[numerics] improve dAJLR
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2 changed files with 26 additions and 13 deletions
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@ -2,23 +2,30 @@
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layout: default
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math: true
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lang: en
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subtitle: Curves with modulated stiffness
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---
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## Parameters:
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- $N = 180$
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- $L = 2π$
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- $M = 0$
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- $\mu = 10^{-2}$
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|$N$|$L$|$M$|$\mu$|
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|$180$|$2\pi$|$0$|$10^{-2}$|
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{:.bordered.center}
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## Results ($c_0 = 0$):
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- $\beta \equiv 1$: [movie](/s/numerics/dAJLR/beta=1.mp4)
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- symmetric double well ($\beta(x) = 1.01 + (x - 1)^2 (x + 1)^2$): [movie](/s/numerics/dAJLR/sym.mp4)
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- asymmetric double well ($\beta(x) = 1.2 + (x - 1)^2 (x + 1)^2 + x$): [movie](/s/numerics/dAJLR/asym.mp4)
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## Results:
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## Results $(c_0 > 0$):
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|$c_0$|$\beta$|$t_{max}$, iter$_{max}$|result|comment|
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|$0$|const.||[movie](/s/numerics/dAJLR/beta=1.mp4)|
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|$10$|const.||[movie](/s/numerics/dAJLR/const_c0=10.mp4)
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|$0$|SDW[^1]||[movie](/s/numerics/dAJLR/sym.mp4)|
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|$0.1$|SDW||[movie](/s/numerics/dAJLR/sym-c0=0.1.mp4)
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|$1$|SDW||[movie](/s/numerics/dAJLR/sym-c0=1.mp4)
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|$0$|ADW[^2]||[movie](/s/numerics/dAJLR/asym.mp4)|
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{:.bordered.center}
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- symmetric, $c_0 = 0.1$: [movie](/s/numerics/dAJLR/sym-c0=0.1.mp4)
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- symmetric, $c_0 = 1$: [movie](/s/numerics/dAJLR/sym-c0=1.mp4)
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- constant, $c_0 = 10$: [movie](/s/numerics/dAJLR/const_c0=10.mp4)
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[^1]: ($\beta(x) = 1.01 + (x - 1)^2 (x + 1)^2$))
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[^2]: ($\beta(x) = 1.2 + (x - 1)^2 (x + 1)^2 + x$))
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