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Y. Bouligand, in Physique des Défauts/Physics of Defects, Proceedings of the Les Houches Summer School of Theoretical Physics, Session XXXV, 1980, edited by, R. Balian, M. Kléman, and, J.-P. Poirier, (North-Holland, Amsterdam, 1981).
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Alexander, G.P.1
Marenduzzo, D.2
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77951724391
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In Ref., we showed that with other choices of the field direction ([100] and [110]), disclination lines eventually annihilate to result in a helical (cholesteric) state without disclinations. We also note that for positive a, the final director profile is a uniform one parallel to E without disclination, irrespective of the field direction. This is the reason why in the present study we concentrate on the case with negative ?a and the field along [111], where annihilation of disclination is not observed (see [10] below).
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In Ref., we showed that with other choices of the field direction ([100] and [110]), disclination lines eventually annihilate to result in a helical (cholesteric) state without disclinations. We also note that for positive a, the final director profile is a uniform one parallel to E without disclination, irrespective of the field direction. This is the reason why in the present study we concentrate on the case with negative ? a and the field along [111], where annihilation of disclination is not observed (see [10] below).
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12
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77951707130
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We should mention that this regular array of -1/2 and +1/2 disclination lines must be regarded as a transient, not a stable, state. The ground state under E is a helical state with its pitch axis parallel to E. In simulations in the present Rapid Communication and, we could not observe a helical state as a final structure, possibly due to the perfectness of the prepared initial condition; threefold symmetry of the defect array (Fig. ) remains unchanged, though a gradual increase of the defect distance is observed. A small perturbation would be necessary for the system to reach a helical state.
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We should mention that this regular array of - 1 / 2 and + 1 / 2 disclination lines must be regarded as a transient, not a stable, state. The ground state under E is a helical state with its pitch axis parallel to E. In simulations in the present Rapid Communication and, we could not observe a helical state as a final structure, possibly due to the perfectness of the prepared initial condition; threefold symmetry of the defect array (Fig.) remains unchanged, though a gradual increase of the defect distance is observed. A small perturbation would be necessary for the system to reach a helical state.
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13
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77951760425
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It is not clear enough from Fig. that the initial profile (Fig. ) is that of a -1/2 disclination. It is because the plane of the contour (the plane of Fig. ) is not perpendicular to the disclination line.
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It is not clear enough from Fig. that the initial profile (Fig.) is that of a - 1 / 2 disclination. It is because the plane of the contour (the plane of Fig.) is not perpendicular to the disclination line.
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