jaxdem.integrators.velocity_verlet

Velocity Verlet Integrator.

Classes

VelocityVerlet()

Implements the Velocity Verlet integration method.

class jaxdem.integrators.velocity_verlet.VelocityVerlet

Bases: LinearIntegrator

Implements the Velocity Verlet integration method.

static step_before_force(state: State, system: System) → tuple[State, System]

Advances the simulation state by one half-step before the force calculation using the Velocity Verlet scheme.

The update equations are:

\[\begin{split}& v(t + \\Delta t / 2) &= v(t) + \\Delta t a(t) / 2 \\\\ & r(t + \\Delta t) &= r(t) + \\Delta t v(t + \\Delta t / 2) \\Delta t\end{split}\]

where:

• \(r\) is the particle position (jaxdem.State.pos)

• \(v\) is the particle velocity (jaxdem.State.vel)

• \(a\) is the particle acceleration computed from forces (jaxdem.State.force)

• \(\\Delta t\) is the time step (jaxdem.System.dt)

Parameters:

• state (State) – Current state of the simulation.

• system (System) – Simulation system configuration.

Returns:

The updated state and system after one time step.

Return type:

Tuple[State, System]

static step_after_force(state: State, system: System) → tuple[State, System]

Advances the simulation state by one half-step after the force calculation using the Velocity Verlet scheme.

The update equations are:

\[\begin{split}& v(t + \\Delta t) &= v(t + \\Delta t / 2) + \\Delta t a(t) / 2 \\\\\end{split}\]

where:

• \(v\) is the particle velocity (jaxdem.State.vel)

• \(a\) is the particle acceleration computed from forces (jaxdem.State.force)

• \(\\Delta t\) is the time step (jaxdem.System.dt)

Parameters:

• state (State) – Current state of the simulation.

• system (System) – Simulation system configuration.

Returns:

The updated state and system after one time step.

Return type:

Tuple[State, System]