By E.I. Kats, V.V. Lebedev
Liquid crystals, popular in monitors for digital apparatus and different purposes, have hugely strange homes bobbing up from the anisotropy in their molecules. it seems that a few features of the fluid dynamics of liquid crystals, equivalent to their viscosity, will be understood basically by way of contemplating the function performed via thermal fluctuations. with the intention to supply a theoretical framework for figuring out the experimental effects, the authors commit a wide a part of the ebook to a derivation of the nonlinear dynamic equations and to a dialogue of linearized equations for a number of the sorts of liquid crystals. The diagrammatic and different options they use are of normal use in condensed topic physics, and this exposition may still hence be of curiosity to all condensed-matter theorists.
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Extra resources for Fluctuational Effects in the Dynamics of Liquid Crystals
12). In the one-loop approximation these corrections are determined both by the diagram of the type given in Fig. 10 and by the diagrams of the type given in Figs. 11, 12, and 13. 16). This result is quite natural. 10), due to the rotational 40 3. Fluctuation Effects in Smectic Liquid Crystals FIGURE 1l. Fluctuation correction to the third-order vertex. FIGURE 12. Fluctuation correction to the fourthorder vertex. FIGURE 13. Correction to the vertex with density and specific entropy fluctuations taken into account.
40) brings forth the dispersion equation w 2 + i[r(CX3q; - + cx1qi) + p-l('12qI + '13q;)]W p-lr(CX 3 q; + cx l qIH'12qI+ '13Q;) - p-l(CX 3 Q; + cxlqI)qI = o. 3. Linear Eigenmode Spectrum of Smectics 35 Naturally, it is not difficult to write the dispersion law defined by this equation in the general form. 25). l 2J. 18). This mode is analogous to the fast mode of nematics. 43) largely oscillates the angle cpo This mode is analogous to the slow ("director") mode of nematics. 36)). The terms with the coefficient A1 describe coupling of the orientational and shear diffusion modes.
12). 1 - Tp da - Mk Vk dW - Vk(Mik Vi dW) - ot: -dOl OOl ot: --dV
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