PackSim

PackSim is Python program which perform simulations for the flow of ‘soft’ or ‘compressible’ objects under some energy in a periodic domain.

Installing

Currently, this isn’t packaged as a standalone program. Python 3.8+ is needed to use this.

Building

Before running, first install the necessary requirements. A virtual environment is recommended.

pip install -r requirements.txt

It is also necessary to build the Cython components. So, simply run:

foo@bar:/path/to/packsim: ./build.sh

If video output of the simulation is desired, ffmpeg must be installed on system. Otherwise, it’s all ready to go!

Usage

The primary usage is to run packsim.py to output simulation results. There are many parameters, so it’s recommended that you use a JSON configuration file. There are two required sections, calculation and simulation.

Domain

The ‘domain’ section defines the basic setup. The n_objects parameter represents the number of objects in the domain of width by height. The natural_radius parameter is the radius of the circle that represents the natural ‘zero energy’ state of the object. Lastly, the energy parameter is just the type of energy to simulate with. There are currently three: 'area', 'radial-al', 'radial-t'. These parameters can also be overridden by a command line argument.

{
  "domain": {
    "n_objects": 15,
    "width": 10.0,
    "height": 10.0,
    "natural_radius": 4.0,
    "energy": "radial-t",
    "points": [  // Optional
      [1,1], [2,2], [3,3], [4,4], [5,5],
      [1,2], [2,3], [3,4], [4,5], [5,6],
      [1,3], [2,4], [3,5], [3,6], [5,7]
    ]
  },
  //...
}

Simulation

There are currently three simulation modes, and the configuration changes slightly for each one.

Flow

This mode simulates the relaxing of the objects to its equilibrium. The threshold is the sufficient condition where the gradient is sufficiently close to zero. Specifically, the simulation stops when the L1 norm of the gradient divided by the number of objects is less than the threshold. The step-size parameter only represents the initial step size. This is because adaptive step size is employed.

{
  //...
  "simulation": {
    "mode": "flow",
    "step_size": 0.05,
    "threshold": 0.0001
  },
  //...
}

Search

This mode searches for equilibrium until eq_stop_count equilibria are found. Additionally, if the nullity of the Hessian at the equilibrium is greater than 2. (This is due to periodicity, as any translation is another equilibrium.) In this case, the manifold_step_size parameter is used to traverse along it.

{
  //...
  "simulation": {
    "mode": "search",
    "step_size": 0.05,
    "threshold": 0.0001,
    "eq_stop_count": 100,
    "manifold_step_size": 0.1
  },
  //...
}

Shrink

This mode simulates the the change in the equilibrium as the width is decreased. Both the width_change and width_stop parameters should be set as a percentage of the width.

{
  //...
  "simulation": {
    "mode": "shrink",
    "step_size": 0.05,
    "threshold": 0.0001,
    "width_change": 1,
    "width_stop": 0.3
  },
  //...
}

Additionally, a filename is automatically generated by default, but it’s also possible to provide it with the name parameter. The save_sim parameter determines whether or not the .sim file is saved. This allows simulations to be loaded again at a later time, if other processing is desired. Setting points is also possible, with the points parameter.

{
  //...
  "simulation": {
    //...
    "name": "my_awesome_simulation", // Optional
    "save_sim": true
    //...
  }
  //...
}

Diagram

It’s also possible to visualize the data, but this section is optional. It’s possible to output the frames as individual images [img], or as a video [mp4]. (Note: rendering as an mp4 requires ffmpeg to be installed on your system.)

While it’s possible to customize the figures that are drawn and outputted, there are already a few preset modes: animate, energy, stats, and eigs, which outputs the simulation steps as a video, a video with the graph of energy, compiled statistics, and the eigenvalues, respectively.

{
  "diagram": {
    "filetype": "mp4",
    "figures": "animate",
  }
}

Now with, all that configuration nonsense out of the way, to run, simply type

foo@bar:/path/to/packsim: python3 packsim.py my_sim.json

where my_sim.json is your configuration file.

Contributions

This project welcomes contributors, so feel free to make a pull request!

License

GNU GPLv3.0

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