AI Article Synopsis
- The study focuses on the behavior of various transport processes, such as diffusion and self-avoiding walks, on large, randomly branched polymers through a method called renormalized dynamical field theory.
- In particular, it examines the swollen phase and collapse transition where the polymer structures have no loops, leading to statistical behaviors similar to lattice trees.
- The researchers calculate universal scaling exponents, including the diffusion exponent and the fractal dimension of the optimal path, and compare their theoretical findings with available numerical results for validation.
Article Abstract
We study asymptotic properties of diffusion and other transport processes (including self-avoiding walks and electrical conduction) on large, randomly branched polymers using renormalized dynamical field theory. We focus on the swollen phase and the collapse transition, where loops in the polymers are irrelevant. Here the asymptotic statistics of the polymers is that of lattice trees, and diffusion on them is reminiscent of the climbing of a monkey on a tree. We calculate a set of universal scaling exponents including the diffusion exponent and the fractal dimension of the minimal path to two-loop order and, where available, compare them to numerical results.
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| http://dx.doi.org/10.1103/PhysRevE.85.051126 | DOI Listing |
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