The type for binning statistics.

\[f(r) = \frac{48 \vec{r}}{r^2}(\frac{1}{r^{12}} - 0.5 \frac{1}{r^6})\]

Compute the constant volume capacity is using the following equation

\[\langle K^2 \rangle - \langle K \rangle^2 = \frac{3 k_b^2 T^2}{2N}(1-\frac{3k_B}{2C_v})\]

heat_capacity(md)

defined at /home/runner/work/HappyMolecules.jl/HappyMolecules.jl/src/Core.jl:119.

Measure the radial distribtion over a molecular dynamics runtime instance.

Arguments

• md is the molecular dynamics runtime instance.

Keyword argument

• nbins is the number of bins,
• min_distance and max_distance are the minimum and maximum distance of the bins.

measure_gr(md; nbins, min_distance, max_distance)

defined at /home/runner/work/HappyMolecules.jl/HappyMolecules.jl/src/Core.jl:245.

The most common among the ways to measure the pressure $P$ is based on the virial equation for the pressure.

\[P = \rho k_B T + \frac{1}{dV}\langle\sum_{i<j} f(r_{ij}) \cdot r_{ij}\rangle\]

pressure(md)

defined at /home/runner/work/HappyMolecules.jl/HappyMolecules.jl/src/Core.jl:140.

random_locations(box::Box, natoms::Int) -> SVector

Returns a set of random locations in a box

random_locations(box, natoms)

defined at /home/runner/work/HappyMolecules.jl/HappyMolecules.jl/src/Core.jl:22.

The temperature $T$ is measured by computing the average kinetic energy per degree of freedom.

\[k_B T = \frac{\langle 2 \mathcal{K} \rangle}{f}.\]

temperature(md)

defined at /home/runner/work/HappyMolecules.jl/HappyMolecules.jl/src/Core.jl:103.

ticks(bin)

Return the ticks (center of boxes) of bins.

ticks(bin)

defined at /home/runner/work/HappyMolecules.jl/HappyMolecules.jl/src/Core.jl:211.

uniform_locations(box, natoms)

uniform_locations(box::Box, natoms::Int) -> SVector

Returns a set of uniform locations in a box

uniform_locations(box, natoms)

defined at /home/runner/work/HappyMolecules.jl/HappyMolecules.jl/src/Core.jl:39.

lennard_jones_triple_point(
;
    natoms,
    temperature,
    density,
    Nt,
    Δt,
    seed,
    gr_lastn
)

Case study in Chapter 4 of the book "Understanding Molecular Simulation, From Algorithms to Applications". It is about the molecule dynamics simulation of a Lennard-Jones Fluid in a 3D periodic box. The parameters are set close to the triple point.

Keyword arguments

• natoms is the number of atoms.
• temperature is the initial temperature.
• density is the density of atoms.
• Nt is the number of tims steps.
• Δt is the time step.
• seed is the random seed.
• gr_lastn is the number of last n samples for collecting radial distribution.

lennard_jones_triple_point(
;
    natoms,
    temperature,
    density,
    Nt,
    Δt,
    seed,
    gr_lastn
)

defined at /home/runner/work/HappyMolecules.jl/HappyMolecules.jl/src/applications.jl:31.