[numerics] improve dAJLR

This commit is contained in:
Gaspard Jankowiak 2022-01-31 13:10:21 +01:00
commit 4187df3c96
2 changed files with 26 additions and 13 deletions

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