Tails of exit times from unstable equilibria on the line

For a one-dimensional smooth vector field in a neighborhood of an unstable equilibrium, we consider the associated dynamics perturbed by small noise. We give a revealing elementary proof of a result proved earlier using heavy machinery from Malliavin calculus. In particular, we obtain precise vanishing noise asymptotics for the tail of the exit time and for the exit distribution conditioned on atypically long exits. We also discuss our program on rare transitions in noisy heteroclinic networks.

An Agent-Based Simulation of Deep Foundation Pit Emergency Evacuation Modeling in the Presence of Collapse Disaster

With the gradual expansion of high buildings and underground spaces, deep foundation pits have been widely used in these engineering projects, but if they are not well-designed, safety problems occur. Proper deep foundation pit design requires proper exit distribution. However, calculating an adequate number of exit distributions for evaluation is difficult due to the numerous influential factors existing in the deep foundation pit environment. To this end, this paper presents a prototype of a decision-making system that uses agent-based modeling to simulate deep foundation pit evacuation in the presence of collapse disaster. By modeling the collapse occurrence process and agent escape process, an agent-based evacuation model is built, and a modified simulation-based particle swarm optimization algorithm is used to solve the optimization problem of exit distribution. Extensive experiments are conducted to verify the system, and the results show that the system provides a feasible framework for deep foundation pit evacuation.

Nematodes as a source of total coliforms in a distribution system

In a distribution system of a large North American city, recurring total coliforms and atypical coliforms were detected at the exit (distribution pumps) of a storage reservoir. The presence of total coliforms and atypical coliforms was noted when the pumps were in operation and the water temperature was higher than 18 °C. The total coliform and atypical coliform concentrations at the volute pump casings ranged from 0 to 93.5 colony forming units (cfu)/100 mL. Significant concentrations of nematodes were also detected at this sampling location, averaging 12.0 nematodes/L in 2001 and 17.4 nematodes/L in 2002. The hypothesis that coliforms were released from the nematodes during their transit through the high-pressure pump was tested by recovering nematodes by filtering large volumes of water and grinding the nematodes in the laboratory, using various techniques. Total coliform and heterotrophic bacteria concentrations ranged from 0 to 27 cfu/nematode and 0 to 643 cfu/nematode, respectively. The origin of the nematodes was traced back to the sand filters located at the two water treatment plants. The importance of invertebrates in the distribution system should not be dismissed and the associated health risks, if any, should be assessed.