Loop Equations

This collection of Mathematica notebooks and Python scripts supports the enclosed paper Microscopic theory of Decaying Turbulence MDPI (download PDF).

Mathematica notebooks verify analytic solutions, and the Python code in VorticityCorrelation.py simulates the random complex curve with N up to 2*10^8 points of a polygon

and T= 2*10^5 samples.

The formulas are explained in the text of the paper.

The code in VorticityCorrelation.py has two regimes:

1. statistics collection ( script 'run.sh" for a cluster and "run_local.sh" for a laptop/desktop) Output is stored in "FData.T.C.np" files (T is the number of samples, and C is the number of a node that created these samples on a cluster in a parallel run.
2. The second regime (script plot.sh and plot_local.sh, automatically launched in the "submit.sh" script after the statistics collection) is the data processing part\ This processing starts with pooling all the "FData....C.np" files for C =1,... Num_nodes into a single data file. Then this data file is used to plot various distributions

1. cd CPP

2. activate G++ 7 somehow

3. cmake .

4. make