Binormal flow

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August undefined, 2024

WebMay 1, 2009 · Abstract: In this paper we study the stability of the self-similar solutions of the binormal flow, which is a model for the dynamics of vortex filaments in fluids and super-fluids. These particular solutions $\chi_a(t,x)$ form a family of evolving regular curves of $\mathbb R^3$ that develop a singularity in finite time, indexed by a parameter ... WebThe binormal flow is a model for the dynamics of a vortex filament in a 3-D inviscid incompressible fluid. The flow is also related with the classical continuous Heisenberg model in ferromagnetism, and the 1-D cubic Schrödinger equation. We consider a class of solutions at the critical level of regularity that generate singularities in finite ...

Scattering for 1D cubic NLS and singular vortex dynamics

WebThe binormal flow is a model for the dynamics of a vortex filament in a 3-D inviscid incompressible fluid. The flow is also related with the classical continuous Heisenberg … WebThe plane defined by normal and binormal vectors is called the normal plane and the plane defined by binormal and tangent vectors is called the rectifying plane (see Fig. 2.6 ). As … c\u0026f bank towne center drive newport news va

Travelling helices and the vortex filament conjecture in the

WebThe local induction equation, or the binormal flow on space curves is a well-known model of deformation of space curves as it describes the dynamics of vortex filaments, and the complex curvature is governed by the non-linear Schrödinger equation. In this article, we present its discrete analogue, namely, a model of deformation of discrete ... WebIn this proceedings article we shall survey a series of results on the stability of self-similar solutions of the vortex filament equation. This equation is a geometric flow for curves in and it is used as a model for… 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. c\u0026f bank stock price

On the energy of critical solutions of the binormal flow ...

Convergence Rates of the Allen--Cahn Equation to Mean …

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 WebWe study curve motion by the binormal flow with curvature and torsion depending velocity and sweeping out immersed surfaces. Using the Gauss-Codazzi equations, we obtain … ea sports fifa 2017WebApr 13, 2024 · The results show that the proposed method improved the response time required to change the coolant flow direction and led to a coolant temperature difference of 4.90 °C at 90 °C cooling conditions. This result indicates that the proposed system can be applied to existing internal combustion engines to enhance their performance in terms of ... ea sports fifa 19 demo

"WebBinormal definition: (mathematics) A line that is at right angles to both the normal and the tangent of a point on a curve and, together with them, forms three cartesian axes. " - Binormal flow

Scattering for 1D cubic NLS and singular vortex dynamics

Travelling helices and the vortex filament conjecture in the

Binormal flow

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