Page personnelle de Gaspard Jankowiak

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Curves with modulated stiffness

Parameters:

$N$ $L$ $M$
$180$ $2\pi$ $0$

23.03.2022 (loss of convexity for $c_0 \neq 0$)

$\mu$ $c_0$ $\beta$ result comment
$10^{-1}$ $10^{-1}$ $e^{-\rho}$ movie  
$10$ $10^{-1}$ $e^{-\rho}$ movie  
$10^{-1}$ $1 = 2\pi / L$ $e^{-\rho}$ movie  
$10^{-1}$ $4$ $e^{-\rho}$ movie  
$10$ $4$ $e^{-\rho}$ movie  

08.02.2022 (focus on convexity)

Results:

$\mu$ $c_0$ $\beta$ result comment
$10^{-2}$ $0$ $e^{-\rho}$ movie cigar via “circle”
$10^{-1}$ $0$ $e^{-\rho}$ movie cigar via “triangle”
$10^{-1}$ $2.5$ $e^{-\rho}$ movie non embedded curve (neg. curv.) at equilibrium
$10^{-1}$ $2.5$ $e^{-0.7\rho}$ movie embedded curve (neg. curv.) at equilibrium
$10^{-1}$ $1.9$ $e^{-\rho}$ movie $\dot{E}{\rho}$ and $\dot{E}{\theta}$ do not have a sign
$10^{-1}$ $2$ $e^{-\rho}$ movie “cigar”-like (neg. curve) at equilibrium
$10^{-1}$ $3$ $e^{-\rho}$ movie non embedded curve (neg. curv.) at equilibrium
$10^{-1}$ $5$ $e^{-\rho}$ movie timestep too large?
$10^{-1}$ $10$ $e^{-\rho}$ movie clipped

31.01.2022

Results:

$\mu$ $c_0$ $\beta$ $t_{max}$, iter$_{max}$ result comment
$10^{-2}$ $0$ const.   movie  
$10^{-2}$ $10$ const.   movie  
$10^{-2}$ $0$ SDW1   movie  
$10^{-2}$ $0.1$ SDW   movie  
$10^{-2}$ $1$ SDW   movie  
$10^{-2}$ $0$ ADW2   movie  
  1. ($\beta(x) = 1.01 + (x - 1)^2 (x + 1)^2$)) 

  2. ($\beta(x) = 1.2 + (x - 1)^2 (x + 1)^2 + x$)) 


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