On the sensitivity of the N-body problem to small changes in initial conditions. II

Details On the sensitivity of the N-body problem to small changes in initial conditions. II On the sensitivity of the N-body problem to small changes in initial conditions. II

Feb 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992apj...386..635k&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 386, Feb. 20, 1992, p. 635-645.

Statistics

Computation

17

Computational Astrophysics, Many Body Problem, Perturbation Theory, Computerized Simulation, Equilibrium, Numerical Analysis

Scientific paper

Attention is given to the microscopic instability of the gravitational N-body problem toward small changes in initial conditions, with emphasis on the scale invariance of the nonlinear evolution of an initial perturbation, the effects of allowing for a system comprised of two mass species (m1 and m2 = 5m1), and possible differences arising for special initial conditions corresponding to a collisionless equilibrium. In a precise sense, scale invariance is found to obtain for simulations with an initial virial ratio Z0 = 1.0, which entail no systematic expansion or contraction. Allowing for two mass species is seen to introduce no systematic effects on short time scales of the order of the average e-folding time. This complication does have an effect at later times, at least for simulations with Q0 = 0.5, resulting in a systematic increase in the rate at which initial perturbations grow, and in differences in the behavior of the two mass components which correlate with the phenomenon of mass segregation.

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