Small dilatation pseudo-Anosov homeomorphisms and 3-manifolds

The main result of this paper is a universal finiteness theorem for the set of all small dilatation pseudo-Anosov homeomorphisms ?:S→S, ranging over all surfaces S. More precisely, we consider pseudo-Anosov homeomorphisms ?:S→S with |χ(S)|log(λ(?)) bounded above by some constant, and we prove that, after puncturing the surfaces at the singular points of the stable foliations, the resulting set of mapping tori is finite. Said differently, there is a finite set of fibered hyperbolic 3-manifolds so that all small dilatation pseudo-Anosov homeomorphisms occur as the monodromy of a Dehn filling on one of the 3-manifolds in the finite list, where the filling is on the boundary slope of a fiber.     

Density functional theory investigation of competitive free-radical processes during the thermal cracking of methylated polyaromatics: estimation of kinetic parameters

Density functional B3LYP and BH&HLYP calculations with the 6-31G** basis set have been performed to investigate elementary reactions playing an important role in the pyrolysis of 1-methylnaphthalene. The pathways describing the destiny of the main radicals, H, methyl, hydromethylnaphthyl and methylnaphthyl, have been studied. At low temperature, addition of H atoms on the aromatic ring is favored over hydrogen abstraction. Except at low temperature (below 400 K), the hydromethylnaphthyl radical undergoes preferentially a loss of hydrogen rather than a bimolecular hydrogen transfer with methylnaphthalene or addition reaction on methylnaphthalene forming a hydrogenated dimer. In the range 400-750 K, the formation of methane by hydrogen abstraction of methyl radical on methylnaphthalene is predominant compared to the formation of hydrodimethylnaphthalenes by addition reaction. Rate constants of reactions describing the formation of heavy products like methyldinaphthylmethanes or dimethylbinaphthalenes have been calculated and discussed. They are also compared to recombination reactions from the literature. Rate constants of these reactions have been computed using transition state theory and can be integrated in kinetic radical schemes of methylated polyaromatic compounds pyrolysis from geological to laboratory conditions.     

Two-generator subgroups of the pure braid group

We show that any two elements of the pure braid group either commute or generate a free group, settling a question of Luis Paris. Our proof involves the theory of 3-manifolds and the theory of group actions on trees.     

Communication: Bond length alternation of conjugated oligomers: Another step on the fifth rung of Perdew's ladder of functional

In this work, we present the application of the hybrid short-range density functional theory/long-range MP2 energy gradients to the bond length alternation in polymethineimine and polyacetylene conjugated oligomers. Compared to other density functional calculations, our results are quite superior, even to fourth rung functionals, usually better than MP2 and very close to the available CCSD(T) values.     

Accuracy of the multipole expansion applied to a sphere in a creeping flow parallel to a wall

An example system is studied to discuss precision of the multipoleexpansion, applied to determine forces exerted on particlesby a viscous low-Reynolds-number fluid flow. A single spherein an ambient flow (pure shear, quadratic, and modulated shear)parallel to a close plane wall is considered. Forces and torquesexerted by the ambient flow on a motionless sphere are evaluated.Their precision is determined and related to a multipole orderof the truncation. Similar analysis is performed for a movingsphere with no ambient flow and for a freely moving sphere.Relative motion of the sphere with respect to the wall givesrise to strong lubrication interactions. It is analysed howthese interactions affect accuracy of the pure multipole expansion,and what are the smallest distances where it becomes insufficient.An alternative precise method is applied, in which lubricationexpressions are subtracted from the hydrodynamic forces andtorques, and the residue is evaluated as a fast-convergent seriesof inverse powers of the distance between the sphere centreand the wall. The accuracy of this procedure is carefully analysed.