Summary: We study the impact of topological disorder on the mechanical response of hyperbranched macromolecules from a theoretical and numerical perspective. The polymer models are generated using a bond switching algorithm, and the emerging systems are described within the Zimm and Rouse pictures of macromolecular dynamics. The topological disorder is manifest in the frequency‐dependent dynamic moduli, . These are clearly distinct from that of regular hyperbranched fractals of the same size, and they do not obey simple scaling rules. The dynamic moduli reflect the short‐range order inherent in the model, and we thus suggest that the extent of disorder in branched tree‐like polymers may be well‐estimated experimentally using .
The aim of this paper is to generalize two important results known for the Stratonovich and Itô integrals to any stochastic integral obtained as limit of Riemann sums with arbitrary evaluating point: the ordinary chain rule for certain nonlinear functions of the Brownian motion and the Wong–Zakai approximation theorem. To this scope we begin by introducing a new family of products for smooth random variables which reduces for specific choices of a parameter to the pointwise and to the Wick products. We show that each product in that family is related in a natural way to a precise choice of the evaluating point in the above mentioned Riemann sums and hence to a certain notion of stochastic integral. Our chain rule relies on a new probabilistic representation for the solution of the heat equation while the Wong–Zakai type theorem follows from a reduction method for quasi-linear SDEs together with a formula of Gjessing’s type. 相似文献
