HistoricDisks

This repository accompanies the work Hard-disk pressure computations—a historic perspective. It provides the pressure data of the hard-disk model extracted from the literature since 1953, and also the set of high-precision pressures that are presented in the work above. Furthermore, this repository contains naive Markov-chain Monte Carlo and molecular dynamics implementations (with or without pressure estimation) for the hard-disk model, as well as a state-of-the-art implementation of the hard-disk event-chain Monte Carlo algorithm.

List of programs

This repository contains:

Pressure data, equations of states
- Pressure data files (CSV, see the DigitizedData directory)
- Equations of states visualization (Python, requires matplotlib, see the synopsis directory)
Four-disk non-periodic-box programs (Python)
- Sampling program using Metropolis algorithm (Python, see the Python/four-disk/Metropolis_disks_box.py script)
- Sampling program using Molecular dynamics with pressure estimators (Python, see the Python/four-disk/molecular_disks_box.py script)
- Sampling program using straight ECMC with pressure estimators (Python, see the Python/four-disk/ECMC_straight_disks.py script)
- Sampling program using reflective ECMC (Python, see the Python/four-disk/ECMC_reflective_disks_box.py script)
- Sampling program using forward ECMC (Python, see the Python/four-disk/ECMC_forward_disks_box.py script)
- Sampling program using Newtonian ECMC (Python, see the Python/four-disk/ECMC_Newtonian_disks_box.py script)
Naive periodic-box programs
- Sampling program using Metropolis algorithm (Python, see the Python/naive/Metropolis.py script)
- Sampling program using Molecular dynamics (Python, see the Python/naive/molecular_dynamics.py script)
- Sampling program using straight ECMC with pressure estimators (Python, see the Python/naive/ECMC_straight.py script)
- Sampling program using reflective ECMC (Python, see the Python/naive/ECMC_reflective.py script)
- Sampling program using forward ECMC (Python, see the Python/naive/ECMC_forward.py script)
- Sampling program using Newtonian ECMC (Python, see the Python/naive/ECMC_Newtonian.py script)
State-of-the-art hard-disk programs
- Sampling program using straight ECMC with pressure estimators (C++, see the CPP/StraightECMC directory)
Analysis
- Pressure calculation using the fitting formula (Python, see the Python/four-disk/fitting.py script)
- Global Orientational order parameter calculation (Python, requires numpy, scipy, see the Python/analysis/psi6.py script)
- Confidence-interval calculation (Python, requires numpy, stresampling, see the Python/analysis/error_bar.py script)
- Analysis for straight ECMC runs stored in the HDF5 format (Python, requires numpy, stresampling, h5py, see the Python/analysis/analysis_h5.py script)

Installing

All Python scripts can be executed with any Python3 implementation (e.g., standard CPython or PyPy3).

The sampling programs do not have any further requirements. The script for the pressure calculation using the fitting formulas (see Python/four-disk/fitting.py) relies on NumPy.

In addition to NumPy, the analysis programs rely on h5py to read and store data in the HDF5 data format. SciPy is used to compute the orientational order parameter of a hard-disk configuration, and matplotlib is used for visualization. The stresampling package estimates error bars by using stationary bootstrap.

The requirements can also be found in the List of Programs. All external dependencies for the Python programs are included in requirements.txt.

We recommend setting up a virtual environment and installing the correct versions of the external dependencies by running the following commands (replace python3 by the Python3 interpreter of your choice):

python3 -m venv historic_venv
source historic_venv/bin/activate
python3 -m pip install -U pip setuptools
python3 -m pip install -r requirements.txt

Please refer to the README.md of the C++ program for its compilation requirements.

Authors

Check the AUTHORS.md file to see who participated in this project.

License

This project is licensed under the GNU General Public License, version 3 (see the LICENSE file).

Contact

If you have questions regarding the HistoricDisks software package, just raise an issue here on GitHub or contact us via mail (see the AUTHORS.md file). We are happy to help you!

Citation

If you use (parts of the) the programs in published work, please cite the following reference (see [Li2022] in References.bib):

Botao Li, Yoshihiko Nishikawa, Philipp Höllmer, Louis Carillo, A. C. Maggs, Werner Krauth;
Hard-disk pressure computations—a historic perspective.
J. Chem. Phys. 21 December 2022; 157 (23): 234111. https://doi.org/10.1063/5.0126437