Simple models for mesoscopic systems: from slender structures to stochastic resetting

TL;DR

This thesis explores mesoscopic models to understand buckling in slender structures due to thermal effects and develops optimized search strategies using stochastic resetting, addressing practical constraints and partial information.

Contribution

It introduces a minimal mesoscopic model for buckling under thermal load and analyzes stochastic resetting strategies for efficient search with costs and partial knowledge.

Findings

Buckling behavior is influenced by elastic-electronic coupling.

Optimal resetting strategies improve search efficiency under constraints.

Models provide insights into mesoscopic phenomena in physical systems.

Abstract

The objective of this thesis is to advance the understanding of complex physical phenomena through the lens of statistical physics. Specifically, it addresses two fundamental questions: What types of interactions can induce buckling of slender structures when their temperature is increased? And, how can we devise an optimal strategy for locating a hidden target? The thesis is divided into two distinct parts, both employing mesoscopic descriptions -- neither fully microscopic nor fully macroscopic -- to capture the essential interactions and behaviours that qualitatively govern the phenomena under investigation. In the first part, we examine the buckling behavior of low-dimensional materials under thermal load. To this end, we develop a comprehensive model that characterises the system using a minimal setup for mimicking: (i) elastic and electronic degrees of freedom, and (ii) coupling between the elastic and the electronic modes. In the second part, we investigate stochastic resetting processes as a means to formulate efficient search strategies. We explore various resetting mechanisms to understand how to optimise the search performance in real scenarios, where: (i) resetting involves a finite cost, and (ii) the target location is only partially known.