Discussion summary: Fictitious domain methods

Fictitious Domain methods are constructed in the following manner: Suppose a partial differential equation is to be solved on an open bounded set, Omega, in 2-D or 3-D. Let R be a rectangle domain containing the closure of Omega. The partial differential equation is first solved on R. Using the solution on R, the solution of the equation on Omega is then recovered by some procedure. The advantage of the fictitious domain method is that in many cases the solution of a partial differential equation on a rectangular region is easier to compute than on a nonrectangular region. Fictitious domain methods for solving elliptic PDEs on general regions are also very efficient when used on a parallel computer. The reason is that one can use the many domain decomposition methods that are available for solving the PDE on the fictitious rectangular region. The discussion on fictitious domain methods began with a talk by R. Glowinski in which he gave some examples of a variational approach to ficititious domain methods for solving the Helmholtz and Navier-Stokes equations

Generation of Reactive Oxygen Metabolites by the Varicose Vein Wall

AbstractObjectives: to evaluate the content of lipid peroxidation products (expressed by the concentration of thiobarbituric acid-reactive substances; TBARS), the content of myeloperoxidase (MPO), and the localisation of xanthine oxidase (XO) in varicose veins (vv), varicose veins with superficial thrombophlebitis and unchanged saphenous veins.Methods: varicose saphenous veins, varicose veins with superficial thrombophlebitis and normal saphenous veins obtained during varicose vein surgery on 36 patients as well as healthy saphenous veins from cadaver organ donors (control). Homogenates were prepared in which TBARS concentration and MPO content were determined. Immunohistochemical staining to detect XO was also performed.Results: the highest concentration of TBARS occurred in vv with superficial thrombophlebitis, the lowest in donor vein. The highest content of MPO was observed in vv and slightly lower – in varicose veins with thrombophlebitis. A positive reaction for XO was seen in vv wall endothelium. Specimens of vv with thrombophlebitis revealed strong, intense staining in endothelium as well as in vasa vasorum.Conclusions: varicose veins, especially those complicated with superficial thrombophlebitis revealed increased free radical generation. Its sources might be neutrophils, and in vv complicated with superficial thrombophlebitis–xanthine oxidase

Continuation-conjugate gradient methods for the least squares solution of nonlinear boundary value problems

We discuss in this paper a new combination of methods for solving nonlinear boundary value problems containing a parameter. Methods of the continuation type are combined with least squares formulations, preconditioned conjugate gradient algorithms and finite element approximations. We can compute branches of solutions with limit points, bifurcation points, etc. Several numerical tests illustrate the possibilities of the methods discussed in the present paper; these include the Bratu problem in one and two dimensions, one-dimensional bifurcation and perturbed bifurcation problems, the driven cavity problem for the Navier–Stokes equations

Toward a model of computational attention based on expressive behavior: applications to cultural heritage scenarios

Our project goals consisted in the development of attention-based analysis of human expressive behavior and the implementation of real-time algorithm in EyesWeb XMI in order to improve naturalness of human-computer interaction and context-based monitoring of human behavior. To this aim, perceptual-model that mimic human attentional processes was developed for expressivity analysis and modeled by entropy. Museum scenarios were selected as an ecological test-bed to elaborate three experiments that focus on visitor profiling and visitors flow regulation