Moment decay rates of solutions of stochastic differential equations

The objective of this paper is to investigate the p-ίh moment asymptotic stability decay rates for certain finite-dimensional Itό stochastic differential equations. Motivated by some practical examples, the point of our analysis is a special consideration of general decay speeds, which contain as a special case the usual exponential or polynomial type one, to meet various situations. Sufficient conditions for stochastic differential equations (with variable delays or not) are obtained to ensure their asymptotic properties. Several examples are studied to illustrate our theory.

Predicting HCl concentrations in fire enclosures using an HCl decay model coupled to a CFD-based fire field model

The amount of atmospheric hydrogen chloride (HCl) within fire enclosures produced from the combustion of chloride-based materials tends to decay as the fire effluent is transported through the enclosure due to mixing with fresh air and absorption by solids. This paper describes an HCl decay model, typically used in zone models, which has been modified and applied to a computational fluid dynamics (CFD)-based fire field model. While the modified model still makes use of some empirical formulations to represent the deposition mechanisms, these have been reduced from the original three to two through the use of the CFD framework. Furthermore, the effect of HCl flow to the wall surfaces on the time to reach equilibrium between HCl in the boundary layer and on wall surfaces is addressed by the modified model. Simulation results using the modified HCl decay model are compared with data from three experiments. The model is found to be able to reproduce the experimental trends and the predicted HCl levels are in good agreement with measured values