Modelling of fusion-reaction protons measurements within TEXTOR facility

This paper describes the computation of fusion protons detection efficiency, which has been carried out by means of the known GOURDON code. For this purpose an analytical model of the tokamak magnetic field has been used. Computer simulations of different trajectories of charged particle, on the basis of the motion equations, have been performed with the GOURDON code. Detection efficiency, defined as the ratio of the number of detected particles to that of particles emitted from plasma, has been calculated. The transparency function of the detector system has been derived for given geometry of the ion-pinhole camera. Calculations have been carried out for the detector position used in recent experiments. The poloidal-and toroidal-symmetry of plasma and standard fusion-product source profile have been assumed. The computed detection efficiency is presented as a function of the main radius and particle pitch-angle for different spatial orientations of the detector head.     

Dynamic updates of the barrier parameter in primal-dual methods for nonlinear programming

We introduce a framework in which updating rules for the barrier parameter in primal-dual interior-point methods become dynamic. The original primal-dual system is augmented to incorporate explicitly an updating function. A Newton step for the augmented system gives a primal-dual Newton step and also a step in the barrier parameter. Based on local information and a line search, the decrease of the barrier parameter is automatically adjusted. We analyze local convergence properties, report numerical experiments on a standard collection of nonlinear problems and compare our results to a state-of-the-art interior-point implementation. In many instances, the adaptive algorithm reduces the number of iterations and of function evaluations. Its design guarantees a better fit between the magnitudes of the primal-dual residual and of the barrier parameter along the iterations.     

Damaging processes in polypropylene compound: Experiment and modeling

The aim of this paper is to present a procedure of construction of constitutive equations within the framework of Continuum Mechanics. The main focus of our effort is to introduce the geometric change at a high level of strain and the damage which are generally developed in simple tests (tension, shear) of polymeric materials such as polypropylene compounds or copolymers (PP). High-resolution strain-mapping techniques are employed to determine the surface strain fields and, consequently, a measurement of the volume change. A phenomenological model based upon experimental observations was developed to reproduce the main behavior, e.g., the stress strain curves, including the volume change and their consequences. State Variables are defined and related to their evolution in relation with the state laws. The identification of the resulting model was made by reproducing the data issued from basic tests (Tension, Iosipescu Shear). Published in Russian in Vysokomolekulyarnye Soedineniya, Ser. A. 2008, Vol. 50, No. 5, pp. 850–861. This article was submitted by the authors in English.     

Groupoids with quasigroup and Latin square properties

Connections of some groupoid identities with the quasigroup and Latin square properties are investigated using combinatorial methods.     

Vanishing Results for Toric Varieties Associated To GL n and G2

Toric varieties associated with root systems appeared very naturally in the theory of group compactifications. Here they are considered in a very different context. We prove the vanishing of higher cohomology groups for certain line bundles on toric varieties associated to GL _n and G₂. This can be considered of general interest and it improves the previously known results for these varieties. We also show how these results give a simple proof of a converse to Mazur’s inequality for GL _n and G₂ respectively. It is known that the latter imply the nonemptiness of some affine Deligne–Lusztig varieties. Dedicated to Scarlett MccGwire and Dr. Christian Duhamel     

Correlating surface microstructures with reactivity on commercially pure zirconium using scanning electrochemical microscopy and scanning electron microscopy

Scanning electrochemical microscopy and scanning electron microscopy were employed to correlate the surface microstructures with surface reactivity of commercially pure zirconium. It was found that heightened reactivity was associated with iron impurities lying beneath the oxide surface. This could result in failure of nuclear reactor components fabricated using zirconium alloys due to hydrogen ingress and corrosion. COMSOL multiphysics software was used to quantify the electrochemical kinetic constants associated with the differences in surface reactivity.     

Digital image correlation and biaxial test on composite material for anisotropic damage law identification

The purpose of the work is to extend the use of non-conventional tests and full field measurements to the identification of an anisotropic damage law. A Digital Image Correlation technique based on a finite element discretization is used to extract planar displacement fields. The reconditioned Equilibrium Gap Method is then used to retrieve a damage law that accounts for shear softening, a specific form suited to the present application. The identification is shown to reduce to a linear system. The example of a biaxial shear test performed on a cruciform specimen is considered. The approach is first qualified by using displacement fields resulting from a non-linear computation with a known damage law. A good agreement is observed between the prescribed and identified laws for distinct parameter settings, even when significant noise is added to the displacement fields. The reconstructed displacement fields coincide perfectly with the measurements. The complete scheme is finally tested considering images taken during an experiment performed on a carbon/carbon composite. The identified damage pattern and the corresponding damage values are similar to post-processed maps using classically identified parameters. The reconstructed displacement field accounts for 95% of the fluctuations observed in the measurements.