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

Alejandra León

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.

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

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.
Paper Structure (10 sections, 4 equations, 5 figures)

This paper contains 10 sections, 4 equations, 5 figures.

Table of Contents

  1. Introduction:
  2. Model Description:
  3. Model Validation and Proof of Concept:
  4. Conclusions and Future Work:
  5. Acknowledgments:
  6. References:

Figures (5)

  • Figure 1: Thermal conductivity of pristine AGNRs as a function of width and temperature. The figure also includes a schematic of the physical system, including the thermal reservoirs.
  • Figure 2: Thermal conductivity as a function of temperature for an AGNR with a length of 110 Å and a width of 40 lines, corresponding to 50 Å. The figure also displays the results for the system with vacancies and irregular edges. Additionally, temperature maps for both cases are included.
  • Figure 3: Effective thermal conductivity as a function of the length of the central region of the structure. Temperature maps are also included for six representative values out of the nine shown in the thermal conductivity plot: $Crf=2.1,\;2.2,\;2.3,\;2.4,\;3.0\;y\;4.0$.
  • Figure 4: Thermal gradient and temperature maps for two S-shaped structures. The two panels on the left correspond to a factor $\mathrm{Crf}=2.1$, while the panels on the right correspond to $\mathrm{Crf}=3.0$.
  • Figure 5: Model scalability study. The graph displays the execution time in seconds as a function of the total number of atoms in the simulated system. The dark points represent transversal scalability (increasing nanoribbon width with constant length), while the light points represent longitudinal scalability (increasing length with constant width). In both studies, 1% vacancies and irregular edges with 5% penetration were considered.