Performance and analysis of saddle point preconditioners for the discrete steady-state Navier-Stokes equations

Summary. We examine the convergence characteristics of iterative methods based on a new preconditioning operator for solving the linear systems arising from discretization and linearization of the steady-state Navier-Stokes equations. With a combination of analytic and empirical results, we study the effects of fundamental parameters on convergence. We demonstrate that the preconditioned problem has an eigenvalue distribution consisting of a tightly clustered set together with a small number of outliers. The structure of these distributions is independent of the discretization mesh size, but the cardinality of the set of outliers increases slowly as the viscosity becomes smaller. These characteristics are directly correlated with the convergence properties of iterative solvers. Received August 5, 2000 / Published online June 20, 2001     

Trace pollutants analysis in soil by a time-resolved laser-induced breakdown spectroscopy technique

The results of a joint experiment of IFAM-Pisa and ENEA-Frascati for the detection of traces of pollutants in soil by a time-resolved laser-induced spectroscopy technique are reported. Using samples of soil with known pollutants' concentration [Geochemical Exploration Reference (GXR) silicate from US Geological Survey], we were able to estimate the sensitivity of this Laser-Induced Breakdown Spectroscopy (LIBS) technique to be of the order of some parts per million for a vast class of metallic pollutants, including extremely dangerous soil pollutants such as copper, lead and chromium.ENEA guest with HC&M fellowship     

Comparison of the DNA Damage Photoinduced by Fenofibrate and Ketoprofen, Two Phototoxic Drugs of Parent Structure

Fenofibrate and ketoprofen (KP) are two drugs of similar structure derived from that of benzophenone. Both are photoallergic and promote cross reactions in patients. However, the cutaneous photosensitizing properties of KP also include phototoxic effects and are more frequently mentioned. To account for this difference in their in vivo properties, their in vitro photosensitizing properties on DNA were compared. First, it was shown that under irradiation at 313 nm, fenofibric acid (FB), the main metabolite of fenofibrate, photosensitized DNA cleavage by a radical mechanism similar to that proposed for KP but with a 50 times lower efficiency. Furthermore, FB did not photosensitize the formation of pyrimidine dimers into DNA in contrast to KP, which did promote this type of DNA damage. Their difference in efficiency as DNA breakers was compared to their relative photochemical reactivity and the quantum yield of FB photolysis was found to be eightfold lower than that of KP. The reactivity of these drugs cannot explain alone the difference in their photosensitizing properties. Other factors such as the magnitude of the ionic character of the pho-todecarboxylation pathway of these benzophenone-like drugs are considered in the discussion.     

Physical aging of a polyetherimide: Creep and DSC measurements

Creep and differential scanning calorimetry (DSC) measurements have been used to study the physical aging behavior of a polyetherimide. Isothermal aging temperatures ranged from 160°C to T_g with aging times ranging from 10 min to 8 days. The only measurable effect of physical aging on the short-time creep curves is a shift of the creep compliance to longer times. Andrade plots of the compliance versus the cube root of time are linear at short times with the slope β decreasing with increasing aging time to a constant value once equilibrium is reached. Log β³ is related directly to the degree to which the creep curves shift to longer times with physical aging, and is used in this work as a measure of physical aging. A reduced curve of log β³ versus log aging time is obtained for the aging temperatures investigated by appropriate vertical and horizontal shifts. The enthalpy change during aging increases linearly with the logarithm of the aging time, t_a, leveling off at equilibrium at values which increase with decreasing aging temperature. Hence, both nonequilibrium and equilibrium temperature shift factors can be calculated from the DSC data. Good agreement is observed between the equilibrium temperature shift factors obtained from the creep and DSC data. The temperature dependence of the nonequilibrium temperature shift factors is found to be an order of magnitude smaller than that of the equilibrium shift factors. The time scales to reach equilibrium for enthalpy and for mechanical measurements are found to be the same within experimental error. © 1995 John Wiley & Sons, Inc.     

Some Invariance Principles for Random Vectors in the Generalized Domain of Attraction of the Multivariate Normal Law

For independent identically distributed random vectors belonging to the generalized Domain of Attraction of the multivariate normal law, we define two partial sum processes analogous to that of Donsker's Theorem. We prove that each converges in distribution to a Brownian Motion in the space of continuous functions. One process uses nonrandom operator normalization, and the other is a studentization of the first, using normalization by the empirical covariance operator.