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Treating the relaxation dynamics of an ensemble of random hyperbranched macromolecules in dilute solution represents a challenge even in the framework of Rouse-type approaches, which focus on generalized Gaussian structures (GGSs). The problem is that one has to average over a large class of realizations of molecular structures, and that each molecule(More)
We consider the dynamics of Vicsek fractals of arbitrary connectivity, models for hyperbranched polymers. Their basic dynamical properties depend on their eigenvalue spectra, which can be determined iteratively. This paves the way for theoretical studies to very high precision for regular, finite, arbitrarily large hyperbranched structures.
In these lectures, we discuss the influence of weak quenched disorder on the critical behavior in condensed matter and give a brief review of available experimental and theoretical results as well as results of MC simulations of these phenomena. We concentrate on three cases: (i) uncorrelated random-site disorder, (ii) long-range-correlated random-site(More)
We analyze the effective triplet interactions between the centers of star polymers in a good solvent. Using an analytical short distance expansion inspired by scaling theory, we deduce that the triplet part of the three-star force is attractive but only 11% of the pairwise part even for a close approach of three star polymers. We have also performed(More)
We characterize the multifractal behavior of Brownian motion in the vicinity of an absorbing star polymer. We map the problem to an O(M)-symmetric phi(4)-field theory relating higher moments of the Laplacian field of Brownian motion to corresponding composite operators. The resulting spectra of scaling dimensions of these operators display the convexity(More)
We examine the demixing transition in star-polymer-colloid mixtures for star arm numbers f=2,6,16,32 and different star-polymer-colloid size ratios 0.18< or =q< or =0.50. Theoretically, we solve the thermodynamically self-consistent Rogers-Young integral equations for binary mixtures using three effective pair potentials obtained from direct molecular(More)
We explore the rich scaling behavior of copolymer networks in solution. We establish a eld theoretic description in terms of composite operators. Our 3rd order resummation of the spectrum of scaling dimensions brings about remarkable features: Convexity of the spectra allows for a multifractal interpretation. This has not been conceived for power of eld(More)
We analyze the scaling laws for a set of two different species of long flexible polymer chains joined together at one of their extremities (copolymer stars) in space dimension D=2. We use a formerly constructed field-theoretic description and compare our perturbative results for the scaling exponents with recent conjectures for exact conformal scaling(More)