Shape and fluctuations of positively curved ribbons
نویسندگان
چکیده
منابع مشابه
Shape and Shape Fluctuations of incompatible Ribbons
Geometrically incompatible ribbons are ubiquitous in nature, from the growing of biological tissues, to the self assemblies of peptides and lipids. These exhibit unusual characteristics such shape bifurcations, and abnormal mechanical properties. When considering nano and micro ribbons, thermal fluctuations convert these properties into nontrivial statistics. We derive a reduced quasi-one-dimen...
متن کاملPositively Curved Combinatorial 3-Manifolds
We present two theorems in the “discrete differential geometry” of positively curved spaces. The first is a combinatorial analog of the Bonnet-Myers theorem: • A combinatorial 3-manifold whose edges have degree at most five has edgediameter at most five. When all edges have unit length, this degree bound is equivalent to an angle-deficit along each edge. It is for this reason we call such space...
متن کاملNon-positively Curved Cube Complexes
Let Γ be a discrete group, defined by a presentation P = 〈ai | rj〉, say, or as the fundamental group of a connected CW-complex X. Remark 1.1. Let XP be the CW-complex with a single 0-cell E , one 1-cell E i for each ai (oriented accordingly), and one 2-cell E 2 j for each rj , with attaching map ∂E j → X (1) P that reads off the word rj in the generators {ai}. Then, by the Seifert–van Kampen Th...
متن کاملA Positively Curved Manifold Homeomorphic
Spaces of positive curvature play a special role in geometry. Although the class of manifolds with positive (sectional) curvature is expected to be relatively small, so far there are only a few known obstructions. Moreover, for closed simply connected manifolds these coincide with the known obstructions to nonnegative curvature which are: (1) the Betti number theorem of Gromov which asserts tha...
متن کاملConstructing Non-positively Curved Spaces and Groups
The theory of non-positively curved spaces and groups is tremendously powerful and has enormous consequences for the groups and spaces involved. Nevertheless, our ability to construct examples to which the theory can be applied has been severely limited by an inability to test – in real time – whether a random finite piecewise Euclidean complex is non-positively curved. In this article I focus ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physical Review E
سال: 2018
ISSN: 2470-0045,2470-0053
DOI: 10.1103/physreve.98.022502