Indépendance Linéaire sur Q de logarithmes P-adiques de nombres algébriques et rang P-adique du groupe des unités d'un corps de nombres

Following Ax's method a lower bound for the p-adic rank of the group of units in the general case of a Galois number field over the rationals is given. In some nontrivial special cases the result gives Leopoldt's conjecture. The same method is also applied to the case of p-units.     

The Haemers partial geometry and the Steiner system S(5, 8, 24)

Haemers has constructed a partial geometry with parameters s = 4, t = 17, and α = 2, using properties of the Hoffman-Singleton graph. We describe this geometry in terms of the Steiner system S(5, 8, 24).     

Theory of C2Hx species on Pt{110}(1x2): structure, stability, and thermal chemistry

The adsorption of C2Hx (x=0-5) hydrocarbon fragments on Pt{110}(1x2) has been investigated using calculations based on density functional theory. For all the species, the most stable adsorption site identified completes the tetravalency of each carbon atom and involves the maximum possible number of Pt atoms subject to that constraint. The most stable adsorption sites for C2Hx fragments of stoichiometry x=2-5 involve ridge atoms, while trough sites stabilize C2H and C2 species. The relative stability of the fragments involved is compared via a free energy picture.     

Tilted and helical columnar phases for an axially symmetric discoidal system

We report novel phase behavior for a system of disclike ellipsoidal particles interacting via a pair potential. We identify a structural phase transition between two hexagonal columnar phases, both tilted, induced by spatial ordering of the tilt about the columnar axis and positional correlations between neighboring columns upon cooling. The local minima of the potential energy surface support irregular helical arrangements of the discoids about the columnar axis for the high-temperature hexagonal columnar phase, and a tilted arrangement for both phases. Our study demonstrates that dispersion-repulsion forces corresponding to oblate ellipsoids are sufficient to produce a columnar phase that is tilted and helical.     

Theory of C2Hx species on Pt{110} (1x2): reaction pathways for dehydrogenation

A complete reaction sequence for molecular dissociation at a surface has been characterized using density functional theory. The barriers for sequential ethane dehydrogenation on Pt{110} are found to fall into distinct energy sets: very low barriers, with values in the range of 0.29-0.42 eV, for the initial ethane dissociation to ethene and ethylidene at the surface; medium barriers, in the range of 0.72-1.10 eV, for dehydrogenation of C(2)H(4) fragments to vinylidene and ethyne; and high barriers, requiring more than 1.45 eV, for further dehydrogenation. For dissociation processes where more than one pathway has been found, the lowest energetic route links the most stable reactant adsorbed state at the surface to a product state involving the hydrocarbon moiety adsorbed in its most stable configuration at the surface. Hence there is a clear link between surface stability and kinetics for these species.     

Energy landscapes for water clusters in a uniform electric field

The behavior of small water clusters, (H2O)n, n=2-5 and n=8, in a uniform electric field is investigated for three related rigid-body models. Changes in the properties of the low-lying potential energy minima and the rearrangement pathways between them are examined. Results for certain structural transitions are compared with recent ab initio calculations. The models are found to give qualitatively similar trends, and there is some evidence that as the applied field strength is increased the quantitative differences between the models are also reduced.