Wittmer, J. P., Kriuchevskyi, I., Cavallo, A., Xu, H., & Baschnagel, J. (2016). Shear-stress fluctuations in self-assembled transient elastic networks. *Phys. Rev. E*, *93*(6), 11 pp.

Focusing on shear-stress fluctuations, we investigate numerically a simple generic model for self-assembled transient networks formed by repulsive beads reversibly bridged by ideal springs. With Lambda t being the sampling time and t(star)(f) similar to 1/f the Maxwell relaxation time (set by the spring recombination frequency f), the dimensionless parameter Delta x = Delta t/ t(star) (f) is systematically scanned from the liquid limit (Delta x >> 1) to the solid limit (Delta x << 1) where the network topology is quenched and an ensemble average over m-independent configurations is required. Generalizing previous work on permanent networks, it is shown that the shear-stress relaxation modulus G(t) may be efficiently determined for all Delta x using the simple-average expression G(t) = mu(A) – h(t) with mu(A) = G(0) characterizing the canonical-affine shear transformation of the system at t = 0 and h(t) the (rescaled) mean-square displacement of the instantaneous shear stress as a function of time t. This relation is compared to the standard expression G(t) = (c) over tilde (t) using the (rescaled) shear-stress autocorrelation function (c) over tilde (t). Lower bounds for the m configurations required by both relations are given.