Self-similar self-avoiding structures: Models for polymers

Self-avoiding flexible polymers under spherical confinement.

We compute the free energy of confinement for a flexible self-avoiding polymer inside a spherical cavity. Accurate numerical results allow us to arbitrate between three competing scaling predictions. For moderate confinement, the free energy exhibits a power-law dependence on cavity size that is different from what is observed for planar and cylindrical confinement. At high monomer concentratio...

Rouse modes of self-avoiding flexible polymers.

Using a lattice-based Monte Carlo code for simulating self-avoiding flexible polymers in three dimensions in the absence of explicit hydrodynamics, we study their Rouse modes. For self-avoiding polymers, the Rouse modes are not expected to be statistically independent; nevertheless, we demonstrate that numerically these modes maintain a high degree of statistical independence. Based on high-pre...

Self-similar Traffic Models

The Domino Problem for Self-similar Structures

We define the domino problem for tilings over self-similar structures of Z given by forbidden patterns. In this setting we exhibit non-trivial families of subsets with decidable and undecidable domino problem.

Active Tile Self-assembly, Self-similar Structures and Recursion

We present an active tile assembly model which extends Winfree’s abstract tile assembly model [31] to tiles that are capable of transmitting and receiving binding site activation signals. In addition, we introduce a mathematical framework to address self-similarity and recursion within the model. The model is applied to show a recursive assembly of an archetypal self-similar aperiodic tiling kn...