Convergence to Equilibrium of Gradient Flows Defined on Planar Curves
نویسندگان
چکیده
We consider the evolution of open planar curves by the steepest descent flow of a geometric functional, under different boundary conditions. We prove that, if any set of stationary solutions with fixed energy is finite, then a solution of the flow converges to a stationary solution as time goes to infinity. We also present a few applications of this result.
منابع مشابه
Gradient Flows as a Selection Procedure for Equilibria of Nonconvex Energies
For atomistic material models, global minimization gives the wrong qualitative behaviour; a theory of equilibrium solutions needs to be defined in different terms. In this paper, a concept based on gradient flow evolutions, to describe local minimization for simple atomistic models based on the Lennard-Jones potential, is presented. As an application of this technique, it is shown that an atomi...
متن کاملOn the Geometric Flow of Kirchhoff Elastic Rods
Recently, rod theory has been applied to the mathematical modeling of bacterial fibers and biopolymers (e.g. DNA), to study their mechanical properties and shapes (e.g. supercoiling). In static rod theory, an elastic rod in equilibrium is the critical point of an elastic energy. This induces a natural question of how to find elasticae. In this paper, we focus on how to find the critical points ...
متن کاملTraveling Waves of Some Symmetric Planar Flows of Non-Newtonian Fluids
We present some variants of Burgers-type equations for incompressible and isothermal planar flow of viscous non-Newtonian fluids based on the Cross, the Carreau and the power-law rheology models, and on a symmetry assumption on the flow. We numerically solve the associated traveling wave equations by using industrial data and in order to validate the models we prove existence and uniqueness of ...
متن کاملConvergence Properties of Curvature Scale Space Representations
Curvature Scale Space (CSS) representations have been shown to be very useful for recognition of noisy curves of arbitrary shapes at unknown orientations and scales [10,14]. This paper contains a number of important results on the convergence properties of CSS representations and on the evolution and arc length evolution of planar curves [6,12]. The processes which convolve arc length parametri...
متن کاملA constitutive framework for the non-Newtonian pressure tensor of a simple fluid under planar flows.
Non-equilibrium molecular dynamics simulations of an atomic fluid under shear flow, planar elongational flow, and a combination of shear and elongational flow are unified consistently with a tensorial model over a wide range of strain rates. A model is presented that predicts the pressure tensor for a non-Newtonian bulk fluid under a homogeneous planar flow field. The model provides a quantitat...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013