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Jamming of deformable particles with sinusoidal preferred angles

Using the main file main/jam/bidisperseSinusoidalParticleJamming.cpp, you can generate jammed packings (at a specified pressure) of bidisperse, purely repulsive, deformable particles with lobed shapes sets by a sinusoidally-varying preferred angle profile.

See some example jammed configurations below.

Particles drawn with empty circles are "rattlers" i.e. are not part of the force-bearing backbone of the packing.

Input

Once you compile the main file, run the simulation using the generated binary file. The input parameters are:

  • NCELLS: integer number of particles
  • nsmall: integer number of vertices on small particles, n on large particles is set by the 1.4:1.0 size ratio.
  • calA0: preferred shape parameter of all particles
    • defined as calA0 = p_0^2/(4 * pi * a_0), where p_0 and a_0 are the preferred perimeter and areas of the particles, respectively
    • Note that input calA0 should be greater than or equal to 1 always.
  • kl: mechanical constant for perimeter
  • kb: mechanical constant for curvature
  • thA: amplitude of sinusoidal preferred angles
  • thK: wavenumber of sinusoidal preferred angles (sets number of lobes)
  • Ptol: pressure tolerance, jammed configs with final pressure P satisfy Ptol < P < 2 * Ptol
  • Ftol: force tolerance of energy minimization protocol
  • seed: integer to seed random number generator
  • positionFile: path to file to store position data for jammed configuration.

To generate the above images, run a compiled binary bin.o using

  • left: ./bin.o 12 24 1.04 1.0 0.01 3.0 3.0 1e-7 1e-12 1 pos.test

  • right: ./bin.o 12 24 1.20 1.0 0.01 10.0 5.0 1e-7 1e-12 1 pos.test

Output

The final input to the main file, positionFile (above called pos.test), will store the positions of all vertices in the jammed state as well as some other useful information about the state of the system.

Each row in this file starts with a five-character keyword that denotes what information that row contains. The keywords are:

  • NEWFR: starts frame
    • If the code prints multiple configurations, this can be used to identify the start of a new configuration.
  • NUMCL: number of cells
  • PACKF: packing fraction (particle areas / box area)
  • BOXSZ: box lengths Lx and Ly
  • STRSS: components of the virial stress tensor, sorted as Sxx, Syy, Sxy
  • CINFO: information about cell
  • VINFO: information about vertex
  • ENDFR: ends frame

CINFO

There is one CINFO row per cell. For a given cell mu, the row is formatted as:

CINFO nv zc zv a0 a p

where

  • nv number of vertices on cell mu
  • zc number of cell-cell contacts on cell mu.
  • zv number of vertex-vertex contacts on cell mu.
  • a0 preferred area of cell mu
  • a instantaneous area of cell mu
  • p instantaneous perimeter of cell mu

VINFO

There is also one VINFO row per vertex. For a given vertex i on cell mu, the row is formatted as:

CINFO mu i x y r l0 t0

where mu and i refer to the cell and vertex indices, respectively, and

  • x: x coordinate of vertex
  • y: y coorindate of vertex
  • r: radius of vertex
  • l0: preferred length of edge between vertices i and i+1
  • t0: preferred angle for angle centered on vertex i

Running on the cluster

To run an ensemble of jammed configurations on a remote cluster, use the following steps. Note: currently only supports clusters that use the Slurm workload manager.

Using the submit_ bash script

To clone the repository to your remote cluster, ssh onto the login node and use

>> git clone https://github.com/jacktreado/dpm.git

The bash script submit_bidisperseSinusoidalParticleJamming.sh submits an ensemble of simulations to the cluster as an array job.

NOTE: All data will be placed in project on Grace if using Yale HPC. If using a different file storage system, edit outputdir to the desired location for data output.

  1. Once you have logged in to the remote cluster, cd to ~/dpm/bash/jam.
  2. Use >> cat submit_bidisperseSinusoidalParticleJamming.sh to see the input list, which is:
# ====================
#       INPUTS
# ====================
# 1. NCELLS
# 2. n
# 3. calA0
# 4. kb
# 5. thA (lobey preferred angle amplitude)
# 6. thK (lobey preferred angle wavenumber)
# 7. partition
# 8. time
# 9. number of runs (number of array entries, i.e. arraynum)
# 10. start seed (end seed determined by number of runs)
  1. Jobs are submitted with >> bash submit_bidisperseSinusoidalParticleJamming.sh [INPUTS] where [INPUTS] must match the list above. See input description below.

Bash script inputs

  1. NCELLS: integer number of particles
  2. n: integer number of vertices on small particles (nsmall above)
  3. calA0: preferred shape parameter of all particles
  4. kb: mechanical constant for curvature
  5. thA: amplitude of sinusoidal preferred angles
  6. thK: wavenumber of sinusoidal preferred angles (sets number of lobes)
  7. partition: Slurm partition to queue + run jobs
  8. time: Slurm time limit
  9. numSeedsPerRun: number of jobs in batch submission
  10. startSeed: first seed in array, last seed is startSeed + numSeedsPerRun

Data storage

By default, data will be stored in your Grace project folder.

Each file will begin with lobes_, with the parameters for the ensemble following. For example, an ensemble with NCELLS=16, n=24, calA0=1.10, kb0.01, thA=3.0, and thK=3.0 will be stored in the directory

~/project/dpm/jam/lobes_N16_n24_calA01.10_kb0.01_thA3.0_thK3.0

Each file will begin with the string lobes_N16_n24_calA01.10_kb0.01_thA3.0_thK3.0 and will end with _seed[seedNumber].pos, where seedNumber denotes the seed used in the random number generator. This differentiates different members of the particular ensemble.

Data processing (Slurm scheduler only)

The MATLAB function processJammedDPMEnsemble will aggregate statistical data stored the ensemble folder (i.e. ~/project/dpm/jam/lobes_) and save it to a .mat file (see MATLAB documentation stored in ~/project/dpm/jam/matfiles.

To submit this function to the cluster, use the Slurm script slurm_bidisperseSinusoidalParticleJamming.slurm. This script must be edited via the command line, so open the file using a command line editor like vim or emacs.

Slurm-specific options, like partition or time are controlled by the #SBATCH headers. See this Slurm cheatsheet for all cluster options.

Simulation options are set by these variables:

# matlab input information
NCELLS=16
nsmall=24
calA0=1.10
kb=1.0
thA=3.0
thK=3.0

To process a given set of simulations, edit these variables & the Slurm headers appropriately, then use sbatch to submit the script to the cluster:

>> sbatch slurm_bidisperseSinusoidalParticleJamming.slurm

A matfile with ensemble statistics will be saved in the folder ~/project/dpm/jam/matfiles with the same name as the ensemble folder.