Related papers: Moebius energy of thick knots
The energy of extended classical objects, such as vortices, depends on their shape. In particular, we show that the curvature energy of a kink in two spatial dimensions, as a prototype of extended classical solutions, is always negative. We…
An analysis of extensive simulations of interacting self-avoiding polygons on cubic lattice shows that the frequencies of different knots realized in a random, collapsed polymer ring decrease as a negative power of the ranking order, and…
The energy- and flux budget (EFB) turbulence closure theory for the atmospheric surface layers in convective and stably stratified turbulence has been developed using budget equations for turbulent energies and fluxes in the Boussinesq…
We study stationary points of the bending energy of curves $\gamma\colon[a,b]\to\mathbb{R}^n$ subject to constraints on the arc-length and the curve's holonomy while simultaneously allowing for a variable bending stiffness along the…
Macromolecules can gain special properties by adopting knotted conformations, but engineering knotted macromolecules is a challenging task. Here we surprisingly observed that knotting can be very effectively produced in active polymers.…
We investigate kinetic energy properties of an irrotational deep-water Stokes wave. By introducing a conformal hodograph transform, we perform complex analysis in the new variables, and show that the existence of the streamline time-period…
Knot theory provides a powerful tool for the understanding of topological matters in biology, chemistry, and physics. Here knot theory is introduced to describe topological phases in the quantum spin system. Exactly solvable models with…
Unusual chemical bonds are proposed. Each bond is almost covalent but is characterized by the thread of a small radius $\sim 0.6\times 10^{-11}$cm, between two nuclei in a molecule. The main electron density is concentrated outside the…
It is understood in a general sense that turbulent fluid motion below the shock front in a core-collapse supernova stiffens the effective equation of state of the fluid and aids in the revival of the explosion. However, when one wishes to…
We propose that the knots of the large-scale jets in powerful radio sources represent moving and separate portions of the jet matter, with the excess kinetic power. This can explain many morphological properties of quasar jets - like high…
We give a solution to the inverse problem of Moebius geometry on the circle. Namely, we describe a class of Moebius structures on the circle for each of which there is a hyperbolic space such that its boundary at infinity is the circle, and…
We generalize the descriptions of vortex moduli spaces in \cite{Br} to more than one section with adiabatic constant $s$. The moduli space is topologically independent of $s$ but is not compact with respect to $C^\infty$ topology. Following…
The Willmore energy plays a central role in the conformal geometry of surfaces in the conformal 3-sphere \(S^3\). It also arises as the leading term in variational problems ranging from black holes, to elasticity, and cell biology. In the…
Knotted and tangled structures frequently appear in physical fields, but so do mechanisms for untying them. To understand how this untying works, we simulate the behavior of 1,458 superfluid vortex knots of varying complexity and scale in…
This an article about some elementary geometric and combinatorial natures of various knot energies. A related "new" knot invariant -- the X-crossing number -- is introduced.
The O'Hara energies, introduced by Jun O'Hara in 1991, were proposed to answer the question of what is a "good" figure in a given knot type. A property of the O'Hara energies is that the "better" the figure of a knot is, the less the energy…
Quantum mechanics is a successful theory that describes the behavior of photons, electrons, and other atomic- and molecular-scale objects. However, it is far from being well understood. In this paper, a new theory - knot physics for…
The curves of zero intensity of a complex optical field can form knots and links: optical vortex knots. Both theoretical constructions and experiments have so far been restricted to the very small families of torus knots or lemniscate…
The ribbonlength Rib$(K)$ of a knot $K$ is the infimum of the ratio of the length of any flat knotted ribbon with core $K$ to its width. A twisted torus knot $T_{p,q;r,s}$ is obtained from the torus knot $T_{p,q}$ by twisting $r$ adjacent…
We generalize the notion of integral Menger curvature introduced by Gonzalez and Maddocks by decoupling the powers in the integrand. This leads to a new two-parameter family of knot energies $intM^{p,q}$. We classify finite-energy curves in…