Harmonic Circuit Self-Assembly in cTAM Models

We explore algorithmic self-assembly models for nanomanufacturing of electronic circuits akin to models for DNA self-assembly. Growth is controlled by thresholding of the energy required for attachments of new components to a growing assembly. We introduce two new families of such systems in one dimension (1D) and 2D, the so-called harmonic self-assemblers that generalize the new circuit tile assembly model (cTAM), and answer fundamental questions about the size and energy distribution of the assembly sequences and their steady state. As an application, we fully resolve the 1D electric circuit ladders.