Fast regularized linear sampling for inverse scattering problems

A new numerical procedure is proposed for the reconstruction of the shape and volume of unknown objects from measurements of their radiation in the far field. This procedure is a variant and the linear sampling method has a very acceptable computational load and is fully automated. It is based on exploiting an iteratively computed truncated singular‐value decomposition and heuristics to extract the desired signal from the background noise. Its performance on a battery of examples of different types is shown to be promising. Copyright © 2010 John Wiley & Sons, Ltd.     

Asymptotic analysis of the steady stokes equation with randomly perturbed viscosity in a thin tube structure

The Stokes equation with the nonconstant viscosity is considered in a thin tube structure, i.e., in a connected union of thin rectangles with heights of order ε ≪ 1 and bases of order 1 with smoothened boundary. An asymptotic expansion of the solution is constructed. In the case of random perturbations of the constant viscosity, we prove that the leading term for the velocity is deterministic, while for the pressure it is random, but the expectations of the pressure satisfies the deterministic Darcy equation. Estimates for the difference between the exact solution and its asymptotic approximation are proved. Bibliography: 11 titles. Illustrations: 3 figures.     

H2 Convergence of Solutions of a Biharmonic Problem on a Truncated Convex Sector Near the Angle π

We consider a biharmonic problem Δ²u_ω = f_ω with Navier type boundary conditions u_ω = Δu_ω = 0, on a family of truncated sectors Ω_ω in ?² of radius r, 0 < r < 1 and opening angle ω, ω ∈ (2π/3, π] when ω is close to π. The family of right-hand sides (f_ω)_{ω∈(2π/3, π]} is assumed to depend smoothly on ω in L²(Ω_ω). The main result is that u_ω converges to u_π when ω → π with respect to the H²-norm. We can also show that the H²-topology is optimal for such a convergence result.

     

Sol-gel preparation and properties of interpenetrating, encapsulating and blend silica-based urea-formaldehyde hybrid composite materials

Four different silica-based urea-formaldehyde (UF/SiO₂) composite materials were prepared by various sol-gel synthetic procedures to yield an interpenetrating (IPN-UF/SiO₂), a micro-size UF resin encapsulated inside silica shell (Encap-UF/SiO₂), a micro-size silica encapsulated inside UF shell (Encap-SiO₂/UF), and a blend mixture (Blend-UF/SiO₂) hybrid systems. The thermal properties of the obtained organic-inorganic hybrid composite materials were examined by thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC). The structure and morphology of the obtained systems were investigated by infrared spectroscopy (FT-IR), powder X-ray diffraction (XRD) and scanning electron microscopy (SEM) techniques. Their surface porosity and acidity were evaluated from the nitrogen adsorption isotherm and the pH of the corresponding 10% aqueous suspension, respectively. All the results provided evidence for the formation of different hybrid systems with different surface, structural and morphological characteristics.     

Investigation de la gestion de qualité de service dans le réseau UMTS

Bit rate announced for the future standards of telecommunication, as well as the level of integration reached are, as many factors, determining for the establishment of new applications in mobile terminals. Nowadays, mobile video streaming services are possible. Mobile users expect to receive multimedia traffic with some performance guarantees, so we must ensure the necessary quality of service during the video transmission. This paper aims at investigating quality of service issue inUmts network. More specifically, we explore the main challenge of quality of service management to dynamically optimize the distribution of load inUmts networks. Our investigation is organized in the following way. We formalize the optimization problem which is based on the graph theory and modellingUmts network as well as mobile users and applications to be used. The simulation of our optimization model show a clear improvement of the quality of service perceived by anUmts user in terms of bit rate, blocking and connection drop.     

One-dimensional stochastic heat equation with discontinuous conductance

We introduce a new stochastic partial differential equation with second-order elliptic operator in divergence form, having a piecewise constant diffusion coefficient, and driven by a space–time white noise. Such equation could be used in mathematical modeling of diffusion phenomena in medium consisting of two kinds of materials and undergoing stochastic perturbations. We prove the existence of the solution and we present explicit expressions of its covariance and variance functions. Some regularity properties of the solution sample paths are also analyzed.     

General decay for a porous thermoelastic system with a memory

In this paper, we consider a linear damped porous thermoelastic system of memory type where the heat conduction is given by Cattaneo’s Law . We establish a general decay results using an appropriate Lyapunov functional.     

Uniformly stable numerical schemes for the Boltzmann equation preserving the compressible Navier–Stokes asymptotics

In this paper, we develop a numerical method to solve Boltzmann like equations of kinetic theory which is able to capture the compressible Navier–Stokes dynamics at small Knudsen numbers. Our approach is based on the micro/macro decomposition technique, which applies to general collision operators. This decomposition is performed in all the phase space and leads to an equivalent formulation of the Boltzmann (or BGK) equation that couples a kinetic equation with macroscopic ones. This new formulation is then discretized with a semi-implicit time scheme combined with a staggered grid space discretization. Finally, several numerical tests are presented in order to illustrate the efficiency of our approach. Incidentally, we also introduce in this paper a modification of a standard splitting method that allows to preserve the compressible Navier–Stokes asymptotics in the case of the simplified BGK model. Up to our knowledge, this property is not known for general collision operators.     

Optimized FIB silicon samples suitable for lattice parameters measurements by convergent beam electron diffraction

The aim of this paper is to check the effect of artefacts introduced by focused ion beam (FIB) milling on the strain measurement by convergent beam electron diffraction (CBED). We show that on optimized silicon FIB samples, the strain measurement can be performed with a sensitivity of about 2.5 × 10⁻⁴ which is very close to the theoretical one and we conclude that FIB preparation can be suitable for such measurements in microelectronic devices.

To achieve this, we first used CBED and electron energy loss spectroscopy (EELS) which provide a procedure permitting an exact knowledge of the sample geometry, i.e. the thickness of both amorphous and crystalline layers. This procedure was used in order to measure the FIB-amorphized sidewall layer. It was found that if the FIB preparation is optimized one can reduce this amorphous layer down to around 7 nm on each side. Secondly different preparation techniques (cleavage, Tripod™ and FIB) permit to check if the surface damaged layer introduced by FIB influences the strain state of the sample. Finally, it was found that the damaged layer does not introduce measurable strain in pure silicon but reduces appreciably the quality of the CBED patterns.