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Matthen

Emergence

Apr 15th, 2013
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  1. n = 100;
  2. \[Theta]0 = RandomReal[{0, 2 Pi}, n];
  3. \[Theta]p = RandomReal[{0, 0.6}, n];
  4. T = 20 Pi;
  5. \[Lambda] = 0.3;
  6. soln = NDSolve[
  7. Table[{\[Theta][i]'[
  8. t] == \[Theta]p[[i]] - \[Lambda] Sin[(\[Theta][i][t] -
  9. Sum[\[Theta][i][t], {i, 1, n}]/n)], \[Theta][i][
  10. 0] == \[Theta]0[[i]]}, {i, n}],
  11. Table[\[Theta][i], {i, n}], {t, 0, T}];
  12. Manipulate[Graphics[
  13. {
  14. Block[{\[Mu]},
  15. \[Mu] =
  16. If[norm, First[Sum[\[Theta][i][t], {i, 1, n}]/n /. soln], 0];
  17. Table[
  18. {
  19. Opacity[0.5],
  20. ColorData["DarkRainbow"][i/n],
  21. Disk[{Cos[\[Theta][i][t] - \[Mu]], Sin[\[Theta][i][t] - \[Mu]]},
  22. 0.1] /. soln}, {i, n}]
  23. ]
  24. }
  25. , PlotRange -> 1.2]
  26. ,
  27. {t, 0, T},
  28. {norm, {True, False}}]
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