By Roger Fosdick, Eliot Fried
Recent advancements in biology and nanotechnology have motivated a speedily turning out to be curiosity within the mechanics of skinny, versatile ribbons and Mobius bands.
This edited quantity comprises English translations of 4 seminal papers in this subject, all initially written in German; of those, Michael A. Sadowsky released the 1st in 1929, by way of others in 1930, and Walter Wunderlich released the final in 1962.
The quantity additionally comprises invited, peer-reviewed, unique learn articles on similar topics.
Previously released within the magazine of Elasticity, quantity 119, factor 1-2, 2015.
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Extra resources for The Mechanics of Ribbons and Möbius Bands
Sample text
V. Synonymous with ideal point. vi. The order of Figs. 5 and 6 is herein reversed from the original for clarity. vii. The use of X¨ i in the original instead of X¨ appears to be an error. viii. Imaginary circle was chosen for the German nullteiliger Kreis. 1007/s10659-014-9475-4 Gamma-Limit of a Model for the Elastic Energy of an Inextensible Ribbon Nicholas O. Kirby · Eliot Fried Received: 7 November 2013 / Published online: 20 March 2014 © Springer Science+Business Media Dordrecht 2014 Abstract A Γ -convergence result involving the elastic bending energy of a narrow inextensible ribbon is established.
Inst. de Fr. 2, 167–226 (1812) 13. : Sides of the Möbius strip. Arch. Math. 66(6), 511–521 (1996) 14. : Differential geometry of polymer models: worm-like chains, ribbons and Fourier knots. J. Phys. A, Math. Theor. 40(17), 4455 (2007) 15. : Ein elementarer Beweis für die Existenz eines abwickelbaren Möbiusschen Bandes und Zurückfügrung des geometrischen Problems auf ein Variationsproblem. Sitzber. Preussischen Akad. der Wiss. -hist. Kl. 22, 412–415 (1930) 16. : The equilibrium shape of an elastic developable Möbius strip.
The functional F (·, I ) defined by (18) is called the Sadowsky functional. 1 Existence of Γ -Limit In particular, following De Giorgi [6], given any sequence {εj } with εj > 0 and εj → 0 and any element u ∈ X: 1. for every sequence {uj } with uj ∈ X such that uj → u in X, F (u, I ) is bounded above in accord with F (u, I ) ≤ lim inf Fεj (uj , I ); (19) j →∞ 2. there exists a sequence {uj } converging to u such that F (u, I ) is bounded below in accord with F (u, I ) ≥ lim sup Fεj (uj , I ). (20) j →∞ For any such sequence {εj }, it is possible to extract a decreasing subsequence {εjk }.