The required first-passage probabilities are computed using a novel efficient Monte Carlo based simulation technique called asymptotic sampling.
Using the estimated passage position effect, the adjusted difficulty of each item linked to passage 5 can be computed.
Expected passage times can be computed from the fundamental matrix x N = (I − x P )−1.
For such a one-dimensional diffusion problem, the mean first passage time can be computed in closed form (Gardiner 2004) and this formula has been used in Stephan et al. (1993) and Gordo and Charlesworth (2000) to estimate the rate of the ratchet.
The adoption of suitable absorbing and reflecting boundary conditions enables the evolution of the first-passage probability to be computed.
Flip angles for state-space rotations on passage of a transition can generally be computed from the critical adiabaticity by the Landau-Zener-Stückelberg-Majorana expression.
Several multi-fluid problems, including the breakup of a water cylinder induced by the passage of a shock wave were computed in order to demonstrate the capability of the proposed method.
Within each blade passage, several time-linearized unsteady solutions, each of which have different frequencies and interblade phase angles, are computed.
We replace the mean-first-passage-time criterion by the distance to (un desirable attractor states of the underlying Markov chain, which can be computed efficiently.
