That is a simple molecular dynamics simulation for one type of atom (especially Argon) interacting with van der Waals' forces. One may observe the solid → gas phase transition and investigate thermodynamical properties that characterise the gas state.
Referring to Wikipedia:
"Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of the system. In the most common version, the trajectories of atoms and molecules are determined by numerically solving Newton's equations of motion for a system of interacting particles, where forces between the particles and their potential energies are often calculated using interatomic potentials or molecular mechanics force fields."
More about Molecular Dynamics.
- Simulation of dynamics for an any ideal gas which satisfies the ideal gas law and the Maxwell-Boltzmann distribution.
- Simulation of melting the crystals.
- Calculations of fundamental properties of the system.
- Observations of simulations may be provided by an open-source viewer Jmol.
More about Maxwell-Boltzmann Distribution and Ideal Gas Law.
- Length: 1 nm (10-9 m).
- Time: 1 ps (10-12 s).
- Mass: 1 u (1.66 x 10-27 kg).
- Temperature: 1 K.
The primary program control is done by setting the system parameters. Parameters to set in program:
- n - Number of atoms along the crystal edge (default 6).
- m - Atomic mass (default 40.0 - Argon).
- e - Minimum of the potential (default 1.0).
- R - Interatomic distance for which occurs minimum of the potential (default 0.38).
- k - Boltzmann constant (default 8.31e-3).
- f - Elastic coefficient of sphere which confines molecules (default 1e4).
- L - Radius of sphere which confines atoms (default 6.0).
- a - Interatomic distance (default 0.38).
- T0 - Initial temperature (default 1e4).
- tau - Simulation time step (default 1e-3).
- So - Initial number of steps for thermalization of the system (default 5000).
- Sd - Number of steps for mainly simulation (default 50000).
- Sout - Interval with which information about the system are saved (default 500).
- Sxyz - Interval with which positions of the molecules are saved (default 500).
C++ code to set in main file:
// Usage: ./main <1> <2> <3> <4> <5> <6> <7>
// Where:
// <1> - input file with parameters in `Config` folder e.g. parameters.txt
// <2> - output file with initial positions to save in `Out` folder e.g. r0_init.txt
// <3> - output file with initial H, T, P to save in `Out` folder e.g. htp_init.txt
// <4> - output file with initial momenta to save in `Out` folder e.g. p0_init.txt
// <5> - output file with positions from the whole simulation to save in `Out` folder e.g. rt_sim.txt
// <6> - output file with H, T and P from the whole simulation to save in `Out` folder e.g. htp_sim.txt
// <7> - output file with initial momentum histogram to save in `Out` folder e.g. hist.txt
// Create object first.
Argon *A = new Argon;
// Call function `setParameters()` is optional.
// If you do not give file with own parameters, then simulation suppose default values.
A->setParameters(argv[1]);
// Call function `checkParameters()` is optional.
// It is only to information if system is properly set.
A->checkParameters();
// Call function `initialState()` is required if you want to get to simulation.
A->initialState(argv[2], argv[3], argv[4]);
// Get absolute values of momenta, its size and calculated temperature
// is required if you want to calculate statistics.
// You may call this function after `initialState()` or after `simulateDynamics()`.
usint N;
double *pAbs, T, k, m;
std::tie(pAbs, N, T, k, m) = A->getMomentumAbs();
// Call function `simulateDynamics()` is optional.
// But obviously it is the core of entertainment and playing with the system.
// That At the end of the simulation, the program checks if the ideal gas law is
// fulfilled (It is if the value is around 1). Moreover, while the whole simulation,
// the total energy should be constant.
A->simulateDynamics(argv[5], argv[6]);
// Do not forget to release memory
delete A;
// Calculate statistics from Maxwell-Boltzmann distribution is optional.
// That provides calculation of most probable momentum, mean momentum,
// mean square momentum and kinetic energy.
Stats *S = new Stats;
S->setInputFromArgon(pAbs, N, T, k, m);
S->evaluateHist(argv[7]);
delete S;| Dynamics of 216 molecules at temperature 104 K: | Crystal of 15625 molecules at temperature 102 K: |
|---|---|
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Momentum distribution fulfils Maxwell distribution:
