Affine cellularity of affine Hecke algebras of rank two

We show that affine Hecke algebras of rank two with generic parameters are affine cellular in the sense of Koenig-Xi.Comment: 24 pages, 4 figures and 14 tables. New version: added references, corrected typos. Final versio

Kazhdan-Lusztig cells in affine Weyl groups with unequal parameters

Hecke algebras arise naturally in the representation theory of reductive groups over finite or p-adic fields.  These algebras are specializations of Iwahori-Hecke algebras which can be defined in terms of a Coxeter group and a weight function without reference to reductive groups and this is the setting we are working in.  Kazhdan-Lusztig cells play a crucial role in the study of Iwahori-Hecke algebras.  The aim of this work is to study the Kazhdan-Lusztig cells in affine Weyl groups with unequal parameters.  More precisely, we show that the Kazhdan-Lusztig polynomials of an affine Weyl group are invariant under “long enough” translations, we decompose the lowest two-sided cell into left cells and we determine the decomposition of the affine Weyl group of type Ğ2 into cells for a whole class of weight functions.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Homology rings of affine grassmannians and positively multiplicative graphs

Let $\mathfrak{g}$ be an untwisted affine Lie algebra with associated Weyl group $W_a$. To any level 0 weight $\gamma$ we associate a weighted graph $\Gamma_\gamma$ that encodes the orbit of $\gamma$ under the action $W_a$. We show that the graph $\Gamma_\gamma$ encodes the periodic orientation of certain subsets of alcoves in $W_a$ and therefore can be interpreted as an automaton determining the reduced expressions in these subsets. Then, by using some relevant quotients of the homology ring of affine Grassmannians, we show that $\Gamma_\gamma$ is positively multiplicative. This allows us in particular to compute the structure constants of the homology rings using elementary linear algebra on multiplicative graphs. In another direction, the positivity of $\Gamma_\gamma$ yields the key ingredients to study a large class of central random walks on alcoves.Comment: 36 pages and 19 figure

Kinetic modelling of the thermal decomposition of ettringite into metaettringite

International audienceDespite recent insights into thermal stability of ettringite and structural changes during decomposition, a lack of knowledge on nucleation and growth mechanisms of metaettringite remained. Therefore, a better understanding of the kinetic modelling of this heterogeneous reaction was proposed. Thanks to an experimental approach allowing to check the validity of kinetic assumptions (rate-determining step, expression of the rate as d alpha/dt=k f(alpha)...), a good agreement was found between the calculated and experimental alpha vs. t and d alpha/dt vs. t kinetic curves. The reaction area of the region in which the rate-limiting step occurs was also elucidated. Finally, we demonstrated that the rate-limiting step of the growth process follows an Arrhenius law in non-isothermal conditions

HPMC and HEMC influence on cement hydration

International audienceCellulose ethers such as hydroxyethylmethyl cellulose (HEMC) and hydroxypropylmethyl cellulose (HPMC) are common admixtures in factory made mortars. Nevertheless, their use principally remains empirical, and no cement-admixture interaction mechanism has ever been rigorously demonstrated. The main issue of this publication deals with the control of secondary effects generated by these admixtures such as the retardation of cement hydration. In this frame, a study of the impact of HEMC and HPMC molecule parameters on the modification of cement hydration was carried out. Minor influence of the molecular weight and of the hydroxypropyl or the hydroxyethyl group content was observed. On the contrary, the results emphasize that the methoxyl group content appears as the key parameter of the hydration delay mechanism

Alkaline stability of cellulose ethers and impact of their degradation products on cement hydration

International audienceCellulose ethers are polymers frequently introduced into mortar formulations. This study allows to assess the potential role of cellulose ethers degradation on the alteration of the cement hydration kinetics. A retardation mechanism based on the calcium binding capacity of chelates is often proposed to describe the effects of some polysaccharides (e.g. sugars) on cement hydration. The alkaline stability of cellulose ethers has been poorly studied and may represent one way to understand the hydration delay induced by such admixtures. Identification and quantification of the hydroxy carboxylic acids generated during alkaline degradation were performed. The results indicate that cellulose ethers are very stable in alkaline media. We also show that the ability of cellulose ethers to complex calcium ions is negligible. Finally, degradation of cellulose ethers and its impact on the cement hydration kinetics does not seem to be significant