One-dimensional mechanical networks and crystals

TL;DR

This paper establishes fundamental physical properties like thermal expansion and Hooke's law for crystals using a one-dimensional microscopic model, providing theoretical insights into their mechanical behavior.

Contribution

It introduces a novel one-dimensional microscopic model that rigorously proves thermal expansion and Hooke's law for crystals.

Findings

Proves thermal expansion in 1D crystal models

Demonstrates Hooke's law at microscopic level

Provides a rigorous mathematical framework

Abstract

We prove thermal expansion and Hooke-s law for crystals via an one-dimensional microscopic model.