The analysis methods applied in this study belong to the class of advanced Monte-Carlo simulation methods, with which the computational costs induced by direct simulation can be drastically reduced.
In this paper, an integrated utilization of analytic keyhole theory, B-plane mapping, and planetary encounter geometry, augmented by direct numerical simulation, is shown to be useful in determining the impact risk of an asteroid with the Earth on a given encounter, as well on potential future encounters via keyhole passages.
Although the impact of this approximation cannot be analyzed theoretically, the numerical results in Figure 4 show that the mismatch between the proposed analytical approximation of the RMSE and the RMSE obtained by direct simulation of the communication system is larger in the low SNR region.
Hence the following results are given by direct simulation for the stochastic delay differential equation, i.e., Eq. (10), which can be formally integrated by using a simple forward Eular algorithm with a small time step for time delay.
These viscous unstable experiments have been modelled by direct simulation using a high-accuracy numerical model.
Usually the numerical solutions of the transport equation are obtained by Direct Simulation Monte Carlo (DSMC) approaches with the unavoidable stochastic noise due to the statistical fluctuations.
As an example, the repeated under-prediction of the peak transverse pressure gradient, observed in the results of asymptotic methods and of direct numerical simulations, is explained by the historically neglected consistency of the fringing magnetic field.
The saving percentage values estimated by simulation are confirmed by the direct measures continuously taken on site through energy-meters.
"Simulation is done entirely by a computer," Schumacher said.
This simulation is imperfect.
