Asymptotic Expansions for the Distribution of the Maximum of Gaussian Random Fields

Some asymptotic results are proved for the distribution of the maximum of a centered Gaussian random field with unit variance on a compact subset S of ^N . They are obtained by a Rice method and the evaluation of some moments of the number of local maxima of the Gaussian field above an high level inside S and on the border S. Depending on the geometry of the border we give up to N+1 terms of the expansion sometimes with exponentially small remainder. Application to waves maximum is shown.     

The vacuum ultraviolet absorption spectrum of diatomic calcium

Calcium granules (99.5%) have been heated to 615°C in a tantalum furnace and the absorption spectrum has been observed on the SA 61 beam line of SUFERACO (Orsay) using a 3-metre Balzers monochromator down to the -LiF cut-off (1015 Å). An intense Rydberg series has been observed between 1900 and 1500 Å. This series extends from n = 5 to n = 12 and gives the ionization potential at 63068 cm^?1 (1585.6 Å) or 7.819eV and the quantum defect δ = 1.73.     

An Exact Riemann Solver for Multicomponent Turbulent Flow

The main objective of this paper is to provide some adequate way to compute the non-conservative hyperbolic system which describes a multicomponent turbulent flow. The model is written for an isentropic gas. The exact solution of the Riemann Problem (RP) associated to the hyperbolic system is exhibited. It is composed of constant states separated by rarefaction waves, or shock waves and a contact discontinuity.

The selection of the admissible part of the shock curve is obtained using an entropy criterion. This entropy is the total energy of the system. Thanks to the latter, one may compute the exact solution of the Riemann problem, assuming genuinely non linear fields contain sufficiently weak shocks.     

Computation of Flashing Flows In Variable Cross-Section Ducts

A Finite-Volume scheme which enables computing fast transient single phase and two phase flows in variable cross section ducts is presented. The physical modelling relies on the Homogeneous Relaxation Model. The theoretical framework is briefly presented, together with the main ideas of a new approximate Riemann solver. Numerical results confirm the suitability of the present approach.