Related papers: Equivalent elastica knots
A new type of knot energy is presented via real life experiments involving a thin resilient metallic tube. Knotted in different ways, the device mechanically acquires a uniquely determined (up to isometry) normal form at least when the…
We consider black-string-type solutions in five-dimensional Einstein-Gauss-Bonnet gravity. Numerically constructed solutions under static, axially symmetric and translationally invariant metric ansatz are presented. The solutions are…
We show that the elastic energy $E(\gamma)$ of a closed curve $\gamma$ has a minimizer among all plane simple regular closed curves of given enclosed area $A(\gamma)$, and that the minimum is attained for a circle. The proof is of a…
Constitutive tensors are of common use in mechanics of materials. To determine the relevant symmetry class of an experimental tensor is still a tedious problem. For instance, it requires numerical methods in three-dimensional elasticity. We…
The elliptic integral and its various generalizations are playing very important and basic role in different branches of modern mathematics. It is well known that they cannot be represented by the elementary transcendental functions.…
The elasticity difference tensor, used in [1] to describe elasticity properties of a continuous medium filling a space-time, is here analysed from the point of view of the space-time connection. Principal directions associated with this…
On Boxing Day, 1838, Jacobi found a solution to the problem of geodesics on a triaxial ellipsoid, with the course of the geodesic and the distance along it given in terms of one-dimensional integrals. Here, a numerical implementation of…
Consider a knot $K$ in $S^3$ with uniformly distributed electric charge. Whilst solutions to the Laplace equation in terms of Dirichlet integrals are readily available, it is still of theoretical and physical interest to understand the…
In this report, I will start by first giving a brief introduction on knots to build some intuition before beginning the more rigorous review in the Literature Review section. There, I will define knot equivalence, the Jones polynomial…
We address three related problems in the theory of elasticity, formulated in the framework of double forms: the Saint-Venant compatibility condition, the existence and uniqueness of solutions for equations arising in incompatible…
A new algebraic method to find two special types of exact traveling wave solutions and the solitary type solutions to some conformable fractional partial differential equations is proposed. The two special types of solutions given by the…
Exact solutions with torsion in Einstein-Gauss-Bonnet gravity are derived. These solutions have a cross product structure of two constant curvature manifolds. The equations of motion give a relation for the coupling constants of the theory…
After characterizing the integrable discrete analogue of the Euler's elastica, we focus our attention on the problem of approximating a given discrete planar curve by an appropriate discrete Euler's elastica. We carry out the fairing…
We obtain an analytical solution for the weighted Fermat-Torricelli problem for an equilateral geodesic triangle A_1A_2A_3 which is composed by three equal geodesic arcs (sides) of length Pi/2 for given three positive unequal weights that…
This paper investigates, without any regularization procedure, the sensitivity analysis of a mechanical friction problem involving the (nonsmooth) Tresca friction law in the linear elastic model. To this aim a recent methodology based on…
An efficient method is presented for solving axisymmetric, frictionless contact problems between a rigid punch and an elastically non-homogeneous, power-law graded half-space. Provided that the contact area is simply-connected profiles of…
This is an expository note to give a brief review of classical elastica theory, mainly prepared for giving a more detailed proof of the author's Li--Yau type inequality for self-intersecting curves in Euclidean space. We also discuss some…
In the previous article (J. Geom. Phys. {\bf 43} (2002) 146), we show the hyperelliptic solutions of a loop soliton as a study of a quantized elastica. This article gives some functional relations in a loop soliton as a quantized elastica.
We prove the local existence of solutions to the Einstein-Elastic equations that represent self-gravitating, relativistic elastic bodies with compact support.
We introduce two numerical invariants, the waist and the trunk of knots. The waist of a closed incompressible surface in the complement of a knot is defined as the minimal intersection number of all compressing disks for the surface in the…