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Chapter 2. Geometrical optics
Figure 2.16: N-body interaction and superposition of two-body
interactions.
each particle in the sample. The resulting trajectory displacement
is compared for each particle individually, with the difference between the two simulations recorded. Statistics are then performed
on the differences. It was shown in reference [41] that the two
methods agree within about one percent for a particular severe
case. The reader is referred to this reference for details. Our hypothesis can safely be considered to be vindicated for a wide range
of operating conditions.
The vector superposition of two-body interactions thus represents
a useful basis to proceed. This superposition can be formally represented as a Markov chain. This is intuitively evident from Figure 2.16, in which the vector displacements visually appear like a
succession of random flights. In fact, the mathematical assumptions are the same, and the above analysis applies. We propose to
Chapter 2. Geometrical optics
Figure 2.16: N-body interaction and superposition of two-body
interactions.
each particle in the sample. The resulting trajectory displacement
is compared for each particle individually, with the difference between the two simulations recorded. Statistics are then performed
on the differences. It was shown in reference [41] that the two
methods agree within about one percent for a particular severe
case. The reader is referred to this reference for details. Our hypothesis can safely be considered to be vindicated for a wide range
of operating conditions.
The vector superposition of two-body interactions thus represents
a useful basis to proceed. This superposition can be formally represented as a Markov chain. This is intuitively evident from Figure 2.16, in which the vector displacements visually appear like a
succession of random flights. In fact, the mathematical assumptions are the same, and the above analysis applies. We propose to