Fig. 1: Diagonal components of the gyration tensor.
a–f Diagonal gyration tensor elements \({G}_{\alpha \alpha }(\dot{\gamma })\) for a set of rings, normalised over their equilibrium value \({R}_{{\rm{g}}}^{2}(0)/3\) where Rg is the radius of gyration, against the shear rate \(\dot{\gamma }\) in panels a–c and against Weissenberg number Wi in panels d–f. A more complete discussion of gyration tensor G and the values obtained from it can be found in the Supplementary Methods. g–i Diagonal gyration tensor elements \({G}_{\alpha \alpha }(\dot{\gamma })\) for a set of chains including HI and the N  = 200-ring without HI for reference, normalised over their equilibrium value \({R}_{{\rm{g}}}^{2}(0)/3\) where Rg is the radius of gyration, against Weissenberg number Wi. a Gxx (flow direction) increases with shear rate to some maximum and then drops as rings align into the flow–vorticity plane and experience less strain. b Gzz (vorticity direction) decreases to a minimum and then shoots up at values of \(\dot{\gamma }\) that anticipate the inflation anomaly observed in panel c for the gradient direction. c Gyy (gradient direction) initially decreases with shear rate. For N = 150 and N = 200, an inflation anomaly is observed, which is hardly visible for N = 100. The same anomaly is reproduced for MPCD collision time step h = 0.05 for the N = 150-ring. To highlight this behaviour, shifts δ have been applied along the vertical axis, where δN=100  = 0.0, δN=150 = 0.25 (h = 0.1), δN=150 = 0.5 (h = 0.05) and δN=200 = 0.75. g Gxx (flow direction) increases with shear rate and eventually saturates for chains. Saturation was not yet reached for the N = 200-ring without HI. h Gzz (vorticity direction) decreases continuously. The anomaly of rings with HI presented in panels b and e is absent here. i Gyy (gradient direction) decreases with shear rate. As the anomaly in panels c and f is not shown by chains nor rings without HI, no shift was applied to these data.
