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AbstractAbstract
[en] This PhD thesis deals with the study of fundamental physics phenomena, with applications to nuclear materials of interest. We have developed methods for the study of rare events related to thermally activated structural transitions in many body systems. The first method involves the numerical simulation of the probability current associated with reactive paths. After deriving the evolution equations for the probability current, a Diffusion Monte Carlo algorithm is implemented in order to sample this current. This technique, called Transition Current Sampling was applied to the study of structural transitions in a cluster of 38 atoms with Lennard-Jones potential (LJ-38). A second algorithm, called Transition Path Sampling with local Lyapunov bias (LyTPS), was then developed. LyTPS calculates reaction rates at finite temperature by following the transition state theory. A statistical bias based on the maximum local Lyapunov exponents is introduced to accelerate the sampling of reactive trajectories. To extract the value of the equilibrium reaction constants obtained from LyTPS, we use the Multistate Bennett Acceptance Ratio. We again validate this method on the LJ-38 cluster. LyTPS is then used to calculate migration constants for vacancies and divacancies in the α-Iron, and the associated migration entropy. These constants are used as input parameter for codes modeling the kinetic evolution after irradiation (First Passage Kinetic Monte Carlo) to reproduce numerically resistivity recovery experiments in α-Iron. (author)
[fr]
Cette these aborde l'etude de phenomenes physiques fondamentaux, avec des applications aux materiaux d'interet nucleaire. Nous avons developpe des methodes pour l'etude d'evenements rares concernant des transitions structurales thermiquement activees dans des systemes a N-corps. La premiere methode consiste en la simulation numerique du courant de probabilite associe aux chemins reactifs. Apres avoir derive les equations d'evolution du courant de probabilite, on echantillonne ce courant grace a un algorithme de type Monte Carlo Diffusif. Cette technique, denommee Transition Current Sampling, a ete appliquee pour etudier les transitions structurales d'un agregat de 38 atomes lies par un potentiel Lennard-Jones (LJ-38). Un deuxieme algorithme, denommee Transition Path Sampling avec bias de Lyapunov local (LyTPS), a ensuite ete developpe. LyTPS permet de calculer des taux de reaction a temperature finie en suivant la theorie des etats de transition. Un biais statistique derivant du maximum des exposantes de Lyapunov locaux est introduit pour accelerer l'echantillonnage de trajectoires reactives. Afin d'extraire la valeur des constantes de reaction d'equilibre depuis celle obtenues par LyTPS, on utilise le Multistate Bennett Acceptance Ratio. Nous avons a nouveau valide cette methode sur l'agregat LJ-38. LyTPS est ensuite utilise pour calculer les constantes de migration des lacunes et di-lacunes dans le Fer-α, ainsi que l'entropie de migration associee. Ces constantes de reaction servent de parametre d'input dans des codes de modelisation cinetique (First Passage Kinetic Monte Carlo) pour reproduire numeriquement des recuits de resistivite de Fer-α apres irradiationOriginal Title
Evenements rares dans des systemes a N-corps: chemins reactifs et constantes de reaction dans les transitions structurales
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30 Jan 2012; 159 p; CEA-R--6310; 111 refs.; Available from the INIS Liaison Officer for France, see the 'INIS contacts' section of the INIS-NKM website for current contact and E-mail addresses: http://www.iaea.org/INIS/contacts/; Metallurgie Physique
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