We study the tubular phase of self-avoiding anisotropic membranes. We discuss the renormalizability of the model Hamiltonian describing this phase and derive from a renor-malization group equation some general scaling relations for the exponents of the model. We show how particular choices of renormalization factors reproduce the Gaussian result, the Flory theory and the Gaussian Variational tr...

2014 Self-avoiding walks (SAW) explore the backbone of a fractal lattice, while random walks explore the full lattice. We show the existence of an intrinsic exponent for SAW and examine a simple Flory approximation that uses the spectral dimension of the backbone. Exact results for various fractal lattices show that this approximation is not very satisfactory and that properties of SAW depend o...

Predicting and understanding the phase equilibria or separation in polymer–solvent solutions represent unresolved fundamental problems polymer science. The behavior thermodynamics of miscibility depend on inter- intramolecular interactions a with certain molecular weight distribution mixed solvent. Here, we develop machine-learning framework to achieve highly generalized robust prediction Flory...

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We propose a new form of free energy for polymeric fractals (chain-like, branched or membranes) based on self-similarity arguments and on the existence of a maximum gyration radius. Results are obtained conceming the size exponents at the theta-point and critical point. These two exponents depend on a single parameter only, for which a simple phenomenological expression is provided. A very good...