Parity-violating electron deuteron scattering and the proton's neutral weak axial vector form factor

We report on a new measurement of the parity-violating asymmetry in quasielastic electron scattering from the deuteron at backward angles at Q2=0.038 (GeV/c)2. This quantity provides a determination of the neutral weak axial vector form factor of the nucleon, which can potentially receive large electroweak corrections. The measured asymmetry A=-3.51+/-0.57 (stat)+/-0.58 (syst) ppm is consistent with theoretical predictions. We also report on updated results of the previous experiment at Q2=0.091 (GeV/c)2, which are also consistent with theoretical predictions.     

On the transition moment of the CO2 40°1II-00°0 band near 7740 cm-1

Using intensity measurements on the CO₂ 40°1_II-00°0 band obtained by Valero and Boese, we have expanded the F(m)-factor for the parallel band by using the Herman-Wallis formula. We have calculated the transition moment and determined the coefficients in the expansion of F(m).     

Pointwise gradient estimates of solutions to onedimensional nonlinear parabolic equations

We present here an improved version of the method introduced by the first author to derive pointwise gradient estimates for the solutions of one-dimensional parabolic problems. After considering a general qualinear equation in divergence form we apply the method to the case of a nonlinear diffusion-convection equation. The conclusions are stated first for classical solutions and then for generalized and mild solutions. In the case of unbounded initial datum we obtain several regularizing effects for t > 0. Some unilateral pointwise gradient estimates are also obtained. The case of the Dirichlet problem is also considered. Finally, we collect, in the last section, several comments showing the connections among these estimates and the study of the free boundaries associated to the solutions of the diffusion-convection equation.     

A Hybrid Approach to Scheduling with Earliness and Tardiness Costs

A hybrid technique using constraint programming and linear programming is applied to the problem of scheduling with earliness and tardiness costs. The linear model maintains a set of relaxed optimal start times which are used to guide the constraint programming search heuristic. In addition, the constraint programming problem model employs the strong constraint propagation techniques responsible for many of the advances in constraint programming for scheduling in the past few years. Empirical results validate our approach and show, in particular, that creating and solving a subproblem containing only the activities with direct impact on the cost function and then using this solution in the main search, significantly increases the number of problems that can be solved to optimality while significantly decreasing the search time.     

Étude d'un modèle de fragmentation secondaire pour les brouillards de gouttelettes

In this Note, we first present a model for droplet secondary breakup, in liquid sprays. This model is based on the kinetic theory formalism and uses experimental correlations found in the literature (L.-P. Hsiang, G.M. Faeth, Int. J. Multiphase Flow 19 (5) (1993) 721–735; R. Maxey, J. Riley, Phys. Fluids 26 (4) (1983) 883–889; M. Pilch, C.A. Erdman, Int. J. Multiphase Flow 13 (6) (1987) 741–757) to determine the fragmentation rate and its outcome. We then conduct a mathematical study of the resulting kinetic equation. We prove, under some physically reasonable assumptions, an existence and uniqueness theorem and characterize the long-time behaviour of the solution. To cite this article: G. Dufour et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

The dimension of leaf closures of K-contact flows

For K-contact flows on (2n+1)-dimensional compact manifolds, we show that the dimension of any leaf closure is at most the smaller of (n+1) and 2n+1) minus the rank of the vector space of harmonic vector fields.     

Monitoring cooperative equilibria in a stochastic differential game

This paper deals with a class of equilibria which are based on the use of memory strategies in the context of continuous-time stochastic differential games. In order to get interpretable results, we will focus the study on a stochastic differential game model of the exploitation of one species of fish by two competing fisheries. We explore the possibility of defining a so-called cooperative equilibrium, which will implement a fishing agreement. In order to obtain that equilibrium, one defines a monitoring variable and an associated retaliation scheme. Depending on the value of the monitoring variable, which provides some evidence of a deviation from the agreement, the probability increases that the mode of a game will change from a cooperative to a punitive one. Both the monitoring variable and the parameters of this jump process are design elements of the cooperative equilibrium. A cooperative equilibrium designed in this way is a solution concept for a switching diffusion game. We solve that game using the sufficient conditions for a feedback equilibrium which are given by a set of coupled HJB equations. A numerical analysis, approximating the solution of the HJB equations through an associated Markov game, enables us to show that there exist cooperative equilibria which dominate the classical feedback Nash equilibrium of the original diffusion game model.This research was supported by FNRS-Switzerland, NSERC-Canada, FCAR-Quebec.     

Delayed fracture in porous media

The fracture of porous media subjected to a constant load is studied. Contrary to homogeneous solids in which fracture usually happens instantaneously at a well-defined breaking strength, the fracture of a porous medium can occur with a delay, allowing us to quantify the average lifetime of the unbroken material. We show that the average fracture probability, a key property for risk analysis in civil engineering, is given by the probability of crack nucleation. The nucleation process can be understood qualitatively by calculating the activation energy for crack nucleation, taking into account the porosity of the medium.     

Onset of quark-hadron duality in pion electroproduction

A large data set of charged-pion (pi+/-) electroproduction from both hydrogen and deuterium targets has been obtained spanning the low-energy residual-mass region. These data conclusively show the onset of the quark-hadron duality phenomenon, as predicted for high-energy hadron electroproduction. We construct several ratios from these data to exhibit the relation of this phenomenon to the high-energy factorization ansatz of electron-quark scattering and subsequent quark-->pion production mechanisms.