Self-Assembly of Infinite Structures

We review some recent results related to the self-assembly of infinite structures in the Tile Assembly Model. These results include impossibility results, as well as novel tile assembly systems in which shapes and patterns that represent various notions of computation self-assemble. Several open questions are also presented and motivated

Biomimetic Membranes Realized with Arrays of Carbon Nanofibers

A microfluidic device with imbedded nanoporous membranes, constructed using a novel nanostructured material, was designed, built, modeled, and tested. The membranes were shown to be modular, and by adsorbing monodisperse latex spheres to the fibrous membrane, the pore size could be controlled. A mathematical model of the device was developed based on several existing fluidic models for transport through fibrous materials, and an image processing algorithm was designed to extract the hydrodynamic properties of the device from a series of scanning electron micrographs based on the existing hydrodynamic models. A series of experiments were performed using fluorescent microscopy to quantify the hydrodynamic properties of the device. The results of these experiments suggest that the modeling was accurate. This thesis explores several unique issues. The first is that tortuosity, defined as a particle’s path length divided by its displacement, is the factor that scales the reference diffusion. The second is that the membrane can be thought of as a realization of random fractal. The third is that tortuosity can be related to the resistance scaling factor, a property of a fractal. To support these claims, a close agreement between a classical and a fractal permeability model is shown. In addition, a model is incorporated to approximate surface effects showing that the surface cannot be categorically neglected because of the rather large device dimensions. Finally, the extrapolation of 3-dimensional information from an SEM image is used to determine the model parameters