A test problem for molecular dynamics integrators

We derive a test problem for evaluating the ability of time-steppingmethods to preserve the statistical properties of systems inmolecular dynamics. We consider a family of deterministic systemsconsisting of a finite number of particles interacting on acompact interval. The particles are given random initial conditionsand interact through instantaneous energy- and momentum-conservingcollisions. As the number of particles, the particle density,and the mean particle speed go to infinity, the trajectory ofa tracer particle is shown to converge to a stationary Gaussianstochastic process. We approximate this system by one describedby a system of ordinary differential equations and provide numericalevidence that it converges to the same stochastic process. Wesimulate the latter system with a variety of numerical integrators,including the symplectic Euler method, a fourth-order Runge-Kuttamethod, and an energyconserving step-and-project method. Weassess the methods' ability to recapture the system's limitingstatistics and observe that symplectic Euler performs significantlybetter than the others for comparable computational expense.     

Sur le degré dynamique des transformations de Cremona du plan qui stabilisent une courbe irrationnelle non-elliptique

We show that the first dynamical degree of a Cremona transformation stabilizing an irrational non elliptic curve is 1. Moreover, among these transformations, we characterize those which have finite order. To cite this article: I. Pan, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Structure and Structural Nonrigidity of Tetrachlorodibenzo-p-Dioxin Radical Cations

Ab initio calculations showed that the tetrachlorodibenzo-para-dioxin radical cations (TCDD RCs) with a planar structure have two steady states with asymmetric dioxin cycles. The activation barriers between these states are up to 2 kcal/mole, so that the RCs may be regarded as being structurally nonrigid within the dioxin cycle. The 2,3,7,8-TCDD RC is more stable than the 1,4,6,9-TCDD RC, the energy difference being 5.2 kcal/mole. The adiabatic ionization potential of 2,3,7,8-TCDD (7.54 eV) is 0.1 eV smaller than the corresponding potential of 1,4,6,9-TCDD. These factors account for the increased hemoproteide affinity and hence increased biological activity of 2,3,7,8-TCDD.     

Dicyclopentadienyl complexes of titanium,niobium, and tungsten in the controlled synthesis of poly(methyl methacrylate)

Organometallic compounds Cp₂TiCl₂, (EtC₅H₄)₂NbCl₂, and (PrⁱC₅H₄)₂WCl₂ were assessed as additives that control polymer chain growth in the polymerization of methyl methacrylate. In the presence of compounds mentioned in amounts comparable with that of the initiator, a uniform process with no gel-effect occured and respective linear increase in the molecular weight of the polymer up to high degrees of the monomer conversion was observed.     

Nuclear superstructure {1/2, 0, 1/2} of an La<Subscript>0.93</Subscript>Sr<Subscript>0.07</Subscript>MnO<Subscript>3</Subscript> manganite orthorhombic crystal

The {1/2, 0, 1/2} nuclear superstructure in an La_0.93Sr_0.07MnO₃ manganite orthorhombic crystal is revealed using thermal-neutron diffraction. It is demonstrated that this superlattice belongs to the class of distortion-type structures and is directly associated with a 1/16-type ordering of Mn⁴⁺ and Mn³⁺ ions in a collinear ferromagnetic phase of the La_0.93Sr_0.07MnO₃ manganite.     

Decay of neutron-rich Ga isotopes near N = 50 at PARRNe

The PARRNe facility has been used to produce neutron-rich isotopes ^83,84Gaby the ISOL method. Their decay has been studied, and β-γ coincidence and γ-γ coincidence data were collected as a function of time. The first two excited levels in ⁸³Ge and the first excited level in ⁸⁴Ge have been measured for the first time.     

Fixed points in the family of convex representations of a maximal monotone operator

Any maximal monotone operator can be characterized by a convex function. The family of such convex functions is invariant under a transformation connected with the Fenchel-Legendre conjugation. We prove that there exists a convex representation of the operator which is a fixed point of this conjugation.

     

Fractional Derivatives Applied to Phase-Space Reconstructions

The concept and application of phase-space reconstructions are reviewed. Fractional derivatives are then proposed for the purpose of reconstructing dynamics from a single observed time history. A procedure is presented in which the fractional derivatives of time series data are obtained in the frequency domain. The method is applied to the Lorenz system. The ability of the method to unfold the data is assessed by the method of global false nearest neighbors. The reconstructed data is used to compute recurrences and correlation dimensions. The reconstruction is compared to the commonly used method of delays in order to assess the choice of reconstruction parameters, and also the quality of results.