Stochastic sensitivity analysis applied to gas–surface scattering

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Abstract
The results of the application of sensitivity analysis to the simulation of gas–surface scattering are presented. The simulation technique was the three dimensional generalized Langevin method of Tully, and the sensitivity analysis methods were the coupled solution of system and sensitivity equations approach and a new stochastic sensitivity analysis method. We found that the coupled solution approach only converged when trajectories which involved multiple collisions of the gas with the surface were excluded from the Monte Carlo averaging of this simulation approach. The stochastic sensitivity method was found to give convergent results for both single collision trajectories and multiple collision trajectories. In the stochastic sensitivity method the sensitivity coefficients are computed by selecting the parameters of the system randomly from a given distribution and then performing a linear least-squares analysis of the variations of the output variables of the simulation model with respect to variations of the input parameters. The stochastic sensitivity analysis method should also be applicable to completely deterministic trajectory simulations which however exhibit ergodic behavior in individual trajectories. In addition to first-order coefficients, we also used the stochastic sensitivity analysis method to compute higher order coefficients (selected second and third order) and derived sensitivity coefficients. We have applied both the coupled solution and stochastic sensitivity analysis method to the Ar–Pt (111) scattering system, where we found that the surface corrugation and the steepness of the respulsive two-body interactions were essential features of the interaction potential in determining the quantity of energy transfered.