Biomedical subjects
Publications and source records attributed to Seppo Mikkola.
A chain regularization method is combined with special purpose computer hardware to study the evolution of massive black hole binaries at the centers of galaxies. Preliminary results with up to N = 0.26 x 10(6) particles are presented. The decay rate of the binary is shown to decrease with increasing N, as expected on the basis of theoretical arguments. The eccentricity of the binary remains small.
Symbolic dynamics is applied to the one-dimensional three-body problem with equal masses. The sequence of binary collisions along an orbit is expressed as a symbol sequence of two symbols. Based on the time reversibility of the problem and numerical data, inadmissible (i.e., unrealizable) sequences of collisions are systematically found. A graph for the transitions among various regions in the Poincare section is constructed. This graph is used to find an infinite number of periodic sequences, which implies an infinity of periodic orbits other than those accompanying a simple periodic orbit called the Schubart orbit. Finally, under reasonable assumptions on inadmissible sequences, we prove that the set of admissible symbol sequences forms a Cantor set. (c) 2000 American Institute of Physics.
We have investigated the appearance of chaos in the one-dimensional Newtonian gravitational three-body system (three masses on a line with -1/r pairwise potential). In the center of mass coordinates this system has two degrees of freedom and can be conveniently studied using Poincare sections. We have concentrated in particular on how the behavior changes when the relative masses of the three bodies change. We consider only the physically more interesting case of negative total energy. For two mass choices we have calculated 18 000 full orbits (with initial states on a 100x180 lattice on the Poincare section) and obtained dwell time distributions. For 105 mass choices we have calculated Poincare maps for 10x18 starting points. Our results show that the Poincare section (and hence the phase space) divides into three well defined regions with orbits of different characteristics: (1) There is a region of fast scattering, with a minimum of pairwise collisions. This region consists of 'scallops' bordering the E=0 line, within a scallop the orbits vary smoothly. The number of the scallops increases as the mass of the central particle decreases. (2) In the chaotic scattering region the interaction times are longer, and both the interaction time and the final state depend sensitively on the starting point on the Poincare section. For both (1) and (2) the initial and final states consist of a binary + single particle. (3) The third region consists of quasiperiodic orbits where the three masses are bound together forever. At the center of the quasiperiodic region there is a periodic orbit discovered (numerically) by Schubart in 1956. The stability of the Schubart orbit turns out to correlate strongly with the global behavior.