Figure 3.

(a) Decay of tangent-tangent autocorrelation function, measured from the middle of the chain, for different magnitudes of active forces F_a = 0, 90, 130, 170, and 200 (black, red, green, blue, and orange, respectively), chain length L = 100, L_p = 250, and τ = 1. (Brown) Exponential fit, according to Eq. 20, yields excellent agreement for the value of the persistence length (L_p) for the purely thermal case (F_a = 0). (Pink lines) Fit of the decay, for both short- and long ranges, to the same exponential form, for the correlations in the presence of active forces, thereby yielding L_p,eff. (Vertical dashed line) Length-scale of the onset of the plateau in the correlations. (Inset) Ensemble-averaged bending angles for different bonds along the chain. (b) Comparison of the effective temperatures (T_eff) obtained from the exponential fits of the decay of the orientational correlations from the middle bead, as shown in panel a (red, short range; green, long range). Mean bending energy (black) averaged over all the bonds and mean kinetic energy (lower dashed lines) associated with the components of velocities of the middle bead. (Inset) A typical conformation of the chain that provides visual evidence for the results shown in panel a (inset). (Pink symbols) Higher T_eff (and shorter persistence length) when the orientations are measured with respect to the end of the polymer, and compared to the mean bending energy of the first seven beads of the chain (orange line). (c) Orientational correlations calculated for polymer of different bending modulus κ; (inset) length-scale of the resonance increases as λ_c ∝ κ^1/4 (see Eq. 21). (d) As in panel c, we plot for different values of τ = 0.1, 0.5, 1, and 2 (top to bottom), showing (inset) that the length-scale of the resonance (extracted from a spline fit to the maximum of the plateau) increases in rough agreement with the predicted behavior as λ_c ∝ τ^1/4 (see Eq. 21). To see this figure in color, go online.