期刊
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
卷 34, 期 49, 页码 11069-11082出版社
IOP PUBLISHING LTD
DOI: 10.1088/0305-4470/34/49/322
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The stable profile of the boundary of a plant's leaf fluctuating in the direction transverse to the leaf's surface is described in the framework of a model called a 'surface godets' (SG). It is shown that the information on the profile is encoded in the Jacobian of a conformal. mapping (the coefficient of deformation) corresponding to an isometric embedding of a uniform Cayley tree into the 3D Euclidean space. The geometric characteristics of the leaf's boundary (such as the perimeter and the height) are calculated. In addition, a symbolic language allowing us to investigate the statistical properties of a SG with annealed random defects of the curvature of density q is developed. It is found that, at q = 1, the surface exhibits a phase transition with the critical exponent alpha = 1/2 from the exponentially growing to the flat structure.
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