We report large-scale molecular dynamics simulations of the glass formation from the liquid phase and homogeneous nucleation phenomena of pure zirconium. For this purpose, we have built a modified embedded atom model potential, in order to reproduce relevant structural, dynamic and thermodynamic properties from ab initio and experimental data near the melting point. By means of liquid-solid interface simulations, we show that this potential provides a thermodynamic melting temperature and densities of the solid and liquid state in good agreement with experiments. Using melt-quenching simulations with one million atoms, we determine the glass transition from the temperature evolution of the inherent structure energy as well as the nose of the time-temperature-transformation curve located in the deep undercooling regime. We identify the local structural origin of the glass forming ability as a competition between bcc and five-fold polytetrahedral structures that may represent an impediment of rapid homogeneous nucleation at such high undercoolings. This suggests the ability of single elemental zirconium to form a glass from the melt with cooling rates of at least 10 12 K/s compatible with modern experiments.
Cohomology with twisted coefficients of the classifying space of a fusion system RÉMI MOLINIERWe study the cohomology with twisted coefficients of the geometric realization of a linking system associated to a saturated fusion system F . More precisely, we extend a result due to Broto, Levi and Oliver to twisted coefficients. We generalize the notion of F -stable elements to F c -stable elements in a setting of cohomology with twisted coefficients by an action of the fundamental group.We then study the problem of inducing an idempotent from an F -characteristic (S, S)-biset and we show that, if the coefficient module is nilpotent, then the cohomology of the geometric realization of a linking system can be computed by F c -stable elements. As a corollary, we show that for any coefficient module, the cohomology of the classifying space of a p-local finite group can be computed by these F c -stable elements. 55R40, 55N25, 55R35, 20J06, 20D20, 20J15The notion of saturated fusion systems was introduced by Puig in the 90s in a context of modular representation theory. In topology, saturated fusion systems are used in the study of p-completed classifying spaces of groups. A p-local finite group is a triple (S, F, L) where S is a p-group, F a saturated fusion system over S and L an associated centric linking system. For a p-local finite group (S, F, L), the p-completed nerve of L, |L| ∧ p , is called its classifying space. The theory of p-local finite group has been studied in detail by Broto, Levi, Oliver and others (see [BLO2], [OV1],[5a1] and [5a2]). The linking system and its geometric realization, even without p-completion, play here a fundamental and central role. In fact, for a given saturated fusion system, the existence and uniqueness of a linking system associated to a saturated fusion system were shown more recently by Chermak [Ch] (using the theory of partial groups). The proof of this important conjecture highlights the deep link between group theory and homotopy theory and the importance of linking systems to study p-local structures. We refer to Aschbacher, Kessar and Oliver [AKO] for more details about fusion systems in general.A well-known result of Cartan and Eilenberg (see [CE] Chap XII, Theorem 10.1) expresses the cohomology with mod p coefficients of a finite group as the submodule of stable elements in the cohomology of a Sylow p-subgroup. This submodule of stable elements corresponds to the inverse limit over the fusion system of the group cohomology functor. One important result in the theory of p-local finite groups is an extension of this theorem to any p-local finite group which tells us that the cohomology of the geometric realization of a linking system with trivial coefficients can be computed by F -stable elements.
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