Finite elements for a prefractal transmission problem

In this Note we deal with the finite element approximation of a transmission problem across a prefractal curve approximating the von Koch fractal curve. We construct a mesh adapted to the geometric shape of the interface and we refine it consistently with some estimates in suitable weighted Sobolev spaces. In these spaces we also obtain an approximation error estimate. To cite this article: P. Bagnerini et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

The distance function from the boundary in a Minkowski space

Let the space be endowed with a Minkowski structure (that is, is the gauge function of a compact convex set having the origin as an interior point, and with boundary of class ), and let be the (asymmetric) distance associated to . Given an open domain of class , let be the Minkowski distance of a point from the boundary of . We prove that a suitable extension of to (which plays the rôle of a signed Minkowski distance to ) is of class in a tubular neighborhood of , and that is of class outside the cut locus of (that is, the closure of the set of points of nondifferentiability of in ). In addition, we prove that the cut locus of has Lebesgue measure zero, and that can be decomposed, up to this set of vanishing measure, into geodesics starting from and going into along the normal direction (with respect to the Minkowski distance). We compute explicitly the Jacobian determinant of the change of variables that associates to every point outside the cut locus the pair , where denotes the (unique) projection of on , and we apply these techniques to the analysis of PDEs of Monge-Kantorovich type arising from problems in optimal transportation theory and shape optimization.

     

Bose–Einstein condensation in satisfiability problems

This paper is concerned with the complex behavior arising in satisfiability problems. We present a new statistical physics-based characterization of the satisfiability problem. Specifically, we design an algorithm that is able to produce graphs starting from a k-SAT instance, in order to analyze them and show whether a Bose–Einstein condensation occurs. We observe that, analogously to complex networks, the networks of k-SAT instances follow Bose statistics and can undergo Bose–Einstein condensation. In particular, k-SAT instances move from a fit-get-rich network to a winner-takes-all network as the ratio of clauses to variables decreases, and the phase transition of k-SAT approximates the critical temperature for the Bose–Einstein condensation. Finally, we employ the fitness-based classification to enhance SAT solvers (e.g., ChainSAT) and obtain the consistently highest performing SAT solver for CNF formulas, and therefore a new class of efficient hardware and software verification tools.     

Error estimate for a stabilised domain decomposition method with nonmatching grids

Summary. In this paper, we analyse a stabilisation technique for the so-called three-field formulation for nonoverlapping domain decomposition methods. The stabilisation is based on boundary bubble functions in each subdomain which are then eliminated by static condensation. The discretisation grids in the subdomains can be chosen independently as well as the grid for the final interface problem. We present the analysis of the method and we construct a set of bubble functions which guarantees the optimal rate of convergence. Received May 12, 1998 / Revised version received November 21, 2000 / Published online June 7, 2001     

Absolute (e, 2e) differential cross section measured in coplanar conditions: He

The first measurement of the absolute (e, 2e) five times differential cross section in coplanar symmetric conditions on He are reported. Incident energy is varied from 200 to 4000 eV in order to test different theoretical models.     

Application of electrochemical reactors for industrial waste-water treatment

The effectiveness of electrochemical reactors for industrial wastewater treatment has been improved since three-dimensional electrodes have been introduced; in fact, limitations of mass transfer can arise, due to the low concentrations of pollutants which may be involved in the process. Three-dimensional electrodes offer a very high electrode area per unit electrode volume and they can act as turbulence promoters or give rise to high linear electrolyte velocity, resulting in high values of mass transport coefficient. However, careful selection of operative parameters is needed in order to obtain high performance. This paper examines the results obtained in our laboratory on the cathodic reduction of copper at RVC electrodes; in particular the interference of dissolved oxygen is studied during the removal of copper from extremely diluted solutions (C < 10 ppm). Some results are also discussed on the removal of organic pollutants by electrochemical oxidation at three-dimensional anode consisting of a fixed bed of carbon pellets.     

Detection of a flow induced magnetic field eigenmode in the riga dynamo facility

In a closed volume of molten sodium an intense single-vortex-like helical flow has been produced by an outside powered propeller. At a flow rate of 0.67 m(3)/s a slowly growing magnetic field eigenmode was detected. For a slightly lower flow, additional measurements showed a slow decay of this mode. The measured results correspond satisfactorily with numerical predictions for the growth rates and frequencies.     

Satellite structures and momentum distributions in binary (e, 2e) spectroscopy of N2O

The (e, 2e) coincidence technique has been applied in studying the valence shell of N₂O. The assignment of some satellite structures is discussed.     

Static light scattering,ultraviolet–visible,and fluorescence spectroscopy from fluorescent methyl methacrylate/benzazole dye copolymers displaying an intramolecular proton‐transfer mechanism in the electronically excited state

The solution behavior of new copolymers of methyl methacrylate and benzazole dyes emitting fluorescence because of an intramolecular proton‐transfer mechanism in the electronically excited state has been investigated by static light scattering, fluorescence spectroscopy, ultraviolet–visible, and gel permeation chromatography. In the dilute regime, with tetrahydrofuran (THF) and chloroform as solvents, the copolymers behave as typical polydisperse linear chains in good solvents. The analysis of the osmotic modulus for concentrated solutions in THF (c ≥ 60 g L^?1) indicates the existence of an interchain association mechanism. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 341–350, 2003