Friedemann Schuricht

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Many different physical systems, e.g. super-coiled DNA molecules, have been successfully modelled as elastic curves, ribbons or rods. We will describe all such systems as framed curves, and will consider problems in which a three dimensional framed curve has an associated energy that is to be minimized subject to the constraint of there being no(More)
Minimizers of the total variation subject to a prescribed L 1-norm are considered as eigen-solutions of the 1-Laplace operator. The derivation of the corresponding eigenvalue equation, which requires particular care due to the lack of smoothness, is carried out in a previous paper by using a special Lagrange multiplier rule based on Degiovanni's weak slope.(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)
Many diierent physical systems, e.g. super-coiled DNA molecules, have been successfully modelled as elastic curves, ribbons or rods. We will describe all such systems as framed curves, and will consider problems in which a three dimensional framed curve has an associated energy that is to be minimized subject to the constraint of there being no(More)
This paper treats several aspects of the induced geometrically exact theory of shearable rods, of central importance for contact problems, for which the regularity of solutions depends crucially on the presence of shearability. (An induced theory is one derived from the 3-dimensional theory by the imposition of constraints. Because the role of thickness(More)
In this paper we study the local and global injectivity of spatial deformations of shearable nonlinearly elastic rods. We adopt an analytical condition introduced by Ciarlet & Ne cas in nonlinear elasticity to ensure global injectivity in that case. In particular we verify the existence of an energy minimizing equilibrium state without self-penetration(More)
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