Localization of a random copolymer at an interface: an untethered self-avoiding walk model
We consider two related n-step self-avoiding walk models of a copolymer at an interface between two bulk phases. In one case the walk is confined to start in the interface while in the other this condition is relaxed. We prove that both models have the same limiting free energy (in the n → ∞ limit) and hence that their phase diagrams are identical. We also show that the limits n → ∞ and certain energy parameters going to plus or minus infinity can be interchanged. These latter results are interesting from the viewpoint of numerical studies.
Abstract In this paper, we study the long-time behavior of solutions for a non-autonomous strongly damped wave equation. We first prove the existence of a uniform attractor for the equation with a translation compact driving force and then obtain an upper estimate for the Kolmogorov e -entropy of the uniform attractor. Finally we obtain an upper bound of the fractal dimension of the uniform attractor with quasiperiodic force.