Dislocations loop, defined

For a smectic-A that is confined in the SEA crossed cylinder geometry, there is a competition between the homeotropic alignment on mica and the tendency to form layers of equal thickness d. As a result, dislocations must arise (Fig. 3.18, inset). As the local geometry aroimd the contact point is equivalent to a sphere-plane geometry, the loops are expected to be circular and centered on the contact point. Consider thus an array of torus-like cells, coaxial to the loops (Fig. 3.18, inset). Each cell is defined by an inner radius r, corresponding to a thickness h ri) = Uid, and an outer radius rj+i, with h ri+i) = (rij - - l)d, and contains a circular dislocation loop of radius pi- The cells are independent, because the strain patterns produced by the dislocations decays exponentially outside a parabola of equation = z, where A ... 

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