Equivalent classes of degree sequences for triangulated polyhedra and their convex realization

We define an equivalence on the set of all degree sequences of a triangulated polyhedron with a fixed number of vertices and compute them and their cardinal via an algorithm. We also prove that each class is realizable as a convex polyhedron

Ultracold collisions between Li atoms and Li2 diatoms in high vibrational states

International audienceWe have performed a quantum-dynamical study of vibrational deexcitation and elastic scattering at ultralow collision energies for the bosonic system Li7+Li27 and for the fermionic system Li6+Li26 with diatomic molecules in high vibrational states. Inelastic rates show a strong and irregular dependence on the vibrational state of the diatomic molecule. For the highest vibrational state which lies near the dissociation limit, vibrational deexcitation processes are not suppressed, but rather depleted, for both bosonic and fermionic systems

Ultracold collisions involving heteronuclear alkali metal dimers

We have carried out the first quantum dynamics calculations on ultracold atom-diatom collisions in isotopic mixtures. The systems studied are spin-polarized 7Li + 6Li7Li, 7Li + 6Li2, 6Li + 6Li7Li and 6Li + 7Li2. Reactive scattering can occur for the first two systems even when the molecules are in their ground rovibrational states, but is slower than vibrational relaxation in homonuclear systems. Implications for sympathetic cooling of heteronuclear molecules are discussed.Comment: 4 pages, 3 figure

A detailed quantum mechanical and quasiclassical trajectory study on the dynamics of the H(+) + H2 --> H2 + H(+) exchange reaction

13 pages, 11 figures.-- PACS nrs.: 82.30.Hk; 82.30.Nr.The H(+) + H2 exchange reaction has been studied theoretically by means of a different variety of methods as an exact time independent quantum mechanical, approximate quantum wave packet, statistical quantum, and quasiclassical trajectory approaches. Total and state-to-state reaction probabilities in terms of the collision energy for different values of the total angular momentum obtained with these methods are compared. The dynamics of the reaction is extensively studied at the collision energy of E(coll) = 0.44 eV. Integral and differential cross sections and opacity functions at this collision energy have been calculated. In particular, the fairly good description of the exact quantum results provided by the statistical quantum method suggests that the dynamics of the process is governed by an insertion mechanism with the formation of a long-lived collision complex.Two of the authors (O.R. and T.G.L.) thank the Spanish Ministry of Education (MEC) for financial support through Grants Nos. FIS2004-02461 and CTQ2004-02415. One of the authors (T.G.L.) would like to acknowledge support from the program Ramón y Cajal of Spanish MEC and EU Grant No. MERG-CT-2004-513600. Two other authors (F.J.A. and L.B.) acknowledge financial support through MEC Grant No. CTQ2005-08493-C02-01 and Universidad Complutense- Comunidad de Madrid Grant No. 910729. Another author (N.B.) thanks a postdoctoral fellowship by Spanish MEC under the program "Estancias de jóvenes doctores y tecnólogos extranjeros en España". One of the authors (F.J.A.) thanks the financial support by the programme of "Sabáticos Complutenses" of the Universidad Complutense de Madrid. The EQM calculations were performed on a NEC-SX5 vector supercomputer, through a grant from the "Institut du Développement des Ressources en Informatique Scientifique" (IDRIS-CNRS) in Orsay (France).Peer reviewe

New Theoretical Results Concerning the Interstellar Abundance of Molecular Oxygen

