WebJul 14, 2024 · We make a connection between a famous analytical object introduced in the 1860s by Riemann, as well as some variants of it, and a nonlinear geometric PDE, the binormal curvature flow. As a consequence this analytical object has a non-obvious nonlinear geometric interpretation. We recall that the binormal flow is a standard model … WebMay 25, 2024 · The binormal (curvature) flow, that we refer hereafter as BF, is the classical model for one vortex filament dynamics. It was derived by Da Rios 1906 in his PhD …
Travelling helices and the vortex filament conjecture in the
Webinvestigate various dynamical and kinematical relations connecting the flow quantities with the geometrical parameters of the streamline trajectories. The expressions for the tangent, principal normal and binormal vectors and the curva ture and torsion of the streamlines are given in terms of the velocity components, pressure and density. WebAs a consequence this analytical object has a non-obvious non- linear geometric interpretation. We recall that the binormal flow is a standard model for the evolution of vortex filaments. We prove the existence of solutions of the binormal flow with smooth trajectories that are as close as desired to curves with a multifractal behavior. bilyk pronunciation
Singular solutions of the binormal flow Department of …
The vortex filaments are present in 3-D fluids having vorticity concentrated along a curve, and are a key element of quantum and classical fluid turbulent dynamics. This low regularity framework is difficult to analyze through the Euler and Navier–Stokes equation; it is however at the heart of current investigations (see … See more A classical problem of mathematical analysis is finding real variable functions that are continuous but not differentiable at any point. Although it … See more Let n\in {\mathbb {N}}^*, \nu \in ]0,1], \Gamma >0. Let \chi _n(0) be a polygonal line with corners located at j\in {\mathbb {Z}} with j \le n^\nu , of same torsion \omega _0 and angles \theta _nsuch that located and oriented … See more Our main statement asserts the existence of various families of solutions \{\chi _n\}_{n\in {\mathbb {N}}} of the binormal flow such that the … See more WebMar 11, 2024 · The binormal flow is a model for the dynamics of a vortex filament in a 3-D inviscid incompressible fluid. This flow is also related to the classical continuous … WebBinormal definition, the normal to a curve, lying perpendicular to the osculating plane at a given point on the curve. See more. cynthia tianti