Overall Formalisms of Ion Mobility Calculations

We should also average over the thermal distribution of Vki  

Except for several classic geometric bodies, the integrals in Equations 1.29 and 1.30 with any expression for x must be evaluated numerically. That is done using Monte Carlo schemes, where a large number of gas atoms is shot at an ion with random 0, (p, y, b, their trajectories in the assumed are tracked through the collision event (1.4.3 and 1.4.4) producing x, and contributions to ft are accumulated. As with any Monte Carlo integration, the statistical error scales as (number of 

FIGURE 1.22 Rotating an object around the line of sight does not change its cross section, regardless of the model for ion-molecule interaction. (From Shvartsburg, A. A., Mashkevich, S.V., Baker, E.S., Smith, R.D., J. Phys. Chem. A, 111, 2002, 2007.) 

FIGURE 1.23 The projections of an aircraft propeller on two perpendicular planes increase when the propeller rotates. The shadow of static propeller is in black and that of blurred-out rotating propeller is in grey scale. (From Shvartsburg, A.A., Mashkevich, S.V., Siu, K.W.M., / Phys. Chem. A, 104, 9448, 2000.) 

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