maloufi, Scientific reports 7, (2017).[5] – H. Kriaa, A. Guitton, N. Maloufi, Materials 11 (2018)

International audience; Developing new materials and understanding how they deform is the main challenge of engineers in order to follow and predict the fast evolutions of our society. For instance, in a framework of energetic cost reductions, titanium aluminide (TiAl) alloys have attracted considerable attention due to their unique combination of properties such as high specific strength and stiffness, good creep properties and resistance against oxidation and corrosion, which make them suitable candidate materials for high temperature applications [1]. However, TiAl alloys are brittle at Room Temperature (RT), i.e. below their brittle-to-ductile transition temperature, which lies between 800°C and 1000°C [2]. Furthermore, their complex microstructures (multiphase, different types of microstructures, specific dislocation mechanisms…) with several impacts at different scales are puzzling the materials science community. Despite intense research, literature suffers from a lack of understanding of their elementary deformation mechanisms and the precise role of microstructures [2]. In order to address these questions, we report here, an original and an innovative approach bringing the necessary information, thus allowing linking the multiscale aspects of the mechanical behavior of TiAl alloys at RT. Particularly, we bring new breakthrough on the evolution of deformation microstructures at RT in the vicinity of interfaces in γ phase of a dual-phase bulk TiAl alloy. Plastic deformation is induced locally by µN-nanoindentation. The evolution of the microstructures is characterized comprehensively by accurate Electron Channeling Contrast Imaging (aECCI) before and after deformation [3]. aECCI is a non-destructive groundbreaking procedure offering the ability to provide, inside a SEM, TEM-like diffraction contrast imaging of sub-surface defects (at a depth of about one hundred of nanometers) on centimetric bulk specimen with still unsurpassed resolutions [4]. Defects, such as dislocations, can be characterized by applying the TEM extinction criteria [5]. All features help to explain the poor ductility of the TiAl-based alloys at RT. Accommodation of the deformation is reported and a scenario is proposed [3].References[1] – Y. Kim, D. Dimiduk, JOM 43, (1991).[2] – C. Zambaldi, Thèse, Aachen (2010).[3] – A. Guitton, H. Kriaa, E. Bouzy, J. Guyon, N. Maloufi, Materials 11, 2 (2018)[4] – H. Kriaa, A. Guitton, N. Maloufi, Scientific reports 7, (2017).[5] – H. Kriaa, A. Guitton, N. Maloufi, Materials 11 (2018)

This work focuses on the microstructure evolution of a TiAl alloy during sintering by a process called Spark Plasma Sintering (SPS). The initial powders, elaborated by atomization, consist primarily of a metastable phase. The transformations of the return to equilibrium of the latter during heating are finely characterized using SEM, TEM and EBSD. These phase transformations are then used as a thermal indicator during the SPS densification to estimate the thermal and mechanical gradients. The densification mechanisms responsible for the neck formation and the origins of the microstructure heterogeneities of fully densified samples are discussed. A comparison between the densification mechanisms and the final microstructures of a milled powder and a no milled powder is showed. Finally, the effect of the application of a dynamic stress during the compaction using an original process is presented; Ce travail porte sur l'évolution microstructurale d'un alliage TiAl lors du frittage par un procédé appelé Spark Plasma Sintering (SPS). Les poudres initiales, élaborées par atomisation, sont constituées principalement d'une phase métastable. Les transformations qui accompagnent le retour à l'équilibre de cette dernière durant un chauffage sont finement caractérisées par MEB, MET et EBSD. Ces transformations seront ensuite utilisées comme marqueur thermique lors de la densification SPS afin de mieux estimer les amplitudes des gradients thermiques et mécaniques du procédé de frittage. Les mécanismes de densification responsables de la formation des cous sont discutés, ainsi que les origines des hétérogénéités microstructurales des échantillons complètement densifiés. Un comparatif des mécanismes de densification et des microstructures finales entre une poudre broyée et une poudre non broyée est dressé. Enfin, l'influence de l'application d'une contrainte dynamique pendant la compaction au moyen d'un dispositif original est présentée