Fluctuating torque model

This is a two-body AFPE that is fully equivalent to those described by Stillman and Freed, including both a fluctuating torque effect (matrix f) and a slowly relaxing local structure (interaction potential V) the equivalence of the two approaches will be further investigated in the next section for the case of a planar model. 

The physical mechanism of the instability is related to several coupled phenomena discussed by Helfrich [42]. His elegant calculation of the instability threshold is reproduced here for the simplest steady state one-dimensional model shown in Fig. 11.33a. A homogeneously aligned nematic liquid crystal layer of thickness d is stabilised by the rubbed surfaces of the limiting glasses. The dielectric torque is considered negligible (s = 0). At first, a small director fluctuation 9(x) with a period dh postulated ... 

The simplest model. The physical mechanism of the instability could be described as follows [236], A homogeneously oriented nematic liquid crystal is stabilized by the elastic torque (due to surface anchoring). The dielectric torque is considered to be negligible ( a=0)- Now, let us imagine a small incident director fluctuation with a period of the order of cell thickness d ... 

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