HENRI AUGUSTE DELANNOY, UNE BIOGRAPHIE

Cette biographie traite en annexe du legs de la bibliothèque mathématique de Delannoy à la ville de Guéret.Les travaux du mathématicien Delannoy (1833-1915), qui étaient tombés dans l'oubli, ont suscité récemment un vif intérêt, en raison des nombreux objets qui sont dénombrés par les suites associées à son nom. En effet, ces suites ont émergé dans des travaux aussi divers que la représentation et le raisonnement spatio-temporel en informatique et en linguistique, en biologie ou en physique théorique. Nous nous proposons ici de remettre à l'honneur ce mathématicien méconnu. Son parcours, bien que modeste, nous éclaire sur la société mathématique de la fin du dix-neuvième siècle. Dans ce premier article nous présentons les éléments connus de sa vie, en particulier de son activité de mathématicien. Nous fournissons notamment une revue complète de ses publications. En annexe, le lecteur trouvera la description de la bibliothèque mathématique donnée en héritage par Delannoy à la bibliothèque municipale de Guéret et ce qu'il en est advenu. Dans un second article, nous traiterons de façon approfondie de son apport majeur : l'usage des échiquiers arithmétiques dans la résolution de problèmes combinatoires et probabilistes et les applications actuelles

Prefixes of infinite words and ambiguous context-free languages

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Dynamic simulation of the THAI heavy oil recovery process

Toe-to-Heel Air Injection (THAI) is a variant of conventional In-Situ Combustion (ISC) that uses a horizontal production well to recover mobilised partially upgraded heavy oil. It has a number of advantages over other heavy oil recovery techniques such as high recovery potential. However, existing models are unable to predict the effect of the most important operational parameters, such as fuel availability and produced oxygen concentration, which will give rise to unsafe designs. Therefore, we have developed a new model that accurately predicts dynamic conditions in the reservoir and also is easily scalable to investigate different field scenarios. The model used a three component direct conversion cracking kinetics scheme, which does not depend on the stoichiometry of the products and, thus, reduces the extent of uncertainty in the simulation results as the number of unknowns is reduced. The oil production rate and cumulative oil produced were well predicted, with the latter deviating from the experimental value by only 4%. The improved ability of the model to emulate real process dynamics meant it also accurately predicted when the oxygen was first produced, thereby enabling a more accurate assessment to be made of when it would be safe to shut-in the process, prior to oxygen breakthrough occurring. The increasing trend in produced oxygen concentration following a step change in the injected oxygen rate by 33 % was closely replicated by the model. The new simulations have now elucidated the mechanism of oxygen production during the later stages of the experiment. The model has allowed limits to be placed on the air injection rates that ensure stability of operation. Unlike previous models, the new simulations have provided better quantitative prediction of fuel laydown, which is a key phenomenon that determines whether, or not, successful operation of the THAI process can be achieved. The new model has also shown that, for completely stable operation, the combustion zone must be restricted to the upper portion of the sand pack, which can be achieved by using higher producer back pressure

On Generalized Delannoy Paths

A Delannoy path is a minimal path with diagonal steps in ${\mathbb Z}^2$ between two arbitrary points. We extend this notion to the $n$ dimensions space ${\mathbb Z}^n$ and identify such paths with words on a special kind of alphabet: an S-alphabet. We show that the set of all the words corresponding to Delannoy paths going from one point to another is exactly one class in the congruence generated by a Thue system that we exhibit. This Thue system induces a partial order on this set that is isomorphic to the set of ordered partitions of a fixed multiset where the blocks are sets with a natural order relation. Our main result is that this poset is a lattice