A numerical study of steady state evaporative conditions applied to mine tailings

The suction profile of a desiccating soil is dependent on the water table depth, the soil-water retention characteristics, and the climatic conditions. In this paper, an unsaturated flow model, which simulates both liquid and vapour flow, was used to investigate the effects of varying the water table depth and the evaporation rate on the evaporative fluxes from a desiccating tailings deposit under steady-state conditions. Results obtained showed that at a critical evaporation rate, beyond which evaporation is no longer dictated by climatic conditions, the matric suction profiles remain basically unchanged. The critical evaporation rate varies inversely with the water table depth. It is associated with the maximum evaporative flux that might be extracted from a soil at steady-state conditions. The time required to establish steady-state conditions is directly proportional to the water table depth, and it acquires a maximum value at the critical evaporation rate. A detailed investigation of the movement of the drying front demonstrated the significance of attaining a matric suction of about 3000 kPa on the contribution to flow in the vapour phase.

Using weak nonlinearity under decoherence for macroscopic entanglement generation and quantum computation

Recently, there have been several suggestions that weak Kerr nonlinearity can be used for generation of macroscopic superpositions and entanglement and for linear optics quantum computation. However, it is not immediately clear that this approach can overcome decoherence effects. Our numerical study shows that nonlinearity of weak strength could be useful for macroscopic entanglement generation and quantum gate operations in the presence of decoherence. We suggest specific values for real experiments based on our analysis. Our discussion shows that the generation of macroscopic entanglement using this approach is within the reach of current technology.

Improved algorithms for rare event simulation with heavy tails

The estimation of P(S-n > u) by simulation, where S, is the sum of independent. identically distributed random varibles Y-1,..., Y-n, is of importance in many applications. We propose two simulation estimators based upon the identity P(S-n > u) = nP(S, > u, M-n = Y-n), where M-n = max(Y-1,..., Y-n). One estimator uses importance sampling (for Y-n only), and the other uses conditional Monte Carlo conditioning upon Y1,..., Yn-1. Properties of the relative error of the estimators are derived and a numerical study given in terms of the M/G/1 queue in which n is replaced by an independent geometric random variable N. The conclusion is that the new estimators compare extremely favorably with previous ones. In particular, the conditional Monte Carlo estimator is the first heavy-tailed example of an estimator with bounded relative error. Further improvements are obtained in the random-N case, by incorporating control variates and stratification techniques into the new estimation procedures.