Integers larger multiples

One obvious remedy for this problem is to choose time-step lengths so as to avoid small integer multiples of half-periods of any oscillatory motion. However, it has been demonstrated that the molecular dynamics potential gives rise to motion with a continuum of periods greater than or equal to 10 fs. Furthermore, the energy instability of impulse MTS methods becomes exponentially worse at larger multiples of the half-periods. This rules out the possibility that a fortuitously chosen assortment of impulse multiple time steps longer than 5 fs could yield stable trajectories. 

Now consider the case where the energy is only somewhat larger than the potential in Region II (E > Vn). The sine-squared function in Equation 5-35 varies from a minimum of zero (complete transmission), to a maximum of one (a non-zero reflection probability). Complete transmission of the particle will occur when the width of Region n, a, times the constant ku is equal to some positive integer, n, multiple of n. 

VII.43 Design a deadbeat and Dahlin s controller for the process with the reaction curve data of Table PIV.l. Assume zero-order hold and approximate the process dead time by the nearest larger integer multiple of the sampling period, which is 0.2 min. 

Assume a zero-order hold element and approximate the process dead time by the nearest larger integer multiple of sampling periods. 

The second situation that can occur is that a surface is reconstructed. The surface unit cell is then a multiple of the bulk unit cell, and it is customary to use this larger cell as the unit cell. With respect to this reference, all rods have integer h and k indices, but for the reflections corresponding to the larger surface periodicity (superstructure reflections), the contribution of the bulk, is zero. This is the case because the reconstructed unit cell wiU contain several copies of the smaller bulk unit cell whose contributions are exactly out of phase at these superstructure reflections [11]. Alternatively, one can continue to use the original bulk unit cell. 

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