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2022-02-09 16:20:50 +01:00

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layout math lang subtitle
default true en Curves with modulated stiffness

Parameters:

|$N$|$L$|$M$| |-| |$180$|$2\pi$|$0$| |-| {:.bordered.center}

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| {:.bordered.center}

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| |-| {:.bordered.center}


  1. (\beta(x) = 1.01 + (x - 1)^2 (x + 1)^2)) ↩︎

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