Related papers: Moebius energy of thick knots
Turbulent flows in the presence of walls may be apprehended as a collection of momentum- and energy-containing eddies (energy-eddies), whose sizes differ by many orders of magnitude. These eddies follow a self-sustaining cycle, i.e.,…
Weaving knots are alternating knots with the same projection as torus knots, and were conjectured by X.-S. Lin to be among the maximum volume knots for fixed crossing number. We provide the first asymptotically correct volume bounds for…
The folding pathway and rate coefficients of the folding of a knotted protein are calculated for a potential energy function with minimal energetic frustration. A kinetic transition network is constructed using the discrete path sampling…
Measurements of the energy spectrum and of the vortex-density fluctuation spectrum in superfluid turbulence seem to contradict each other. Using a numerical model, we show that at each instance of time the total vortex line density can be…
In this paper we prove a generalisation of Schlenk's theorem about the existence of contractible periodic Reeb orbits on stable, displaceable hypersurfaces in symplectically aspherical, geometrically bounded, symplectic manifolds, to a…
The kinetic energy of a local system of objects placed in a curved spacetime is gained by the subsequent acceleration of the object following the more contracted region of spacetime. Normally this happens near massive gravitating stars.…
The magnetic structure of neutron vortices in the superfluid cores of neutron stars is determined assuming that the proton condensate forms a type I superconductor. It is shown that the entrainment currents induced by the neutron vortex…
On a Riemannian manifold, lower Ricci curvature bounds are known to be characterized by geodesic convexity properties of various entropies with respect to the Kantorovich-Rubinstein-Wasserstein square distance from optimal transportation.…
We construct a simple analytic model for wall-bounded turbulence, containing only four adjustable parameters. Two of these parameters characterize the viscous dissipation of the components of the Reynolds stress-tensor and other two…
We introduce a novel energy method that reinterprets ``curve shortening'' as ``tangent aligning''. This conceptual shift enables the variational study of infinite-length curves evolving by the curve shortening flow, as well as higher order…
Motivated by our previous work using the Stillinger-Weber potential, which shows that the [$\overline{2}11$] step on 1$\times$1 reconstructed Si(111) has a Schwoebel barrier of 0.61$\pm$0.07 eV, we calculate here the same barrier…
Turbulence in a system of nonlinearly interacting waves is referred to as wave turbulence. It has been known since seminal work by Kolmogorov, that turbulent dynamics is controlled by a directional energy flux through the wavelength scales.…
The nonlinear dynamics of a bundle of magnetic flux ropes driven by stationary fluid motions at their endpoints is studied, by performing numerical simulations of the magnetohydrodynamic (MHD) equations. The development of MHD turbulence is…
The knots in solar prominences are often observed to fall with nearly constant velocity, but the associated physical mechanism is currently not well understood. In this letter, we presented a prominence observed by New Vacuum Solar…
Nonequilibrium active polymers provide a minimal framework to investigate biopolymers such as DNA and chromatin under the action of molecular motors. Here we study active ring polymers with controlled topology and show that knot type…
Here we report the first evidence of the inverse energy cascade in a flow dominated by 3D motions. Experiments are performed in thick fluid layers where turbulence is driven electromagnetically. It is shown that if the free surface of the…
Ribbons are long narrow strips possessing three distinct material length scales (thickness, width, and length) which allow them to produce unique shapes unobtainable by wires or filaments. For example when a ribbon has half a twist and is…
Geometric and topological bounds are obtained for the first energy level gap of a particle constrained to move on a compact surface in 3-space. Moreover, geometric properties are found which allows for stationary and uniformly distributed…
Relatively extremal knots are the relative minima of the ropelength functional in C^1 topology. On the set curves of fixed length, they are the relative maxima of thickness (normal injectivity radius) functional, including the ideal knots.…
Turbulence may appear as a complex process with a multitude of scales and flow patterns, but still obeys simple physical principles such as the conservation of momentum, of energy, and the maximum entropy principle. The latter states that…