Geometry and elasticity of strips and flowers

Details Geometry and elasticity of strips and flowers Geometry and elasticity of strips and flowers

2004-09-06

arxiv.org/abs/cond-mat/0409135v1

Physics

Condensed Matter

Soft Condensed Matter

12 pages and 9 figures, many of them in color

Scientific paper

We solve several problems that involve imposing metrics on surfaces. The problem of a strip with a linear metric gradient is formulated in terms of a Lagrangean similar to those used for spin systems. We are able to show that the low energy state of long strips is a twisted helical state like a telephone cord. We then extend the techniques used in this solution to two--dimensional sheets with more general metrics. We find evolution equations and show that when they are not singular, a surface is determined by knowledge of its metric, and the shape of the surface along one line. Finally, we provide numerical evidence that once these evolution equations become singular, either the surface is not differentiable, or else the metric deviates from the target metric as a result of minimization of a suitable energy functional .

Affiliated with

Also associated with

No associations

Rating

Geometry and elasticity of strips and flowers does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Geometry and elasticity of strips and flowers, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometry and elasticity of strips and flowers will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-532582