Algorithmic design of self-assembling structures

TL;DR

This paper explores how to design simple, convex potential functions to reliably produce specific symmetrical ground states in inverse statistical mechanics, using coding theory and algorithms.

Contribution

It introduces a method to construct decreasing, convex potential functions for targeted ground states, expanding the toolkit for inverse statistical mechanics design.

Findings

Simple potential functions can produce certain symmetrical ground states

Mathematical proof confirms the effectiveness of the designed potentials

An algorithm for constructing potentials with desired ground states is provided

Abstract

We study inverse statistical mechanics: how can one design a potential function so as to produce a specified ground state? In this paper, we show that unexpectedly simple potential functions suffice for certain symmetrical configurations, and we apply techniques from coding and information theory to provide mathematical proof that the ground state has been achieved. These potential functions are required to be decreasing and convex, which rules out the use of potential wells. Furthermore, we give an algorithm for constructing a potential function with a desired ground state.