Results of Triangles Under Discrete Curve Shortening Flow
نویسندگان
چکیده
In this paper, we analyze the results of triangles under discrete curve shortening flow, specifically isosceles triangles with top angles greater than π3 , and scalene triangles. By considering the location of the three vertices of the triangle after some small time , we use the definition of the derivative to calculate a system of differential equations involving parameters that can describe the triangle. Constructing phase plane diagrams and then analyzing them, we find that the singular behavior of discrete curve shorting flow on isosceles triangles with top angles greater than π3 is a point, and for scalene triangles is a line segment.
منابع مشابه
Multiphase flow and tromp curve simulation of dense medium cyclones using Computational Fluid Dynamics
Dense Medium Cyclone is a high capacity device that is widely used in coal preparation. It is simple in design but the swirling turbulent flow, the presence of medium and coal with different density and size fraction and the presence of the air-core make the flow pattern in DMCs complex. In this article the flow pattern simulation of DMC is performed with computational fluid dynamics and Fluent...
متن کامل1-slim triangles and uniform hyperbolicity for arc graphs and curve graphs
We describe unicorn paths in the arc graph and show that they form 1-slim triangles and are invariant under taking subpaths. We deduce that all arc graphs are 7-hyperbolic. Considering the same paths in the arc and curve graph, this also shows that all curve graphs are 17-hyperbolic, including closed surfaces.
متن کاملThe Blow up Analysis of Solutions of the General Curve Shortening Flow
In this paper, a detailed asymptotic behavior of the closed curves is presented when they contract to a point in finite time under the general curve shortening flow.
متن کاملOn the Affine Heat Equation for Non-convex Curves
In the past several years, there has been much research devoted to the study of evolutions of plane curves where the velocity of the evolving curve is given by the Euclidean curvature vector. This evolution appears in a number of different pure and applied areas such as differential geometry, crystal growth, and computer vision. See for example [4, 5, 6, 15, 16, 17, 19, 20, 35] and the referenc...
متن کاملRelaxation of the Flow of Triods by Curve Shortening Flow via the Vector-valued Parabolic Allen-cahn Equation
where uǫ : R n × R+ → R and W : R → R is a positive potential with a finite number of minima. In particular we will concentrate on the case m = n = 2 and W a function with 3 minima. We prove that triods evolving under curve shortening flow can be realized as nodal sets of this equation (for a precise statements and definitions see Section 2). We also include some corollaries derived from this r...
متن کامل