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.     

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.     

Fixed mesh approximation of ordinary differential equations with impulses

When trains of impulse controls are present on the right-hand side of a system of ordinary differential equations, the solution is no longer smooth and contains jumps which can accumulate at several points in the time interval. In technological and physical systems the sum of the absolute value of all the impulses is finite and hence the total variation of the solution is finite. So the solution at best belongs to the space BV of vector functions with bounded variation. Unless variable node methods are used, the loss of smoothness of the solution would a priori make higher-order methods over a fixed mesh inactractive. Indeed in general the order of -convergence is and the nodal rate is . However in the linear case -convergence rate remains but the nodal rate can go up to by using one-step or multistep scheme with a nodal rate up to when the solution belongs to . Proofs are given of error estimates and several numerical experiments confirm the optimality of the estimates. Received March 15, 1996 / Revised version received January 3, 1997     

Pricing and distributed QoS control for elastic network traffic

We study a processor-sharing model in which users choose between a high- and a low-priority service, based on their utility functions and prices charged by the service provider. The latter aims at revenue maximization. The model is motivated by file transmissions in data networks with distributed congestion control.     

Weighted Sobolev embedding with unbounded and decaying radial potentials

We prove embedding results of weighted W1,p(RN) spaces of radially symmetric functions. The results then are used to obtain ground and bound state solutions of quasilinear equations with unbounded or decaying radial potentials.     

Kinetics and mechanisms of chlorine transfer from chloramine to amines in aqueous medium

The kinetics and the equilibrium constant of the chlorine transfer reaction between monochloramine NH₂Cl and the amines: C₂H₅NH₂, (CH₃)₂CHNH₂, (CH₃)₂NH, and (C₂H₅)₂NH are investigated by spectrophotometry in aqueous medium at 25°C, in the pH range from 8 to 13 and for an ionic strength equal to 1.03 ± 0.05M. For a concentration of total ammonia equal to 1M, the observed rate constant is pH independent below 8 and above 12.8 and reaches a maximum located between the pK_as of NH₄⁺ and RR'NH₂⁺. From these results and those obtained earlier for NH₂Cl and CH₃NH₂, the reaction is shown to involve an interaction between neutral molecules NH₂Cl and RR'NH, subject to general acid catalysis. The ability of an interaction corresponding to a specific catalysis and involving NH₃Cl⁺ and RR'NH rather than NH₂Cl and RR'NH₂⁺ is also discussed. The activation parameters are given for each reaction.     

Evolution equations for shapes and geometries

The first object of this paper is to introduce a new evolution equation for the characteristic function of the boundary Γ of a Lipschitzian domain Ω in the N-dimensional Euclidean space under the influence of a smooth time-dependent velocity field. The originality of this equation is that the evolution takes place in an L^p-space with respect to the (N − 1)-Hausdorff measure. A second more speculative objective is to discuss how that equation can be relaxed to rougher velocity fields via some weak formulation. A candidate is presented and some of the technical difficulties and open issues are discussed. Continuity results in several metric topologies are also presented. The paper also specializes the results on the evolution of the oriented distance function to initial sets with zero N-dimensional Lebesgue measure.     

A New Differential Method Applied to the Study of Arbitrary Cross Section Microstructured Optical Fibers

The present work adapts a recent grating theory called “Fast Fourier factorization” to cylindrical coordinates in order to study microstructured optical fibers (MOFs). Compared with the classical differential method, this new differential method takes into account the truncation of Fourier series and the discontinuities of the fields across the diffracting surface with the help of new factorization rules. The main advantage of this method is that the directrix of the diffracting cylindrical surface is arbitrary and permits anisotropic and inhomogeneous media although its numerical application needs longer computation time, compared with other well-known numerical methods. The S-propagation algorithm is used to avoid numerical contaminations. The numerical results are validated and compared with the well-established Multipole method in the case of a MOF with six circular cylinders. Further, a new cross-sectional profile (with sectorial inclusions) that the Multipole method cannot consider is studied.