Extrinsic curvature, geometric optics, and lamellar order on curved substrates
نویسندگان
چکیده
منابع مشابه
Extrinsic curvature, geometric optics, and lamellar order on curved substrates.
When thermal energies are weak, two-dimensional lamellar structures confined on a curved substrate display complex patterns arising from the competition between layer bending and compression in the presence of geometric constraints. We present broad design principles to engineer the geometry of the underlying substrate so that a desired lamellar pattern can be obtained by self-assembly. Two dis...
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We study thin self-assembled columns constrained to lie on a curved, rigid substrate. The curvature presents no local obstruction to equally spaced columns in contrast with curved crystals for which the crystalline bonds are frustrated. Instead, the vanishing compressional strain of the columns implies that their normals lie on geodesics which converge (diverge) in regions of positive (negative...
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We show that smectic order on arbitrary curved substrate can be described by differential form of rank one (1-form), whose geometric meaning is the differential of the local phase field of the density modulation. The exterior derivative of 1-form is shown to be the local dislocation density. Elastic deformations are described by superposition of exact differential forms. More importantly, we us...
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Delamination is considered for thin elastic 'lms that are bonded to cylindrical substrates and subject to an equi-biaxial compressive pre-stress. Results for both positive and negative curvatures are obtained. The 'lm buckles or de2ects (depending on the sign of the curvature) away from the substrate inducing mixed mode stress intensities at the edge of the delamination. The energy release rate...
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ژورنال
عنوان ژورنال: Physical Review E
سال: 2009
ISSN: 1539-3755,1550-2376
DOI: 10.1103/physreve.80.051703