Dispersion analysis of the least‐squares finite‐element shallow‐water system

The frequency or dispersion relation for the least‐squares mixed formulation of the shallow‐water equations is analysed. We consider the use of different approximation spaces corresponding to co‐located and staggered meshes, respectively. The study includes the effect of Coriolis, and the dispersion properties are compared analytically and graphically with those of the mixed Galerkin formulation. Numerical solutions of a test problem to simulate slow Rossby modes illustrate the theoretical results. Copyright © 2003 John Wiley & Sons, Ltd.     

Infinitely renormalizable diffeomorphisms of the disk at the boundary of chaos

We show that, among area contracting embeddings of the 2-disk, infinitely renormalizable maps with a bounded geometry either have positive topological entropy or correspond to a cascade of period doubling.

     

Kinetics of the reactions of the IO radical with dimethyl sulfide,methanethiol, ethylene,and propylene

The reactions of IO radicals with CH₃SCH₃, CH₃SH, C₂H₄, and C₃H₆ have been studied using the discharge flow method with direct detection of IO radicals by mass spectrometry. The absolute rate constants obtained at 298 K are the following: IO + CH₃SCH₃ → products (1): k₁ = (1.5 ± 0.2) × 10^?14; IO + CH₃SH → products (2): k₂ = (6.6 ± 1.3) × 10^?16; IO + C₂H₄ →products (3): k₃ < 2 × 10^?16; IO + C₃H₆ → products (4): k₄ < 2 × 10^?16 (units are cm³ molecule^?1 s^?1). CH₃S(O)CH₃ and HOI were found as products of reactions (1) and (2), respectively. The present lower value of k₁ compared to our previous determination is discussed.     

The ALTO project at IPN-Orsay

The availability of both a tandem deuteron beam and a linac electron beam, the latter converted into Bremsstrahlung, at the new ALTO facility at IPN-Orsay offers a unique opportunity to compare the performance of a laser ion guide under different regimes. The ALTO accelerator has delivered its first electron beam at the end of 2005 and a design for a gas-cell prototype is being studied.     

Optimization technique based on learning automata

Optimization techniques are finding increasingly numerous applications in process design, in parallel to the increase of computer sophistication. The process synthesis problem can be stated as a largescale constrained optimization problem involving numerous local optima and presenting a nonlinear and nonconvex character. To solve this kind of problem, the classical optimization methods can lead to analytical and numerical difficulties. This paper describes the feasibility of an optimization technique based on learning systems which can take into consideration all the prior information concerning the process to be optimized and improve their behavior with time. This information generally occurs in a very complex analytical, empirical, or know-how form. Computer simulations related to chemical engineering problems (benzene chlorination, distillation sequence) and numerical examples are presented. The results illustrate both the performance and the implementation simplicity of this method.Nomenclature c _i penalty probability - cp precision parameter on constraints - D variation domain of the variablex - f(·) objective function - g(·) constraints - i,j indexes - k iteration number - N number of actions - P probability distribution vector - p _i ith component of the vectorP as iterationk - r number of reactors in the flowsheet - u(k) discrete value or action chosen by the algorithm at iterationk - u _i discrete value of the optimization variable in [u _min,u _max] - u _min lowest value of the optimization variable - u _max largest value of the optimization variable - Z random number - x variable for the criterion function - xp precision parameter on criterion function - W(k) performance index unit output at iterationk - ₀, ₁ reinforcement scheme parameters - _p sum of the probability distribution vector components     

Sur une conjecture de M. Kac

Summary We consider the following heat conduction problem. Let K be a compact set in Euclidean space ³. Suppose that K is held at the temperature 1, while the surrounding medium is at the temperature 0 at time 0. Following Spitzer we investigate the asymptotic behaviour of the integral E _K (t) which represents the total energy flow in time t from the set K to the surrounding medium ³–K. An asymptotic expansion is given for E _K (t) which refines a theorem due to Spitzer. This expansion also verifies and improves a formal calculation of Kac. Similar results are proved in higher dimensions. Up to the constant m(K), the quantity E _K (t) can be interpreted as the expected value of the volume of the Wiener sausage associated with K and a d-dimensional Brownian motion. This point of view both plays a major role in the proofs and leads to a probabilistic interpretation of the different terms of the expansion.