[numerics] improve dAJLR
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2 changed files with 26 additions and 13 deletions
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@ -86,10 +86,13 @@ footer { font-size: 75%; padding-bottom: 175px; }
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em { font-style: italic; }
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em { font-style: italic; }
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table { width: 100%; }
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table { width: 100%; }
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thead { color: $dim; }
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/*thead { color: $dim; }*/
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th, td { padding: 0.3em; }
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th, td { padding: 0.3em; }
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tr { border-bottom: 1px dotted $tr-rule; }
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tr { border-bottom: 1px dotted $tr-rule; }
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table.bordered { border-collapse: collapse; }
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table.bordered tr { border-top: 1px solid #bbb; border-bottom: 1px solid #bbb; }
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.publi_table td:nth-child(1) { width: 30%; }
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.publi_table td:nth-child(1) { width: 30%; }
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.publi_table td:nth-child(2) { width: 60%; }
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.publi_table td:nth-child(2) { width: 60%; }
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.publi_table td:nth-child(3) { width: 10%; }
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.publi_table td:nth-child(3) { width: 10%; }
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@ -137,6 +140,9 @@ ol li:hover { border-right: 3px solid $links; padding-right: 7px; }
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#http_code { text-align: center; font-size: 10em; line-height: 1em; }
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#http_code { text-align: center; font-size: 10em; line-height: 1em; }
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.footnotes { font-size: 0.8em; padding-left: 1em; margin-top: 2em;}
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.footnotes ol li { padding: 0; border: none; }
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@media (max-width: $small-width) {
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@media (max-width: $small-width) {
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body { font-size: 80%; }
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body { font-size: 80%; }
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}
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}
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@ -2,23 +2,30 @@
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layout: default
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layout: default
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math: true
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math: true
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lang: en
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lang: en
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subtitle: Curves with modulated stiffness
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---
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---
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## Parameters:
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## Parameters:
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- $N = 180$
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|$N$|$L$|$M$|$\mu$|
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- $L = 2π$
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- $M = 0$
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|$180$|$2\pi$|$0$|$10^{-2}$|
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- $\mu = 10^{-2}$
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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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## Results:
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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 $(c_0 > 0$):
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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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[^1]: ($\beta(x) = 1.01 + (x - 1)^2 (x + 1)^2$))
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- symmetric, $c_0 = 1$: [movie](/s/numerics/dAJLR/sym-c0=1.mp4)
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[^2]: ($\beta(x) = 1.2 + (x - 1)^2 (x + 1)^2 + x$))
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- constant, $c_0 = 10$: [movie](/s/numerics/dAJLR/const_c0=10.mp4)
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