We want to find the biggest term in this bracket. We begin by assuming that 1 is the biggest term and using the fact that k˘0 α >0 and 0 < z ≤ 1 we have, 1 ≥ k˘0 zα ⇒ 1 ≥ z k˘0 α ⇒ 1 ≥ z. (F49) So 1 is indeed the bigger term meaning 1−z...
Here is the instantaneous angle between the dumbbell axis and the normal to the wall, and the angular bracket represents the ensemble average. The value of S ranges between -1 to 1 and characterizes the average orientation of dumbbells. In particular, S = −1 corresponds to the case where...