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Lyapunov in README

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Ian Jauslin 2025-01-31 11:08:20 -05:00
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README.md
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@ -45,6 +45,11 @@ The available commands are
In addition, if alpha has a negative value (even in between `print_freq` In addition, if alpha has a negative value (even in between `print_freq`
intervals), a line is printed with the information. intervals), a line is printed with the information.
* `lyapunov`: to compute the Lyapunov exponents. This command prints
```time instantaneous_lyapunov lyapunov```
where `instantaneous_lyapunov` is computed from the tangent flow only between
the given time and the previous one.
* `uk`: to compute the Fourier transform of the solution. * `uk`: to compute the Fourier transform of the solution.
* `quiet`: does not print anything, useful for debugging. * `quiet`: does not print anything, useful for debugging.
@ -138,13 +143,27 @@ should be a `;` sperated list of `key=value` pairs. The possible keys are
* `print_alpha` (0 or 1, default 0): if this is set to 1, then whenever alpha * `print_alpha` (0 or 1, default 0): if this is set to 1, then whenever alpha
is negative, its value is printed as a comment. is negative, its value is printed as a comment.
* `lyapunov_reset` (double, default: `print_freq`): if this is set, then, when
computing the Lyapnuov exponents, the tangent flow will renormalize itself at
times proportional to `lyapunov_reset`. This option is incompatible with
`lyapunov_maxu`.
* `lyapunov_maxu` (double, default: unset): if this is set, then, when
computing the Lyapnuov exponents, the tangent flow will renormalize itself
whenever the norm of the tangent flow exceeds `lyapunov_maxu`. This option
is incompatible with `lyapunov_reset`.
* `algorithm_lyapunov`: the algorithm used to integrate the tangent flow. Can
be `RK4` for Runge-Kutta 4 (default) or `RK2` for Runge-Kutta 2. Adaptive
step algorithms cannot be used for the tangent flow.
# Interrupting and resuming the computation # Interrupting and resuming the computation
The computation can be interrupted by sending Nstrophy the `SIGINT` signal The `enstrophy` computation can be interrupted by sending Nstrophy the `SIGINT`
(e.g. by pressing `Ctrl-C`.) When Nstrophy receives the `SIGINT` signal, it signal (e.g. by pressing `Ctrl-C`.) When Nstrophy receives the `SIGINT` signal,
finishes its current step and writes the value of uk, either to `savefile` if it finishes its current step and writes the value of uk, either to `savefile`
such a file was specified on the command line (using the `-s` flag), or to if such a file was specified on the command line (using the `-s` flag), or to
`stderr`. In addition, when a `savefile` is specified it writes the command `stderr`. In addition, when a `savefile` is specified it writes the command
that needs to be used to resume the computation (which essentially just sets that needs to be used to resume the computation (which essentially just sets
the appropriate `starting_time` and `init:file:<savefile>` parameters. The data the appropriate `starting_time` and `init:file:<savefile>` parameters. The data