Structures undergoing discrete phase transformation

Discrete phase transformations occur in a wide range of structures and systems, from proteins and sub-cellular components in biological systems to micro-scale structures of standard materials. In this paper we study theoretically the mechanical behavior of these intriguing structures. We reexamine the conventional model of a bi-stable chain by introducing the concept of an ideal bi-stable element, and show that any bi-stable element can be conceptually separated into an ideal bi-stable element connected in series with an elastic spring. This new approach allows relatively simple calculations, important insights, and meaningful results. Emphasis is put on consequences of the discrete nature of these structures, and in particular on finite size effects, non-trivial stability, dissipation ratchets, and escape rates. We also consider the inverse problem of finding micro-level properties from experiments, and propose a novel method which provides sub-pixel resolution that is not subjected to the sampling rule of the Nyquist frequency. Simple experiments are performed in order to demonstrate some of the theoretical concepts.