Binormal flow
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 ... 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 filaments evolving with constant torsion which arise from extremal curves of curvature energy functionals. They are “soliton” solutions in the sense that they …
Binormal flow
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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. 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 ...
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 … Webvector field on is the binormal vector field of, and the sign of the z-dimension of is positive if B is upward and is negative if it is downward. Therefore, we consider the sign of the binormal vector. In 2D the sign of the binormal vector can be obtained using the cross product of the two vectors and as follows: B T u N < < B B (vi) T (vi) N (vi)
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 … WebSep 21, 2024 · In this talk I shall present a connection between a famous analytical object introduced in the 1860s by Riemann, as well as some variants of it, and a nonlinear …
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WebMay 25, 2024 · Finally we prove the existence of a unique solution of the binormal flow with datum a polygonal line. This equation is used as a model for the vortex filaments … how far away was the krakatoa eruption heardWebApr 17, 2024 · The skew-mean-curvature (or binormal) flow in $${\mathbb {R}}^n,\;n\geqslant 3$$ with certain symmetry can be regarded as point vortex motion of these 2D lake equations. We compare point vortex motions of the Euler and lake equations. Interesting similarities between the point vortex motion in the half-plane, … how far away was the ferndale earthquake feltWebSep 1, 2024 · It also plays a surprising role as a physical trajectory in the evolution of regular polygonal vortices that follow the binormal flow. With this motivation, we focus on one more classic tool to measure intermittency, namely, the fourth-order flatness, and we refine the results that can be deduced from the multifractal analysis to show that it ... how far away will doordash deliverThe 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 hiding tonight letraWebJul 20, 2024 · Abstract: The 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 … how far away was the turkey earthquake feltWebThe 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 … hiding to nothingWebAug 8, 1999 · The purely binormal motion of curves of constant curvature or torsion, respectively, is shown to lead to integrable extensions of the Dym and classical sineGordon equations. ... Minarčík J and Beneš M (2024) Minimal surface generating flow for space curves of non-vanishing torsion, Discrete and Continuous Dynamical Systems - B, … hiding to nowhere