Fluctuations of empirical means at low temperature for finite Markov chains with rare transitions in the general case

Summary. The integrated autocovariance and autocorrelation time are essential tools to understand the dynamical behavior of a Markov chain. We study here these two objects for Markov chains with rare transitions with no reversibility assumption. We give upper bounds for the autocovariance and the integrated autocorrelation time, as well as exponential equivalents at low temperature. We also link their slowest modes with the underline energy landscape under mild assumptions. Our proofs will be based on large deviation estimates coming from the theory of Wentzell and Freidlin and others [4, 3, 12], and on coupling arguments (see [6] for a review on the coupling method). Received 5 August 1996 / In revised form: 6 August 1997     

Stokes flow inside and around a fluid drop distorted by the presence of a tube wall

Using a quadratic optimisation process to satisfy the boundary conditions, the drag coefficient and the flow patterns inside and outside a fluid drop translating axially in a tube have been determined accurately even when the drop is clearly elongated. Convincing comparisons with experimental results (flow visualizations, velocity and drag measurements) are presented. The effects of the viscosity and density ratios are examined.     

Variable space search for graph coloring

Let G=(V,E) be a graph with vertex set V and edge set E. The k-coloring problem is to assign a color (a number chosen in {1,…,k}) to each vertex of G so that no edge has both endpoints with the same color. We propose a new local search methodology, called Variable Space Search, which we apply to the k-coloring problem. The main idea is to consider several search spaces, with various neighborhoods and objective functions, and to move from one to another when the search is blocked at a local optimum in a given search space. The k-coloring problem is thus solved by combining different formulations of the problem which are not equivalent, in the sense that some constraints are possibly relaxed in one search space and always satisfied in another. We show that the proposed algorithm improves on every local search used independently (i.e., with a unique search space), and is competitive with the currently best coloring methods, which are complex hybrid evolutionary algorithms.     

The Dynamics of Stretchable Rods in the Inertial Case

Nonlinear amplitude equations for the near-threshold behavior of twisted extensible elastic rods under tension with inertial and dissipative dynamics are derived. In the inertial case localized solutions to the amplitude equations are derived and a linear stability criterion for the pulse solutions is obtained using the Hamiltonian formulation of the problem.     

Preemptive scheduling and antichain polyhedra

We present a theoretical framework, which is based upon notions of ordered hypergraphs and antichain polyhedra, and which is dedicated to the combinatorial analysis of preemptive scheduling problems submitted to parallelization constraints.This framework allows us to characterize specific partially ordered structures which are such that induced preemptive scheduling problems may be solved through linear programming. To prove that, in the general case, optimal preemptive schedules may be searched inside some connected subset of the vertex set of an Antichain Polyhedron.     

Damaging processes in polypropylene compound: Experiment and modeling

The aim of this paper is to present a procedure of construction of constitutive equations within the framework of Continuum Mechanics. The main focus of our effort is to introduce the geometric change at a high level of strain and the damage which are generally developed in simple tests (tension, shear) of polymeric materials such as polypropylene compounds or copolymers (PP). High-resolution strain-mapping techniques are employed to determine the surface strain fields and, consequently, a measurement of the volume change. A phenomenological model based upon experimental observations was developed to reproduce the main behavior, e.g., the stress strain curves, including the volume change and their consequences. State Variables are defined and related to their evolution in relation with the state laws. The identification of the resulting model was made by reproducing the data issued from basic tests (Tension, Iosipescu Shear). Published in Russian in Vysokomolekulyarnye Soedineniya, Ser. A. 2008, Vol. 50, No. 5, pp. 850–861. This article was submitted by the authors in English.     

Amino wagging and inversion in hydrazine: K′ = 1 levels in the first excited state of the antisymmetric wagging vibration

The infrared absorption spectrum of NH₂NH₂ vapor has been observed in the region 899–1077 cm^?1, where the antisymmetric wagging band (v_a = 1 ← 0) appears, by the use of a Fourier transform spectrometer with a practical resolution of 0.003 cm^?1. In the region 925.0–925.6 cm^?1, the spectrum was also observed with a tunable diode laser, and a component, β, of the ^pQ₂ cluster has been further resolved. Most of the absorption lines assignable to β-^pP₂(J″), γ-^pP₂(J″), β-^pQ₂(J″), γ-^rQ₀(J″), β-^rR₀(J″), and γ-^rR₀(J″), where J″ = 2 ～ 15, have been identified. From these observed transition frequencies, in combination with the ground state energy levels given by microwave spectroscopy, the energy level structure of the K′ = 1 rotational states was determined. From this, the following molecular parameters for the v_a = 1 state were determined: molecular asymmetry, B′-C″ = 0.00017 cm^?1; a parameter q₅ describing an umbrella motion Coriolis interaction (q₅K) about the a axis, q₅ = ?0.0030 cm^?1; its J(J + 1) variation, q_5j = 0.00014 cm^?1; and a parameter describing an umbrella-motion K-type doubling g₅J(J + 1), g₅ = 0.000021 cm^?1.     

A photo-induced redox reaction by visible light via a charge transfer complex

The reduction of tropylium cation (Tr⁺) with the concomitant oxidation of O,O′-dialkyldithiophosphate anions (dtp^?) have been achieved by visible irradiation of their acetonitrile solution in presence of a bipyridinium dication ; the later via its charge transfer complex with dtp^? acts as a light-harvest and as an electron relay.     

Degenerate Dirichlet Problems Related to the Invariant Measure of Elasto-Plastic Oscillators

A stochastic variational inequality is proposed to model a white noise excited elasto-plastic oscillator. The solution of this inequality is essentially a continuous diffusion process for which a governing diffusion equation is obtained to study the evolution in time of its probability distribution. The diffusion equation is degenerate, but using the fact that the degeneracy occurs on a bounded region we are able to show the existence of a unique solution satisfying the desired properties. We prove the ergodic properties of the process and characterize the invariant measure. Our approach relies on extending Khasminskii’s method (Stochastic Stability of Differential Equations, Sijthoff and Noordhoff, 1980), which in the present context leads to the study of degenerate Dirichlet problems with nonlocal boundary conditions. This research was partially supported by a grant from CEA, Commissariat à l’énergie atomique and by the National Science Foundation under grant DMS-0705247.