From proteins to grains: a journey through simple models.

Abstract

This thesis is about the study of complex systems through simple models. Our work evidences the relevance of this kind of modeling in science, which provides us with a better understanding of nature at minimum cost. The fundamentals tools for our investigation are those of (nonequilibrium) statistical mechanics. More specically, we thoroughly analyze two minimalistic models, which are motivated by two quite diferent realms: modular biomolecules and granular uids. On the one hand, we look into the elastic response of modular biomolecules. Therein, our main goal is predicting of the unfolding pathway of the molecule. We put forward and check a theoretical framework that is valid in the maximum hysteresis path limit. On the other hand, a model mimicking the shear modes of granular gases is analyzed in depth. Our study embraces a wide range of fundamental aspects, among others: physical stationary states, fuctuations, unite size efects, stability of the stationary solutions, and memory e ects. This analysis is carried out by a combination of numerical and analytical techniques, with the numerical results showing, in general, an excellent agreement with the theory.