Spectral properties and time asymptotic behaviour of linear transport equations in slab geometry

The goal of this paper is to analyse some spectral properties of time‐dependent monoenergetic linear transport equation with perfect reflecting boundary conditions.It is proved that the streaming operator generates a strongly continuous group and its explicit expression is derived. This enables us to investigate in details the compactness properties of the second‐order remainder term of the Dyson–Phillips expansion for a large class of collision operators. The validity of the obtained results for perfect periodic boundary conditions is also discussed. Copyright © 2001 John Wiley & Sons, Ltd.     

Decay rates at low and high frequencies for a plate equation with feedback concentrated in interior curves

In this paper we study the stabilization of plate vibrations by means of piezoelectric actuators. In this situation the geometric control condition of Bardos, Lebeau and Rauch [6] is not satisfied. We prove that we have exponential stability for the low frequencies but not for the high frequencies. We give an explicit decay rate for regular initial data at high frequencies while clarifying the behavior of the constant which intervenes in this estimation there function of the frequency of cut n. The method used is based on some trace regularity which reduces stability to some observability inequalities for the corresponding undamped problem. Moreover, we show numerically at low frequencies, that the optimal location of the actuator is the center of the domain Ω. Research supported by the RIP program of Oberwolfach Institut and by the Tunisian Ministry for Scientific Research and Technology (MRST) under Grant 02/UR/15-01. Research supported by the RIP program of Oberwolfach Institut. (Received: September 17, 2003; revised: February 26, 2004)     

Nonlinear three-point boundary value problems

In the present work, we investigate nonlinear three-point boundary value problems (second-order differential equations with boundary conditions imposed at three consecutive points) in an effort to understand the conditions that must be imposed upon nonlinear perturbations of a linear problem in order to obtain a solution of a three-point problem. Both the noncritical case and the critical case are considered. In the first case, existence and uniqueness results are obtained, and in the second case we deal with local bifurcation problems when the nonlinearities are quadratic and cubic.     

Numerical approximation for a non-linear membrane problem

We present a numerical study of large deformations of non-linearly elastic membranes. We consider the non-linear membrane model obtained by Le Dret and Raoult using Γ-convergence, in the case of a Saint Venant-Kirchhoff bulk material. We consider conforming P₁ and Q₁ finite element approximations of the membrane problem and use a non-linear conjugate gradient algorithm to minimize the discrete energy. We present numerical tests including membranes subjected to live pressure loads.     

Coincidence summing corrections factors calculated for volume 152Eu sources in γ-ray spectromtery using Monte Carlo techniques

Journal of Radioanalytical and Nuclear Chemistry - True coincidence summing (TCS) correction factors were determined for 152Eu volume sources used for γ-ray efficiency calibration as the ratio...     

Competitive adsorption of anionic dyes onto DMOA modified MCM-41

Research on Chemical Intermediates - The single and binary adsorption of two anionic dyes Acid Yellow 17 (AY17) and Naphtol Green B (NGB) onto N–N–Dimethyl-n-octylamine (DMOA) modified...