September 2002

1  Trajectories

The position and velocity of each nucleus is measured by averaging the positions and velocities of a selected subset of particles. Ideally this subset would contain only those particles most tightly bound to the nucleus, but it's expensive to redefine this subset at each time step. However, there's relatively little diffusion in binding energy, so it's possible to sort the particles in each realization by initial binding energy, and use those particles most tightly bound initially to determine fairly accurate nuclear coordinates.

Figure 1: Log of inter-nuclear distance vs. time for all three encounters. Black: γ1 = γ2 = 2. Red: γ1 = 1, γ2 = 2, shifted downward by 0.25. Blue: γ1 = γ2 = 1, shifted downward by 0.5. Dotted lines show low-resolution runs, solid lines show high-resolution runs. Insert shows first passages; these curves are not shifted. Triangle shows pericenter for two point masses on same initial orbit.

Fig. 1 gives an overview of the encounters. All three were launched on the same initial orbit. A pair of point masses started on this orbit would have a single parabolic passage with separation rp = 0.25 at time tp = 40 and then recede to infinity. In practice the first passages of these extended systems are slightly later and somewhat wider than the point-mass trajectory would imply; once they begin to interpenetrate, the acceleration of each nucleus falls below that of a corresponding point mass. There's also some variation among the first passages of these three encounters; for example, the γ1 = 1, γ2 = 2 passage is distinctly closer than the others. This variation is presumably due to fluctuations which transfer momentum within each participant.

2  Animations

γ1 = γ2 = 1γ1 = 1, γ2 = 2γ1 = γ2 = 2
Figure 2: These animations show the evolution of all three encounters between times t = 36 and t = 50. Each frame is 4 length units wide.

γ1 = γ2 = 1γ1 = 1, γ2 = 2γ1 = γ2 = 2
Figure 3: These animations show the second through final passages and mergers of all three encounters. Each frame is 0.5 length units wide.

Joshua E. Barnes (barnes@ifa.hawaii.edu)

Last modified: September 3, 2002