Safescape is a Western Australian company that has recently developed a device for improved safety in open-pit mines. Serious accidents can occur when large trucks veer off the roads running around the edge of the mine. The conventional technique to mitigate the risk is to pile waste rock to form a so-called bund on the edge of the road. This method is not fail safe though as vehicles can, and do, drive completely over the bund. In this paper, we describe a new device that consists of a row of filled polyethylene shell units which are linked together and sit on the road side of the rock bund. The vertical front face of the edge protector prevents out of control dump trucks from climbing over the bund and into the pit, so that they push against the barriers and heave the broken rock behind the bund. The models developed here suggest that the primary resistance to an impacting truck is provided by the large heaving force with the barrier simply facilitating this process. The theory indicates that the total resistance is independent of truck speed, meaning that simple barrier pushing experiments are sufficient to validate the analysis. The conclusions of the theory and field tests suggest that in a worst-case scenario involving the normal impact of a 500 tonne filled dump truck, the barriers and bund move a few metres before coming to rest.

Pricing variance swaps have become a popular subject recently, and most research of this type come under Heston’s two-factor model. This paper is an extension of some recent research which used the dimension-reduction technique based on the Heston model. A new closed-form pricing formula focusing on a log-return variance swap is presented here, under the assumption that the underlying asset prices can be described by a mean-reverting Gaussian volatility model (Ornstein–Uhlenbeck process). Numerical tests in two respects using the Monte Carlo (MC) simulation are included. Moreover, we discuss a procedure of solving a quadratic differential equation with one variable. Our method can avoid the previously encountered limitations, but requires more time for calculation than other recent analytical discrete models.

As a possible model for fluid turbulence, a Reiner–Rivlin-type equation is used to study Poiseuille–Couette flow of a viscous fluid in a rotating cylindrical pipe. The equations of motion are derived in cylindrical coordinates, and small-amplitude perturbations are considered in full generality, involving all three velocity components. A new matrix-based numerical technique is proposed for the linearized problem, from which the stability is determined using a generalized eigenvalue approach. New results are obtained in this cylindrical geometry, which confirm and generalize the predictions of previous recent studies. A possible mechanism for the transition to turbulent flow is discussed.