A curve shortening flow rule for closed embedded plane curves with a prescribed rate of change in enclosed area
نویسندگان
چکیده
منابع مشابه
A curve shortening flow rule for closed embedded plane curves with a prescribed rate of change in enclosed area.
Motivated by a problem from fluid mechanics, we consider a generalization of the standard curve shortening flow problem for a closed embedded plane curve such that the area enclosed by the curve is forced to decrease at a prescribed rate. Using formal asymptotic and numerical techniques, we derive possible extinction shapes as the curve contracts to a point, dependent on the rate of decreasing ...
متن کاملCurve shortening-straightening flow for non-closed planar curves with infinite length
We consider a motion of non-closed planar curves with infinite length. The motion is governed by a steepest descent flow for the geometric functional which consists of the sum of the length functional and the total squared curvature. We call the flow shorteningstraightening flow. In this paper, first we prove a long time existence result for the shortening-straightening flow for non-closed plan...
متن کاملA Higher Order Scheme for a Tangentially Stabilized Plane Curve Shortening Flow with a Driving Force
We introduce a new higher order scheme for computing a tangentially stabilized curve shortening flow with a driving force represented by an intrinsic partial differential equation for an evolving curve position vector. Our new scheme is a combination of the explicit forward Euler and the fully-implicit backward Euler schemes. At any discrete time step, the solution is found efficiently using a ...
متن کاملErgodicity of Stochastic Curve Shortening Flow in the Plane
We study models of the motion by mean curvature of an (1+1) dimensional interface with random forcing. For the well-posedness of the models we prove existence and uniqueness for certain degenerate nonlinear stochastic evolution equations in the variational framework of Krylov-Rozovskĭı, replacing the standard coercivity assumption by a Lyapunov type condition. Ergodicity is established for the ...
متن کاملCurve Shortening Flow in a Riemannian Manifold
In this paper, we systemally study the long time behavior of the curve shortening flow in a closed or non-compact complete locally Riemannian symmetric manifold. Assume that we have a global flow. Then we can exhibit a a limit for the global behavior of the flow. In particular, we show the following results. 1). Let M be a compact locally symmetric space. If the curve shortening flow exists for...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
سال: 2016
ISSN: 1364-5021,1471-2946
DOI: 10.1098/rspa.2015.0629