A cellular automaton model for thermal transport in low-dimensional systems

TL;DR

This paper introduces a cellular automaton model for simulating thermal transport in low-dimensional nanostructures, offering a computationally efficient alternative to traditional methods like BTE, with validated results on graphene nanoribbons.

Contribution

The paper presents a novel cellular automaton approach that efficiently models thermal transport across different regimes and incorporates complex geometries, validated against graphene nanoribbon data.

Findings

Successfully replicates thermal conductivity dependence on width and temperature.

Captures scattering and confinement effects effectively.

Scales linearly with system size.

Abstract

In this work, we formulate a theoretical model based on a cellular automaton (CA) to study thermal transport in low-dimensional nanostructures across ballistic, diffusive, and transition regimes. Unlike computationally intensive methods such as the Boltzmann Transport Equation (BTE), our model stands out for its geometrical robustness, allowing the seamless integration of substitutional impurities, vacancies, and irregular edges. We validated the model using graphene nanoribbons (AGNRs), successfully replicating the dependence of thermal conductivity on ribbon width and temperature. Results demonstrate that the model captures critical scattering and confinement effects with a linear scalability O(N). Given the increasing pressure to optimize computational resources and reduce the carbon footprint associated with AI infrastructure, this CA model emerges as a highly efficient tool for the parametric exploration and design of next-generation thermal devices.