Brownian Motion

What to Install

• python3 -m pip install numpy
• Download and install OVITO from: https://www.ovito.org/

Versions

python 3.8

Configuration

Everything is configured by modifying config.json. Available configuration keys are:

• static_file: static file filepath
• dynamic_file: dynamic file filepath
• N: number of small particles, 100 < N < 150
• L: simulation area side, L > 0
• small_radius: small particle radius, rp >= 0
• small_mass: small particle mass, mp > 0
• big_radius: big particle radius, RP > rp
• big_mass: big particle mass, MP > mp
• max_v_mod: initial max particle speed module, vm > 0
• max_events: maximum amount of events to analyze, maxEvents > 0
• delta_time_animation: minimum timestep between events for animation, dt > 0
• delta_time_analysis: minimum timestep between events for analysis, dt > 0
• delta_time_intercollition: bin width for intercollision plot, dti > 0
• delta_v_mod: timestep between speeds in histogram, dv > 0
• small_dcm_count: number of particles to select for small particle DCM calculation, small_dcm_count > 0
• plot: determines whether to plot or not single analysis, must be true or false

Particle generator

To generate initial particle positions by creating static_file and dynamic_file. Generates N small particles with random positions and speeds, and 1 stopped big particle at the center. If N cannot be reached in a number of iterations, resets and tries again. Run python3 generator.py, using the following parameters from config.json:

static_file, dynamic_file, N, L, small_radius, small_mass, big_radius, big_mass, max_v_mod

Simulation

To generate executable and run the life simulation

1. Run ./prepare.sh in root to generate executable (only required once).

2. Run ./target/tp3-simu-1.0/brownian-motion.sh, using the following parameters from config.json:

   static_file, dynamic_file, max_events

Output will be appended to dynamic_file, adding time and particle position and velocity for each event.

Animation Tool

Generates simu.xyz using information from static_file and dynamic_file. Run python3 animator.py, using the following parameters from config.json:

static_file, dynamic_file, delta_time_animation, max_v_mod

To view the animation, you must open simu.xyz with Ovito: ./bin/ovito simu.xyz.

Particles will be colored in a scale of colors from cian (static particles) to red (high velocity module), showing how fast each particle is going.

Column Mapping

Configure the file column mapping as follows:

• Column 1 - Radius
• Column 2 - Position - X
• Column 3 - Position - Y
• Column 4 - Particle Identifier
• Column 5 - Color - R
• Column 6 - Color - G
• Column 7 - Color - B

Analysis Tools

Analysis can be performed in multiple ways.

analysis.py

Generate plots and metrics given a single simulation file as input. Run python3 analysis.py [out_filename], using the following parameters from config.json:

static_file, dynamic_file, delta_time_analysis, delta_time_intercollition, delta_v_mod, max_v_mod, small_dcm_count, plot

If a filename is provided, some metrics will be written to filename. If plot is false, then no graphs are plotted.

Metrics calculated are:

• Small DCM D (single simulation)
• Collision count
• Collision frequency
• Average time between collisions
• Kinetic energy

Plots shown are:

• Small particles DCM dependant on time for last half
• Probability distribution of times between collisions
• Initial probability distribution of |v|
• Probability distribution of |v| in last third of simulation
• Big particle trajectory (with and without zooming in)

multipleAnalysis.py

Run analysis on multiple simulation files to plot metrics according to the different iterations or values. It receives a root directory, where each folder should correspond to a parameter value (eg: 101) with multiple data simulations of that value. python3 multipleAnalysis.py root_directory (N|T) [save_dir]

The second parameter indicates mode, whether simulations have a varying number of small particles (N) or temperature (T, by changing initial max_v_mod). If save_dir is provided, the plots are saved as .png in that directory.

If mode is N, plots shown are:

• Big particle trajectory, taking one repetition for each N
• Collision count dependant on N
• Collision frequency dependant on N
• Average time between collisions dependant on N

If mode is T, plots shown are:

• Big particle trajectory, taking one repetition for each T
• Small particles DCM D value dependant on initial max_v_mod
• Big particle DCM dependant on time for max_v_mod = 2.0, for last half of simulation
• Big particle DCM D value dependant on initial max_v_mod
• Small particles DCM dependant on time for max_v_mod = 2.0, for last half of simulation
• Small particles DCM D value dependant on initial max_v_mod

multipleN.sh

This script can be used to run generation and simulation multiple times, given a starting N value, a step to increase N each iteration and the number of repetitions (>= 2) to run for each N in range. ./multipleN.sh N_start N_step repetitions

The script runs the simulation for each available N from N_start to the highest N_start + K * N_step that is lower or equal than 136. Then, it runs multipleAnalysis.py with the output data directory. The plots can be found at directory pics_N. Values corresponding to each plot can also be found at file pics_N/outN.txt.

multipleT.sh

This script can be used to run generation and simulation multiple times, given a starting max velocity module value, a step to increase module each iteration, a maximum module and the number of repetitions (>= 2) to run for each module in range. ./multipleT.sh max_v_mod_start max_v_mod_step max_v_mod_stop repetitions

The script runs the simulation for each available velocity module from max_v_mod_start to the highest max_v_mod_start + K * max_v_mod_step that is lower or equal than max_v_mod_stop. Then, it runs multipleAnalysis.py with the output data directory. The plots can be found at directory pics_T. Values corresponding to each plot can also be found at file pics_T/outN.txt.