The low abundance of molecular oxygen in cold cores of interstellar clouds poses a continuing problem to modelers of the chemistry of these regions. In chemical models O_2 is formed principally by the reaction between O and OH, which has been studied experimentally down to 39 K. It remains possible that the rate coefficient of this reaction at 10 K is considerably less than its measured value at 39 K, which might inhibit the production of O_2 and possibly bring theory and observation closer together over a wider range of times. Two theoretical determinations of the rate coefficient for the O + OH reaction at temperatures down to 10 K have been undertaken recently; both results show that the rate coefficient is indeed lower at 10 K than at 39 K, although they differ in the magnitude of the decrease. Here we show, using gas-phase models, how the calculated interstellar O_2 abundance in cold cores is affected by a decrease in the rate coefficient. We also consider its effect on other species. Our major finding is that for standard O-rich abundances, the calculated abundance of O_2 in cold cores is sufficiently low to explain observations only at early times regardless of the value of k_1 in the range investigated here. For C-rich abundances, on the other hand, late-time solutions can also be possible

Interactions and dynamics in Li+Li2 ultracold collisions

A potential energy surface for the lowest quartet electronic state (A′4) of lithium trimer is developed and used to study spin-polarized Li+Li2collisions at ultralow kinetic energies. The potential energy surface allows barrierless atom exchange reactions. Elastic and inelastic cross sections are calculated for collisions involving a variety of rovibrational states of Li2. Inelastic collisions are responsible for trap loss in molecule production experiments. Isotope effects and the sensitivity of the results to details of the potential energy surface are investigated. It is found that for vibrationally excited states, the cross sections are only quite weakly dependent on details of the potential energy surface

Honvault, Pascal Euclidean realizations of triangulated polyhedra. (English) £ ¢ ¡ Zbl 07203374

International audienceThe author studies (not necessarily convex) triangulated polyhedra in three-dimensional Euclidean space and with genus zero. The focus of the paper is to devise an algorithm to construct an explicit realization of such a polyhedron given by its combinatorial data: • the number n + 1 and a labelling v 0 , v 1 ,. .. , v n of its vertices • degree sequence (d 0 , d 1 ,. .. , d n), where d i is the number of edges incident to the ith vertex v i • a triangulation given by a list of triangles (v i , v j , v k) The algorithm is guided by a set of necessary and sufficient conditions on the length of the edges, and the internal and external angles of the triangles in the triangulation. Reviewer: Matthias Schymura (Cottbus) MSC: 52B05 Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) 51N20 Euclidean analytic geometry 52-04 Software, source code, etc. for problems pertaining to convex and discrete geometry 51M20 Polyhedra and polytopes; regular figures, division of space

Time-dependent wave packet and quasiclassical trajectory study of the C(3P)+OH(X 2)CO(X 1+)+H(2S) reaction at the state-to-state level

9 pages, 9 figures, 1 table.The first calculations of state-to-state reaction probabilities and product state-resolved integral cross sections at selected collision energies (0.05, 0.1, 0.5, and 1.0 eV) for the title reaction on the ab initio potential energy surface of [Zanchet et al. J. Phys. Chem. A 110, 12017 (2006)] with the OH reagent in selected rovibrational states (v=0–2, j=0–5) have been carried out by means of the real wave packet (RWP) and quasiclassical trajectory (QCT) methods. State-selected total reaction probabilities have been calculated for total angular momentum J=0 in a broad range of collision energies. Integral cross sections and state-specific rate coefficients have been obtained from the corresponding J=0 RWP reaction probabilities for initially selected rovibrational states by means of a capture model. The calculated RWP and QCT state-selected rate coefficients are practically temperature independent. Both RWP and QCT reaction probabilities, integral cross sections, and rate coefficients are almost independent of the initial rotational excitation. The RWP results are found to be in an overall good agreement with the corresponding QCT results. The present results have been compared with earlier wave packet calculations carried out on the same potential energy surface.Partial financial support from the Spanish Ministry of Education and Science (Project No. CTQ2008-02578/BQU) is gratefully acknowledged. A.Z., P.H., and B.B.-H. acknowledge support from the Institut du Développement des Ressources en Informatique Scientifique (IDRIS) in Orsay (France), the UTINAM laboratory for its fast cluster, and also the Pôle de Sciences Planétaires of Bourgogne Franche-Comté.Peer reviewe