A five-parameter Markov model for simulating the paths of sedimenting particles

The random initial positions of particles in any sedimentation experiment and the extreme sensitivity of the creeping-motion equations to even minute variations in these positions imply that the detailed results from one experiment provide no detailed information about another experiment. However, the five statistical parameters obtained by following the three-dimensional trajectories of spheres form the basis of a Markov model that quickly and accurately simulates the typical behaviour of individual spheres. In this model, velocities are continuous, but nowhere differentiable. The joint position-velocity processes (one for each direction) are both Markov and Gaussian. Thus, no integration is required to produce a position-velocity skeleton. When continuity conditions are imposed, this sequence of values provides all the coefficients of a fourth-degree interpolating polynomial that closely imitates the smooth paths of spheres in real suspensions.