H‐self‐adjoint matrices. Application to radiosity

In computer graphics, in the radiosity context, a linear system Φx=b must be solved and there exists a diagonal positive matrix H such that H Φ is symmetric. In this article, we extend this property to complex matrices: we are interested in matrices which lead to Hermitian matrices under premultiplication by a Hermitian positive‐definite matrix H. We shall prove that these matrices are self‐adjoint with respect to a particular innerproduct defined on ?ⁿ. As a result, like Hermitian matrices, they have real eigenvalues and they are diagonalizable. We shall also show how to extend the Courant–Fisher theorem to this class of matrices. Finally, we shall give a new preconditioning matrix which really improves the convergence speed of the conjugate gradient method used for solving the radiosity problem. Copyright © 2002 John Wiley & Sons, Ltd.     

Development of a compact alpha and beta camera for dismantlement applications

Journal of Radioanalytical and Nuclear Chemistry - A new method has been developed to image surface contamination on-site by short range radiation emitters (such as alpha or beta particle...     

Control of the refractive index in photopolymerizable materials for (2+1)D solitary wave guide formation

We report an experimental and theoretical study on the optimization of (2+1)D self-written waveguide formation inside a photopolymerizable material. The accurate control of the refractive index value inside the bulk of the material during the polymerization process gives us the opportunity to define a virtual core and a virtual cladding for the system. The V value which characterizes the guidance properties of a fiber can be applied to this propagation. The control of the V value allows us to propagate single mode or multimode waveguides on a few centimeters. Numerical simulations of these waveguides based on a paraxial model including both photopolymerization and Kerr effect give very good agreement with our experimental results.     

Characterization of an ytterbium-doped double-clad fiber laser passively mode-locked by nonlinear polarization rotation

The properties of an ytterbium-doped double-clad fiber laser, passively mode-locked by nonlinear polarization rotation are investigated in this work. Cartographies of mode-locking regime versus halfwave plates orientations are presented for several values of the total cavity dispersion and for different pump powers. Bistability between the continuous and the mode-locking regimes is pointed out. The effect of the total group velocity dispersion is described with a master mode-locking equation. PACS 42.55.Wd; 42.65.Re     

Analytical study of a hollow sphere made of plastic porous material and subjected to hydrostatic tension-application to some problems in ductile fracture of metals

A solution to the problem stated in the title is given by treating the porous matrix as a homogeneous material obeying the Gurson-Tvergaard model. As a first application, it is shown that the flow stress under hydrostatic loading of a material containing two populations of voids with very different sizes is almost the same as that of a material with only one population of voids and the same total porosity. As a second application, a self-consistent method is used to derive a value for the parameter introduced by Tvergaard in the original Gurson model to account for the interactions between cavities. Other models are also considered and shown to fail to satisfy the self-consistency requirement, whatever the value chosen for the parameter characterizing interactions between voids.     

Cavitation in holographic sQGP

We study the possibility of cavitation in the non-conformal N=^2?SU(N) theory which is a mass deformation of N=4SU(N) Yang-Mills theory. The second order transport coefficients are known from the numerical work using AdS/CFT by Buchel and collaborators. Using these and the approach of Rajagopal and Tripuraneni, we investigate the flow equations in a (1+1)-dimensional boost invariant set up. We find that the string theory model does not exhibit cavitation before phase transition is reached. We give a semi-analytic explanation of this finding.     

Geometrical disorder of the fronts of a tunnel-crack propagating in shear in some heterogeneous medium

A statistical analysis of the deformation of the fronts of a tensile tunnel-crack propagating in fatigue in some medium with spatially varying Paris constant was recently performed, with special emphasis on the evolution of the power spectra and correlation functions of the fluctuations of the fronts around reference straight lines. This study is extended here to coplanar propagation (along a weak plane) of a tunnel-crack loaded in mode 2+3. The results are rather similar to those previously obtained for mode 1. In particular, just like for tensile loadings, there is an effect of gradual selection in time of Fourier components of the fluctuations of the fronts of large wavelength. One novelty, however, is that for shear loadings, the fronts no longer tend to become symmetrical in time, so that correlations between crack front fluctuations at two points are higher for points located on the same front than for points located on distinct ones.     

Mathematical modelling of transformation plasticity in steels I: Case of ideal-plastic phases

Transformation plasticity in steels (i.e., the anomalous plastic flow observed during the progress of a phase transformation) is usually attributed to two distinct physical mechanisms, which have been proposed by Greenwood and Johnson and Magee. This paper proposes a theoretical approach to the problem, in the case where the Magee mechanism is negligible and the phases are ideal-plastic. An explicit expression for the transformation plastic strain rate is obtained for a steel undergoing a transformation under a small applied stress; this expression is consistent with experiments conducted on various materials. A finite element simulation provides a confirmation of the theoretical formula and allows for a detailed examination of the validity of some physical hypotheses made in the treatment. It also allows for a study of transformation plasticity under high applied stresses. Based on these results, a general (i.e., applicable for all kinds of stresses applied) model is proposed in the case of ideal-plastic phases.