Unfold dynamics of generalized Gaussian structures

We consider the unfold dynamics of generalized Gaussian structures (GGSs) exposed to different kinds of external forces. A GGS consists of $N$ monomers connected by harmonic springs into a network; when its spectral dimension $d_s$ exceeds the critical value of 2 the GGS is in a collapsed state. Sommer and Blumen [J. Phys. A 28, 6669 (1995)] showed that collapsed structures can be unfolded under external forces; they demonstrate this for the case where each monomer is exposed to a force with a random direction: Then networks with a spectral dimension up to 4 become unfolded. In the present paper we focus on the dynamics of such unfold processes. We investigate GGSs exposed to different kinds of external forces (pulling one monomer, uncorrelated forces, long-range correlated forces, and diblocklike forces). We show that external perturbations that act only on a few monomers are not able to unfold a collapsed structure; on the other hand, more general kinds of forces lead to a stretching of GGSs even for $d_s>2\mathrm{}$ as long as $d_s<d_c,$ where $d_c$ depends on the kind of the force field. In general, during the unfold process the size $R$ of the GGS grows via a power law $R\propto t^{\alpha }$ $(0\mathrm{}<~\alpha <~1),$ where α depends on $d_s$ as well as on the kind of force field that is applied.