Packing Class

class Packing(n, dim=2, radius=0, rfac=0.8, params={'central': 0.0005, 'contact': 0.1, 'drag': 0.05}, seed=12)

Bases: object

Class to model a contact network of bidisperse spheres.

Parameters:

  • n (int) – The number of spheres.

  • dim (int) – The dimensionality of the system. Valid options are 2 and 3.

  • radius (float, optional) – The radius of the larger spheres. If 0 (default), a good choice is computed automatically.

  • rfac (float, optional) – Factor by which the smaller sphere radius is scaled relative to large spheres.

  • params (dict, optional) –

    Specifies system parameters. Required keywords are :

    • ’central’: strength of the force pulling spheres toward origin

    • ’drag’: coefficient of isotropic drag

    • ’contact’: strength of contact repulsion

  • seed (int, optional) – A random seed used for initializing the positions of the spheres, and assigning which are large or small.

Variables:

  • n (int) – The number of spheres.

  • dim (int) – The dimensionality of the system.

  • pts (ndarray) – (x,y) coordinates for each sphere.

  • labels (ndarray) – Array of sphere labels (0=large, 1=small).

  • radii (list) – List of sphere radii, indexed by sphere type (0=large, 1=small).

  • traj (ndarray) – The simulated trajectory of the network produced after a call to the generate() routine.

  • t_eval (ndarray) – The corresponding time at each simulated frame.

  • graph (networkx.graph) – Graph specifying the nodes and edges in the final contact network.

animate(spheres=True, edges=True, figsize=(5, 5), skip=1)

Animate the system after a simulation.

Parameters:

  • spheres (bool, optional) – Whether to plot the spheres. Default is True.

  • edges (bool, optional) – Whether to plot the edges connecting spheres in contact. Default is true.

  • figsize (tuple, optional) – The figure size.

  • skip (int, optional) – Use every skip number of frames (skip=1 uses every frame).

Returns:

The resulting animation. In a jupyter notebook, the animation may be visualized with the import from IPython.display import HTML, and running HTML(ani.to_html5_video()).

Return type:

matplotlib.animation.FuncAnimation

coordination()

Compute the coordination information of the network.

Returns:

  • nc (int) – The number of nodes forming a connected network.

  • Ziso (float) – The required average coordination for isostaticity.

  • Z (float) – The average coordination of the network.

  • dZ (float) – The excess coordination, defined as Z - Ziso.

generate(duration=1000.0, frames=200)

Run a packing simulation.

Generates a graph of the resulting contact network at the end.

Parameters:

  • duration (float, optional) – The final integration time.

  • frames (int, optional) – The number of output frames to produce (excluding initial frame).

initialize()

Initialize the sphere positions and radii.

plot(spheres=True, edges=True, figsize=(5, 5), filename=None)

Plot the network, optionally specifying whether to include spheres and edges.

Parameters:

  • spheres (bool, optional) – Whether to plot the spheres. Default is True.

  • edges (bool, optional) – Whether to plot the edges connecting spheres in contact. Default is true.

  • figsize (tuple, optional) – The figure size.

  • filename (str, optional) – The name of the file for saving the plot.

rotate(spheres=True, edges=True, figsize=(5, 5), skip=1)

Animate camera and light rotation about a static scene.

save(filename)

Save the contact network to a file.

Parameters:

filename (str) – The name of the text file to write.

set_frame(fr)

Select a specific simulation frame as the network state.

Parameters:

fr (int) – The frame number.