Fig. 3: Spatial and temporal correlations in experiment and simulations.

a Decay of the spatial correlation functions, \({C}^{x}(r)={\langle \cos 2[{\psi }_{x}(r+{r}_{0},{t}_{0})-{\psi }_{x}({r}_{0},{t}_{0})]\rangle }_{{t}_{0},{r}_{0}}\), where ψ_x represents shape director angle Cⁿ, stress angle C^m, or the mismatch angle C^θ. Comparison of the simulation and the experiment assumes 10LB spatial units ~30 μm. b Decay of the time correlation functions, \({C}^{x}(t)={\langle \cos 2[{\psi }_{x}({r}_{0},t+{t}_{0})-{\psi }_{x}({r}_{0},{t}_{0})]\rangle }_{{t}_{0},{r}_{0}}\), where ψ represents shape director angle Cⁿ or the stress angle C^m. Comparison of the simulation and the experiment assumes 100LB time units \(\sim 10\,\min\). c Using the length-scale that relates experiments and simulations (in part (a)), we can compare the velocity correlation in experiments (solid line) and simulations (dashed line). The velocity correlation in simulations decays on a similar length-scale as in the experiments. The velocity correlation and the error bars are measured in eight experiments. d Magnitude of the stress σ as a function of the misalignment angle θ. The magnitude of the stress is re-scaled with its maximum value in each experiment before averaging. In (a–d) the centre of the error bars show the average data and the error bars show the standard deviation over 11 experiments. The data in each experiment is averaged over 48 frames. Source data are provided as a Source Data file in ref. ⁴⁵.