h2. A closer look: Velocity Verlet Algorithm
We designed sa dynamical simulation to compute the particle positiontrajectories as a function of time. The simulation utilizes the Velocity Verlet algorithm, which calculates positions and velocities of particles by means of Taylor expansion. Because the Newton's equation of motion is second order in relative position (r), the initial condition needs to specify both particle position and velocity at time 0.
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The following equations are used:
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{latex}
\large
$$
{{x(t + \Delta t) }} = {{ x(t) + v(t)\Delta t + (1/2)a(t)\Delta t^2 }}
$$
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\large
$$
{{v(t + \Delta t/2) }} = {{ v(t) + (1/2)a(t)\Delta t }}
$$
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!fig2.png|align=center! | 