The three-dimensional axisymmetry-breaking instability of an axisymmetric convective flow in a vertical cylinder with a partially heated sidewall is studied numerically. The central part of the sidewall is maintained at constant temperature, while its upper and lower parts are thermally insulated. The dependence of the critical Grashof number on the cylinder aspect ratio (A=height/radius) is obtained for a fixed value of the Prandtl number, Pr=0.021, and fixed length of the heated central region, equal to the cylinder radius. Three different modes of the most dangerous three-dimensional perturbations, which replace each other with the variation of the aspect ratio, are found. Comparison with experiment shows a good agreement at the aspect ratio A=8 and 12, while at A=4 a significant disagreement is observed. Possible reasons for this disagreement are discussed. At A=4, the dependence of the critical Grashof number on the Prandtl number is studied in the range 0<Pr<0.05, to rule out the possibility that the disagreement is due to uncertainty in values of fluid properties. The similarities and differences of instabilities in the cylindrical and rectangular geometries are examined. The computations are carried out using two independent numerical approaches, which cross-validate each other.

We investigate the statistics of the decay process in an equal-mass three-body problem with randomized initial conditions. Contrary to earlier expectations of similarity with 'radioactive decay', the lifetime distributions obtained in our numerical experiments turn out to be heavytailed, i.e. the tails are not exponential but algebraic. The computed power-law index for the differential distribution is within a narrow range, approximately from −1.7 to −1.4, depending on the virial coefficient. Possible applications of our results to studies of the dynamics of triple stars known to be at the edge of disruption are considered.

Dynamical evolution of 120 000 equal‐mass rotating triple systems is investigated. The system rotation is described by the parameter w=−L20E0/G2m50, where G is the gravitational constant, m0 is the mass of a body, and L0 and E0 are the angular momentum and the total energy of the triple system, respectively. We consider the values of w= 0.005, 0.1, 1, 2, 4 and 6. For each w, 20 000 triple systems are studied. The initial coordinates and velocities of the components are randomly chosen. The initial data are chosen in two different ways: the first one assumes a hierarchical structure initially and the second one does not. The evolution of each triple system is calculated until either the escape of one of the bodies occurs or the time exceeds 1000 mean crossing times of the system. The orbital parameters of the final binary and the escaper are recorded for each run. We compare the results of numerical simulations and predictions of a statistical escape theory. The statistical theory is based on the assumption of ergodicity, that is, the only information on the initial conditions remaining at the time of the escape of the third body is contained in the conserved total energy, total angular momentum and the mass values. The distributions of various quantities are derived from the allowable phase‐space volumes. The distribution of binary energy agrees with earlier results by Heggie, with the angular momentum dependence of Mikkola & Valtonen being added. The eccentricities are distributed in general accordance with Monaghan's work, while the triple systems break up like in radioactive decay, as was previously found by Valtonen & Aarseth. The escape directions are preferentially perpendicular to the total angular momentum vector; the more so, the greater the angular momentum. The escape‐angle distributions are derived from the statistical theory and are found to be in agreement with the numerical data. The relative orientations and magnitudes of the binary and third‐body angular momenta are also explained based on the statistical theory.

Abstract. We discovered a new component E in the nearby multiple system Gliese 225.2, making it quadruple. We derive a preliminary 24-yr astrometric orbit of this new sub-system C,E and a slightly improved orbit of the 68-yr pair A,B. The orientations of the A,B and C,E orbits indicate that they may be close to coplanarity. The orbit of AB,CE is rather wide and does not allow to determine its curvature reliably. Thus, the 390 yr orbit computed by Baize (1980, Inf. Circ. IAU Comm., 26(80)) was premature. The infrared colors and magnitudes of components A, B, and C match standard values for dwarfs of spectral types K5V, M0V, and K4V, respectively. The new component E, 3 magnitudes below the Main Sequence, has an anomalously blue color index. We estimate its mass as roughly 0.2 solar from the astrometric orbit, although there remains some inconsistency in the data hinting on a higher mass or on the existence of additional components in the system. Large space velocities indicate that Gliese 225.2 belongs to the thick Galactic disk and is not young. This quadruple system survived for a long time and should be dynamically stable.

The problem of three stars arises in many connections in stellar dynamics: three-body scattering drives the evolution of star clusters, and bound triple systems form long-lasting intermediate structures in them. Here we address the question of stability of triple stars. For a given system the stability is easy to determine by numerical orbit calculation. However, we often have only statistical knowledge of some of the parameters of the system. Then one needs a more general analytical formula. Here we start with the analytical calculation of the single encounter between a binary and a single star by Heggie (1975). Using some of the later developments we get a useful expression for the energy change per encounter as a function of the pericenter distance, masses, and relative inclination of the orbit. Then we assume that the orbital energy evolves by random walk in energy space until the accumulated energy change leads to instability. In this way we arrive at a stability limit in pericenter distance of the outer orbit for different mass combinations, outer orbit eccentricities and inclinations. The result is compared with numerical orbit calculations.