Conical Surfaces and Crescent Singularities in Crumpled Sheets
نویسندگان
چکیده
We analyze the geometry and elasticity of the crescentlike singularity on a crumpled elastic sheet. We give a physical realization of this in terms of a free-boundary contact problem. An analytical solution is given for the universal shape of a developable cone that characterizes the singularity far from the tip, and some of its predictions are qualitatively verified experimentally. We also give a scaling relation for the core size, defined as the region close to the tip of the cone where the sheet is not developable. [S0031-9007(98)05465-9]
منابع مشابه
Ricci flow on surfaces with conical singularities Hao Yin
This paper studies the normalized Ricci flow on surfaces with conical singularities. It’s proved that the normalized Ricci flow has a solution for a short time for initial metrics with conical singularities. Moreover, the solution makes good geometric sense. For some simple surfaces of this kind, for example, the tear drop and the football, it’s shown that they admit Ricci soliton metric. MSC 2...
متن کاملIntrinsically anomalous roughness of randomly crumpled thin sheets.
We study the effect of folding ridges on the scaling properties of randomly crumpled sheets of different kinds of paper in the folded and unfolded states. We found that the mean ridge length scales with the sheet size with the scaling exponent mu determined by the competition between bending and stretching deformations in the folded sheet. This scaling determines the mass fractal dimension of r...
متن کاملExtremal Hermitian Metrics on Riemann Surfaces with Singularities
0. Introduction. It is a well-known consequence of the classical uniformization theorem that there is a metric with constant Gaussian curvature in each conformal class of any compact Riemann surface. It is natural to ask how to generalize this classical uniformization theory to compact surfaces with conical singularities and with nonempty boundary, or to find a “best metric” on such surfaces. H...
متن کاملEmergent Conformal Symmetry of Quantum Hall States on Singular surfaces
We show that quantum Hall states on surfaces with conical singularities behave as conformal primaries near the singular points, with a conformal dimension controlled by the gravitational anomaly. We show that the electronic fluid at the cone tip possesses an intrinsic angular momentum equal to the conformal dimension, in units of the Planck constant. Finally, we argue that the gravitational ano...
متن کاملConical diffraction and the dispersion surface of hyperbolic metamaterials
Hyperbolic metamaterials are materials in which at least one principal dielectric constant is negative. We describe the refractive index surface, and the resulting refraction effects, for a biaxial hyperbolic metamaterial, with principal dielectric constants 1 < 0, 0 < 2 = 3. In this general case the two sheets of the index surface intersect, forming conical singularities. We derive the ray des...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1998