18 - Small-N experiments  pp. 323-349

Small-<i>N</i> experiments

By Sverre J. Aarseth

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In this last chapter, we return to the subject of numerical experiments in the classical sense. Using the computer as a laboratory, we consider a large number of interactions where the initial conditions are selected from a nearly continuous range of parameters. Such calculations are usually referred to as scattering experiments, in direct analogy with atomic physics. Moreover, the results are often described in terms of the physicist's cross sections, with the results approximated by semi-analytical functions. The case of three or four interacting particles is of special interest. However, the parameters space is already so large that considerable simplifications are necessary. In addition to the intrinsic value, applications to stellar systems provide a strong motivation. Naturally, the conceptual simplicity of such problems has also attracted much attention.

In the following we discuss a number of selected investigations with emphasis on those that employ regularization methods. It is convenient to distinguish between simulations and scattering experiments, where in the former case all particles are bound. The aim is to obtain statistical information about average quantities such as escape times and binary elements, and determine their mass dependence. Small bound systems often display complex behaviour and therefore offer ample opportunities for testing numerical methods. On the other hand, scattering experiments are usually characterized by hyperbolic relative velocities, the simplest example being a single particle impacting a binary.