MCFTLE: Monte Carlo Rendering of Finite-Time Lyapunov Exponent Fields

2016 ◽  
Vol 35 (3) ◽  
pp. 381-390 ◽  
Author(s):  
Tobias Günther ◽  
Alexander Kuhn ◽  
Holger Theisel
Keyword(s):  
Monte Carlo ◽  
Lyapunov Exponent ◽  
Finite Time ◽  
Finite Time Lyapunov Exponent ◽  
Monte Carlo Rendering

scholarly journals Shape Coherence and Finite-Time Curvature Evolution

2015 ◽  
Vol 25 (05) ◽  
pp. 1550076 ◽  
Author(s):  
Tian Ma ◽  
Erik M. Bollt
Keyword(s):  
Lyapunov Exponent ◽  
Dynamical Systems ◽  
Coherent Structures ◽  
Finite Time ◽  
Large Curvature ◽  
Nonautonomous Dynamical Systems ◽  
Finite Time Lyapunov Exponent ◽  
Close Proximity ◽  
Definition Of ◽  
Curvature Growth

We introduce a definition of finite-time curvature evolution along with our recent study on shape coherence in nonautonomous dynamical systems. Comparing to slow evolving curvature preserving the shape, large curvature growth points reveal the dramatic change on shape such as the folding behaviors in a system. Closed trough curves of low finite-time curvature (FTC) evolution field indicate the existence of shape coherent sets, and troughs in the field indicate the most significant shape coherence. Here, we will demonstrate these properties of the FTC, as well as contrast to the popular Finite-Time Lyapunov Exponent (FTLE) computation, often used to indicate hyperbolic material curves as Lagrangian Coherent Structures (LCS). We show that often the FTC troughs are in close proximity to the FTLE ridges, but in other scenarios, the FTC indicates entirely different regions.

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