A Reliable Residual Based A Posteriori Error Estimator for a Quadratic Finite Element Method for the Elliptic Obstacle Problem

A residual based a posteriori error estimator is derived for a quadratic finite element method (FEM) for the elliptic obstacle problem. The error estimator involves various residuals consisting of the data of the problem, discrete solution and a Lagrange multiplier related to the obstacle constraint. The choice of the discrete Lagrange multiplier yields an error estimator that is comparable with the error estimator in the case of linear FEM. Further, an a priori error estimate is derived to show that the discrete Lagrange multiplier converges at the same rate as that of the discrete solution of the obstacle problem. The numerical experiments of adaptive FEM show optimal order convergence. This demonstrates that the quadratic FEM for obstacle problem exhibits optimal performance.

A Remark on the A Posteriori Error Analysis of Discontinuous Galerkin Methods for the Obstacle Problem

We revisit the a posteriori error analysis of discontinuous Galerkin methods for the obstacle problem derived in 25]. Under a mild assumption on the trace of obstacle, we derive a reliable a posteriori error estimator which does not involve min/max functions. A key in this approach is an auxiliary problem with discrete obstacle. Applications to various discontinuous Galerkin finite element methods are presented. Numerical experiments show that the new estimator obtained in this article performs better.

Influence of Obstacle-Produced Turbulence on Development of Premixed Flames

An investigation into influence of obstructions on premixed flame propagation has been carried out in a semi-open tube. It is found that there exists flame acceleration and rising overpressure along the path of flame due to obstacles. According to the magnitude of flame speeds, the propagation of flame in the tube can be classified into three regimes: the quenching, the choking and the detonation regimes. In premixed flames near the flammability limits, the flame is observed first to accelerate and then to quench itself after propagating past a certain number of obstacles. In the choking regime, the maximum flame speeds are somewhat below the combustion product sound speeds, and insensitive to the blockage ratio. In the more sensitive mixtures, the transition to detonation (DDT) occurs when the equivalence ratio increases. The transition is not observed for the less sensitive mixtures. The dependence of overpressure on blockage ratio is not monotonous. Furthermore, a numerical study of flame acceleration and overpressure with the unsteady compressible flow model is performed, and the agreement between the simulation and measurements is good.

A Note on Risk Acceptance, Bankruptcy Avoidance and Riskiness Measures

In this work we clarify the relationships between riskiness, risk acceptance and bankruptcy avoidance. We distinguish between the restriction on the current wealth required to make a gamble acceptable to the decision maker and the restriction on the current wealth required to guarantee no bankruptcy if a gamble is accepted. We focus on the measure of riskiness proposed by Foster and Hart.

Is inbreeding avoidance driving female mate choice in Verreaux's sifaka lemurs?

Females of different species might exert female mate choice for different reasons, one of them the aim of avoiding inbreeding. In this study I examine the implication of inbreeding avoidance as a mechanism driving female mate choice in Verreaux’s sifaka lemurs (Propithecus verreauxi). In fact, in this species females are dominant and appear to be able to choose certain males to mate with, while observations indicate that rank, body size, canine size and proportions of fights won are not factors influencing female mate choice. So I hypothesized that females mate choice is driven by inbreeding avoidance in Verreaux’s sifaka lemurs. Tissue and fecal samples were collected in the Kirindy Mitea National Park in western Madagascar as a source of DNA. Parentage was assigned for a sample of the population and relatedness coefficients between dams and sires were estimated and compared to those of between random female and male pairs, dams and other candidate sires within the population and within the groups were the offspring were conceived. I found that there were no significant differences in none of the comparisons which means that Verreaux’s sifaka females do not mate more with males that are more distantly related to them. I concluded that inbreeding avoidance does not appear to be the main force driving female mate choice in Verreaux’s sifaka lemurs and I addressed explanations for these findings. With this study I contribute to our knowledge of female mate choice in lemurs.

Avoidance of common problems on ponds and lakes.

This report looks at the events that results in fish deaths on ponds and lakes, and how to control and avoid them. Problems include de-oxygenation of the water, algal growth, water temperature, excessive fish stocks, excessive weed growth and excessive zooplankton

Effect of paradoxical sleep deprivation and stress on passive avoidance behavior

Previous studies have shown that several types of stress can induce memory impairment. However, the memory effects of paradoxical sleep deprivation (PSD), a stressor in itself, are unclear. We therefore compared passive avoidance behavior of rats undergoing PSD and PSD stress yoked-control (PSC) using the "reversed flowerpot method." When rats were kept isolated on a PSC platform for 24 It immediately after criterion training, retention trials showed impaired aversive memory storage. When delayed for 24 h after criterion training, PSC stress did not disrupt retention performance. In rats subjected to PSD, either immediately or 24 It after criterion training, there was no disruption of aversive memory consolidation. These results suggest that, during stress, paradoxical sleep plays a role in erasing aversive memory traces, in line with the theory that we "dream in order to forget." (C) 2003 Elsevier Inc. All rights reserved.

Ketamine affects memory consolidation: Differential effects in T-maze and passive avoidance paradigms in mice

The effects of ketamine, an N-methyl-D-aspartate (NMDA) antagonist, on memory in animals have been limited to the sub-anesthetic dose given prior to training in previous studies. We evaluated the effects of post-training anesthetic doses of ketamine to se