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We prove isoperimetric inequalities for general parametric variational double integrals F , whose Lagrangians F depend on the position vector X and on the surface normal N. As an essential tool we introduce Sauvigny's F-conformal parameters adapted to the parametric integrand and use the notion of generalized mean and Gaussian curvature adapted to the… (More)

We derive the Euler-Lagrange equations for nonlinearly elastic rods with self-contact. The excluded-volume constraint is formulated in terms of an upper bound on the global curvature of the centre line. This condition is shown to guarantee the global injectivity of the deformation of the elastic rod. Topological constraints such as a prescribed knot and… (More)

We consider the problem of minimizing the bending energy Eb = R 2 ds on isotopy classes of closed curves in IR 3 to model the elastic behaviour of knotted loops of springy wire. A potential of Coulomb t ype with a small factor as a measure for the thickness of the wire is added to the elastic energy in order to preserve the isotopy class. With a direct… (More)

- Henryk Gerlach, Heiko von der Mosel
- The American Mathematical Monthly
- 2011

What is the longest rope on the unit sphere? Intuition tells us that the answer to this packing problem depends on the rope's thickness. For a countably infinite number of prescribed thickness values we construct and classify all solution curves. The simplest ones are similar to the seamlines of a tennis ball, others exhibit a striking resemblance to Turing… (More)

The attractive and spacing interaction between pairs of filaments via cross-linkers, e.g. myosin dimers connecting actin filaments, is modeled by global integral kernels for negative binding energies between two intersecting stiff and long rods in a (projected) 2-dimensional situation, for simplicity. Whereas maxima of the global energy functional represent… (More)

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