caa a22 4500 467893098 CHVBK 20180406152754.0 cr unu---uuuuu 170328e20061201xx s 000 0 eng 10.1007/s10955-006-9087-x doi (NATIONALLICENCE)springer-10.1007/s10955-006-9087-x Geometry and Elasticity of Strips and Flowers [Elektronische Daten] [M. Marder, N. Papanicolaou] 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 Lagrangian 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 by minimizing a suitable energy functional that once these evolution equations become singular, either the surface is not differentiable, or else the metric deviates from the target metric. Springer Science+Business Media, Inc., 2006 pattern formation nationallicence elasticity nationallicence metric nationallicence surfaces nationallicence differential geometry nationallicence Marder M. Center for Nonlinear Dynamics and Department of Physics The University of Texas at Austin, 78712, Austin, TX, USA aut Papanicolaou N. Department of Physics, University of Crete, and Research Center of Crete, Heraklion, Greece aut Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 125/5-6(2006-12-01), 1065-1092 0022-4715 125:5-6<1065 2006 125 10955 https://doi.org/10.1007/s10955-006-9087-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9087-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Marder M. Center for Nonlinear Dynamics and Department of Physics The University of Texas at Austin, 78712, Austin, TX, USA aut NATIONALLICENCE 700 1- Papanicolaou N. Department of Physics, University of Crete, and Research Center of Crete, Heraklion, Greece aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 125/5-6(2006-12-01), 1065-1092 0022-4715 125:5-6<1065 2006 125 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer