miopoortvliet / cop-molecular-dynamics

COP-Molecular-Dynamics

Authors: Jonah Post, Mio Poortvliet

COP-Molecular-Dynamics is a molecular dynamics simulation implemented in Python 3.8 as an assignment for the course Computational Physics, part of the Leiden University physics master's.

The simulation is carried out mostly by making smart use of Numpy arrays and uses some Numba here and there too. ####Dependencies The simulation relies on three standard scientific packages that are not part of the Python base.

• Numpy
• Matplotlib
• Numba

All examples are verified to work on the latest Windows build (as of 2021-03-17, Python 3.8). It is important that the root path is this folder when executing a file.

##How to use Below a quick-start guide is written talking you through how to use the simulation and simultaneously how it works. ###Initialization First initialize the simulation by calling Simulation() from the file src/molecular_dynamics.py. The simulation initializes a system of particles in fcc unit cells. The amount of unit cells along an axis is determined by unit_cells_along_axis (default is 3 in 3 dimensions making for 108 particles). This fcc lattice is created at a density of unitless_density (alternatively pass along density in SI units instead, the simulation will do a conversion). Then starting velocities are drawn from a maxwellian distribution at unitless_temperature (or alternatively temperature in SI units). This will run for steps time steps with a unitless timestep length of time_step (default is 1e-3).

###Thermalizing the system Upon calling run_sim() the system is first thermalized. This is done by running the simulation for 100 steps, computing the mean kinetic energy and comparing this to the expected energy gotten from the equipartition theorem. The velocities are rescaled appropriately if the relative difference is within treshold (pass this to Simulation(), default is 0.1).

###Simulating After thermalization the system is calculated forward in time by steps time steps, writing data every steps_between_writing steps. This is written to a folder in /data/ named as the ISO time code of the time when Simulation() was called.

###Finishing up All data is written to the folder in sequential files. The path of the folder is returned. Using the IO_utils.py function load_and_concat(fpath, 'positions') the positions array is read from the files. The same can be done for 'velocities' and 'potential_energy'.

These arrays can be fed into the functions in process_results.py and plotting_utilities.py.

All functions have type annotations and a comprehensive docstring.

###Examples In the folder /examples/, scripts making use of the /src/ files are located.

• energy.py plots the energy, velocity distribution and a 1D projection of the paths of the simulation. It also plots the correlation function.
• rhoT-plot.py makes a plot with temperature on the horizontal axis and density on the vertical axis. The z-variable is the pressure. All these quantities are in terms of the unitless quantities used by the simulation.
• statistics_pressure_and_correlationfunction.py runs the simulation N times and produces a pressure along with an error estimation, along with a plot of the correlation function.
• animation.py runs the simulation and plots the positions in an interactive animated plot.

###Todo

• More tests
• Create a GUI to run the simulation from and process results in.