期刊
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
卷 468, 期 2143, 页码 1851-1864出版社
ROYAL SOC
DOI: 10.1098/rspa.2011.0627
关键词
soap films; minimal surfaces; Elastica
资金
- NSF Harvard MRSEC
- Harvard Kavli Institute for Nanobio Science and Technology
- Wyss Institute
- MacArthur Foundation
- Division Of Materials Research
- Direct For Mathematical & Physical Scien [820484] Funding Source: National Science Foundation
In mathematics, the classical Plateau problem consists of finding the surface of least area that spans a given rigid boundary curve. A physical realization of the problem is obtained by dipping a stiff wire frame of some given shape in soapy water and then removing it; the shape of the spanning soap film is a solution to the Plateau problem. But what happens if a soap film spans a loop of inextensible but flexible wire? We consider this simple query that couples Plateau's problem to Euler's Elastica: a special class of twist-free curves of given length that minimize their total squared curvature energy. The natural marriage of two of the oldest geometrical problems linking physics and mathematics leads to a quest for the shape of a minimal surface bounded by an elastic line: the Euler-Plateau problem. We use a combination of simple physical experiments with soap films that span soft filaments and asymptotic analysis combined with numerical simulations to explore some of the richness of the shapes that result. Our study raises questions of intrinsic interest in geometry and its natural links to a range of disciplines, including materials science, polymer physics, architecture and even art.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据