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The local ordering inside a vortex cluster is extremely fast in comparison to its migration because the intervortex force decreases exponentially with the separation. The stability of the final configuration was tested by running the simulation from this configuration for 200000 more time steps with step duration four times larger.
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The upper bound is equal to (1-δ∫×a3/ δ∫×a2)/2 that is numerically estimated to 0.346 (δ∫ stands for the variation of the integral as d grows to infinity). The lower bound 3(ζ8(2)-ζ6(2))/4(ζ6(2)-ζ4(2))-1≈-0.4 with the values of the constants ζn(2) is given by Ref. 9.
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