منابع مشابه
Knot Types, Homotopies and Stability of Closed Elastic Rods
The energy minimization problem associated to uniform, isotropic, linearly elastic rods leads to a geometric variational problem for the rod centerline, whose solutions include closed, knotted curves. We give a complete description of the space of closed and quasiperiodic solutions. The quasiperiodic curves are parametrized by a two-dimensional disc. The closed curves arise as a countable colle...
متن کاملKirchhoff Rods with Nonhomogeneous Cross Section
The Kirchhoff’s theory for thin, inextensible, elastic rods with nonhomogeneous cross section is studied. The Young’s and shear moduli of the rod are considered to vary radially, and it is shown that an analytical solution for the constitutive relations can be obtained for circular cross section and constant Poisson’s ratio. We comment on possible applications of our results.
متن کاملOn the Geometric Flow of Kirchhoff Elastic Rods
Recently, rod theory has been applied to the mathematical modeling of bacterial fibers and biopolymers (e.g. DNA), to study their mechanical properties and shapes (e.g. supercoiling). In static rod theory, an elastic rod in equilibrium is the critical point of an elastic energy. This induces a natural question of how to find elasticae. In this paper, we focus on how to find the critical points ...
متن کاملOn Generalized Knot Groups
Generalized knot groups Gn(K) were introduced first by Wada and Kelly independently. The classical knot group is the first one G1(K) in this series of finitely presented groups. For each natural number n, G1(K) is a subgroup of Gn(K) so the generalized knot groups can be thought of as extensions of the classical knot group. For the square knot SK and the granny knot GK, we have an isomorphism G...
متن کاملThe 2-generalized Knot Group Determines the Knot
Generalized knot groups Gn(K) were introduced independently by Kelly (1991) and Wada (1992). We prove that G2(K) determines the unoriented knot type and sketch a proof of the same for Gn(K) for n > 2. 1. The 2–generalized knot group Generalized knot groups were introduced independently by Kelly [5] and Wada [10]. Wada arrived at these group invariants of knots by searching for homomorphisms of ...
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ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2019
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216519400108