Related papers: Constructing many-twist M\"obius bands with small …
The equilibrium shape of a thin, elastic, inextensible ribbon minimizes its bending energy. It has been shown that, as the width of the ribbon tends to zero, the bending energy Gamma-converges to the so called Sadowsky functional. In this…
We compute the real part of the semi-classical limit of the sequence of quantum hyperbolic invariants (QHI) of the figure-eight knot complement $M$. We show that it is rigid, in the sense that it does not depend on the choice of holonomy…
Determining the equilibrium configuration of an elastic M\"{o}bius band is a challenging problem. In recent years numerical results have been obtained by other investigators, employing first the Kirchhoff theory of rods and later the…
Every knot can be embedded in the union of finitely many half planes with a common boundary line in such a way that the portion of the knot in each half plane is a properly embedded arc. The minimal number of such half planes is called the…
It is shown that if a link in 3-space bounds a proper oriented surface (without closed component) in the upper half 4-space, then the link bounds a proper oriented ribbon surface in the upper half 4-space which is a renewal embedding of the…
Quantum confinement and interference often generate exotic properties in nanostructures. One recent highlight is the experimental indication of a magnetic phase transition in zigzag-edged graphene nanoribbons at the critical ribbon width of…
We present a fiber-ring resonator that realizes an ultra-narrowband, high-extinction, low-loss, tunable optical filter. It consists of a pair of commercial variable ratio directional couplers that allow precise adjustment of the filter…
This paper demonstrates numerically and experimentally that it is possible to tailor flexural band gaps in the low-frequency regime by appropriate choice of cutout characteristics. The finite element method is used to obtain the numerical…
We derive the precise relation between level matching condition and fractional instanton numbers in six dimensional, abelian and supersymmetric orbifolds of E8 x E8 heterotic string theory. The fractional part of the two E8 instanton…
The off-diagonal magnetoimpedance in field-annealed CoFeSiB amorphous ribbons was measured in the low-frequency range using a pick-up coil wound around the sample. The asymmetric two-peak behavior of the field dependence of the off-diagonal…
Suppose $K$ is a knot in a closed 3-manifold $M$ such that $\bar{M-N(K)}$ is irreducible. We show that for any positive integer $b$ there exists a triangulation of $\bar{M-N(K)}$ such that any weakly incompressible bridge surface for $K$ of…
We enumerate and show tables of minimal diagrams for all prime knots up to the triple-crossing number equal to five. We derive a minimal generating set of oriented moves connecting triple-crossing diagrams of the same oriented knot. We also…
Given a thin strip of paper, tie a knot, connect the ends, and flatten into the plane. This is a physical model of a folded ribbon knot in the plane, first introduced by Louis Kauffman. We study the folded ribbonlength of these folded…
Miniaturizing nonlinear optical components is essential for integrating advanced light manipulation into compact photonic devices, enabling scalable and cost-effective applications. While monocrystalline lithium niobate thin films advance…
We determine the band structure of graphene under strain using density functional calculations. The ab-initio band strucure is then used to extract the best fit to the tight-binding hopping parameters used in a recent microscopic model of…
Twisted magnons (TMs) carrying orbital angular momentum (OAM) have attracted much attention from the magnonic community. The fabrication of such novel magnon state however is still challenging. Here we present a simple method to generate…
In this paper we discuss the applications of knotoids to modelling knots in open curves and produce new knotoid invariants. We show how invariants of knotoids generally give rise to well-behaved measures of how much an open curve is…
We characterize all compact embedded stable minimal capillary surfaces with capillary angle close to either $0$ or $\pi$ that are supported on a complete embedded minimal surface with finite total curvature that is not an affine plane.…
A long standing open conjecture states that if a link $\mathcal{K}$ is alternating, then its ropelength $L(\mathcal{K})$ is at least of the order $O(Cr(\mathcal{K}))$. A recent result shows that the maximum braid index of a link bounds the…
The Whitney embedding theorem gives an upper bound on the smallest embedding dimension of a manifold. If a data set lies on a manifold, a random projection into this reduced dimension will retain the manifold structure. Here we present an…