From the Boltzmann equation to the Stokes‐Fourier system in a bounded domain

We prove that the renormalized solutions of the Boltzmann equation considered in a bounded domain with different types of (kinetic) boundary conditions converge to the Stokes‐Fourier system with different types of (fluid) boundary conditions when the main free path goes to zero. This extends the work of F. Golse and D. Levermore [9] to the case of a bounded domain. © 2003 Wiley Periodicals, Inc.     

Aluminium electron-phonon relaxation-time measurement from subpicosecond nonlinear single-photon photoelectric emission at 248 nm

The sensitivity of photoelectric emission of polycrystalline aluminium, produced by 248 nm laser pulses with p-polarization and 450 fs duration, under incidence angles = 74–86°, has been measured. A nonlinear increase of photoemission efficiency, as a function of the incident laser peak intensity in the range of 1–50 GW/cm², was displayed, which confirms earlier observations with gold and tungsten. This nonlinearity is consecutive to the non-thermal distribution of electron gas of laser-heated metal on the time scale of the electron-phonon relaxation time. Analysis of experimental data, using the model previously developed by us [1], gives a value of electron-phonon relaxation time 0.55 ± 0.11 ps.     

Global solutions for 2D quadratic Schrödinger equations

We prove global existence and scattering for a class of quadratic Schrödinger equations in dimension 2 with small and localized data. The proof relies on the idea of space–time resonance.     

The zero surface tension limit two‐dimensional water waves

We consider two‐dimensional water waves of infinite depth, periodic in the horizontal direction. It has been proven by Wu (in the slightly different nonperiodic setting) that solutions to this initial value problem exist in the absence of surface tension. Recently Ambrose has proven that solutions exist when surface tension is taken into account. In this paper, we provide a shorter, more elementary proof of existence of solutions to the water wave initial value problem both with and without surface tension. Our proof requires estimating the growth of geometric quantities using a renormalized arc length parametrization of the free surface and using physical quantities related to the tangential velocity of the free surface. Using this formulation, we find that as surface tension goes to 0, the water wave without surface tension is the limit of the water wave with surface tension. Far from being a simple adaptation of previous works, our method requires a very original choice of variables; these variables turn out to be physical and well adapted to both cases. © 2005 Wiley Periodicals, Inc.     

Numerical solution for exterior problems

Summary We solve the Helmholtz equation in an exterior domain in the plane. A perfect absorption condition is introduced on a circle which contains the obstacle. This boundary condition is given explicitly by Bessel functions. We use a finite element method in the bounded domain. An explicit formula is used to compute the solution out of the circle. We give an error estimate and we present relevant numerical results.     

Influence of the Coulomb forces on the thermodynamic and transport properties of non stoichiometric cerium dioxide

Abstract

In this study, it is demonstrated that the Coulomb interactions explains the essential of experimental thermodynamic and transport thermodynamic results.     

Dependence of photoemission efficiency on the pulsed laser cleaning of Tungsten photocathodes, part 1: Experimental

3+ :YAG laser with 5^th harmonic generator, generating 16 ps duration pulses at 213 nm, with energies up to 0.5 mJ. Experimental results concerning the action of laser pulses, as well as the effects of residual pressure on the cleanliness of the photocathodes surface are presented and discussed. Influence of laser pulses and residual pressure on the work function of the metal are also investigated. Received: 15 April 1996/Accepted: 5 November 1996     

Computation of high order derivatives in optimal shape design

Summary. In shape optimization problems, each computation of the cost function by the finite element method leads to an expensive analysis. The use of the second order derivative can help to reduce the number of analyses. Fujii ([4], [10]) was the first to study this problem. J. Simon [19] gave the second order derivative for the Navier-Stokes problem, and the authors describe in [8], [11], a method which gives an intrinsic expression of the first and second order derivatives on the boundary of the involved domain. In this paper we study higher order derivatives. But one can ask the following questions: -- are they expensive to calculate? -- are they complicated to use? -- are they imprecise? -- are they useless? \medskip\noindent At first sight, the answer seems to be positive, but classical results of V. Strassen [20] and J. Morgenstern [13] tell us that the higher order derivatives are not expensive to calculate, and can be computed automatically. The purpose of this paper is to give an answer to the third question by proving that the higher order derivatives of a function can be computed with the same precision as the function itself. We prove also that the derivatives so computed are equal to the derivatives of the discrete problem (see Diagram 1). We call the discrete problem the finite dimensional problem processed by the computer. This result allows the use of automatic differentiation ([5], [6]), which works only on discrete problems. Furthermore, the computations of Taylor's expansions which are proposed at the end of this paper, could be a partial answer to the last question. Received January 27, 1993/Revised version received July 20, 1993     

Genetic diversity and haplotype structure of 21 Y‐STRs,including nine noncore loci,in South Tunisian Population: Forensic relevance

Y chromosome STRs (Y‐STRs) are being used frequently in forensic laboratories. Previous studies of Y‐STR polymorphisms in different groups of the Tunisian population identified low levels of diversity and discrimination capacity (DC) using various commercial marker sets. This definitely limits the use of such systems for Y‐STRs genotyping in Tunisia. In our investigation on South Tunisia, 200 unrelated males were typed for the 12 conventional Y‐STRs included in the PowerPlex® Y System. Additional set of nine noncore Y‐STRs including DYS446, DYS456, DYS458, DYS388, DYS444, DYS445, DYS449, DYS710, and DYS464 markers were genotyped and evaluated for their potential in improving DC. Allele frequency, gene diversity, haplotype diversity (HD), and DC calculation revealed that DYS464 was the most diverse marker followed by DYS710 and DYS449 markers. The standard panel of 12 Y‐STRs (DC = 80.5%) and the nine markers were combined to obtain DC of 99%. Among the 198 different haplotypes observed, 196 haplotypes were unique (HD = 99.999). Out of the nine noncore set, six Y‐STRs (DYS458, DYS456, DYS449, DYS710, DYS444, and DYS464) had the greatest impact on enhancing DC. Our data provided putative Y‐STRs combination to be used for genetic and forensic applications.