homepage/numérique/dAJLR.markdown

layout	math	lang	subtitle
default	true	en	Curves with modulated stiffness

Parameters:

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

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|| {:.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}

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

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