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h2. A closer look: Velocity Verlet Algorithm

We designed s dynamical simulation to compute the particle position as a function of time. The current theory of plate settlers predicts the failure for a specific sedimentation tank and plate settler sp 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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{latex}
\large
$$
{{x(t + \Delta t) }} = {{ x(t) + v(t)\Delta t + (1/2)a(t)(\Delta t)^2t^2    }}
$$
{latex}
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{latex}
\large
$$
{{v(t + \Delta t/2) }} = {{ v(t) + (1/2)a(t)(\Delta t)    }}
$$
{latex}


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!fig2.png|align=center!