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Open Boundary 12-fold Symmetric Quasicrystal Simulator

This repository contains the simulation code used in the paper:
“Defects Enhance Stability in 12-fold Symmetric Soft-Matter Quasicrystals.”

Supported Operating Systems

The code is designed to run on Linux and macOS.

Compilation Instructions

To compile the code, use the following command:

gcc -o rhombi -Wall -std=c99 -O3 rhombi.c -lm

Usage

To run the simulation, use:

./rhombi <st_D> <st_I> <gamma> <eps_rh>

Parameters

  1. st_D: Parameter of the randomized $[D,I]$-Stampfli inflationary tiling used as the initial configuration.
  2. st_I: Parameter of the randomized $[D,I]$-Stampfli inflationary tiling.
  3. gamma: Line tension value in $\beta\gamma a$.
  4. eps_rh: Energy cost of adding a rhombus to the system ($\beta\epsilon_R$).

Output

The code generates a directory in the same path as the executable, named:

data_size_<st_D>_<st_I>_gamma_<gamma>_epsRh_<eps_rh>

Inside this directory, two files are created:

  1. state.csv: Contains details of the state point.
  2. measurements.csv: Contains simulation measurements.

state.csv Format

This file contains the following columns:

  1. Number of vertices
  2. $D$ parameter of Stampfli tiling
  3. $I$ parameter of Stampfli tiling
  4. Line tension ($\beta\gamma a$)
  5. Energy cost of adding a triangle ($\beta\epsilon_{Tr}$)
  6. Energy cost of adding a square ($\beta\epsilon_{Sq}$)
  7. Energy cost of adding a rhombus ($\beta\epsilon_R$)

measurements.csv Format

This file contains the following columns:

  1. Monte Carlo Sweep
  2. Number of squares
  3. Number of triangles
  4. Number of rhombi
  5. Boundary length
  6. Number of directed edges in each direction ($e_1, e_2, \ldots, e_{12}$)

Citation

If you use this code, please cite the associated paper: “Defects Enhance Stability in 12-fold Symmetric Soft-Matter Quasicrystals”

@article{ulugol2024defects,
  title={Defects Enhance Stability in 12-fold Symmetric Soft-Matter Quasicrystals},
  author={Ulug{\"o}l, Alptu{\u{g}} and Hardeman, Robert J and Smallenburg, Frank and Filion, Laura},
  journal={arXiv preprint arXiv:2408.08168},
  year={2024}
}

Contact

For questions or issues, please contact:

Alptuğ Ulugöl

[e-mail address is stated in the paper]